The proceedings of the 18th Annual Conference of China Electrotechnical Society: Volume VII 9789819710720, 9819710723

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Lecture Notes in Electrical Engineering 1169

Qingxin Yang Zewen Li An Luo   Editors

The proceedings of the 18th Annual Conference of China Electrotechnical Society Volume VII

Lecture Notes in Electrical Engineering

1169

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, University of Karlsruhe (TH) IAIM, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dipartimento di Ingegneria dell’Informazione, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Intrinsic Innovation, Mountain View, CA, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Subhas Mukhopadhyay, School of Engineering, Macquarie University, Sydney, NSW, Australia Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Department of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Federica Pascucci, Department di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Kay Chen Tan, Department of Computing, Hong Kong Polytechnic University, Kowloon Tong, Hong Kong

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Qingxin Yang · Zewen Li · An Luo Editors

The proceedings of the 18th Annual Conference of China Electrotechnical Society Volume VII

Editors Qingxin Yang Tianjin University of Technology Tianjin, Tianjin, China

Zewen Li East China Jiaotong University Nanchang, Jiangxi, China

An Luo Hunan University Changsha, Hunan, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-97-1071-3 ISBN 978-981-97-1072-0 (eBook) https://doi.org/10.1007/978-981-97-1072-0 © Beijing Paike Culture Commu. Co., Ltd. 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Contents

RUL Prediction Method of Series Battery Based on Improved Limit Learning Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sidong Hu Impulse Flashover Characteristics of High-Voltage Post Insulators in High Altitude Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Sun, Siyi Chen, Hailin Shi, Yanjie Cui, Zhijin Zhang, and Guohui Pang Multi-agent Distributed Cooperative Control of Multi-energy Complementary Microgrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rui Ma, Hui Fan, Jianfeng Li, and Xiaoguang Hao Effect of Low Temperature on Impulse Discharge Characteristics of Insulator String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lei Wang, Yu Su, Jian Zhang, Xiuyuan Yao, Bingxue Yang, Zhiwei Li, and Yujian Ding Research on Rapid Cooling Technology for High Temperature Copper Parts . . . Gou Xueke, Geng Hao, and Wu Lizhou Optimal Dispatching of Distribution Network Considering Inverter Air Conditioner Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dian Yuan, Qinran Hu, Yuanshi Zhang, Xu Jin, Shunjiang Wang, and Peng Qiu

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Research on Coding Method of Polarization PLC System Based on Upper Bound of Bhattacharyya Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wangbin Cao, Yijin Ren, Xiaolin Liang, Zhengwei Hu, and Zhiyuan Xie

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A Preventive Maintenance Strategy of Wind Turbine Gearbox Based on Stochastic Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Yuqi and Su Hongsheng

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Research Status of Contact on Breaking Performance of High Voltage Circuit Breaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pang Zhen, Mao Guanghui, Zhang Congrui, Han Yu, Gao Meijin, Chen Baoan, Liu Tan, Gao Jianfeng, and Ding Yi

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Simulation of Flow Characteristics in High-Voltage Circuit Breakers . . . . . . . . . . 103 Yujiao Qiao, Shanika Matharage, and Zhongdong Wang Optimal Configuration of Hybrid Energy Storage Capacity Based on Improved Compression Factor Particle Swarm Optimization Algorithm . . . . . 114 Dengtao Zhou, Libin Yang, Zhengxi Li, Tingxiang Liu, Wanpeng Zhou, Jin Gao, Fubao Jin, and Shangang Ma A Novel SVM-Based Transient Protection Algorithm for Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Zhenwei Guo, Yingcai Deng, Jiemei Huang, Qian Huang, and Zebo Huang Effect of Ion Types on Arc Erosion of Circuit Breaker Contact: Molecular Dynamics Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Xin Wang, Shanika Yasantha Matharage, Ruoyu Xu, Mingyu Zhou, Yuzhen Zhou, Yi Ding, and Zhongdong Wang Research on the Delay Characteristics of 5G Communication Networks for Regional Protection in Power Distribution Grids . . . . . . . . . . . . . . . . . . . . . . . . 139 Chen Linhan, Wei Qi, Ge Wei, and Hong Weijun Distributed Reactive Power Control Scheme for Parallel Inverters Based on Virtual Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Rui Ma, Hui Fan, Jianfeng Li, Xiaoguang Hao, Changbin Hu, and Shanna Luo On Line Estimation of Power Line Channel Impedance Based on Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Hu Zhengwei, Xia Siyi, Wang Wenbin, Xie Zhiyuan, and Cao Wangbin Research on Insulator Defect Detection Based on Improved YOLOv7 . . . . . . . . . 173 Bing Li, Mingjie Xu, Zhongxin Xie, Donglian Qi, and Yunfeng Yan Field Application of Switchgear Abnormal Noise Detection Based on Acoustic Imaging Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Jun Xiong, Shengya Qiao, Qiang Pang, Hongling Zhou, Guangmao Li, and Wangwei Ji Compensation Capacitor Status Monitoring Research Based on Feature Fusion and SVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Jianqiang Shi, Youpeng Zhang, and Guangwu Chen

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Study on Acid Thermal Aging Characteristics of Composite Insulator Core Rod Material Based on TGA and SEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Dandan Zhang, Yuwei You, Wenwu Pan, Ming Lu, and Chao Gao Research on Cumulative Fatigue Damage for Vortex-Induced Vibration of Steel Tube Tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Songsong Yu, Zhongwei Hou, Quan Liu, Jiang Liu, and Yu Cao A Model for Predicting the Flashover Voltage of Ice-Covered DC Insulator Strings Based on Extreme Learning Machine Neural Network . . . . . . . . . . . . . . . 217 Xiaoyi Wang, Hao Shen, Chao Zhou, and Hui Liu A Grid-Friendly Bidirectional Electric Vehicle Charger Based on CLC Resonant Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Ziqian Ren, Xinqi Li, Qiaozhi Xue, Jiang Shang, Nanzhe Wei, and Chunguang Ren Operation Strategy of Battery Swapping-Charging System for Electric Vehicle Based on Multi-material Flow with Space-Time Coupling Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 Zhijian Liu, Jing Dai, Lingrui Yang, and Hang Dong Analysis of Unrecoverable Breakdown Ground Fault Scenarios in the Internal Insulation of Large Generator Stators . . . . . . . . . . . . . . . . . . . . . . . . 240 Li Li, Kun Yu, Xiangjun Zeng, Lisi Chen, and Chenyu Wu Investigation on the Effect of the Self-generated Metal Vapour on the Cathode Spot Formation in Vacuum Arc by Molecular Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 Haonan Yang, Shuhang Shen, Ruoyu Xu, Mingyu Zhou, and Zhongdong Wang Study on Electromagnetic Radiation Phenomenon in Electrical Wire Explosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Ruoyu Han, Menglei Wang, Wei Yuan, Juan Wu, Manyu Wang, Pengfei Li, and Xi Chen Measurement and Analysis of Multiple Parameters of Enhanced Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Zihao Tian, Lihua Zhu, Jianying Hao, and Ping Liu Mathematical Modeling of Electrical Energy Storage System and Off-Grid Wind Turbine System Based on Load Demand Response . . . . . . . . . . . . . . . . . . . . 273 Haseeb Shams and Jie Yu

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Consumption Modeling and Influencing Factors Analysis of Alkaline Water Electrolyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Rui Wang, Zhaoran Xu, Zhuocheng Dai, Lei Yang, and Xiaojun Shen A Model Predictive Control Approach for Reconfigurable Battery Energy Storage Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 Bo Yan, Tinghua Wang, Jingyun Wu, and Darui He Stability Analysis on Large-Scale Adiabatic Compressed Air Energy Storage System Connected with Power Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Chengqian Xiao, Yanbing Zhang, Shu Zhang, Xiaoya Zhen, Zihao Jia, and Jiaxin Ding Handwritten Table Recognition Method Based on Multi-head Attention Mechanism and Knowledge Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Chao Tong, Jijing Yan, Ziwei Zhu, Fan Li, Xing Zhang, Hua Hua, Yucong Mei, and An Hu Research on the Planning Method for EV Charger Allocation in Highway Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Hengjie Li and Tianyi Liu Multi-fidelity Data Fusion for Electromagnetic Field Prediction of Electromagnetic Railgun Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Liang Jin, Shuo Shi, Juheng Song, and Chenyuan Zhang An Online Battery Electrochemical Impedance Spectroscopy Measuring Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Yu Zhang, Haojing Wang, Cheng Peng, Xinyue Liu, and Rui Li Research on Location Determination and Capacity Optimization Method for Large-Scale Energy Storage Station in Regional Power Grid . . . . . . . . . . . . . . 359 Liming Zhai, Chengqian Xiao, Xiaohang Li, and Yanbing Zhang Research on the Transient Temperature Field of the High-Speed Permanent-Magnet Motor for Dragging Pulsed Alternator . . . . . . . . . . . . . . . . . . . 370 Yuan Wan, Xu Zhang, Yuqi Jia, Jian Guo, and Wenlong Li Effect of Pre-qualification Test on Properties of Semi-conductive Shielding of High Voltage XLPE AC Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Xueqi Huang, Man Xu, Hengyi Liu, Fa Xie, Ruofei Wang, Shuai Hou, and Yunpeng Zhan Study on Noise Characteristics of Scaled Capacitor Stacks . . . . . . . . . . . . . . . . . . 398 Li Long, Xiaoyan Lei, Lingyu Zhu, and Jinyu Li

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Insulator Defects Detection and Classification Method Based on YOLOV5 . . . . 407 Yingbin Gu, Peifeng Huang, Juan Wang, Lize Tang, Jia Weng, and Xiaofeng Wang Design and Implementation of Indirect Lightning Protection for Airborne Electronic Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Zhifei He, Xinyao Li, and Kai Dong Optimization of Non-Destructive Testing of Power Equipment Based on X-ray Backscattered Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Zihao Cao, Ruohan Wu, Weiping Zhu, Peng Gu, Yong Yang, and Zhengzheng Liu Visual Positioning Method for Unmanned Aerial Vehicle Charging Platform Using Cooperative Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Jiahao Lu, Wei Yang, Hengxing Zhou, Shaoqi Ma, Yuanshang Fan, Zhongbiao Ling, Jianwen Zhong, and Ruifeng Chen Statistical Distribution Law of CVT Test Data in Guangzhou Power Grid . . . . . . 440 Hongling Zhou, Shengya Qiao, Guocheng Li, Wangwei Ji, Sen Yang, Guangmao Li, Jun Xiong, and Feng Luo A Transformer Insulation Life Assessment Method Considering Variational Annual Load Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Chenying Yi, Qianyi Chen, Qingfa Chen, Dechao Li, and Chen Wang Die Matching Performance of Ultra-Thin Titanium Sheet Driven by Polyurethane During Electromagnetic Forming . . . . . . . . . . . . . . . . . . . . . . . . . 457 Runze Liu, Xiaotao Han, Pengxin Dong, and Zelin Wu Analysis of the End Electric Field of 66 kV Dry Transformer in Offshore Wind Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 Ke Xu, Xinhan Qiao, Wei Li, Jiliang Yi, Xia Li, Xiaoquan Zhang, and Wenfeng Chen Research Status and Development Trend of Gravity Energy Storage Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Chen Qimei, Gou Yurong, and Wang Tangrong Research on Control Strategy of Permanent Magnet Synchronous Motor Speed Sensorless System Based on New Wide Band Gap Devices . . . . . . . . . . . . 482 Jun Jiang, Chengsheng Wang, Wei Duan, Zhiming Lan, Fan Li, and Qiongtao Yang

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Submodule Capacitance Dimensioning for Cascaded H-bridge STATCOM with Film Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 Hengyi Wang Design of Electromagnetic Detection System for Underground Cultural Relics Protection Based on Spread Spectrum Coding . . . . . . . . . . . . . . . . . . . . . . . 503 Shiqiang Li, Guoqiang Liu, Wenwei Zhang, Zhiguang Lv, and Lijuan Guo Electric Field Analysis and Research of 1000 kV AC Transformers High Voltage Direct Type Exit Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Xiangjun Li, Yanyan Hou, Xiaoyang Zhang, Yuzhe Lu, Penghong Guo, and Xinbing Wang Analysis of Current and Voltage Characteristics of 500 kV Noninverting Parallel Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 Zhifang Zhu, Dongmei Fan, Jingjing Huang, and Weiwei Liu Characteristic of the Power-Frequency Induced Current and the Corresponding Power Loss on the OPGW of 220 kV Overhead Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Qi Wei, Guangxiang Jin, Yong Wei, Jinxin Cao, Xianchun Wang, Wenhao Zhang, Yufei Chen, and Jianguo Wang Construction and Application of Knowledge Graph in Electric Power Field . . . . 555 Huapeng Chen, Shuo Yu, Tian Cao, and Xinyu Cao Study on Characteristic and Optimization of Eddy Current Damper Under Impact Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 Chao Zhang, Xin-ke Ma, Xiao-ming Han, and Qiang Li SOH Prediction for Lithium-Ion Batteries Based on SSABP-MLR . . . . . . . . . . . . 572 Xueqin Zheng, Ning Su, and Weibiao Huang Integrated Design and Optimization of SSPC Current Measurement Module Based on AMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 Feiran Xu, Li Wang, and Kaijun Wang Multi-Vibration Sensor Fusion of Flexible DC Converter Transformer Based on Adaptive Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590 Dong Xie, Hong Zheng, Meijun Bao, Guowei Zhou, and Jiangyang Zhan Parameter Identification of Retired Batteries Based on Improved Adaptive Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 Liang Li, Jingyun Chen, Shiqi Nie, Yuan Li, Yanwei Li, and Jialing Li

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A Bidirectional DC-DC Converter and Fast-GMPPT Algorithm for Photovoltaic Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Lianggang Xu, Baoxian Ji, Lijuan Lu, and Wenming Liu Power Analysis and Experimental Study of Vortex-Excited Vibrating Ocean Current Energy Generation Based on a Cylindrical Permanent Magnet Linear Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 Liguo Fan, Guoqiang Liu, Xianjin Song, Wenwei Zhang, Lipeng Wu, and Hui Xia Research Review of Non-invasive Load Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 628 Dan Chen, Wenxuan Liu, Sheng Ding, and Chen Zhang Harmonic Coordination Suppression Strategy of Hybrid Grid-Connected System in Complex Grid Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638 Tailin Huang, Fei Rong, Xiaobin Mu, Guofu Chen, Xiang Wang, and Yalei Yuan Study on Partial Discharge Characteristics of Epoxy Resin Under Bipolar High-Frequency Square Wave Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 Yongsheng Xu, Bing Luo, Jiaju Lv, Qihang Jiang, and Weiwang Wang Partial Discharge Pattern Recognition of High Voltage GIS Defects by Using GWO-SVM Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 Tianbao Wu, Huan Bai, Jiayi Wang, Jianyang Huang, Yue Yu, and Weiwang Wang Modeling High Concealment LR Attack Based on Linearization of Signal Space Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Wengen Li, Lu Zhou, Xingyu Shi, Huan Guo, and Duange Guo Design and Analysis of a Novel Type of Double Stator Switched Reluctance Wind Turbine Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 Wenju Yan, Jiangpeng Hu, Wenwen Sun, Hailong Li, Hao Chen, and Hongwei Yang Research on Short-Circuit Withstand Capability of Transformer Considering the Mechanical Accumulation Characteristics of Insulation Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684 Zhihao Liao, Zhongxiang Li, Zhiqin Ma, Dan Zhou, and Xiang Shu Calculation and Analysis of Temperature Field Characteristics of Power Transformers in Oil During Short Circuit Processes . . . . . . . . . . . . . . . . . . . . . . . . 693 Linglong Cai, Bin Tai, Zhiqin Ma, Yuhui Jin, Shuo Jiang, and Zhongxiang Li

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Refinement of Short-Circuit Withstand Capability Calculation for Power Transformers and Application in Fault Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Yuhui Jin, Xian Yang, Zhiqin Ma, Chunyao Lin, Jiangnan Liu, and Zhongxiang Li Image-Based Modeling and Numerical Simulation Analysis of Transmission Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 710 Lizhong Qi, Yaping Zhang, Xiaohu Sun, Jingguo Rong, Weijing Ma, and Hui Xiao Analysis of Mechanical Properties of Polypropylene Cable Insulation at Different Aging Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Fanwu Chu, Tao Xu, Chao Peng, Kai Deng, Mingzhong Xu, and Zhenpeng Zhang Influences of Secondary Width on Forces and Losses in Linear Induction Motors with Transversally Asymmetric Secondary . . . . . . . . . . . . . . . . . . . . . . . . . 731 Dihui Zeng, Ke Wang, and Qiongxuan Ge Current Characteristics and Overcurrent Suppression in Segmented Power Switching Process of Long Primary Dual Three-Phase Linear Motors . . . . . . . . . 740 Yanfei Li, Zixin Li, Cong Zhao, Fei Xu, Liming Shi, and Yaohua Li Short-Term Wind Power Prediction Based on AVMD-SMA-LSSVM Combined Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756 Dan Zhang, Pijiang Zeng, Changsheng He, Xiongbiao Wan, Botao Shi, and Yiming Han Design of Grid Model Parameter Test System for New Energy Power Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766 Shoude Jiang, Deshun Wang, and Haojie Yu Parametric Design of Railgun Armature Based on Functional Zoning . . . . . . . . . 780 Bo Gao, Xuan Li, Liang Chen, and Qunxian Qiu Study on the Optimizing Impact of Hydrogen Equipment in Integrated Energy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792 Yue Cheng Design of Variable Stress Fatigue Strength for Mechanical Parts of Gun Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801 Qunxian Qiu, Haitong Song, Jun Xu, and Pengfei Li

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Optimization Configuration of Energy Storage System Considering the Cost of Retired Power Battery Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809 Yuan Jiang, Suliang Ma, Qian Zhang, Wenzhen Chen, and Qing Li Calculation of Electric Field for UAV Cross-Inspection in 220 kV Substation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818 Ying Zhang, Jianming Liu, Duanjiao Li, Yongchao Liang, Jianhong Su, Kaixuan Chen, and Wensheng Li Magnetic Field Safety Analysis of UAV Inspection in 220 kV Substation . . . . . . 827 Yun Chen, Ying Zhang, Duanjiao Li, Jianming Liu, Zihan Yang, and Wensheng Li Insulated Bucket Arm Vehicle Bucket Arm Spatial Motion Path Planning and Algorithm Analysis Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 Cong Hu, Wanying Zhang, Xin Yang, Li Cai, Jianguo Wang, and Yadong Fan Simulation Modeling and Forward/Inverse Kinematic Analysis of Insulated Bucket Arm Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845 Cong Hu, Wanying Zhang, Qiao Shi, Xin Yang, Li Cai, Jianguo Wang, and Yadong Fan Optimization of Insulated Bucket Arm Vehicle Bucket Arm Motion Trajectory and Analysis of Collision Detection Algorithms . . . . . . . . . . . . . . . . . . 855 Cong Hu, Wanying Zhang, Xin Yang, Qiao Shi, Li Cai, Jianguo Wang, and Yadong Fan Research on Winding Electrodynamic Force and Hot Spot Temperature Rise of Environmental Stereo Wound Core Transformer . . . . . . . . . . . . . . . . . . . . . 864 Junchao Wu, Haipeng Tian, Wei Cheng, Zhitao Song, Qing Wu, and Chi Yuan Maintenance Strategy of Microgrid Energy Storage Equipment Considering Charging and Discharging Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 872 Xi Cheng, Yafeng Liang, Lihong Ma, Jianhong Qiu, Rong Fu, Zaishun Feng, Yangcheng Zeng, and Yu Zheng Research on Application of Carbon Fiber-Steel Materials in Lightweight Gun Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880 Jun Xu, Qunxian Qiu, and Chao Zhang Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889

RUL Prediction Method of Series Battery Based on Improved Limit Learning Machine Sidong Hu(B) Faculty of Electrical and Control Engineering, Liaoning Technical University, Fuxin, China [email protected]

Abstract. The conventional RUL prediction method for series type batteries mainly relies on particle filter algorithms, which have poor tracking effect on battery status, resulting in low prediction accuracy. Therefore, a RUL prediction method for series battery systems based on an improved extreme learning machine is proposed. Firstly, by analyzing the capacity decay process of the battery during charging and discharging, the decay parameters are extracted. Then, an improved extreme learning machine algorithm is used to establish a battery RUL prediction model, where the decay parameters are used as input information to obtain the predicted values, and the uncertainty of the predicted values is quantitatively analyzed. Finally, calculate the dispersion of battery capacity and track the battery status to achieve RUL prediction based on the distribution interval of the predicted results. The experimental results show that applying this method to RUL prediction of series batteries has high prediction accuracy. Keywords: improve the limit learning machine · Series battery · RUL prediction · Method design

1 Introduction If you want to extend the duration of power supply, you need a battery to provide highpower load support. However, it is difficult to do this with a single battery. Therefore, it is necessary to combine multiple batteries in a series connection to form a series-type battery system. Series-connected battery systems have the advantages of high output power and cyclic energy storage, and have been widely used in automation, industrial control and other fields. However, during cycling, the performance of batteries gradually deteriorates or even fails due to the decomposition of the internal electrolyte, aging of the electrodes and other factors. Therefore, fast and accurate prediction of the remaining service life of the battery is of great significance to improve the utilization rate of the battery and the safety of electric equipment. In order to estimate the Remaining Useful Life (RUL) of the battery system, literature [1] uses the SQKF algorithm to predict the remaining life of the battery system by simulating its cyclic operating state and analyzing its life decay process by combining with the single-particle physical machine model simulation. Literature [2] sampled the principal component analysis to extract the battery health factor from the constant © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 1–15, 2024. https://doi.org/10.1007/978-981-97-1072-0_1

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current stage and constant voltage stage of battery charging and discharging, and used the correlation analysis to analyze the specific relationship between the factor and the capacity, and constructed a prediction method based on the health factor. Literature [3], on the basis of analyzing the characteristic parameters of the battery life state, takes the equal-voltage drop discharge time as the indirect health factor, and uses genetic algorithm to optimize the parameters of the limit learning machine model, so as to establish the indirect prediction model of the remaining battery life. However, in practical application, it is found that the above traditional methods generally have a drawback, that is, they all use a single degradation model to simulate the battery capacity decay process, which has certain application limitations. Based on this, this paper samples the improved limit learning machine algorithm for battery RUL prediction, and extends the range interval of the prediction results by establishing a prediction model and quantifying the uncertainty of the predicted values. This method has certain reference value for the maintenance of battery system.

2 Extraction of Characteristic Parameters of Series-Connected Battery Recession The degradation of properties is irreversible during continuous cyclic charging and discharging of series-type batteries [3]. When a characteristic degrades to a critical point, the battery is considered to be ineffective, and by extracting and analyzing the characteristic parameters of the degradation, the degradation patterns and trends of the battery can be identified. These patterns and trends can provide valuable information for the RUL prediction algorithm to better understand the battery’s degradation pattern and thus more accurately predict the battery’s remaining life. In this paper, based on the expertise and previous studies related to series-type electricity to understand the mechanism of battery performance degradation, the key factors affecting the battery life, and the feature parameters used in previous studies, five features are extracted, including the energy of the voltage and current signals in each cycle, the charging voltage rise interval, the standard deviation, the charging current drop interval, and the skewness, which are expressed as follows. 2.1 Energy Signature The energy parameters extracted from the battery dataset can be calculated by the following equation: t1   xi2 dt ej =

(1)

t0

In the above formula, j indicates a sampling moment; ej indicates a signal energy of an input value x j at the moment; I represents a data source of the input energy value as a voltage, a current, or a temperature, and v represents a voltage, c represents a current, t represents a temperature, for example, ev as a signal energy of a voltage, ec as a signal

RUL Prediction Method of Series Battery

3

energy of a current, and et as a signal energy of a temperature. T 0 is an initial discharge or charging time; t 1 is an end time of the discharge or charging. Integrating the amplitude squares of the input values x i during this period gives the input energy signal ej for this charging or discharging cycle. 2.2 Time Interval for Charging Voltage Rise In charging mode, the degree of battery polarization can affect the charging time, and in practical applications, since users do not wait until the battery is depleted before charging, the charging time between the initial voltage and the final voltage can be used as a battery recession characteristic to characterize the health of the battery [4]. The trend of battery charging voltage under different charging and discharging cycles is shown in Fig. 1.

Charging Voltage/V

4.5 4.2 4.0

recession process

voltage rise

3.5 30 cycles 60 cycles 90 cycles 3 0

2000

4000

6000

8000

10000

time/s

Fig. 1. Battery constant current charging process

According to the above figure, it can be found that with the repeated use of the battery, the battery charging time gradually slows down the phenomenon, therefore, the charging voltage rise time interval is calculated as follows:   (2) tj = tv0 − tv , j = 1, 2, ..., k In the above equation, t j denotes the time interval data of the corresponding charging voltage rise under the j charging and discharging cycle; t v0 denotes the moment of selecting the initial voltage; and t v denotes the moment of the end of constant current charging. 2.3 Standard Deviation Signal (Electronics) The signal standard deviation characteristic parameters extracted from the battery data can be calculated by the following equation:   n 1

 dj =  xi − mj (3) n i=0

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In the above equation, n is the number of input signals x i ;mj is the mean value of the signal obtained at the sampling moment j; x i is the input signal. The input value is subtracted from the mean value, and then the sum of squares is divided by the number of inputs, and the open root sign is the signal standard deviation d j . Among them, the formula for the signal mean value is: 1 xi n

mj =

(4)

2.4 Charge Current Drop Interval The actual capacity loss of the battery is high percentage in the charging phase, and battery aging can affect the energy embedding ability. Figure 2 depicts the trend of current changes in charging mode for different number of cycles. 2.0 30 cycles 60 cycles 90 cycles

Charging Current

1.5 1.0 recession process 0.5

0.1 0

current drop

2000

4000

6000

8000

10000

time/s

Fig. 2. Battery constant voltage charging process

As shown in the above figure, the rate of change of current gradually becomes slower with the deepening of battery degradation, resulting in a tendency for the charging time to increase during constant voltage charging [5]. Therefore, the charging current drop is selected as a characteristic parameter reflecting the battery degradation, and the calculation formula is as follows: aj = |aI − a100 |, i = 1, 2, ..., k

(5)

In the above equation, α I denotes the starting moment of the CV charging stage; α 100 denotes the moment when the current decreases to 100 mA. 2.5 Skewness Signal The skewness signal of the battery energy can reflect the degree of deviation between the battery charging current difference and the theoretical value to a certain extent, and

RUL Prediction Method of Series Battery

5

the larger the value, the more serious the battery decline phenomenon [6], which can be calculated using the following equation:    n

 1 xi − mj (6) sj =  n dj3 i=0

In the above equation, d j denotes the signal standard deviation. Through the above analysis and calculation, the eigenvalues obtained by using Eq. (1) to Eq. (6) are the characteristic parameters of battery energy decline selected in this paper, but due to the characteristics of non-uniformity of the magnitude in the eigenparameters, it is necessary to normalize the extracted data in order to facilitate the RUL prediction and simplify the prediction process [7]. The principle of normalization calculation is to map all the parameters to a data distribution where the difference between the mean and the variance does not exceed 1. The calculation method is as follows: rj =

fj − min fj max fj − min fj

(7)

In the above equation, f j denotes the battery degradation characteristic parameter; r j denotes the data normalization result; min f j and max f j denotes the minimum and maximum values of the characteristic parameter, respectively. By normalizing the above extracted battery energy degradation characteristic parameters, the final characteristic parameter r j is obtained, which not only reduces the complexity of the data structure, but also lays the foundation for the subsequent RUL prediction [8].

3 RUL Prediction Method for Series-Connected Batteries 3.1 Establishment of Battery RUL Prediction Model Based on Improved Limit Learning Machine As the traditional single-layer feed-forward neural network needs to continuously adjust and optimize the structural parameters and hyperparameters of the model when performing model training, which makes the algorithm’s operation time longer when facing a larger data capacity, and it is difficult to be applied to prediction occasions with high requirements for efficiency [9]. For this reason, this paper adopts the improved limit learning machine algorithm, utilizing its advantages of fast learning speed and no need to adjust the parameters, to establish a series-type battery RUL prediction model, and realize the accurate prediction of battery RUL. The model structure of the improved limit learning machine algorithm is shown in Fig. 3. In the figure, the input data of the input layer is the characteristic parameter r j of the battery energy recession extracted and normalized in the previous section; k j denotes the model output results; β 1 , β i , and β L denote the weight matrices corresponding to the input unit, hidden unit, and output unit, respectively. When applying the extreme learning machine for prediction, it is crucial to correctly carry out the selection of its parameters to influence the prediction results [10]. The

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Fig. 3. Model Structure of Improved Extreme Learning Machine Algorithm

parameter selection of the extreme learning machine mainly includes the selection of input parameters and internal parameters, the input parameters are mainly the selection of the amount of input data, where the internal parameters are selected as the activation function. Since the parameter dataset may be mixed with some invalid data, so in order to facilitate the prediction, combined with the Kernel Principal Component Analysis (KPCA) to reduce the dimensionality of the dataset, dimensionality reduction can reduce the feature redundancy, reduce the burden of the model computation, and improve the algorithm to improve the accuracy of the identification, so based on the KPCA algorithm to improve the dimensionality reduction of the input layer of the feature library of the Extreme Learning Machine model. Let there be N sets of samples X = [x 1 ,x 2 ,…,x n ], where x i are all qi -dimensional column vectors, as xi ⊂ Rqi . φ(xi ) is a nonlinear mapping that maps the data from the sample space to a high-dimensional feature repository, realizes Rq1 → Rq2 , where q2 ≥ q1 , and Ø(x i ) is unknown. The data in the feature library is Ø(X) = [Ø(x 1 ), Ø(x 2 ),…,Ø(x n )]. Then, the data Ø(X) in the feature library is downscaled. It is assumed that the data satisfies the centrality condition, i.e.: N

φ(X ) = 0

(8)

i=1

When using PCA for dimensionality reduction, it is necessary to find an axis on which the data. The projection on it is the most dispersed, i.e., the variance D of the projected coordinates is the largest. Let the unit direction vector of this axis be v and the variance of the projected coordinates of Ø(X) on v be D. The objective function for dimensionality reduction can be expressed as: v = arg max vT Dv v∈Rk v=1

(9)

RUL Prediction Method of Series Battery

7

The maximum value of Eq. (9) can be found by the Lagrange multiplier method. Define the kernel function k(x i ,x j ) = Ø(X i )T Ø(X j ) as the inner product of the highdimensional vectors Ø(X i ) and Ø(X j ) in the feature library, and the kernel matrix k = Ø(X)Ø(X)T . The eigenvalue η of k is related to the unit eigenvector μ by: Kμ = ημ Ø(X i ) the coordinates of the nonlinear mapping projection to v are: ⎤ ⎡

k x1 , xj 1 vT φ(xi ) = √ μT ⎣ · · · ⎦ 

λ k x1 , xj

(10)

(11)

In summary, the input layer of the extreme learning machine is improved by the KPCA algorithm to reduce the redundancy of features in the input layer and improve the computational efficiency of the algorithm. One-dimensional data based on the above reduced  dimensionality of the characteristic parameters of the series-type battery recession rj rj |j = 1, 2, ..., N , a reconstruction of the m-dimensional space is performed, i.e., it is considered that there exists a particular functional relationship between the future values of this one-dimensional data and the previous m values, so that a set of phase-space quantities, i.e., the input data quantities, is obtained:   (12) y = r|r1 , r2+τ , ..., rN (m−1)τ In the above equation, τ denotes the sampling delay; m denotes the spatial dimension; N(m-1)τ denotes the number of data vectors. After determining the input and output parameters of the Extreme Learning Machine, it is also necessary to determine the internal parameters of the Extreme Learning Machine because the activation function has a greater impact on the Extreme Learning Machine’s ability to generalize the prediction. The more the number of nodes of the activation function Gi (x), the better the prediction model can approximate all the training samples with zero error, that is to say, the better the results obtained by applying the improved extreme learning machine model prediction [11]. Assuming that the improved limit learning machine model with P hidden nodes can be represented by the following equation: Gi (x) = rj

P

(ai , bi ) · βL

(13)

i=1

In the above equation, r j denotes the battery energy recession characteristic parameter; Gi (.) denotes the minimum activation function of the node I; α i denotes the hidden layer state of the I node; bi denotes the intermediate state of the I node; and β L denotes the connection weight matrix of the output layer. Based on the above calculations, the input parameters and internal parameters of the improved limit learning machine prediction model are obtained, so under the premise of battery energy recession feature parameter extraction, the specific construction and

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Fig. 4. Battery RUL prediction process based on improved extreme learning machine

implementation process of predicting battery RUL using the improved limit learning machine algorithm is shown in Fig. 4. According to the above figure, the derived RUL prediction process based on the improved limit learning machine can be summarized in the following steps: (1) Input the battery energy degradation characteristic parameter r j , and normalize the data. Since the parameter data set may be mixed with some invalid data, the data set is reduced and streamlined to facilitate prediction, and the sampling frequency is usually set to N, with the value of N depending on the effect of battery use [12]. (2) Initialize the original structural parameters of the prediction model and the tracking set TS. Under the condition that the data of the experimental part is known, the historical data with large capacity scale is generally selected as the tracking sample set. (3) Train all data samples, remove noisy distributed data, optimize the best parameters of the model, and update the model. (4) The proposed distribution is corrected by combining the state-tracking optimal measure information, and the data are sampled for ordinal importance using the activation function of the model [13]. (5) Calculate the weights. Set up a resampling mechanism to re-estimate the battery health state to get the state estimate at the current moment. (6) Repeat the above steps to iteratively update the tracking set and the estimation set to determine whether the battery health state meets the set battery failure threshold. If it meets, the algorithm terminates and outputs the prediction result.

RUL Prediction Method of Series Battery

9

Through the prediction step of the above algorithm, the remaining life of the battery is predicted and the predicted value of RUL of the battery at any moment is obtained [14]. However, since the prediction result of the prediction model is only a point estimate that cannot reflect the uncertainty of the predicted value, the final result obtained should be subjected to uncertainty quantification to obtain the prediction state interval to refine the predicted value. 3.2 Quantification of Uncertainty in Forecast Results In order to confine the model prediction results to a fixed range interval, a regularization algorithm is introduced into the prediction results and the internal and structuring parameters of the prediction model are considered as observed variables obeying a normal distribution [15]. Where X denotes the training data set of the model and Y denotes the actual RUL value of the battery. The internal parameters of the model are denoted by θ (W,b), where the probability distribution of θ and the distribution of the variables are denoted by p(θ ) and q(θ ). Then the optimal approximation of the distribution is obtained by minimizing the value of the scatter between the two. Therefore, under Q2 regularization, the objective function is optimized as: Qdp =

1 θ (W , b) + λ(X , Y ) p p∈s

(14)

In the above equation, λ denotes the regularized decay coefficient; s denotes the subset of training samples; and p denotes the number of subsets. Based on the regularized objective function, the updated model input data X* is optimized to obtain the range interval of the distribution of the model’s prediction of the battery RUL, i.e.:

 1 w X ∗, Y = Qdp T

(15)

In the above equation, T denotes the number of cyclic sampling. The uncertainty of the prediction results of the prediction model is quantified by the above equation, the state distribution interval of the prediction results is obtained, and the predicted value of the battery RUL is determined according to the actual demand.

4 Analysis of Experimental Arguments 4.1 Experimental Preparation The series-type batteries selected for the experiments were commercially available 18650-type batteries that can be recharged and discharged in a cyclic manner.

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The main parameters of the selected battery are shown in Table 1. Table 1. Experimental battery parameters parameters

descriptive

model number

18650

kind

tandem type (chemistry)

Individual size

10 × 62 × 120 (mm)

standard voltage

14.8V

quantitative (science)

≥ 7.2v·h

Charging Voltage

4.2V

weights

160 g

Minimum discharge voltage

2.75V

A total of four identical 18650-type batteries, numbered A1 ~ A4, were selected for the experiment, and a six-month aging experiment was conducted on the experimental batteries in the laboratory environment. The hardware configuration of the computer selected for the experiment is as follows: 32GB of memory, R7-3700X (3.6GHz) processor, and Windows 10 as the operating system. The relevant data of the battery are collected with the help of multifunctional sensors and integrated into a complete data set, and the information of charging, discharging, and measuring resistance is recorded in each data set, and the charging mode is set to be constant-current and then constantvoltage, and the discharge mode is constant-current discharging. Mode for constantcurrent discharge. The charging and discharging data collected by the sensors are saved into a database to record all the data of a single charging and discharging experiment. In order to establish a RUL prediction model with better prediction performance, this paper removes the battery data with abnormal status in the experiment and retains the battery data with more realistic trends, and establishes a battery RUL prediction model based on the valid data. 4.2 Description of the Experiment Based on the battery data collected by the sensors, the internal relationships are analyzed. In order to better understand the internal structure and working principle of the battery, an equivalent model is established to characterize the performance degradation trend of the battery. According to the actual working process of the battery, an equivalent model that can characterize the battery performance degradation trend is established, as shown in Fig. 5. In Fig. 5, C DL denotes the equivalent capacitance of the circuit; V C denotes the rated voltage of the circuit; RCT denotes the DC resistance of the circuit; RW denotes the dry-circuit impedance; I R denotes the output current of the battery; RE denotes the resistance of the electrolytic tank; I L denotes the value of the current change; V L denotes the value of the voltage change; and OCV denotes the open-circuit voltage.

RUL Prediction Method of Series Battery IL

11

RE

+ RCT

CDL RW

IR

+ V − C

VL

OCV

−

Fig. 5. Battery Equivalent Circuit Model

Considering the cyclic nature of the battery life in the experiment, the battery capacity declines to 60% of the initial capacity as the threshold of battery failure. The relevant parameters in the improved extreme learning machine algorithm are set as follows: the learning rate is 0.01, the hidden layer nodes are set to 32, the number of neurons in the output layer is 20, the number of training times is 500, 200 random data segments are included on the input layer, and the activation function is chosen as the S function. Based on the actual extracted battery capacity degradation signal, the uncertainty quantification calculation of the predicted value is carried out by using the state prediction results of the previous time to get the battery RUL distribution range interval at the prediction time, and finally realize the battery RUL prediction and evaluation process. 4.3 Analysis of Projected Results In order to comprehensively analyze the effectiveness of this paper’s method, the SQKFbased residual life prediction of lithium-ion batteries from literature [1] (Method 1), the indirect prediction of RUL of lithium-ion batteries based on principal component analysis from literature [2] (Method 2) and the traditional comparative learning machine method (Method 3) are selected as the comparative methods for this paper’s prediction method in the experiments. The three methods are utilized to predict the RUL of four series-connected batteries respectively, and the starting point of the prediction is 0. The predicted values are obtained through 500 cycle predictions, and the prediction results under different cycle periods are shown in Fig. 6. Analyzing Fig. 6, it can be seen that under different charge/discharge cycle cycles, the prediction results obtained by using this paper for RUL prediction of four batteries are closer to the actual aging of the battery, the capacity degradation curves are very close to the real capacity degradation curves, and the predicted starting point of the failure threshold of the battery is consistent with the actual value. Compared with Method 2 and Method 3, the gap between the prediction results obtained by Method 1 and the real capacity of the battery is larger, and the prediction errors of Method 1, Method 2 and Method 3 are significantly larger than those of the methods in this paper. This shows that the prediction accuracy of the battery RUL prediction method designed in this paper is high.

S. Hu failure threshold

Predicted values of the method in this paper Method 1 predicted values

actual value

Method 2 predicted values

3.0

quantitative/Ah

2.9 2.8 2.7 2.6 2.5

0

100

200

300

500

400

Charge and Discharge Cycle/cyclicality

A1 failure threshold

Predicted values of the method in this paper Method 1 predicted values

actual value

Method 2 predicted values

3.0

quantitative/Ah

2.9 2.8 2.7 2.6 2.5

0

100

200

300

400

500

Charge and Discharge Cycle/cyclicality

A2 Predicted values of the method in this paper Method 1 predicted values

failure threshold actual value

Method 2 predicted values

3.0 2.9

quantitative/Ah

12

2.8 2.7 2.6 2.5

0

100

200

300

400

Charge and Discharge Cycle/cyclicality

A3 Fig. 6. Prediction result curves of battery

500

RUL Prediction Method of Series Battery

13

Predicted values of the method in this paper Method 1 predicted values

failure threshold actual value

Method 2 predicted values

3.0

quantitative/Ah

2.9 2.8 2.7 2.6 2.5

0

100

200

300

400

500

Charge and Discharge Cycle/cyclicality

A4 Fig. 6. (continued)

The metric of relative error was chosen to assess the predictive performance of different prediction methods, which was calculated using the following formula:   n 1 (12) ε= (Ci − Ci ) n i=1

where C i and C i’ denote the actual and predicted battery capacity values, respectively; n denotes the number of samples. Three prediction methods are utilized to predict the experimental cells A1 ~ A4RUL, and the number of experimental simulations is set to 30, the relative errors of the predictions of different prediction methods are counted, and the comparative results are shown in Fig. 7.

Fig. 7. Comparison of prediction relative error results of different algorithms

Analyzing the above figure, it can be seen that compared with Method 1, Method 2 and Method 3, the method designed in this paper predicts the RUL of the four batteries and

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obtains a smaller relative error of prediction, which are all below 0.03. Since the other two methods need to perform multiple random resampling of the battery capacity degradation data when building the prediction model, it makes it impossible to provide the model with the optimal number of predictions during the iteration process, which reduces the prediction accuracy. By comparing the lifespan, the prediction method designed in this paper can predict the battery RUL more accurately.

5 Summarize In this paper, a new RUL prediction method for series-type batteries is designed by utilizing the improved limit learning machine algorithm. In the study of this paper, the capacity decline parameters of series-type battery systems during charging and discharging are firstly extracted. On this basis, the advantages of the improved limit learning machine algorithm, which has the advantages of fast learning speed and no need to adjust the parameters, are utilized to establish a battery RUL prediction model, input the recession parameters into the model, and calculate the battery capacity dispersion and track the battery state, so as to obtain the prediction results of the battery RUL. The introduction of the improved limit learning machine algorithm effectively makes up for the shortcomings of low prediction accuracy of traditional methods and improves the prediction effect. In the future research, we will consider enriching the types and conditions of the battery recession dataset, and carry out an in-depth study on the RUL prediction of series-connected batteries under different operating conditions. Acknowledgement. This research is supported by Liaoning Applied Basic Research Program (2023JH2/101300138); Basic Research Program of Liaoning Provincial Department of Education (Key Research Projects) (LJKZZ20220046) ; Liaoning BaiQianWan Talents Program (2021921083); Liaoning Technology University Discipline Innovation Team Funding Program (LNTU20TD-29).

References 1. Huang, M., Hu, L., Zhang, Q.: Square-root quadrature Kalman filtering for remaining useful life prediction in lithium-ion battery. J. Xi’an Univ. Sci. Technol. 42(05), 994–1002 (2022). (in Chinese) 2. Zhu, C., Wang, H., Wu, Z.: Indirect prediction of RUL for li-ion batteries based on principal component analysis. J. Hebei Polytech. Coll. 22(01), 30–36 (2022). (in Chinese) 3. Chen, W., Li, F., Lin, Y.: Indirect prediction method of RUL for lithium-ion battery based on GA-ELM. Acta Metrologica Sinica 2041(06), 735–742 (2020). (in Chinese) 4. Xing, Z., Zhang, F., Wu, M.: Remaining life prediction of lithium-ion batteries based on WD-GRU. Chin. J. Power Sources 46(08), 867–871 (2022). (in Chinese) 5. He, N., Qian, C., Li, R.: RUL prediction for lithium-ion batteries via adaptive modeling and improved particle filter. J. Harbin Inst. Technol. 54(09), 111–121 (2022). (in Chinese) 6. Wending, Z., Shijian, B., Fangmin, X., et al.: Remaining useful life prediction of lithium-ion batteries using a fusion method based on Wasserstein GAN. J. China Univ. Posts Telecommun. 27(01), 1–91005–8885 (2020)

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7. Zhang, H., Hu, C., Du, D.: Remaining useful life prediction method of lithium-ion battery based on Bi-LSTM network under Multi-State influence. Acta Electronica Sinica 50(03), 619–624 (2022). (in Chinese) 8. Wei, M., Wang, Q., Ye, M., Xu, X.: An indirect remaining useful life prediction of lithium-ion batteries based on a NARX dynamic neural network. Chin. J. Eng. 44(03), 380–388 (2022). (in Chinese) 9. Song, Y., Liu, D., Hou, Y., et al.: Satellite lithium-ion battery remaining useful life estimation with an iterative updated RVM fused with the KF algorithm. Chin. J. Aeronaut. 31(01), 31–40 (2018) 10. Wang, B., Lei, M., Liang, J.: An IPSO-GRU-Based prediction of Remaining Useful life of lithium-ion batteries. J. Hunan Univ. Technol. 36(04), 23–30 (2022). (in Chinese) 11. Liao, Z., Yu, L., Li, S.: Remaining life prediction of lithium battery based on Stochastic Configuration Network. Combined Mach. Tool Autom. Mach. Technol. (05), 146–150 (2022). (in Chinese) 12. Zhou, Y., Guo, B., Wang, Y.: A remaining useful life prediction method for lithium-ion battery based on PF-ARIMA. Chin. Battery Ind. 26(01), 19–22 (2022). (in Chinese) 13. Ouyang, M., Qu, Q.: Remaining useful life prediction of lithium-ion battery based on SAEEEMD-GRU. J. Jiamusi Univ. (Natural Science Edition) 40(02), 43–49 (2022). (in Chinese) 14. Xu, Q., Wu, M., Khoo, E., et al.: A hybrid ensemble deep learning approach for early prediction of battery remaining useful life. IEEE/CAA J. Autom. Sin. 10(01), 177–187 (2023) 15. Jianfang, J., Keke, W., Xiaoqiong, P., et al.: Multi-scale prediction of RUL and SOH for lithium-ion batteries based on WNN-UPF Combined model. Chin. J. Electron. 30(01), 26–35 (2021)

Impulse Flashover Characteristics of High-Voltage Post Insulators in High Altitude Areas Yong Sun1 , Siyi Chen2 , Hailin Shi2 , Yanjie Cui1 , Zhijin Zhang2(B) , and Guohui Pang2 1 Maintenance and Test Centre of EHV Power Transmission Company of China Southern

Power Grid, Guangzhou, China 2 Xuefeng Mountain Energy Equipment Safety National Observation and Research Station of

Chongqing University, Chongqing University, Chongqing 400044, China [email protected]

Abstract. High-altitude areas present challenges for external insulation design due to the dry climate and thin air. This paper conducts high-voltage flashover experiments on a ceramic post insulator in a multifunctional artificial climate laboratory. Also, to better compare the characteristic of the testing insulator, the same experiments are performed on a reference post insulator which is commonly used in transmission lines. In order to simulate complex climate in different highaltitude areas, air pressure and absolute humidity are adjusted corrodingly. The research includes two types of voltage sources with positive and negative polarities. It is found that the testing insulator has a higher flashover voltage when a negative lightning testing voltage is applied. Besides, the influence of air pressure is studied. Further, a flashover voltage correction function and factor are given in this paper, based on the experiment results and cross comparison analysis on existing highaltitude insulator flashover studies. In conclusion, this paper provides a technical method of external insulation calculation for post insulators in high-altitude area. Keywords: Post Insulators · Lightning Impulse · Operating Impulse · Impulse Flashover Characteristics

1 Introduction China has a large land area and diverse topography. More than 70% of China’s land area has an altitude of more than 1 km.The average altitude of Qinghai-Tibet Plateau is more than 4 km. With the increase of altitude, the air density and air pressure decrease, which will lead to changes in the insulation strength of air. From previous experiences, the air insulation strength in high altitude areas is lower than that in plain areas. This will bring challenges to the external insulation of electrical equipment in high altitude areas. Low temperature, low air pressure and other factors at high altitude will affect the external insulation performance of insulators. Therefore, it is of great significance to study the pollution flashover characteristics of post insulators at high altitude. Scholars have carried out a lot of research on the flashover characteristics and influencing © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 16–27, 2024. https://doi.org/10.1007/978-981-97-1072-0_2

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factors of post insulators at high altitude, and have achieved certain research results. Lu [1] has carried out test researches on 110 kV post insulators in a multi-functional climate laboratory, and studied the measures to improve the ice flashover characteristics of post insulators by adding a climbing skirt. The relationship between the minimum AC flashover voltage of the standard pillar insulator and the conductivity and surface pollution of the ice-water coating is obtained. Jiang et al. [2] simulated the DC discharge characteristics of ice-coated smooth post insulators in a multi-function climate laboratory. The results show that the flashover voltage is different if there is ice. Sun et al. [3] conducted DC flashover test on post insulators in the artificial climate laboratory. According to the test results, the relationship between DC discharge voltage of power-station post insulators and altitude, rain rate, rain conductivity, pollution degree, was obtained. Yang et al. [4] conducted DC pollution flashover tests on four kinds of composite post insulators and two kinds of porcelain post insulators by using the up and down method at the actual altitude of 1970m. The effects of pollution, insulator material and geometry on DC pollution flashover characteristics were also studied. Nelson et al. [5] proposed that the design and application of electrical systems at the altitude over 1 km need to understand the influence of atmospheric conditions on each specific component. A lack of consideration for the high-altitude environment in the design and application of equipment can lead to aging and failure of electrical equipment. Sun et al. [6] proposed that the selection of electrical insulation clearance in the tunnel at high altitude above 4000 m. For the area with an altitude of 1000–4000 m, the correction coefficient can still be applied. Wan et al. [7] conducted flashover tests under low air pressure to simulate the situation at high-altitude areas, and proposed correction formulas. Zhang et al. [8] studied the lightning flashover characteristics of railway post insulators and discovered that tested insulators were unqualified for insulation requirements at certain region. Meng et al. [9] discussed AC flashover characteristics post insulators and proposed correction method of unevenly contaminated post porcelain insulators. Wang et al. [10] conducted switching impulse flashover test on uneven polluted insulators in natural environment and discovered that the polarity effect is obvious. However, for the area with an altitude above 4000 m, there is no corresponding reference standard at home and abroad for the selection of electrical external insulation, so it is necessary to conduct experimental research. Based on the experimental data of the influence of air pressure on the characteristics of AC discharge in short air gap, this paper systematically analyses the law of the influence of air pressure on the characteristics of AC discharge in short air gap between 100 and 310 mm. Post insulator is an important part of the power transmission system and external insulation equipment. The operation status of post insulator can be affected by natural environment, such as rain and fog weather. If the equipment is not cleaned timely, flashover accidents are very likely to occur in timid air. Thus, it is important to study the external insulation characteristics of post insulators and learn how to effectively prevent flashover accidents. The research on the external insulation characteristics and altitude correction can help to improve the safety level of transmission line.

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2 Methodology 2.1 Test Equipment In order to study the lightning and operating impulse flashover characteristics of sample post insulator at high altitude. All flashover tests are conducted in a multi-functional artificial climate laboratory at Chongqing University. Weather parameters such as air pressure and humidity can be changed in the laboratory to simulate climate conditions at different altitudes.

Fig. 1. Impulse voltage generator.

Fig. 2. Multi-functional artificial climate laboratory

As shown in Fig. 1, the impulse voltage generator has 16 stages. The nominal voltage of generator is ±3200 kV, and the nominal energy is 30 kJ. It can generate the standard

Impulse Flashover Characteristics of High-Voltage Post Insulators

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lightning wave (1.2 ± 30%/50 ± 20%µS) and the operating wave (250 ± 20%/2500 ± 30%µS) at different voltage levels. The output voltage can be adjusted by changing the resistance value of the wave head and wave tail along with the number of input capacitor stages. The multi-functional artificial climate laboratory is shown in Fig. 2. The laboratory has an inner diameter of 7.8 m and a height of 11.6 m. The laboratory consists of four main components, including the refrigeration system, the evacuation system, the spraying system and the wind speed adjustment system. The temperature of the laboratory can various from −45 ˚C to + 70 ˚C, which the precise control deviation of temperature is ± 0.5 ˚ C. The air pressure can be controlled from 35 kPa to 97 kPa, which can meet the demand of simulating climates at high-altitude areas. The spray and wind speed adjustment system can be used to adjust the humidity and water droplet diameter of the climate laboratory. The system consists of fourteen IEC standard recommended spray nozzles and ten fans with adjustable wind speed. The droplet particle diameter can be controlled between 10−120µm, and the wind speed range is 1−12 m/s. During testing, the voltage is introduced from the 330 kV through-wall bushing installed on the side of the laboratory. In brief, the laboratory can provide various of test conditions. 2.2 Test Setup The impulse testing equipment consists of impulse voltage generator, multi-functional artificial climate laboratory and measuring equipment. The testing schematic diagram is shown in Fig. 3.

Fig. 3. Test main equipment and wiring diagram.

2.3 Test Sample As shown in Fig. 4 and Fig. 5, the test sample is a ceramic post insulator, which is numbered as Sample A. And the lightning tests were also performed on a reference post insulator: sample B, which is commonly used in transmission lines. The relevant technical parameters are shown in Table 1, and the technical parameter diagram is shown in Fig. 6.

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Y. Sun et al. Table 1. Technical parameters of post insulators.

Sample

H (mm)

D0 (mm)

D1 (mm)

D2 (mm)

Sample A

2180

70.5

101.5

141.5

Sample B

1200

148

266

300

Fig. 4. Post insulator sample A.

Fig. 5. Post insulator sample B.

Impulse Flashover Characteristics of High-Voltage Post Insulators

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Fig. 6. Technical parameters diagram.

2.4 Test Procedure The flashover testing method meets requirement recommended by IEC60507 [11], GB/T4585 [12], DL/T859 [13] standards. The voltage was applied following the up and down method [14], which means that at least 15 valid tests were performed on the sample insulator for one test setup. First, the breakdown voltage of the insulator was estimated, and the impulse voltage generator was set and charged according to this expected voltage. If the insulator breakdown, then the single-stage voltage was decreased by 5 kV. Otherwise, the singlestage voltage was increased by 5 kV. The procedure continues until the flashover (or not flashover) happens four times continuously of the same tolerance. The U 50 was obtained using 15 valid values. The U 50 and its relative deviation error (σ ) were calculated as follows:  Ui ni (1) U50 = N   N  σ = (U − U )2 /(N − 1)/U × 100% (2) i

50

50

i=1

where U i is the applied voltage, ni is the number of the tests performed at the same applied voltage level U i , N is the number of valid tests.

3 Results 3.1 Lightning Impulse Flashover Testing Results All tests were conducted in the multi-functional climate laboratory in Chongqing University. Weather conditions at different altitudes were simulated by changing the air pressure using the laboratory, and the corresponding relationship between altitude and

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air pressure is shown as Table 2. Tests on both positive and negative polarity lightning impulse dry flashover were conducted by the method mentioned above, and the results are shown in Table 3 and Table 4, where P is the air pressure of the test, P0 is the standard atmosphere pressure (P0 = 101.3 kPa), h is absolute humidity, U 50 (+) is the 50% flashover voltage under positive polarity impulse voltage, U 50 (−) is the 50% flashover voltage under negative polarity impulse voltage. Table 2. Conversion relationship between altitude and air pressure. Altitude (m)

232

1000

3500

4000

Air Pressure (kPa)

97.9

89.8

65.8

61.7

Table 3. Lightning impulse (positive) flashover test results of sample A. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

19.02

1221.63

0.49

2

89.8

0.89

17.75

1122.60

0.55

3

65.8

0.65

14.78

859.16

0.65

4

61.7

0.61

15.67

813.88

0.88

Table 4. Lightning impulse (negative) flashover test results of sample A. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

20.84

−1646.94

0.53

2

89.8

0.89

23.35

−1504.51

0.40

3

65.8

0.65

18.00

−1136.75

0.70

4

61.7

0.61

17.42

−1062.51

0.74

Table 5. Lightning impulse (positive) flashover test results of sample B. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

19.44

631.09

0.72

2

89.8

0.89

16.33

583.13

0.68

3

65.8

0.65

17.99

439.00

0.77

4

61.7

0.61

24.86

422.40

1.45

Impulse Flashover Characteristics of High-Voltage Post Insulators Table 6. Lightning impulse (negative) flashover test results of sample B. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

21.54

−882.99

0.53

2

89.8

0.89

17.71

−839.11

0.34

3

65.8

0.65

15.39

−685.10

0.54

4

61.7

0.61

17.28

−655.49

0.59

Fig. 7. Relationship between P/P0 under positive lightning impulse voltage.

Fig. 8. Relationship between P/P0 under negative lightning impulse voltage.

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To better compare the flashover characteristic of samples, the lightning flashover tests were also performed on sample B following the same procedure. The test results are shown in Table 5 and Table 6. And Fig. 7 and Fig. 8 shows the comparison of flashover voltage between sample A and B under the same polarity of lightning impulse voltage. In the Fig. 7 and Fig. 8, R2 is the fitting correlation coefficient, and the closer R2 is to 1, the better fitting of linear formula is. As can be seen in Fig. 7 and Fig. 8, the conclusion can be drawn as: 1. At the same altitude, the breakdown voltages of sample A are higher than that of sample B. In other words, when sample A and B are set up at the same altitude, sample B is more likely to flashover. The U 50 (+) of sample A is 93.64% higher than the U 50 (+) of sample B, while U 50 (-) of sample A is 73.43% more than U 50 (-) of sample B. From the analysis of the insulator structure, sample A has more sheds and is higher than sample B, resulting in a greater creepage distance. 2. According to the test results, the relationship between air pressure and flashover voltage of sample insulators can be described as equations in Fig. 7. As the area altitude increases, the air pressure decreases, which obviously affects the U 50 . Especially for sample A, the influence factor of air pressure of positive lightning impulse voltage is 0.87, and the influence factor of negative lightning impulse voltage is 0.93. For sample B, the influence factors are 0.88 and 0.64 respectively. Besides, the fitting correlation coefficients R2 of the fitting curves are close to 1, which indicates that the fitting errors are small. The fitting function can well describe the relationships. 3. By comparing the test data, it is found that the U 50 of sample A is more affected by the pressure under the lightning impact of negative polarity than that of positive polarity. 3.2 Operating Impulse Flashover Testing Results As shown in Table 7 and Table 8, the operating impulse flashover tests were carried out in order to study the flashover characteristics of sample A. Table 7. Operating impulse (positive) flashover testing results for sample A. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

25.10

879.57

0.95

2

89.8

0.89

22.19

854.03

0.40

3

65.8

0.65

18.01

682.87

0.10

4

61.7

0.61

18.05

633.76

0.88

Impulse Flashover Characteristics of High-Voltage Post Insulators

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Table 8. Operating impulse (negative) flashover testing results for sample A. Number

P/kPa

P/P0

h/g/m3

U 50 (+)/kV

σ /%

1

97.9

0.97

14.86

−1237.11

0.68

2

89.8

0.89

17.61

−1124.03

0.91

3

65.8

0.65

19.72

−949.36

0.71

4

61.7

0.61

18.67

−861.25

0.55

Fig. 9. Relationship between P/P0 and U 50 under operating impulse for sample A.

Fig. 10. Comparison of U 50 under lightning impulse and operating impulse tests of sample A

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As it can be seen in Fig. 9 the relationship between P/P0 and U 50 under operating impulse can be expressed by fitting function. And Fig. 10 shows the comparison U 50 of sample A under different kind impulse voltage. The conclusion can be drawn as: 1. For sample A, the influence factors of air pressure of positive and negative operating impulse are both 0.70, which shows that air pressure P has the same degree of influence on U 50 for both polarity cases. The fitting correlation parameters of the function R2 are 0.976 and 0.988 respectively. Comparing to the lightning impulse test results, the operating impulse tests results less well fitted the equation. 2. For sample A, the absolute value of U 50 (-) is up to 1237.11 kV. The flashover voltage of sample A at 4000 m altitude was only 69.62% of that at atmospheric air pressure. And it can be seen that air pressure has a great influence on flashover voltage. In general, the flashover voltage of sample A is higher than that of positive polarity. Meanwhile, sample A is easier to breakdown under operating impulse tests than under lightning impulse tests.

4 Conclusion The lightning impulse and operating impulse voltage test of ceramic post insulator was conducted in a multi-functional climate laboratory, and the results were present above. The conclusion can be drawn as follows: 1. This paper provides a method to calculate porcelain post insulator flashover voltage in high-altitude area based on air pressure. For the lightning impulse voltage tests, the flashover voltage U 50 of sample A can be described using following function: P 0.87 ) P0 P U50 (−) = −1686.84 × ( )0.93 P0 U50 (+) = 1249.54 × (

(3) (4)

For operating impulse: P 0.70 ) (5) P0 P U50 (−) = −1247.30 × ( )0.70 (6) P0 The negative lightning impulse flashover voltage of insulator is most affected by the change of air pressure among the four cases. U50 (+) = 910.70 × (

2. For the two tested samples, the flashover voltage of both polarity lightning impulse of sample A is higher than sample B by 93.64% and 73.43% respectively. And for sample A, the negative lightning impulse flashover voltage is averagely 333.36 kV higher than the positive lightning impulse flashover voltage. As for operating impulse, the higher value is 280.38 kV. Acknowledgements. The research is supported by the Key Science and Technology Projects of China Southern Power Grid Corporation, grant number CGYKJXM20210338.

Impulse Flashover Characteristics of High-Voltage Post Insulators

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References 1. Lu, J.: Research on AC flashover characteristics and Anti-ice flashover measures of 110kV post insulators covered by ice. Master Thesis, Chongqing University (2008). (in Chinese) 2. Yuan, J., Jiang, X., Zhang, Z.: Experimental study on DC discharge characteristics of iced smooth post insulators. High Voltage 1, 8–10 (2006) 3. Sun, C., et al.: DC discharge characteristics of power station type pillar insulators in high altitude, rain and dirty environment. Trans. China Electrotechnical Soc. 1, 41–45+64 (1991). (in Chinese) 4. Yang, H., et al.: DC pollution flashover characteristics of ±800kV composite post insulators in high altitude areas. High Voltage 35(04), 749–754 (2009). (in Chinese) 5. Nelson, J.P.: High-altitude considerations for electrical power systems and components. IEEE Trans. Ind. Appl. IA-20(2), 407–412 (1984) 6. Sun, C., et al.: Characteristics and voltage correction of short gap AC discharge above 4000. Proc. CSEE 22(10), 116–120 (2002). (in Chinese) 7. Wan, X., et al.: AC pollution flashover characteristics of post insulators under low air pressure. In: 2023 IEEE 4th International Conference on Electrical Materials and Power Equipment (ICEMPE), pp. 1–4, IEEE, China (2023) 8. Zhang, Z., et al.: Flashover characteristics and altitude correction of railway insulators at high altitude and polluted areas. Electr. Power Syst. Res. 224, 109724 (2023). https://doi.org/10. 1016/j.epsr.2023.109724 9. Meng, H., et al.: AC flashover characteristics of post porcelain insulators with non-uniform pollution on top and bottom surfaces. Electr. Eng. 15, 207–210 (2022) 10. Wang, M., et al.: Switching impulse flashover performance of nonuniform pollution insulators in natural environment. IEEE Trans. Dielectr. Electr. Insul. 30(2), 844–851 (2023) 11. IEC 60507: Artificial pollution tests on high-voltage ceramic and glass insulators to be used on AC systems (2013) 12. GB/T 4585: Artificial pollution tests on high-voltage insulators to be used on AC. systems (2004). (in Chinese) 13. DL/T859: Artificial pollution tests on composite insulators used on high-voltage AC systems (2015). (in Chinese) 14. Zhang, Z., et al.: AC flashover performance of different shed configurations of composite insulators under fan-shaped non-uniform pollution. High Voltage 3(3), 199–206 (2018). (in Chinese)

Multi-agent Distributed Cooperative Control of Multi-energy Complementary Microgrid Rui Ma1(B) , Hui Fan2 , Jianfeng Li1 , and Xiaoguang Hao1 1 State Grid Hebei Electric Power Research Institute, Shijiazhuang 050021, China

[email protected]

2 State Grid Hebei Electric Power Company, Shijiazhuang 050021, China

[email protected]

Abstract. With the increasing use of distributed energy, the concept of microgrid has been proposed and used to coordinate the management of single distributed energy and load. For the large grid, the microgrid is represented as a single manageable unit, which meets the reliability and security requirements of customers. The microgrid can be connected to the power grid or disconnected from the main power grid, and operates in island mode in case of grid failure or need. Therefore, it is very important to ensure the power quality in the island microgrid. However, few people have studied multi-agent distributed cooperative control of multi-energy complementary microgrid (MECM for short here), so this paper focused on this topic. Firstly, this paper introduced the MECM and microgrid control mode, then analyzed the multi-agent system, and then discussed the distributed generation and distributed management control system. At the end of this paper, the multi-agent distributed cooperative control of building MECM was analyzed, and the feasibility conclusion was drawn. In the micro-grid scenario of load change in grid-connected operation mode, this paper simulated the coordination and scheduling process of each agent layer and found that the coordination control system proposed in this paper had great stability. In the island operation mode, the multi-agent distributed cooperative control system based on MECM can well adapt to the sudden change of microgrid load even in the autonomous operation. The power of micro-source without radio wave change was maintained at 80kW. At present, microgrid had a relatively wide application space, and also had a relatively broad application prospect in the development of collaborative control system. Keywords: Distributed Cooperative Control · Multi-energy Complementary Microgrid · Circuit Analysis · Multi-Intelligent Body

1 Introduction With the shortage of fossil fuels and the aggravation of pollution, the shortcomings of traditional energy grid are becoming more and more obvious. Microgrid based on renewable energy such as solar energy and wind energy began to develop rapidly. It needs to manage the microgrid reasonably and effectively to ensure the reliable operation © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 28–41, 2024. https://doi.org/10.1007/978-981-97-1072-0_3

Multi-agent Distributed Cooperative Control

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of energy. Moreover, the MECM has gradually come into the public’s view at present, and there is more in-depth research in the use of energy, but no one has applied it to the research of multi-agent distributed collaborative control. Therefore, it is of practical significance to study this aspect. At present, microgrid is widely used, and many scholars have studied this field. Wang YL studied the optimal operation of MECM based on moth-flame optimization algorithm [1]. Bai, Kaifeng analyzed the optimal configuration of MECM based on wind power and photovoltaic output scenario generation [2]. Teng Y studied the model of electrothermal hybrid energy storage system for improving the autonomous control capability of multi-energy microgrid [3]. Wang X analyzed the equilibrium state of the multi-energy market with micro-grid bidding [4]. Chen X conducted research on the land-sea relay fishery network microgrid in the context of network-physical integration [5]. Jithendranath. J believed that the island microgrid with uncertain multi-energy demand and renewable energy power generation was randomly planned [6]. Kaifeng, Bai designed the optimal configuration of MECM based on wind power and photovoltaic output scenario generation [7]. There was no research on collaborative control in the research on microgrid. Multi-agent is also widely used in life, and this technology has greatly facilitated people’s life. Cheedella. N used multiple intelligent technology to automatically control the wheelchair [8]. However, many scholars rarely apply multi-agent to the analysis of collaborative control. In order to improve the stability of distributed cooperative control, the system design method is adopted to build a multi-agent distributed cooperative control system for MECM. Through the simulation of grid-connected operation mode and island operation mode, this paper finally obtained that the multi-agent distributed cooperative control system based on MECM had high adaptability to the dynamic change of microgrid load. This paper made use of MECM and multi-agent, and combined them to apply to distributed collaborative control, which had certain reference value.

2 Multi-energy Complementary Microgrid and Microgrid Control Mode The micro-grid represented by the distributed generation system can realize the diversification and intelligent utilization of renewable energy, which can better meet users’ requirements for power quality and reliability. When the MECM microgrid is incorporated into the power system, the traditional distribution system mode has also changed. Especially when the number of micro-grids is large, the distribution system has changed from the original role of only responsible for distribution to a new type of energy system. When deploying the microgrid, attention should be paid to the application scale according to the load characteristics, so that customers can use thermal and electric energy. According to the type of buildings, the operating standards used and the weather conditions in each region, different customer load conditions may bring some problems to the actual operation of the system. Therefore, it should keep in mind the changes in customers’ actual needs, energy prices sold, weather conditions, and equipment prices sold, and constantly adapt to the microgrid. In addition, since the use of clean and

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renewable energy and micro-grid depends on policies, the energy structure needs to be adjusted over time to conform to existing policies, so as to maximize economic benefits. 2.1 Main Advantages of Microgrid Over Traditional Grid Power Supply The distributed energy in the microgrid is mostly clean and renewable energy, with the characteristics of low pollution. It helps to solve the mismatch between energy demand and scarcity, energy consumption and environmental protection. Microgrid eliminates the disadvantages of grid connection of distributed energy, makes full use of distributed energy, and can flexibly connect or disconnect, reflecting “plug and play” [9]. If one or more distributed energy resources fail, they should coordinate and manage the distributed energy resources in the microgrid. This can not only make the remaining distributed energy resources continue to meet the energy demand of the entire microgrid, but also ensure the stability and security of grid operation and improve the reliability of energy supply. 2.2 Microgrid Control Strategy A key technology in microgrid research is microgrid energy management [10, 11]. The basic requirement of microgrid power management is to be able to coordinate microgrid power and load, and independently select the operation point. It can operate stably in grid-connected and isolated modes, and make a smooth transition between the two modes. It can independently control active and reactive power, and can independently correct voltage deviation and system imbalance. Master-Slave Control Strategy. When connected to the grid, the output of each distributed power supply must be adjusted to a constant level. When the power system is not running and enters the isolation mode, one of the distributed power sources (the main power supply) switches to V/f regulation to maintain a constant voltage and its own output power, which increases or decreases power according to the load change. In this way, the main distributed power supply can ensure that the voltage and frequency in the isolation system are maintained, while other distributed power supplies are not responsible for regulation. If the distributed power supply controlled by V/f has problems in island mode, the whole system cannot continue to operate normally. Therefore, the stability of the microgrid in the island mode completely depends on the main distributed power supply, and highly depends on it [12, 13]. The primary and secondary control depends on reliable communication and requires the ability to accurately detect the time of network failure. Without effective communication, such control would fail or fail, and communication equipment would increase the cost and complexity of microgrid [14]. The power fluctuation caused by load fluctuation must be compensated by the master distributed power supply first, and such distributed power supply needs a large amount of rotating power reserve. Peer Control Strategy. The peer-to-peer control strategy is based on the plug-and-play and peer-to-peer control concepts of power electronics. Each distributed power supply is “equal” and there is no subordinate relationship. In peer-to-peer microgrid management,

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each microgrid is managed in a delayed manner. Once the bias coefficient, active and reactive power and voltage reference values are determined, each managed distributed power supply would be controlled according to these determined parameters to ensure the stability of the microgrid voltage and frequency. In the peer-to-peer control strategy, each distributed power supply controller operates on the basis of local information, and only needs to measure the electrical quantity at the output end of the inverter, without receiving the communication data of other distributed power supplies. Therefore, it participates in voltage and frequency regulation independently and responds to load changes in a predetermined manner. Since the peer-to-peer control strategy only considers the primary frequency control and does not consider the secondary control of the conventional generator, the recovery process of the microgrid system is not controlled. This may cause the voltage and frequency to not return to the original state. Therefore, if the microgrid is seriously damaged, the system frequency would fluctuate greatly, and normal load operation cannot be guaranteed. In addition, this method is only applicable to the control of distributed power generation based on power electronics technology.

2.3 Microgrid Control Mode The existing microgrid control methods can be roughly divided into two types: centralized management and decentralized management. The traditional centralized control is usually controlled by a central controller to control all terminals in the microgrid. The system relies heavily on the central controller, and its reliability, scalability and flexibility are not enough, so it is difficult to meet the management requirements of today’s rapidly growing distributed generation. Decentralized control usually has no central controller, and the control of the micro system is distributed to all distributed terminals. Each distributed terminal makes control decisions independently according to local information, and there is the most basic communication mechanism between terminals. Completely decentralized control is prone to power supply and load management being out of sync, which may lead to the microsystem not conforming to the specification in serious cases. Therefore, it must not only meet the needs of the microsystem for its own physical equipment to meet the electrical constraints, but also meet the overall coordination of the entire microsystem, which inevitably leads to the conflict between these two requirements. Pure distributed control makes independent decisions and controls on each distributed terminal in the microgrid based on local information, reducing the amount of information between the slave controller and the central controller. However, it is very sensitive to asynchronous power supply and load control. In serious cases, it may cause the microsystem not to be listed. Therefore, it needs to recognize that the physical equipment of the microsystem needs to meet the electrical requirements and the overall coordination needs of the whole microsystem, which inevitably leads to conflicts between the two.

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2.4 Typical Microgrid Control Technology Typical microgrid control technologies are divided into “plug and play” and “peer to peer” control based on power electronics technology, control based on power management system and microgrid control based on multi-agent technology, which are summarized in Fig. 1: Power electronics-based "plug-and-play" and "peer-to-peer" control

Power management system with different microgrid control strategies depending on voltage fluctuation characteristics, voltage regulation, load reactive power compensation

Simple, reliable and easy to implement as it requires any communication channel between microgrids

Control based on power management systems

Microgrid control based on multi-intelligence technologies

Smartbody has good autonomy, flexibility, spontaneity and sociality

Fig. 1. Typical microgrid control technology

“Plug and Play” and “Peer to Peer” Control Based on Power Electronics Technology. This method uses the characteristic attenuation curve similar to the ordinary generator attenuation curve. According to the control requirements of the microgrid, it controls the active and reactive power of each microgrid source in the microgrid. This can enable each microgrid source to reasonably absorb the unbalanced power in the microgrid, so as to achieve the supply and demand balance and frequency stability of the microgrid. This method does not need any communication channel between microgrids, so it is simple, reliable and easy to implement, but it does not take into account the voltage and frequency recovery of the system. Therefore, the power quality of the system cannot be guaranteed when the external environment causes serious interference to the microgrid. Control Based on Power Management System. This method separates active power and reactive power and controls them separately to meet the adaptive control requirements of microgrid. At the same time, it adds a voltage and frequency recovery algorithm to adjust the power balance of the microgrid and meet the power quality requirements of the microgrid. For different reactive power requirements in the microgrid, the power management system adopts different microgrid control strategies according to voltage fluctuation characteristics, voltage regulation and load reactive compensation. These control strategies allow more flexible microgrid management and more coordinated management between microgrids. Microgrid Control Based on Multi-agent Technology. This method introduces intelligent multi-agent technology into the field of microgrid control system. The agent has

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good autonomy, flexibility, spontaneity and sociality, which just meets the needs of distributed microgrid management. The smart trunk network can deploy different management modes. When each smart trunk network joins the network, other smart trunk networks can adapt to their own management modes according to a set of logical connections. This makes them suitable for systems that do not require frequent presence of managers. However, the existing multi-agent technology in microgrid mainly focuses on coordinating market transactions and energy management, while the research on frequency, voltage and power management in microgrid is still underdeveloped.

3 Multi-agent System (MAS) MAS is generally defined as an interconnected intelligent system network with specific communication, computing, sensing, communication and execution capabilities. The basic idea is that the whole is greater than the sum of the parts, because the higher level interaction is based on the very limited intelligence of individuals, which represents a distributed, coordinated and cooperative system. The control strategy of distributed microgrid can be realized by using consistency algorithm. The consistency algorithm refers to the mutual connection between each microgrid and its adjacent nodes, and finally makes the state of each microgrid consistent. The solution to the consistency problem is based on the structure of multi-agent. The agents cooperate with each other to complete tasks that cannot be completed by a single agent. Economic allocation achieves economic objectives by optimizing the operation of the microgrid and minimizing the total cost of generators by satisfying constraints. The performance of MAS is mainly achieved through the interaction of agents. Agents can solve problems that cannot be solved by a single agent. In practical applications, the characteristics of agents and agent control methods make multiple agents have incomparable advantages in complex systems and have broad market potential. Therefore, compared with traditional power grid control methods, MAS conforms to the trend of power grid distribution and makes better use of distributed energy resources. MAS has better coordinated the operation of microgrid and microgrid, microgrid and supergrid. The implementation of MAS enhances the support of microgrid to the main grid.

4 Distributed Generation and Distributed Management Control System The so-called distributed control is to build a network so that information can only be exchanged between adjacent nodes, which would lead to a unified response of the entire network. Through this control mode, nodes can operate in a “plug and play” mode, and the blocking of an information channel would not affect the stability of the entire system. Due to the pollution and shortage of fossil energy, many people are gradually turning their attention to clean and sustainable energy, such as wind energy, solar energy and gas micro-turbines. Clean energy has the characteristics of intermittent, unregulated and

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distributed due to its regional environment, which makes it an ideal choice for distributed supervision. The principle of selecting the address is to be as close to the user or load as possible. The generator set is usually a generator of tens of kilowatts to tens of megawatts. It only needs to provide services for specific users to achieve economic, efficient and reliable power generation technology. Today, distributed generation is actually used as a backup power source. Distributed power generation is also known as distributed or embedded power generation in many documents. It has low pollution, high energy efficiency, and low requirements for installation space. It can be installed anywhere. This effectively improves the peak-valley characteristics of the power grid, effectively complements the shortcomings of the power grid, and greatly enhances the reliability of the power grid. Compared with the traditional centralized power plant, its operation cost is low and the power grid loss is also reduced. Therefore, distributed generation is a trend of energy system. The distributed control system can also be used to control the microgrid. Compared with the traditional centralized control mode, the distributed coordinated control of the typical agent system excludes the large system. Each small system exists independently. While receiving the instructions of the main control unit, it can realize self-control and make final decisions after combination. This means faster response and higher accuracy than centralized control.

5 Design of Collaborative Control System 5.1 Microgrid Collaborative Control Technology The microgrid is connected to the grid through the grid switch, and the control of its operation mode depends on the flexibility of the control strategy of each distributed energy converter in the microgrid. On the other hand, it depends on the control strategy of the grid-connected microgrid converter and the coordinated control between the grid switches. The accurate and rapid coordination between them provides an important basis for controlling the operation mode of the microgrid. This also means that the strategy used to implement cooperative control would have a significant impact on the management of microgrid operation mechanism. At present, the research on microgrid collaborative control can be divided into two categories: “with communication” collaborative control technology and “without communication” collaborative control technology. “with Communication” Collaborative Control Technology. “Communication” collaborative control means that the operation information of each distributed energy in the microgrid should be sent to the central control center, which would analyze and make decisions. It then sends distribution information to each distributed energy to coordinate the operation of each distributed energy. This requires that the microgrid has enough communication lines to transmit control information. “without Communication” Collaborative Control Technology. Non-communication collaborative control means that each distributed energy resource in the microgrid is controlled independently according to its local operation information, without communication links, and allows the connection and disconnection of distributed

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energy resources. Compared with cooperative communication control, non-interactive cooperative control has many advantages.

5.2 Microgrid Control Strategy Based on Multi-agent Distributed Algorithm Cooperative control without communication means that each distributed energy resource in the microgrid is controlled independently according to its local operation information, without communication links, and allows the connection and disconnection of distributed energy resources. Due to the lack of inertia in the microsystem control, the interference mitigation ability is poor, and the connection is complex and heterogeneous. Therefore, for complex microsystem control, the strategy is divided into the following three layers, as shown in Fig. 2:

Second layer Third layer

First layer

Control layer

Based on the tradional distributed power control strategy, acve frequency and reacve voltage are controlled to achieve power and frequency distribuon and voltage regulaon

Stabilization layer

Eliminates frequency and voltage deviations caused by the primary control layer and maintains frequency and voltage near the rated value.

Distribuon layer

Controls the flow of energy between individual distributed energy sources and between the microgrid and the outside world.

Fig. 2. Microgrid control strategy based on multi-intelligent distributed algorithm

The first layer is the control layer: the control layer is mainly based on the traditional distributed power control strategy to control the active frequency and reactive voltage, and realize the distribution of power and frequency and voltage regulation. The second layer is the stabilization layer: the main purpose of this layer is to eliminate the deviation of frequency and voltage caused by the primary control layer, and maintain the frequency and voltage near the rated value. The third layer is the distribution layer, which controls the energy flow between distributed energy sources and between the microgrid and the outside world. The traditional hierarchical control is based on the centralized control center, which is not flexible enough, while the distributed control algorithm can consider hierarchical control. Because they only need a small number of communication links and information exchange to achieve global control, they are more suitable for the needs of microgrid in terms of cost-effectiveness and robustness. 5.3 System Design Scheme The main controller is used to respond to sudden changes between power supply and load to balance power supply and load. Unlike synchronous generators, the output frequency

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of Virtual Switch Interface (VSI) is independent of other power supplies. Therefore, after measuring the power delivered by each VSI, the bias controller can be used to change the output frequency in a certain proportion. In this paper, a primary controller is installed in each VSI, and its frequency and droop characteristics are as follows: ⎧ ∗   w = w0j − λqj Rhj − R0j ⎪ ⎪ ⎨ j   Ucj∗ = Uc0j − λ Shj − S0j (1) ⎪ ⎪ ⎩ U∗ = 0 pj

In the formula, w* j and U* cj refer to the frequency and voltage commands sent to the jth inverter; In synchronous rotation, U* pj is 0 in the coordinate system, referring to the output voltage; Rhj and S hj respectively represent the active and reactive output of the ith power supply: ⎧  wdj  ⎪ ⎪ ⎨ Rhj = P + wdj Tcj jcj + Tpj jpj (2) P ⎪ ⎪ (Tpj jpj − Tcj jcj ) ⎩ Shj = P + wdj In the formula, T cj , T pj , jcj , jpj represent the components of voltage and current in the direct-axis direction and quadrature axis respectively; wdj represents the cut-off frequency of the low-pass filter. hypothesis wj ≈ wj∗ , Ucj ≈ Ucj∗ , Upj ≈ Upj∗ then



  wj = w0j − λqj Rhj − R0j   Ucj = Uc0j − λ Shj − S0j

(3)

(4)

In the formula, Rhj , R0j , w0j , U c0j represent the dynamic parameters of the main controller. In order to achieve coordination, the input of the coordination control system: uwj =

α(βNF − βMDD ) α 2 (βNF − βMDD ) + αt αt 2

(5)

6 Simulation Experiment of Cooperative Control In order to verify the adaptability and efficiency of the multi-agent distributed cooperative control system for MECM proposed in this paper, this paper simulates the coordination and scheduling process of each agent layer under the microgrid scenario of load change in grid-connected operation mode and isolated operation mode. The five micro-sources selected are marked as A, B, C, D and E.

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6.1 Grid-Connected Operation Mode During grid-connected operation, the initial output of micro-source A, B, C, D, E and the initial demand power of load A, load B, load C, load D, and load E can be seen in Table 1: Table 1. Microsource output and load power under grid-connected operation scenario Microsource

Rated power(kW)

Output power(kW)

Load

Load demand power(kW)

A

120

80

Load A

80

B

120

80

Load B

80

C

120

80

Load C

80

D

120

80

Load D

80

E

120

80

Load E

120

The constant power control strategy is adopted for LAN (local area network) control A, LAN control B, LAN control C, LAN control D, and LAN control E. At 0 ~ 0.6s, the microgrid operates stably, and the load B of micro-source B controlled by the local area network suddenly increases by 40kW in 0.6s ~ 1.0s. Load B remains unchanged for 1.0s ~ 1.6s, and load B decreases by 80kW for 1.6–2.0s. This paper checks whether the microgrid control system can respond to sudden load changes when it is not connected to the grid. According to this condition, the output of each micro-source and distribution network in case of sudden load change under grid-connected operation mode is recorded in Fig. 3:

Fig. 3. Each micro-source and grid output in grid-connected operation mode (a) A.A (b) B.B (c) C.C (d) D.D

In Fig. 3, A represents the active power and reactive power output of A under gridconnected operation mode, and B represents the active power and reactive power output of B under grid-connected operation mode. C represents C active power and reactive

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power output under grid-connected operation mode, and D represents D active power and reactive power output under grid-connected operation mode. The coordination and planning process of each layer of the microgrid control system is as follows: From 0 to 0.6s, when each agent is in control mode, the power of each microgrid is 80kW, and the total power is 400kW. Since the total load is 440kW, the power provided by the microgrid is insufficient to meet the local load demand. Therefore, 40kW power needs to be obtained from the distribution network. From 0.6s to 1.0s, the load of LoadB suddenly increased by 40kW. When LoadAgentB checks the demand power change of the load, it sends the current demand information of LoadB to the top-level LocalAgentB. After receiving the information, LocalAgentB extracts the information from the information and calculates the power difference according to the principle of regional autonomy. The first step is to calculate the power difference according to the principle of regional autonomy, and determine whether the output power control range of micro-resources in the region matches the load demand. In this local area, the rated capacity of micro-source B is 120kW, and the total load demand of LoadB is 120kW, so micro-source B can use its maximum capacity to meet the load demand of LoadB. The power supply and demand in this region are balanced, while the power of other micro sources A, C and D is 80kW. From 1.0s to 1.6s, LoadB has no change. The total demand of LoadB reaches 120kW. LoadAgentB checks the power change and sends the current demand information of LoadB to the superior LocalAgentB. Then the LocalAgentB sends a coordination request to the superior MASAgent to enter the global coordination mode. Then, MASAgent enters the global coordination mode. According to the capacity feedback of each microagent and the load demand of each LocalAgent, MASAGENT determines the global capacity gap, and increases the capacity interaction with the distribution network by increasing the capacity of 40kW to balance the capacity demand and supply of the microgrid, while the capacity of other micro-agents is not affected. After 1.6–2.0s, LoadB dropped sharply by 80kW. After receiving the load demand change information, LocalAgentB calculates and analyzes according to the principle of regional autonomy, and determines that the output power of micro-agent B exceeds the demand. So the local agent B adjusted the predetermined power value of the constant power control strategy and set it to 80kW, 0kVar. At the same time, it sends the load change information to the upstream MASAGENT to reduce the energy interaction with the distribution network according to the principle of global cooperation. During operation, each LocalAgent uses a constant power control strategy, and the voltage and frequency of the microgrid are maintained according to the distribution network parameters. Based on the grid-connected operation mode, it can be seen that the multi-agent distributed cooperative control system based on MECM has high adaptability to the dynamic change of microgrid load. The microgrid control system can jointly control agents at all levels according to load changes, and dynamically adjust the power of each microgrid and distribution network. This can maintain the balance of power supply and demand of the microgrid, help to stabilize the overvoltage of the distribution network, and reduce the scheduling difficulty of the large-capacity microgrid.

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6.2 Island Operation Simulation During island operation, the initial output of micro-source A, B, C, D and E and the initial demand power of load A, B, C, D and E can be seen in Table 2: Table 2. Micro-source output and load power under islanding operation scenario Microsource

Rated power(kW)

Outputpower(kW)

Load

Load demand power(kW)

A

120

80

Load A

80

B

120

80

Load B

80

C

120

80

Load C

80

D

120

80

Load D

80

E

120

80

Load E

80

Local area control B follows the V/f management strategy, and all other local area controls follow the constant power control strategy. At the time of 0 ~ 0.6s, the microgrid operates stably. At the time of 0.6s ~ 1.0s, the load at B end rapidly increases by 40kW. At the time of 1.0s ~ 1.4s, the load at B end basically remains unchanged. At the time of 1.4s ~ 1.8s, the load at B end decreases by 80kW, which controls the response of the microgrid control system to the sudden change of island load. This paper studies the response ability of microgrid control system to sudden load changes in island mode. According to this condition, the performance of each microgrid and distribution network when the unexpected load changes in island mode is shown in Fig. 4:

Fig. 4. Each microsource and grid output in islanded operation mode (a) A.B (b) B.C (c) C.D (d) D.E

In Fig. 4, A represents the active power and reactive power output of B in island operation mode, and B represents the active power and reactive power output of C in island operation mode. C represents D active power and reactive power output in island operation mode, and D represents E active power and reactive power output in island operation mode.

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It can be seen from the island operation mode that the multi-agent distributed cooperative control system based on MECM can well adapt to the sudden change of microgrid load even in autonomous operation. The microgrid control system can adjust the set point of power management strategy of each local controller according to the change of load, and coordinate the power of each microgrid resource to balance the microgrid power and load power demand.

7 Conclusions In order to analyze the adaptability and efficiency of the multi-agent distributed cooperative control system of MECM proposed in this paper, this paper used MECM and multiagent to design the distributed cooperative control system. At the same time, this paper designed experiments to analyze the stability of the system in grid-connected operation mode and island mode, and finally found that the multi-agent distributed cooperative control system based on MECM had high adaptability to the dynamic changes of microgrid load in grid-connected operation mode. In island mode, multi-agent distributed cooperative control system based on MECM can quickly respond to power changes to meet the demand of voltage changes. In the future, MECM would be widely used in public life, and more and more people would make rational use of MECM. Acknowledgements. This work is supported in part by the Science and Technology Project of Hebei Electric Power Company (kj2021–002).

References 1. Wang, Y.L.: Optimal operation of microgrid with multi-energy complementary based on moth flame optimization algorithm. Energy Sources Part A 42(7), 785–806 (2020) 2. Bai, K.F.: Optimal allocation for MECM based on scenario generation of wind power and photovoltaic output. Autom. Electr. Power Syst. 42(15), 133–141 (2018). (in Chinese) 3. Teng, Y.: A model of electro-thermal hybrid energy storage system for autonomous control capability enhancement of multi-energy microgrid. CSEE J. Power Energy Syst. 5(4), 489– 497 (2019) 4. Wang, X., Ying, Z., Zhang, S.H.: Equilibrium analysis of multi-energy markets with microgrids bidding. IEEJ Trans. Electr. Electron. Eng. 15(7), 1020–1031 (2020). (in Chinese) 5. Chen, X., Ju, Y.T., Zhang, R.S.: Land-sea relay fishery networked microgrids under the background of cyber-physical fusion: Characteristics and key issues prospect. Inf. Process. Agric. 9(1), 159–169 (2022) 6. Jithendranath, J., Das, D.: Stochastic planning of islanded microgrids with uncertain multienergy demands and renewable generations. IET Renew. Power Gener. 14(19), 4179–4192 (2020) 7. Bai, K.F.: Optimal allocation for multi-energy complementary microgrid based on scenario generation of wind power and photovoltaic output. Autom. Electr. Power Syst. 42(15), 133– 141 (2018). (in Chinese) 8. Cheedella, N., Andanapalli, K., Cheepurupalli, R.: Automatic controlled wheel chair using multi-intelligence technique. J. Comput. Theor. Nanosci. 17(5), 2273–2278 (2020)

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9. Michael, S.: Planning and implementation of bankable microgrids. Electr. J. 32(5), 24–29 (2019) 10. Zhang, L.: A review on protection of DC microgrids. J. Mod. Power Syst. Clean Energy 6(6), 1113–1127 (2018) 11. Gao, F.: Primary and secondary control in DC microgrids: a review. J. Mod. Power Syst. Clean Energy 7(2), 227–242 (2019) 12. Elshaari, A.W.: Hybrid integrated quantum photonic circuits. Nat. Photonics 14(5), 285–298 (2020) 13. Steve, P.: Why microgrids are becoming an important part of the energy infrastructure. Electr. J. 32(5), 17–21 (2019) 14. Joshua, A.: Electricity intensity of internet data transmission: untangling the estimates. J. Ind. Ecol. 22(4), 785–798 (2018)

Effect of Low Temperature on Impulse Discharge Characteristics of Insulator String Lei Wang1 , Yu Su2(B) , Jian Zhang1 , Xiuyuan Yao2 , Bingxue Yang3 , Zhiwei Li3 , and Yujian Ding2 1 State Grid Heilongjiang Electric Power Co., Ltd Electric Power Research Institute,

Harbin 150030, China 2 China Electric Power Research Institute Co., Ltd., Beijing 100192, China

[email protected] 3 North China Electric Power University, Beijing 102206, China

Abstract. Due to the geographical location, many transmission lines operate in cold conditions for a long period of the year. However, the existing standards are mostly only applicable for the correction of the discharge voltage of the external insulation above 5 °C. The relevant basic data under low temperature are lacking and there is no targeted optimization and improvement for the external insulation. In this paper, switching impulse discharge and lightning impulse discharge tests on insulator strings using XWP-70 insulator are carried out at normal temperature and low temperature respectively. The results show that the switching impulse discharge voltage of insulator string is lower than that of lightning impulse discharge. With the decrease of temperature, both the witching impulse discharge voltage and the lightning impulse discharge voltage increase, and the increase of lightning impulse discharge voltage is greater than that of witching impulse. It indicates that the external insulation configuration at low temperatures can be optimized. The research results can provide theoretical support for the design and optimization of external insulation of transmission lines under perennial low temperature environment. It has important reference value for ensuring the safe operation of power grid, improving the stability of electrical equipment and reducing operation and maintenance costs in extremely cold areas. Keywords: Low temperature · Insulator string · Switching impulse · Lightning impulse · Discharge characteristics

1 Introduction The insulator is an important part of the UHV DC transmission system, and its impulse discharge characteristics can affect the lightning performance of the DC transmission line, which is one of the long-term concerns in the field of high voltage engineering [1, 2]. The discharge characteristics of insulator strings are affected by various factors such as size structure and atmospheric environment, and there are different degrees of difference in impulse discharge voltage under different altitudes and temperature and humidity conditions [3–5]. Studying the impulse discharge characteristics of insulator © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 42–49, 2024. https://doi.org/10.1007/978-981-97-1072-0_4

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strings under different environmental conditions has very important guiding significance for the external insulation design of UHV transmission lines. Literature [6] studied the artificial snow flashover characteristics of 110kV AC post insulators, and analyzed the arc discharge and flashover characteristics during the flashover process. The experiment obtained the change law of flashover voltage under different pollution salt density and different snow thickness. Literature [7] and [8] obtained the lightning and switching impulse flashover characteristics of insulators with non-uniform pollution respectively, and the results showed that the discharge voltage of the insulator was negatively correlated with the non-uniform pollution ratio. Literature [9] conducted a study on the flashover characteristics and mechanism of insulators under wind and sand environment. The influence of wind speed, sand flow and sand particle diameter on the flashover characteristics of insulators is studied by means of experiments, and the flashover mechanism of insulators in the air flow field is analyzed. Literature [10] studied the DC pollution flashover characteristics of large-scale composite post insulators in UHV converter stations in high-altitude areas. The numerical relationship between salt density, gray density and DC pollution flashover voltage of insulators at high altitudes are obtained through analysis. Literature [11] completed a large number of flashover tests under artificially simulated rainwater conditions, and studied the characteristics and mechanism of DC pollution and rain flashover of post insulators. Based on the classic insulator pollution flashover discharge model, a discharge model describing post insulator pollution rain flashover is established. Literature [12] studied the pollution flashover characteristics of five kinds of post insulators with different umbrella structures under salt spray conditions. And the effects of the umbrella structure such as the equivalent diameter and whether there is a rib under the umbrella on the pollution flashover voltage of the insulator under salt spray conditions are given. Researchers at home and abroad have conducted a large number of tests and mechanism studies on the flashover characteristics of insulators in various special environments such as rainfall, wind and sand, high altitude, salt spray, snow, pollution, etc. However, the discharge characteristics of insulator strings under extremely low temperature conditions are still blank. When the temperature decreases, the movement of molecules in the air slows down, and the average kinetic energy of air molecules decreases, which is not conducive to the generation of impact ionization, resulting in an increase in the discharge voltage of the air gap [13]. Studying the impulse discharge characteristics of insulator strings under low temperature conditions is beneficial to reduce the excessive margin in the external insulation design. And improve the economical efficiency of construction on the premise of ensuring the safe and stable operation of UHV power transmission and transformation projects. In this paper, for 70kN double-umbrella cap and pin insulator, the insulator string impulse discharge characteristic test at low temperature was carried out at the outdoor test site of Mohe 220kV substation. The corresponding discharge characteristic curve was obtained and the law of discharge voltage changing with temperature was analyzed. The results can provide certain reference for the external insulation design of UHV engineering under extreme temperature environment.

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2 Test Arrangement and Method 2.1 Sample 70kN double-umbrella cap and pin insulator was selected for the test, and the insulator string contained 3 to 7 pieces of insulator. The structure graphing and physical picture of the insulator are shown in Fig. 1, and its basic parameters are shown in Table 1. The structure height of the single insulator is 146 mm. The arcing distance of 3 to 7 insulators is 577 mm, 723 mm, 869 mm, 1015 mm, and 1161 mm, respectively.

Fig. 1. Insulator structure graphing.

Table 1. Insulator parameters. Type

Structure height/ mm

Cap diameter/ mm

Creepage distance/ mm

XWP-70

146

280

450

2.2 Experimental Setup and Method The test was carried out at the outdoor test site of Mohe 220kV substation. Low temperature test was completed in January to February 2023, and normal temperature test was completed in July 2023. The experimental setup is shown in Fig. 2. 110kV analog wire was suspended below the insulator string and connected to the divider of the impulse voltage generator. The top of the insulator string was grounded with copper wire. CDYL1200kV/90kJ impulse voltage generator was used in the test, as shown in Fig. 2. The rated voltage is ±1200kV, and the main body consists of 12 levels, which can be adjusted according to the insulation distance of the insulator string.

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Fig. 2. Experimental setup.

The test was carried out according to GB/T 16927.1–2011 “High-voltage test techniques - Part I: General definitions and test requirements” and GB/T 16927.2−2013 “High-voltage test techniques - Part II: Measuring system”. The switching impulse test was carried out 40 times per group, and the lightning impulse test was carried out 30 times. Meteorological conditions were also recorded during the tests. (1) The applied voltage waveform is positive 250µs/2500µs standard switching impulse wave and positive 1.2µs/50µs standard lightning impulse wave; (2) 50% discharge voltage U 50% is calculated by using the up-and-down method, and the calculation formula is as follows: U50% =



(ni ×Ui ) n

(1)

where U i is the voltage applied, ni is the number of tests under the same applied voltage U i , n is the total number of valid tests. (3) The standard deviation σ of the test is calculated according to formula (2):    n  (Ui − U50% )2  i=1 (2) σ = n−1

3 Test Results and Analysis In this paper, low temperature tests were carried out at −20.45 ~ −3.80 °C from January to February 2023, and normal temperature tests were carried out at 22.35 ~ 32.45 °C in July 2023. The switching impulse and lightning impulse discharge tests were performed on insulator string of 3 to 7 insulators. The results of the switching impulse tests are shown in Fig. 3, and lightning impulse tests’ are shown in Fig. 4. The total results are shown in Table 2. It can be seen from the test results that the lightning impulse discharge

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Fig. 3. Results of switching impulse discharge tests under different temperatures.

voltage of insulator string is greater than the switching impulse discharge voltage either at normal temperature or low temperature. The lightning impulse discharge voltage is 1.8% ~ 9.2% higher than the switching impulse discharge voltage in room temperature environment, and 12.5% ~ 17.3% higher in low temperature environment.

Fig. 4. Results of lightning impulse discharge tests under different temperatures.

For the switching impulse discharge test, the 50% discharge voltage increases a little with the decrease of temperature. In the test temperature range, the U 50% of the insulator string at low temperature is increased by 0.7% ~ 5.5% compared with that at normal temperature. As for the lightning impulse discharge test, the 50% discharge voltage increases obviously with the decrease of temperature. In the test temperature range, the

Effect of Low Temperature on Impulse Discharge Characteristics

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U 50% of the insulator string at low temperature is increased by 9.4% ~ 16.0% compared with that at normal temperature. The effect of temperature on lightning impulse discharge voltage is greater than on switching impulse discharge voltage. At the same time, we can also see that the deviation of the switching impulse discharge voltage is larger than that of the lightning impulse discharge voltage at different temperatures. The insulator configuration under low temperature conditions is in accordance with the standard meteorology, without considering the influence of low temperature. As can be seen from the test results, the impulse discharge voltage at low temperature is higher than that at normal temperature, indicating that low temperature has no adverse impact on external insulation characteristics. So the effect of low temperature can be ignored when configuring external insulation in most cases. For areas with perennial low temperature, there is room for optimizing the external insulation configuration. Table. 2 Results of impulse discharge tests for insulator string. U 50% (kV)

σ (%)

29.70

349.52

5.24

−10.95

357.59

2.75

29.70

419.53

4.93

−12.50

426.33

3.93

−20.45

442.40

3.02

5

29.35

510.53

4.58

−14.70

528.77

4.67

6

29.40

559.00

4.57

−9.70

585.93

4.66

7

22.35

657.23

4.51

−3.80

662.00

4.04

31.95

378.81

3.46

−14

414.60

1.81

4

32.45

458.06

2.02

−18.95

511.00

1.65

5

31.15

523.78

2.26

−12.4

595.00

1.55

30.50

598.61

1.60

−15.05

681.30

1.35

28.50

669.28

2.08

−13.1

776.30

1.09

Impulse type

Number of insulators

T (°C)

Switching impulse

3 4

Lightning impulse

3

6 7

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4 Conclusions In this paper, the impulse discharge characteristics of double-umbrella cap and pin insulator strings in the temperature range of −20 ~ 32 °C are studied, and the following conclusions are drawn. (1) Under both low and normal temperature conditions, the lightning impulse discharge voltages of the insulator string are higher than the switching impulse discharge voltages. (2) In the temperature range of −20 ~ 32 °C, with the decrease of temperature, the switching impulse and lightning impulse discharge voltage of insulator string are increased, and the lightning impulse varies more with temperature. (3) At low temperature, the impulse discharge voltage of the insulator string is higher than that at normal temperature, indicating that there is some room for optimizing the external insulation configuration at low temperature. The results can provide theoretical support for the external insulation design of transmission lines under extreme environment with perennial low temperature. Acknowledgments. This work was funded by technology project of State Grid Heilongjiang Electric Power Co., Ltd (52243722000Z): Experimental study on discharge characteristics of typical external insulation structure of power transmission and transformation equipment at low temperature.

References 1. Zeng, R., Zhuang, C., Yu, Z., et al.: Challenges and achievement in long air gap discharge research. High Voltage Eng. 40(10), 2945–2955 (2014). (in Chinese) 2. Tang, J., Ding, Z.: Simulation calculation and experimental study on impulse flashover voltage of 110 kV insulator. Electr. Eng. Mater. 04, 37–39 (2021). (in Chinese) 3. Yang, B., Ding, Y., Lu, Z., et al.: Intelligent computing of positive switching impulse breakdown voltage of rod-plane air gap based on extremely randomized trees algorithm. Electr. Eng. 103(6), 3177–3187 (2021) 4. Wang, Y., Wen, X., Lan, L., et al.: Breakdown characteristics of long air gap with negative polarity switching impulse. IEEE Trans. Dielectr. Electr. Insul. 21(2), 603–611 (2014) 5. Qiu, Z., Ruan, J., Huang, D., et al.: A prediction method for breakdown voltage of typical air gaps based on electric field features and support vector machine. IEEE Trans. Dielectr. Electr. Insul. 22(4), 2125–2135 (2015) 6. Mei, H., Shi, Q., Lu, M., et al.: Flashover characteristics of 110 kV snow-covered post insulators. High Voltage Eng. 44(12), 3944–3950 (2018). (in Chinese) 7. Jiang, X., Wang, M., Yuan, Y., et al.: Lightning impulse flashover characteristics of insulator with non-uniform pollution. Trans. China Electrotechnical Soc. 1–10 (2023). https://doi.org/ 10.19595/j.cnki.1000-6753.tces.221644. (in Chinese) 8. Jiang, X., Liao, Y., Yuan, Y., et al.: Switching impulse flashover characteristics of insulator with extremely non-uniform pollution. High Voltage Eng. 1–10 (2022). https://doi.org/10. 13336/j.1003-6520.hve.20211256. (in Chinese)

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9. Sun, C., Zhang, Z., Fan, C., et al.: Study on flashover characteristics and mechanism of insulator in Wind-sand environment. High Voltage Apparatus 57(10), 182–188 (2021). (in Chinese) 10. Gu, Y., Yang, L., Zhang, F., et al.: DC pollution flashover performance of Ultra high voltage convert stations large-size composite post insulators at high altitude areas. Trans. China Electrotechnical Soc. 31(10), 93–101 (2016). (in Chinese) 11. Zhang, C., Meng, X., Zhang, F., et al.: Research on the DC rain flashover mechanism of polluted post insulators. Proc. CSEE 34(09), 1481–1489 (2014). (in Chinese) 12. Wang, L., Li, J., Mei, H., et al.: Flashover characteristics of post insulators under fog and haze conditions. High Voltage Eng. 45(02), 433–439 (2019). (in Chinese) 13. Ge, X., Ding, Y., Yao, X., et al.: Computation of breakdown voltage of long rod-plane air gaps in large temperature and humidity range under positive standard switching impulse voltage. Electr. Power Syst. Res. 187, 106518 (2020)

Research on Rapid Cooling Technology for High Temperature Copper Parts Gou Xueke, Geng Hao(B) , and Wu Lizhou The 713 Research Institute of CSSC, Zhengzhou 450015, China [email protected], [email protected]

Abstract. In high voltage and high current fast discharge devices, copper conductors that carry high current generate significant heat and require rapid cooling to reduce temperature. In this article a cooling test system using active heat pipe cooling technology is developed based on the nonlinear temperature rise distribution and cooling requirements of copper parts in use. The cooling test system has the function of simulating the temperature rise distribution of copper parts and can quickly cool the copper parts from 400°C to below 100°C within 50 s. It has good cooling effect, which verifies the feasibility of using active heat pipe cooling technology on the heating components of high-voltage and high current fast discharge devices. Keywords: active-type heat-pipe technology · copper piece · cooling; test system

1 Introduction High-strength and high-conductivity copper alloy structural parts (hereinafter referred to as copper parts) are the core conductive components in the high-voltage and large-current fast discharge device [1–3]. Their service life and safety directly affect the reliability of the whole device. After long-term test, it can be seen that the transient high temperature produced by copper part during discharge has the greatest impact on its service life and safety. Copper parts are subjected to instantaneous large pulse current [4, 5] during use. Due to the skin effect of metal conductor transmitting current, certain resistance heat will be generated at the outer edge of copper parts, especially at arc angles, resulting in temperature rise. The accumulation of heat [6] generated by a heated copper part that is energized several times in a short period of time can cause the temperature of the copper part to rise dramatically leading to overheating and failure [7] of the copper part or the surrounding structural parts. Therefore, it is necessary to study the corresponding cooling test system that provides high efficiency cooling of the copper part during the intervals. When the copper part is not in operation and has insulating properties [8]. Due to the compact structure and long length of copper parts, the cooling effect of common natural air convection and forced liquid convection cooling methods is not good. Therefore, in this paper, the active heat pipe cooling technology [9–11] is adopted, that is, a reflux © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 50–56, 2024. https://doi.org/10.1007/978-981-97-1072-0_5

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pump is used to add driving force to the cooling medium between the condensation section and the evaporation section, so that the cooling medium can quickly conduct the heat of copper parts through phase change heat transfer, thus achieving the purpose of efficient cooling of copper parts.

2 Heating Analysis of Copper Part 2.1 Heating of Copper Part The structure of a copper part itself is relatively simple, which is a single-sided arc surface structure. However, the temperature rise generated under the service conditions in the system is complex and closely related to its pulse current [12] and pulse interval. Through the coupling simulation of electromagnetic field-temperature field [13–15], the cumulative temperature rise and temperature distribution of copper part under service conditions are obtained. The simulation results are shown in Fig. 1.

Fig. 1. Figure of Temperature Rise Simulation for Copper Parts

It can be seen from the figure that the temperature rise of copper part is mainly at the arc corners on both sides of the structure, and most core part of copper part still maintain the set room temperature without temperature rise. The distribution of temperature rise cross section along the length direction is basically consistent, which is caused by resistance heat generated by the current density distribution of pulse current transmitted in the structure. The results of simulation analysis show that the temperature rise at the arc corner of the copper part can reach nearly 400 °C under continuous working condition, and the heat flux shows a nonlinear distribution. Therefore, this study mainly focuses on high-efficiency cooling test research for this part of the copper part. 2.2 Phase Change Cooling Scheme According to the heat dissipation principle of the heat pipe, the liquid cooling medium enters the evaporation end of the copper part from the liquid-phase header, that is, the heated part of the copper part. After heat absorption, an evaporation phase change occurs, and the heat is quickly spread out to the whole inner cavity of the copper part in a vapor state, and discharged from the copper part through the vapor-phase pipeline.

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The working medium steam in the vapor-phase pipeline flows to the condenser under the push of pressure difference, and the working medium in the condenser transfers heat to external cooling water through inter-wall heat transfer. Thus, the transmission of large heat flow under a certain temperature difference can be realized and the temperature of copper part can be quickly reduced.

3 Cooling Device and Test 3.1 Principle of Active Phase Change Cooling The calculation formula of phase change cooling is as follows [5]:   Q = M Cp (Tm − Ti )+H

(1)

where, M is the mass of medium, kg; Q is the heat absorbed by medium, J; C p is the specific heat capacity of medium, J/(kg·K); T m is the boiling point temperature of medium, °C; T i is the initial temperature of medium, °C; H is the latent heat of phase change of medium, J/kg. The latent heat of evaporation of tetrafluoroethylene used in this test is 2.16*105 J/kg, and as a comparison, the latent heat of evaporation of water is 40.8kJ/kg. The cooling calculation formula for wind convection heat dissipation is: Q = hAT

(2)

where T is the temperature difference between air inlet and outlet, h is the coefficient of convective heat transfer, and A is the contact area. Due to convection heat dissipation and small area of high-temperature components, less heat can be taken away by air. The coefficient of convective heat transfer and heat dissipation efficiency of phase change heat transfer are the highest (Table 1). Table 1. Comparison Table of Performance of Different Cooling Fluids Cooling Medium

Initial Temperature

Temperature of Copper Part to be Cooled

Cooling Mode

Latent Heat of Evaporation (J/kg)

Remarks

Tetrafluoroethylene

100°C

Phase change heat dissipation

~2.16 × 105

Best

Water

~20°C

>100°C

Phase change heat dissipation

~4.08 × 104

Better

Air

~20°C

>100°C

Convection heat dissipation

–

Poor

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By comparing the theoretical results of different heat dissipation modes, it can be concluded that tetrafluoroethylene is the best working medium for active phase change cooling. However, this calculation method is on the basis of completely effective heat dissipation. In the actual heat dissipation process, affected by various factors such as actual contact area, medium flow rate and local temperature difference, there are differences between the actual heat exchange and theoretical derivation. Therefore, a simulated heat dissipation test platform for copper parts is built for testing. 3.2 Test Platform Construction and Test The active heat pipe cooling system design of the copper part includes simulation heating device, structural design of evaporation section and condensation section, selection of medium and determination of liquid filling amount and pressure. Considering the length, structural layout and heating mode of the copper part, this cooling system adopts active heat pipe technology, which is characterized by the conformal design of inner cavity of copper part and heat pipe. The condensed liquid medium returns from the cooling section to the evaporation section along the liquid phase header by the power of reflux pump. Figure 2 shows the structure of the active heat pipe cooling test system.

Fig. 2. Structure Diagram of Active Heat Pipe Cooling Test System

The cross section of copper part is 0.2 m long and 0.05 m high. Tetrafluoroethane is selected as the cooling medium in the cooling test system, with a liquid flow rate of 0.2 ~ 0.25 m3 /min. The medium transmission pipeline and copper part are made of the same material, which is copper alloy. Due to the long size and compact structure of this cooling test system, compared with the air-cooled and liquid-cooled devices of traditional launching weapons, this system is characterized by high technology content and relatively complicated manufacturing process, but the system has high heat transfer efficiency, significant cooling effect, long service life, and insulation of the copper part from other components, which can satisfy the cooling needs of this copper part (Fig. 3).

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Fig. 3. Figure of Active Heat Pipe Cooling Test System Structure

4 Analysis of Test Results In this paper, oxyacetylene flame is used to simulate the temperature rise of the copper part. The cooling effect of active phase change cooling is analyzed by simulating the heating condition up to 400 °C for the copper part. In the whole heating-cooling test process, the infrared temperature measuring device is used to measure the temperatures of multiple points on the heated side and the opposite side of the copper part in real time, and the temperature of arc corners of the copper part is taken as a sign that the heating test is performed in place. When the arc angle reaches the predetermined temperature, all flame spray guns are shut quickly by shutting off the master gas valve, and then the copper part stops being heated. If the active heat pipe cooling system is not started at this time, the initial surface temperature state of the heating test for copper part can be obtained, as shown in Fig. 4 below:

Fig. 4. Figure of Initial Surface Temperature State of Copper Parts during Heating Test. (a) Distribution of temperature measurement points for copper parts (b) Initial temperature distribution diagram of copper parts after heating

The temperature change with time in the comparative test of natural cooling and phase change cooling of copper part is shown in Fig. 5, where Tmax and Tmin respectively represent the actual temperature changes at the highest and lowest temperatures of copper part.

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Fig. 5. Figure of Temperature Variation over Time during Rapid Cooling Test of Copper Parts

It can be seen from the figure that under the natural cooling condition, the temperature at the maximum temperature of copper part slowly drops from 400 °C and remains above 270 °C after 50 s. When the arc corners reaches the predetermined temperature, all flame spray guns are quickly turned off. At this time, the active heat pipe cooling system keeps working. The maximum temperature of copper part is continuously and rapidly reduced from 400 °C. Within the first 10 s of cooling, the temperature drop is greater than 100 °C. After 50 s of cooling, the maximum temperature point of copper part is lower than 100 °C, and the minimum temperature position has cooled to room temperature. The test results show that the active heat pipe cooling system has the characteristics of quick response, good heat transfer performance and high heat exchange efficiency, and can quickly adjust the temperature difference between the evaporation section and the condensation section.

5 Conclusion According to the requirements of heat management for copper parts in high-voltage and large-current fast discharge device, a cooling test system for copper parts is designed and developed based on efficient active heat pipe cooling technology. The heating device in the system is used to heat the copper part and simulate the temperature rise distribution of the copper part under actual working conditions. By using efficient active heat pipe cooling technology, the heat of the copper part can be quickly taken away with good cooling effect. During the cooling process of the copper part, the temperature drops very obviously. The maximum temperature of the copper part is continuously and rapidly reduced from 400 °C. Within the first 10 s of cooling, the temperature drop is greater than 100 °C. After 50 s of cooling, the temperature of the copper part is lower than 100 °C, and the minimum temperature position has cooled to room temperature. The cooling test system has the characteristics of high-efficiency cooling of copper parts and insulation from external structures, with advantages such as high thermal conductivity, quick thermal response, compact structure and good heat transfer stability. It verifies the feasibility of active heat pipe cooling technology and provides a technical basis for the subsequent thermal management design of heating components of high-voltage and large-current rapid discharge devices.

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References 1. Ma, W.M., Lu, J.Y.: Research progress and challenges of electromagnetic launch technology. Trans. China Electrotechnical Soc. 38(15), 3943–3959 (2023) 2. He, X., Cao, Q.S.: Development and critical techniques of electromagnetic launch technology. J. China Acad. Electron. Inf. Technol. 6(2), 130–135 (2011) 3. Pu, X.L.: Research on Orbit Damage Characteristics of Copper Alloy under Simulated Electromagnetic Emission Condition. Shandong University, Wang Weimin (2020) 4. Wang, X.F., Sun, Z.J., Wu, C.Z., et al.: Experimental study on gravity heat pipe radiator for electronic device cooling. J. Electron. 27(3), 393–396 (2004) 5. Fair, H.D.: Progress in electromagnetic launch science and technology. IEEE Trans. Magn. 43(1), 93–98 (2007) 6. Agostini, B.: State of the art of high heat flux cooling technologies. Heat Transfer Eng. 28(4), 258–281 (2007) 7. Li, J.W., Dai, S.G.: Research progress and prospect of high temperature heat pipe technology. China Space Sci. Technol. 39(03), 30–42 (2019) 8. He, D.X., Zhang, T., Chen, X.G., Gong, W.J., Li, Q.Q.: Summary of research on insulation charge characteristics of power electronic equipment under pulse voltage. Trans. China Electrotechnical Soc. 36(22), 4795–4808 (2021) 9. Hu, Y.F.: Heat pipe technology and its application in engineering. Phys. Eng. 12(3), 42–44 (2002) 10. Lv, A.Q., Li, J., Zhang, Z.P., Song, H., Lin, X.B.: Finite element analysis of the influence of clamps on thermal characteristics of high voltage insulated cables. Trans. China Electrotechnical Soc. 37(1), 283–290 (2022) 11. He, B., Wang, P., Wu, K., Hu, X.B., Yang, D.: Overview of study on phase dynamics behavior of impurities in contaminated insulating oil in multiple physical fields. Trans. China Electrotechnical Soc. 37(1), 266–282 (2022) 12. Wang, Z.J., Chen, L.X., You, P.H., Lan, X.Y., Ge, Y.F.: Current distribution characteristics of armature-rail interface considering velocity skin effect and contact resistance influence. Trans. China Electrotechnical Soc. 37(19), 5003–5010 (2022) 13. Cheng, C., et al.: Research on transient temperature measurement of positive lead discharge channel in the initial stage based on pulse quantitative schlieren system. Trans. China Electrotechnical Soc. 38(23) 6483–6493 (2023) 14. Li, J., Zhao, R.Y., Du, B.X., Hao, L.C., Bian, K.: Research progress of nondestructive detection methods for defects of electrical epoxy insulators. Trans. China Electrotechnical Soc. 36(21), 4598–4607 (2021) 15. Jia, S.Y., Zhao, Z.M., Shi, B.C., Zhu, Y.C.: Numerical modeling and analysis of electromagnetic interference in power electronics systems. Trans. China Electrotechnical Soc. 36(11), 2383–2393 (2021)

Optimal Dispatching of Distribution Network Considering Inverter Air Conditioner Aggregation Dian Yuan1 , Qinran Hu1(B) , Yuanshi Zhang1 , Xu Jin1 , Shunjiang Wang2 , and Peng Qiu3 1 School of Electrical Engineering, Southeast University, Nanjing, China

[email protected]

2 State Grid Liaoning Electric Power Co., Ltd., Shenyang, China 3 Jinzhou Power Supply Branch State Grid Liaoning Electric Power Supply Co. Ltd., Jinzhou,

China

Abstract. The proportion of distributed energy resource (DER) in the distribution network has been increasing year by year to realize “carbon peaking and carbon neutrality goals”. However, new energy power generation is random and intermittent, and with the increasing peak-to-valley difference in loads, it is difficult to satisfy the peak shifting demand with only traditional power generation side resources. Therefore, it is essential to fully exploit the external characteristics of distributed energy sources on the user’s side and engage them in distribution network optimization dispatching. In this paper, the inverter air conditioner on the user’s side is modeled and aggregated. Based on the mathematical model, the regulation potential and external characteristic curves of the inverter air conditioner aggregation were evaluated and analyzed. The effectiveness of the proposed external characteristics of inverter air conditioner aggregation are verified in the IEEE 33-node distribution network model. It turns out that the aggregation of userside inverter air conditioners can efficiently participate in distribution network optimization and improve distribution network reliability. Keywords: Inverter Air Conditioner · Distributed Energy Resource · External Characteristics · Distribution Network

1 Introduction In order to address the challenges of energy shortages and environmental pollution [1], China has promised to peak its carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060 [2]. To realize “carbon peaking and carbon neutrality goals”, the proportion of distributed energy in the power system is increasing year by year [3]. However, renewable energy and power generation such as wind power and photovoltaic are intermittent and random, and their high penetration rate will bring threats to the stability of the power system [4]. At the same time, with the development of social economy, the power load continues to climb, and the load peak-to-valley difference is increasing. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 57–65, 2024. https://doi.org/10.1007/978-981-97-1072-0_6

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In this case, it is difficult to meet the power system balance and regulation needs by relying only on traditional generation-side resources. In this regard, the traditional distribution network has gradually shifted from a reactive mode to an active mode [5], and it is urgent to fully exploit the regulation characteristics of distributed energy resources to help maintain the real-time power balance of the power system [6]. Among them, air conditioner loads of customer side have the advantages of flexible scheduling, fast response speed, and large regulatory potential [7]. The existing studies on the regulatory potential of customer-side air conditioner loads are dominated by fixed-frequency air conditioners [8, 9], and fewer studies have been conducted for inverter air conditioners. However, in recent years, the market volume of inverter air conditioners has been gradually increasing. With the advantages of small room temperature fluctuation, low power consumption, and high comfort [10], there is an urgent need to model inverter air conditioners, explore their regulatory potential, and generate their external characteristics [11]. In this paper, the first section introduces the research background and the urgency of exploiting the potential of air conditioner load aggregation. The second section establishes a mathematical model of inverter air conditioner during demand response based on the equivalent thermal parameter model. The third section evaluates the demand response regulation potential of inverter air conditioner aggregation considering user comfort. In the fourth section, a typical scenario is set up in the IEEE-33 node distribution network, and the air conditioner load aggregation is added as a distributed energy source to the relevant node when participating in the distribution network optimization scheduling. The simulation results show that the air conditioner load aggregation has good potential for peak shifting.

2 Mathematical Model of Inverter Air Conditioner Aggregation and Optimization 2.1 Room Thermal Modeling Currently, the most commonly used model for thermodynamic simulation of airconditioned rooms is the equivalent thermal parameter (ETP) model. The original differential equations are too complicated and are not a major focus of this paper, so the first-order equations for room temperature are obtained by simplification as shown in Eq. (1). Troom (t + 1) = Tout (t + 1) − Q(t)R − (Tout (t + 1) − Q(t)R − Troom (t))e−t/RC (1) where Troom (t) is the indoor temperature at time t; Tout (t) is the outdoor temperature at time t; Q(t) is the air conditioner cooling capacity at time t and the unit of Q(t) is kW; R is the thermal resistance of the air-conditioned room and the unit of R is °C/kW; C is the equivalent heat capacity of the air-conditioned room and the unit of C is kJ/°C. 2.2 Electrical Parameter Relationships The relationship between compressor frequency and air conditioner electric power can be obtained by curve fitting according to the image in reference [12], as is shown in

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Eq. (2). Meanwhile, the relationship between compressor frequency and air conditioner cooling capacity can be obtained, as is shown in Eq. (3). PAC = mf + n

(2)

QAC = af 2 + bf + c

(3)

where f is the air conditioner compressor frequency. PAC is the air conditioner electric power, and QAC is the air conditioner cooling capacity. The unit of PAC and QAC is kW, while a, b, c, m, and n are the parameters of the fitted curve. 2.3 Demand Response Control Strategy The frequency control method is used to model the demand response scenario of the air conditioner. Firstly, assuming that the outdoor temperature Tout and the air conditioner set temperature Tset remain unchanged for a short period of time, the cooling capacity QAC required to maintain the room temperature at the set temperature can be calculated according to Eq. (1), as is shown in Eq. (4). QAC (t) =

Tout (t + 1) − Tset R

(4)

By taking the value of cooling capacity QAC into (3), (4) is solved to obtain the value of air conditioner compressor frequency fAC . . The physical meaning of (5) is that the air conditioner needs to operate at fAC (Tout , Tset ) in order to maintain the set temperature Tset when the outdoor temperature is Tout .  set ) −b + b2 − 4a(c − Tout −T R fAC (Tout , Tset ) = (5) 2a

2.4 Objective Function The objective function is to minimize the dispatch cost of the distribution network. min f = CLA + Closs

(6)

In Eq. (6), CLA is the cost of load aggregator participation in distribution, and Closs is the costs of power losses in the distribution network. 2.5 Constraints 1) Distributed power output constraints min In Eq. (7), PDG,j (t) is the actual active power output of distributed power j, PDG,j max and PDG,j are respectively the upper and lower limits of the power output. min max PDG,j ≤ PDG,j (t) ≤ PDG,j

(7)

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2) Node voltage constraints In Eq. (8), Vi is the voltage of node i, Vimax is the upper limit of node voltage, and min Vi is the lower limit of node voltage. Vimin ≤ Vi ≤ Vimax

(8)

3) Branch flow constraints min and In Eq. (9), PLi is the power delivered by line L in the distribution network, PLi max are respectively the upper and lower branch power limits. PLi min max PLi ≤ PLi ≤ PLi

(9)

4) Power balance constraint The total power purchase of the distribution network from the main grid at each moment satisfies the power balance with the uncontrollable loads in the distribution network and the distributed power output with the controllable loads. PTG,t = Pcl,t − PDG,t + PLA,t

(10)

In Eq. (10), PTG,t is the active output power of the conventional unit at time t, Pcl,t is the active power required by the uncontrollable load at time t, PDG,t is the active power output of the distributed power supply at time t, PLA,t is the active output of the load aggregator at time t, which is negative for curtailment of electricity use.

3 Regulatory Potential Assessment and External Characterization This section evaluates the regulatory potential of inverter air conditioner aggregations when they participate in demand response. To simplify the modeling, it is assumed that 100% of the users contracted with the load aggregator (LA) respond to demand response signals. The effects of different factors on the regulatory potential of the air conditioner aggregation are analyzed, while external characteristic curves are generated. 3.1 Parameter Initialization The number of air conditioners in the aggregation is N and the number of air conditioners is consistently the same as the number of rooms. The sampling period is 1 s. The room parameters are as follows: the thermal resistance of the air-conditioned room R is 10 °C/kW, and the equivalent heat capacity of the air-conditioned room C is 200 kJ/°C. The initial room temperature was set to a normal distribution with a mean room temperature of 24 °C and a variance of 1 [12]. The air conditioner parameters are set as follows: the initial setting temperature set by the user is a uniformly distributed random number between 22–28 °C. The minimum frequency of a single air conditioner is 5 Hz, and the maximum frequency is 110 Hz. The secondary coefficient of air conditioner cooling is −0.23, the primary coefficient is 50, and the constant coefficient is 200. The primary coefficient of power is 18, and the constant coefficient is 50. Considering the user’s comfort level, the maximum set temperature of the air conditioner is 28 °C, and the minimum set temperature is 22 °C. Outdoor temperature is 35 °C during the demand response period and the demand response time is 10 min.

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3.2 Load Reduction with Different Number of Air Conditioners A typical air conditioner cooling scenario in summer is set up to explore the relationship between the number of air conditioners and the amount of load reduction. The temperature up-regulation according to the demand response signal is 0.5 °C, 1.0 °C, 1.5 °C, and 2.0 °C, respectively. The number of air conditioners varies between 0–2000 units. The result is plotted according to the experimental data in Fig. 1.

Fig. 1. Relationship between the number of air conditioners and load reduction

In Fig. 1, there is a linear relationship between the number of air conditioners and load reduction. In a typical scenario, the number of air conditioners increases and the load reduction increases proportionally. The results of this example are also consistent with the mathematical logic of the air conditioner power expression. 3.3 Load Reduction with Different Outdoor Temperature A typical scenario of air conditioner cooling in summer is set up to explore the relationship between outdoor temperature and load reduction. The number of air conditioners is 1000. The temperature up-regulation according to the demand response signal is 0.5 °C, 1.0 °C, 1.5 °C, and 2.0 °C, respectively. The outdoor temperature varies between 32–38°C, and the image is plotted according to the experimental data as shown in Fig. 2.

Fig. 2. Relationship between the outdoor temperature and load reduction.

It is shown in Fig. 2 that, for the same regulation temperature, the load reduction increases with the increase in outdoor temperature and the growth rate slows down.

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In this case, the increase in outdoor temperature increases the air conditioner cooling capacity and the air conditioner frequency. Then, the air conditioner operates at higher power and the total steady-state aggregated power increases, corresponding to higher load reduction. 3.4 Load Reduction with Different Temperature Regulation A typical scenario of air conditioner cooling in summer is set up to explore the relationship between different temperature regulation and load reduction. The number of air conditioners in a regional aggregation is 1000. The temperature regulation amount of the demand response signal varies between 0–7 °C with an interval of 0.5 °C, and the image is plotted based on the experimental data as shown in Fig. 3.

Fig. 3. Relationship between different upward temperatures and load reduction.

As shown in the figure, the air conditioner load reduction increases with the increase of the upward temperature, but the growth rate of the load reduction slows down with the increase of the upward temperature and reaches the saturation value at the upward temperature of 6 °C. This phenomenon occurs because the user comfort is considered. The relationship between the air conditioner load reduction potential and the upregulation temperature can be approximated as a quadratic function. The curve fitting result is: PRC = a(Tset )2 + bTset + c, where PRC is the value of power that can be cut by the up-regulation of the temperature during the demand response period, while a = −3.52, b = 43.61, and c = 0.40. In the scenario set out above, the maximum load reduction potential of the air conditioner aggregation is 134 kW.

4 Numerical Results 4.1 Example Settings In this section, the distribution network model containing distributed power sources is constructed on the basis of the IEEE-33 nodal system [13], as shown in Fig. 4. Due to the connection of distributed power sources, the operational reliability of the distribution network decreases and the difficulty of load peaking increases. In this regard, two load aggregators are added to load node 10 and node 26, respectively, to assist peak shifting through demand response.

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Fig. 4. Improved IEEE-33 node system.

From the evaluation in Sect. 3, it can be concluded that the maximum load reductions for different air conditioner aggregations can be calculated for each time period. The parameters of each air conditioner aggregation are shown in Table 1, including the number of air conditioners, the demand response period, the minimum response interval, the maximum total response hours per day, and the subsidized price for demand response. Table 1. AC aggregators information. AC Aggregators

Number of AC

Response Time Period

Minimum response interval/h

Maximum response time h/day

Demand Response Subsidized Pricing yuan/h

LA1-AC1

1000

9:00–20:00

1

4

88

LA1-AC2

500

13:00–18:00

1

3

95

LA2-AC3

1500

10:00–21:00

1

4

80

LA2-AC4

1000

11:00–19:00

2

5

85

4.2 Optimized Scheduling Results The objective function of this distribution network optimization scheduling problem is economically optimal on the basis of ensuring power balance as shown in Sect. 2. The load curves before and after the participation of the load aggregator are shown in Fig. 5, and it can be found that with the participation of the conditioner aggregation in the optimal scheduling of the distribution network, the load has been cut down in the peak hour of electricity consumption from 12:00 to 22:00 and the peak shaving rate achieves 2.86%. The load reduction and reduction periods obtained from the optimization for each air conditioner aggregation are shown in Fig. 6. The demand response information obtained from the optimization is given to the load aggregator. The load aggregator gives control instructions to the aggregated loads depending on the control time period and control

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Fig. 5. Comparison of load curves before and after AC aggregation.

power, which is specifically signaled as the air conditioner temperature upward adjustment amount, and the value can be derived from the aggregation curve fitting function in Sect. 3.

Fig. 6. Reduction period and amount of AC aggregation.

5 Conclusion This paper proposes a novel method of generating external characteristics of air conditioner aggregation. Meanwhile, the relationship between inverter air conditioner aggregation power and the number of air conditioners, outside temperature and up-regulation temperature was analyzed. Then, the air conditioner aggregations are ultilized as distributed energy resources in the IEEE33-node system to participate in the optimal scheduling of the distribution network. To summarize, the established air conditioner aggregation model has a certain peak shifting effect, and the proposed air conditioner aggregation external characteristic curve is operable and efficient. In the subsequent research, issues such as the regional characteristics of air conditioner aggregations and the demand corresponding subsidy mechanism can continue to be explored to further improve the modeling and application of distributed energy aggregation external characteristics.

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Acknowledgment. This work is supported by Science and Technology Project of State Grid Corporation (5108-202328048A-1-1-ZN).

References 1. Hasanuzzaman, M., Zubir, U.S., Ilham, N.I., et al.: Global electricity demand, generation, grid system, and renewable energy polices: a review. Wiley Interdisc. Rev. Energy Environ. 6(3), e222 (2017) 2. Xiao, X., Zheng, Z.: New power systems dominated by renewable energy towards the goal of emission peak & carbon neutrality: contribution, key techniques, and challenges. Adv. Eng. Sci. 54(1), 47–59 (2022). (in Chinese) 3. Zhang, Z., Kang, C.: Challenges and prospects for constructing the new-type power system towards a carbon neutrality future. Proc. CSEE 42(8), 2806–2819 (2022). (in Chinese) 4. Hu, Q., Liang, Y., Ding, H., et al.: Topological partition based multi-energy flow calculation method for complex integrated energy systems. Energy 244, 123152 (2022) 5. Hu, Q., Han, R., Quan, X., et al.: Grid-forming inverter enabled virtual power plants with inertia support capability. IEEE Trans. Smart Grid 13(5), 4134–4143 (2022) 6. Hu, Q., Li, F.: Hardware design of smart home energy management system with dynamic price response. IEEE Trans. Smart Grid 4(4), 1878–1887 (2013) 7. Song, M., Gao, C., Su, W.: Air conditioning load modeling and control for demand response applications. Autom. Electric Power Syst. 40(14), 158–167 (2016). (in Chinese) 8. Lu, N.: An evaluation of the HVAC load potential for providing load balancing service. IEEE Trans. Smart Grid 3(3), 1263–1270 (2012) 9. Hui, H., Ding, Y., Liu, W., et al.: Operating reserve evaluation of aggregated air conditioners. Appl. Energy 196, 218–228 (2017) 10. Yang, J., Shi, K., Cui, X., et al.: Group peak-shaving method of frequency conversion air conditioner under demand response. Autom. Electric Power Syst. 42(24), 44–52 (2018). (in Chinese) 11. Yang, Z., Ding, X., Lu, X., et al.: Inverter air conditioner load modeling and operational control for demand response. Power Syst. Prot. Control 49(15), 132–140 (2021). (in Chinese) 12. Ding, X.: Regulating Strategy and Effect Evaluation of Inverter Air-Conditioner Applied in Demand Response.Southeast University, Nanjing (2016). (in Chinese) 13. Deng, X.: Research on Optimal Dispatching of Active Distribution NETWORK Considering "Source-Load-Storage” Collaborative Interaction. North China Electric Power University, Beijing (2019). (in Chinese)

Research on Coding Method of Polarization PLC System Based on Upper Bound of Bhattacharyya Parameter Wangbin Cao1,3(B) , Yijin Ren1,3 , Xiaolin Liang2,3 , Zhengwei Hu1 , and Zhiyuan Xie1 1 School of Electrical and Electronic Engineering, North China Electric Power University,

Baoding 071003, China [email protected] 2 School of Electronic and Information Engineering, Hebei University, Baoding 071002, China 3 Hebei Key Laboratory of Power Internet of Things Technology, Baoding 071003, China

Abstract. Power Line Communication (PLC) channels are characterized by strong pulse interference, significant impedance changes, and severe signal attenuation. In order to effectively enhance the communication quality of PLC, channel coding emerges as a crucial technology. Polar codes have gained significant attention in the field of channel coding because of their simple encoding and decoding processes, as well as their potential to achieve the Shannon limit. A polarization PLC channel coding system is proposed to reduce the impact of pulse noise on information transmission in PLC channels. This system combines polar code and Orthogonal Frequency Division Multiplexing (OFDM). The initial value of the Bhattacharyya parameter under the PLC channel is determined using the Bhattacharyya parameter method and the PLC channel state information. The upper bound recursive method of Bhattacharyya parameter is used to estimate the reliability of polarization PLC sub-channel in the recursive construction range of Bhattacharyya parameter, so as to obtain the optimal information bit selection scheme. The validity of the Bhattacharyya parameter bounds in the PLC channel is verified by studying the performance of polar code with different parameters in the polarization PLC channel coding system. The performance is compared with that of Turbo code and low-density parity check code under the same conditions. The results show that the polar code coding structure in the polarization PLC channel coding system is clear. The decoding complexity of polar codes is low, and they perform better under certain SNR conditions, resulting in higher coding gain. The polarization PLC channel coding system can effectively improve the transmission reliability of PLC, and has a broad application prospect in the complex PLC channel. Keywords: Polar code · PLC · Bhattacharyya Parameter Boundary · OFDM

1 Introduction Power Line Communication (PLC) is a communication method in which the power line is used as an information transmission medium for voice or data transmission. It is an important method for achieving the integration of the smart grid [1–3]. PLC has the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 66–80, 2024. https://doi.org/10.1007/978-981-97-1072-0_7

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advantages of wide coverage, low operation and maintenance cost, and a large number of users [4, 5]. However, compared with wireless channels, PLC channel characteristics include a high channel noise level, complex noise types, large impedance changes, and serious multi-path fading [6–8]. Improving PLC reliability through channel coding is an important research direction for PLC. In order to enhance the transmission quality of the PLC system, M. Babic et al. utilized convolutional codes and Reed-Solomon codes as channel codes in PLC to enhance system performance [9]. In literature [10], dual-binary Turbo code is used in OFDM-PLC system to improve system performance and obtain considerable coding gain. Literature [11] uses Low Density Parity Check Code (LDPC) as the coding method in PLC system to effectively reduce the impact of pulse noise on system performance. All of the aforementioned schemes have the potential to enhance the performance of the PLC system. However, it is worth noting that the internal interleaver of Turbo code introduces a significant decoding delay, which may be deemed excessive in practical applications. Additionally, the implementation of Turbo code may incur substantial patent fees. The encoding complexity of LDPC codes exhibits an exponential relationship with respect to the code length. When the length of the code is excessively long, it results in complex construction and high system delay, which hinders effective implementation. In 2008, Arikan introduced the notion of channel polarization during the International Symposium on Information Theory (ISIT) [12]. Subsequently, in 2009, Arikan further developed the polar code by leveraging the principles of channel polarization theory. It is proved for the first time that the channel capacity is asymptotically reachable by the constructional method [13]. The polar code has a clear coding structure, no need to design a specific check matrix, and the coding complexity is low. Its error correction performance has a strict parsing range and does not require iterative decoding. Decoding complexity is low, and it has played an important role in the field of channel coding. The development of polar code technology for PLC communication reliability has pointed out a new path. In literature [14] and [15], polar codes are used in PLC systems. They consider the impact of pulse noise on the performance of polar codes. In the construction stage of polar code, the Bhattacharyya parameter method for the Binary Erasure Channel (BEC) is adopted, and the initial value of the Bhattacharyya parameter is set to a fixed value. The characteristics of the PLC channel itself have not been fully considered. In order to quantitatively study the impact of polar codes on the reliability of PLC channels, this paper combined polar codes with Orthogonal Frequency Division Multiplexing (OFDM) technology to establish a polarization PLC channel coding system. Based on Bhattacharyya parameter method combined with PLC channel state information, the initial value of Bhattacharyya parameter under PLC channel is calculated, and the upper bound of Bhattacharyya parameter is used as the recursive construction scheme of polar code in the polarization PLC channel coding system according to the boundary range of Bhattacharyya parameter, in order to obtain the optimal information bit selection scheme, so that Bhattacharyya parameter method is suitable for the polarization PLC channel. The application range of polar code is extended. In order to verify the effectiveness of the Bhattacharyya parameter bound in the PLC channel, we studied the performance of different parameters of polar code in the polarization PLC channel coding system.

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We compared the performance of the polarization PLC channel coding system with that of LDPC and Turbo codes, which are mature and have superior performance under the same conditions. This comparison verified the superiority of the polarization PLC channel coding system.

2 Basic Principle of Polar Code Channel polarization is the phenomenon wherein a set of N = 2n independent BinaryInput Discrete Memoryless channels (B-DMC) W are transformed into N interdepen(i) dent sub-channels {WN : 1 ≤ i ≤ N } through the processes of channel merging and channel separation. After undergoing channel polarization, the channels are denoted (1) (2) (N ) as {WN , WN , ..., WN }, with each sub-channel exhibiting polarized reliability. This phenomenon becomes increasingly evident as the number of channels, denoted as N , continues to rise. As N approaches infinity, certain sub-channels exhibit a capacity that tends towards 0, while others demonstrate a capacity that tends towards 1. However, the overall channel capacity remains unchanged (Fig. 1).

Fig. 1. Channel polarization process

The implementation of polar code channel coding involves three distinct steps: Code word construction, Encoding, and Decoding. 2.1 Code Word Construction In polar codes, the fundamental aspect of constructing the code lies in the procedure of channel selection. Firstly, N independent channels W are polarized to obtain N interrelated polarization channels. Subsequently, a reliability measurement is conducted on N sub-channels following the polarization operation. Finally, among the N metrics, the sub-channel with the highest reliability (K ≤ N ) is chosen to accommodate K information bits. The remaining N − K sub-channels are used to transmit the frozen bits, which are known by both the sender and receiver, in order to obtain the original transmission sequence. The specific process is depicted in Fig. 2.

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Fig. 2. Code word construction flowchart

2.2 Encoding Polar code is a typical linear block code. The length of a polar code is typically a power of 2, denoted as N = 2n , where n is a positive integer. The encoding process of the polar code can be mathematically represented as follows: x1N = u1N GN

(1)

GN = BN F ⊗n

(2)



10 F= 11

 (3)

where, x1N is the encoding bit sequence, u1N is the original information bit sequence. GN is a generated matrix. For any N = 2n , n = 1, 2, ..., GN can be represented by formula (2), where BN is a bit flip matrix, and F ⊗n represents the Kronecker product of n degrees of matrix F. 2.3 Decoding The Successive Cancellation (SC) algorithm is commonly employed for the decoding of polar codes. This decoding process is executed in a bit-by-bit manner, resulting in a time complexity of O(N log2 N ). For the polar code of (N , K, A, uAC ), the work of SC decoding is to combine the information bit set A, the frozen bit uAC , and the output bit sequence y1N to calculate the estimated value of the original information bit sequence based on the Logarithm Likelihood Ratio (LLR) of the polarization channel. Define the initial LLR: (1)

L1 (yi ) = ln

W (yi |0) W (yi |1)

(4)

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Given that the transfer probability of the subchannel can be calculated recursively, and LLR here is solely dependent on the channel transfer probability (CTP), the LLR of each polarization subchannel can be obtained recursively using the following two formulas: (y1N , uˆ 12i−2 ) = L(2i−1) N

(i)

N /2

LN /2 (y1 (i)

N /2

LN /2 (y1

(i)

2i−2 2i−2 2i−2 , uˆ 1,o ⊕ uˆ 1,e ) · LN /2 (yNN /2+1 , uˆ 1,e )+1 (i)

2i−2 2i−2 2i−2 , uˆ 1,o ⊕ uˆ 1,e ) + LN /2 (yNN /2+1 , uˆ 1,e ) N /2

2i−2 N N ˆ 12i−1 ) = L(i) ˆ 1,e ) · L(i) L(2i) N (y1 , u N /2 (yN /2+1 , u N /2 (y1

2i−2 2i−2 1−2ˆu2i−1 , uˆ 1,o ⊕ uˆ 1,e )

(5) (6)

According to the LLR of each polarization channel, the decision criteria of the SC decoder for u1N can be expressed as follows: ⎧ ⎪ i ∈ AC ⎨ ui , (i) N uˆ i = (7) 0 LN (y1 , uˆ 1i−1 ) ≥ 0 ⎪ ⎩ 1 L(i) (yN , uˆ i−1 ) < 0 1 1 N

3 Polarization PLC Channel Coding System

Fig. 3. Polarization PLC channel coding system

The polarization PLC channel coding system designed in this paper is shown in Fig. 3. The information bit and freezing bit are determined according to the construction process of polar code under the PLC channel. The information bit is randomly generated and placed in the information bit, while the frozen bit, known to both the transmitter and the receiver, is placed in the freezing bit. On this basis, polarization coding, BPSK mapping, and OFDM modulation are carried out to generate OFDM modulation signals X . OFDM symbols X are transmitted to the receiving end through PLC channels. In the transmission process, the signal is subject to interference from two types of noise. The first type of noise is background noise, typically characterized by Additive White Gaussian Noise (AWGN) that conforms to a Gaussian distribution. The second type of interference is pulse noise, which significantly impacts the performance of the PLC system and is considered the most crucial interference. At the receiving end, the signal undergoes demodulation and decoding processes in order to retrieve the original sequence of information bits.

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3.1 Transfer Probability of the PLC Channel For PLC channel, the initial LLR of SC decoding algorithm is directly related to the transfer probability of channel output data. The subsequent value represents the initial LLR decoding of the PLC channel using BPSK mapping. The signal is transmitted in PLC channel, and the signal received at the receiving end can be expressed as: Yi = Hi × Xi + Wi i = 0, 1, ..., N − 1

(8)

where, Xi is the input symbol, Hi is the channel transmission function, and Wi is the PLC channel noise. For OFDM-PLC systems, the pulse LLR is not applicable due to the inability to estimate LLR after FFT transformation [16]. Additionally, when the number of OFDM subcarriers is sufficiently large, the pulse noise after FFT transformation resembles Gaussian distribution noise. As a result, the variance of noise in the frequency domain can be approximated as [15]: σZ2 = σG2 (1 +

1 ) = σG2 + σI2 γ

(9)

where σG2 represents AWGN noise power and σI2 represents pulse noise power. If the system uses BPSK mapping, the PLC CTP can be expressed as: 1

W (Yi |xi = 1, Hi ) =  e 2π σZ2 W (Yi |xi = −1, Hi ) = 

1

−

e

|Yi −Hi |2 2σZ2

−

(10)

|Yi +Hi |2 2σZ2

(11)

2π σZ2

The initial LLR for decoding can be obtained using the following formula: (1) L1 (Yi )

− 1 W (Yi |xi = 1, Hi ) = ln[  = ln e W (Yi |x = −1, Hi ) 2π σ 2

|Yi −Hi |2 2σZ2

/

Z

1 2π σZ2

e

−

|Yi +Hi |2 2σZ2

]

(12)

3.2 Reliability Estimation of Polarization PLC Channels Arikan introduced the concept of the polar code and employed the Bhattacharyya parameter method for its construction. The Bhattacharyya parameter was observed to satisfy [17]: (i)

(2i−1)

Z(WN ) ≤ Z(W2N

(i)

(i)

) ≤ 2Z(WN ) − Z(WN )2

(13)

The aforementioned mathematical relationship offers an opportunity for the utilization of the Bhattacharyya parameter method in the context of general channel reservation. Based on the aforementioned information, this paper presents a novel approach known as

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the Bhattacharyya parameter boundary method, which is specifically designed to address the unique characteristics of PLC channels: (1) The Bhattacharyya parameter under B-DMC can be defined using equation:

Z(W ) = W (y|0)W (y|1) (14) y∈ϒ

Under a continuous channel similar to PLC, probability distribution density is used to replace probability distribution, and integral is used to replace summation. The calculation expression of Bhattacharyya parameters is shown in Eq. (15): 

W (y|0)W (y|1)dy (15) Z(W ) = According to the transmission function of the PLC channel, as well as the state information of background noise power and pulse noise power, Eqs. (10) and (11) representing the PLC channel transfer probability are substituted into Eq. (15). The initial value of the Bhattacharyya parameter Z1 (W ) under the PLC channel is determined. In the above formula, the channel state information is mainly obtained through channel estimation at the receiving end and noise power measurement without signal transmission, and then the information is transmitted through the communication feedback link. (2) Under B-DMC, the recursive structure of the Bhattacharyya parameter is (2i−1)

Z(W2N

(i)

(i)

) ≤ 2Z(WN ) − Z(WN )2 (2i)

(i)

Z(W2N ) = Z(WN )2

(16) (17)

If and only if the channel is BEC, the Eq. (16) is valid. Due to the unique nature of the PLC channel, the aforementioned recursive structure cannot be directly applied to the PLC channel. In theory, restricting the recursive structure of Bhattacharyya parameters to the boundary range can fulfill the polar code construction scheme under the PLC channel. However, it becomes more complex to enumerate all the recursive structures that meet the boundary range. Therefore, the recursive structure of the upper bound, median, and lower bound of the Bhattacharyya parameter are used to compare the performance of formula (16). The polar code construction scheme under the PLC channel uses the recursive structure with the best performance. The upper bound, median value, and lower bound of the Bhattacharyya parameter are calculated as follows: Upper bound of the Bhattacharyya parameter: (2i−1)

Z(W2N

(i)

(i)

) = 2Z(WN ) − Z(WN )2

(18)

Lower bound of the Bhattacharyya parameter: (2i−1)

Z(W2N

(i)

) = Z(WN )

(19)

The median value of the Bhattacharyya parameter: (2i−1) Z(W2N )=

1 × (Z(WN(i) ) − Z(WN(i) )2 ) 2

(20)

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The Bhattacharyya parameter of the PLC channel is determined in step (1), and subsequently, the Bhattacharyya parameter value of each polarization channel is calculated using the recursive formula in step (2). The reliability estimation of the polarization PLC channel is then accomplished by comparing the values of each Bhattacharyya parameter.

4 Simulation Experiment and Result Analysis 4.1 PLC Channel Simulation Model 4.1.1 PLC Channel Attenuation Model Zimmermann and K. Dostert introduced a top-down multipath transmission attenuation model for PLC channels, aiming to elucidate the signal attenuation and frequency selection characteristics in PLC channels. The channel transmission function can be mathematically represented as shown in Eq. (18): H (f ) =

N

gi · A(f , di ) · e−j2π f τi

(21)

i=1

A(f , di ) = e−(a0 +a1 ·f

k )·d

i

(22)

√ di ε di = τi = v c0

(23)

In the formula, N denotes the total number of signal transmission paths in the PLC channel, while f represents the signal frequency transmitted by the PLC. The weight coefficient of the i path is denoted by gi , and the channel attenuation function is represented by A(f , di ). Additionally, the attenuation parameters are denoted by a0 and a1 , while the attenuation factor index is represented by k. Lastly, the transmission distance of the i path is denoted by di . τi represents the propagation delay of the i path, ε is the transmission line dielectric constant, and c0 is the propagation speed of light. 4.1.2 PLC Channel Pulse Noise Model The Middelton Class A noise model [19] contains white Gaussian noise component and pulse noise component, which can better characterize the noise characteristics of PLC channel. Its Probability density function (PDF) is as follows: f (x) = e−A σm2 =

∞

2

− |x| Am

e 2σm2 2 m=0 m! 2π σm

(σG2 + σI2 )(m/A + γ ) 1+γ γ =

σG2 σI2

(24)

(25) (26)

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In the given formula, the value σm2 represents the power of pulse noise in the m state. The value γ denotes the ratio of Gaussian noise power to pulse noise power. Lastly, the value A represents the pulse index, which is a measure of the product of the average number of pulses received per unit time and the average pulse time. This index provides a description of the sustained characteristics of noise. The parameter set for this article is A = 0.1, γ = 0.1. 4.2 Result Analysis The effectiveness of Bhattacharyya parameter bounds in the PLC channel is verified by studying the performance of different parameters of polar code in the polarization PLC channel coding system. This is done based on the PLC channel attenuation model and pulse noise model. The simulation parameters for the polarization PLC channel coding system are shown in Table 1. Table 1. Simulation parameters of polarization PLC channel coding system Simulation parameter

Parameter setting

Channel attenuation model

Zimmermann

Noise model

Middleton Class A

Modulation mode

BPSK

Subcarrier number

32

FFT length

64

CP length

16

4.2.1 Comparison of Recursive Schemes of Bhattacharyya Parameter Bounds In order to obtain the optimal performance of PLC polarization coding, the code length of N = 512 and code rate of R = 0.5 are set as the simulation parameters. The performance comparison of the polarization PLC coding under the three recursive structures is depicted in Fig. 4. The figure clearly demonstrates that the recursive structure of the upper bound of the Bhattacharyya parameter outperforms both the recursive structure of the lower bound and the recursive structure of the middle value of the Bhattacharyya parameter in the polarization PLC channel. Hence, to achieve the maximum efficiency of polarization PLC channel coding, the recursive structure of the upper bound of Bhattacharyya parameters is employed as the construction scheme for PLC channel polar code. 4.2.2 Performance Comparative Analysis of Channel Polarization Degree Polar code length determines the degree of polarization of the channel, the longer the code length, the higher the degree of polarization. In order to compare the influence of the

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Fig. 4. Performance graph of different recursion modes

degree of PLC channel polarization on the performance of polar code, the performance simulation of the polarization PLC system with different code lengths was carried out under the condition of bit rate R = 0.5, and the results were shown in Fig. 5. As depicted in the figure, it is evident that as the signal-to-noise ratio improves, the code length of the polar code increases, resulting in enhanced error correction performance. The construction of the polar code relies on the choice of the fully polarized channel as the information bit. Under the constraint of a limited code length, it has been observed that as the code length increases, the polarization degree of the channel also increases. Consequently, the reliability of the polarization channel, where the information bit is located, is enhanced.

Fig. 5. Performance comparison of different code lengths

4.2.3 Comparative Analysis of Performance of Completely Polarization SubChannels with Different Proportions of Information Bits The anti-noise performance of the polar code is influenced by the number of information bits, given a specific code length. In order to conduct a comparative analysis of the performance of information bits occupying different proportions of fully polarization sub-channels, a simulation was performed. The simulation considered a code length of N = 512, and the results are presented in Fig. 6.

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Fig. 6. Performance comparison of different coding efficiency

As can be seen from the figure, the low bit rate polar code has obvious performance improvement. The polar code with a bit rate of R = 0.25 has a gain of 2dB and 4dB, respectively, compared to the polar code with bit rates of R = 0.5 and R = 0.75. This is because, under the condition of a certain code length, the information bit of the low bit rate polar code selects a lower proportion of the polarization channel with low reliability in the process of code word construction. 4.2.4 Comparative Analysis of Decoding Mode Performance In order to assess the impact of various decoding algorithms on performance in the PLC channel, this study introduces the Belief Propagation (BP) decoding algorithm and the Cyclic Redundancy Check-Successive Cancellation List (CRC-SCL) decoding algorithm. The simulation parameters for each decoding algorithm are presented in Table 2. Table 2. Parameter settings for different decoding methods Decoding method

Parameter setting

BP

Maximum iterations 50

CRC-SCL

CRC 4 List length L = 2 CRC 4 List length L = 8

Under the given conditions of a code length of 512 and a code rate of 0.5, a comparison was made to assess the impact of various decoding algorithms on performance in the context of PLC. The simulation results are presented in Fig. 7. As depicted in Fig. 7, it is evident that the performance of the CRC-SCL decoding algorithm surpasses that of the SC decoding algorithm. Furthermore, the performance of the CRC-SCL decoding algorithm gradually improves as the number of search paths in the decoding list increases. On the other hand, the performance of the BP decoding algorithm is inferior to that of the SC decoding algorithm. However, the BP decoding

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Fig. 7. Performance comparison of different decoding modes

algorithm offers the advantage of being a parallel decoding algorithm, which results in lower delay and higher throughput compared to the SC decoding algorithm. 4.2.5 Comparative Analysis of Encoding Performance To assess the benefits of incorporating polar codes into the PLC system, this study will conduct performance and complexity analyses, comparing polar codes with the currently utilized Turbo codes and LDPC codes, which are known for their superior performance. The comparative analysis of polar codes, LDPC codes, and Turbo codes is conducted to evaluate their performance in the presence of the PLC channel. The evaluation is carried out using a code length of N = 512 and a code rate of R = 0.5. The simulation results are depicted in Fig. 8. Table 3. Comparison of encoding and decoding complexity of different encoding schemes Method

Encoding Complexity

Decoding Method

Decoding Complexity

Polar Code

SC

O(N log2 N )

Turbo

O(N log2 N ) O(mN )

BCJR

O(Imax (4N m ))

LDPC

O(N 2 )

BP

O(Imax (N d v + M d c ))

From the presented figure, it is evident that when subjected to low signal-to-noise ratio conditions, the performance of polar codes exhibits a slight disadvantage compared to LDPC and Turbo codes. The performance of the SC decoder is significantly affected by the forward dependency of the decoded bits in polar codes, resulting in a sharp deterioration. Under high signal-to-noise ratio conditions, the performance of polar codes is better than Turbo codes and LDPC, and the performance advantage becomes more pronounced as the signal-to-noise ratio increases. Table 3 presents a comparison of the encoding and decoding complexity of polar codes, LDPC codes, and Turbo codes. From the analysis presented in Table 3, it is evident that polar codes exhibit a marginally higher encoding complexity compared to Turbo codes, yet significantly lower than LDPC codes. In the context of decoding, polar codes employ the SC decoding algorithm,

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Fig. 8. Performance comparison of different encoding modes

which exhibits significantly lower complexity when compared to the iterative procedures employed by Turbo codes and LDPC. This characteristic confers a distinct advantage to polar codes.

5 Conclusion The polar code is applied to the PLC channel with a poor channel environment in this paper, establishing a polarization PLC channel coding system. The study aims to verify the effectiveness of constructing the polar code’s Bhattacharyya parameter boundary under the PLC channel. It examines the performance of various parameters of the polar code in the polarization PLC channel coding system. The specific conclusions are as follows: (1) The polar code aims to assign the information bit to the polarization channel with high reliability and the frozen bit to the polarization channel with low reliability. The upper bound, median, and lower bound of the Bhattacharyya parameter are the most effective construction schemes for estimating the reliability of the polarization PLC sub-channel. The recursive construction scheme with an upper bound on the Bhattacharyya parameter is the most effective for the PLC channel. (2) As the length of the code increases, the channel polarization effect improves, resulting in a decrease in the bit error rate. As the coding efficiency improves, there is an increase in the proportion of information bits that occupy unreliable channels, leading to a degradation in the bit error rate. By employing various decoding techniques, it has been observed that the CRC-SCL decoding algorithm outperforms the SC decoding algorithm. Furthermore, the performance of the CRC-SCL decoding algorithm improves as the decoding list length increases. The performance of the BP decoding algorithm is inferior to that of the SC decoding algorithm.. (3) Polar codes outperform LDPC and Turbo codes in terms of error rate performance, particularly under specific signal-to-noise ratio conditions. In terms of encoding complexity, polar codes have a slightly higher complexity than Turbo codes but are much lower than LDPC codes. Polar codes utilize the SC decoding algorithm, which has low complexity compared to the iterative calculations used by Turbo codes and LDPC, making it highly advantageous in terms of decoding.

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This article aims to validate the practicality of polar codes in PLC applications by conducting simulation analysis. The utilization of the polar PLC channel coding system has been shown to significantly enhance the transmission reliability of PLC and exhibits promising potential for application in intricate PLC channels. Acknowledgements. This paper received support from the National Natural Science Foundation of China (62001166), the Natural Science Foundation of Hebei Province (E2019502186), and the Central University Basic Research Fund (2021MS073).

References 1. Zhang, W., Li, T.: Relative impacts of channel characteristics and noise characteristics on the performance of a power line communication system. Power Syst. Prot. Control 50(07), 145–152 (2022). (in Chinese) 2. Cao, W., Kang, H., Xie, Z., et al.: Research on coding method of mimo-plc direct sequence spread spectrum system. Proc. CSEE 41(S1), 121–129 (2021). (in Chinese) 3. Pu, H., Liu, X., Han, M., et al.: Distributed opportunity relay selection for cooperative nonorthogonal multiple access systems in power line communication channels. Trans. China Electrotech. Soc. 35(11), 2306–2318 (2020). (in Chinese) 4. Rouissi, F., Vinck, A.J.H., Gassara, H., et al.: Statistical characterization and modelling of impulse noise on indoor narrowband PLC environment. In: 2017 IEEE International Symposium on Power Line Communications and its Applications (ISPLC), Madrid, pp.1–6 (2017) 5. Wang, Y., Zhang, M., Ma, Z., et al.: Analysis of influencing factors of power line channel communication characteristics. J. Electric Power Sci. Technol. 36(03), 157–164+173 (2021). (in Chinese) 6. Wang, Y., Hu, X.-T., Hou, X., et al.: Hardware implementation of Markov-Middleton pulse Noise Model. Autom. Electric Power Syst. 43(16), 168–174 (2019). (in Chinese) 7. Hu, S., Wang, L., Yang, S.: Research on Modeling method of power line channel system noise. Electr. Meas. Instrument. 55(17), 88–93 (2018). (in Chinese) 8. Jin, X., Xiao, Y., Zeng, Y., et al.: Modeling and error compensation of Low voltage Power line wideband carrier communication channel. Proc. CSEE 40(09), 2800–2809 (2020). (in Chinese) 9. Babic, M., Bausch, J., Kistner, T., et al.: Perfomance analysis of coded OFDM systems at statistically representative PLC channels. In: 2006 IEEE International Symposium on Power Line Communications and Its Applications, Orlando, pp. 104–109 (2006) 10. Eun, C.K., Seo, S.I., Jun, H., et al.: Performance of double binary turbo coding for high speed PLC systems. IEEE Trans. Consum. Electron. 56(3), 1211–1217 (2010) 11. Wang, X.,Hong, H,M., Wang, K., et al.: Performance of LDPC and turbo coded power line communication over multipath channel and narrowband noise. In: 2022 2nd Asia-Pacific Conference on Communications Technology and Computer Science (ACCTCS), Shenyang (2022) 12. Erdal, A.: Channel polarization: a method for constructing capacity-achieving codes. In: 2008 IEEE International Symposium on Information Theory, Toronto, pp. 1173–1177 (2008) 13. Erdal, A.: Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans. Inf. Theory 55(7), 3051–3073 (2009)

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14. Jin, L., Li, Y., Li, B., et al.: Performance of polar coding for the power line communications in the presence of impulsive noise. IET Commun. 9(17), 2101–2106 (2015) 15. Ammar, H., Khaled, M.R., Emad, A.: Polar codes based OFDM-PLC systems in the presence of middleton class-a noise. In: 2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), Prague, pp.1–6 (2016) 16. Oh, H.M., Young, J.P., Sungsoo, C., et al.: Mitigation of performance degradation by impulsive noise in LDPC coded OFDM system. In: 2006 IEEE International Symposium on Power Line Communications and Its Applications, Orlando, pp. 331–336 (2006) 17. Shi, P., Tang, W., Zhao, S., et al.: Performance of polar codes on wireless communication channels. In: 2012 IEEE 14th International Conference on Communication Technology, Chengdu, pp. 1134–1138 (2012) 18. Zimmermann, M., Dostert, K.: A multipath model for the powerline channel. IEEE Trans. Commun. 50(4), 553–559 (2002) 19. Middleton, D.: Statistical-physical models of electromagnetic interference. IEEE Trans. Electromagn. Compatibil. EMC 19(3), 106–127 (1977)

A Preventive Maintenance Strategy of Wind Turbine Gearbox Based on Stochastic Differential Equation Li Yuqi1(B) and Su Hongsheng1,2 1 School of Automation and Electrical Engineering, Lanzhou Jiaotong University,

Lanzhou 730070, China [email protected] 2 Rail Transit Electrical Automation Engineering Laboratory of Gansu Province, Lanzhou 730070, China

Abstract. Due to the double carbon target in China, the use of wind power in practical applications is becoming more and more widespread. Therefore, the preventive maintenance (PM) of wind turbine equipment has become an important research topic. At present, PM mainly focuses on time based maintenance (TBM), supplemented by state based maintenance (CBM), each with its own advantages and disadvantages. Therefore, this paper proposes the joint preventive maintenance of TBM and CBM, mathematically modelling, simulating and analyzing the TBM and CBM strategies based on stochastic differential equations (SDE), and deriving the joint maintenance strategy of the two to make use of their respective advantages and avoid the disadvantages. Eventually, the usability and validity of the proposed model and the soundness of the preventive maintenance strategy are verified and analyzed through examples. Keywords: PM · TBM · CBM · Stochastic Differential Equation

1 Introduction With the increase of global environmental awareness, wind energy as an environmentally friendly, clean, and sustainable renewable resource has gained widespread attention, and the capacity has been installed of wind turbines added 77.6GW in 2022 [1]. Due to the gearbox being a vulnerable component in wind power generation equipment, it is necessary to repair it and optimize its maintenance strategy, which in turn leads to increased equipment availability, reduced downtime and reduced maintenance costs. Nowadays, Corrective Maintenance (CM) and Preventive Maintenance (PM) are the main maintenance method for wind turbines.CM refers to maintenance measures similar to rescue measures for equipment after a malfunction occurs. PM refers to a series of maintenance activities carried out on equipment before a malfunction occurs to ensure the equipment running in a safe state.[2].Currently, PMs are divided into TBM and CBM based on the running time of maintenance time or the state of equipment during © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 81–88, 2024. https://doi.org/10.1007/978-981-97-1072-0_8

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maintenance. TBM sets fixed maintenance intervals and invests sufficient maintenance resources at points of maintenance in time. CBM determines whether to repair the equipment by monitoring and measuring the condition of the equipment, predicts the change trend of the unit condition, and formulates the maintenance plan in advance to improve the progressiveness of the equipment. In the literature [3, 4], the characteristics about CBM and TBM are analyzed through the established state model, the CBM model is established by introducing the state value function, and the maintenance strategy based on TBM as the main and CBM as the auxiliary is obtained after its simulation. Since wind turbines are often built in remote areas or even in the sea and the monitoring system is also prone to errors [5, 6], this paper establishes a state degradation model for gearboxes considering random external factors based on SDE, conducts modelling and simulation, analyses the validity of the model and compares it with other models to prove its feasibility and superiority [7]. On this basis, the joint preventive maintenance of TBM and CBM is proposed, and its strategy is simulated and verified in the example analysis, which proves its practicality in actual production. The structure of this article is as follows: the first section models the gearbox state degradation model under SDE and solves the parameters in it analytically. Section 2 simulates and analyses the TBM and CBM strategies under the model has been established, and explains the relationship between them under the mathematical model. Section 3 presents a example of wind turbine to demonstrate the feasibility and superiority of the combined TBM and CBM repair strategy.

2 Gearbox State Degradation Model 2.1 Model of SDE Setting the random function x(t) indicates the state value of a gearbox. According to the actual production state of the gearbox, and its assumed that x(t 1 ) = 1 indicates good as new condition of gearbox at time t 1 , and x(t 2 ) = 0 indicates indicates the completely damaged state of gearbox at time t 2 . And in this paper, we consider that as long as the preventive maintenance is carried out, the state of the gearbox will be restored as new, i.e., x(t) = 1. The state degradation model of the gearbox based on the SDE is established as shown below. dx(t) = λ(x(t), t)dt + μ(x(t), t)dB(t)

(1)

In Eq. (1), λ(x(t),t)dt and μ(x(t),t)dB(t) denote the gearbox’s own recession and exposure to external random disturbances, respectively; λ(x(t),t)dt is the drift coefficient, and it denotes that the gearbox is subjected to its own failure rate. μ(x(t),t)dB(t) is the diffusion coefficient, and it denotes that the gearbox is subjected to random disturbances; and B(t) denotes the Brownian motion [8]. 2.2 Failure Rate Model Λ(x(t),t) is defined as failure rate model of the gearbox, which composed by time and state of itself in this paper. For time, it is inevitable to increase the failure rate over time

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for gearbox. And for the state of the gearbox itself; devices with better state values for the same operating time have lower failure rates. Therefore, the failure rate is divided into two mathematical form parts: one part is the basic failure rate which is affected by time, and the other part is the state-influenced rate which is the change of the basic failure rate caused by the self-generated state of the gearbox. Thus λ(x(t),t) = h(t)*g(x(t)), where h(t) denotes the base failure rate and g(x(t)) denotes the state impact rate. The fundamental failure rate h(t) of the gearbox is chosen as the Weibull distribution due to its characteristics.   β t β−1 (2) h(t) = η η In Eq. (2), h means a scale parameter, b means a shape parameter, and t means a device operating time. g (x(t)) represents the influence about state of gearbox on the failure rate. It is a continuous function with a value range of [0,1]. According to Weierstrass’s theorem and Taylor’s expansion [9], the state influence rate can be expressed as: g(x(t)) =

1 α · x(t) + 1

(3)

In Eq. (3), a indicates the effect of gearbox state on the failure rate function, also called as the regression coefficient. 2.3 Stochastic Perturbation Model Gearbox in the operation process either by the environment, monitoring equipment errors and other external random interference, are unrelated to operating time, and it has an effect on the state of gearbox, called the state fluctuation rate, and the current operating moment of the gearbox related to the current state. Thus, the state fluctuation rate is as follows: μ(t, x(t)) = k · x(t)

(4)

where k is a random perturbation parameter. 2.4 Parameter Solution We can get the reliability function of the model from the failure rate model of the gearbox, it can be express as follows:     1 t β R(x(t), t) = exp − (5) η 1 + α · x(t) Due to the definition of the fault density function F(x(t),t) = R(x(t),t)*λ(x(t),t), the likelihood function can be constructed as follows:       n  ti β β ti β−1 α α · exp − · (6) L(β, η, α) = η η 1 + x(ti ) η 1 + α · x(ti ) i=1

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The parameters η, β, α of the failure rate model are then solved using the NewtonRaphson method [10]. Solving the stochastic disturbance k, both sides of the SDE are integrated. In period (0,T ) with step size t and 0 ≤ nt ≤ T, x n (t) as the change in state value during the time period t to obtain Eq. (7)  t  t kxn (t)dB(t) = xn (t)− λ(xn (t), t)dt (7) 0

0

At this point, the failure rate will be considered as some fixed values λn (t), when t tends to 0, will be brought into the Eq. (7) can be expressed: N xn (t)−λn (t)·t k = kav =

n=0

xn (t)−Bn (t)

N

(8)

3 Analysis of Preventive Maintenance Strategies Based on Condition Modelling 3.1 Theoretical Analysis of CBM Strategies With the addition of the condition monitoring indicator parameters, the CBM model is as follows:   β t β−1 exp{γ · Z(t)}dt + k · x(t)dB(t) (9) dx(t) = − · η η 1 − α · x(t) where Z(t) denotes a true state information of each component of the gearbox, which is generally collected by the monitoring system, and this indicates that CBM determines its state value by observing real-time parameters of the gearbox. γ is the weight share of each parameter of the component [11]. The CBM is the implementation of maintenance activities guided by information about the state of the gearbox. This implies the existence of a preventive maintenance state threshold X thr , and due to the X thr if at time t = τ there is: x(τ ) ≤ Xthr

(10)

3.2 Theoretical Analysis of TBM Strategies TBM is a preventive maintenance of equipment at fixed maintenance intervals, the essence of which is to take the mean value of multiple model tracks of a CBM, i.e., all the information prior to maintenance is known and thus an average value of t is obtained to obtain the TBM’s time interval. T TBM is time interval threshold, for TBM, it is defined through the average of n times CBM stops. n

1 

TTBM = E E τi |fτ = E τi |fτ n i=1

(11)

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According to the above analysis, TBM is based on the average about almost CBM sample trajectories, and it replies that TBM is not only maintained depended on a few time intervals, and the TBM time intervals obtained from a great quantity of CBM sample trajectories.

4 Example Analyses The practicality and validity of the model will be verified by taking each component of the wind turbine gearbox as an example [9]. According to the data in Tables I and II obtained from the monitoring system, the parameters η = 16238, β = 2.12, α = -0.41, k = 0.0013 are obtained by the parameter solving method in Sect. 2.4. Table 1. Sample of gearbox partial fault data Numb

1

2

3

4

5

Failure time/h

5231

5251

4923

4823

5013

Number

6

7

8

9

10

Failure time/h

5443

4692

4982

4732

4632

Table 2. Sample of gearbox partial fault data Numb

running time/h

oil temperature/°C

shaft temperature/°C

amplification/mm

1

100

24.4

26.2

0.321

2

420

24.8

28.2

0.403

3

820

28.1

31.4

0.462

4

1400

31.4

36.8

0.527

5

1750

37.4

41.3

0.594

6

2650

39.3

46.2

0.831

7

3550

47.4

50.5

1.401

8

4050

54.4

57.8

1.923

9

4850

59.1

63.7

2.135

10

5150

68.4

72.1

3.234

The state model of the gearbox under CBM can be given by: dx(t) = −

 1.12 t 2.12 1 · exp{γ · Z(t)}dt + 0.0013x(t)dB(t) · 16238 16238 1 − 0.41 · x(t) (12)

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Based on the data of Table 1, and the mean time to failure of the state of CBM, we get the state model of the gearbox under TBM can be given by:    1.73 2.73 t · x∗ (t) dt (13) dx∗ (t) = − 16623 16623 We used Euler’s method [9] to solve the numerical solution of the above model and obtained the results of the state models of three conditions for the current instance. This is shown in Fig. 1, where the true state is obtained after processing through the SCADA monitoring system.

Fig. 1. State deterioration diagram of gearbox

From Fig. 1, it can be seen that both the TBM model and the CBM model are in good agreement with the real state values of the gearbox. However, it is also clear that the stochastic nature of the CBM is more in line with the actual trend of the real state, with a higher degree of fit, which proves the properties of the CBM model, i.e., it is able to describe more accurately the current state values of the gearbox. Figure 2 shows multiple sampling trajectories for the TBM and CBM state. From Fig. 2, it can be seen that there is an error between the state trajectory under TBM and a certain state trajectory under CBM, and TBM clearly tends towards the average value of an infinite number of CBM samples. The above analysis shows that both CBM and TBM have their own advantages and disadvantages, so we combine CBM and TBM to obtain a joint preventive maintenance strategy, whose state is shown in Fig. 3. T TBM is set to 4801h, and X thr is 0.9. In each TBM cycle, we decide whether or not to carry out CBM by comparing the state mainly to whether it is lower than X thr or not, whereas time reaches T TBM , TBM is performed directly. Some conditions are set at T TBM to avoid TBM and CBM at the same time and reduce over-maintenance.

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Fig. 2. Multitrack state degradation diagram under CBM

Fig. 3. The Joint Maintenance Strategy for TBM and CBM

5 Conclusion In this paper, a state model of a gearbox is developed based on SDE to mathematically describe the evolutionary behaviour of the state of the gearbox during operation. According to the models established and the different maintenance strategies of CBM and TBM, the state model under TBM and CBM is established, and A joint preventive maintenance strategy of TBM and CBM is proposed by simulating and analyzing the TBM and CBM strategies, combining the advantages of the two and analyzing the characteristics of the various strategies from the point of view of SDE. Finally, the modeling and analyzing results are validated by a sample of the wind turbine that a strategy of joint TBM and CBM is proved to be necessary.

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Acknowledgments. This work is funded by National Natural Science Foundation of China, grant number (61867003).

References 1. Global wind energy council: China leads global growth in offshore wind power for third consecutive years. China Oil Gas 28(3), 63 (2021) 2. Zichuan, Q., et al.: Reliability evaluation of key components of wind turbines based on improved Weibull distribution. Electr. Meas. Instrum. 58(3), 68–73 (2021). (in Chinese) 3. Su, H., et al.: Maintenance decision of wind turbine gearbox based on stochastic differential equation. Energies 13(17), 4480 (2020) 4. Li, C., et al.: Preventive maintenance model analysis on wind-turbine gearbox under stochastic disturbance. Energy Reports 8, 224–231 (2022) 5. Su, H.: Maintenance Decision of Wind Turbine Gearbox Based on Stochastic Differential Equation. Energies 13(17), 4480 (2020) 6. Aafif, Y., et al.: Optimal preventive maintenance strategies for a wind turbine gearbox. Energy Reports 8, 803–814 (2022) 7. Zhao, H., et al.: Preventive opportunistic maintenance strategy for wind turbines based on reliability. Proc. CSEE 34(22), 3777–3783 (2014) (in Chinese) 8. Klebaner, F.C.: Introduction to Stochastic Calculus with Applications Third Edition, pp. 133– 134. Imperial College Press (2012) 9. Wang, R.S.: Functional Analysis and Optimization Theory, 1st ed., pp. 66–68. Beijing University of Aeronautics and Astronautics Press, Beijing (2003) 10. Syamsundar, A., et al.: Estimating maintenance effectiveness of a repairable system under time-based preventive maintenance. Comput. Ind. Eng. 156, 107278 (2021) 11. Su, H., Zhao, Y., Wang, X.: Analysis of a state degradation model and preventive maintenance strategies for wind turbine generators based on stochastic differential equations. Mathematics 11(12), 2608 (2023)

Research Status of Contact on Breaking Performance of High Voltage Circuit Breaker Pang Zhen1 , Mao Guanghui2 , Zhang Congrui1(B) , Han Yu1 , Gao Meijin3 , Chen Baoan1 , Liu Tan1 , Gao Jianfeng1 , and Ding Yi1(B) 1 State Key Laboratory of Advanced Transmission Technology, State Grid Smart Grid Research

Institute, Beijing 102209, China [email protected], [email protected] 2 State Grid Corporation of China, Beijing 100032, China 3 State Grid Zhejiang Electric Power Co., Ltd., Economic and Technological Research Institute, Hangzhou 030001, China

Abstract. Circuit breaker is the key control and protective equipment in the power system, widely used in various fields of the national economy, accurate assessment of circuit breaker breaking performance, better establishment of new energy as the main body of the new power system, strengthen the safe and reliable operation of the power system is of great significance. Contact is the core component of circuit breaker responsible for making and breaking circuit, and its performance directly affects the breaking ability of circuit breaker. This paper reviews the current research status and direction development of high-voltage circuit breaker. Based on the breaking requirements of high-voltage circuit breaker, the influence law of contact characteristics on the breaking performance is summarized, and the research progress of contact in nanometer preparation and doping modification technology is analyzed. The future development direction and problems of contact materials are prospected. Keywords: Electrical Contact · Interruption Performance · Primary Cut-out

1 Introduction In recent years, global climate issues and low-carbon energy development have attracted more and more attention. In 2020, China also put forward the goals of “carbon peak” in 2030 and “carbon neutrality” in 2060, promoting the transformation of the power industry to low-carbon and sustainable development and building a new power system with new energy as the main body [1]. In this context, more and more attention has been paid to the development and application of wind power, solar power, nuclear power and other new energy sources, but new energy power generation is characterized by randomness, volatility and gap [2], which brings major challenges to the economy, safety and reliability of the power system. With the gradual grid-connection of large power supplies and the completion of UHV ring networks, the problem of excessive short-circuit current in power supply and load-intensive areas is prominent, which has © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 89–102, 2024. https://doi.org/10.1007/978-981-97-1072-0_9

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become a prominent factor restricting the load growth and development of the power grid. For example, in the power grid of Huanjing, East China and South China, where the load is concentrated, the short-circuit current in many 550 kV substations exceeds the maximum breaking capacity of the circuit breaker (63 kA). It seriously threatens the safe and stable operation of power grid. Circuit breaker is the core control and protection equipment in the power system, which plays the role of closing, carrying, breaking normal current and cutting off fault current to protect the system, and its breaking ability directly affects the operation safety of the power system. The function of the contact in the circuit breaker is to realize the current in the circuit to switch on and off, is the core part of the circuit breaker, and plays a crucial role in the breaking performance of the circuit breaker, and its performance has become one of the key factors restricting the domestic development of ultra-high voltage and large capacity SF6 circuit breaker. In the process of opening and closing, the contacts have to experience the ablation of thousands of degrees of high-temperature arc, the erosion of SF6 gas and the friction caused by insertion and removal [3]. With the increase of power grid load, high performance requirements and long service life are proposed. The comprehensive performance of the current contacts is difficult to meet the requirements. Achieving collaborative performance improvement has always been a bottleneck problem in the contact industry. At present, the domestic and foreign high-voltage circuit breaker contact materials and technology are mainly based on the copper tungsten alloy material technical route, this technical route has been developed since the 1960s, because it has high voltage strength and low electrical ablation, thus becoming the key material to promote the use of highvoltage electrical switch voltage level and power. Domestic and foreign scholars have summarized the four characteristics that ideal circuit breaker contacts should have [4]: Low contact resistance; b. Excellent arc welding resistance; c. Low ablation rate; d. Good arc root migration Based on the introduction of the development and current situation of high voltage circuit breaker, the influence mechanism of contact characteristics on the breaking performance of high voltage circuit breaker is summarized. This paper summarizes and analyzes the latest research progress of contacts, points out the hot spots and existing problems in the research, in order to provide practical and effective reference for the further development of contacts. 1 High voltage circuit breaker research. 1.1 High Voltage Circuit Breaker Development History High-voltage circuit breakers have gone through the development process of oil circuit breakers and compressed air circuit breakers, and the first two have been gradually eliminated, and the latter two have become the mainstream of the power system [5]. Since 1926, oil circuit breakers have been used in 154 kV systems in Japan, but there are low breaking capacity, short service life, It is easy to cause fire and other defects, so it gradually changes to the air circuit breaker. In 1953, ABB took the lead in using

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24 kV air circuit breakers, and gradually developed to 50 kA and 550 kV equipment with multiple breaks, but the air circuit breaker was gradually eliminated due to problems such as violent explosion operating sound and poor seismic performance. At present, the application of SF6 circuit breakers in the high-voltage field is more common, and the high-voltage switches above 40 kV in China are basically in use, which use SF6 as the arc extinguishing medium and have high cutting capacity. In the early SF6 circuit breaker, there are two gas pressures in the arc extinguishing chamber, called double-pressure SF6 circuit breaker, the SF6 gas is compressed by the compressor, and the high-speed air flow is formed in the arc extinguishing chamber nozzle to put out the current over zero. Because of its need for pressure pumps and pressure devices, complex structure, poor environmental adaptability, has been eliminated. On this basis, domestic and foreign manufacturers developed a single voltage SF6 circuit breaker. Compared with the double-voltage SF6 circuit breaker, it has the advantages of simple structure, low inflation pressure, good arc quenching performance and low production cost, but the required operation power is large, the opening time is long, the mechanical life is short, and the cut-off overvoltage is easy to be generated when the small inductance current and small capacitance current are broken. In order to solve the above problems, the SF6 circuit breaker with “self-energy” arc extinguishing function is developed. When the short circuit current is broken, the SF6 gas is heated by the energy of the short circuit current arc itself, and the high pressure required for arc extinguishing is generated. The circuit breaker has the advantages of strong breaking ability, small operating power, reliable operation, long mechanical life and short inherent opening time. It has been widely used in the 110–500 kV voltage level of China’s power system, which greatly improves the reliable, stable and economic operation level of the power system. Foreign ABB [6] and Siemens have successfully developed 245 kV single break, 550 kV double break rated short circuit breaking current up to 80 kA and 100 kA SF6 circuit breakers. In addition, the United States Westinghouse, ITE company also has 80 kA high-voltage circuit breaker products, but its production of 80 kA high-voltage circuit breaker multi-oil and SF6 double-voltage circuit breaker, due to its large size, need to consume a lot of steel and transformer oil, transportation and installation is more difficult, the technology is relatively backward, has tended to be eliminated. So far, there are no domestic manufacturers can produce 550 kV/80 kA high-voltage circuit breakers. Taking ABB as an example, it has a relatively complete 80kA high-voltage circuit breaker products, including 145 kV ~ 245 kV single-break circuit breakers and 420 kV, 550 kV double-break circuit breakers. In 1984, ABB developed 420 kV/80 kA doublebreak outdoor SF6 circuit breaker (single dynamic pressure gas interrupter), on this basis, combined with the PA type 245 kV/63 kA tank circuit breaker and GIS circuit breaker that have been developed and put into engineering application. In 1992, the company developed the first GIS 80kA interrupter (single dynamic pressure gas type), but its maximum voltage can only achieve 170 kV, and realized the 145 kV and 170 kV single-break circuit breakers, 245 kV double-break circuit breakers and 550 kV three-break circuit breakers. In the early 21st century, ABB developed a 245 kV single break interrupter (still a single dynamic pressure gas type) based on the improvement of the original 80 kA interrupter nozzle, air flow channel, circuit breaker tank and external capacitance. Completed the development of 245 kV single break, 420 kV and 550 kV double break

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GIS and tank circuit breaker products. Siemens has provided 17 550 kV/100 kA tank circuit breakers and GIS circuit breakers for the Canadian power system, using doublebreak single-voltage interrupter, the interrupter has the following three characteristics: 1) in the interrupter mode using a fixed opening distance, the fixed opening distance has the advantage of large breaking current; 2) The nozzle and arc ring are made of graphite material. After breaking the short circuit current 20 times, the surface of the graphite nozzle does not become rough, because the graphite is directly sublimed from the solid state. 3) Arc extinguishing chamber adopts double action transmission structure, fast opening speed and short breaking time. Siemens also has a new generation of 8DQ1 420 kV/80 kA circuit breaker, which uses a double-break self-energizing double-action structure arc extinguishing chamber. So far, there are no domestic manufacturers can produce 550 kV/80 kA high-voltage circuit breakers. In 2014, the team of Academician Pan Yuan of Huazhong University of Science and Technology, together with Guangzhou Power Supply Bureau and XD and other units, based on the high coupling hollow split reactor, after four years of technical research, overcome the problems of transverse insulation under high coupling reactor, dynamic thermal stability and temperature rise under large current, and the elimination of circulating current between high coupling parallel coils. By using two 252 kV/63 kA porcelain post circuit breakers, the scheme design of 252 kV/100 ka large-capacity breaking device was realized by using 2-phase parallel arrangement, and the 100 kA (RMS) short-circuit current breaking test was passed in Xi ‘an National High Voltage Electrical Products Quality Supervision and Inspection Center in September 2019. Pinggao Group has successfully passed the 550 kV/80 kA symmetrical shortcircuit current breaking test, 80 kA (3s) short-time withstand current test, 200 kA peak withstand current test and insulation test, and has accumulated test experience in 80kA high-current breaking. A 550 kV/80 kA circuit breaker prototype based on new electrical contacts was developed in cooperation with State Grid Smart Grid Research Institute. In foreign countries, represented by large switching equipment enterprises such as ABB and Siemens in Europe, it is in the forefront of the world in terms of high-voltage and large-capacity SF6 circuit breakers, and has 420 kV/80 kA double-break SF6 circuit breakers, 550 kV/100 kA GIS and other advanced and mature products. At present, the rated short circuit breaking current of 252 kV circuit breakers in China has been generally increased to 63 kA, but there is no mature 550 kV voltage level 80 kA and above short circuit current circuit breakers, the relevant electrical contact technology has become one of the key factors restricting the development of super and UHV large capacity SF6 circuit breakers. 1.2 Life Evaluation Status of High Voltage Circuit Breakers The number of high-voltage circuit breakers is large, the maintenance workload is huge, and its maintenance cost accounts for more than half of the substation maintenance cost. Therefore, it is a practical problem to accurately predict the life of the high-voltage circuit breaker and correctly evaluate the overall performance, and obtain the balance between safe use and economy. The research on the method and technology of circuit breaker life evaluation has not been interrupted at home and abroad [7]. In the 1990s, the United States first proposed the concept of “electrical life”, I. Benfatto and A. De Lorenzi

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through the analysis of the wear of the contacts after the high-voltage vacuum circuit breaker was broken 50 kA, it was concluded that the experiment 2000 times of breaking times can be achieved. C. Neumann et al. calculated the failure rate curve of a certain type of high-voltage circuit breaker and divided it into three stages: early failure period, accidental failure period and wear failure period. A. Pons et al. studied the electrical life and reliability of high-voltage circuit breakers. The results showed that the breaking current of the contacts of high-voltage circuit breakers directly determined the wear condition of the contacts, and then affected the breaking times of high-voltage circuit breakers. The relationship curve and function relationship between the breaking times of high-voltage circuit breakers and the ratio of rated breaking current to actual breaking current were given. Chinese researchers are still in the initial stage of evaluating the life of high-voltage circuit breakers [7]. According to the defect statistics of high-voltage circuit breakers, some researchers obtained the failure types and proportions of each component, and established the failure analysis model of high-voltage circuit breakers, such as the life model of SF6 sealing components based on Weibull distribution. Some researchers have proposed an electrical life evaluation method using the cumulative wear of contacts as the basis for judging the electrical life. 1.3 Reliability Evaluation Status of High Voltage Circuit Breakers The stable operation of circuit breaker directly affects the safety and reliability of power system operation, and its reliability evaluation is an important part of the whole power system reliability evaluation. Since the 1970s, the international academic community has paid attention to reliability research. Texas A&M University of the United States proposed A method for automatic detection and analysis of circuit breaker operation. United States Consolidated Electrnics, Inc. The SM6 series circuit breaker online inspection system developed by the company and the GIS online inspection system developed by the Swiss ABB company have been applied and achieved good economic benefits [8]. Similar work in China is still in its initial stage [9]. In recent years, China Electric Power Research Institute and China Southern Power Grid Company have carried out many statistics on the defects and faults of switchgear, but they mainly counted the fault data in the operation of the equipment, did not analyze the specific failure causes, and lacked the guidance to effectively improve the reliability of the equipment. Tsinghua University, Xi ‘an Jiaotong University, North China Electric Power University and many other universities, Ningbo Institute of Technology, Beijing Huizhi and other condition monitoring technology enterprises, as well as XD Group, Pinggao Group and other power equipment manufacturers have carried out the research work of power equipment condition monitoring and evaluation. The state evaluation of SF6 high-voltage circuit breaker is mainly based on its external state, including current characteristics monitoring of the switching coil, operating characteristics monitoring and analysis of the circuit breaker mechanism, and SF6 gas density monitoring [10]. It is not possible to diagnose the internal state of the high voltage circuit breaker in operation, such as the insulation state, the ablative state of the conductive and arc extinguishing elements, so the elimination of defects is usually very difficult. In addition, the monitoring and condition evaluation of high-voltage circuit breakers mostly adopt a single parameter, and rarely

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adopt multi-parameter synthesis method, which cannot accurately study the change law of the health state of high-voltage circuit breakers during operation [11].

2 Influence of Contact Characteristics on Breaking Performance 2.1 Contact Resistance The temperature rise of the contact directly depends on the contact resistance value, and the contact should have a low contact resistance. Under high contact resistance, the increase of temperature is easy to lead to short circuit, fusion welding, and even fire and other problems, causing great damage to the power system. This paper focuses on the research direction of contact materials and the factors affecting contact resistance. At present, the research of contact resistance is divided into two main directions: (1) theoretical calculation. A mathematical model or calculation formula was established to simulate the contact resistance. Du Yongguo [12] studied the contact resistance formulas of contact surfaces of different specifications (round, circular, square, etc.). Chen Senchang [13] introduced a new G-W contact resistance model. (2) Equipment development. Developed high-precision contact resistance test equipment. Ren Wanbin [14] designed a batch contact resistance measurement system for contact materials with a resolution of 0.1m; Chen Zhi [15] developed an ICT system suitable for the contact resistance detection of relay contacts. There are many factors affecting the contact resistance of the contact material in practical applications, mainly including the property of the contact material itself, surface roughness, contact surface shape, etc. In order to obtain low contact resistance, the contact material is required to have low resistivity, low hardness and high chemical stability to prevent the corrosion layer in the arc drawing process. The perfectly clean, ideal contact model is a point of radius r, which is calculated as follows: R=

ρ 2r

(1)

where R is the contact resistance, ρ is the resistivity of the contact material, and r is the radius of the contact point [16]. But in reality, the ideal point contact does not exist, and the contact resistance is also affected by the contact force and the contact area. At the microscopic level, when the force acts on the surface of a pair of contacts, the most prominent point on the surface first contacts, and then under the action of elastic deformation, more microscopic points contact together. In the process of increasing the number of contact points, the contact resistance will decrease significantly. CIGRE SC13 [17] gives an empirical formula for the contact force between contacts: F = k · H · Ar

(2)

where H is the hardness of the contact material, Ar is the contact area, and k is a coefficient between 0.1 and 0.3. The proportional constant k first needs to consider the surface finish of the contact, and secondly, the actual hardness is not constant, but there is a highly localized stress at the microscopic contact point, so it needs to be obtained by repeated experiments for the specific application of the material.

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Although it is currently impossible to determine the contact area with great precision, knowing the approximate area of contact is essential for correctly understanding and designing electrical contact. It is shown that the contact resistance is a function of the contact point density and the total real contact area within two meshing full contact surfaces. In a uniformly distributed region, the current will diffuse to fill all available conductive regions, but in actual contact, the region is greatly limited because it is impossible to have such high accuracy in alignment, and it is impossible to obtain and maintain such high smoothness. In the above contact pressure, the contact area is determined only by the hardness of the material and the force pushing the contact. Since the original simplified equation of contact resistance is given in terms of the resistivity of the material and the radius of the contact point, the contact radius can be replaced by an expression of the contact force. Ar = π r 2

(3)

Assuming that the resistance of the oxide layer on the surface of the contact is RF, the formulas (2) and (3) are substituted into formula (1) to see that the calculation formula of the actual contact resistance RT is:  ρ π kH RT = + RF (4) 2 F Formula (4) explains that low contact resistance requires the contact material to have low resistivity and low hardness. At the same time, it is necessary to pay attention to the fact that higher contact force will bring more mechanical wear. Therefore, it is necessary to find the balance point of parameters combined with engineering practice in the process of designing contacts. 2.2 Resistance to Arc Welding and Low Ablation Rate The arc welding resistance and low ablation rate of circuit breaker contacts require the contact material to have high melting point and high hardness. In fact, it is the consideration of the heat and temperature processing capacity of the contact. The following relationship can be established between the voltage drop measured through the contact and its temperature. This is based on the analogy that exists between electric and thermal fields, and assumes that there is no radiant heat loss near the contact point. θ=

VC2 8λρ

(5)

where θ represents the temperature, λ represents the thermal conductivity of the contact material, and ρ represents the resistivity of the contact material. Formula (5) is valid only in the range of lower temperatures. At higher temperatures, metal materials tend to soften and produce more severe elastic deformation. When the temperature rises further, the melting point of the metal is reached. Table 1 summarizes the softening points and melting points of common metals and their corresponding voltage drops. The table shows the maximum current of a particular material at which the contacts soften or melt, so that appropriate design can be made to avoid contact melting and

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contact materials

electrical resistivity·cm·10–6

hardness kg/cm2 ·103

softening point Temperature, voltage drop K,mV

softening point Temperature, voltage drop K,mV

Au

2.2

2–7

373

80

1336

450

Ag

1.63

3–7

423

90

1233

350

Al

2.9

1.8–4

423

10

931

300

Zn

6.16

3–4

443

10

692

170

Cu

1.8

4–7

463

120

1356

430

Ni

9.0

7–20

793

220

1728

650

Pt

11.0

4–8

813

250

2046

700

Mo

4.8

18

1172

340

2883

960

W

5.5

12–40

1273

400

3653

1000

welding. The maximum softening and melting currents corresponding to the material are:  F 2Vs IS = (6) ρ πH  2Vm F (7) Im = ρ πH The script s in the formula represents softening and m represents melting. The electrical ablation of the contact is an inevitable consequence of arc breaking, mainly caused by the evaporation of the cathode and anode electrodes. According to the theory of W. Wilson [18], the pressure drop at the contact end causes local high temperature to cause contact gasification. Based on its evaporation rate equation, the distribution of different materials in the air from the minimum to the maximum amount of electrical corrosion was obtained (Fig. 1) [19]. The empirical formula of metal ablation rate is as follows: R=

1000(Ec + EA ) ρJH

(8)

where R represents the ablation rate (ml/kA-sec), Ec represents the cathode pressure drop (V), EA represents the anode pressure drop (V), J represents the Joule-calorie conversion coefficient (4.18 Cal/J), H represents the heat of gasification (cal/g), and represents the material density (g/ml). 2.3 Arc Root Migration There is arc root migration on the surface of the contact in the arc extinguishing room of the circuit breaker. When there is an arc, the contact of the circuit breaker should

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Fig. 1. Electrical ablation rate of various metal materials

separate a main arc into several small arcs under high arc, so as to reduce the ablation of a single arc point on the surface of the contact. J. McBride et al. [20] Many researchers found that in actual operation, the arc often remains motionless for a period of time and continues to burn the specific position of the contact, which limits the arc breaking capacity and significantly increases the ablation rate of the contact. In order to increase the arc voltage drop and reduce the electric ablation, it can be achieved by increasing the breaking rate on the mechanical level. S. N. Kharin et al. [21] summarized the rule of arc root migration and metal vapor density during arc breaking, and found that the two are inversely proportional, that is, metals with higher gasification points produce less metal vapor, and thus play a role in improving arc root migration. 2.4 Dam a River The cut-off phenomenon refers to the phenomenon that when the AC circuit breaker breaks a small current, the arc current decreases from the peak to the zero with the breaking of the contact, and the current value (usually less than 5A) drops to 0 immediately after reaching a certain current value. In the case of breaking inductive load, due to the current lag voltage of 90 degrees, the current near the zero crossing is just the moment when the end to ground voltage is close to the peak. If the current drops to zero instantaneously, the inductance and capacitor in the system will be stimulated to produce overvoltage. If the fracture does not have sufficient dielectric strength, breakdown and reignition will occur, causing high-frequency shock and damaging the circuit breaker. Closure exists in both SF6 and vacuum circuit breakers, but the triggering mechanism is different, the vacuum circuit breaker is affected by the contact material and the SF6 circuit breaker is affected by the bypass capacitance.

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In the vacuum circuit breaker, the contact material determines the life cycle of a single arc, and the factors that affect the life cycle of the arc are mainly the following three aspects. a. Metal vapor pressure of contact material In most cases, materials with higher vapor pressure produce a larger amount of vapor, which helps to maintain the stability of the arc, thereby shortening the life cycle of the arc. b. The product of boiling point and thermal conductivity of the contact material. Higher material boiling points (Tb) and thermal conductivity (λ) generally result in higher cut-off values. Table 2 shows the relationship between the cut-off values of some common metal materials. The electrode material made of alloy is more complex: it is not just the average of the two materials, but in most cases, lower than the average of each element acting alone. For example, the cut-off value of W80%-Cu20% alloy is between 5A and 6A, which is lower than tungsten and copper respectively; The cut-off value of Cu50%-Cr50% alloy is between 4 A and 5 A, which is also lower than the corresponding cut-off value of copper and chromium. Table 2. The Relationship between the Product of Boiling Point Thermal Conductivity and the Interception Value of Different Metal Materials material

λ·Tb (cal·cm−1 ·s)

Ich (A)

Mo

1280

5.7–6.7

W

2820

12–21

Ag

1150

7–7.5

Cu

2140

16–18

Al

935

12–13

Sn

350

1–2.3

c. Peak current of the load to be switched off When the peak value of the load current is above a certain threshold, the average life of the arc is greater than 10 ms, which means that at 50 Hz, half a cycle of the power supply frequency and longer, in which case the interception cannot be observed.

3 Research Status of Electric Contacts At present, the research on contact materials at home and abroad mainly focuses on three directions: (1) Developing new contact material system; (2) Add new elements or compounds to improve performance when the matrix is unchanged; (3) Explore new preparation technology.

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3.1 Nano-Contact Materials In order to solve the problems of low density, more defects and limited performance of traditional contact materials, the development of fine crystal/nano contact materials has become one of the hot research directions. When the grain refinement reaches nanometer level, the arc ablation resistance, electrical and thermal conductivity and mechanical properties of the material can be significantly improved. Nano-contact materials are generally made of ultrafine or nano-level mixed powder sintered in solid phase. The preparation of mixed powder can be made by high-energy ball milling, co-reduction, sol-gel, electroless plating, etc. Zhao Jingjing et al. [22] used sodium tungstate and copper nitrate to obtain regular spherical WCu20 composite powder with copper-coated tungsten structure by hydrothermal synthesis and co-reduction method, with a particle size of 70 nm. Zhao Ming et al. [23] prepared tungsten-copper composite powder with final particle size of 100 nm by sol-gel method using ammonium metatungstate and copper nitrate as raw materials and citric acid as complexing agent. Nanometer powder sintering activity is large, solid phase sintering can reach more than 98% density. Qiu et al. [24] prepared WCu20 nano-powder by high-energy ball milling method (400 r/min, 40 h), and after hot pressing sintering at 1050°C and 40 MPa, CuW alloy with nanocrystalline structure was obtained, with a density of up to 99.2% and a hardness of 310 HV. Elsaved et al. [25] used nano tungsten and copper powder to prepare nano WCu30 material by vacuum plasma sintering process at 950°C, with dense microstructure and good mechanical properties. 3.2 Doped Modified Contact Material Doping modification is another research focus, additives include: rare earth metals and oxides, third phase particles, activator elements, new carbon materials and so on. Rare earth elements La, Ce, Y and their corresponding oxides can improve the arc burning resistance of contact materials. Qian et al. [26] prepared La2 O3 -doped tungstencopper composite by in-situ synthesis method. When the mass fraction is 0.75%, the hardness of the contact is 220 HB, the conductivity is 45%IACS, and the arc ablation resistance is significantly enhanced, and the vacuum dielectric strength and arc mobility are increased by 36.9% and 46.6% respectively. The doping of the third phase particles such as WC, A12 O3 and graphene can improve the mechanical properties, welding resistance and arc ablation resistance of the materials. Zhang et al. [27] prepared WC-doped tungsten-copper contacts with high thermal conductivity and hardness. Dong et al. [28] added graphene into WCu30 alloy, studied its arc ablation performance through vacuum electrical breakdown test, and found that its breakdown strength increased by 45.5%, with only slight copper spatter on the surface of tungston-copper contacts and small flat cathode forming pits. Activator elements such as Ni, Co and Cr can improve the fusion and sintering properties of each component. Zhuo et al. [29] prepared nickel-coated tungsten fiber reinforced tungsten-copper composite electrical contacts, whose breakdown strength and tensile strength increased by 65.3% and 15.8%, respectively. Ahang et al. [30] studied the effect of Co on liquid-phase sintering of WCu40, and the results showed that Co reacts with W during sintering to form W6 Co7 compound phase, which reduces the Cu-W wetting Angle and has good activation effect.

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4 Conclusion This paper introduces the development history of high-voltage circuit breaker, starts with the ideal performance index of circuit breaker contacts, and puts forward its requirements for contact materials. By analyzing the properties of contact resistance, arc welding ablation resistance, arc root migration and cut-off, it summarizes the main parameters that affect the breaking performance of circuit breaker, and introduces the development status of contact materials. To summarize: 1) The resistivity of the material is the main factor affecting the contact resistance, low resistivity will obtain low contact resistance; The contact force will affect the contact resistance, and the contact force is inversely proportional to the contact resistance and proportional to the hardness of the material. 2) The hardness of the material also affects the contact resistance, mechanical wear and arc welding resistance, so it is necessary to find the best balance in the design process of the contact material. 3) The metal vapor density is inversely proportional to arc root migration, and the higher the gasification point, the better the arc root migration. Contact density is inversely proportional to the metal ablation rate, the higher the density, the lower the metal ablation rate, corresponding to better ablation resistance. 4) The higher the pressure of metal vapor, the lower the cut-off value, but the higher the pressure, the higher the vapor density, which affects the arc root migration, the best balance point needs to be found in the design process. 5) In the future, the research and development of high-voltage grade contact materials should be oriented towards the breaking performance, burn resistance, fusion and welding resistance of contact materials. The new material strengthening method and preparation technology. Acknowledgments. This work is supported by State Grid Co., LTD. Technology project (project code: 5500-202158363A-0–0-00). Research on the electrical contact materials of high voltage circuit breaker.

References 1. Gao, H., Guo, M., Liu, T., et al.: Review of power balance analysis for new power systems. High Voltage Technol. 49(07), 2683–2696 (2023) 2. Han, X., Li, T., Zhang, D., Zhou, X.: New problems and key technologies of new power system planning under dual-carbon target. High Voltage Technol. 47(9), 3036–3046 (2021) 3. Yang, R., Zhang, X., Peng, Y.N., et al.: Study on solid decomposition products during SF6 circuit breaker breaking. High Voltage Electr. Apparatus 58(12), 21–27+36 (2022) 4. Mutzel, T., Niederreuther, R.: Development of contact material solutions for low-voltage circuit breaker applications. In: 2010 Proceedings of the 56th IEEE Holm Conference on Electrical Contacts. IEEE (2011) 5. Zhiqiang, D., Baoshi, W., Xuedong, T.: Current situation and development trend of SF6 high-voltage circuit breakers in China. J. Shenyang Inst. Technol. 7(01), 50–52 (2011) 6. Jianji, L.I.: ABB high voltage circuit breaker technology. Electric Age 02, 64–65 (2003)

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7. Luo Yanyan, L., Jianguo, L.Z.: Overview of circuit breaker reliability research at home and Abroad. Low Voltage Electr. Apparatus 2, 3–6 (2001) 8. Zhang, X.: Research on Detection and Test Technology of Characteristic Parameters of Moulded Case Circuit Breaker. Hebei University of Technology (2011) 9. Zhou, H., Meng, C., Zhang, Z., Hua, F., Wang, P.: Development of smart grid and high voltage switchgear technology. Electrical Technology 25–27 (2010) 10. Sun, Y.S., Zhang, W.T., Zhang, Y.M., Yu, W.J., Liu, Y.F.: Research on the mechanical state evaluation method of high voltage switchgear Basedon on Kendall correlation coefficient. Electr. Autom. 36, 86–88 (2014) 11. Yabin, S.H.I., et al.: Development and application of the high-voltage switchgear reliability database. High Voltage Apparatus 6, 133–138 (2014) 12. Yongguo, D., Zhang, W., Junsui, H.: Electrical contact and electrical contact materials. Electrotechnical Mater. 3, 42–46 (2005) 13. Senchang, C., Yanhui, C., Ping, Z.: Research progress of electrical contact phenomenon and contact resistance model. J. Guangdong Teachers’ Univ. Technol. 36(02), 40–44 (2015). (in Chinese) 14. Wanbin, R., Chen, Y., Shengjun, X.: Research on automatic contact resistance measurement system for new contact materials. Electrotechnical Mater. 4, 39–42 (2013) 15. Zhi, C., Ruile, Z.: Discussion on relay contact test. Mech. Electr. Compon. 30(3), 36–37 (2010) 16. Garzon, R.D.: High Voltage Circuit Breakers. CRC Press (2002). https://doi.org/10.1201/978 0203910634 17. CIGRE SC13: High Voltage Circuit Breaker Reliability Data for use in System Reliablity Studies. CIGRE Publication (1991) 18. Wilson, W.R.: High-current Arc erosion of electric contact materials [includes discussion]. Trans. Am. Inst. Electr. Eng. Part III 74(3), 657–664 (1955). https://doi.org/10.1109/AIE EPAS.1955.4499130 19. Lee, T.H.: Physics and Engineering of High Power Switching Devices. MIT Press (1975) 20. McBride, J., Weaver, P., Jeffery, P.: Arc root mobility during contact opening at high current. IEEE Trans. Compon. Packag. Manuf. Technol. Part A 21, 61–67 (1998) 21. Kharin, S.N., Nouri, H., Miedzinsky, B.: Phenomena of arc root immobility in electrical contacts. In: 2012 IEEE 58th Holm Conference on Electrical Contacts (Holm). IEEE (2012) 22. Zhao, J., Li, J., Zhang, P., et al.: Preparation and structure of W-20%Cu complex by hydrothermal synthesis and co-reduction method. Powder Metall. Mater. Sci. Eng. 9(4), 628–634 (2014) 23. Zhao, M., Wang, J., Liu, W., et al.: Study on sol-gel preparation and reduction behavior of WCu composite powder. Rare Metal Mater. Eng. 40(2), 362–366 (2011) 24. Qiu, W.T., Pang, Y., Xiao, Z., et al.: Preparation of W-Cu alloy with high density and ultrafine Gruins by mechanical alloying and high pressure sintering. Int. J. Refract. Metals Hard Mater. 61, 91–97 (2016) 25. Elsayed, A., Li, W., el Kady, O.A., et al.: Experimental investigations on the synthesis of W-Cu nanocomposite through spark plasma sintering. J. Alloy. Compd. 639, 373–380 (2015) 26. Qian, K., Liang, S., Xiao, P., et al.: In situ synthesis andelectrical properties of CuW-La2 O3 ; composites. Int. J. Refract. Metals Hard Mater. 31(3), 147–151 (2012) 27. Zhang, C.C., Luo, G.Q., Zhang, J., et al.: Synthesis and thermal condutivity improvernent of W-Cu composites modified with WC interfiacial Jayer. Mater. Design 127, 233–242 (2017) 28. Dong, L.L., Chen, W.G., Deng, N., et al.: Investigation on are erosion behaviors and mechanism of W70Cu30 electrical contact materials adding graphene. J. Alloy. Compd. 696, 923–930 (2017)

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29. Zhuo, L., Zhang, Y., Chen, Q., et al.: Fabrication and properties of the W-Cu compasites reinforced with un-coated and nickel-coated tungsten fibers. Int. J. Refract. Metals Hard Mater. 71, 175–180 (2018) 30. Ahangarkani, M., Borgi, S., Abbaszadeh, H., Rahmani, A.A., Zangeneh-Madar, K.: The effect of additive and sintering mechanism on the microstructural characteristics of W–40Cu composites. Int. J. Refract. Metals Hard Mater. 32, 39–44 (2012). https://doi.org/10.1016/j. ijrmhm.2012.01.006

Simulation of Flow Characteristics in High-Voltage Circuit Breakers Yujiao Qiao, Shanika Matharage(B) , and Zhongdong Wang Centre for Smart Grid, University of Exeter, Exeter EX4 4PY, UK [email protected]

Abstract. Gas-insulated high voltage circuit breakers are used in the power network to protect the equipment and to isolate the system from the fault. Modelling and simulation are nowadays a key part of the HVCB development process, and understanding the arc quenching process in the nozzle through modelling is important. This paper investigated the first stage of arc quenching process. A comprehensive COMSOL Multiphysics model was developed, in which flow pattern in the nozzle and downstream is investigated without arc condition. Characteristics of supersonic flow including shock position, Mach number distribution and pressure distribution were studied. Results show that the flow behaviour is influenced by gas type, position of downstream electrode and the outlet geometry. Keywords: Supersonic flow · Flow characteristics · Circuit breakers

1 Introduction Gas-insulated high voltage circuit breakers are used in the power network to protect the equipment and to isolate the system. SF6 is the most commonly used gas insulation due to its excellent dielectric strength and arc extinguishing capabilities [1]. However, due to its high global warming potential, the power industry is in search of alternative environmentally friendly gases. Modelling and simulation can help to evaluate these new materials as well as new structures without conducting prototype tests [2]. The first step of simulation of arc quenching process is to implement the cold flow simulation, which predicts the air flow pattern in the nozzle area without the occurrence of an arc. Results from this stage can become the initial solution for later stage simulations which include arcing conditions. In addition, the experiments of SF6 circuit breakers show that the flow is turbulent in the nozzle area, [3]. Typically, the Laval nozzle structure is used in gas circuit breakers as the flow can reach Mach number 1 at the nozzle throat developing supersonic flow [4]. As the flow pattern plays a critical role in the arc quenching process, it is essential to study flow behavior under various conditions and explore the interactions between flow and key factors, such as gas pressure, nozzle geometry, inlet and outlet boundary conditions. Therefore, a model that can predict these processes with a certain accuracy is required for research on arc quenching. Many studies have been conducted related to cold flow, such as investigating the flow characteristics with different models comparing performance of laminar and different © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 103–113, 2024. https://doi.org/10.1007/978-981-97-1072-0_10

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turbulent models [5, 6]; optimizing the design and performance of circuit breakers [7]; investigating the impact of solvers on shock at different opening strokes [8]. Overall, the characteristics of cold flow has been investigated, but the influence of factors on the flow needs more study, this paper focus on the influence of factors including inlet pressures, smoothness of nozzle throat, position of downstream electrode, outlet boundary condition and outlet geometry. Supersonic flow is a key area of research in HVCB, because it can improve the performance and reliability of devices. With the influence of supersonic flow, the gas is compressed rapidly in nozzle and the arc extinguish effectively. As a fundamental research of arc quenching process, the research on supersonic flow has help on understanding the interaction between gas and arc. Besides, the design of the structure of circuit breaker can affect the flow pattern, therefore, the accurate model can help to optimizing the nozzle shape.

2 Methodology 2.1 Governing Equations For the simulation of the arc, one of the most important assumptions is local thermal equilibrium (LTE), which means every point reaches thermodynamic equilibrium. The conservation equation based on the LTE is shown as follows [9]: Mass conservation:  − ∂ρ → +∇ · ρV =0 ∂t where t is time, ρ is the instant density, V is the instant velocity vector. Momentum conservation equation:  − ∂ − → →− → − → ρ V + ∇ · ρ V V = −∇p + ∇ · τ + F ∂t − → where p is the pressure, τ is the stress tensor, the last term F is the additional force. Energy conservation equation:   − ∂ − → → (ρ ∈) + ∇ · V (ρ ∈ +p) = ∇ · (kl + kt )∇T + τ · V + S ∂t where the thermal conductivity includes molecular k l and turbulent thermal conductivity k t , T is the temperature, S is the source term, ∈ is the total enthalpy and can be calculated as follows:  − →2 V   p ∈= h − + ρ 2 where h is the internal energy, which is determined by T.

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2.2 Supersonic Flow Earlier studies have shown that the flow in the downstream nozzle area is in supersonic region [10]. Therefore, turbulent model is used to simulate gas flow in the nozzle [11]. The most widely used turbulence model is k-E model, which has been applied to simulate arc quenching process [12]. The k-E model has two transport equations, which describes the conservation of turbulent kinetic energy per unit mass, and turbulence dissipation rate [13]:     μt ∂ − → ∇ke + Gk − ρε μl + (ρke) + ∇ · ρke V = ∇ · ∂t σke     − ∂ ε μt ε2 → ∇ε + C1ε Gk − C2ε ρ μl + (ρε) + ∇ · ρε V = ∇ · ∂t σke ke ke where μl is the molecular viscosity, μt is the turbulence viscosity, Gk is generation of turbulence kinetic energy shown below [14]: ke2 ε        v 2  ∂w ∂v  ∂v 2 ∂w 2 + +2 +2 + Gk = μt 2 ∂z ∂r r ∂r ∂z Mt = ρCu

where w and v are respectively the axial and radial velocity components. Apart from that, Mach number is a key parameter used to represent flow compressibility, it is calculated as follows: u M = c where u is flow velocity, c is the speed of sound in medium. Typically, a flow with a Mach number higher than 1 (a flow velocity that is 30% of the velocity of sound in the media) is called a supersonic flow and such flow regime has a strong coupling among velocity, pressure, and temperature fields [7]. In circuit breaker nozzles most of the nozzle throat area has Mach number higher than 0.3 and hence the Navier-Stokes equation and continuity equations are solved together with the energy equation for heat transfer in fluids using high Mach number module in COMSOL Multiphysics [8]. The energy equation predicts the temperature, which is required to compute the temperaturedependent material properties. In addition, the ideal gas law is can be used in cold flow simulation, as the temperature is below 1000 K. 2.3 Nozzle Geometry and Boundary Conditions 2.3.1 Nozzle Geometry The prototype of the circuit breaker used for computations is from the experiments of Benenson and Frind [15]. Figure 1 shows the nozzle structure with upstream and downstream electrode. The upstream electrode has a round tip and the outer diameter is identical to the nozzle throat diameter. The downstream electrode is hollow. The model was built as 2D symmetry, detailed parameters are shown in Table 1.

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Fig. 1. Nozzle geometry

Table 1. Dimensional parameters for the nozzle Geometry

Value (mm)

Downstream electrode (Inner diameter)

d1

3.6

Downstream electrode (Outer diameter)

d2

Nozzle throat

d3

12.7

Upstream electrode

d4

12.7

Nozzle inlet

d5

25.4

Nozzle outlet

d6

38.1

6.35

2.3.2 Boundary Conditions The boundary conditions were specified at the nozzle inlet, the nozzle outlet, the symmetrical axis, and the nozzle wall. (1) The inlet boundary conditions are set up to assume gas in an isotropic process when entering the nozzle. The axial velocity and density are iteratively computed according to the calculated inlet static pressure from a reservoir with stagnation pressure (P0) and stagnation temperature (T0). (2) The exit static pressure (Pe) is given as input data in the simulation. The axial gradients of enthalpy and velocity are set to zero. The diffusion of momentum and energy at the exit is very small in comparison with convection and could be neglected. (3) Solid surface is applied as the non-slip boundary condition for velocity. Furthermore, the surface was set to be adiabatic. 2.4 Simulation Conditions Cold flow simulation aims to predict the flow pattern in the nozzle area without a burning arc. Hence the simulations were conducted without a heat input into the model [14]. Under these conditions the flow is driven by a pressure gradient between the nozzle inlet and nozzle outlet [5]. Impact of inlet pressure, position of downstream electrode, outlet boundary, gas type and nozzle throat conditions on the flow patterns were studied. Furthermore, the values of the parameters for smooth fillet at nozzle throat indicated in Table 2 were derived from experiments [6].

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Table 2. Simulation conditions and settings Simulation condition

Settings

Inlet pressure (P0) (atm)

37.5

Electrodes distance (mm)

21.5, 62

Gas type

Air, SF6

Outlet geometry

With tank, without tank

Outlet condition (atm)

2, 0.25*P0

3 Results and Discussion 3.1 Features of the Cold Flow in the Nozzle Area Flow in the nozzle area start with subsonic at the nozzle inlet, then reach transonic state before nozzle throat [14]. The presence of downstream electrode generates shock in the supersonic flow region. Figure 2 shows the flow distribution in SF6 gas for an inlet pressure of 21.4 atm. It can be seen that the Mach 1 is reached at the nozzle throat and shock, and supersonic velocities are reached in the expanding region after the smallest cross-section of the outflow path.

(a) Nozzle

(b) Shock

Fig. 2. SF6 gas Mach number distribution in the nozzle. P0 = 37.5 atm, Pe = 0.25*P0.

The contour in front of the flat tip of the downstream electrode is dense which shows the existence of the shock. The shock generates in the downstream of supersonic flow when the flow is forced to separate from the nozzle wall. The shape of nozzle and velocity of gas flow are the primary factors causing these phenomena. Figure 3 shows the flow characteristic along arc axial in the nozzle obtained for SF6 with an inlet pressure of 37.5 atm and the electrodes distance is 21.5mm. Mach number is lower than 1 at the nozzle inlet, Mach number reach 1 at the nozzle throat, then increase to higher than 1 in the downstream area [14, 16]. The inlet pressure can significantly affect the flow behavior and the performance of the circuit breaker as shown in Fig. 4. Three different inlet pressures are compared to find the interaction between inlet pressure and shock in the nozzle. The inlet pressures are 11.2 atm, 21.4 atm, 37.5 atm from the experiments [6]. Higher inlet pressure can lead

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Fig. 3. Flow characteristic along arc axial, variables are normalized with their throat values.

to higher Mach number. With the increase of inlet pressure, the shock position moves towards downstream electrodes.

Fig. 4. Mach number distribution along the axial direction. Pe = 0.25*P0, d = 21.5 mm.

In addition, the rise in velocity is associated with a pressure drop. Pressure decreases in the radial direction from the tip of the downstream electrode. Higher inlet pressure can cause larger pressure drops. To compare the influence of other factors on flow pattern, we choose the basic condition as inlet pressure is 37.5 atm, outlet pressure is 0.25 times of inlet pressure, opening distance is 21.5 mm. 3.2 The Influence of Outlet Condition The outlet condition includes exit boundary and tank after downstream nozzle. Therefore, two exit boundaries are compared to figure out the influence of outlet pressure on flow pattern, which is 2 atm and 0.25*P0 shown in Fig. 7. The previous simulations were conducted under the condition of nozzle with tank, whereas the simulation in this section is being performed without tank. By comparing these two geometries, we aim to identify

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the influence of change of exit geometry on the flow in the nozzle area. The outlet boundary condition for the nozzle without tank is 0.25*P0 at nozzle exit. The flow pattern in the nozzle area is influenced by the existence of tank. Figure 5 shows that the nozzle with tank has higher flow velocity at shock area, and position of shock is moved to the downstream electrode. Figure 6 presents that with the existence of tank, the gas in the tank is sucked into the nozzle and flow pattern become more complex.

Fig. 5. Mach number distribution with and without tank. P0 = 37.5 atm, Pe = 0.25*P0, d = 21.5 mm.

(a) with tank

(b) without tank

Fig. 6. Flow pattern at downstream nozzle, P0 = 37.5 atm, Pe = 0.25*P0, d = 21.5 mm.

Therefore, the computed velocity and pressure distribution in the nozzle at the nozzle exit plane with a dumping tank are substantially different from those computed assuming constant exit pressure. The condition with tank is closer to the real circuit breakers, therefore, the geometry with tank is used for the other simulations. The outlet pressure should be higher than ambient pressure to guarantee the existence of shock. In the experiments, outlet pressure is set as 0.25*P0 [15]. Therefore, the outlet boundary is set as 2 atm and 0.25*P0 separately in the simulation. The results show that the flow pattern shows no difference between two outlet boundary conditions, in other words, with the promise of shock exist, the outlet boundary influence on the flow can be neglected.

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Fig. 7. Mach number distribution with outlet boundary condition. P0 = 37.5 atm, d = 21.5 mm.

3.3 The Influence of the Smoothness Geometry of Nozzle Throat The smoothness of nozzle throat affects the flow by at high Reynolds number conditions. In such conditions, any small perturbation will grow under the action of the average flow amount, thus has the possibility inducing a new flow structure. This phenomenon can occur in the nozzle upstream area. The change of smoothness of nozzle throat also changes the geometry of upstream wall. Therefore, two types of nozzle throat geometry are compared to investigate the influence of smoothness on flow pattern, one is smooth throat geometry, and the other one is discontinuous throat geometry. The smooth throat shows in Fig. 8 (a) fillet with radius 6.35mm.

(a) Smooth throat geometry

(b) Discontinuous throat geometry

Fig. 8. Two types of throat geometry.

Mach number distribution along x-axial in Fig. 9 indicates that under the simulated conditions smoothness of nozzle throat has limited influence on flow pattern. While the model with discontinuous throat has slightly higher Mach number at up-stream electrode, the highest Mach number, shock location and shock strength appear to be same under two conditions. Therefore, the change of smoothness of nozzle throat can slightly change the flow pattern in the area upstream near the throat, but it almost has no influence on the downstream supersonic flow. Therefore, only the smooth throat nozzle is considered for further simulations.

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Fig. 9. Mach number distributions on the axis with smoothness of nozzle throat. P0 = 37.5 atm, Pe = 0.25*P0, d = 21.5 mm.

3.4 The Influence of Position of Downstream Electrodes The opening distance between two electrodes are simulated to investigate the influence of position of downstream electrodes on the flow. In the simulation, two opening distances have been compared, which are 21.5 mm and 62 mm based on the experiments conducted on the prototype [15]. Figure 10 shows the opening distance has influence on mostly the downstream flow pattern, including shock position and strength, while the upstream flow pattern remains the same. As the shock is generated by the downstream electrode, larger opening distance provides more space for gas to accelerate to higher speed. In addition, with increase in opening distance, the shock position moves with electrode towards downstream, and the contour of velocity becomes sparse. In other words, the velocity drop at shock position is quicker when the opening distance is smaller.

Fig. 10. Mach number distributions along the axis with opening distance between two electrodes. P0 = 37.5 atm, Pe = 0.25*P0.

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4 Conclusion The cold flow in the nozzle of HVCB has been investigated using high-Mach number module. The model has good performance on coupling heat transfer and fluid dynamics to solve conservation equations of supersonic flow in the nozzle. Impact of several design and operating conditions on the flow patterns were investigated. Results indicated that the gas type, moving electrode position and outlet type may impact the downstream flow patterns while they have minimal impact on the upstream flow. The next step of the simulation will incorporate arc conditions into the simulation model to develop a complete model that can study the arc-flow interactions. This will facilitate the prediction and optimisation of the arc quenching process in circuit breakers under new alternative gases, without expensive experiments.

References 1. Ito, H.: Switching Equipment. Paris, France: CIGRE (2019) 2. Franck, C.M., Engelbrecht, J., Muratovi´c, M., Pietrzak, P., Simka, P.: Comparative test program framework for non-Sf6 switching gases. B&H Electr. Eng. 15(1), 19–26 (2021). https:// doi.org/10.2478/bhee-2021-0002 3. Aabid, A., Khan, S.A., Baig, M.: A critical review of supersonic flow control for high-speed applications. Appl. Sci. 11(15), 6899 (2021). https://doi.org/10.3390/app11156899 4. Gremmel, H.: Switchgear Manual, 10th ed. ABB (1999) 5. Franck, C.M., Mantilla, J.D., Seeger, M.: Measurements and simulations of cold gas flows in high voltage gas circuit breakers geometries. In: Presented at the IEEE International Symposium on Electrical Insulation (2008) 6. Ye, X., Dhotre, M.: CFD simulation of transonic flow in high-voltage circuit breaker. Int. J. Chem. Eng. 2012, 1–9 (2012). https://doi.org/10.1155/2012/609486 7. Gonzalez, J.J., Freton, P.: Flow behavior in high-voltage circuit breaker. IEEE Trans. Plasma Sci. 39(11), 2856–2857 (2011). https://doi.org/10.1109/tps.2011.2129538 8. Tsonev, P., Ivanov, V., St Kolev, K.H., Tarnev, T.P.: Turbulent flow influence on the discharge parameters of a magnetically-stabilized gliding arc discharge. J. Phys. Conf. Ser. 2240(1), 012035 (2022). https://doi.org/10.1088/1742-6596/2240/1/012035 9. Zhang, Q., Yan, J.D., Fang, M.T.C.: The modelling of an SF6 arc in a supersonic nozzle: I. Cold flow features and dc arc characteristics. J. Phys. D Appl. Phys. 47, 17 (2014). https:// doi.org/10.1088/0022-3727/47/21/215201 10. Hermann, W., Kogelschatz, U., Niemeyer, L., Ragaller, K., Schade, E.: Experimental and theoretical study of a stationary high-current arc in a supersonic nozzle flow. J. Phys. D Appl. Phys. 7, 22 (1974) 11. Zhang, Q., Liu, J., Yan, J.D.: Flow structure near downstream electrode of a gas-blast circuit breaker. IEEE Trans. Plasma Sci. 42(10), 2726–2727 (2014). https://doi.org/10.1109/TPS. 2014.2309174 12. Yan, J.D., Nuttall, K.I., Fang, M.T.C.: A comparative study of turbulence models for SF6 Arcs in a supersonic nozzle. J. Phys. D Appl. Phys. 32, 1401–1406 (1999) 13. Bini, R., Basse, N.T., Seeger, M.: Arc-induced turbulent mixing in an SF6 circuit breaker model. J. Phys. D Appl. Phys. 44(2), 025203 (2011). https://doi.org/10.1088/0022-3727/44/ 2/025203

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14. Zhang, J.F., Fang, M.T.C.: Dynamic behavior of high-pressure Arcs near the flow stagnation point. IEEE Trans. Plasma Sci. 17(3), 10 (1989) 15. Benenson, D.M., Frind, G., Kinsinger, R.E., Nagamatsu, H.T., Noeske, H.O., Sheer, R.E.: Fundamental Investigation of Arc Interruption in Gas Flows. General Electric Company, New York (1980) 16. Dhotre, M.T., Ye, X., Kotilainen, S., Schwinne, M., Bini, R.: CFD simulation for a self-blast high voltage circuit breaker: mixing and heat transfer. In: Presented at the Electrical Insulation Conference. Annapolis, Maryland (2011)

Optimal Configuration of Hybrid Energy Storage Capacity Based on Improved Compression Factor Particle Swarm Optimization Algorithm Dengtao Zhou1 , Libin Yang2,3 , Zhengxi Li2,3 , Tingxiang Liu2,3 , Wanpeng Zhou2,3 , Jin Gao2,3 , Fubao Jin1(B) , and Shangang Ma1 1 School of Energy and Electrical Engineering, Qinghai University, Xining 810016, China

[email protected]

2 Economic and Technological Research Institute of State Grid Qinghai Electric Power

Company, Xining 810016, China 3 Clean Energy Development Research Institute of State Grid Qinghai Electric Power Company,

Xining 810016, China

Abstract. Wind power generation and solar thermal power generation are unstable and intermittent. The use of energy storage devices can suppress the power fluctuations caused by wind and solar power generation. In order to improve the economy of wind power-photothermal combined power generation energy storage system, the capacity configuration model of energy storage system is studied. Firstly, lithium battery and flywheel are used as energy storage devices of power generation system. The capacity optimization configuration model of hybrid energy storage system is established with the whole life cycle cost model as the objective function and the system load power shortage rate, lithium battery characteristics and flywheel energy storage characteristics as constraints. Secondly, based on the dynamic changes of inertia factor and acceleration factor, the compression factor is introduced to improve the particle swarm optimization algorithm, and the simulation is solved on Matlab. The results show that the improved compression factor particle swarm optimization algorithm has faster convergence speed and lower system cost. Keywords: Hybrid Energy Storage · Capacity Optimization · Total Life Cycle Costs · Compression Factor · Particle Swarm Algorithm

1 Introduction Wind power generation and photothermal power generation have low predictability and intermittence and Wind power-photothermal combined power generation system can effectively solve the above problems [1]. Reasonable configuration of energy storage capacity for wind power-photothermal combined power generation system is of great significance to the development of new energy. Hybrid energy storage system (HESS), © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 114–122, 2024. https://doi.org/10.1007/978-981-97-1072-0_11

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which consists of flywheel and lithium battery, can make full use of the characteristics of large energy of lithium battery, high power and long life of flywheel energy storage system to achieve complementary advantages. Nowadays, many researchers have done a lot of work on the solution method of HESS capacity allocation. Reference [2] uses improved whale optimization algorithm to solve HESS model by introducing power function control parameters and adaptive weights. Reference [3] used elite reverse learning to initialize the population, combined with particle swarm optimization to improve the sparrow position update equation to solve the HESS model. In reference [4], based on the nonlinear optimization of step size parameters, the sparrow search algorithm is improved to improve the convergence speed to solve the optimal solution of HESS. Reference [5] improved the asymmetric acceleration factor of the particle swarm optimization algorithm, and found that the convergence speed and optimization ability were improved. The traditional particle swarm optimization algorithm has the defects of low precision, easy to be premature and lead to local optimum [6]. Based on the dynamic changes of inertia factor and acceleration factor, this paper introduces compression factor to improve the particle swarm optimization algorithm, takes the whole life cycle cost of the energy storage device as the optimization objective, optimizes the system capacity by rationally allocating the energy storage quantity of lithium battery and flywheel. The simulation results show that the improved particle swarm optimization algorithm has better optimization ability and more reasonable capacity allocation.

2 The Constitution of Energy Storage Model 2.1 Hybrid Energy Storage System Topology The main research object of this paper is to optimize the configuration of energy storage capacity of wind power-photothermal combined power generation system, and mix flywheel and lithium battery as energy storage device. The system structure is shown in Fig. 1, which is composed of large power grid, AC to DC, DC to DC, DC to AC and energy storage control system.

Flywheel

PMSM

AC/DC DC/AC

Energy Storage Control System

Lithium Battery

DC/DC

Fig. 1. Topology diagram of hybrid energy storage system.

Grids

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3 Optimization Objectives and Constraints 3.1 Full Life Cycle Costs Life Cycle Cost (LCC), also known as Life Cycle Cost, is defined as the sum of a series of costs generated during the product life cycle from manufacturing to waste. The LCC model of the system is constructed by using the cost decomposition structure [7]. At this time, LCC is: LCC = CP + C0 + CM + CH

(1)

In the above equation, C P , C O , C M and C H are the costs of equipment purchase, operation, maintenance and treatment respectively. 3.2 Objective Function The mathematical model of LCC of hybrid energy storage system is as follows: min C = CP + CO + CM + CH = (1 + fob + fmb + fdb )Nb Pb + (1 + fof + fmf + fdf )Nf Pf

(2)

Table 1 describes the parameters. Table 1. Parameter meanings Parameter

Lithium battery and flywheel parameter description

f ob , f of

Operating coefficient

f mb , f mf

Maintenance factor

f db , f df

Handling factor

N b, N f

Number of pieces

Pb , Pf

Unit price

3.3 Electricity Supply Reliability Indicators Loss of Power Supply Probability (LPSP) is the reference index for the stable operation of the whole power generation system [8]. The formula is shown in Eq. (3), where E LPS represents the power shortage of the load and E L represents the demand of the load side: fLPSP =

K  k=1

ELPS (k)/

K 

EL (k)

(3)

k=1

The rated storage energy of lithium battery is E bn (in mWh), and the lower limit value of capacity of lithium battery is E bmin , which is calculated as follows: Ebn = Nb · Cb · Ub /106

(4)

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Eb min = Nb · Cb · Ub · (1 − dod )/106

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(5)

C b , U b , dod for the purchase of lithium battery set parameters are respectively rated capacity, rated voltage, maximum discharge depth. The capacity of the flywheel energy storage device is determined by Eq. (6) [9]: E=

1 2 Jω 2

(6)

In the above equation: J is the rotational inertia of the flywheel; ω is the angular velocity of the flywheel rotation. 3.4 Restrictive Condition (1) The reliability of the power supply is reflected by the load loss rate: fLPSP ≤ fLPSPmax

(7)

where f LPSPmax is the maximum permissible shortage rate for the load. (2) Energy storage constraints for energy storage systems: Ebmin < Eb (k) < Ebn Ef min < Ef (k) < Ef

max

(8) (9)

(3) E is mainly composed of two parts: high-frequency fluctuation part and lowfrequency fluctuation part, of which the low-frequency fluctuation part is borne by the lithium battery, that is, to meet the following conditions: Eb (k) ≤ α · E

(10)

4 Solution Method 4.1 Particle Swarm Algorithm Particle Swarm Optimization (PSO) is an algorithm inspired by the foraging activities of birds in nature. In order to improve the convergence of the algorithm, inertia factor ω [10] is introduced to form a standard particle swarm optimization algorithm. In order to obtain a more accurate global optimal solution, The inertia factor can be changed linearly [11], and the calculation expressions of speed update, position formula and dynamic change of inertia factor are shown in Eqs. (11), (12) and (13): k+1 k k k k k = ωνid + c1 r1 (pid − xid ) + c2 r2 (pgd − xid ) νid

(11)

k+1 k+1 k xid = xid + νid

(12)

ω = ωmax − t(ωmax − ωmin )/Tmax

(13)

The meaning of specific parameters is shown in Table 2.

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Parameter

Meaning

ω

Inertia factor

c1 , c2

Acceleration factor

r1, r2

Random number of [0–1]

k、t

Iteration number and current iteration number

T max

Maximum number of evolutionary generations

vid k /vid k+1 x id k /x id k+1 pid k 、pgd k

Particle velocity

d

dth dimension

Particle position Individual extremes and global extremes

4.2 Improved Compression Factor Particle Swarm Algorithm The acceleration factor dynamic change strategy is adopted to adjust the value of the acceleration factor, which indicates the strength of information exchange between particles. The adjustment equation is as follows. c1 = 2.5 − 1.5t/Tmax

(14)

c2 = 1 + 1.5t/Tmax

(15)

Based on the dynamic changes of inertia factor and acceleration factor, the compression factor [12] is introduced in this paper, which can effectively balance the search ability of particles before and after iteration, and avoid falling into the problem of local optimization. k+1 k k k k k νid = ζ [ωνid + c1 r1 (pid − xid ) + c2 r2 (pgd − xid )]

where ζ is the compression factor, expressed in Eq. (17).      ζ = 2/2 − ϕ − ϕ 2 − 4ϕ  ϕ = c1 + c2

(16)

(17) (18)

5 Example Simulation and Discussion 5.1 Parameter Setting of Example It is proposed to optimize the energy storage capacity of the wind power-photothermal combined power generation system in a certain area of Northwest China. The maximum shortage rate LPSP of the system is set to be 0.02, the efficiency of the inverter is 0.95, and Fig. 2 shows the power generation of the power system as well as the power consumed by the load in the region. The parameters of the lithium battery and the flywheel are shown in Table 3.

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Photothermal power generation Wind power generation

Electric quantity mWH

180000

Load consumption

160000 140000 120000 100000 80000 60000 40000 20000 1

2

3

4

5

6 7 month

8

9

10

11

12

Fig. 2. Electricity generated by the power generation system and consumed by the loads

Table 3. Parameters of the energy storage device Lithium Battery

Value

Flywheel

Value

Rated Voltage/V

12

Maximum energy storage/kwh

3

Rated Capacity/Ah

100

Maximum speed/rpm

9000

Charging efficiency

0.85

Charging efficiency

0.96

Discharge efficiency

0.85

Discharge efficiency

0.96

Discharge depth

0.4

Discharge depth

0.75

Operation coefficient

0.1

Operation coefficient

0.01

Maintenance factor

0.02

Maintenance factor

0

Handling factor

0.08

Handling factor

0.05

Cycle life

4000 times

Cycle life

20 years

Unit price/yuan

400

Unit price / ten thousand yuan

50

5.2 Simulation Results and Analysis of Examples According to the objective function and constraint conditions set above, the standard particle swarm optimization algorithm and the improved compression factor particle swarm optimization algorithm are used to simulate and analyze in Matlab. (1) Standard particle swarm algorithm Setting the population size as 100, the maximum evolutionary generations as 400, c1 = c2 = 2.05, ωmax = 0.9, ωmin = 0.4, the optimal individual fitness for the evolutionary generations and fitness is obtained as shown in Fig. 3, and it can be seen from the curves that the convergence requires about 37 iterations. (2) Improved compression factor particle swarm algorithm

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1.092530

1.092528

1.092526

Fitness

1.092524

1.092522

1.092520 X: 37 Y: 10925170

1.092518

1.092516 0

50

100

150

200

250

300

350

400

Evolutionary generations

Fig. 3. Based on traditional particle swarm algorithm

Also set the population size of 100, the maximum number of evolutionary generations is 400, c1 = c2 = 2.05, ωmax = 0.9, ωmin = 0.4, the optimal individual fitness is obtained as shown in Fig. 4, and it can be seen that the improved particle swarm algorithm, the speed of convergence is significantly accelerated, and it converges in about 13 iterations. Optimal individual fitness

107

1.0879420

1.0879415

Fitness

1.0879410

1.0879405

1.0879400 X: 13 Y: 10879395 1.0879395 0

50

100

150

200

250

300

350

400

Evolutionary generations

Fig. 4. Particle swarm algorithm based on improved compression factor

The full life cycle costs of the standard PSO and the modified compression factor PSO were obtained and are shown in Table 4. Table 4. Optimization results for both cases Optimize parameters

Standard PSO

Improved compression factor PSO

Lithium battery / piece

47100

38479

Flywheel / piece

297203

296024

LPSP

0.0152

0.0111

Minimum cost / yuan

10925170

10879395

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From Figs. 3 and 4, it can be seen that the improved compression factor particle swarm optimization algorithm has a faster convergence speed than the standard particle swarm optimization algorithm. From Table 4, it can be seen that compared with the standard particle swarm optimization algorithm, the improved compression factor particle swarm optimization algorithm reduces the total life cycle cost by 4.19%, the number of lithium batteries to be configured by 18.3%, the number of flywheels by 3.97%, and the load power shortage rate by 27%. Therefore, the improved compression factor particle swarm optimization algorithm has better optimization ability.

6 Conclusion This paper optimizes the capacity configuration of lithium battery and flywheel hybrid energy storage device with the goal of minimizing the life cycle cost of the power generation system and taking the power shortage rate and other operating indicators as constraints. Based on the dynamic changes of inertia factor and acceleration factor, the particle swarm optimization algorithm is improved by introducing compression factor. The simulation results show that the convergence speed is faster, the minimum life cycle cost is reduced by 4.19%, and the load power loss is reduced by 27%, which shows that the optimization ability is better, and the local optimization problem of the particle swarm optimization algorithm is well avoided. Therefore, the improved compression factor particle swarm optimization algorithm has certain reference value for the stable operation of wind power-photothermal combined power generation system and the economy of capacity configuration. Acknowledgments. This work was supported by the Open Fund of the State Key Laboratory of Power System Operation and Control (SKLD22KM10) and 2023 Open Topic Project of Qinghai Province Key Laboratory of Photovoltaic grid connected power generation technology (SGQHJY00NYJS2310220).

References 1. Ziyu, W., Shuqiang, Z., Yuchen, F.: Optimization operation strategy for thermal storage system of solar thermal power plants to suppress short-term output fluctuations of wind solar combined systems. Grid Technol. 45(03), 881–892 (2021). (in Chinese) 2. Kun, D., Yongjun, W., Pan, H., et al.: Research on hybrid energy storage capacity configuration of microgrid based on improved whale optimization algorithm. Intell. Comput. Appl. 13(02), 194–199 (2023). (in Chinese) 3. Wang, Y., Chen, J.: Optimization configuration of hybrid energy storage capacity for optical storage microgrids based on ISSA. Smart Power 51(04), 23–29+53 2023 (in Chinese) 4. Shangjun, Y.: Optimization configuration of hybrid energy storage capacity based on improved sparrow search algorithm. Electron. Technol. Software Eng. 19, 134–137 (2022). (in Chinese) 5. Yang, G., Zhu, X., Ma, Y., et al.: Capacity optimization of hybrid energy storage systems based on improved particle swarm optimization algorithm. Electr. Meas. Instrum. 52(23), 1–5+10 (2015) (in Chinese)

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6. Kai, H., Yongfang, G., Zhigang, L.: High precision lithium-ion battery model parameter identification based on information feedback particle swarm optimization. J. Electr. Eng. Technol. 34(S1), 378–387 (2019). (in Chinese) 7. Leiva-Maldonado, S.L., Bowman, M.D.: Superstructure bridge selection based on life-cycle cost analysis for short and medium span bridges. Eng. Struct. 285, 116031 (2023). https:// doi.org/10.1016/j.engstruct.2023.116031 8. Qi, L., Zhao, S., Yuchen, P., et al.: Optimization of capacity configuration for hybrid energy storage microgrids considering electric hydrogen coupling. J. Electr. Technol. 36(03), 486– 495 (2021). (in Chinese) 9. Zhongrui, L., Ziling, N., Sheng, A., et al.: An optimized charging control strategy for flywheel energy storage system based on nonlinear disturbance observer. J. Electr. Technol. 38(06), 1506–1518 (2023). (in Chinese) 10. Iqbal, A., Singh, G.K.: PSO based controlled six-phase grid connected induction generator for wind energy generation. CES Trans. Electr. Mach. Syst. 5(1), 41–49 (2021) 11. Wu, J., Sun, X., Zhu, J.: Accurate torque modeling with PSO-based recursive robust LSSVR for a segmented-rotor switched reluctance motor. CES Trans. Electr. Mach. Syst. 4(2), 96–104 (2020) 12. Li, X., Shuanghe, Y.: Three-dimensional path planning for AUVs in ocean currents environment based on an improved compression factor particle swarm optimization algorithm. Ocean Eng. 280, 114610 (2023). https://doi.org/10.1016/j.oceaneng.2023.114610

A Novel SVM-Based Transient Protection Algorithm for Transmission Lines Zhenwei Guo(B) , Yingcai Deng, Jiemei Huang, Qian Huang(B) , and Zebo Huang School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541000, China [email protected], [email protected]

Abstract. Based on the support vector machine (SVM), this paper presents an innovative transient protection algorithm for ultra-high voltage lines. Busbar’s distributed capacitance to the ground has significant effects on bypass shunting. Highfrequency transient currents are significantly attenuated when they pass through the busbar. Accordingly, the difference of instantaneous-mplitude- integral of the initial inherent mode function (DIAI-IMF1 ) of the transient fault currents from two lines connected to the same busbar generally varies significantly when a fault happens within the protected area or outside of it. In addition, the DIAI-IMF1 varies depending on the initial fault angle or transient resistance. In the proposed algorithm, the vector containing the DIAI-IMF1 , initial fault angle, and transient resistance is utilized as the SVMs’ input dataset. It means that different relay-action values are used to determine the fault under varying fault conditions using trainedSVMs, thereby significantly enhancing the protection’s reliability and sensitivity. Importantly, only typical data that is usually produced during critical fault scenarios were required for SVMs training, enabling the implementation of the presented algorithm in the actual project. The procedure is evaluated using ATP/EMTP, and the statistical outcomes are provided. Keywords: Momentary amplitude integral difference · Initial fault angle · Transient resistance · SVM · Transmission line protection

1 Introduction When a transmission line experiences a fault, it produces a large number of transient High-frequency currents at the same time. These transient high-frequency currents serve as the basis for transient protection. Not only does transient protection offer an ultra-fast response, but it also demonstrates exceptional capabilities. This includes being able to function normally even when the current transformer (CT) becomes saturated, or when there are power system oscillations or changes in the system’s operating mode [1]. For over a decade, researchers from all over the world have conducted thorough investigations into transient protection [2–4]. The main focus of conventional studies on single-terminal transient protection is to analyze and address transient signals caused by faults, employing specific signal processing techniques. A range of approaches has been © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 123–130, 2024. https://doi.org/10.1007/978-981-97-1072-0_12

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utilized in transient protection algorithms, including mathematical morphology, artificial neural network (ANN), S-transform, and wavelet transformation (WT), as mentioned in articles [5–7]. Moreover, certain signal processing methods used in transient protection have been enhanced in previous studies [8–10]. Overall, the transient protection methods seldom make a breakthrough in fundamental principles, and the effects of fault start angle and fault resistance on the transient protection are left out of consideration during developing the protection algorithm [11], which has always been a severe defect in the transient protection method. Consequently, the previous transient protection methods exhibit unfavorable reliability and unstable protection performance and thus cannot be popularized. More seriously, some studies indicate that the existing single-end transient protections are not enough to ensure the complete protection of the entire line [12]. In the article, the high-frequency transient current is detected from the head of both lines connected to the busbar. Appling empirical mode decomposition (EMD), each fault transient current is deconstructed to obtain the first inherent modal function (IMF1 ). The momentary amplitude of IMF1 is determined and then integrated using the Hilbert Transform. Furthermore, the fault feature variable is the difference in the instantaneousamplitude integrals of the IMF1 s from the two transient currents. When a fault occurs within the protection area, the difference in the instantaneous-amplitude integrals of the IMF1 (DIAI-IMF1 ) is substantial. In contrast, it is modest when a fault happens beyond the protection region. Furthermore, DIAI-IMF1 fluctuates significantly depending on the initial fault angle and transient resistance. SVM is used for fault diagnosis in this paper. Inputs of SVMs included DIAI-IMF1 , the initial fault angle, and the transient resistance. SVMs were trained using typical fault data caused under specific fault conditions. These trained-SVMs had the ability to differentiate between faults within the protected area versus those outside it. Additionally, a general ultra-high-voltage power system was created by applying ATP-Draw, and the effectiveness of the presented protection algorithm was validated through numerous simulations.

2 Constructing the Presented Algorithm 2.1 High Frequency Signal Propagation Characteristics of Busbars A multitude of transient high-frequency signals were generated when a fault happened on a line. These transient signals began at the point of fault and propagate along the line towards both ends of the line. The busbar possesses a significant distributed capacitance to ground, which results in the shunting effects on the transient high frequency component [13]. 2.2 Algorithm of the Presented Protection Figure 1 depicts a typical grid with a rated voltage of 500 kV, wherein the relay unit is situated at the busbar C and provides protection for lines BC, line CD, and busbar C. Line BC is designated as the forward protected zone, while line CD is designated as the backward protected zone. Current transformer CT1 and current transformer CT2 are positioned at the starting points of BC and CD, respectively. The fault current values

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detected by CT1 and CT2 are labeled as I 1 and I 2 respectively, and their IMF1 (the high-frequency components), IMF1I1 and IMF1I2 are extracted using HHT. The fact that the momentary amplitude of IMF1 changes quickly is widely recognized. Thus, to enhance the presented algorithm’s stability, we integrate the momentary amplitude of IMF1 using Eq. (1). The momentary amplitude values of IMF1I1 and IMF1I2 are denoted as a1I1 and a1I2 correspondingly, while their integrated values are denoted as IA1I1 and IA1I2 respectively.  IA1 = a1 dt (1) Then, the momentary amplitude integral difference, labeled as IAD12 , is calculated according to (2), which is defined as the fault feature variable. IAD12 = IA1I 1 − IA1I 2

(2)

Fig. 1. Simulated Ultra-high-voltage power system

The busbar’s equivalent distributed capacitance has high by-pass shunting effects on transient high-frequency components. When a grounding fault is happening in the forward protected area, such as at point F1 of line BC, the amplitude integral of IMF1 detected at the near side is typically greater than the amplitude integral detected at the distant side of the fault, which is IA1I1 > IA1I2 . IAD12 is consistently positive, meaning IAD12 > 0, and it has a significantly high value. Conversely, if a fault happens beyond the forward protected area, such as at point F2 of the line A, we can still obtain a similar result, i.e. IA1I1 > IA1I2 and IAD12 > 0, but the value of IAD12 is quite small. Hence, according to the value of IAD12 , it is can be determined whether a fault happens within or outside the forward protected zone. When a fault is happening in the backward protected zone, such as at point F3 of the line C, there are IA1I1 < IA1I2 and IAD12 < 0, with a considerable absolute value for IAD12. Conversely, when a fault is happening in outside the backward protected zone, such as point F4 of line D, there are IA1I1 < IA1I2 and IAD12 < 0, but with a small absolute value for IAD12. Hence, it is easy to detect whether the fault is happening within or outside the backward-protected zone, according to IAD12. To sum up, based on the value of IAD12 , it can be determined whether faults happened within the forward protected region BC, the reverse protected zone CD, or beyond the protected zone. Unfortunately, both initial fault angle and transient resistance impose important effects on the fault-induced transient current. To increase the reliability of

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the protection algorithm, it is necessary to eliminate any adverse effects during fault diagnosis. The proposed algorithm’s framework is illustrated in Fig. 2. The fault feature variable together with the corresponding initial fault angle and transient resistance was adopted as SVMs’ inputs, and subsequently, the SVMs were trained and used for fault diagnosis. In The proposed algorithm, SVM#1 and SVM#2 are constructed to identify whether the fault occurs on line BC or CD. The vector, consisting of IAIDIMF1 , transient resistance, and start fault angle, is adopted as the data entry in the presented algorithm. SVM #1 is trained using fault data inside and outside the protected line BC, while SVM #2 is trained by fault data inside and outside the protected line CD. According to the fault diagnosis procedure, we should first use SVM#1 to estimate whether the fault is occurring on line BC. If yes, the fault diagnosis procedure is finished; else, we should use SVM#2 to further estimate whether there is a fault on line CD. Current sampl atiom & HHT Instantaneous amplitude integral difference

Initial fault angle

Transient resistance

SVM#1

Whether the fault occurs on the line BC? Yes

No

SVM#2 Whether the fault occurs on the line CD?

Fig. 2. Framework of the presented algorithm

3 Algorithm Application Verification As displayed in Fig. 2, the ultra-high-voltage power system model with many transmission lines was selected from the 500-kV Power Grid [14]. The distance from bus A to bus B, from bus B to bus C, and from bus C to bus D is 150, 192, 180, and 115 km, respectively. The protection was implemented at busbar C, aiming to protect the BC and CD lines. The sampling frequency of 200 kHz was selected for the simulations. 3.1 Simulation Cases In order to acquire the necessary testing and training datasets, by altering the fault locations, initial fault angles, or transient resistances, we conducted numerous simulations in the power grid displayed in Fig. 1. The fault type was the A-phase ground fault, with the fault locations assigned as the following: the point F1 on line BC, the point F2 on line AB, the point F3 on line CD, and the point F4 on line DE.

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For the simulations, the initial fault angle values were limited to the range of 0 ◦ to

90 ◦ , while the transient resistance values varied within the range of 1 ~ 300 . To make our description more concise, only a section of simulation data were listed below.

1. Faults occurring at the point F1 of line BC When point F1 is 1 km away from busbar C, transient resistance is 50  and start fault angle is 45°, IAD12 is displayed in Fig. 3. At the fault moment, the IAD12 increased steeply to 1962.

Fig. 3. Point F1 fault with 1 km, 50 and 45°

When the distance from F1 to busbar C is respectively 1 km and 192 km, the maximum IAD12 under different initial fault angles and transient resistances are listed in Table 1. Table 1. IAD12 values for faults occurring on line BC θf (◦ )

R() 1

50

150

300

0

3711

2733

1777

1167

45

2664

1962

1276

837.2

85

382.5

281.5

183.2

120.2

90

56.78

41.68

27.13

17.85

l 1 = 1km

l 1 = 192km 0

4746

3567

2325

1528

45

3567

2632

1716

1128

85

636.2

469.5

306.0

201.0

90

212.3

156.6

102.1

67.09

2. Faults occurring at F2 point on line AB When point F2 is 1 km away from busbar C, transient resistance is 50 , and start fault angle is 45°, IAD12 is displayed in Fig. 4. At the fault moment, the IAD12 increased steeply to 95.58.

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Fig. 4. Point F2 fault with 1 km, 50 and 45°

When the distance between F2 and the busbar B is respectively 1 km and 150 km, the maximum IAD12 under different initial fault angles and transient resistances are listed in Table 2. Table 2. IAD12 values for faults occurring on line AB θf (◦ )

R() 1

50

150

300

0

176.6

129.4

83.76

54.76

45

130.4

95.58

61.84

40.44

85

23.28

17.07

11.07

7.258

90

7.817

5.744

3.748

2.489

0

165.7

126.1

84.64

56.66

45

122.5

93.23

62.61

41.95

85

22.13

16.86

11.37

7.659

90

7.637

5.842

3.973

2.717

l 2 = 1km

l 2 = 150km

3 Faults occurring at F3 point on line CD When point F3 is 1 km away from busbar C, transient resistance is 50 , and start fault angle is 45°, IAD12 is displayed in Fig. 5. At the fault moment, the IAD12 increased steeply to -1956. When the distance from F3 to the bus C is respectively 1 km and 180 km, the maximum IAD12 under different initial fault angles and transient resistances are listed in Table 3. 3.2 Fault Diagnosis Using SVM Input of SVM in the algorithm includes the fault feature variable (IAIDIMF1 ), initial fault angle, and transient resistance. In a fault diagnosis, we should first use SVM#1

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Fig. 5. Point F3 fault with 1 km, 50 and 45° Table 3. IAD12 values for faults occurring on line CD θf (◦ )

R() 1

50

150

300

0

-3710

-2724

-1768

-1159

45

-2664

-1956

-1270

-832.2

85

-384.3

-283.1

-184.9

-122.4

90

-60.14

-45.37

-31.18

-22.27

0

-4985

-3663

-2379

-1558

45

-3653

-2685

-1743

-1142

85

-618.5

-455.0

-295.7

-194.3

90

-181.9

-134.2

-87.99

-58.63

l 3 = 1km

l 3 = 180km

to identify whether the fault occurred on line BC. If the fault occurred on line BC, the program is finished; else, we further used SVM#2 to identify whether the fault occurred on line CD. During the simulation cases mentioned above, the training datasets consisted of data with start fault angles of 0°, 85°, and 90°, while the testing datasets consisted of data with a start fault angle of 45° for fault judgment. The results of the tests showed that all fault judgments were accurate.

4 Conclusions A novel SVM-based transient protection algorithm for the extra-high-voltage transmission lines was proposed. The input vector of SVMs included the momentary amplitude integral difference, the initial fault angle, and the transient resistance. This meant that when the trained SVMs were used to identify faults, different protection operating values were set for different fault conditions. As a result, the negative effects caused by the transient resistance and initial fault angle were successfully minimized, resulting in

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significantly improved sensitivity and reliability of the protection system. In the the proposed algorithm, two transmission lines connected to the same busbar could be protected simultaneously, and the protected area was twice as large as that by using the traditional protection algorithm. Acknowledgment. This research was supported by National Natural Science Foundation of China (No. 52067005) and Guangxi of China Natural Science Foundation (No. 2021GXNSFAA220061).

References 1. Bo, Z.Q., Weller, G., Dai, F.T., Yang, Q.X.: Transient based protection for transmission lines. IEEE Power Syst. Tech. 2, 1067–1071 (1998) 2. da Silva França, R.L., da Silva Júnior, F.C., etc., Traveling Wave-based transmission line earth fault distance protection,” IEEE Trans. Power Del., 36(2), 544–553 (2021) 3. Etingov, D.A., Zhang, P., Tang, Z., Zhou, Y.: AI-enabled traveling wave protection for microgrids. Electr Power Syst. Res. 108078(210), 1–9 (2022) 4. Lei, A., Dong, X., Terzija, V.: An Ultra-High- speed directional relay based on correlation of incremental quantities. IEEE Trans. Power Del. 33(6), 2726–2735 (2018) 5. Wu, H., Dong, X., Ye. R.: A new algorithm for busbar protection based on the comparison of initial traveling wave power, IEEE J. Trans. 14, 520–533 (2019) 6. Gonzalez-Sanchez, V.H., Torres-García, V., Guillen, D.: Fault location on transmission lines based on travelling waves using correlation and MODWT. Electr. Power Syst. Res. 197, 1–8 (2021) 7. Zhang, D.J., Wu, Q.H., Zhiqian, Q.: Bo, Transient positional protection of transmission lines using complex wavelets analysis, IEEE Trans. Power Del., 18(3), 705–710 (2003) 8. He, Z., Liu, X., Li, X., Mai, R.: A novel traveling-wave directional relay based on apparent surge impedance. IEEE Trans. Power Del. 30(3), 1153–1161 (2015) 9. Nayak, K., Jena, S.A., Pradhan, K.: Travelling wave based directional relaying without using voltage transients, IEEE Trans. Power Del., 36(5), 3274–3277(2021) 10. Bernadi´c, A., Leonowicz, Z.: Fault location in power networks with mixed feeders using the complex space-phasor and Hilbert-Huang transform. Electr. Power Energy Syst. 42, 208–219 (2012) 11. Costa, F.B., Monti, A., Lopes, F.V., et al.: Two-terminal traveling-Wave-based transmissionline protection, IEEE Trans. Power Del., 32(3), 1382–1393(2017) 12. Guo, Z., Yao, J., Yang, S., Zhang, H.: Tian mao and thanh long duong, A new method for nonunit protection of power transmission lines based on fault resistance and fault angle reduction, Electr. Power Energy Syst. 55, 760–769(2014) 13. Jafarian, P., Sanaye-Pasand, M.: High-frequency transients-based protection of multiterminal transmission lines using the SVM technique. IEEE Trans. Power Del. 28(1), 188–196 (2013) 14. Lin, X., Liu, P., Liu, S. and Yang, C.: A novel integrated morphology wavelet filter algorithm used for Ultra-high speed protection of power systems. Proc. CSEE 22(9), 19–24 (2002) (in Chinese)

Effect of Ion Types on Arc Erosion of Circuit Breaker Contact: Molecular Dynamics Simulation Study Xin Wang1 , Shanika Yasantha Matharage1 , Ruoyu Xu2 , Mingyu Zhou2 , Yuzhen Zhou2 , Yi Ding3 , and Zhongdong Wang1(B) 1 Centre for Smart Grid, Department of Engineering, University of Exeter, Exeter EX4 4PY, UK

[email protected]

2 Global Energy Interconnection Research Institute Europe GmbH, Kantstr. 162, 10623 Berlin,

Germany 3 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., 18 Binhe Avenue, Beijing 102209, China

Abstract. SF6 circuit breakers are commonly used as switchgear devices in highvoltage power systems. During arcing process, the particles in arc plasma are mostly positive ions (metal ions, S ions, and F ions) and electrons at temperatures beyond 15000 K. Arc erosion on the cathode surface is dominantly determined by positive ion bombardment. Thus, studying the effect of ion type and energy on arc erosion of different contacts is helpful for understanding the failure mechanisms. The current research undertakes an investigation into the impacts of Cu, S, and F ions, all with a constant energy of 50 eV, on both Cu and graphene-covered Cu substrates. Utilising molecular dynamics (MD) simulation, results reveal that S ions induce more substantial damage to the Cu substrate than Cu and F ions. Cu ions have a high sticking probability to the Cu surface, and the larger size and heavier weight of S ions mean more damage than F ions with the same incident ion energy. Moreover, graphene on the surface significantly mitigates the damage caused by all three ion types, as graphene aids in energy dissipation by oscillating waves, thereby reducing the energy acting on the underlying Cu. This research provides insights into the interaction between different plasma ions and contact materials, contributing to the improvement of contact materials. Keywords: SF6 circuit breaker · Arc plasma · Ion bombardment · Molecular dynamics simulation

1 Introduction Circuit breakers are critical components in electrical systems designed to interrupt current flow in case of an overload or short circuit [1]. Since Thomas Edison’s early patent in 1879, insulating mediums within circuit breakers have evolved from oil and air to modern vacuum and SF6 . SF6 is a thermally stable and inert gas [2], which helps prevent internal parts of the circuit breaker from corroding and thus extends the operating © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 131–138, 2024. https://doi.org/10.1007/978-981-97-1072-0_13

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time without maintenance. Moreover, the risk of fire and explosion is also significantly reduced, as SF6 is non-flammable. Besides, SF6 has excellent insulating properties, even at relatively low pressure [3]. The above advantages make SF6 circuit breakers uniquely used in high-voltage applications. An electric arc generates within the gap between contacts once they separate. The interaction between arc and contacts leads to the gradual decomposition of solid contact materials, termed arc erosion. Arc erosion within electrical contacts is a multifaceted phenomenon. The initial arc formed during the separation process originates from the metal vapour emitted due to the rupture of a molten metal bridge. As the gap between contacts increases, surrounding gases enter the arc and eventually dominate the ionised particles within the arc [4]. The positive ions obtain energy after passing through the cathode space charge sheath and subsequently hit the cathode surface [5]. It is acknowledged that ions are recombined with electrons to be atoms when they are approaching the cathode surface. However, this paper maintains the term “ion bombardment”, as this term is commonly known in the switching arc community. The primary cause of contact failure is the erosion of contact materials, which is directly influenced by the total energy imparted to the contact surface [6]. Among the two electrodes, the conditions in the cathode are generally more complex than the anode as the cathode involves a flow of positive ions onto it and the extraction of electrons from it [7]. Therefore, far more research has been devoted to the cathode. The energy required to maintain the arc cathode spot mainly comes from (i) positive ion bombardment, (ii) conductive and radiative heat transfer from the cathode constriction; (iii) Joule heating. Of these, positive ion bombardment stands out as the dominant energy contributor [6]. Within the arc plasma, ions consist of both gaseous ions and ions derived from contact materials. The specific impacts of distinct ion types on arc erosion remain unclear. Consequently, investigating the effects of ion types on cathode materials assumes significance in comprehending the underlying mechanisms of arc erosion. In this work, molecular dynamics (MD) simulation is used to study the effects of ion types on arc erosion at the micro-level. SF6 and Cu, commonly used insulating gas and contact material, are chosen as the research objectives. Additionally, a graphene-covered Cu model was also used as a substrate considering the emerging trend of employing graphene as a reinforcement to improve the arc resistance of contact materials.

2 Positive Ions in SF6 arc Plasma SF6 gas decomposes into lower fluorides of sulphur by-products under the presence of an arc. Figure 1 illustrates the temperature-dependent equilibrium particle densities within an SF6 plasma [8]. Starting from 3000 K, the concentrations of charged particles, specifically S+ ions and electrons, exhibit a rapid increase. As temperatures exceed 15000 K, particles in arc plasma consist mostly of positive ions (S+ , S2+ , and F+ ) and electrons. Measurements taken at the core of a high-current arc have recorded temperatures of about 20000 K [9]. Regarding Cu contact materials, the arc plasma includes contributions from Cu vapour, with Cu+ and Cu2+ ions being the primary ionic species. As a result, this study concentrates on ions of S, F, and Cu ions. To accurately simulate the ion bombardment process, the incident energy ranges of S, F, and Cu ions were estimated by combining thermal energy, kinetic energy and

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Fig. 1. Equilibrium particle densities in an SF6 plasma as a function of temperature [8].

ionisation energy. The average thermal energy (E th ) of the ions in the arc ranges from around 0.85 eV to around 2.5 eV derived from the high temperature of the arc column [10]. Additionally, ions undergo acceleration through a voltage drop (V c ) (typically ranging from 10 to 20 V) at the cathode region. The gained kinetic energy (E V ) is given by: EV = ZeVc

(1)

where Z is the number of charges of an ion. e is the elementary charge (≈ 1.602 × 10−19 C). Ultimately, ions attain the ionization energy (E i ) by recombining with emitted electrons before impacting the cathode surface. Therefore, an incident ion’s total energy (E total ) equals E th + E V + E i . Table 1 summarises the total energy of involved positive ions in SF6 plasma, showing that the incident energies of Cu, S, and F ions approximately range 18.58–62.79 eV, 21.21–65.83 eV, and 28.27–39.92 eV, respectively. Taking into account the energy fluctuations of the ions within the arc, and for the simplicity of simulation scenarios, the incident ion energy value of 50 eV is selected for all three ion types to study the impacts of varying ion types on arc erosion of circuit breaker contact materials.

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Table 1. Incident energy of involved positive ions before hitting Cu contact surface, the ionisation energy of ions is from [11] Ion types

Thermal energy E th (eV)

Kinetic energy E V (eV)

Ionisation energy E i (eV)

Total energy (eV)

Cu+

0.85–2.5

10–20

7.73

18.58–30.23

Cu2+

0.85–2.5

20–40

20.29

41.14–62.79

S+

0.85–2.5

10–20

10.36

21.21–32.86

S2+

0.85–2.5

20–40

23.33

44.18–65.83

F+

0.85–2.5

10–20

17.42

28.27–39.92

3 Simulation Methodology This study utilises two substrate models for the ion bombardment simulation as depicted in Fig. 2 (a) and (b). The z-direction adheres to a fixed boundary condition, while the x and y-directions adopt periodic boundary conditions. Additionally, the three bottom layers of the Cu substrate are fixed. The initial step involves energy minimisation, followed by a relaxation period of 30 ps at 300 K before commencing ion bombardment on the surface. During ion bombardment, three atom layers at four vertical faces were fixed at 300 K.

Fig. 2. Simulation models: (a) pure Cu; (b) graphene-covered Cu. (c) the space independently occupied by each incident ion.

In the simulation, the incident energy of three ion types (S, F, and Cu ions) is set at 50 eV, corresponding velocities of ions are 123.2 Å/ps for Cu ions, 173.4 Å/ps for S ions and 225.3 Å/ps for F ions. Ions are generated from random sites within a circular region with a diameter of 10 nm and hit the model surface one by one. 600 incident ions bombard the model surface one by one, and the time interval between continuous incident ions is 0.1 ps. Figure 2 (c) shows the space independently occupied by each incident ion. Calculated particle densities (average number of particles in unit volume) of Cu, S and F ions in the simulation are 1.03 × 1019 cm−3 , 7.35 × 1018 cm−3 , and 5.65 × 1018 cm−3 , respectively. Considering the contraction of the cathode region, the current density is much higher than that of the arc column (maybe as much as 100 times greater) [10]. Therefore, the particle densities in this work are in a reasonable magnitude order compared with the particle density in the arc column shown in Fig. 1.

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Throughout the ion bombardment process, an NVE (constant Number of particles, Volume, and Energy) ensemble is employed. The timestep employed in the simulation varies depending on the energy of the incident ions. Following the completion of the bombardment phase, the models are subsequently cooled to a temperature of 300 K. MD simulations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The interaction between Cu atoms is described by the embedded atom method (EAM) potential, combined with the Ziegler Biersacke Littmark (ZBL) repulsive potential [12]. The adaptive intermolecular reactive empirical bond order (AIREBO) potential [13] describes the interactions between C atoms in graphene. The 12–6 Lennard-Jones (L-J) potential is used to describe the van der Waals force between Cu and C atoms. The well depth ε = 0.019996 eV, and equilibrium distance δ = 3.225 Å [14]. Additionally, ZBL repulsive potential [15] is used to calculate the forces between the incident S and F atoms with other atoms.

4 Results and Discussion Figure 3 presents the surface morphologies of pure Cu systems subsequent to bombardment by distinct ions and subsequent cooling to 300 K. Notably, S ions induced a larger pit on the Cu substrate surface than Cu ions and F ions. Besides, the number of lost atoms in the Cu system bombarded by S ions is much higher than others, as shown in Table 2. This outcome can be attributed to several factors. Firstly, incident Cu ions possessing an incident energy of 50 eV have a high probability of sticking on the Cu substrate surface because the strong metal bond will be formed between incident Cu ions and substrate Cu atoms. As a result, Cu ions can become trapped in the attractive mean field of the surface long enough to dissipate their energy and stick. This observation corresponds with findings in [16], where the 100% sticking probability of Cu atoms with 50 eV impacting a Cu surface perpendicularly at 300 K was measured. Consequently, the sputtering yield of Cu atoms triggered by Cu ions is comparatively lower in comparison to the effects of S and F ions.

Fig. 3. (a-c) are pure Cu models after completion of ion bombardment and being cooled to 300 K; Red atoms in (a) are deposited Cu atoms. (a1 -c1 ) are corresponding surface mesh. Width and depth of erosion crater are marked in black and white, respectively. (colour figure object)

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Furthermore, the larger atomic size and greater weight of S ions relative to F ions contribute to their heightened capacity for inflicting damage upon the Cu surface during their collision with the Cu surface. Table 2. Number of lost atoms in each system Heading level

Number of lost atoms

Cu@Cu ions

38 Cu atoms

Cu@S ions

237 Cu atoms

Cu@F ions

162 Cu atoms

G-Cu@Cu ions

0

G-Cu@S ions

0

G-Cu@F ions

0

Figure 4 illustrates the surface morphologies of G-Cu systems following bombardment by different ions and subsequent cooling to 300 K. Compared to pure Cu models, G-Cu models keep almost the original surface structure. Firstly, graphene, with its exceptional mechanical properties and high melting point, serves as a strong barrier that intercepts and diverts the trajectory of the incident ions away from the Cu surface [17]. Therefore, graphene on the surface protects the substrate against direct bombardment by incident ions. On the other hand, graphene can dissipate part of incident energy in the form of waves. Figure 5 shows a cycle of wave movement with a graphene layer. As ions collide with the graphene surface, the central C atoms within the graphene layer exhibit an upward rebound. Subsequently, a continuous upward motion of C atoms propagates from the centre to the edges of the graphene shown as (a)-(d), transmitting the incident energy. Then graphene layer gradually moves downwards shown as (d)-(f), and repeats this process in the whole ion bombardment process. The amplitude of the wave within the graphene layer measures approximately 3.5 Å, which is close to the thickness of a single graphene layer of 3.4 Å [18]. Additionally, the time for a complete wave movement cycle is approximately 8 ps in this simulation, and with a graphene length of 25 nm, the speed of wave movement is approximately 3 nm/ps. Therefore, graphene on the substrate surface is able to decrease damages due to ion bombardment in the form of waves.

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Fig. 4. (a-c) are G-Cu models after completion of ion bombardment and being cooled to 300 K; (a1 -c1 ) are corresponding surface mesh.

Fig. 5. A cycle of wave movement within graphene from the top view. The colour shows the height of C atoms in the vertical direction in the model.

5 Conclusion In conclusion, this work studied the effects of ion types (Cu, S, F ions) on arc erosion of circuit breaker contact. Pure Cu and graphene-covered Cu were set as substrates. The results derived from MD simulations indicated that S ions induce more substantial damage in the Cu substrate compared to Cu and F ions. In the case of Cu ions bombardment, low sputtering yield was triggered by Cu ions with 50 eV due to their high sticking probability to the Cu surface. Moreover, the larger size and weight of the S ions than F ions are attributed to the increased physical impact during their collision with the Cu surface. In addition, graphene on the surface significantly reduced the damage caused by all three ion types, as graphene can dissipate energy in the form of waves, thereby

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reducing the energy acting on the underlying Cu. This work provides insights into the interaction between different plasma ions and contact materials. Acknowledgement. This work was supported by the State Grid Corporation of China science and technology Foundation (5500-201958505A-0–0-00).

References 1. Mohammadi, F., et al.: HVDC Circuit Breakers: a comprehensive review,” IEEE Trans. Power Electron., vol.36, no. 12, pp.13726–13739, 2021 2. Kim, Y.-J., Lee, J.-C.: Computations on the thermal characteristics of SF 6 and CO 2 switching Arcs on a microscopic scale. J. Nanosci. Nanotechnol. 20(11), 7201–7205 (2020) 3. Zeng, F., Li, H., Cheng, H., Tang, J., Liu, Y.: SF6 decomposition and insulation condition monitoring of GIE: a review. High Volt. 6(6), 955–966 (2021) 4. Slade, P.G.: Opening electrical contacts: the transition from the molten metal bridge to the electric arc. IEICE Trans. Electron. 9, 1380–1386 (2010) 5. Benilov, M.S.: Theory and modelling of arc cathodes. Plasma Sources Sci. Technol. 11(3A), A49–A54 (2002) 6. Rich, J.A.: Resistance heating in the arc cathode spot zone. J. Appl. Phys. 32, 1023–1031 (1961) 7. Guile, A.E., Eng, C.: Arc-electrode phenomena. Proc. Inst. Electr. Eng. 118(9R), 1131–1154 (1971) 8. Frie, W.: Berechnung der Gaszusammensetzung und der Materialfunktionen von SF6. Zeitschrift für Phys. 201(3), 269–294 (1967) 9. Airey, D.R.: Axial and radial heat transport in a high-temperature SF 6 arc. J. Phys. D Appl. Phys. 12(1), 113–125 (1979). https://doi.org/10.1088/0022-3727/12/1/012 10. Slade, P.G.: Electrical contacts: Principles and applications, second edition. CRC Press, pp.578–583, 2014 11. I. Wolfram Research, “Ionization energies of the elements data. https://periodictable.com/Pro perties/A/IonizationEnergies.html 12. Demkowicz, M.J., Hoagland, R.G.: Simulations of collision cascades in Cu-Nb layered composites using an EAM interatomic potential. Int. J. Appl. Mech. 1(3), 421–442 (2009) 13. Stuart, S.J., Tutein, A.B., Harrison, J.A.: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112(14), 6472–6486 (2000) 14. Fan, Y., Xiang, Y., Shen, H.-S.: Temperature-dependent mechanical properties of graphene/Cu Nanocomposites with In-plane negative poisson’s ratios. Research 2020, 1–12 (2020) 15. Ziegler, J.F., Biersack, J.P.: The Stopping and Range of Ions in Matter. In: Allan Bromley, D. (ed.) Treatise on Heavy-Ion Science, pp. 93–129. Springer US, Boston, MA (1985). https:// doi.org/10.1007/978-1-4615-8103-1_3 16. Coronell, D.G., Hansen, D.E., Voter, A.F., Liu, C.L., Liu, X.Y., Kress, J.D.: Molecular dynamics-based ion-surface interaction models for ionized physical vapor deposition feature scale simulations. Appl. Phys. Lett. 73(26), 3860–3862 (1998) 17. Xu, R., et al.: A molecular dynamics simulation study on the role of graphene in enhancing the arc erosion resistance of Cu metal matrix. Comput. Mater. Sci. 212, 111549–111560 (2022) 18. Scarpa, F., Adhikari, S., Srikantha Phani, A.: Effective elastic mechanical properties of single layer graphene sheets, Nanotechnology, vol.20, no. 6, pp.065709–065720, 2009

Research on the Delay Characteristics of 5G Communication Networks for Regional Protection in Power Distribution Grids Chen Linhan1(B) , Wei Qi2 , Ge Wei1 , and Hong Weijun1(B) 1 Beijing University of Posts and Telecommunications, Beijing 100013, China

{chenlh,gewei,hongwj}@bupt.edu.cn

2 State Grid Economic and Technological Research Institute Co., Ltd., Beijing 102200, China

[email protected]

Abstract. The integration of new energy sources has led to bidirectional power flows in distribution grids. Investigating delay characteristics in 5G networks is crucial for supporting centralized regional protection services in these grids. This study analyzes inherent, NR, propagation, and queuing delays in 5G networks within the architecture of centralized regional protection. By examining delays from the control center to protection terminals, we provide theoretical support for digitally transforming distribution grids using 5G technology. Keywords: Power Distribution Grid · Regional Protection · 5G · Delay

1 Introduction With the integration of renewable energy sources into distribution grids for localized consumption, these grids are undergoing changes. The complexity and multi-source nature of distribution grids present challenges for their safe operation, requiring improvements in reliability and carrying capacity [1]. As distributed energy capacity continues to expand, distribution grids experience bidirectional power flows and complex topologies. Traditional protection methods are no longer applicable [2, 3]. Regional protection, a novel strategy enables information sharing and coordination among switches within a specific region [4]. It effectively isolates fault areas and minimizes their impact. Area protection is essential for protecting grids with distributed renewable energy. However, it requires high communication performance. 5G technology plays a crucial role with its high bandwidth, low delay, reliability, and flexibility. Delay is a key indicator for normal operation. Extensive research has been conducted on communication network delay [5, 6]. This paper analyzes the principles, architecture, and methods of regional protection. It provides theoretical analysis of communication delays, including inherent and NR delays, propagation and queuing delays, and delays to master stations. It discusses the architectural framework of regional protection and presents detailed analysis of time delay. Finally, conclusions are drawn. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 139–147, 2024. https://doi.org/10.1007/978-981-97-1072-0_14

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2 Distribution Network Area Protection Architecture The architectural of regional protection in power distribution grids can be categorized into three types: intelligent distributed architecture, centralized architecture, and regional centralized architecture [7]. 2.1 Centralized Architecture The centralized architecture includes three components: the main station, terminals, and a communication network. Terminals gather and transmit data to the main station. In the event of a fault, the main station analyzes fault information from terminals using predefined algorithms, identifies the fault location, and implements fault isolation for the handling process. As fault processing tasks concentrate at the main station, it leads to extended fault processing times (Fig. 1).

Fig. 1. Distribution network centralized protection architecture

2.2 Intelligent Distributed Architecture The intelligent distributed protection architecture facilitates information exchange among adjacent terminals, enhancing power system reliability, flexibility, and security through shared status information and intelligence. While this architecture meets fast protection needs, its scope is confined to straightforward power topologies. To extend its utility to complex networks, further enhancements are necessary (Fig. 2).

Fig. 2. Distribution network intelligent distributed architecture

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2.3 Regional Centralized Architecture In the regional centralized architecture, A substation is deployed in a selected switchgear room, while multiple substations are connected to the main station. The other distribution rooms act as service recipients for the substations. During a fault, the substation act as the main station in the centralized architecture. Besides, telecontrol information is transmitted to the main station from the substation. The regional centralized architecture achieves a balance between network control complexity and communication performance indicators, making it ideal for large-scale communication networks (Fig. 3).

Fig. 3. Distribution network centralized regional protection architecture

3 5G Bearing Area Protection Distribution network area protection requires a transmission delay of less than 40ms and a minimum bandwidth of 64Kbit/s [8]. 5G networks have low delay and high bandwidth, and define three types of sliced applications: enhanced Mobile Broadband (eMBB), massive Machine Type Communications (mMTC), and ultra-Reliable and Low-Delay Communications (uRLLC). The uRLLC slice is primarily used in distribution network area protection. The end-to-end network slice consists of three sub-slices: core network, wireless network, and transmission network, which are managed uniformly through an end-to-end slice orchestration and management system. The end-to-end delay of the service is mainly divided into four parts: inherent delay, NR delay, propagation delay, and queuing delay [9]. Inherent Delay T1 . The inherent delay components can be abbreviated as follows: • Packaging and Uploading Delay: d1 • Unpacking Delay: d2 • Base Station Delay: d3 These abbreviations represent the different components that contribute to the overall inherent delay experienced during the data transmission process. Typically, the values of

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these delay components are small and consistent, ranging in the order of microseconds. The inherent delay can be expressed as T1 = d1 + d2 + h ∗ d3

(1)

where h represents the number of base station passed from the sender to the receiver. NR Delay T2 . The NR delay refers to the delay of the transmission from the CPE to the base station. The uncertainty of the NR Delay, uplink and downlink slot ratio, and retransmission Are the main differences between wired and wireless communications. According to the 3GPP standard, the 5G NR Delay can be calculated using T2 = Tt + Ts + Ta

(2)

where Tt represents transmission delay, Ts represents processing delay, and Ta represents additional delay. Propagation Delay T 3 . Propagation delay is the time for a data signal to travel through the medium. The value of T3 depends on the physical characteristics of the transmission medium and the propagation distance [10]. The propagation speed of optical signals in optical fibers is 2/3 of the speed of light, which means a delay of 5μs per kilometer. Queuing Delay T 4 . Queuing delay refers to the waiting time of data packets in the queue before they are processed and transmitted. Previous studies [11] have shown that data packet arrivals in a slice follow a Poisson distribution, with arrival time intervals and service times following exponential distributions. Each virtual base station node can be considered as an M/M/1 queuing system. In the slice network, the set of virtual nodes is represented as V = {v0 , v1 , · · · , vm }, with only one link between any two nodes. The source node sends n data flows F = {f1 , f2 , · · · , fN }, all transmitted along the optimal path Pk . The service order of all power system services in the network follows the FIFO principle and has the same priority. for Node vi , the arrival rate of data packets is λi , and the service rate is μi . The utilization of node vi , ρi is calculated as λi μi

ρi =

(3)

The average number of data packets at node vi can be calculated as E(Qi ) =

ρi 1 − ρi

(4)

Assuming that any data flow fk (k = 1, 2, · · · , N ) passes through h base station nodes on path Pk , since the nodes in the network are independent of each other, the total queue length on path Pk is the sum of the queue lengths of each base station node, denoted as Lk =

h  i=1

E(Qi )

(5)

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According to Little’s Law, the average delay of data flow fk passing through path Pk is denoted as τk (k = 1, 2, · · · , N ), and the average value of the delay is represented as  ρi Lk = λi 1 − ρi h

E(τk ) =

(6)

i=1

Therefore, the average end-to-end delay of the service data flow can be expressed as: Tavg = T1 + T2 + T3 + E(τk )

(7)

4 Regional Protection Delay Analysis 4.1 Centralized Protection Delay In the centralized protection architecture, the one-way delay between the terminal and the main station can be expressed as: Tcentralized = T1 + T2 + T3 + E(τk )

(8)

As all terminal data is uploaded to the main station, there is an increase in reception and processing delay at the main station (Fig. 4).

Fig. 4. Communication model of centralized architecture for distribution network

4.2 Intelligent Distributed Protection Delay In the intelligent distributed architecture, data is shared between terminals. The communication delay between power terminals can be expressed as: Tdistributed = T1 + T2 + T3 + E(τk )

(9)

The fault processing delay is relatively small for it doesn’t need to upload fault data or wait for action signals from higher-level (Fig. 5).

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Fig. 5. Communication model of intelligent distributed architecture for distribution network

4.3 Regional Centralized Protection Delay In the regional centralized protection architecture, it illustrates the communication process from terminals to substations and then to main stations for area protection in the power distribution network. In this networking mode, by sinking the UPF user plane network element equipment, local diversion of various types of power network data within the region is achieved, providing better delay support for real-time services (Fig. 6).

Fig. 6. Communication model for centralized architecture in distribution network.

When there is communication between a substation and a main station, the inherent delay between the communication devices is T1 , as shown in Eq. (1). The propagation delay is defined as T3 , and the queuing delay can be defined by Eq. (10). Therefore, the communication delay between the substation and the main station is: Tsubstation = T1 + T3 + E(τk )

(10)

And the one-way communication delay between the terminal and the main station is: Tmaster = 2T1 + T2 + 2T3 + 2E(τk )

(11)

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5 Simulation and Analysis 5.1 Different End-to-End Delays of Three Architectures When the packet size is the same, the distributed architecture has the shortest end-to-end delay, while the centralized architecture has the longest end-to-end delay. The regional centralized architecture falls in between. Additionally, as the packet size increases, the centralized architecture experiences a larger increase in delay due to the need to upload all data to the distribution network main station. For transmitting 10,000 data packets, the centralized architecture has approximately 3ms higher delay than the regional centralized architecture (Fig. 7).

Fig. 7. Delay of three architectures for different numbers of data packets

5.2 Different End-to-End Delay with Varying Routing Parameters in Regional Centralized Architecture Delay for Different λ Values of Data Packets λ represents the arrival rate of a queuing system. The simulation results show that, with the unchanged data processing capacity, a higher λ (i.e., a greater number of data packets arriving per unit time) leads to increased delay, which aligns with practical observations. Delay for Different μ Values of Data Packets μ represents the data processing efficiency in the transmission network. The simulation results indicate that a higher μ (i.e., a greater number of data packets processed per unit time) results in lower delay, which is consistent with real-world scenarios (Fig. 8).

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Fig. 8. Delay for different λ and μ values

6 Conclusion We have conducted an analysis on the core principles, application architectures, and protection methods of distribution network area protection. In addition, we have investigated the delay in three different distribution network architectures within 5G networks. By considering factors such as inherent delay, NR Delay, propagation delay, and queuing delay in various architecture topologies, we were able to determine the unidirectional delay between terminals and main station. Furthermore, through simulation analysis, we evaluated the delay of the three architectures and examined how the delay varies with different parameters in the regional centralized architecture. This analysis provides valuable insights into understanding the delay requirements for 5G network slicing access in distribution network zone protection.

References 1. Cao, Q., Jiang, Y., Liu, C., et al.: Research on fault analysis of multi-source distribution network based on adaptive protection. In: 2022 7th Asia Conference on Power and Electrical Engineering (ACPEE), pp. 1342–1346, Hangzhou, China (2022) 2. Chu, T., Wang, G., Wang, T., et al.: Distributed relay protection for distribution network based on hybrid power method and current method. Energy Rep. 8(5), 749–756 (2022) 3. Zhou, M.: Principle and test of fiber optic differential protection for transmission lines. Electr. Age 2021(07), 49–51 (2021). (in Chinese) 4. Xiao, W., Xia, M., Tang, N.: A new regional protection scheme for distribution network considering the introduction of multi-DGs. Power Syst. Prot. Control 42(09), 103–109 (2014). (in Chinese) 5. Wei, L., et al.: Research on the network slicing delay modeling method for electric power service based on FlexE and MTN technology. In: 2022 IEEE 10th International Conference on Information, Communication and Networks (ICICN), pp. 286–291, Zhangye, China (2022) 6. Abbou, A.N. Taleb, T., Song, J.: Towards SDN-based Deterministic Networking: Deterministic E2E Delay Case. In: 2021 IEEE Global Communications Conference (GLOBECOM), pp. 1–6, Madrid, Spain (2021)

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7. Gu, Z.: Modeling of regional protection and self-healing control system for distribution network and performance analysis of its communication network. M. S. thesis, South China University of Technology, Guangzhou, China, 2020. (in Chinese) 8. Zhou, X., Shen, B., Jiang, X.: A quick action scheme of differential protection for a distribution network with 5G communication. Power Syst. Prot. Control 50(16), 163–169 (2022). (in Chinese) 9. Stahlhut, J.W., Browne, T.J., Heydt, G.T., et al.: Latency viewed as a stochastic process and its impact on wide area power system control signals. IEEE Trans. Power Syst. 23(1), 84–91 (2008) 10. Shahraeini, M., Javidi, M.H., Ghazizadeh, M.S.: Comparison between communication infrastructures of centralized and decentralized wide area measurement systems. IEEE Trans. Smart Grid 2(1), 206–211 (2011) 11. Abbou, A.N., Taleb, T., Song, J.: Towards SDN-based deterministic networking: Deterministic E2E Delay Case. In: 2021 IEEE Global Commun. Conf. (GLOBECOM), pp. 1–6, Madrid, Spain (2021)

Distributed Reactive Power Control Scheme for Parallel Inverters Based on Virtual Impedance Rui Ma1(B) , Hui Fan2 , Jianfeng Li1 , Xiaoguang Hao1 , Changbin Hu3 , and Shanna Luo3 1 State Grid Hebei Electric Power Research Institute, Shijiazhuang 050021, China

[email protected]

2 State Grid Hebei Electric Power Company, Shijiazhuang 050021, China

[email protected]

3 School of Electrical and Control Engineering, North China University of Technology,

Beijing 100144, China [email protected]

Abstract. Droop control is an important control strategy for microgrids with multiple inverters in parallel. Adding virtual impedance to droop control can effectively increase the voltage of the common coupling point and achieve equal sharing of reactive power. However, in practical engineering, due to line aging and environmental changing, line parameters will change, which will affect the traditional virtual impedance control performance, making it difficult to divide reactive power accurately. To address this issue, we propose a distributed optimization compensation control scheme based on dynamic virtual impedance. Using the reactive power output by an inverter as a communication signal, based on the multi-agent consensus, we optimize the virtual impedance, which effectively compensates the influence of line impedance mismatch, realizes the uniform sharing of load reactive power, and compensates the line voltage drop. When the line parameters change due to the factors such as aging and damage, the scheme can still realize the uniform share of reactive power and compensate the voltage drop on the line. The addition of secondary regulation to the droop control can significantly suppress the variations of the bus voltage and frequency when the load changes. The effectiveness of the scheme is verified by the MATLAB/Simulink simulation software and a RTDS-based hardware-in-the-loop simulation platform. Keywords: Droop Control · Line Impedance Mismatch · Dynamic Virtual Impedance · Distributed Optimization · Secondary Regulation

1 Introduction However, the fluctuation and intermittency of the output power of distributed power generation affect safe and stable power grid operation. To better connect distributed power sources to a power grid and take advantage of renewable energy power generation, microgrid systems have emerged. As representative power electronic con-version © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 148–164, 2024. https://doi.org/10.1007/978-981-97-1072-0_15

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devices, inverters are hubs of distributed power sources and microgrids. They can efficiently and flexibly convert renewable energy into electrical energy and have the important function of adjusting the voltage and frequency of the entire system in island mode. Therefore, these devices are highly promoted by many researchers [2]. When multiple inverters in the microgrid are operating in parallel, due to the different output characteristics of each inverter, the output voltage of each inverter is different. The created voltage difference results in the generation of circulation, which can eventually reduce the system operating efficiency and the life of the equipment [3]. Droop control is an important control scheme for a multi-inverter parallel connection in microgrids. Droop control can ensure the stability of the bus voltage and make each inverter evenly share the load power according to its rated capacity. However, in real-world engineering, due to the effects of line impedance parameters, it is difficult for traditional droop control to achieve reactive power sharing, and the existence of line impedance also makes the voltages at common nodes deviate from the ideal control values. Therefore, the addition of virtual impedance to multi-inverter droop control can raise bus voltages and allow for reactive power sharing. However, due to line aging and environmental factors, line parameters vary, affecting the accuracy of traditional virtual impedance control and making the accurate sharing of reactive power difficult. There have been many studies on the above problems to improve the accuracy of inverter reactive power distribution. In adaptive virtual impedance control proposed in Ref. [4], adaptive virtual impedance was generated according to the inverter output overcurrent and the scheduling command of the central controller, the power angle is adjusted according to its change intensity for adaptive control, and the power distribution accuracy of parallel inverters in the microgrid was improved. In the control scheme proposed in Ref. [5] that automatically adjusted a droop coefficient, each inverter sent its output power information to the central controller, calculated the given power, and automatically adjusted the droop coefficient through a PI regulator, improving the power distribution accuracy. Ref. [6] proposed an enhanced droop control method through online virtual impedance adjustment. This method adjusts the virtual impedance of distributed power sources at fundamental positive sequence, fundamental negative sequence and harmonic frequencies, and uses a low-bandwidth communication bus to send compensation commands from the central controller. Microgrid to the local controller of the unit to achieve precise power distribution under steady state. In the adaptive droop control scheme proposed in Ref. [7], the micro-sources in microgrids were calculated separately and the adaptive reactive power droop coefficient was applied to achieve reactive power accurate distribution among the micro-sources in islanded microgrids, but the problem of line voltage drop was not considered. An reactive power accurate distribution scheme considering the line impedance mismatch of an islanded AC microgrid was proposed in Ref. [8]. This scheme was based on the optimal adjustment of the virtual impedance of each inverter, and it was not necessary to determine the actual line impedance in advance, but the ability to deal with failures was mainly studied. The aforementioned methods in the above literature can make inverters share the load reactive power evenly. However, some methods need to rely on a central controller, and their centralized control methods have a simple structure and risk of a single point of failure problem, which reduces the system’s robustness. Distributed control does not need

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to rely on a central controller. It only needs to exchange information with its neighbors to achieve accurate power distribution. It has no single point of failure problem, and a node failure will not affect the system operation. Thus, the system performance is significantly improved. The robustness of the method has attracted great attention [9, 10]. Ref. [11] proposed a multi-loop control scheme with a virtual negative inductive reactance component and adaptive virtual impedance. This compensated for the inductive component of the inverter output impedance, dynamically adjusted the parameters of the equivalent impedance of the inverter, and improved the accuracy of power distribution. By improving the droop control loop, the voltage of the common node was raised. However, the main goal was to improve power distribution accuracy. Ref. [12] proposed a circulating current suppression scheme based on dynamic virtual impedance. It introduced the reactive power and voltage output to the adaptive virtual impedance controller, improved the accuracy of the reactive power distribution, and thus suppressed the reactive circulating current. By adding voltage compensation items to eliminate line voltage drops, the scheme improved the traditional droop control scheme and further suppressed reactive circulating currents. However, the main research goal was the suppression of circulating currents, and the calculation of voltage compensation items was complicated. Ref. [13] proposed an adaptive virtual impedance droop non-communication control scheme. This scheme introduced voltage and reactive power output by each inverter into an adaptive virtual impedance controller. It improved the accuracy of the reactive power distribution, but it presented an asynchronous regulation problem. Ref. [14] proposed an improved droop control scheme based on adaptive virtual impedance. The scheme improved the efficiency of the reactive power distribution accuracy. The average reactive power was obtained using a local information consensus algorithm. However, the calculation was complex and additional voltage compensation items were required. Ref. [15] proposed a new reactive power distribution method for a resistive island microgrid based on the online estimation of the line impedance and performed accurate self-adaptive optimization of the virtual impedance of parallel inverters so that reactive power could be evenly divided. However, single-phase inverters were mainly studied. Ref. [16] proposed a distributed optimization algorithm based on original dual gradient. This algorithm uses the microsource output voltage as the control variable, voltage regulation and reactive power distribution as the objective function, and achieves the optimal balance of voltage regulation and reactive power distribution. However, voltage control was mainly studied. To improve load reactive power accuracy shared by parallel inverters in a microgrid and raise the voltage of a common node, we propose a dynamic virtual impedance control scheme for parallel inverters with distributed optimization based on traditional virtual impedance. First, we establish a mathematical model of the circulating current of parallel inverters in the microgrid, use droop control to suppress the circulating current, analyze the process of the droop control suppressing the circulating current and show that the droop control cannot make each inverter share the load reactive power evenly. Second, we analyze the traditional virtual impedance and the distributed optimized virtual impedance without communication, which can make each inverter share the load reactive power evenly but has its own shortcomings. Then, to overcome these shortcomings, we use the reactive power that is output by each inverter as a form of communication to construct virtual impedance so that the reactive power output can be

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evenly divided. We also add a secondary regulation in the droop control loop to suppress the increase or decrease in the bus voltage and frequency caused by load changes. Finally we design a parallel simulation experiment of three inverters with different rated capacities on the MATLAB/Simulink simulation software and the RTDS-based hardware-in-the-loop simulation platform to verify the proposed control scheme.

2 Microgrid Parallel Inverter Model Considering Circulating Current As shown in Fig. 1, in an islanded microgrid, n distributed power sources are connected to the bus through power electronics, filters, and lines, and the output power of each inverter is rationally distributed using droop control.

Fig. 1. Topology of parallel inverter network

According to Kirchhoff’s law at a common node, the current on the lines of the i-th inverter is ⎡

⎤

⎡

⎤

⎡

⎤

⎡

1 Z1

⎤

Io,1 Ix,1 Ic,1 ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥=⎢ . ⎥+⎢ . ⎥=⎢ . ⎥ ⎣ . ⎦ ⎣ . ⎦ ⎣ . ⎦ ⎣ . ⎦ 1 Io,i Ix,i Ic,i Zi

Upcc ZLoad 1 Z1

+

1 Z2

+ ··· +

1 Zi

⎡ 

i 1 ⎢ m=1 Z1 +Zm ⎢ ⎢ . . +⎢ ⎢ . ⎢

⎣ 1 − Z1 +Z i



⎤ 1 ⎡ ⎤ · · · − Z1 +Z i ⎥ Uo,1 ⎥ ⎥ ⎢ ⎥ . .. ⎥⎢ .. ⎥ . ⎥⎣ . ⎦ . .

⎥ i ⎦ Uo,i  1 ··· Zi +Zm m =i

(1) where I x,i and I c,i are the steady-state current component, the circulating current component in the output current I o,i of the i-th inverter, respectively. Z i , and U o,i are the line impedance of the filter and the voltage at the filter capacitor terminal for the i-th inverter, respectively. Z Load is the load impedance and U pcc is the voltage of the common node [17]. In this work, the line impedance in the parallel inverter topology is inductive. To suppress the circulating current in the above parallel inverter model, all inverters adopt “active power-frequency / reactive power-voltage” droop control and are at the same rated frequency and rated voltage, with the droop coefficients inversely proportional to the rated capacity. The control structure of the i-th inverter with droop control is shown in Fig. 2.

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Fig. 2. Structure of droop control of inverter

Since the line impedance is inductive, the output reactive power of the i-th inverter is Qi =

2 Uo,i Upcc − Upcc

Xi

(2)

where Xi is the line inductance of the i-th inverter and Qi is the reactive power output by the i-th inverter. From the above reactive power equation, Qi =

2 Uo,i Upcc − Upcc

Xi

(3)

Because it is much smaller than U2 pcc, Qi X i can be ignored. The above equation be-comes 2 2 Qi Xi + Upcc Upcc Uo,i = ≈ =1 2 2 Uo,j Qj Xj + Upcc Upcc

(4)

It can be seen from the above equation that the droop control can make the output voltages of each inverter in the parallel inverter topology approximately equal, eliminating the voltage difference, namely by suppressing the circulating current. Although droop control can suppress the circulating current and allow the active power output to be shared evenly by each inverter. Due to the mismatch of line parameters, it is difficult to make the reactive power output from each inverter equally divided[18]. Therefore, virtual impedance needs to be added to eliminate the effect of line impedance on reactive power equalization.

3 Analysis of Reactive Power Distribution Problems 3.1 Analysis of Reactive Power Distribution Problem Based on Virtual Impedance To address the problem that conventional sag control does not allow each inverter to share the load reactive power according to its capacity, a virtual impedance is added so that the equivalent impedance is zero, eliminating the effect of line impedance. This method does not require an additional control scheme to bring the common node voltage to the desired control value. After adding the virtual impedance to the conventional sag control, the control structure of the i-th inverter is shown in Fig. 3.

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Fig. 3. Structure of control of inverter after the addition of virtual impedance

From the above figure, it can be seen that the output load current of the i-th inverter is Io,i =

Uref ,i − Upcc P ∗ Upcc == n i  ∗ ZLoad Zi + Z0,i Pi

(5)

i=1

where U ref,i , Z 0,i , and P* i are the droop control output voltage, virtual impedance, and rated active power, respectively. Obtained from the above equation, the virtual impedance of the i-th inverter is  Uref ,i − Upcc Upcc Pi∗ − Zi (6) Z0,i = n  ZLoad Pi∗ i=1

To make the voltage at the common node equal to the ideal control value, U ref,i = U pcc is set. Then Z 0,i = -Z i is the initial value of the virtual impedance that remains constant, and the virtual impedance can fully compensate for the voltage drop on the line. This method requires accurate line impedance parameters. However, in real-world engineering, the line parameters are difficult to obtain accurately, and when a line is aged or damaged, the line parameters may change while the virtual impedance does not change accordingly. In this case, Z 0,i = -Z i . Thus, it is impossible to make each inverter share the load reactive power evenly according to the capacity, and the voltage of the common node is not equal to the ideal control value. In conclusion, the conventional virtual impedance makes it difficult to distribute the load reactive power equally in each inverter. 3.2 Analysis of Distributed Reactive Power Distribution with Virtual Impedance Without Communication To overcome the shortcomings of the traditional virtual impedance, the virtual impedance can be optimized as a dynamic virtual impedance. When the line impedance parameters change, the virtual impedance can be automatically adjusted to match the line impedance [19]. In the absence of communication between inverters, in order to optimize the virtual

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impedance of each inverter separately, the adaptive virtual impedance is expressed as [12]. 

 Zvi,i = Rvi,i + jXvi,i = Rvi,i + j a1,i Xset + Kv a1,i Qi (7) where Rvi,i is the virtual resistance. A negative line resistance value is assigned to offset the effect of the line resistance so that the equivalent output impedance of the system is inductive. X vi,i is the virtual reactance, a1,i is the ratio of the reactive power droop coefficient between the i-th inverter and the first inverter, X set is the given value of the virtual reactance, and K v is the reactive power feedback coefficient. The reference voltage of the droop control output of the i-th inverter is given by Uref ,i = Upcc +

Pi∗

n 

i=1

Upcc  Zi + Zvi,i ∗ ZLoad

(8)

Pi

where Z vi,i is the adaptive virtual impedance. The value of the virtual impedance of the inverter is negative line impedance. When the line impedance parameters of the i-th inverter change, Eq. (8) can be changed to Uref ,i = Upcc +

Pi∗ Upcc  Zi + Zi + Zvi,i n  ∗ ZLoad Pi

(9)

i=1

After this, the virtual impedance of the i-th inverter is adaptively adjusted, and the reference voltage of the droop control output of the i-th inverter changes. If the virtual impedance of the other inverters is not adaptively adjusted, the reference voltages of the droop control outputs of other inverters remain unchanged. Then a voltage difference is generated between the i-th inverter and other inverters and a circulating current is generated. In summary, when the virtual impedances of the inverters are not optimized simultaneously, a voltage difference between the inverters may be generated, which leads to an occurrence of circulating current.

4 Distributed Optimization Control Scheme for Parallel Inverters 4.1 Distributed Optimization Virtual Impedance Control Theory To tackle the above problems, it is necessary to establish communication between the inverters to increase the system performance. The distributed control scheme only relies on the reactive power information of the local and adjacent inverters for communication. When communication for an inverter fails, the operation of other inverters should not be affected, saving communication costs and having a “plug-and-play” performance. Therefore, a control scheme for distributed consensus optimization based on traditional virtual impedance is proposed. The theory of optimization for distributed virtual impedance control is described below.

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In the proposed control scheme, by adding virtual impedance to each inverter in the parallel inverter model and only communicating with the reactive power information output with adjacent inverters, the virtual impedance is optimized so that the equivalent impedances become matched, enabling an accurate sharing of the reactive power. The control scheme is still applicable even if the line parameters change due to factors such as line aging or damage. To solve the problem of bus voltage drop caused by the line, the line impedance can be calculated according to the current on the line and the voltages at both ends. Letting the initial value of the virtual impedance be the negative line impedance, the voltage drop on the line can be compensated for, raising the voltage at the common node. If the line parameters are changed due to aging or damage to the line, it is only necessary to calculate the rough value of the line impedance again and modify the initial value of the virtual impedance. The block diagram of the distributed control of the i-th inverter is shown in Fig. 4.

Fig. 4. Inverter control block diagram based on distributed optimal virtual impedance

Through the control block diagram in Fig. 4, it can be noted that in the distributed virtual impedance control module, the reactive power information Qi and Qj output by the inverter are used to construct Z C2V,i , and Z C2V,i is automatically adjusted to the appropriate value according to the reactive power information, the given voltage is superimposed on the compensation voltage of Z C2V,i , which can change the output voltage of the inverter and match the equivalent impedance, further changing U pcc and achieving reactive power sharing. The controller of i-th inverter is composed of K 1 (s) and K 2 (s). Among them, K 1 (s) represents the current loop PI control and PWM, K 2 (s) represents the voltage loop PI control, the controlled object is composed of G1 (s) and G2 (s), G1 (s) is the filter inductance, and G2 (s) represents the filter capacitor. Expressed with droop coefficients, the output reactive power of each inverter in the parallel connection model of n inverters is defined as ⎡ c⎤ ⎡ ⎤ n1 Q1 Q1 ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ c⎥ ⎢ ⎥ c ⎥ ⎢ ⎥ (10) Q =⎢ ⎢ Qi ⎥ = ⎢ ni Qi ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎢ . ⎥ ⎣ . ⎦ ⎣ . ⎦ Qnc

nn Qn

where ni is the reactive power droop coefficient of the i-th inverter. According to the distributed control theory, the control strategy proposed treats the entire parallel inverter

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system as a multi-agent system, in which each inverter is an agent, Qc i is a reactive power signal transmitted in the communication network, and each inverter only needs to obtain its own Qc i to communicate locally with adjacent inverters. Based on consistency algorithm, the control target of evenly dividing the reactive power output of each inverter is equivalent to achieving the consensus of Qc i, which is equivalent to making Qc i for each inverter equal, namely, making the product of the output reactive power and droop coefficient of each inverter equal [20]. According to the typical distributed consensus algorithm equations, the virtual impedance in the distributed control scheme proposed is expressed as ⎤ ⎡  

aij Qic − Qjc ⎦dt + Zv0,i (11) Zv,i = KI ⎣ j∈Ni

where K I is the integral coefficient, N i is the set consisting of all adjacent units, Z v0,i is the initial virtual impedance, which is the negative line impedance, and aij is the element of the adjacency matrix A. aij represents whether the j-th inverter is an adjacent unit of the i-th inverter. If it is an adjacent unit, then aij = 1; otherwise, aij = 0 [21, 22]. From Eq. (11), it can be seen that the virtual impedance of the i-th inverter at the next moment is determined by its current reactive power information and that of the adjacent inverters. Then the modulus value of the virtual impedance of each inverter in the parallel system of n inverters is ⎡ ⎡ ⎛ ⎡ ⎤ ⎤⎞ ⎤ Zv0,1 n1 Q1 Zv,1 ⎢ . ⎥ ⎢ . ⎥ ⎜ ⎢ . ⎥⎟ ⎢ . ⎥ ⎢ . ⎥ ⎜ ⎢ . ⎥⎟ ⎢ . ⎥ ⎢ . ⎥  ⎜ ⎢ . ⎥⎟ ⎢ ⎢ ⎜ ⎢ ⎥ ⎥⎟ ⎥ ⎢ Zv0,i ⎥ ⎢ ⎟ ⎜ ⎥ ⎥ Z n Q dt + L = K (12) Zv = ⎢ I ⎢ ⎢ v,i ⎥ ⎜ ⎢ i i ⎥⎟ ⎥ ⎢ ⎢ . ⎥ ⎜ ⎢ . ⎥⎟ ⎥ ⎢ .. ⎥ ⎢ . ⎥ ⎜ ⎢ . ⎥⎟ ⎣ . ⎦ ⎣ . ⎦ ⎝ ⎣ . ⎦⎠ Zv,n

nn Qn

Zv0,n

where L is the Laplacian matrix. 4.2 Distributed Optimization Process of Virtual Impedance From Fig. 4, it can be seen that each inverter adds a distributed optimal virtual impedance. After distributed optimization, the virtual impedance can exactly compensate for the effect of the virtual impedance so that the output reactive power of each inverter is evenly divided and the voltage of the common node reaches an ideal control value. The optimization process of the virtual impedance is as follows. Step 1. Calculate the equivalent value of line impedance based on the voltage at both ends of the line and the current on the line. Step 2. Calculate the initial virtual impedance according to the equivalent line impedance, which is for obtaining the optimal solution of the virtual impedance faster and enable the system to achieve stability faster. Step 3. The reactive power information of each inverter is examined and compared with the reactive power information of adjacent inverters; that is, Qc i and Qc j are

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compared, which is for detecting reactive power allocation error and prepare for the next step of calculation. Step 4. If Qc i > Qc j, Z v,i is increased, thereby reducing the output voltage and in turn reducing the output current of the i-th inverter, and finally reducing Qc i. If Qc i < Qc j, Z v,i is reduced, thereby increasing the output voltage and in turn increasing the output current of the i-th inverter, and finally increasing Qc i, in order to adjust the virtual impedance according to the reactive power allocation error, thereby adjusting the reactive power output of the inverter. Step 5. Repeating Steps 3 and 4 until achieving the reactive power sharing, that is, until Qc i = Qc j, and the virtual impedance no longer changes, in order to optimize the virtual impedance and equalize the reactive power. Step 6. When the line impedance parameters change due to factors such as line aging, the above steps are repeated, this is for the case of perturbation of line parameters. When the parallel system is stable, the virtual impedance of each inverter no longer changes. At this point, LQc = 0

(13)

According to the consensus theory of intelligent agent control, the right eigen-vector of L is (1)n = [1,1,…,1]T , that is, the above equation has only a unique solution vector (1)n . Therefore, when the parallel inverter system is stable, the control scheme proposed can cause the product of reactive power and droop coefficient of each inverter equal, that is, n1 Q1 = · · · = ni Qi = · · · = nn Qn

(14)

4.3 Secondary Regulation of Voltage and Frequency In response to the issue of deviation of bus voltage and frequency from the ideal control value caused by droop control, secondary regulation of voltage and frequency has been added in droop control. When the load changes, the bus voltage and frequency reach the ideal control value. The control block diagram of secondary control is shown in Fig. 5.

Fig. 5. Block diagram of improved droop control

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when the load changes, the change in the load for each inverter is obtained by subtracting the new load from the initial load and is then distributed according to the droop coefficient. This is expressed for the i-th inverter as PLi =

1 mi 1 m1

+

1 m2

+ ··· +

1 mi

(PLi − PL0 ),QLi =

1 ni 1 n1

+

1 n2

+ ··· +

1 ni

(QLi − QL0 ) (15)

where PLi and QLi are the load changes for the i-th inverter. PLi , PL0 , QLi , and QL0 are the active load, initial active load, reactive load, and initial reactive load, and mi is the active power droop coefficient. The improved droop control of the i-th inverter as    ∗       ∗  f mi 0 Pi Pi PLi fi = i∗ − − + (16) Ui Ui Qi Qi∗ QLi 0 ni where f i , U i , f * i, U* i, P* i, and Q* i are the frequency, voltage, given frequency value, given voltage value, given active power value, and given reactive power value. The overall architecture of the parallel inverter control scheme proposed is shown in Fig. 6.

Fig. 6. Overall architecture of the parallel inverter control scheme

5 Experiment and Simulation Analysis To verify the effectiveness and reliability of the distributed optimization virtual impedance control scheme and the secondary regulation scheme of parallel inverters, the parallel topology of three inverters is used as example, and the rated capacity ratio is 1:2:3. As shown in Fig. 7, an island microgrid multi-inverter parallel system is built. The three inverters jointly supply power to the load through the improved Droop control, and each inverter communicates only with information from local and adjacent inverters. The active and reactive power output of the load is 30 kW and 30 kVar, respectively. To reflect the superior performance of the control scheme, the traditional virtual impedance control of parallel inverters and the distributed optimization virtual impedance control are compared utilizing the same parameters in the parallel system. The parameters of each inverter used in this experiment are shown in the table below, and set up three interconnected inverters with a capacity ratio of 1:2:3 as shown in Fig. 8 on the RTDS platform for experiments (Table 1).

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Fig. 7. Overall architecture of the parallel inverter control scheme

Table 1. Parameters of parallel inverters Parameter

DC-AC1

DC-AC2

DC-AC3

Rated active power (kW)

5

10

15

Rated reactive power (kVar)

5

10

15

Rated voltage (V)

311

311

311

Rated frequency (Hz)

50

50

50

DC voltage (V)

600

600

600

Active droop coefficient (10−5 )

1.2

0.6

0.4

Reactive droop coefficient (10−4 )

5

2.5

1.67

Fig. 8. Schematic diagram of RTDS hardware-in-the-loop experiment platform. The considered elements were the (1) GTAO board, (2) TMS320F28335 controller, (3) GTDI board, (4) optical fiber, (5) GPC processor, (6) signal line, (7) FPGA board, (8) RSCAD GUI, (9) Rack.

Operating condition 1: Three inverters with a capacity of 1:2:3 operate in parallel. When the line parameters are disturbed due to aging or damage to the line, it is difficult to determine the accurate parameters of the lines of the two inverters after the disturbance. The impedance becomes mismatched. In this situation, the value of the virtual

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impedance in the traditional control scheme remains unchanged, but the initial value in the distributed optimization virtual impedance control scheme can be adjusted to an appropriate value to match the line impedance after the line parameter disturbance. When using traditional virtual impedance control and distributed optimized virtual impedance control, the simulation results of the active power, reactive power, and common node voltage output by the inverter are as shown in the Fig. 9.

Fig. 9. Comparison of power distribution and common node voltage of two control schemes. Active power of parallel inverters with (a) traditional (b) distributed optimized virtual impedance scheme; traditional reactive power of parallel inverters with (c) traditional (d) distributed optimization virtual impedance; (e) common node voltage with traditional virtual impedance; (f) common node voltage with distributed optimized virtual impedance.

Figure 9 depicts the comparison of power distribution and common node voltage of two control schemes. Under the operating conditions 1, because the droop control is used, the active power output of each inverter is not related with the line impedance. Therefore, both the traditional virtual impedance scheme and the distributed optimized virtual impedance scheme can cause the output active power of each inverter to be evenly divided according to capacity. However, the disturbance of the line parameters results in the virtual impedance value of the traditional scheme no longer accurately matching the line impedance, so the reactive power cannot be divided evenly according to the capacity and the voltage drop cannot be fully compensated for. The distributed optimization virtual impedance scheme does not require the line parameters to be accurate. It only requires the approximate modulus value of the line impedance from the calculation, and it modifies the initial value and then adjusts the virtual impedance adaptively according to the active

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power information output by each inverter to match the line impedance. Therefore, the reactive power can be shared evenly, even when the line parameters are disturbed, and the voltage drop can be fully compensated for as long as the initial value is modified to an appropriate value.

Fig. 10. Comparison diagram of reactive power distribution of load switching and switching between two control strategies in RTDS platform. Reactive power under (a) traditional droop control strategy; (b) distributed virtual impedance optimization strategy

As can be seen from Fig. 10, the parallel inverters under the traditional droop control strategy are affected by the disturbance current when the load is switched, and contain circulating current, so that the reactive power cannot be shared proportionally for a short time. Under the distributed virtual impedance optimization strategy, the disturbance current of each inverter is effectively compensated, the output voltage of each inverter is basically not affected by the disturbance current, the circulating current is reduced, and the reactive power of parallel inverters It can achieve fast proportional equalization. Operating condition 2: Three inverters with a capacity of 1:2:3 operate in parallel. The active power of the initial load is 30 kW and the reactive power is 30 kVar. Add a load of 30 kW active power and 30 kVar reactive power in the 2nd second. Based on the distributed optimized virtual impedance, the simulation results of bus d-axis voltage and frequency and simulation results of virtual impedance of the system before and after load changes with and without the secondary regulation added to the traditional droop control loop are as shown below. It can be seen from the above Fig. 11 that under operating condition 2, when the load increases without secondary regulation, after the addition of the load of 30 kW active power and 30 kVar reactive power, due to the influence of traditional droop control, the d-axis frequency and voltage of the busbar will decrease. In the case of the addition of secondary regulation, when the load increases, the addition of a value equal to the load change in the droop control can compensate for the load change, thereby significantly suppressing the drops of the bus voltage and frequency. The virtual impedance is only related to the line parameters, therefore, the virtual impedance of the system before and after load changes is equal under steady-state conditions. Operating condition 3: Three inverters with a capacity of 1:2:3 operate in parallel. In the second, a certain inverter malfunctioned and was cut off. Based on the distributed optimization virtual impedance control strategy, the simulation results of the output power of each inverter before and after the inverter is cut off are shown in the following Fig. 12.

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Fig. 11. Comparison of two different control schemes in operating condition 2. (a) Bus d-axis voltage without secondary regulation; (b) bus d-axis voltage with secondary regulation; (c) bus frequency without secondary regulation; (d) bus frequency with secondary regulation; (e) virtual impedance of the system before and after load changes

(b) Q / Var

P/W

(a)

Fig. 12. Simulation results of the output power of each inverter before and after the removal of the faulty inverter (a) Active power (b) Reactive power

From Fig. 12, it can be seen that under condition 3, before a certain inverter malfunctions and is cut off, each inverter operates normally and the output power is evenly distributed according to capacity. After a certain inverter malfunctions and is cut off, the output power of the cut off inverter becomes 0, and the other inverters increase their output and evenly share the load power. This proves that when one inverter malfunctions and is cut off, it does not affect the performance of other inverters.

6 Conclusion In this paper, an improved virtual impedance control scheme based on a distributed algorithm is proposed to solve the problem that reactive power cannot be distributed equally according to capacity due to the mismatch and uncertainty of line impedance.

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In addition, by incorporating secondary regulation in the sag control loop, the increase and decrease of bus voltage and frequency can be significantly suppressed when the load changes. The experimental results show that the proposed distributed optimized virtual impedance control scheme can effectively improve the accuracy of the reactive power allocation of the output of each inverter and adequately compensate the voltage drop on the line. The proposed secondary regulation scheme can reduce the variation of bus voltage and frequency. Compared with other control schemes, this control scheme does not require accurate line impedance values. Instead, it only requires communication with neighboring inverters, which saves communication cost and realizes the “plug-and-play” function of inverters. However, the line impedance in the parallel inverter topology used in the strategy proposed in this paper is inductive. When the sum of the inverter output impedance and the line impedance is not inductive, the conventional droop control strategy is not applicable, and more generalized methods need to be investigated in the future. Acknowledgements. . This work is supported in part by the Science and Technology Project of Hebei Electric Power Company (kj2020–47).

References 1. Wang, E.Y., Wang, S.: Low voltage microgrid droop control strategy based on adaptive virtual resistance. Power Syst. Prot. Control 48(2), 144–149 (2020). (in Chinese) 2. Hu, C.B., Shi, X.Y., Luo, S.N., et al.: Decentralized dynamic disturbance compensation control strategy for multiple parallel inverters in microgrid. Proc. CSEE 41(13), 4425–4439 (2021). (in Chinese) 3. Qian, Q., Wei, Q., Xie, S.J., et al.: Multi-frequency impedance model of single-phase gridconnected inverter and its application in analysis of resonant circulating. Autom. Electr. Power Syst. 43(15), 159–165 (2019). (in Chinese) 4. Dai, W., Qin, W.P., Ren, C.G., et al.: Adaptive virtual impedance control based on decoupling droop in microgrid with synchronous generators. Proc. CSEE 40(14), 4486–4496 (2020). (in Chinese) 5. Sun, X.F., Yang, Y.L., Zhao, W., et al.: An adaptive droop control method for inverters in microgrid. Power Grid Technol. 38(09), 2386–2391 (2014). (in Chinese) 6. He, J., Li, Y.W., Blaabjerg, F.: An enhanced islanding microgrid reactive power, imbalance power, and harmonic power sharing scheme. IEEE Trans. Power Electron. 30(6), 3389–3401 (2015). https://doi.org/10.1109/TPEL.2014.2332998 7. Gupta, Y., Chatterjee, K., Doolla, S.: A simple control scheme for improving reactive power sharing in islanded microgrid. IEEE Trans. Power Syst. 35(4), 3158–3169 (2020) 8. Mohammed, N., Lashab, A., Ciobotaru, M., et al.: Accurate reactive power sharing for droopbased islanded AC microgrids. IEEE Trans. Industr. Electron. 70(3), 2696–2707 (2023) 9. Rahbari-Asr, N., Ojha, U., Zhang, Z., et al.: Incremental welfare consensus algorithm for cooperative distributed generation/demand response in smart grid. IEEE Trans. Smart Grid 5(6), 2836–2845 (2014) 10. Achyut, S., Natarajan, J.: Optimal cluster head selection framework to support energy aware routing protocols of wireless sensor network. Int. J. Netw. Virtual Organ. 18(2), 144–165 (2018)

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11. Zhang, J.H., Zhao, R., Liu, Y.F., et al.: Resistive inverters output impedance parallel operation strategy in low-voltage microgrid. High Voltage Technol. 48(01), 136–146 (2022). (in Chinese) 12. Wang, J.K., Mu, L.H., Liu, X.: Control strategy based on dynamic virtual impedance to suppress circulating current between multiple parallel inverters. Power Autom. Equipment 41(4), 94–100 (2021). (in Chinese) 13. Fan, B.S., Li, Q.K., Wang, W., et al.: A novel droop control strategy of reactive power sharing based on adaptive virtual impedance in microgrids. IEEE Trans. Industr. Electron. 69(11), 11335–11347 (2021) 14. Yan, L., Mi, Y., Sun, W., et al.: Reactive power distribution control strategy in islanded AC microgrid based on improved droop control. J. Solar Energy 42(08), 7–15 (2021). (in Chinese) 15. Mohammed, N., Ciobotaru, M.: An accurate reactive power sharing strategy for an islanded microgrid based on online feeder impedance estimation. IEEE Ind. Electron. Soc. 2525–2530 (2020) 16. Mohiuddin, S.M., Qi, J.J.: Optimal distributed control of AC microgrids with coordinated voltage regulation and reactive power sharing. IEEE Trans. Smart Grid 13(3), 1789–1800 (2022) 17. Vishwakarma, R., Monani, R., Hedayatipour, A., et al.: Reliable and secure memristorbased chaotic communication against eavesdroppers and untrusted foundries. Discov. Internet Things 3, 2 (2023) 18. Khezri, R., Golshannavaz, S., Shokoohi, S., et al.: Toward intelligent transient stability enhancement in inverter-based microgrids. Neural Comput. Appl. 30, 2709–2723 (2018) 19. Keddar, M., Doumbia, M.L., Belmokhtar, K., et al.: Enhanced reactive power sharing and voltage restoration based on adaptive virtual impedance and consensus algorithm. Energies 15(10), 3480 (2022) 20. Guo, Q., Lin, L.Y., Wu, H.Y., et al.: Distributed power control strategy for microgrids considering adaptive virtual impedance. Power Syst. Autom. 40(19), 23–29 (2016). (in Chinese) 21. Wang, B.H., Chen, W.S., Zhang, B., et al.: Cooperative control-based task assignments for multiagent systems with intermittent communication. IEEE Trans. Industr. Inf. 17(10), 6697– 6708 (2021) 22. Habib, M., Ladjici, A.A., Harrag, A.: Microgrid management using hybrid inverter fuzzybased control. Neural Comput. Appl.Comput. Appl. 32, 9093–9111 (2020)

On Line Estimation of Power Line Channel Impedance Based on Transfer Function Hu Zhengwei(B) , Xia Siyi, Wang Wenbin, Xie Zhiyuan, and Cao Wangbin Department of Electronic and Communication Engineering, North China Electric Power University, Baoding 071003, China [email protected], {zhiyuanxie,wbin.cao}@ncepu.deu.cn

Abstract. A method of channel impedance estimation based on the characteristics of channel transfer function is proposed. According to the characteristics of different impedance with different reflection coefficients, which leads to different channel transfer functions, the mapping relationship between transfer function and channel impedance is established by using neural network. Compared with the existing methods, this method does not need special impedance measuring circuit, and can realize communication and impedance measurement at the same time. The maximum cross correlation of the transmission function of the received and received signals is taken as the feature sample of the neural network, which improves the accuracy under the noise condition. The feasibility and effectiveness of this method are verified from software model and hardware implementation. Keywords: Power line communication · Impedance measurement · Artificial intelligence · Neural network

1 Introduction PLC (Power Line Communication) technology is one of the important communication modes of the power Internet of things, which is an important solution to realize the interconnection of massive electrical equipment. However, due to the random switching of the working state of a large number of electrical equipment, the impedance change of power line is random, and it is difficult to achieve the optimal impedance matching, which leads to the random characteristics of the receiving power at the receiver and affects the communication quality seriously. In order to enhance the communication quality of PLC, a lot of research work has been done on impedance matching, including impedance measurement [1, 2], matching circuit design [3], matching algorithm [4–7]. The work in this paper belongs to impedance measurement. Accurate impedance measurement is an important prerequisite for impedance matching. At present, there are two methods to measure the impedance of power line channel. One is to measure the impedance of PLC lines with special impedance testing equipment, and the impedance characteristics of the lines can be directly output by the equipment. The other method is to design the impedance measurement system according to the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 165–172, 2024. https://doi.org/10.1007/978-981-97-1072-0_16

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principle of impedance measurement with DDS signal source generates sine wave of specific frequency. Through measuring the impedance value, reflection coefficient or Voltage Standing Wave Ratio of the load, the microprocessor performs matching algorithm to realize the impedance matching according to measured parameters. Although these two methods can fulfill measurement and estimation of line impedance, there are two shortcomings: one is that the measurement system and PLC system are two independent systems, which are not only high cost, but also due to the difference of impedance characteristics of two systems, there will be deviation between the measurement results and the actual impedance characteristics. Second, impedance measurement and communication can not be carried out at the same time. In order to overcome the shortcomings of the existing methods, this paper proposes a method based on neural network to identify the received signal characteristics of power line communication and estimate the channel impedance. In the on-line measurement, the noise has a great impact on the estimation results. Considering that the actual PLC system mostly adopts OFDM technology, this paper extracts the characteristics of the cross-correlation operation results between the received signal and the preamble sequence in the OFDM data frame to realize the accurate estimation of the impedance under the noise condition.

2 Theoretical Basis Equation (1) is the transfer function expression of Phillips model [8]. H (f ) =

N 

ρi e−j2π f τi

(1)

i=1

where N is the number of possible signal transmission paths, τ I is the delay of the i-th path, and parameter ρ i is the product of transmission and reflection factors. From Eq. (1), it can be found that the transfer function H ( f ) depends on two parameters τ i and ρ i . Taking the power line communication network shown in Fig. 1 as an example, the relationship between impedance and parameters τ i and ρ i is given. The internal relationship between impedance and transfer function can be established by combining formula (1). A

B

d1

ZS

C

VS

ZL2

d3 d2

D ZL3

Fig. 1. Example of PLC network

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In Fig. 1, Vs and ZS are the source voltage and source impedance, ZL2 and ZL3 are the load impedance at nodes C and D, and the transmission line lengths are d1 , d2 and d3 , respectively. ⎧ (N = 1) ⎨ 12 ρi = 12 ρ2C 23 (2) (N = 2) ⎩ N −1 N −2 ρ2B 23 (N ≥ 3) 12 ρ2C τi =

d1 + 2(N − 1)d2 + d3 vp

(3)

Formula (2)–(3) gives the calculation expressions of parameters τ i and ρ i in the network shown in Fig. 1. Among them, G13 is the transmission factor of line 1 to 3, ρ 13 is the reflection factor of line 1 to 3, G12 and G23 are the transmission factors of line 1 to 2 and 2 to 3, and ρ 2C and ρ 2B are the reflection factors of line 2 at point C and point B. The expressions of transmission factors and reflection factors: 13 = 1 + ρ13 , 12 = Z3 //Z1 −Z2 3 −Z1 1 + ρ12 , 23 = 1 + ρ23 , ρ1B = ρ13 = ρ12 = ZZ22 //Z //Z3 +Z1 , ρ2B = ρ23 = ρ21 = Z3 //Z1 +Z2 ,

−Z2 ρ2C = ZZL2 . Z1 , Z2 and Z3 are characteristic impedances of line 1, line 2 and line 3 L2 +Z2 respectively. The change of load ZL2 can be regarded as the load change of PLC network. Therefore, the channel impedance information of PLC network can be obtained by channel transfer function H ( f ). Since the total specific impedance information of the whole topology network is monitored, the whole PLC network can be equivalent to a black box with variable impedance Z CH , as shown in Fig. 2.

TX Terminal ZS Terminal impedance

RX Terminal Power line communication network with specific topology

ZL Terminal impedance

ZCH Send data

Receive data

Fig. 2. Structure of power line channel impedance measurement system

3 Impedance and Transfer Function Mapping Based on Neural Network Model In order to estimate the channel impedance according to transfer function, it is necessary to establish the relationship between transfer function and channel impedance. This paper introduces artificial neural network model to establish the mapping relationship between impedance and transfer function.

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Parameter

Value

Description

ZS

50

Resistance of transmitter

ZL3

50

Resistance of receiver

ZL2

Random value

Resistance of load

d1

100 m

Distance from transmitter to branch node

d2

10 m

Branch length

d3

100 m

Distance from receiver to branch node

f

20kHz ~ 10MHz

Communication frequency

3.1 Parameters of PLC Network Model The simulation model of PLC network is built based on MATLAB. The topology is shown in Fig. 1. The specific parameters are shown in Table 1. The cable model is H07V-U, and the cable parameters are c = 15 pF/m, l = 1.08μH/m, R = 1.2 × 10–4 × f 0.5 /m, G = 2πf × 30.9 × 10–14 S/m. In order to simulate the fluctuation of power grid load, the impedance of ZL2 is set as complex value, in which the imaginary part is the normal distribution with N(10,12 ). The real part is normal distribution random variable with N(100,402 ). Figure 3 shows the distribution of 2000 impedance generated samples. The abscissa and ordinate in Fig. 3 represent the real part and the imaginary part respectively.

Fig. 3. Impedance sample distribution

3.2 BP Neural Network Parameters The BP neural network [9, 10] is built and trained in MATLAB. This paper uses OSS algorithm, which is more suitable for this data samples. The learning rate is 0.001.

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3.3 Analysis of Training and Test Results 2000 training samples and 100 test samples are selected to train and test BP neural network. Figure 4 shows the relative error of 100 test samples.

a

amplitude

(b) Phase

Fig. 4. Relative error of impedance estimation

4 Hardware Test 4.1 Sample Collection The 12V DC power PLC system based on FPGA is used as hardware platform. One branch node is set. The length of the branch node, the sending terminal, the receiving terminal and the load are all 10 cm.

Fig. 5. Comparison of transfer functions of five kinds of loads

Figure 5 shows the transfer function under different load conditions measured on the hardware platform. It can be found that the measured transfer function is different with different load.

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4.2 Sample Processing In order to eliminate the error, this paper presents the processing scheme: (1) intercept the low-frequency part of the transfer function; (2) perform IFFT transformation on the intercepted part; (3) perform the same interception and IFFT transformation on the p symbol in the preamble sequence of OFDM; (4) perform cross-correlation operation on the IFFT results obtained in (2) and (3).

Fig. 6. Distribution of maximum value of cross correlation of different loads

Figure 6 shows the distribution of the maximum cross-correlation of different load. It can be found that the impedance values of different loads can be estimated by identifying the range of cross-correlation values. 4.3 Impedance Identification One BP neural network with three layers was implemented on Terasic’s FPGA board de10_nano. Nodes in input layer, invisible layer and output layer is 1, 100 and 5 respectively. 1000 samples were sampled for each load and total samples are 5000, 4500 training samples and 500 test samples. Figure 7 shows the training and testing results of the original sample. Figure 8 compares training and test results of the original samples and samples with 20dB noise. The abscissa represents the training time, and the ordinate represents the samples of successful recognized. The training time required to achieve 100% recognition success rate is increased.

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Fig. 7. Training and test results

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Fig. 8. Influence of noise

5 Conclusion Based on the theoretical relationship between impedance and transfer function, an on-line channel impedance estimation method is proposed by measuring the transfer function of the received signal. The feasibility of the proposed method is verified by theoretical modeling and hardware platform. The method proposed in this paper has engineering reference for improving the quality of PLC and the application of artificial intelligence in smart grid. Acknowledgments. This work is supported by the National Natural Science Foundation of China (52177083) and National Natural Science Youth Foundation of China (62001166).

References 1. Jiasheng, L., Damao, L., Xufei, S.: Impedance measurement and matching of low voltage power line channel. Mod. Electron. Technol. (07), 169–171174 (2011). (in Chinese) 2. Xing, Z., Mingxing, D., Kexin, W.: An impedance test method with dual current probe. Electron. Instrum. Customer 25(5), 5–8 (2018). (in Chinese) 3. Yihe, G., Sisi, D.: Design of impedance matching circuit for medium voltage power line communication. Power Syst. Prot. Control 45(11), 102–107 (2017). (in Chinese) 4. Wang, B., Cao, Z., Shi, S., et al.: Design and evaluation of modifiable impedance matching coupler for narrowband DC power line communications. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E101.A(12), 2328–2337 (2018) 5. Wang, B., Cao, Z., Luan, Z., et al.: Design and evaluation of band-pass matching coupler for narrow-band DC power line communications. J. Circ. Syst. Comput. 28(7), 19 (2019) 6. Changho, H., YongUn, J., Suhwan, K., et al.: An 18-Gb/s/pin single-ended PAM-4 transmitter for memory interfaces with adaptive impedance matching and output level compensation. Electronics 10(15), 1768–1768 (2021) 7. Jinguo, Z., Jinbin, Z., Junwei, Z., Ling, M., Keqing, Q.: Maximum efficiency tracking study of active impedance matching network discontinuous current mode in wireless power transfer system. Trans. China Electrotechnical Soc. 37(1), 24–35 (2022) (in Chinese)

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8. Hensen, C., Schulz, W.: Time dependence of the channel characteristics of low voltage powerlines and its effects on hardware implementation. AEU-Int. J. Electron. C. 54(1), 23–32 (2000) 9. Liben, H.: Evaluation method for thermal stability of smart pole power supply based on BP neural network model. Electr. Technol. 24(06), 47–56 (2023). (in Chinese) 10. Yang, X., Zitao, Z.: Medium and long-term power load forecasting based on genetic simulated annealing algorithm improved BP neural network. Electr. Technol. 22(09), 70–76 (2021). (in Chinese)

Research on Insulator Defect Detection Based on Improved YOLOv7 Bing Li1(B) , Mingjie Xu1 , Zhongxin Xie1 , Donglian Qi2 , and Yunfeng Yan2 1 School of Electrical and Automation Engineering, Hefei University of Technology,

Hefei 232009, China [email protected], [email protected] 2 School of Electrical Engineering, Zhejiang University, Hangzhou 310058, China {qidl,Yvowech}@zju.edu.cn

Abstract. Insulators are crucial components of the transmission and distribution networks, and they are prone to self-explosion under the influence of bad weather. Self-explosion defect diagnosis of insulators has always been an important task in power inspection. To solve this problem, an insulator defect detection algorithm model based on YOLOv7 algorithm is introduced in this article. Firstly, the attention mechanism is integrated into the network framework of the algorithm to enhance the algorithm’s capacity for feature extraction. BiFPN was used for feature fusion to reduce the computational load. Secondly, the improved loss function optimization algorithm is used to train the process. According to the experimental findings, the improved detection model’s accuracy and average accuracy are 97.2% and 97.4%, respectively. Keywords: Insulator Self-explosion Defect · Improved YOLOv7 · CBAM Attention Module · BiFPN · Focal-EIoU loss function

1 Introduction The safety and reliability of the power system relates to the future development of our national economy and the progress of society. How to ensure that the equipment on the power lines can operate safely and for a long time becomes a serious problem. As a basic component of a transmission line, insulators fix the transmission wires insulatively on the poles and towers, and play an important role in current insulation and mechanical support [1]. Hanging in the external environment for a long time, insulators are often affected by bad weather, coupled with the loss of components themselves, making insulators prone to failure, among which self-explosion defect is the most common and threatening failure [2]. Therefore, the inspection of insulator defects is very necessary. The traditional manual inspection method [3] needs to climb the pole and tower for inspection, which has high requirements for staff, heavy workload, long time and poor safety. As technology continues to advance and evolve, UAV inspection has been widely used. Compared with manual inspection, UAV inspection has improved the inspection efficiency, but the efficiency of manual interpretation is very low, and visual fatigue is © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 173–180, 2024. https://doi.org/10.1007/978-981-97-1072-0_17

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easy to occur, resulting in wrong detection, missed detection and other phenomena. The method based on deep learning provides a new research idea to solve this problem. At present, the target detection algorithm for insulators has been widely used. Literature [4] proposes a method combining edge detection with YOLOv2, which can improve the identification speed of insulators, but there is a certain gap with YOLOv3 in loss function. In literature [5], while adjusting the ratio of RPN candidate regions on the original model of Faster R-CNN, Res Net101 is used to replace the VGG16 network used in Faster RCNN, which improves the detection accuracy of insulators under complex background, but the detection speed is relatively slow. In literature [6], shufflenet v2 network and the deep convolutional module were integrated into the network structure of YOLOv5 to achieve the purpose of lightweight, but the detection accuracy was slightly improved. Since the YOLOv7 algorithm was first proposed, it has received extensive study in many fields due to its improved accuracy and speed compared with YOLOv5 [7, 8]. This work suggests an insulator defect detection algorithm based on the improved YOLOv7 algorithm. This approach incorporates the attention mechanism to improve the algorithm’s ability to extract features on the foundation of the original algorithm. Replacing the bidirectional fusion PANet structure of the original network with the weighted bidirectional feature pyramid network BiPAN [9]. Finally, the convergence process of the loss function optimization algorithm is improved.

2 Algorithm Improvement Based on YOLOv7 YOLOv7 is an object detection algorithm published by wang et al. [10] based on the improvement of YOLOv5, the model reparameterization is introduced into the network architecture, and the training method of auxiliary head is proposed. The accuracy is improved without affecting the subsequent inference time. Backbone ELAN

Neck CBAM

Head

SPPCSPC

MPConv ELAN

CBS

Concat

ELAN

Upsample CBAM

40*40*255 MPConv

Concat

MPConv CBS

ELAN

ELAN

Concat

ELAN

RER&Conv

`·

`·

CBS

MPConv ELAN

20*20*255

RER&Conv

CBAM

MPConv CBS

CBS*4

80*80*255

Upsample

Input 640*640*3

Concat

ELAN

RER&Conv

Fig. 1. Improved YOLOv7 model network architecture diagram

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The backbone feature extraction network, the feature fusion layer, and YOLOHead make up the majority of the YOLOv7 model. In view of the problems such as complex background and insufficient resolution in insulator detection pictures, the YOLOv7 network is prone to missing detection. Based on the original model, the CBAM [11] attention module is added, and the feature weighting enhances the algorithm model’s accuracy. The improved YOLOv7’s structure is depicted in Fig. 1. 2.1 Improvement of Attention Mechanism In the actual test, due to bad weather, complex background and other factors, the algorithm will produce a certain amount of invalid features in the process of feature extraction of input images. Convolutional Block Attention Module (CBAM) improves the weight of the model to the important features of the image in both channel and space dimensions, and improves the recognition accuracy. CBAM module adopts the mode of first channel attention and then space attention module, it can combine the advantages of the two kinds of attention, and improve the attention to the recognized object while suppressing the feature interference. The model structure is depicted in Fig. 2.

Input Feature

Conv Operaon

F

H C

Channel Aenon Module

Spaal Aenon Module

Output Feature

H W

C

W

H C

W

Fig. 2. CBAM module structure diagram

For the input feature graph F ∈ RC×H ×W , the channel attention and spatial attention modules are calculated as follows: Mc (F) = σ (MLP(AvgPool(F)) + MLP(MaxPool(F)))       c  c = σ W1 W0 Favg + W1 W0 Fmax

(1)

where σ is the Sigmoid function; MLP is a multi-layer perceptron. AvgPool(F) represents the average pooling operation of the middle feature map. MaxPool(F) indicates the maximum pooling operation for the intermediate feature map. W0 ∈ RC/r×C , W0 ∈ RC×C/r is the weight coefficient, r is the attenuation rate.       s s Ms (F) = σ f 7×7 AvgPool(F); MaxPool(F) (2) = σ f 7×7 Favg ; Fmax where σ is the Sigmoid function; f 7×7 means that the convolution kernel is 7 × 7; Fsavg , Fsmax represent the feature graphs after average and maximum pooling operations for channel directions.

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2.2 Improvement of the Feature Pyramid Since the CNN network extracts target features through layer by layer abstraction, The shallow layer of the network contains the location information of the image, while the deep layer of the network mostly contains the semantic information of the image, Multi-scale feature fusion can aggregate features at different resolutions and combine the shallow and deep information of the network. The feature fusion structure used by YOLOv7 algorithm is PANet, which significantly improves the network’s capacity to combine features. However, PANet structure does not contain the initial feature data from the backbone network, it is easy to cause errors in training process, which reduces the detection accuracy. Therefore, BiFPN structure is introduced to carry out feature fusion in the article. Compared with PANet structure, BiFPN structure deletes nodes with only one input edge, reduces the calculation amount, and adds skip connections to fuse more features (Fig. 3).

Fig. 3. Structure diagram of PANet and BiPAN

2.3 Adjustment of Loss Function The loss function in YOLOv7 network can be divided into target confidence loss, coordinate loss and classification loss. Lossobject = Lossloc + Lossconf + Lossclass Coordinate loss is calculated through CIoU, as shown in Eq. (4).   ρ 2 b, bgt LCIoU = 1 − IoU + + av c2

(3)

(4)

In order to improve the accuracy and performance of the algorithm model, this experiment uses Focal-EIoU [12] loss function to replace the CIoU loss function in the

Research on Insulator Defect Detection Based on Improved YOLOv7

old network. The calculation formula of Focal-EIoU is shown in Eqs. (5)–(7).   ρ 2 b, bgt LEIoU = LIoU + Ldis + Lasp = 1 − IoU + c2    ρ 2 w, wgt ρ 2 h, hgt + + cw2 ch2

2 , 0 < x ≤ 1; 1/e ≤ β ≤ 1 − ∞x [2 ln(βx)−1] 4 Lf (x) −α ln(β)x + C, x > 1; 1/e ≤ β ≤ 1 LFocal−EIoU = IOU γ LEIoU

177

(5) (6) (7)

Among them, x represents the difference between the predicted value and the true value; β is the radian of the control curve; γ is the parameter of outlier control suppression degree.

3 Experimental Result and Analysis 3.1 Production of Data Sets In this experiment, the open source insulator defect data set and the image of insulator self-explosion defect collected by a regional power grid are used to make the data set of the algorithm model. The data set contains a total of 878 images, of which 278 are insulator images with self-detonation defects. The target detection task requires a large amount of data, so it is decided to expand the data set by means of data enhancement, and convert it by means of blur, brightness adjustment, rotation, etc., and finally obtain 6585 images, including 4500 images of normal insulators and 2085 images of defective insulators. The data set is divided into training set and verification set according to 4:1. 3.2 Configuration of the Experimental Environment The experiment uses python language as the programming language, deep learning framework is pytorch, the operating system is 64-bit win10, and the GPU is NVIDIA Geforce RTX 3070. 3.3 Test Index Compare the detection accuracy of different detection models for insulator defects. The experimental evaluation indexes are accuracy and average accuracy. The result is calculated using Eqs. (8) and (9): TP (8) FP + TP C APi (9) mAP = i=1 C Among them, TP(True Positive) is the amount correctly predicted by the positive sample; FP(False Positive) is the number of false predictions in the positive sample; mAP indicates average accuracy. P=

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3.4 Analysis of Experimental Results Figure 4 shows the model accuracy curve of YOLOv7 and the improved YOLOv7. As shown in the graph that the accuracy and average accuracy of the improved YOLOv7 are better than those of the model before the improvement.

(a) Curve of [email protected]

(b) Curve of precision Fig. 4. The Curve of Model Accuracy

For the sake of analyzing the improved model more directly, the detection results of the algorithm before and after the improvement are compared in this article, and Fig. 5 displays the outcomes of the experiment. As demonstrated in the figure, the updated model has increased the accuracy of insulator body and defect identification in comparison to the original model, and the improvement is more obvious for insulators in complex backgrounds.

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At the same time, the updated model was compared with the YOLOv5 model. The results of various performance indicators are shown in Table 1.

(a)(b) YOLOv7 detection effect

(c)(d) Improved YOLOv7 detection effect Fig. 5. Comparison of detection effect

Table 1. Comparison of different detection models Network Model

Precision

[email protected]/%

YOLOv5

93.6

92.8

YOLOv7

94.6

96.1

Improved YOLOv7

97.2

97.4

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4 Conclusion In this article, an improved detection model based on YOLOv7 is proposed for insulator self-detonation defects. There are three main ways to improve: 1) For complex background, CBAM module is introduced to enhance feature extraction capability; 2) BiFPN structure was introduced for feature fusion to replace PANet structure in the original model and accelerate multi-scale feature fusion; 3) Choose Focal-EIoU loss function to replace CIoU loss function in the original network to improve the accuracy and performance of the algorithm model. According to the experimental findings, the accuracy of the improved model has increased by 2.6 percentage points, while the average accuracy has increased by 1.3% points. To sum up, the paper presents an improved YOLOv7 model with higher accuracy and better recognition of complex backgrounds, which can meet the application in inspection. Acknowledgment. This research is supported by Science and Technology Project of Zhejiang Province (2022C01056).

References 1. Miao, X., Liu, X., Chen, J., Zhuang, S., et al.: Insulator detection in aerial images for transmission line inspection using single shot multibox detector. IEEE Access 7, 9945–9956 (2019) 2. Lv, Z.: Summary of common fault analysis and detection methods for transmission lines. Autom. Instrum. 161–164+168 (2020). (in Chinese) 3. Nguyen, V.N., Jenssen, R., Roverso, D.: Automatic autonomous vision-based power line inspection: a review of current status and the potential role of deep learning. Int. J. Electr. Power Energy Syst. 99(JUL.), 107–120 (2018) 4. Lai, Q., Yang, J., Tan, B., et al.: An automatic recognition and defect diagnosis model of transmission line insulator based onYOLOv2 network. Electr. Power. (2019) 5. Zhang, T., Guo, Z.: Research on insulator detection of transmission line based on improved Faster RCNN. Electron. Eng. Product World 28(10), 63–67+77 (2021). (in Chinese) 6. Huang, S., Dong, X., Yang, H.: Rapid insulator detection based on improved YOLOv5. Mod. Inf. Technol, 7(06), 73–76 (2023). (in Chinese) 7. Liu, S., Wang, Y., Yu, Q., et al.: CEAM-YOLOv7: improved YOLOv7 based on channel expansion and attention mechanism for driver distraction behavior detection. IEEE Access 10, 129116–129124 (2022) 8. Li, S., Yu, J., Wang, H.: damages detection of aeroengine blades via deep learning algorithms. IEEE Trans. Instrum. Meas. 72, 1–11 (2023) 9. Li, Y., Yang, M., Hua, J., et al.: A channel attention-based method for micro-motor armature surface defect detection. IEEE Sens. J. 22, 8672–8684 (2022) 10. Wang, C.Y., Bochkovskiy, A., Liao, H.Y.M.: Trainable bag-of-freebies sets new state-of-theart for real-time object detectors. arXiv, 2207.02696 (2022) 11. Wang, L., et al.: Investigation into recognition algorithm of helmet violation based on YOLOv5-CBAM-DCN. IEEE Access 10, 60622–60632 (2022) 12. Zhou, M.: Contraband recognition in passive terahertz images based on Focal-EIOU function. J. Terahertz Sci. Electron. Inf. Technol. 20(08), 810–816 (2022). (in Chinese)

Field Application of Switchgear Abnormal Noise Detection Based on Acoustic Imaging Technology Jun Xiong1,2 , Shengya Qiao2(B) , Qiang Pang3 , Hongling Zhou2 , Guangmao Li2 , and Wangwei Ji2 1 School of Electrical Engineering and Automation, Wuhan University, Hubei 430072, China 2 CSG Guangdong Guangzhou Power Supply Bureau, Guangdong 510620, China

[email protected], [email protected] 3 Nanjing Shanghua Power Technology Co., Ltd., Nanjing, China Abstract. In order to realize the non-contact acoustic imaging location and identification of switchgear abnormal noise type, this paper mainly combines three cases of abnormal noise defect caused by mechanical looseness or internal discharge of on-site switchgear, and uses the acoustic imaging method to locate the noise source. At the same time, the time-domain, time-frequency and frequency spectrum characteristics of mechanical looseness and discharge are analyzed. It is obtained that after filtering out the frequency of 10 kHz and below, the waveform shows obvious pulse form in the case of discharge abnormal noise, while the waveform is irregular noise in the case of mechanical looseness. Whether it is mechanical looseness or internal discharge, its energy is mainly concentrated below 2 kHz.For abnormal noise of mechanical looseness, 0–2 kHz energy ratio accounts for more than 99%, 10–20 kHz energy ratio accounts for less than 0.5%, while for abnormal noise of internal continuous stable discharge, 10–20 kHz energy ratio accounts for more than 2%. In this paper, a feasible method is provided for the preliminary identification of abnormal noise defect type through time domain waveform, time-frequency diagram, energy ratio and frequency spectrum diagram. Keywords: Switchgear · abnormal noise · mechanical looseness · partial discharge

1 Introduction Switchgear is an important equipment of power system, it has the characteristics of reliable operation and convenient operation, and it is widely used in distribution network, and its running safety directly affects the power supply reliability of the whole substation [1, 2]. In the process of operation, abnormal noise may be caused by discharge or mechanical looseness. At present, the detection methods mainly include transient earth voltage (TEV), ultrasonic detection, ultra high frequency (UHF) and other methods, which have high accuracy for the location of partial discharge, but cannot directly and quickly display the location of noise source, and the identification effect of mechanical looseness is poor [3–5]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 181–189, 2024. https://doi.org/10.1007/978-981-97-1072-0_18

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At present, acoustic imaging technology has been gradually applied in the power grid, but the research on abnormal noise location and type recognition is mainly focused on transformer and GIS equipment [6–11]. For the acoustic imaging method of switchgear abnormal noise, it is mainly used as noise source location in the research at home and abroad, combined with other testing methods to identify the abnormal noise type, but there is a lack of research on the direct use of acoustic imaging to identify the abnormal noise type, and mainly aimed at the laboratory simulation research, but the research on the on-site practical application is less [12]. Based on the acoustic imaging method, this paper mainly analyzes the time domain, frequency domain and time-frequency diagram of three on-site switchgear abnormal noise cases, and obtains the abnormal noise characteristics, which provides a reference for the field test of the switchgear abnormal noise.

2 Detection Method In this paper, from the viewpoint of time domain and frequency domain, the following eigenvalues are used to analyze the acoustic imaging characteristics of on-site switchgear. 1) The fundamental frequency ratio: The ratio of 100 Hz component amplitude square to the sum of all component amplitude squares. 2) Main frequency: the frequency at which the maximum amplitude in the signal spectrum is located. 3) Main frequency ratio: The ratio of the squared amplitude of the main frequency component to the sum of all component amplitudes. 4) Odd ratio or even ration: The proportion of 50 Hz odd frequency power or 50 Hz even frequency power in the total power. 5) Energy ratio: the ratio of acoustic cumulative power to total acoustic power in 0– 2000 Hz, 2000–10000 Hz, 10000–20000 Hz frequency band. In order to ensure the consistency of the test method, the acoustic imaging characteristics are mainly analyzed when the switchgear door is closed. The 64-channel handheld array acoustic imaging instrument is used on the spot, and the parameters of the acoustic imaging sensor are as shown in the Table 1. Table 1. Eigenvalue result Parameter

Value

Parameter

Value

Signal-noise ratio

65 dB

Sensitivity

−26 dBFS 50 mV/Pa

Response range

10 Hz–24 kHz

Dynamic range

33 dB–120 dB

Range

90 dB SPL

Resolution ratio

24 bits

Response error

±1 dB

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3 On-Site Case Aiming at three cases of abnormal noise caused by mechanical looseness or internal partial discharge in 10 kV switchgear, this paper uses acoustic imaging technology combined with other methods to locate the abnormal noise source, analyze the characteristics of abnormal noise defect and identify the type. 3.1 Case 1-Abnormal Noise of Mechanical Looseness In the process of the inspection, the staff found that there was an obvious audible abnormal noise in the gap between the two switchgears. The switchgear model is PIX12-011 and the production date is September 2008. The field passed the UHF, ultrasonic detection, TEV and acoustic imaging tests, the on-site schematic diagram and result are shown in the Figs. 1, 2, 3 and Table 2, among them, position 1, 2, 3, 4 represents the middle of the switchgear front door, the top, middle and bottom part of the switchgear back door, respectively.

Fig. 1. Schematic diagram Table 2. Test result TEV/dB Position

1

Background value

13

502A

Ultrasonic detection/dBuV 2

3

4

1

3

11

13

14

11

−5

−5

52AC

18

16

15

14

−4

−4

#2 52BC

10

16

15

15

−2

−4

−5

In Fig. 2 and Table 2, through the test results of TEV, ultrasonic detection and UHF, the abnormal noise can be excluded from the partial discharge. In Fig. 3, it can see that the noise source is located at the top of the middle seam of the two switchgears. For the frequency filtering of 10 kHz and below, the original waveform and filtered waveform are obtained as shown in Fig. 4. In Fig. 4, the peak value of the original waveform is 0.0535 Pa, and the waveform has no characteristics. After filtering out the frequency of 10 kHz and below, the peak

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(a) 52AC

(b) 502A

Fig. 2. UHF result

Fig. 3. Acoustic imaging diagram

(a) Original waveform

(b) 0.1s filtered waveform

Fig. 4. Time domain waveform

value is 0.0049 Pa, and the waveform has no pulse. Through acoustic imaging, combined with UHF, TEV, ultrasonic detection and other methods, it is considered that there is no discharge inside the switchgear. At the same time, combined with Fig. 3 and equipment structure, it is considered that the main reason for the abnormal noise is that the insulation between the main bus and the two switchgears is not tightly fixed. In Fig. 5 and Table 3, the main frequency of abnormal noise in the case of mechanical looseness is 100 Hz, accounting for more than 88%, odd ratio is close to 0, and the energy is concentrated below 2 kHz, more than 99%.

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0.01

Amplitude/Pa

0.008 0.006 0.004 0.002 0

0

500

1000

1500

2000

Frequency/Hz

(a) Time-frequency diagram

(b) Frequency spectrum diagram

Fig. 5. Time-frequency and frequency spectrum diagram

Table 3. Eigenvalue result Eigenvalue

Value

Eigenvalue

Value

Fundamental frequency ratio

100 Hz

Main frequency/Hz

88.1%

Main frequency ratio

88.1%

Odd ratio

0.22%

Even ratio

91%

0–2 kHz energy ratio

99.46%

2–10 kHz energy ratio

0.09%

10–20 kHz energy ratio

0.45%

3.2 Case 2-Abnormal Noise of Mechanical Looseness Abnormal noise can be obviously heard in a high-voltage switchgear room, and the approximate area can be judged by human ear auscultation. Figures 6, 7 and Table 4 are obtained by acoustic imaging test.

Fig. 6. Acoustic imaging diagram

In Figs. 6 and 7, the noise source is located at the lower left corner, and there is no high frequency component signal in the time-frequency diagram. The energy is mainly concentrated below 2 kHz, and the dominant frequency of vibration is not an integer multiple of 100 Hz or 50 Hz, the main reason may be acoustic reflection and environmental interference. In Table 4, the energy is concentrated below 2 kHz, accounting for 99.67%, while the proportion of other frequency band is negligible.

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1200

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1600

1800

2000

Frequency/Hz

(a) Time-frequency diagram

(b) Frequency spectrum diagram

Fig. 7. Time-frequency and frequency spectrum diagram

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Value

Eigenvalue

Value

0–2 kHz energy ratio

99.67%

2–10 kHz energy ratio

0.22%

10–20 kHz energy ratio

0.11%

10

2

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Filtered waveform

Original waveform

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Amplitude/Pa

Amplitude/Pa

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0

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(b) 0.1s filtered waveform

Fig. 8. Time domain waveform

In Fig. 8, the original waveform has no obvious law. After filtering out the frequency of 10 kHz and below, the filtered waveform is also irregular. Open the switchgear door on the spot and identify the noise source location as shown in Fig. 9 (a). After using the rod to support the noise source position, the test result is shown in Fig. 9 (b). It can be seen that the noise source has disappeared, indicating that the abnormal noise is caused by the looseness of the screws at this position. 3.3 Case 3-Abnormal Noise of Internal Discharge The switchgear has a continuous and stable abnormal noise during operation. The acoustic imaging positioning device is used to test the switchgear on the spot, and its acoustic imaging diagram, time-frequency diagram and time-domain waveform are obtained as shown in the Figs. 10, 11, 12 and Table 5. In Fig. 10, the noise source can be clearly located in the middle of the front of the switchgear. In Fig. 11, the main energy is still below 2000 Hz, but there are obvious high

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(a) The rod is not in support

187

(b) The rod is in support

Fig. 9. Acoustic imaging diagram

Fig. 10. Acoustic imaging diagram 0.01

0.008

Amplitude/Pa

0.006

0.004

0.002

0 0

200

400

600

800

1000

1200

1400

1600

1800

2000

Frequency/Hz

(a) Time-frequency diagram

(b) Frequency spectrum diagram

Fig. 11. Time-frequency and frequency spectrum diagram Table 5. Eigenvalue result Eigenvalue

Value

Eigenvalue

Value

0–2 kHz energy ratio

95.39%

2–10 kHz energy ratio

2.02%

10–20 kHz energy ratio

2.58%

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frequency components, and the frequency is between 12–14 kHz. The main frequency is less than 100 Hz, and the frequency is mainly concentrated below 100Hz, which may be due to the indoor sound reflection of the switchgear, indicating that for the abnormal noise judgment, the abnormal noise type cannot be effectively identified only by the frequency spectrum diagram. In Table 5, the proportion of 0–2 kHz energy decreases to 95.39%, while that of 2–10 kHz, 10–20 kHz increases to 2.02% and 2.58%, respectively.

(a) Original waveform

(b) 0.1s filtered waveform

Fig. 12. Time domain waveform

In Fig. 12, for the original waveform, there is no obvious law, and the peak value is 0.15 Pa. After filtering out the frequency of 10 kHz and below, it can see that there is an obvious discharge pulse waveform, the peak value is 0.013 Pa, and the discharge period is 20 ms, which indicates that the interior may be corona discharge. Combined with Table 5, when the internal continuous stable discharge, the proportion of 10–20 kHz energy will exceed 2.58%, and there is a clear high frequency component.

4 Conclusion In this paper, through the analysis of three cases of acoustic imaging detection of switchgear abnormal noise, the following conclusions are drawn: 1) For the abnormal noise of switchgear discharge, there are obvious discharge pulses in the time domain waveform above 10 kHz frequency, and 10–20 kHz energy ratio accounts for more than 2%, which is far more than the case of mechanical looseness, At the same time, there is obvious 12–14 kHz energy in the time-frequency diagram; 2) For the abnormal noise of the switchgear mechanical looseness, the time domain waveform above 10 kHz frequency has no obvious characteristics, and the waveform is irregular noise, and its energy is mainly concentrated below 2 kHz, more than 99%, at the same time, the 10–20 kHz energy ratio is less than 0.5%.

References 1. Dong, P., Yang, X., Yang, P.F., et al.: Improve method the safety performance of 10kV high voltage switchgear. Trans. China Electrotech. Soc. 37(11), 2733–2742 (2022). (in Chinese)

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2. Hu, J.L., Lai, J.J., Li, Y.Y., et al.: Evaluation method of switchgear insulation state based on adaptive density based spatial clustering of applications with noise algorithm. Trans. China Electrotech. Soc. 36(S1), 344–352 (2021). (in Chinese) 3. Ren, M., Peng, H.D., Tao, X.Q., et al.: Comprehensive detection of partial discharge in switchgear using TEV. High Volt. Eng. 36(10), 2460–2466 (2010). (in Chinese) 4. Zheng, J., Zhang, J., Yang, F.D., et al.: Research on imaging technology of ultrasonic echo applied to live detection of switchgear insulation defects. In: 2022 12th International Conference on Power, Energy and Electrical Engineering (CPEEE), pp. 27–33. IEEE (2022) 5. Montanari, G.C., Ghosh, R., Cirioni, L., et al.: Partial discharge monitoring of medium voltage switchgears: self-condition assessment using an embedded bushing sensor. IEEE Trans. Power Delivery 37(1), 85–92 (2021) 6. Shao, Y.Y., Wang, X., Peng, P., et al.: Research on defect detection method of power equipment based on acoustic imaging technology. China Meas. Test 47(07), 42–48 (2021). (in Chinese) 7. Li, X.G., Wu, X.T., Shi, Y.H., et al.: Charged detection system of GIS mechanical fault based on the acoustical imaging. High Volt. Apparatus 55(05), 42–46 (2019). (in Chinese) 8. Si, W.R., Fu, C.Z., Xu, P., et al.: Research on loose detection of transformer core based on acoustic imaging and image processing. High Volt. Apparatus 57(11), 180–186 (2021). (in Chinese) 9. Lin, Q., Yang, J.J., Xu, Z.T., et al.: Modeling and structural optimization of acoustic imaging sensor unit for detecting abnormal noises of dry-type transformer. In: 2021 International Conference on Power System Technology (POWERCON), pp. 2388–2392 (2021) 10. Zhao, L., Wang, S., Yang, Y., et al.: Detection and rapid positioning of abnormal noise of GIS based on acoustic imaging technology. In: The 10th Renewable Power Generation Conference (RPG 2021), pp. 653–657 (2021) 11. Xiong, Q., Zhao, J., Guo, Z., et al.: Mechanical defects diagnosis for gas insulated switchgear using acoustic imaging approach. Appl. Acoust.Acoust. 174, 107784 (2021) 12. Xiu, Z., Jin, B., Lei, C., et al.: Location and analysis of an intermittent discharge fault of switchgear. In: 2023 8th Asia Conference on Power and Electrical Engineering (ACPEE), pp. 2150–2154. IEEE (2023)

Compensation Capacitor Status Monitoring Research Based on Feature Fusion and SVM Jianqiang Shi1,2(B) , Youpeng Zhang1 , and Guangwu Chen1,2 1 School of Automation and Electrical Engineering, Lanzhou Jiaotong University,

Lanzhou 730070, China [email protected], [email protected] 2 Key Laboratory of Gansu Province High Altitude Traffic Information Engineering and Control, Lanzhou Jiaotong University, Lanzhou 730070, China

Abstract. In order to meet the needs of railway electrical departments for “state repair” of track circuit compensation capacitors and timely and effective monitoring of compensation capacitor status, this paper proposes a new method that combines the feature quantities decomposed from CEEMD and LMD algorithms and utilizes support vector machines for compensation capacitor status monitoring. Firstly, a ZPW-2000A track circuit model is established using KCL, KVL, and transmission line theory. By changing the capacitance value of the compensation capacitor, the shunt current curves of the compensation capacitor in each state are simulated. Then, the shunt current curves are decomposed into each order component using CEEMD and LMD, and fuzzy entropy is calculated and combined into a new feature vector. Finally, it is input into a trained multi-class SVM model for state monitoring. The experimental results show that the accuracy of compensating capacitor state monitoring is improved to 91% for a single decomposed feature after fusion. Keywords: Compensation Capacitance · Status Monitoring · CEEMD · Fuzzy Entropy · SVM

1 Introduction As the rapid development of high-speed railways, ensuring the safe operation of trains is the primary task. As one of the key signaling equipment, track circuits play a crucial role in ensuring the safe operation of trains. Compensation capacitors are an important component of track circuits, used to make the transmission effects of track circuits tend to be resistive and balance the high inductance of the rail. In the adjustment state, a fault in the compensation capacitor will cause a red light band; In the shunting state, compensating capacitor faults can cause the train to "drop code" and endanger the safety of train operation. Compensation capacitor faults mainly include wire breakage and capacity decrease, which belong to progressive faults. The greater the capacity decrease, the greater the impact on the train. The current inspection method for compensating capacitors in the electrical department is to use regular inspections by electrical inspection © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 190–197, 2024. https://doi.org/10.1007/978-981-97-1072-0_19

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vehicles, which cannot detect faults in compensating capacitors in a timely manner within the interval between inspections. Compensation capacitor state monitoring is a prerequisite for achieving the transition from “regular maintenance” and “fault maintenance” to “state maintenance” of track circuits. Therefore, it is necessary to conduct state monitoring research on compensating capacitors, and a large number of scholars at home and abroad have conducted extensive research on fault diagnosis and capacitance estimation of compensating capacitors. In foreign countries, reference [1] proposed a method for detecting compensation capacitor faults based on partial least squares regression, neural networks, and transfer confidence models. Reference [2] proposes compensation capacitor fault detection based on Dempster Shafer evidence fusion theory and trend analysis. Reference [3] proposed a life prediction method for ZPW-2000A track circuits based on support vector data description and grey prediction. Reference [4] proposes a neural network-based fault diagnosis method for track circuit tuning regions, which achieves the extraction of induced voltage amplitude envelope features. In China, Sun Shangpeng et al. proposed using the phase space reconstruction theory to process the shunt current curve, obtain a pseudo phase diagram, and extract the characteristics of compensating capacitor faults [5]. Zhao Linhai et al. used simulation to fit the induced voltage curve with the actual data curve trend, and used genetic algorithm to search for capacitance parameters to estimate the compensation capacitance value [6]. Meng Jinghui extracted the attenuation coefficient, fluctuation coefficient, and correlation coefficient characteristics of the induced voltage curve through linear fitting, and transformed them into a trend chart to monitor the compensation capacitor status through trend changes [7]. Feng Dong estimated the capacitance value of the compensation capacitor by calculating the area under the induced voltage curve corresponding to different capacitance values, analyzing the corresponding relationship between the capacitance value of the compensation capacitor and the induced voltage curve [8]. Zhang Youpeng constructed a knowledge base through fuzzy qualitative trend analysis of the shunt current curve, calculated the matching degree between the actual signal and the knowledge base, and achieved fault diagnosis of the compensation capacitance and tuning area of the track circuit [9].Jiao Meimei et al. proposed a genetic algorithm optimized variational mode decomposition based fault feature extraction method with envelope entropy as the optimization objective [10]. Lin Junting et al. proposed a deep confidence network and ocean predator algorithm optimized least squares support vector machine fault diagnosis method [11]. Yu Xiaoying et al. proposed a diagnosis strategy based on evidence fusion using three methods: grey correlation analysis, fuzzy comprehensive evaluation, and backpropagation neural network, to compensate for the shortcomings of a single fault diagnosis method [12]. Chen Guangwu et al. combined simulated annealing algorithm with particle swarm least squares support vector machine to overcome the problems of low accuracy and unstable diagnostic results in track circuit fault diagnosis[13].This article proposes to fuse the results of two different time-frequency decomposition methods into a new set of feature vectors, establish a multi classification SVM model for compensating capacitor state monitoring, and achieve compensating capacitor state monitoring.

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2 Modeling the Amplitude Envelope of Shunt Current 2.1 Main Track Modeling The jointless track circuit consists of the main track and the tuning area. The transmitter signal is sent to both ends of the main track and tuning area through a transmission cable. The signal in the main track section is compensated by a capacitor and reaches the main track receiver. When the train passes through the track circuit, a corresponding short-circuit current is formed at the first wheelset of the train. Assuming that the location of the train passing through the current section’s branching point is x, according to literature [4], the branching circuit signal can be expressed as: Us  (1) I(x) =  N11 (x)Rf + N12 (x) In Eq. (1): Us is the amplitude of the frequency shift signal output by the transmitter, Rf is the equivalent shunt resistance of the train, N11 (x) and N12 (x) is the parameters of the equivalent two-port network for the transmission characteristics between the transmitter and the train shunt point x.   N11 (x) N12 (x) N(x) = (2) = Np × Nt × Ng (x) N21 (x) N22 (x) The equivalent transmission matrix of the compensation capacitor two-port network is as follows:   1 0 Nc = (3) j2π fC 1 By modifying the size of compensation capacitor capacitance C in formula (3), simulate the shunt current curves under different compensation capacitor capacitance states, and obtain the required fault data. 2.2 Main Track Modeling According to the jointless track circuit adjustment table, the corresponding simulation parameters are set using the same simulation conditions as reference [8]: track circuit signal carrier frequency fc = 2600 Hz, track circuit length lg = 1099 m, number of compensation capacitors nc = 11, standard capacitance value of compensation capacitors Cv = 40 µF, ballast resistance rd = 1.5  · km, and shunt resistance Rf = 0.15 . This article selects a C6 compensation capacitor, and the normalized simulation results for the shunt current curves of C6 with different capacitance values are shown in Fig. 1. Under different capacitance states of compensating capacitor C6, the decay trend of the shunt current curve at C6 position increases with the increase of capacitance decrease. The amplitude change of the shunt current is between the normal compensation capacitor and the broken compensation capacitor, and the curve fluctuates greatly. Features can be extracted from the curve as a basis for monitoring the status of the compensation capacitor.

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Fig. 1. Shunt current curve of compensation capacitor C6 in different states

3 Feature Extraction of Shunt Current Curve 3.1 CEEMD Algorithm CEEMD involves adding a pair of positive and negative Gaussian white noise sequences to the original signal to form two sets of signals to be decomposed. The two sets of signals are then EMD decomposed to obtain a series of IMF components and residual components with different feature information [14]. 3.2 LMD Algorithm LMD local mean decomposition is an adaptive time-frequency analysis method. For a signal, local mean decomposition can decompose it into a series of physically significant PF components, each of which is a single component amplitude modulation frequency signal obtained by multiplying an envelope signal and a pure frequency modulation signal[15]. 3.3 Fuzzy Entropy The fuzzy entropy algorithm is an improvement on the sample entropy algorithm, which uses the fuzzy membership function to calculate the similarity between two vectors and to some extent improves the anti-interference ability of the original signal.

4 Multi Classification SVM Compensation Capacitor Status Monitoring 4.1 Feature Fusion Based on the CEEMD algorithm, the shunt current signal is decomposed to obtain IMF components of different orders, and fuzzy entropy is calculated for each IMF component of different orders. Using the LMD algorithm to decompose the shunt current signal, obtain PF quantities with different physical meanings, and sequentially calculate fuzzy entropy for the PF components. Extract the fuzzy entropy as the feature vector, and combine two different decomposition methods to obtain a new set of feature vectors based on the fuzzy entropy, which serves as the feature quantity for compensating the capacitor state.

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4.2 SVM Principle Support vector machine is a binary classification model, whose main idea is to establish a hyperplane, so that the greater the "distance" between data points and the hyperplane, the greater the confidence of classification. Support vector machines have the advantage of strong generalization ability in solving small sample, nonlinear, and high-dimensional data models. 4.3 Multi-class SVM Multi-class SVM considers multi classification as multiple binary classifications, using the SVM classification model multiple times. For example, in an N-classification problem, first select one class as a positive class and the other N-1 classes as negative classes. After the first SVM classification, select another positive class from the remaining N-1 classes and cycle multiple times until all classes are separated. The multi classification SVM structure is similar to a binary tree. In this paper, the state of compensation capacitors is selected into 5 categories. By training the SVM model with the fused feature vectors, the state monitoring of compensation capacitors is achieved.

5 Experimental Analysis and Results Simulate the main track model of the track circuit using MATLAB, and based on the compensation capacitor C6 standard capacitance value 40 µF, simulate 100 branch current data in decreasing steps of 0.4 µF. This data serves as the raw data to verify the feasibility and accuracy of the proposed method in this article. The compensation capacitor state is divided into 5 states, which will be represented by numbers 1–5. Annotate and label 100 simulation data to prepare for subsequent training of multi classification SVM models. Randomly shuffle the annotated 100 pieces of data, select 65 pieces of data as training sample data, and use the remaining data as the testing model. Select the CEEMD decomposition results of the shunt current data with normal compensation capacitance and a decrease in capacitance value to 12 µF as a comparison. Table 1. Correlation coefficient between IMF component and original signal.

Correlation coefficient

IMF2

IMF3

IMF4

IMF5

IMF6

0.0282

0.0913

0.2597

0.1331

0.2408

Obtain the correlation coefficients between each IMF component and the original signal after CEEMD decomposition, and screen the components. Taking the abnormal signal of compensation capacitance (capacitance 12 µF) as an example, the correlation coefficient calculation results are shown in Table 1. Perform LMD decomposition on the shunt current to obtain 2 PF components, and still select the LMD decomposition results of the shunt current data with normal compensation capacitor capacitance and a decrease in capacitance to 12 µF as a comparison.

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Calculate the fuzzy entropy of IMF components (IMF4, IMF5, IMF6) filtered through CEEMD decomposition and PF1 and PF2 components decomposed through LMD. In the process of calculating fuzzy entropy, the spatial dimension is set to 2, and the similarity tolerance limit is 0.2 times the standard deviation of the original signal. List the fuzzy entropy values of the decomposed components corresponding to the five states of the compensation capacitor. FuzzyEn1-FuzzyEn3 is the fuzzy entropy value calculated by the IMF component, and FuzzyEn4-FuzzyEn5 is the fuzzy entropy value calculated by the PF component, as shown in Table 2. Table 2. The fuzzy entropy of components is obtained by decomposition. Capacitive state

FuzzyEn1

FuzzyEn2

FuzzyEn3

FuzzyEn4

FuzzyEn5

1

0.1267

1.0948

1.1513

0.1085

0.0863

2

0.1243

1.0854

1.1213

0.1079

0.0945

3

0.1176

1.0687

1.0901

0.0921

0.4500

4

0.1126

1.0262

1.0661

0.0783

0.4368

5

0.1070

0.9816

1.0431

0.0616

0.3347

As shown in Fig. 2, the results of the multi classification SVM test are shown. The vertical axis numbers 1–5 represent five states of the compensation capacitor throughout its entire lifecycle. This test effectively monitored the normal state, broken line s-state, and moderate capacitance decrease state of the compensation capacitor. The predicted and true samples in the mild capacitance decrease state and severe capacitance decrease state of the compensation capacitor were different, with a classification accuracy of 91.43%, which effectively achieved the monitoring of the compensation capacitor state.

Fig. 2. Multi-class results of compensation capacitor state

Select CEEMD and fuzzy entropy, LMD and fuzzy entropy, CEEMD_ Comparison of the accuracy of multi classification SVM under three different methods of feature extraction using LMD and fuzzy entropy feature fusion. As shown in Table 3, the

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CEEMD selected in this article_ The LMD and fuzzy entropy feature extraction methods have significantly improved the recognition of compensating capacitor states in multi classification SVM models. Table 3. Accuracy comparison of various methods. Feature Vector Extraction Method

Method for monitoring the state of compensating capacitor

Accuracy

CEEMD and fuzzy entropy

Multi-class SVM

88.57%

LMD and fuzzy entropy

Multi-class SVM

85.71%

CEEMD_ LMD fuzzy entropy fusion

Multi-class SVM

91.43%

6 Conclusion This article analyzes the influence of different compensation capacitor capacitance states on the curve based on the shunt current curve of the track circuit. Through the degree of curve difference, it is proposed to use the components obtained from CEEMD and LMD decomposition algorithms to calculate fuzzy entropy separately. The fuzzy entropy is combined into a new feature vector, which is input into a multi classification SVM model to achieve state monitoring of the compensation capacitor. Simulation experiments have shown that this method can effectively monitor the state of compensating capacitors with an accuracy of 91.4%. It can provide a good theoretical basis for the implementation of equipment "state repair" in the electrical department and improve maintenance efficiency. Acknowledgments. This research was funded by the Gansu Provincial Science and Technology Plan Project (21ZD4WA018, 22YF7GA140) and by the National Railway Group Science and Technology Plan Project (N2023G064).

References 1. Debiolles, A., Oukhellou, L., Aknin, P.: Combined use of partial least squares regression and neural network for diagnosis tasks. In: 17th International Conference on Pattern Recognition on Proceedings, pp. 573–576. IEEE Computer Society, New York (2004) 2. Debiolles, A., Denoeux, T., Oukhellou, L., et al.: Output coding of spatially dependent subclassifiers in evidential framework. Application to the diagnosis of railway track/vehicle transmission system. In: 9th International Conference on Information Fusion on Proceedings, pp. 1–6. IEEE, New York (2006) 3. Wang, R., Jia, N.: Life prediction of ZPW-2000A track circuit equipment based on SVDD and gray prediction. J. Meas. Sci. Instrum. 9(4), 373–379 (2018) 4. Zhao, L.-H., Zhang, C.-L., et al.: A fault diagnosis method for the tuning area of jointless track circuits based on a neural network. Proc. Inst. Mech. Eng. Part J. Rall Rapid Transit. 227(4), 333–343 (2013)

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5. Sun, S., Zhao, H.: Fault detection method for compensating capacitors in jointless track circuits based on phase space reconstruction. J. China Railway Soc. 34(10), 79–84 (2012). (in Chinese) 6. Zhao, L., et al.: A comprehensive fault diagnosis method for jointless track circuits based on genetic algorithm. China Railway Sci. 31(03), 107–114 (2010). (in Chinese) 7. Meng, J., Xie, B., Gao, L.: Transmission characteristics of interval track circuits based on linear fitting. China Railway Sci. 32(01), 112–117 (2011). (in Chinese) 8. Feng, D., Zhao, L.: Estimation method of JTC compensation capacitance based on TCR monitoring data. J. China Railway Soc. 38(02), 89–95 (2016). (in Chinese) 9. Zhang, Y., et al.: JTC comprehensive fault diagnosis method based on fuzzy qualitative trend analysis. J. Chongqing Univ. 42(03), 65–75 (2019). (in Chinese) 10. Jiao, M., Shi, L., et al.: Feature extraction of tuning zone and compensation capacitor faults in uninsulated track circuits based on GA-VMD. J. Beijing Jiaotong Univ. 47(03), 149–158 (2023). (in Chinese) 11. Lin, J., Wang, S.: Research on fault diagnosis of jointless track circuit based on DBN-MPALSSVM. J. Electron. Meas. Instrum. 36(09), 37–44 (2022). (in Chinese) 12. Yu, X., Dong, Y., Dong, Y.: Track circuit fault diagnosis based on multi method evidence fusion. J. China Railway Soc. 43(02), 86–94 (2021). (in Chinese) 13. Chen, G., et al.: Track circuit fault diagnosis based on adaptive mutation SAPSO-LSSVM. J. Beijing Jiaotong Univ. 45(02), 1–7 (2021). (in Chinese) 14. Zhang, Y., Zhang, Y.: Fault feature extraction in the tuning zone of jointless track circuits based on CEEMD. J. Railway Sci. Eng. 15(09), 2385–2393 (2018). (in Chinese) 15. Zhang, X., et al.: EEG signal feature extraction method based on LMD and fuzzy entropy fusion CSP. Chin. J. Sci. Instrum. 41(08), 226–234 (2020). (in Chinese)

Study on Acid Thermal Aging Characteristics of Composite Insulator Core Rod Material Based on TGA and SEM Dandan Zhang1,2,3(B) , Yuwei You1,2,3 , Wenwu Pan1,2,3,4 , Ming Lu5 , and Chao Gao5 1 School of Electrical and Electronic Engineering, Huazhong University of Science and

Technology, Wuhan 430074, China [email protected] 2 Key Laboratory of Pulsed Power Technology Ministry of Education, Huazhong University of Science and Technology, Wuhan 430074, China 3 State Key Laboratory of Strong Electromagnetic Engineering and New Technology, Huazhong University of Science and Technology, Wuhan 430074, China 4 Jiaxing Power Supply Company, State Grid Zhejiang Electric Power Co. Ltd., Jiaxing 314000, China 5 Henan Key Laboratory of Power Transmission Line Galloping Prevention and Control Technology, State Grid Henan Electric Power Research Institute, Zhengzhou 450052, China

Abstract. In recent years, a novel “decay-like fracture” has emerged in China’s transmission line composite insulators, posing risks to safe operation. These insulators encounter combined acid, heat, and water effects during use. Research mainly focuses on heat or acid, not reflecting actual external stresses on composite insulators. Hence, this study considers acid, heat, and water, conducting vacuum and acid thermal aging tests on bisphenol An epoxy resin. TGA and SEM analyze degraded samples. Findings show similar reaction mechanisms in intact epoxy resin at different heating rates. Changes minimally affect mass loss, keeping reaction mechanism stable. Acid thermal aging reduces activation energy, lowering the “threshold” for thermal stress erosion, degrading epoxy resin at lower temps. High-temp vacuum aging and low-temp acid aging form bubbles on epoxy resin, resembling decay. This explains minor temp rises yet severe epoxy resin degradation in decayed insulators. Keywords: Composite insulator · Epoxy resin · Vacuum thermal aging · Acid thermal aging · Activation energy

1 Introduction In recent years, a new form of fracture of composite insulators termed “decay-like fracture” has emerged, which is a threat to the stable operation of the power grid. Decaylike fractures result from the combined effects of moisture, discharge, current, acidic medium, and mechanical stress [1, 2]. The core rod is a composite material, primarily epoxy resin and glass fiber. The glass fiber is stable. Hence, the pivotal aspect in studying decay-like composite insulators lies © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 198–206, 2024. https://doi.org/10.1007/978-981-97-1072-0_20

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in the examination of epoxy resin degradation. The actual decay-like insulators generally have abnormal heating. Cai conducted a study on vacuum thermal aging of the core rod and found that after thermal degradation, the surface of the core rod exposed glass fibers, with a maximum exposure level of up to 80% [3]. Secondly, the aging research of core rod materials with moisture participation mainly focuses on hot and humid aging and acid aging at room temperature. Wang conducted wet-heat cyclic aging on epoxy resin and analyzed its macro and micro-level mechanical properties [4]. Shen performed Thermogravimetric Analysis (TGA) on the acid-aged core rods, indicating a reduction in epoxy resin content with higher nitric acid concentration [5]. Derek used PY-GC-MS to investigate the degradation mechanism of different epoxies and their copolymers [6]. Pang conducted an electrical erosion test in an acidfog environment and analyzed the core rod’s macroscopic results and physicochemical properties [7].In summary, current research mainly focuses on wet and thermal aging of core rod and epoxy resin, examining morphology pre- and post-aging. Limited study on cured epoxy resin under acid and heat conditions, differing from actual composite insulator stress. Regarding core rod pyrolysis, scholars employ TGA, but quantitative thermal stability analysis is lacking. Based on the above analysis, core rod degradation is primarily attributed to epoxy resin aging. To replicate early-stage heat impact and later-stage effects of acid, water, and heat on epoxy resin deterioration, an experimental setup for bisphenol A cured epoxy resin aging was established. Vacuum and acid aging experiments were conducted, considering aging traits of epoxy resin under acid, heat, and water conditions. Samples post-aging were analyzed via TGA and SEM for quantitative pyrolysis traits. Changes in activation energy and microstructure of cured epoxy resin after aging were compared and analyzed. This study forms the basis for understanding the mechanism behind core rod decay-like fracture.

2 Samples and Experimental Methods 2.1 Experimental Procedure This study focused on bisphenol A epoxy resin provided by a core rod manufacturer, cured at 120 °C. Circular epoxy resin sheets (28 mm diameter, 2 mm thickness) were prepared. Epoxy resin sheets were uniformly heated in a tube furnace to ensure consistent sample heating. A setup using a grinding flask containing nitric acid was established. The sample was immersed in the nitric acid solution, while the bottom of the flask was heated by a sealed electric furnace. A condensation tube, preventing nitric acid decomposition, was fitted at the top. Epoxy resin degradation initiates at 300 °C [3]. Vacuum thermal aging conducted at temperatures: 200 °C, 240 °C, 280 °C, 300 °C, 340 °C, and 380 °C, each for 1, 2, 3, and 5 h. Acid thermal aging was performed at room temperature, 60 °C, and 80 °C, with nitric acid concentrations of 1M, 3M, and 5M. Samples were immersed for 288 h (12 days), with retrieval every 48 h (2 days) for time efficiency. The thermogravimetric experiment of epoxy resin was carried out by analyzer (Pyris 1 TGA). The carrier gas was high purity nitrogen, the heating rate was 10 K/min,

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15 K/min, 20 K/min and 25 K/min, and the temperature range was from room temperature to 800 °C.

3 Model and Calculation of Activation Energy Core rod aging primarily involves epoxy resin degradation and chemical reactions. Kinetic parameters like activation energy, chemical reaction mechanism function, and pre-exponential factor can characterize the aging state. Activation energy signifies reaction difficulty and represents the minimum energy required. Higher activation energy implies a faster reaction rate. Lower activation energy means reactant molecules are more likely to overcome energy barriers, facilitating reactions. Lower epoxy resin activation energy indicates higher susceptibility to deterioration and a faster reaction rate. The Arenius equation, using TG and DTG curves at varying heating rates, helps obtain sample activation energy in thermogravimetric experiments. The reaction kinetics equation of solid state reaction heterogeneous system suitable for epoxy resin material can be expressed as formula (1) under non-Isothermal conditions [8, 9]: A dα = f (α) exp(−E/RT ) dT β f (α) =

(1)

1 1 = G  (α) d [G(α)]/d α

(2)

In this formula, α is the conversion of the sample,%; T is the absolute temperature of the reaction, K; A refers to the pre-factor; β is the heating rate, K/min; and f (α)is the differential and G(α) is integral form of the reaction mechanism function; E is the activation energy, kJ/mol; R is the general gas constant, R = 8.314 × 10−3 kJ/mol. The formula (1) can be solved by Kissinger method and Flynn-Wall-Ozawa method. Compared with Kissinger method, Flynn-Wall-Ozawa method does not need to assume the mechanism function of chemical reaction in advance to calculate the activation energy E of chemical reaction, so this paper uses Flynn-Wall-Ozawa method to solve the problem. First of all, order: E RT

u= From T =

E Ru ,

(3)

you can get the following formula: dT = −

E du Ru2

(4)

By transforming formula (1) into (2)–(4), we can get: A G(α) = β



T 0

AE E )dT = exp(− RT βR



u −∞

−e−u AE du = u2 βR



+∞ E RT

e−u AE · P(u) du = u2 βR (5)

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Because the ratio of E ≤ R is constant, the integral problem of temperature becomes  u −u the problem of finding functions. The Doyle approximate formula P(u) = ∞ −eu2 du expresses the approximate relationship between activation energy E and P (u). The expression is as follows: ln PD (u) = −2.315 − 0.4567

E RT

(6)

The pyrolysis kinetics equation of Flynn-Wall-Ozawa can be obtained by combining vertical (5) and formula (6) [10]: lg β = lg(

E AE ) − 2.315 − 0.4567 RG(α) RT

(7)

At different heating rates β, if the intact epoxy resin is at the peak temperature, T p The conversion of the sample is approximately equal, that is, G (α) is a constant value, so lg β and 1/1 /T p The activation energy E of the sample can be obtained by linear relationship.

4 Experimental Results and Discussion 4.1 Thermogravimetric Analysis The thermogravimetric curve (TG) and its first order differential curve (DTG) of intact epoxy resin at different heating rates are shown in Fig. 1. DTG curve reflects the weightlessness rate of the sample.

Residual mass(%)

10K/min 15K/min 20K/min 25K/min

80 60 40 20

Weight loss rate(%/°C)

2.0

100

10K/min 15K/min 20K/min 25K/min

1.5

1.0

0.5

0.0

0 0

100

200

300

400

500

600

Aging Temperature(°C)

(a) TG curve

700

800

100

200

300

400

500

600

Aging Temperature(

700

800

)

(b) DTG curve

Fig. 1. A figure caption is always placed below the illustration. Short captions are centered, while long ones are justified. The macro button chooses the correct format automatically.

Figure 1(a) TG curve shows conversion rate at different heating rates is nearly uniform. Figure 1(b) DTG curve shows weight loss rate of epoxy resin sharply rises at 300 °C, indicating onset of vigorous decomposition. The initial mass serves as the base point, setting the residual mass ratio at 100%. Deviation from this ratio marks the initial decomposition temperature, and the temperature of maximum weight loss signifies termination decomposition. In Fig. 1(b), T p represents the peak temperature where maximum weight loss rate is attained.

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With rising heating rate, TG and DTG curves shift rightward, indicating increased temperatures for epoxy resin’s initial decomposition, termination decomposition, and T p . This is attributed to the heat transfer process in TGA. As the Al2 O3 crucible’s overall temperature climbs, it creates a temperature difference with the epoxy resin. Higher heating rates intensify this effect, resulting in a rightward curve shift [11, 12]. Additionally, TG curves at varying heating rates exhibit similarity, with comparable T p . This indicates a consistent reaction mechanism function for epoxy resin within this temperature range. Although altering heating rates impacts material reaction rates, potentially leading to distinct reaction paths and products, when TG curves obtained under different heating rates are similar, it suggests that, in this temperature range, changes in reaction rate have a relatively minor impact on material mass loss. The reaction mechanism function remains relatively stable. 4.2 Activation Energy Analysis At different heating rates, lg β is taken as the longitudinal coordinate and the reciprocal of the peak temperature is 1/1.T p For transverse coordinates, the least square method is used to fit the data in Fig. 1. The fitting results are shown in Fig. 2, and the fitting formula (8) is as follows: lg β = −5278.90599

1 + 8.87106 Tp

(8)

lg

The correlation coefficient of fitting straight line is 0.81773, which indicates that lg β and 1/1 /T p There is a strong linear correlation. The slope of the straight line in Fig. 3 is-5278.9060. By comparing formula (7) and formula (8), the activation energy of the intact epoxy resin can be calculated to be 96.1 kJ/mol.

1/ Tp (1/ K)

Fig. 2. Fitting curve of intact epoxy resin

The activation energy of epoxy resin after vacuum thermal aging with different heating time and temperature was obtained by the same method, as shown in Fig. 3. In Fig. 3(a), As time increases, the activation energy of epoxy resin first decreases, then rises, and finally decreases again. The initial drop in epoxy resin’s activation energy is mainly due to initial polymers undergoing post-curing reactions from heat exposure. This leads to increased epoxy resin polymerization, resulting in subsequently lower

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activation energy. The final drop indicates the reduce of the polar particles and free radicals, resulting in a shallower trap depth and decreased activation energy. This may not be advantageous for the actual operation of composite insulators, which implies decreased energy for epoxy resin’s chemical reactions in the core rod, making it more susceptible to thermal stress erosion, consequently accelerating the aging process [13]. 145 190.71

Activation energy(kJ/mol)

Activation energy(kJ/mol)

200 180 160 140

137.00 134.156

120 100

96.10 93.04

80

0

1

2

3

4

5

141.40 140 135

132.60 134.16

130 125 120

118.87

115

240

Aging time(d)

260

280

300

Aging temperature(

320

340

)

(a) Under different degradation time at 280

(b) Under different heating temperatures

°C

at 5h

Fig. 3. Activation energy results of vacuum thermal aging

In Fig. 3(b), epoxy resin’s activation energy varies initially decreasing then increasing. Epoxy resin’s activation energy drops at 240 °C due to curing reaction. Beyond 300 °C, violent decomposition occurs, leading to the emergence of polar particles and free radicals, which readily adsorb other polar particles. 100 84.79

80

65.12

60 40

23.45

20 0

22.49

0

50

100

150

200

250

300

Aging time (h)

(a) Under different aging time at 80 °C-3 mol/L

90

100 96.10

Activation energy (kJ/mol)

96.10

Activation energy(kJ/mol)

Activation energy (kJ/mol)

100

89.32

80

76.86

70 60 50 40 30

25.59

20 10 0

96.1

90 82.41

80 70 60 50

46.86

40 30 22.49

20 0

1

2

3

4

5

Intact

Nitric acid(mol/L)

(b) Under different nitric acid concentrations at 60 °C-12 d

25

60

80

Aging temperature (°C)

(c) Under different aging temperature at 3 mol/L-12 d

Fig. 4. Activation energy results of acid thermal aging

Similarly, the activation energy of epoxy resin post-acid thermal aging can be determined, as depicted in Fig. 4. This figure illustrates a decrease in epoxy resin’s activation energy with rising aging time, nitric acid concentration, and aging temperature. This suggests that epoxy resin is more susceptible to chemical reactions with heightened levels of acid and thermal aging. In the vacuum aging, the lowest activation energy for epoxy resin is about 300 °C. Compared to acid aging, epoxy resin has lower activation energy at lower temps. This

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indicates that the combination of acid, heat, and water lowers the aging threshold for epoxy resin, enabling aging at lower temperatures. This indicates that even if the temperature rise is not very high, the combined action of acid and water, among other factors, can lower the activation energy of epoxy resin, potentially leading to degradation of the epoxy resin in the core rod. 4.3 Microscopic Morphology Analysis The SEM observation of epoxy resin after vacuum thermal aging and acid thermal aging is shown in Fig. 5. Before 300 °C, the surface of epoxy resin showed minimal change. At 300 °C, violent decomposition occurred, resulting in numerous bubbles and pores after only 3 h of heating. Due to thermal stress, the newly exposed epoxy resin began to pyrolyze after the surface layer fell off, leading to the formation of small bubbles. Additionally, uneven stress distribution caused some cracking in the epoxy resin.

Fig. 5. Comparison of SEM test results of epoxy resin in intact, different deterioration conditions and actual decaying insulators

At 60 °C, with a concentration of 3 mol/L, and a duration of 12 days, the bubble structure on the surface of epoxy resin resembled that seen in vacuum thermal aging at 300 °C. This indicates that, under acid thermal aging conditions, epoxy resin also produces gas, aligning with the morphology characteristics of “decay” to some extent. This reaffirms that with the addition of acid, the activation energy for epoxy resin chemical reaction is lower than with heat alone, facilitating easier deterioration reactions. This also explains why actual “decay” composite insulators experience only a slight temperature rise but significant epoxy resin degradation.

5 Conclusion In this paper, the thermogravimetric test and calculation of bisphenol A epoxy resin after vacuum thermal aging and acid thermal aging were carried out, and the following conclusions were obtained. (1) At different heating rates, the reaction mechanism functions of intact epoxy resin are similar.

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(2) After acid thermal aging, the activation energy of epoxy resin decreases with increasing aging time, nitric acid concentration, and aging temperature. This lowers the “threshold” for thermal stress erosion and may shift the point of severe epoxy degradation to the left. (3) Both vacuum and acid thermal aging induce bubbles on the epoxy resin surface, reflecting its degraded morphology to some extent. Considering the actual operation of composite insulators, despite only experiencing a temperature rise of a few dozen degrees, the combined effects of acid and water lead to a reduction in epoxy resin’s activation energy. This may result in degradation of the epoxy resin within the core rod. This explains why crispy composite insulators exhibit only a slight temperature increase, yet experience significant epoxy resin deterioration. Acknowledgments. This work is supported by Science and Technology Project of State Grid Corporation (5500-202024073A-0-0-00).

References 1. Liang, X., Gao, Y.: Study on decay-like fracture of composite insulators (i): main characteristics, definition and criterion of decay-like fracture. Proc. CSEE 36(17), 4778–4786 (2016). (in Chinese) 2. Li, X., Li, G., Yang, J., Yang, S., Du, G.: Research on invasion of moisture into the crimping interface of insulator under hygrothermal environment. High Volt. Apparatus 58(6), 24–30 (2022). (in Chinese) 3. Cai, X., Gao, C., Zhang, D., et al.: Study on the effect of thermal degradation on the morphology characteristics of composite insulator mandrel under vacuum condition. In: Liang, X., Li, Y., He, J., Yang, Q. (eds.) The Proceedings of the 16th Annual Conference of China Electrotechnical Society 2016. LNCS, vol. 890, pp. 309–320. Springer, Singapore (2022). https://doi.org/10.1007/978-981-19-1870-4_33 4. Wang, G., Sun, Y., Jiang, H., et al.: Influences of cyclic hygrothermal-thermal aging on properties of epoxy vinyl ester resin/glass fiber composites. Eng. Plast. Appl. 48(9), 121–126 (2020). (in Chinese) 5. Shen, H.: Study on the Decay-Like Degradation Mechanism of Epoxy Resin in the Core Rod of Composite Insulator. Shandong University, Jinan (2020). (in Chinese) 6. Dwyer, D.B., et al.: Influence of temperature on accessible pyrolysis pathways of homopolymerized bisphenol A/F epoxies and copolymers. J. Anal. Appl. Pyrol. 153, 104978 (2021) 7. Pang, G., Zhang, Z., Jiang, X., Lu, M., Gao, C.: Effect of electrical erosion on composite insulator core rod under acidic environment. J. Market. Res. 22, 3525–3535 (2023) 8. Vyazovkin, S.V.: Alternative description of process kinetics. Thermochim. Acta 211, 181–187 (1992) 9. Šesták, J., Berggren, G.G.: Study of the kinetics of the mechanism of solid-state reactions at increasing temperatures. Thermochim. Acta 3(1), 1–12 (1971) 10. Hu, R., Shi, Q.: Thermal Analysis Kinetics. Science Press, Beijing (2008). (in Chinese) 11. Liu, J., Chen, W., Qi, Q.: Study on spontaneous combustion tendency of coal based on activation energy index. J. China Coal Soc. 30(1), 67–70 (2005). (in Chinese)

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12. Zhang, Z., Liang, P., Ren, P., Wang, J.: Thermodegradation kinetics of epoxy/DDS/POSS system. Polym. Compos. 28(6), 755–761 (2007) 13. Zhang, H., Jin, H., Zhang, S., Liu, P., Peng, Z.: Electrode polarization in graphene oxide/epoxy resins nanocomposites. Trans. China Electrotech. Soc. 33(23), 5591–5599 (2018). (in Chinese)

Research on Cumulative Fatigue Damage for Vortex-Induced Vibration of Steel Tube Tower Songsong Yu1(B) , Zhongwei Hou2 , Quan Liu2 , Jiang Liu1 , and Yu Cao1 1 Central Southern China Electric Power Design Institute Limited Liability Company of China

Power Engineering Consulting Group, Wuhan 430071, China [email protected] 2 State Grid State Power Economic Research Institute, Beijing 102200, China

Abstract. The vortex-induced vibration of steel tube towers greatly affects the operation of transmission lines. The method of accumulation damage is one of the key in fatigue research. In this study, the applicability of cumulative fatigue damage theories is researched for steel tube tower under vortex-induced vibration. An improved Manson-Halford model is proposed based on the concept of equivalent cyclic ratio. The fatigue experiments of typical C-type and X-type joints of the steel tube towers are carried out, the S-N curves and multi-stage loading fatigue experiment data are obtained. The Miner-Palmgren model, improved Ye Duyi model, Manson-Halford model and improved Manson-Halford model are used to estimate the remain fatigue life of the typical joints respectively. The results reveal that the improved Manson-Halford model has certain advantages in the prediction accuracy of remain fatigue life. Keywords: Vortex-induced vibration · Steel tube tower · Nonlinear fatigue damage accumulation · Improved Manson-Halford model

1 Introduction Compared with the angle steel tower, the steel tube tower has the characteristics of low wind pressure and high stiffness. It can give full play to the bearing capacity of the material. The performance advantages make the steel tube tower more suitable for the ultra high voltage (UHV) transmission projects. However, there are significant vortexinduced vibration of steel tube towers in engineering, especially the member bars with larger slenderness ratio and horizontal disposition [1, 2]. In history, there have been many fatigue failure accidents caused by vortex-induced vibration of steel tube tower [3]. It greatly affects the operation of transmission lines. The method of accumulation damage is one of the key in fatigue research. The fatigue damage of steel tube tower members caused by vortex-induced vibration is controlled by wind load. Severe vibration may cause the fatigue stress to approach the plastic range. The fatigue damage degree of structures may be significantly different under different loading conditions [4]. At present, the fatigue caused by vortex-induced © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 207–216, 2024. https://doi.org/10.1007/978-981-97-1072-0_21

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vibration of steel tube towers are not mature in design standards [5, 6]. Some scholars [7, 8] evaluate the safety of steel tube tower under vortex-induced vibration by comparing the constant amplitude fatigue stress of members with the allowable stress. However, the fatigue residual life of the structures can not be obtained by this way. Some scholars [9, 10] evaluate the key joints remain fatigue life of steel tube towers by the theory of Miner-Palmgren cumulative fatigue damage [11]. Although the Miner fatigue damage accumulation is widely used in engineering because of its reliable calculation accuracy and simple calculation method [12], the theory can hardly reflect the effect of loading state, loading sequence and interaction between loads on structural fatigue damage. In order to overcome the limitations, some nonlinear fatigue damage accumulation theories are proposed based on the concept of continuous damage mechanics, thermodynamics, energy method and so on [13–16]. Due to the complexity of theory and model parameters, many theories are not capable of engineering application at present. The Manson-Halford model and Ye Duyi model are the tow relatively mature theories. Manson et al. [14] proposed a damage curve model (Manson-Halford model) based on the power index law of fatigue damage. Ye et al. [15] proposed a nonlinear fatigue damage accumulation model (Ye Duyi model) based on the evolution rule of material toughness with fatigue. The above models can express the effect on the loading sequence. After years of development, the Manson-Halford model and Ye Duyi model have been well developed and verified by engineering application. In this study, the theory of cumulative fatigue damage is researched for the vortexinduced vibration of steel tube tower. The Miner-Palmgren model, Ye Duyi model and Manson-Halford model are selected to analyze the applicability of cumulative fatigue damage theory in the steel tube tower structures. An improved Manson-Halford model is proposed based on the concept of equivalent cyclic ratio. Multi-stage loading fatigue experiments of steel tube tower typical joints are carried out to verify the performance of the improved model. The primary purpose is to supply the theoretic support for the design and security operation of UHV steel tube tower.

2 Methods 2.1 Miner-Palmgren Model The fatigue damage at the selected typical joints in the structures during a stationary short-term condition can be evaluated by applying the linear Palmgren-Miner equation [11], which is given by the following expression:  ni k Di = D= (1) (i = 1, 2, . . . . . . k) i=1 Ni Its failure criterion is as follows: D=

 ni =1 Ni

(2)

where D is the fatigue damage accumulated during the stationary short-term condition, ni is the number of stress cycles for the stress range Si , which is given by the spectrum of load; Ni is the number of stress cycles to failure for the stress range Si , which is given by S-N curves.

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2.2 Ye Duyi Model The Ye Duyi model can be used for the nonlinear fatigue damage accumulation under multi-stage loading [15]. After the first-stage load σ1 cycles n1 times, the remain fatigue life n2 /Nf 2 under the second-stage load σ2 is as follows:  lnNf 2  n1 lnNf 1 n2 = 1− Nf 2 Nf 1

(3)

where Nf 1 is the fatigue life under stress σ1 , Nf 2 is the fatigue life under stress σ2 . The Ye Duyi model has a simple form and does not require other test constants. However, the model can hardly reflect the interaction between loads. Wang et al. [16] proposed an improved model by adding the ratio square of the front and next stress. The expression of remain fatigue life n2 /Nf 2 under the second-stage load σ2 is as follows:  lnNf 2  n2 n1 lnNf 1 = 1− Nf 2 Nf 1



 σ1 2 σ2

 −



1 Nf 2



 σ1 2 σ2

(4)

2.3 Manson-Halford Model After the first-stage load σ1 cycles n1 times, the remain fatigue life n2 /Nf 2 under the second-stage load σ2 in the Manson-Halford model [14] is as follows: n2 =1− Nf 2





n1 Nf 1



Nf 1 Nf 2

0.4

(5)

By analogy, the expression of fatigue failure under multiple loads is:  a

ai−1,i  n1 a1,2 n2 2,3 ni−1 ni + + ··· + + =1 Nf 1 Nf 2 Nf (i−1) Nf (i)   Nf (i−1) 0.4 ai−1,i = Nfi

(6) (7)

2.4 Improved Manson-Halford Model The effect of loading sequence is well considered in the Manson-Halford model. However, different loads will interact with each other and affect the cumulative fatigue damage during loading [17]. Therefore, an improved Manson-Halford model is proposed based on the concept of equivalent cyclicratio. Use the equivalent cycle ratio nS2 /NS2 eq instead of the cycle ratio nS2 /NS2 . The cumulative model of fatigue damage under the R-th load Sk is as follows: a0 + (0.18 − a0 ) DS R =

   23 NSR 0.4 n

0.18

Sk

NSR

eq

(8)

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Let a0 = 0, refer to the derivation procedure of the special case of multistage variable amplitude loading. When the first-stage load σ1 cycles nS1 times, the cumulative fatigue damage is:  D1 =

nS1 NS1

 2 NS 3

0.4

1

(9)

The equivalent cycle nS2,eq is as follows:  D1 =

nS1 NS1

 2 NS 3



0.4

1

=

 2 NS

nS2,eq

3

0.4

2

(10)

NS2

eq

So the D2 is:  D2 =

nS2,eq + nS2 NS2

 2 NS 3

0.4

2

(11) eq

The DR is:  DR =

nSR,eq + nSR NSR

 2 NS 3

0.4

R

(12) eq

Combine the following formula: 

nSi,eq



 =

NSi

eq

nSi,eq

 Ln4 (Si−1 ) Ln4 (Si )

(13)

NSi

The improved Manson-Halford model based on the equivalent cyclic ratio is as follows:  DS i =

nSi + nSi,eq NSi

 2 Ln4 (Si−1 ) NS 0.4 3

Ln4 (Si )

i

(14)

3 Fatigue Experiment Data Due to the advantages of convenient construction and concise force transmission, the tube-gusset Joints are widely used in the UHV steel tube towers. However, there is few recommendations about the fatigue analysis and s-n curves for the tube-gusset joints of steel tube tower. Refer to the engineering case of vortex-induced vibration of steel tube towers, the C-type and X-type tube-gusset joints are selected as the fatigue experimental analysis objects. The joint forms are shown in the following Fig. 1.

Research on Cumulative Fatigue Damage for Vortex-Induced Vibration

(a) C-type tube-gusset joint.

211

(b) X-type tube-gusset joint.

Fig. 1. The typical joints diagram.

30 groups of fatigue tests are completed for the X-type and C-type joints. The stress range covers 140-340Mpa. The fatigue S-N curve of C-type tube-gusset joint is as follows: log10 N = 12.49 − 3.089log10 σ

(15)

The fatigue S-N curve of X-type tube-gusset joint is as follows: log10 N = 12.70 − 3.213log10 σ

(16)

A total of 8 multi-stage loading fatigue tests of X-type and C-type joints are carried out. The primary purpose is to verify the applicability of the cumulative fatigue damage theory under the vortex-induced vibration of steel tube tower. The experimental conditions are shown in the following table (Tables 1 and 2). Table 1. Multi-stage loading experiment results of C-type joints Serial number

Loading

Stress amplitude (Mpa)

Loading frequency (Hz)

Loading times

Number of stress cycles

C6-1

First-stage loading

200

15

120528

486775

Second-stage loading

130

15

Till failure

First-stage loading

130

15

456035

Second-stage loading

200

15

Till failure

C6-2

607456

(continued)

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Serial number

Loading

Stress amplitude (Mpa)

Loading frequency (Hz)

Loading times

Number of stress cycles

C6-3

First-stage loading

200

15

80352

437795

Second-stage loading

165

15

145569

Third-stage loading

130

15

Till failure

First-stage loading

130

15

304023

Second-stage loading

165

15

145569

Third-stage loading

200

15

Till failure

C6-4

563745

Table 2. Multi-stage loading experiment results of X-type joints Serial number

Loading

Stress amplitude (Mpa)

Loading frequency (Hz)

Loading times

Number of stress cycles

X5-1

First-stage loading

200

15

101335

364902

Second-stage loading

140

15

Till failure

First-stage loading

140

15

318757

Second-stage loading

200

15

Till failure

First-stage loading

200

15

67556

Second-stage loading

170

15

113879

Third-stage loading

140

15

Till failure

First-stage loading

140

15

212505

X5-2

X5-3

X5-4

440232

333867

420915 (continued)

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Table 2. (continued) Serial number

Loading

Stress amplitude (Mpa)

Loading frequency (Hz)

Loading times

Second-stage loading

170

15

113879

Third-stage loading

200

15

Till failure

Number of stress cycles

4 Results Based on the experimental results, the Miner cumulative fatigue damage model, improved Ye Duyi model, Manson-Halford model and improved Manson-Halford model are used to estimate the remain fatigue life of the C-type and X-type joints respectively. The results are shown in the following tables (Tables 3, 4, 5, 6, 7, 8, 9 and 10). Table 3. The loading times comparison of theoretical and experimental on the C-type joints by Miner cumulative fatigue damage model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

C6-1

576565

486775

18.44

C6-2

576564

607456

5.09

C6-3

529947

437795

21.05

C6-4

529945

563745

6.00

Table 4. The loading times comparison of theoretical and experimental on the X-type joints by Miner cumulative fatigue damage model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

X-–1

420094

364902

15.13

X5-2

420093

440232

4.57

X5-3

393945

333867

17.99

X5-4

393942

420915

6.41

It shows that the prediction accuracy of remain fatigue life has higher accuracy under the loading sequence of first small and then large, compared with the loading sequence of first large and then small. The average error of the Miner cumulative fatigue damage model is 11.83%, the Ye Duyi model is 20.37%, the Manson-Halford model is 5.84%, and the improved model is 4.789%.

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Table 5. The loading times comparison of theoretical and experimental on the C-type joints by Ye Duyi model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

C6-1

268790

486775

44.78

C6-2

641076

607456

5.53

C6-3

285992

437795

34.67

C6-4

594081

563745

5.38

Table 6. The loading times comparison of theoretical and experimental on the X-type joints by Ye Duyi model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

X5-1

237020

364902

35.05

X5-2

467328

440232

6.15

X5-3

244324

333867

26.82

X5-4

440419

420915

4.63

Table 7. The loading times comparison of theoretical and experimental on the C-type joints by Manson-Halford model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

C6-1

425523

486775

12.58

C6-2

623042

607456

2.57

C6-3

399003

437795

8.86

C6-4

574552

563745

1.92

Table 8. The loading times comparison of theoretical and experimental on the X-type joints by Manson-Halford model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

X5-1

327559

364902

10.23

X5-2

453711

440232

3.06

X5-3

312973

333867

6.26

X5-4

426032

420915

1.22

Further statistics are made on the calculated results, as shown in the following table. Whether C-type joints or X-type joints, the improved model has certain advantages in

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Table 9. The loading times comparison of theoretical and experimental on the C-type joints by improved Manson-Halford model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

C6-1

517547

486775

6.32

C6-2

593105

607456

2.36

C6-3

477108

437795

8.98

C6-4

545459

563745

3.25

Table 10. The loading times comparison of theoretical and experimental on the X-type joints by improved Manson-Halford model Serial number

Theoretical loading times

Experimental loading times

Average error (%)

X5-1

381614

364902

4.58

X5-2

433013

440232

1.64

X5-3

359408

333867

7.65

X5-4

406040

420915

3.53

the prediction accuracy of remain fatigue life for steel tube tower fatigue under vortexinduced vibration (Table 11). Table 11. The prediction accuracy comparison of remain fatigue life for steel tube tower fatigue under vortex-induced vibration Theory

Average error (%) C-type joints

X-type joints

Miner model

12.64

11.03

Improved Ye Duyi model

22.59

18.16

Manson-Halford model

6.48

5.19

Improved Manson-Halford model

5.23

4.35

5 Conclusions In this study, the applicability of cumulative fatigue damage theories is researched for steel tube tower under vortex-induced vibration. An improved Manson-Halford model is proposed based on the concept of equivalent cyclic ratio. The fatigue experiments of typical C-type and X-type joints are carried out, the S-N curves and multi-stage loading fatigue experiment data are obtained. The Miner cumulative fatigue damage model,

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improved Ye Duyi model, Manson-Halford model and improved Manson-Halford model are used to estimate the remain fatigue life of the C-type and X-type joints respectively, based on the experimental data. The results reveal that the improved Manson-Halford model has certain advantages in the prediction accuracy of remain fatigue life for steel tube tower fatigue under vortex-induced vibration. The prediction accuracy satisfies the project requirements. Acknowledgments. This work was funded by the Management Technology Project of the Headquarters of the State Grid (5200-202156071A-0-0-00) Research on the vortex-induced vibration fatigue and control technology of steel tube tower in transmission line considering environmental factors.

References 1. Liu, S.Z., Ma, Y.G., et al.: Hazard and influence analysis of UHV transmission lines under aeolian vibration. J. Power Syst. Equip. 1, 46–47 (2021). (in Chinese) 2. Li, C.M., Yang, Y.W., et al.: Mechanism research on prevention and control of pipe members aeolian vibration. J. Sci. Technol. Innov. 12, 149–150 (2021). (in Chinese) 3. Hou, Z.W., Wei, P., et al.: Cracking causes and breezy vibration prevention measures of UHV steel tube tower. J. Electr. Power Surv. Des. 5, 17–23 (2022). (in Chinese) 4. Aid, A., Amrouche, A., et al.: Fatigue life prediction under variable loading based on a new damage model. J. Materails Des. 32, 183–191 (2011) 5. DL/T 5154-2012 Technical Regulations for Tower Structure Design of Overhead Transmission Lines. (in Chinese) 6. GB50017-2017 Code for Design of Steel Structures. (in Chinese) 7. Yang, J.B.: LI Z: the influence on structural safety of steel tube tower breeze vibration. J. Vibr. Test. Diagn. 27(3), 208–211 (2007). (in Chinese) 8. Wu, H.Y., Bao, Y.Z., et al.: Analysis of breeze vibration of steel tube tower members of transmission lines. J. Electr. Constr. 30(9), 42–45 (2009). (in Chinese) 9. Yao, J.: Time domain analysis of UHV steel tube tower fatigue life. J. Jiangxi Sci. 30(2), 181–184 (2012). (in Chinese) 10. Deng, P.W.: Time domain analysis of 1000KV UHV steel tube tower fatigue life. J. Ind. Technol. Innov. 3(3), 435–438 (2016). (in Chinese) 11. Miner, M.A.: Cumulative damage in fatigue. J. Appl. Mech. 12(3), A159-164 (1945) 12. Lu, X.W., Liu, Z.G., et al.: Fatigue damage estimation method of aluminum electrolytic capacitors based on cumulative damage theory. Trans. China Electrotechn. Soc. 26(4), 13–18 (2011). (in Chinese) 13. Yang, X.H., Yao, W.X., et al.: The review of ascertainable fatigue cumulative damage rule. J. Eng. Sci. 5(4), 81–87 (2003). (in Chinese) 14. Manson, S.S., Halford, G.R.: Practical implementation of the double linear damage rule and damage curve approach for treating cumulative fatigue damage. Int. J. Fract. 17(2), 169–192 (1981) 15. Ye, D.Y., Wang, D.J., et al.: A new approach for studying fatigue damage. J. Exp. Mech. 14(1), 80–88 (1999). (in Chinese) 16. Wang, X., Liu, M.Z., et al.: Nonlinear fatigue damage accumulation model based on load interaction effects. J. Constr. Mach. 16(4), 74–77 (2018). (in Chinese) 17. Esin, A.: Stress-interaction effects in cumulative fatigue damage. J. Nuclear Eng. Des. 6, 139–146 (1967)

A Model for Predicting the Flashover Voltage of Ice-Covered DC Insulator Strings Based on Extreme Learning Machine Neural Network Xiaoyi Wang1 , Hao Shen2(B) , Chao Zhou2 , and Hui Liu2 1 State Grid of China Technology College, Jinan 250001, China 2 State Grid Shandong Electric Power Research Institute, Jinan 250002, China

[email protected]

Abstract. Icing tests of insulator string are limited by many factors, such as geographical location, climate conditions and test equipment. Therefore, this paper proposes a new model for applying artificial neural network to select the external insulation on the basis of the experimental data obtained, that is, the mapping relationship between complex environmental conditions and the Flash loop voltage of dc insulator is developed in view of the extreme learning machine neural network. When the neural network is verified and trained, It can be used to forecast ice flash pressure. By comparing the prediction results obtained by extreme learning machine neural network with the experimental results, the relative error between them is less than 4.46%. The method accurately predicts flashover stresses of insulators with ice and reasonably predicts the flashover stresses of icing insulators. The implementation of this project has very important theoretical and practical significance for the prevention and control of flood and drought disasters in our country. Keywords: Ice-covered insulator · Flashover voltage · Extreme learning machine · Neural network · Prediction model

1 Introduction Freezing is a common phenomenon in nature. In low temperature weather, the supercooled droplets flowing in the air will condense into ice when they hit the insulators and wires, which brings great harm to power system security. Ample insulator flashover accidents caused by ice accretion have been reported worldwide [1–10]. With the implementation of China’s “West-East Power Transmission, North-South Power Exchange, and National Grid Interconnection” strategy and extra-high voltage transmission projects, power transmission lines inevitably pass through areas with ice and snow, high altitudes, pollution, and other adverse conditions, placing insulators at even greater risk of ice flashover. Therefore, study of electrical properties of insulators at high altitude, polluted, and ice accretion environments is of great significance for evaluating the safety status of insulators and preventing ice flashover accidents. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 217–223, 2024. https://doi.org/10.1007/978-981-97-1072-0_22

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Currently, power lines under complex environmental conditions such as ice accretion, snow accumulation, pollution, and high altitudes relies mainly on laboratory artificial climate chamber tests. Both domestic and international standards for ice accretion on insulators have been initially established [11, 12], and a substantial amount of experimental data on the flash loop characteristics of insulators has been obtained [10, 13–18]. References [13, 14] examined the influence of icing conductance on flash loop voltage and it tends to saturate as the conductance increases. References [15–17] investigated the development process of flashovers on ice insulator surfaces and proposed that the flash loop voltage during the melting time is lower than during the ice covering period. Reference [10] studied the variation of the equivalent conductivity of insulator surfaces, applied it to ice flashover voltage prediction models, and con-ducted experimental verification. Reference [18] studied the influence of different arrangements of insulators on AC flash loop characteristics, indicating that the inverted V-shaped or flower-like arrangement of insulators. The flashover problem of icing insulators is familiarly related to factors, e.g. pollution, ice thickness, air pressure, and the length of insulator strings. However, the selection of external insulation in such complex environments is a com-plex research topic due to the multiple influencing factors and randomness involved. Therefore, establishing a model for ice flashover voltage of insulators in intricate environments has important aca-demic and engineering reference value. Currently, external insulation re-lies on the results of laboratory tests, using conventional empirical methods, statis-tical methods, and simplified statistical methods [19, 20]. So new methods must be explored based on actual conditions. Due to the ability of neural networks to learn the best approximation of nonlinear mappings, they have shown significant advantages over traditional methods and have been widely applied in various engineering fields [21, 22]. Reference [21] used artificial neural networks to fit the relationship between flash loop time and voltage, resistance, and plate length in the pollution model, and verified the results through experiments. Reference [22] utilized an synthetic artificial network model to simulate the influence of individual and analyzed the simulation results. Traditional neural networks have drawbacks such as slow convergence speed and easily falling into local minima. However, Extreme Learning Machine (ELM) neural networks outperform traditional neural networks in terms of approximation capability and learning speed. This study selects ELM neural networks based on dc ice flash (of lightning, metals etc.) data under complex environmental conditions to establish a predictive model. This model is used to analyze the electrical characteristics of insulators in complex environments.

2 Icing Insulator Flashover Voltage Prediction Model 2.1 Establishment of ELM Neural Network Prediction Model Neural networks possess high levels of self-learning, self-organization, and adaptability, and they are widely applied in pattern recognition, fault diagnosis, trend prediction, etc. [23, 24]. ELM is a machine learning algorithm proposed by Guangbin Huang in 2006. It solves the drawbacks of slow training speed and poor generalization performance,

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thereby determining the output of the hidden layer without iterative parameter tuning, thus improving the efficiency of the training algorithm. In the study, a flashover voltage prediction model for icing insulators is established based on the ELM neural network. ELM is a single-layer feedforward neural network with a large number of hidden layer neurons. ELM has faster learning speed and can overcome the problems of overfitting, inappropriate learning rate selection in traditional gradient algorithms, and it has better generalization ability [25] (Fig. 1).

Fig. 1. Typical structure of ELM

Assuming the grid has p input layer neurons and l hidden layer neurons, between the input layer and the hidden layer, there is an activation function called f . The data sample  1 2 p T set is {xi , ti }N ∈ Rp , where N is the sample set’s overall i=1 , where xi = xi , xi , . . . , xi sample count. The mathematical relationship between input and output is as follows: l    f Wj · Xi + bj ηj = oi i = 1, 2, . . . , N

(1)

j=1

T  where Wj = wj,1 , wj,2 , ..., wj,n is the input weight, wj,n and ηj is the input weight, bj is the jth threshold, oi is the ith sample’s output. The objective of learning can be expressed as: N 

oi − ti  = 0

(2)

i=1

There exist ηj , W j and bj : l    f Wj · Xi + bj ηj = yi i = 1, 2, . . . , N

(3)

j=1

The matrix is represented as: Hη = T

(4)

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There are [25]: H (W1 , · · · , Wl, b1 , · · · , bL, Xl , · · · , Xl ) ⎤ ⎡ g(W1 · X1 + b1 ) · · · g(Wl · X1 + bl ) ⎥ ⎢ .. .. =⎣ ⎦ . ··· . g(W1 · XN + b1 ) · · · g(Wl · XN + bl ) ⎡ T⎤ ⎡ T⎤ η1 T1 ⎢ .. ⎥ ⎢ .. ⎥ η=⎣ . ⎦ T =⎣ . ⎦ ηlT



TNT

l×m

(5) N ×L

N ×m

It is desired to obtain W j , bj and ηj , such that:       H (W j , bj )ηj − T  = min H (Wj , bj )ηj − T 



(6)

W ,b,η

where j = 1,…,l. The above equation can be equated to: ⎛ ⎞2 N l   ⎝ E= f (Wj · Xi + bj )ηj − ti ⎠ i=1

(7)

(8)

j=1

For this kind of problem, a new method is commonly used, but all the parameters need to be modified when solving this method. The output matrix H of the hidden layer is uniquely determined when the input weighted wj and the hidden layer weighted bj are selected at random. A straightforward set of linear equations is created from the learning of a single neural network. Further, the output weighted eta can be determined:

η = H †T

(9)

2.2 Selection of Activation Function and Normalization Processing The activation function is chosen as the sigmoid function, where the variable is u. 1 (10) 1 + e−u U fm of insulators is the result of the interaction of string length, icing water conductivity, air pressure, and contamination salt density. Therefore, the number of insulator discs, icing water conductivity, air pressure ratio, and contamination salt density are selected as the input layer of the neural network, and the flashover voltage is the output layer. For a neural network, the convergence speed and accuracy of the learning process mainly rely on the range of input data. Then, before training the data, normalization of the input and output data needs to be performed according to Eq. 11. f (u) =

xi = where xi is the normalized result of x i .

xi − xmin xmax − xmin

(11)

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3 Network Training and Analysis of Results Based on the experimental data from [20], 78 sets of data were randomly selected for network training, and the remaining 15 sets of data were used to verify the effectiveness of the neural network. The relative error is calculated according to Eq. 12. δ=

S −A × 100% A

(12)

where δ represents the relative error, while S and A represent the predicted and measured values of flashover voltage for ice-covered insulator string, respectively. The units for S and A are both in kV. From Fig. 2 and Table 1, The absolute values of the relative errors between the predicted and experimental results are all less than 4.46%. It is of great significance for preventing icing flashover accidents. Table 1. Test and simulating results. Number

Test results

Predicted results

δ/%

1

50.5

49.73

−1.527

2

79.5

79.47

−0.037

3

45.8

46.71

1.977

4

43.1

42.91

−0.448

5

86.9

86.02

−1.015

6

74

7

108.9

8

43.7

73.67 108.1 44.84 112.6

−0.452 −0.740 2.597

9

112.5

10

102.2

99.86

−2.291

0.114

11

46.2

48.26

4.460

12

67.1

68.79

2.518

13

79

78.66

−0.429

14

83.5

83.62

0.140

15

54.8

52.39

−4.390

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0

2

4

6

8

10

12

14

16

Fig. 2. Test results and predictive results

4 Conclusion The ELM neural network was employed in this study to establish a flashover voltage prediction model for DC insulators under complex environmental conditions such as icing, pollution, and low air pressure. Through the comparison and analysis of the results of experimental and ELM neural network prediction model, it is verified that the absolute value of the relative error between them is less than 4.46%, which validates the effectiveness of the prediction model. The ELM artificial neural network flashover voltage prediction model overcomes the limitations of geographical location, climatic conditions, and experimental equipment on icing tests.

References 1. A CIGRE Task Force 33.04.09: Influence of ice and snow on the flashover performance of outdoor insulators, part I: effect of Ice. Electra 187, 91–111 (1999) 2. Farzaneh, F.: Atmospheric Icing of Power Networks, pp. 1–4. Springer, Heidelberg (2008). https://doi.org/10.1007/978-1-4020-8531-4 3. Xu, Z.H., Jia, Z.D., Li, Z.N., et al.: Anti-icing performance of RTV coatings on porcelain insulators by controlling the leakage current. IEEE Trans. Dielectr. Electr. Insul. 18(3), 760– 766 (2011) 4. Jiang, X., Lu, J., Wan, J., Luo, L., Zhang, Z.: Study on measures to prevent icing flashover of insulation strings. Power Syst. Technol. 32(14), 19–24 (2008). (in Chinese) 5. Jiang, Z., Lu, J., Lei, H., Huang, F.: Analysis of the causes of tower collapses in Hunan during the 2008 ice storm. High Volt. Eng. 34(11), 2468–2474 (2008). (in Chinese) 6. China Southern Power Grid Corporation: Power Grid Ice Prevention and Melting Technology and Application, pp. 13–15. China Electric Power Press, Beijing (2010).(in Chinese)

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7. Farzaneh, M., Zhang, J., Volat, C.: Effect of insulator diameter on AC flashover voltage of an ice-covered insulator string. IEEE Trans. Dielectr. Electr. Insul. 13(2), 264–271 (2006) 8. Zhang, Z., Jiang, X., Hu, J., Shen, Q., Chen, L., Liu, F.: Influence of environment parameters on the icing accretion on the surface of insulator. High Volt. Eng. 36(10), 2418–2423 (2010). (in Chinese) 9. Zhao, S., Jiang, X., Zhang, Z., Hu, J., Hu, Q.: Impact of environmental parameters on the icing process of 110 kV composite insulators. High Volt. Eng. 38(10), 2575–2581 (2012). (in Chinese) 10. Farokhi, S., Farzaneh, M., Fofana, I.: Experimental investigation of the process of arc propagation over an ice surface. IEEE Trans. Dielectr. Electr. Insul. 17(2), 458–464 (2010) 11. Meghnefi, F., Farzaneh, M., Volat, C.: Measurement of the evolution of dripping water conductivity of an ice-covered insulator during a melting period. In: Conference on Electrical Insulation and Dielectric Phenomena, pp. 236–239. IEEE, US (2008) 12. Ma, J., Jiang, X., Zhang, Z., Hu, J., Shu, L.: Influence of the icing period with voltage on the icing and electric field characteristics of impendent insulators. High Volt. Eng. 36(8), 1936–1941 (2010). (in Chinese) 13. Khalifa, M., Morris, R.: Performance of line insulators under rime ice. IEEE Trans. Power Appar. Syst. 86(6), 692–698 (1968) 14. Volat, C., Farzaneh, M., Mhaguen, N.: Improved FEM models of one- and two-arcs to predict AC critical flashover voltage of ice-covered insulators. IEEE Trans. Dielectr. Electr. Insul. 18(2), 393–400 (2011) 15. Sabri, Y., Farzaneh, M., Zhang, J.: Application of identification methods for predicting the flashover voltage of contaminated insulators covered with ice. IEEE Trans. Dielectr. Electr. Insul. 17(2), 451–457 (2010) 16. Sun, C., Shu, L., Jiang, X., Sima, W., Gu, L.: AC/DC flashover performance and its voltage correction of UHV insulators in high altitude and icing and pollution environments. Proc. CSEE 22(11), 115–120 (2002). (in Chinese) 17. Jiang, X., Xiang, Z., Zhang, Z., Hu, Q., Bi, M., Zhao, S.: Influence of icing degree on AC icing flashover performance of porcelain, glass and composite insulators. Proc. CSEE 33(31), 227–233 (2013). (in Chinese) 18. Zhang, Z., Jiang, X., Hu, J., Sun, C.: Influence of the type of insulators connected with alternately large and small diameter sheds on ac icing flashover performance. Trans. China Electrotech. Soc. 26(1), 170–176 (2011). (in Chinese) 19. Zhang, W., He, J.L., Gao, Y.M.: Overvoltage Protection and Its Insulation. Tsinghua University Press, Beijing (2002). (in Chinese) 20. Shi, Y., Jiang, X., Wan, J.: Flashover voltage forecasting mode of iced insulator based on RBF network. High Volt. Eng. 35(3), 591–596 (2009). (in Chinese) 21. Ghosh, P.S., Chakravorti, S., Chatterjee: Estimation of time to flashover characteristics of contaminated electrolytic surface using artificial neural network. IEEE Trans. Dielectr. Electr. Insul. 2(6), 1064–1074 (1995) 22. Yuan, Y., Jiang, X., Du, Y., Ma, J., Sun, C.: Predictions of the AC discharge voltage of short rod-plane air gap under rain conditions with the application of ANN. High Volt. Eng. 38(1), 102–108 (2012). (in Chinese) 23. Li, Y., Teng, Y., Yuan, S., Leng, O.: Study on snow covered insulator flashover characteristics and its improved QNN prediction model. Power Syst. Technol. 42(8), 2725–2732 (2018). (in Chinese) 24. Wu, Q., Huang, X.: Study on short-term prediction of transmission line ice cover based on RBF neural network. Guizhou Electr. Power Technol. 19(11), 57–60 (2016). (in Chinese) 25. Huang, G., Zhu, Q., Siew, C.K.: Extreme learning machine: theory and applications. Neurocomputing 70, 489–501 (2006)

A Grid-Friendly Bidirectional Electric Vehicle Charger Based on CLC Resonant Converter Ziqian Ren(B) , Xinqi Li, Qiaozhi Xue, Jiang Shang, Nanzhe Wei, and Chunguang Ren College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan, China [email protected]

Abstract. With the increasing frequency of interaction between electric vehicles and the power grid, the key to the development of electric vehicles lies in improving the friendly interaction between electric vehicles and the power grid, and the bidirectional charging and discharging efficiency of electric vehicles. In this paper, a CLC bidirectional isolated resonant converter based on virtual synchronous machine control technology is proposed. On the one hand, the charging and discharging stability of the electric vehicle is enhanced by the converter, which facilitates the friendly interaction of the high-power interface converter with the power grid. On the other hand, the efficiency of the converter is improved by the zero-voltage turn-on and zero-current turn-off characteristics of the rectifier. Simultaneously, a single high/low level switch can be used to control the power flow of the interface converter, which simplifies the mode conversion operation of EVs and enhances the operability of the charge-discharge mode conversion. The effectiveness and accuracy of the proposed control strategy are verified by simulation. Keywords: Electric vehicle · VSM · Resonant converter · Bidirectional converter

1 Introduction The pace of vehicle electrification has been accelerated by fossil fuel shortages and the concerns about air pollution. The integration of a large number of electric vehicles with the power grid will help stabilize the impact of intermittent renewable energy on the power grid and also serve as an effective alternative solution for emergency power supply, which has been widely recognized and welcomed worldwide [1–4]. The performance of electric vehicle charging and discharging systems is a key factor in ensuring efficiency, speed, and friendly interaction with the power grid, which has received a lot of attention from both domestic and international researchers. The bidirectional interface converter, which enables adjustable bidirectional power flow, is an important component of electric vehicle chargers. For the bidirectional interface converter, on one hand, a good interaction characteristic between the electric vehicle charging/discharging equipment and the grid is required to have high stability and steadystate accuracy when the distribution grid experiences transient faults. The bidirectional © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 224–231, 2024. https://doi.org/10.1007/978-981-97-1072-0_23

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droop control method is proposed which controls the power flow direction by controlling the frequency and voltage on the AC side and DC side to achieve balanced load sharing on the AC and DC sides. However, with the gradual increase in EV penetration, EV batteries and grid stability may be affected by droop control [5, 6]. On the other hand, the goal that the charging and discharging process of electric vehicle charging equipment should be fast and efficient has been proposed, which can improve the service life and operational safety of electric vehicle power batteries, as well as reduce the energy loss in the charging and discharging process. For high voltage and high power operation of bidirectional converters, the DAB (Dual Active Bridge) structure has been proposed. However, the traditional DAB converter exhibits a large reactive current, which generates electrical stress on switching elements and increases power losses, leading to a decrease in the overall efficiency of the converter [6]. To improve the interaction characteristics between bidirectional interface converters and the grid, as well as the charging/discharging efficiency, an grid-friendly isolated bidirectional Electric Vehicle (EV) charger based on CLC resonant converter is proposed in this paper. A resonant converter is incorporated into the traditional DAB structure to improve efficiency during high-power operations. Furthermore, virtual synchronous machine control strategy is employed which improves the performance of convertergrid interaction. The direction of flow of power in the system is controlled by a single device, simplifying electric vehicle mode shift operations. Finally, the correctness and effectiveness of the proposed method is verified by MATLAB/Simulink simulation.

2 Charger and Discharger Working Principle The V2G charging and discharging machine, which consists of AC/DC stage and DC/DC stage, is designed to achieve two-directional energy flow. To match the DC bus and the electric vehicle battery, the structure of a DAB converter is employed in the DC/DC stage of the interface converter in this paper, meeting the requirements of high power and wide output voltage range [7, 8]. However, to address the issue of high reactive current leading to power losses in traditional DAB converters, a CLC resonant module is added. This allows zero-voltage turn-on and zero-current turn-off for the switching devices in the interface converter, thereby enhancing the overall efficiency of the converter. The structure topology of the bidirectional interface converter is illustrated in Fig. 1. The AC bus of the grid is connected to the AC side of the interface converter through the line impedance Z ac and the LC filter (L ac is the filter inductance, C ac is the filter capacitor, and Rac is the filter resistor). The DC side of the interface converter is connected to the DC/DC converter through the DC capacitor C dc . The primary and secondary sides of the DC side of the interface converter are interconnected via the CLC resonant module, and then connected to the power battery through the voltage-stabilizing capacitor C f and filter inductor L f . 2.1 AC/DC Interface Control Strategy To improve the interaction characteristics between the bidirectional interface converter and the electrical grid, stabilize the voltage input to the power battery from the DC side

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Fig. 1. Topological structure of charge-discharge machine.

during transient elevation and drop of grid voltage, and ensure high stability and inertia of the whole system when the grid power fluctuates significantly, a virtual synchronous motor control strategy is adopted in the AC/DC converter. The entire electric vehicle charging pile is equivalently treated as a synchronous machine from the grid-connected point, adaptively responding to the voltage and frequency disturbances of the grid and providing necessary inertia and damping for the grid. The control strategy for the AC interface is divided into two parts: frequency-voltage control and virtual excitation control. Based on the structural similarity between the three-phase synchronous motor model and the three-phase converter, the three-phase converter can be equivalently treated as a synchronous motor, realizing the modeling of the virtual synchronous motor. Frequency-Voltage Control. The torque equation of the virtual synchronous machine can be represented as follows, assuming that the number of pole pairs is set to 1: ⎧ dω ⎪ = Pm − Pe − kω (ω − ωN ) ⎨ J ωN dt ⎪ ⎩ dδ = ω dt

(1)

In the equation, J represents the inertia of the synchronous motor, measured in kg·m2 , ωN refers to the rated angular velocity of the grid, measured in rad/s. Pe and Pm denote the electromagnetic and mechanical power of the synchronous motor, respectively. D is the damping coefficient, which equals the first-droop coefficient of AC frequency regulation (k ω ) when the effect of the damping winding is disregarded. δ is the power angle of the generator, measured in rad, and ω is the virtual rotor angular velocity of the synchronous motor, measured in rad/s. Due to the presence of rotating inertia J, the charging/discharging machine can exhibit mechanical inertia capabilities when grid voltage fluctuations occur. When the AC droop coefficient is chosen, an increase in rotating inertia J can enhance the inertia of the AC frequency, but an excessively large J might decrease system stability, hence it should not be too large. Similarly, an increase in the damping coefficient D can enhance the inertia of the entire system, but an excessively large D might affect system stability. The specific values for each variable in Eq. (1) can be referenced from References [9, 10]. Virtual Excitation Control. In the virtual excitation control section, the control and adjustment of the AC voltage and reactive power are simulated by mimicking the generator’s excitation control. Reactive power generation is achieved by adjusting the effective value E of the virtual potential of the virtual synchronous motor model. The effective

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value E of the virtual potential of the virtual synchronous motor is composed of three parts. ΔE Q represent the adjustment of the reactive power, can be denoted as: EQ = kq (Qref − Q)

(2)

In this equation, k q represents the reactive-voltage droop coefficient, whereas Qref and Q denote the instantaneous reactive power reference value and the actual value of the AC interface output, respectively. ΔE U represent the adjustment of the machine terminal voltage, can be equated to the automatic excitation regulator of the synchronous motor, and is denoted as: EU = kv (Uref − U )

(3)

In this equation, k v represents a voltage regulation coefficient; U ref and U denote the reference value and the actual value of the line voltage effective measure at the converter terminal, respectively. E 0 represents the effective value of the no-load potential of the motor. Thus, the effective value of the virtual potential of the motor can be expressed as: E = E0 + EQ + EU

(4)

The vector value of the virtual potential of the electric motor is represented as: ⎡ ⎤ E sin(δ) ⎢ ⎥ eabc = ⎣ E sin(δ − 2π/3)⎦ (5) E sin(δ + 2π/3) The electromagnetic equations of a synchronous motor can be represented as: diabc = eabc − uabc − Riabc (6) dt In this equation, uabc represents terminal voltage of the synchronous motor and the stator inductance and resistance of the synchronous motor are denoted by L and R, respectively. It should be noted that the stator inductance L and resistance R correspond to the filtering inductance L ac and filtering resistance Rac of the AC interface. L

2.2 DC/DC Interface Control Strategy The bidirectional DC/DC converter consists of 8 switches, namely M1 to M8 as shown in Fig. 3. The resonant structure, composed of resonant capacitor Cr and resonant inductor Lr, is located on the secondary side for resonant PWM operation. The capacitor Cv on the primary side is used for voltage boosting operation. The proposed bidirectional charger maintains the structural advantages similar to the DAB converter, However, this converter operates in buck type regardless of the direction of the power flow, which makes it difficult for the converter to form a bidirectional power flow. To solve this problem, the proposed converter employs a voltage doubling rectifier structure to increase the voltage to double in the case of discharge operation, which can be achieved by keeping M3 in the on state during discharge operation, thus realizing bi-directional power flow.

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Fig. 2. Virtual synchronous motor control strategy,

Fig. 3. DC/DC control strategy.

3 Simulation Verification The simulation model of the electric vehicle charging and discharging machine, which is built on the MATLAB/Simulink simulation platform, is shown in Fig. 4. It is composed of a distribution grid, an electric vehicle power battery, and an interface converter. The AC and DC sides are interconnected by the interface converter.

Fig. 4. Simulation model of electric vehicle charging and discharging.

When the inverter initially operates in the inverter mode, the parameters of the inverter controlled by the virtual synchronous machine are selected as J = 0.76 kg·m2 and D

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= 200. In the simulation, after the inverter is grid-tied, the initial active power is set to 10 kW and the reactive power is set to 0 var. At t = 3 s, the inverter transitions to the rectifier mode while the active power remains at 10 kW and the reactive power abruptly increases from 0 var to 2 k var. This state is maintained for 3s. At t = 6 s, the inverter transitions back to the inverter mode, with the active power remaining at 10 kW and the given reactive power remaining at 2 k var. Throughout the simulation process, the grid voltage remains constant.

Fig. 5. Simulation waveform of mode switching.

The simulation waveforms of the DC voltage udc , active power P, and reactive power Q of the interface converter during the mode transition (J = 0.76 kg·m2 , D = 200) are shown in Fig. 5. The amplitude variations during the voltage rise and drop are 2 V and 2.1 V, respectively. The time for power increase and decrease changes is 430 ms and 460 ms, respectively. From the figure, it can be observed that the operation mode of the interface converter can be flexibly adjusted based on the charging and discharging variations of the DC/DC control strategy, enabling bidirectional power flow between the power grid and the electric vehicle.

Fig. 6. Soft switch and charging current waveform during charging.

When discharging operation is performed, the simulation results of the voltages V cr across the capacitor Cr in the tuned circuit and the switching waveform of the switching device M5 of the interface converter are shown in the left graph of Fig. 6. The simulation results of the charging current ip on the secondary side and the switching waveform of

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the switching device M1 of the interface converter are shown in the right graph of Fig. 6. From the graph, it can be observed that zero voltage turn-on and zero current turn-off are achieved by the switching devices, with a high efficiency of up to 98.1%.

Fig. 7. Soft switch and charging current waveform during discharging.

When discharge operation is performed, the simulation results of the voltages V cr across the capacitor Cr in the tuned circuit and the switching waveform of the switching device M4 of the interface converter are shown in the left graph of Fig. 7. The simulation results of the discharging current on the secondary side and the switching waveform of the switching device M8 of the interface converter are shown in the right graph of Fig. 7. From the graph, it can be observed that zero voltage turn-on and zero current turn-off can be achieved by the switching devices, with a highest efficiency of up to 97.1%.

4 Conclusion A bidirectional isolated PWM resonant converter based on the CLC type and its control strategy was proposed for the charging/discharging requirements of friendly interaction between electric vehicles and the grid. The soft-switch function of the converter and the transformation of charging and discharging modes were simulated, verifying that the proposed CLC type bidirectional isolated resonant converter can achieve friendly interaction with the grid, implement the soft-switch function, and improve the efficiency of the converter. Furthermore, the change in the charging and discharging state can be effectively controlled by a single switch change, which can be easily operated and improves safety in practical engineering applications. This paper provides a new idea and solution for the problem of grid-connected charging and discharging operation of electric vehicles. Acknowledgment. This work was supported by the National Nature Science Foundation of China under grant 51807130 and Key Research and Development Program of Shanxi Province (202102060301012).

References 1. Kumar, S., Khan, K.R., Srinivas, V.L., Shankar, G., Saket, R.K., Jana, K.C.: Electric vehicle fast charging integrated with hybrid renewable sources for V2G and G2V operation. In: 2023 IEEE IAS Global Conference on Emerging Technologies (GlobConET), London, United Kingdom, pp. 1–6 (2023)

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2. Mozina, C.: Impact of green power distributed generation. IEEE Ind. Appl. Mag. 16(4), 55–62 (2010) 3. Yuan, J., Dorn-Gomba, L., Callegaro, A.D., Reimers, J., Emadi, A.: A review of bidirectional on-board chargers for electric vehicles. IEEE Access 9, 51501–51518 (2021) 4. El Chehaly, M., Saadeh, O., Martinez, C., et al.: Advantages and applications of vehicle to grid mode of operation in plug-in hybrid electric vehicles. IEEE Electrical Power & Energy Conference (EPEC), Montreal, pp. 1–6 (2009) 5. Loh, P., Li, D., Chai, Y., et al.: Autonomous operation of hybrid microgrid with AC and DC subgrids. IEEE Trans. Power Eelctron. 28(5), 2214–2223 (2013) 6. Qin, D., Sun, Q., Wang, R., Ma, D., Liu, M.: Adaptive bidirectional droop control for electric vehicles parking with vehicle-to-grid service in microgrid. CSEE J. Power Energy Syst. 6(4), 793–805 (2020) 7. Xu, G., Sha, D., Xu, Y., Liao, X.: Hybrid-bridge-based DAB converter with voltage match control for wide voltage conversion gain application. IEEE Trans. Power Electron. 33(2), 1378–1388 (2018) 8. Liao, Y., et al.: An LLC-DAB bidirectional DCX converter with wide load range ZVS and reduced switch count. IEEE Trans. Power Electron. 37(2), 2250–2263 (2022) 9. Liu, G., Li, D., Zjang, J.Q., Jia, M.L.: High efficiency wide range bidirectional DC/DC converter for OBCM application. In: Proceedings of the PEAC, pp. 1434–1438 (2014) 10. Kan, J., Wu, Y., Tang, Y., Zhang, B., Zhang, Z.: Dual active full-bridge bidirectional converter for V2G charger based on high-frequency AC Buck-boost Control Strategy. Proc. IEEE ITECAP, pp. 46–50(2016)

Operation Strategy of Battery Swapping-Charging System for Electric Vehicle Based on Multi-material Flow with Space-Time Coupling Characteristics Zhijian Liu(B) , Jing Dai, Lingrui Yang, and Hang Dong Faculty of Power Engineering, Kunming University of Science and Technology, Kunming 650000, China [email protected]

Abstract. With the development of electric vehicles (EVs) and renewable energy sources, there is an urgent need for a flexible and convenient battery power supply system to achieve energy space-time complementarity. Therefore, this paper proposes a battery charge-swapping system (BSCS) operation strategy. Firstly, based on the spatio-temporal coupling relationship of material flow (battery flow/energy flow) carried by different operating entities in BSCS, a multi-material flow spatiotemporal coupling BSCS framework is proposed. Then, the joint scheduling optimization model of BSCS is constructed. The model takes the minimization of the economic operation of each subject of BSCS as the objective function, and comprehensively considers the vehicle routing planning of the battery transporter (BT), the battery swapping plan between BT and battery swapping station/charging station, and the fine charging management of charging station based on charging range division. Finally, aiming at the characteristics of high dimension and large computational complexity of the established model variables, an improved penalty alternating direction multiplier method is proposed for efficient solution. The space-time flexibility and operation economy of the model are verified by the case study. Keywords: Electric vehicles · Battery charging-swapping system · Vehicle routing planning · Penalty alternating direction multiplier method

1 Introduction The pursuit of carbon neutrality to cope with global climate change has become a global consensus. The transport sector accounts for 21.2% of global carbon emissions [1]. As a mainstream transportation electrification solution, electric vehicles (EVs) have the characteristics of zero emission and high operating efficiency. However, EVs rely on supporting infrastructure to charge their batteries, an efficient, flexible, and convenient EV battery power system is essential to promote EV adoption and the integration of renewable energy sources. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 232–239, 2024. https://doi.org/10.1007/978-981-97-1072-0_24

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There are two main ways to supply batteries, namely battery charging station (BCS) and battery swapping station (BSS) [2]. BCS usually obtain electricity through traditional transmission methods, which are limited by transmission line congestion and power quality control of the grid [3], which hinder the widespread promotion of EV. For cities with high population density, the construction of additional charging stations and charging piles and the expansion of transmission lines [4] will not only increase the financial burden, but also make the limited land resources and the saturated power grid transmission architecture face greater challenges. Considering the above problems, BSS is widely used in EV battery power supply system [5]. In order to make full use of the convenience and efficiency of BSS, a battery swapping charging station (BSCS) was developed for crowded cities based on the integration of established BCS [6]. In this system, the battery is centrally charged in the BCS and locally changed in the BSS, the intermediate transfer process being completed by the BT. Therefore, the battery power supply process of the BSCS system is jointly completed by the three operating entities of BSS, BCS and BT. Taking dynamic electricity price into account, [7] established a charge and discharge optimization scheduling model to maximize the revenue of charging stations and minimize the interactive power fluctuation between charging stations and distribution network as the objective function, and realized the load leveling of distribution network. As a bridge between the battery supply side and the demand side, BT’s battery transfer logistics involves the path planning strategy on the road network side and the battery supply and distribution decision on the power grid side. On the basis of considering the problem of BT path planning, [8] constructs a charge-exchange system based on large-scale wind power plants, and makes the wind farm power generation plan and the battery charging and discharging plan of centralized charging stations, [9] studies the optimal path planning of EV and selects the best BSS with sufficient full battery stock for EV users. In order to alleviate the EV queuing problem caused by insufficient BSS inventory, reference [10] designed a Lyapunov optimization framework based on queuing theory. However, the specific practice of strategies to guide EV travel behavior is often challenged by EV users’ cooperative attitude. Based on the above analysis, this paper proposes a BSCS spatiotemporal coupling operation scheme that is practical and meets the convenience requirements of EV users. For the mixed integer programming (MIP) problem, the improved Penalty alternating direction multiplier (PADM) algorithm is used to efficiently solve the model, and the economy and effectiveness of the proposed BSCS operating mechanism are verified by a numerical example.

2 Space-Time Operation Mechanism In order to make battery supply flexible across time and space and meet the convenience needs of electric vehicle users, BT is proposed to cooperate with BSS, BCS and the information control center (ICC) to jointly achieve the effective operation of BSCS. ICC, as the interactive core of the information flow, connects each single BSCS operating entity through the information flow. First of all, the information of each BSCS operating subject is collected in a unified manner, including: public grid electricity price,

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distributed renewable energy generation capacity equipped with each BCS, local nonelectric vehicle load, BSS battery inventory data, BT location information and other data. Then, according to the collected information, the mathematical model established by the coupling material flow between each subject in the system is solved, and the coupling coordination between each material flow is fully mined, and the operation schemes such as BT path transfer planning, battery loading and unloading plan, BCS fine charging plan, and BSS battery inventory dynamic management are obtained. The operation strategy is formulated by ICC, BSS directly supplies EV battery demand, BCS prepares full battery recharge for BSS, and BT connects the energy supply of the entire BSCS system in the form of battery transfer. Since the energy supply and demand of the battery are disassembled in space and time, the operational freedom of each agent is enhanced, so it is necessary to build a joint scheduling optimization model of BSCS according to the spatio-temporal coupling relationship of the material flow corresponding to each operating agent. In this section, the BSCS framework of multi-material flow coupling is proposed, and the space-time operation strategy model of BSCS is described, which includes the path transfer of BT, battery loading and unloading constraints, the dynamic change constraints of BSS battery inventory, the fine management model of BCS rechargeable battery based on charging range, and the economic operation objective function of BSCS. Equation (1) is the space-time state uniqueness constraint, Eq. (2) is the transfer state constraint, Eqs. (3)–(4) are the instantaneous action state constraint, and Eqs. (5)–(6) is the battery loading and unloading of BT:   λtmn + αnt = 1 (1) m,n∈N

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BT. C 1 c,t-1 and C nj c,t-1 respectively represent the number of first-charge batteries and the t /FBt and DBt /DBt represent the number number of nj -charge batteries in BCS c. FBBT BT b b of full and empty batteries of BT/BSS in the t period respectively. In addition to taking into account the battery interaction with BT, the update of the full and empty battery stock of the changing station is also determined by the number of EVs arriving at time t. FBbt =FBbt−1 +ubt − Dbt , DBbt =DBbt−1 +Dbt − lbt

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Equation (8) indicates that the number of all rechargeable batteries cannot exceed max the number of charging piles nch, of BCS. t j represents the time for the j-charging c range to complete charging. Equation (8) also represents the charging power constraint. Part of the energy of the charging station comes from the locally equipped distributed renewable energy output Pc RE,t , and part comes from the purchase of Pc grid,t from the public grid. The power of the public grid is limited by the transmission capacity Pc L,max of the transmission line, Ej is the power required to complete the j charging range. The objective function includes the operating costs of BT, BCS and BSS, of which F BT mainly considers the route transfer cost of BT, F BCS mainly considers the power purchase cost and battery charging loss cost within BCS, and F BSS mainly considers the EV replacement service income. min FBSCS = FBT + FBCS −FBSS ⎧  ⎪ FBT =C tra t λtmn ⎪ ⎪ ⎪ ⎪ m,n∈N ,t∈T ⎪ ⎪ ⎪ ⎪ ⎨   Ej · Cjt grid,t FBCS = C grid,t tPc + C deg ηch ⎪ ⎪ t∈T ,c∈C t∈T ,c∈C ,j∈J ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ F = C battery,t Dbt ⎪ ⎩ BSS

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t∈T ,b∈B

where C tra , C grid,t , C deg and C battery,t respectively correspond to the unit price of route transfer cost, the electricity price of public grid, the unit price of battery charging loss cost, and the service fee for single battery replacement. The space-time operation model of BSCS can be summarized as follows: ⎧ min f (xI , xC ) ⎪ ⎨ x MIP : s.t. G(xI ) ≥ 0 (11) ⎪ ⎩ H (xC , xI ) = 0

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  where x I represents integer variables, xB = αnt , λtmn , δnt , βnt , θnt and gen t including t , DBt , ut , l t , ut , l t , and x reperalized integer variable xI \B = FBb , DBbt , FBBT C BT c c b b grid,t resents continuous variable, that is, Pc . The objective function is Eq. (10), and G(x I ) represents the constraint containing only integer variables, H(x C , x I ) represents the constraint of coupling continuous variables with integer variables.

3 Solution Algorithm The above model is a mixed integer optimization problem (MIP), which takes a long time to solve using solvers. Therefore, based on the penalty alternating direction multiplier method (PADM) in [11], this paper proposes a restart mechanism and a penalty coefficient updating mechanism based on distance difference to improve PADM. Thus, the rapid solution of BSCS model with multiple running agents can be realized. The linear programming problem is easy to solve, so the relaxation of the original problem is conducive to improving the solving speed, but the original problem MIP includes a large number of integer variables, so it is necessary to design an approximation function as the objective function to approximate the relaxation solution to the integer feasible solution of the original problem. By relaxing all integer variables x I in the original problem Eq. (11) into continuous variable x I ’ , defining auxiliary integer variable y, and introducing the approximation function χ(x, y; ρ), the original problem MIP is transformed into Eq. (12). √ ⎧ |I | ⎪ min (x, y; ρ, w) = ∇fw·(x0,0 f (x) + (1 − w) · χ ⎪ ) ⎪ x,y ⎪ ⎪ ⎪ ⎨ s.t. L(x) ≥ 0 (12) rlx - MIP : y = xI , y ∈ Z ⎪ ⎪

 ⎪ ⎪ ⎪ ρ i xi − yi + ρ i xi − yi ⎪ ⎩ where, χ (x, y; ρ)= i∈I

where, L(x) contains the post-relaxation constraints corresponding to G(x I ) and H(x C , x I ). ρ i and ρ i represent the up and down penalty coefficients corresponding to the i-th integer variable. w is weight factor which can balance the original optimization objective function and the approximation function. According to [12], PADM consists of an inner and an outer cycle: the inner cycle uses the alternating direction multiplier method to solve the local minimum of Eq. (12) under fixed parameters w and ρ; After considering the convergence condition of the outer loop, the w and ρ parameters are updated, so as to update the objective function of the inner loop neutron problem. A penalty coefficient updating mechanism based on distance difference is introduced into the outer loop, so the penalty that does not meet y = x I is gradually aggravated. By introducing inc(•) = (•) · (1 + |xik,m − yik,m |) and dec(•) = (•)/(1 + |xik,m − yik,m |), the updating step of the penalty coefficient can be written as follows: ⎧  ⎨ ρ k+1 = inc(ρ k ),ρ k+1 = dec(ρ k ), when yk,m+1 = xk,m+1 i i i i i i (13) ⎩ ρ k+1 =dec(ρ k ), ρ k+1 = inc(ρ k ) otherwise i i i i

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1) Considering that under the effect of the distance difference between integer variables and continuous variables, the update of the above penalty coefficient may increase exponentially, which will lead to the cycle/stall problem caused by excessive approximation function [20], restart operation is introduced. 2) By iterating the inner loop, when the inner and outer loops converge at the same time, yk,m+1 is the suboptimal solution of Eq. (12), and x∗I = yk,m+1 is brought into the original Eq. (11) for solving, then the original problem is solved immediately.

4 Example Analysis In this section, with the planning period of 24 h and the time slice length set to 15 min, we built a 24-node network system. In Table 1, A is the number of FB and DB carried by BT at the initial time, B is the FB and DB stocks of each BSS, C is the random arrival of EV, D is the initial SOC compliance of empty batteries, E is battery capacity. Table 1. Parameter setting A

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(2) Charge control for BCS The proposed model can monitor the state of battery power in each pile on the BCS, so as to carry out fine management of the battery on the BCS. Take the battery management of BCS2 as an example to analyze (as shown in Fig. 2), when the number of divided charging ranges is finer, the charging power control of the battery is more accurate, so

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that it can more accurately capture and respond to the fluctuation of electricity price over time. (3) Economic analysis of BSCS operation

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In general, it can be seen from the analysis of each section of the path that under the primary requirement of ensuring timely supply of BSS stock, BT absorbs excess new energy output from various places as much as possible. In a few cases, in order to meet the demand of charging and supplying FB, BT will choose to purchase electricity from the grid when the price is low (as shown in Fig. 3 (a)). As can be seen from Fig. 3 (b), during the operation cycle of 96 periods, BT helped the three distributed new energy sources absorb 16.95% of the excess output, that is, a total of 1089.714 kWh of electricity, which fully met the total disordered EV load demand of 1344kWh.

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Fig. 3. The purchasing power of BSCs and the consumption of renewable energy

Where (a) in Fig. 3 represents the purchasing situation of each charging station under the fluctuation of electricity price, (b) in Fig. 3 represents New energy consumption of each charging station.

5 Conclusion In this paper, a multi-agent integrated system BSCS is introduced, and the joint scheduling optimization of each agent in the system is studied. The main conclusions are as follows: (1) BT, which has the flexibility of energy storage and space-time movement, connects the energy supply of the entire BSCS system in the way of battery transfer, so that each subject in the BSCS system has a certain degree of operational autonomy and realizes the coordination of energy supply and demand. (2) For the constructed MIP, an improved PADM algorithm is used to efficiently solve the model. Effectively solve the strong coupling problem between integers and continuous decision variables, which will not cause large convergence time and dimension problems when applied to large-scale systems.

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In the future, we will pay attention to the cooperation of multiple BTS in the battery charging and replacement system, and consider more uncertainties to build multi-stage robust optimization or random optimization to improve the model. In addition, crossregional BSCS can match more new energy and EV batteries, and even supply energy for utility-level loads. These are all directions that the model can be extended to in the future. Acknowledgments. This work was funded by Yunnan basic research project (202301AS070055) and the National Key R&D Program of China (2022YFB2703500).

References 1. AGENCY I E. Net Zero by 2050[M/OL] (2021) 2. Liang, Y., Ding, Z., Zhao, T., et al.: Real-time operation management for battery swappingcharging system via multi-agent deep reinforcement learning. IEEE Trans. Smart Grid 14(1), 559–571 (2023) 3. Elliott, R.T., Fernandez-Blanco, R., Kozdras, K., et al.: Sharing energy storage between transmission and distribution. IEEE Trans. Power Syst. 34(1), 152–162 (2019) 4. Yan, J., Lai, F., Liu, Y., et al.: Multi-stage transport and logistic optimization for the mobilized and distributed battery. Energy Convers. Manage. 196, 261–276 (2019) 5. Zhan, W., Wang, Z., Zhang, L., et al.: A review of siting, sizing, optimal scheduling, and cost-benefit analysis for battery swapping stations. Energy 258, 124723 (2022) 6. Cui, D., Wang, Z., Liu, P., et al.: Operation optimization approaches of electric vehicle battery swapping and charging station: a literature review. Energy 263, 126095 (2023) 7. Cheng, S., Zhao, M., Wei, Z.: Optimal scheduling of electric vehicle charging and discharging with dynamic electricity price. Proc. CSU-EPSA 33(10), 31–36+42 (2021). (in Chinese) 8. BAN M. Joint optimal scheduling for electric vehicle battery swapping-charging system based on wind farms. CSEE J. Power Energy Syst. (2020) 9. You, P., Low, S.H., Tushar, W., et al.: Scheduling of EV battery swapping—Part I: centralized solution. IEEE Trans. Control Network Syst. 5(4), 1887–1897 (2018) 10. Yan, J., Menghwar, M., Asghar, E., et al.: Real-time energy management for a smartcommunity microgrid with battery swapping and renewables. Appl. Energy 238, 180–194 (2019) 11. Geissler, B., Morsi, A., Schewe, L., et al.: Penalty Alternating Direction Methods for MixedInteger Optimization: A New View on Feasibility Pumps[M/OL]. arXiv, 2017[2022–07–29] 12. He, G., Michalek, J., Kar, S., et al.: Utility-scale portable energy storage systems. Joule 5(2), 379–392 (2021)

Analysis of Unrecoverable Breakdown Ground Fault Scenarios in the Internal Insulation of Large Generator Stators Li Li1(B) , Kun Yu1 , Xiangjun Zeng1 , Lisi Chen2 , and Chenyu Wu1 1 School of Electrical and Information Engineering,

Changsha University of Science and Technology, Changsha 410114, China [email protected] 2 Hunan Sanmood Electric Co., Ltd., Yi Yang 413001, China

Abstract. Due to the complex physical structure and numerous equipment at the generator stator, the stator ground fault scenarios are complex and variable. The mechanism of single-phase ground fault breakdown is difficult to clarify. Starting from a typical stator ground fault scenario, this article explores the types of dielectric breakdown and degree of damage caused by internal grounding faults in large generators. These faults are mainly caused by excitation such as internal insulation defect discharge and slot gap discharge. As the internal insulation is mainly composed of solid insulation materials such as mica and semiconductors, such faults are often accompanied by permanent insulation damage. Analyze the theory of irreparable stator insulation grounding faults in typical scenarios. Study the effect of grounding residual current on core burning and melting. Compare and analyze the reliability of the allowable operating range of stator safe grounding current under different grounding methods. The simulation model is established to verify the effectiveness of the method. Keywords: Generator Stator · Ground Fault · Unrecoverable Insulation · Melting of Stator Core

1 Introduction The proportion of large generators in modern power systems is significant, and stator single-phase grounding arc faults occur frequently. The continuous burning arc is prone to burn or melt the stator winding insulation and iron core, so unit is tripping and shutdown. The safe and stable operation of the power system is seriously threatened [1]. Due to the complex structure and manufacturing process of the stator, it is very difficult to repair the grounding arc burning iron core. The stator winding has been subjected to complex operating conditions such as high temperature and high voltage, strong magnetic field for a long time [2]. Single-phase grounding arc faults are often caused by air gap breakdown caused by insulation damage between the stator winding and the iron core. According to statistics, in recent years, stator grounding arcing faults have occurred multiple times in Ertan, Longkaikou, and Dongwude power generation units [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 240–247, 2024. https://doi.org/10.1007/978-981-97-1072-0_25

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In the context of low-carbon energy, the increase in single machine capacity leads to a sharp increase in stator to ground capacitance current. The increasing single-phase to ground fault current further exacerbates the impact of grounding arc breakdown of winding insulation and burning of stator core. The combustion scenario of stator grounding arc belongs to the parallel arc of the medium voltage system based on the arc energy level and arc properties. After finite element modeling and analysis of the stator grounding arc, the burning process of the grounding arc on the stator core can be clearly defined [4–6]. The maximum stator grounding arc current under different voltage levels is analyzed in reference [7]. But the mechanism of the voltage level acting on the grounding arc resistance did not further is revealed. Reference [3] analyzed the iron core burn situation under the cumulative effect of stator grounding current and time based on temperature field modeling. However, in the stator grounding arc scenario, the characteristics of the breakdown gap arc during continuous voltage changes have not been clarified. Method for studying the effect of insulation aging on stator temperature rise based on operating experience and calculations [8]. The consistency between the calculation results and the long-term operation and testing experience of the generator is difficult to have universality [9]. Therefore, it is necessary to further analyze the interaction relationship between the voltage change at the stator grounding arcing point. Following the development trend of research on the mechanism of stator ground faults, the characteristics of insulation damage changes in stator ground faults are analyzed. By analyzing the arc power of irreparable grounding faults in the internal insulation of the stator, the thermal effect of the fault point current burning the iron core is combined. And the boundary conditions for the temperature rise of the stator iron core are established considering the gap changes during the aging process of the main insulation of the stator bar. The impact of stator grounding fault core burning is verified in the MATLAB simulation environment. A theoretical foundation for achieving safe disposal of generator stator grounding arc faults has been laid.

2 Physical Scenario Analysis of Stator Ground Fault 2.1 Unrecoverable Breakdown Grounding Fault Scenario of Stator Insulation Due to the complex production and manufacturing process of generator stator winding bars, there may be poor overall insulation performance. Under long-term operation, weak insulation points inside the bars are prone to internal discharge. So, leading to further electrical and thermal aging of the winding main insulation, the breakdown fault points in stator main insulation is formed [10, 11]. The internal discharge cross-section of the generator stator bar is shown in Fig. 1. The stator winding of the generator mainly uses alkali free glass fiber reinforced epoxy mica as the main insulation material[12]. And the type of material is generally designed to have a lifespan of over several decades within the voltage range that can be withstood. During the manufacturing process of generator stator winding main insulation, the production process of stator winding main insulation inevitably produces air gaps. When the generator is put into operation, the main insulation of the stator will withstand the rated potential. Under this electric field, gas breakdown will occur in the air gap of the winding, forming an internal discharge phenomenon.

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9

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Fig. 1. Cross section diagram of internal discharge of stator bar

The internal air gap discharge of the stator winding main insulation is initially excited by local high-frequency pulse discharge. During the discharge process, many gas molecules ionize, producing positive ions, negative ions, and free electrons. A space charge environment composed of many charged particles is formed in the internal air gap. Under the action of the electric field formed by the voltage of the generator air gap, space charges migrate to the air gap wall to establish an electric field opposite to the voltage applied by the generator. As the discharge process further occurs, the space charge gradually increases, forming a superposition of internal and external electric fields. And weakening the field strength between the air gaps, causing the electric field between the air gaps to be lower than the initial field strength of the discharge. When the voltage in the air gap increases again, a second discharge occurs. The accumulation of heat leads to thermal aging of the winding insulation. During the operation of the generator, the stator bar will generate a radial electromagnetic force with a frequency of 100 Hz in the slot. Sharp silicon steel laminations will cut the semi conductive layer on the surface of the windings. The air gap in the stator winding slot is caused by vibration. Under the action of a strong electric field, the gap gas is ionized. The forming ozone that can react chemically with nitrogen, and then producing acidic substances that cause chemical corrosion of the insulation, accelerating insulation aging. At the same time, the air gap generated in the slot will block normal heat conduction. Due to the continuous occurrence of partial discharge, the temperature of the winding will increase, accelerating the aging of insulation. Coil conductor Insulator Air gap

Core

Ground fault channel

Fig. 2. Cross section diagram of internal discharge of stator bar

Under the influence of multiple factors such as the main insulation air gap and slot gap, the generator stator voltage will completely breakdown the stator insulation

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material. The internal breakdown of the stator winding forms a grounding fault channel. The grounding fault channel forms a stable discharge circuit from the bar conductor to air gap, and iron core. The discharge channel is hidden inside the slot and is tangent to the thermal cooling cycle of the winding. The thermal effect of the grounding fault current is eliminated to result in the inability. The insulation damage area is exacerbated further, and the safety of the iron core is threatened. Due to the breakdown of solid insulation materials through the entire fault channel, once the breakdown occurs, its insulation performance cannot be restored, forming a permanent insulation damage fault that requires shutdown and repair. 2.2 Analysis of Arc Current Power for Stator Ground Fault In the scenario of irreparable stator insulation grounding fault, the heating effect of extremely short gap arc in the grounding fault current circuit is prominent [11]. The heating effect of grounding arc current on stator core burning seriously threatens the safe operation of the generator. Firstly, the relationship between stator grounding arc current and arc power is analyzed. There are many factors that affect the process from stator insulation degradation to breakdown, and the stable arcing stage of ground faults has the most significant impact on stator core damage. To eliminate random effects, the stable arcing stage of ground faults is taken as the analysis object. According to the analysis of arc energy, if the temperature of the grounding arc column of the very short gap stator does not change with time and space, the arc channel current only changes with the diameter of the arc channel. When the arc current increases, the thermal effect of the arc increases. So, the cross-sectional area of the arc increases, the arc resistance decreases. Therefore, the effective value of the arc voltage decreases with the increase of the current. The empirical formula for the static characteristics of short gap medium voltage arc and its volt ampere characteristics can be expressed  Ua = A + B Ian . U a is the arc voltage. I a is the arc current. To further confirm the size of parameters A, B, and n. A large amount of experimental data was linearly fitted, indicating that the short gap arc n = 1. In the equation, A = 74, B = 79, therefore, calculating the arc power based on voltage and current can obtain [3]. Parc = 74Iarc + 79

(1)

In formula (1), Parc is the stator grounding arc power. AC arc has a certain randomness due to the presence of ignition and extinction processes. However, in the scenario of internal breakdown faults where insulation cannot be restored, the arc power and current can be approximated as a linear relationship. For the decay process of arc power over time during the arc burning process, arc power data under different conditions are used for fitting. The fitting function is used Parc = kt x . k and x are the coefficients to be fitted, respectively. The coefficient k can be regarded as a factor that varies with the test current. The coefficient x is taken as a constant of −0.15 in the case of stator irreparable ground fault scenarios. It is assumed that the decay function of arc power over time does not change with the magnitude of arc current. By combining formula (1) with the decay function of arc power over time, the expressions for arc power and arc combustion time can be obtained. Parc = (74Ia + 79)t −0.15

(2)

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In the formula (2), Parc is the arc power.

3 Thermal Effect Damage Mechanism of the Unrecoverable Ground Fault Current in Stator Insulation In the scenario of stator ground fault, due to the good conductivity of the stator iron core, the grounding arc will directly discharge the iron core after breakdown. Therefore, a thermodynamic analysis is conducted on the burning of the iron core by the grounding arc current. The irreparable grounding fault scenario of stator insulation is as shown in Fig. 2. Combined with on-site accidents and test records, it is shown that after insulation breakdown fault occurs in the stator core. The area of insulation damage on the wire rod is small, and the burning effect on the stator at a short time scale is hemispherical. And the stator core laminations are melted, causing insulation damage between the laminations and forming lamination melting. Therefore, the burning of the stator ground fault point to the iron core can be equivalent to the heat transfer model of a stationary point heat source to an infinite conductor. The heat transfer hemisphere of the stator ground fault point heat source is equivalent as shown in Fig. 3. Stator winding Insulation Gap

R

Stator core Iron core burning point dR

Fig. 3. Equivalent schematic diagram of heat source conduction at stator ground fault point

To simplify the analysis process, it is assumed that the flow field after the melting of the stator core is not considered. And no phase transition occurs in the initial stage of the grounding fault current, ignoring the thermal radiation and convection of the grounding arc. According to the physical properties of iron core metal materials, the thermal coefficients of each conductor in their three-dimensional space are basically the same. Based on the temperature rise process, an expression for the temperature field of a semi-infinite conductor is established. −R2

2Q0 e 4at  dt dT = ρC0 (4π at)3

(3)

In formula (3), dT is the temperature change of the conductor. t is the action time of the point heat source. Q0 is the heat of the point heat source. C 0 is the specific heat capacity of the stator core. ρ is the material density. R is the distance from the point heat source. a is the thermal diffusivity and satisfies a = λ ρC0 . λ is the thermal conductivity. From formula (3), the temperature change of the stator core varies with the thermal conductivity time. As time increases, the temperature change of the iron core gradually stabilizes, and the initial temperature change is the most significant. The

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instantaneous heat of the point heat source satisfies Q0 = Parc dt. Parc is the instantaneous power of the point heat source, which can be integrated into formula (3) to obtain the temperature change value T as T = Parc (2π λR). To reduce the difference between the assumed conditions of the analytical solution and the actual situation, the accuracy of the calculation results is improved. Boundary conditions are studied for the scenario of stator irreparable insulation. Considering the changes in thermal conductivity after insulation aging, the gap between the original stator core and the insulation surface will disappear based on the looseness of the insulation layer. And the thermal conductivity of the insulation material will decrease. Furthermore, when the insulation of the stator bar is peeled off, the thermal conductivity further changes, which can be expressed as the equivalent thermal coefficient. λ=

(δ1 + δ2 )λ1 λ2 δ2 λ1 + δ1 λ2

(4)

In formula (4), λ1 is the thermal conductivity of the material after insulation aging. λ2 is the thermal conductivity of the air in the breakdown gap. δ1 is the gap between the main insulation and the slot wall of the stator core. δ2 is the size of the gap after insulation delamination. As shown in Fig. 3, the point heat source of power Parc continues to act. Substituting formula (2) and formula (4) into formula (3) can obtain the temperature rise expression of the stator core. Under the action of the breakdown arc current at time t from the heat source R in the hemispherical region, the fault arc current is Iarc. T (t, R, Iarc ) =

(74Ia + 79)t −0.15 2π λR

(5)

According to formula (5), the temperature rise of the iron core is inversely proportional to the radius from the center of the electric heat source. The farther away from the point heat source, the smaller the temperature rise of the iron core. Under the action of a continuous point heat source, the radius of the melting area of the iron core reaches a stable value. The power of the heat source and conforms to the actual burning situation of the stator iron core is proportional. Therefore, as the action time of the grounding fault current increases, the temperature rise component area stabilizes. And the temperature change is the most severe during the initial fault.

4 Simulation Analysis According to the stator grounding fault current and protection action setting time under different grounding methods of the generator, the relationship between arc power, current and time can be obtained as shown in Fig. 4. The grounding fault current is closely related to the grounding method. According to regulations, under different generator capacities, the capacitance current is generally larger under the resistance grounding method. However, to ensure the repairability of iron core burning, the maximum current is generally set below 25 A. The safe grounding minimum current is generally less than 1 A. The fault removed, the load transfer and shutdown demagnetization time should be considered. The time is generally less than 15 s. The time from breakdown to arc stability should be taken as 10 s for analysis.

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Parc/W

2000 1500

1000 500 0 0

1

2

3

4

t/s

5

6

7

8

9

10

0

5

10

20

15

25

Iarc/A

Fig. 4. Relationship diagram of arc power under changes in arc action time

As shown in Fig. 4, the arc power shows a linear increase trend as the arc current increases. The arc power decays exponentially with the arc extinction time. After the arc enters the stable combustion stage in the early stage of grounding fault, the arc power reaches its maximum. Due to the existence of thermal inertia, the final arc power region is stable. Under the condition of a ground fault current of 25 A, the maximum arc power can reach 2.724 kW. The fault removal time is within 10 s, and the minimum arc power can be controlled below 1.5 kW. According to the simulation analysis of different stator ground fault scenarios, the degree of damage to the stator core is shown in Table 1. The table discusses the variation of thermal conductivity based on the gap length after different insulation aging. Table 1. Temperature changes caused in the stator core by various factors of grounding faults. Number

λ/(W/cm·°C)

t/s

I/A

R/mm

T /°C

1

0.015

10

10

30

2050

2

0.020

10

5

20

1264

3

0.015

15

5

20

1190

4

0.020

15

5

10

2380

5

0.015

30

1

10

1623

From Table 1, under the same heat dissipation coefficient, the longer the current action time, the smaller the distance from the point heat source radius, and the higher the temperature. Therefore, reducing the fault current and reducing the action time of the current are the key factors to prevent iron core burns.

5 Conclusion The paper starts from the scenario of stator insulation irreparable grounding faults and analyzes the power analytical expression of stator grounding arc. Using the heat dissipation coefficient of the grounding fault material and the action time of the stator grounding fault current, the damage degree of the stator grounding fault current on the iron core

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lamination is studied. And through simulation, it was verified that the main indicators of grounding fault current burning the iron core are the current action time and current size. The farther away from the radius point power source, the lower the degree of burning. Acknowledgments. This work is supported by the Hunan Provincial Science and Technology Talent Recruitment Project (2023TJ-X86), Graduate Scientific Research Innovation Project of Hunan Province (CX20210789), Yiyang Science and Technology Talent Recruitment Project and Xiaohe Talent Project.

References 1. Wang, W.J.: Principle and application of relaying protection for main electrical equipment, 2nd edn. China Electric Power Press, Beijing (2002). (in Chinese) 2. Wang, W.J., Wang, X.H., Wang, Z.J.: Internal Fault Analysis and Relay Protection for Large Generator Transformer. China Electric Power Press, Beijing (2006). (in Chinese) 3. Gong, H., Gui, L., Zhou, G.H., et al.: Arc Burning Process of Stator Core Under Stator SinglePhase Grounding Fault of Generator. Electric Power Autom. Equip. 42(12), 197–203 (2022). (in Chinese) 4. Wu, A.Y.: MV generator ground fault arcing power damage assessment. IEEE Trans. Ind. Appl. 54(19), 12–915 (2018) 5. Edmonds, J., Daneshpooy, A., Murray, S.J., et al.: Turbo generator stator core study. In: 2007 IEEE International Symposium on Diagnostics for Electric Machines, Power Electronics and Drives, Cracow, Poland, 441–446. IEEE (2007) 6. Gao, C.X., Miao, Z., Chen, H., et al.: Mathematical model based on coil sub-element for permanent magnet synchronous motor with health and stator winding short-circuit fault. Trans. China Electrotechn. Soc. 38(04), 957–969 (2023). (in Chinese) 7. Rong, J.G.: Analysis and test of generator core burning by arc. High Volt. Eng. 19(2), 18–22 (1993) 8. Lin, X., Wang, N., Xu, J.Y.: Calculation and analysis of very fast transient over-voltage characteristic on the condition of dynamic arcing model. Proc. CSEE 32(16), 157–164 (2012). (in Chinese) 9. Li, D.J., Bai, Y.M., Wang, S.Y.: The influence of insulation ageing on stator temperature rise. Large Electric Mach. Hydraulic Turb. (06), 25–33+38 (1988) 10. Recommended practice for system grounding of industrial and commercial power systems. In: IEEE Std 3003.1™-2019. IEEE 3003 Standards: Power Systems Grounding. New York, June 2019, pp. 53–63 (2019) 11. Tai, N.L., Stenzel, J.: Differential protection based on zero-sequence voltages for generator stator ground fault. IEEE Trans. Power Del. 22(1), 116–121 (2007) 12. Yuan, Z., Jia, S., Liang, D., Wang, X., et al.: Research on slot-pole combination in high-power direct-drive pm vernier generator for fractional frequency transmission system. CES Trans. Elect. Mach. Syst. 6(4), 445–453 (2022)

Investigation on the Effect of the Self-generated Metal Vapour on the Cathode Spot Formation in Vacuum Arc by Molecular Dynamics Simulation Haonan Yang1(B) , Shuhang Shen1 , Ruoyu Xu2 , Mingyu Zhou3 , and Zhongdong Wang1 1 Centre for Smart Grid, University of Exeter, Exeter, UK

[email protected]

2 Global Energy Interconnection Research Institute Europe GmbH, Berlin, Germany 3 State Key Laboratory of Advanced Power Transmission Technology, Beijing,

People’s Republic of China

Abstract. Contact erosion is one of the key problems that limit the development of vacuum circuit breakers at higher voltage levels. Contact erosion in vacuum arc is the result of the plasma-surface interactions, located at the positions of cathode spots. Simulation studies on cathode spot dynamics have been of great significance in investigating the mechanism of contact erosion. Previous cathode spot simulations commonly assumed that the leftover plasma ions have a constant density function, which initiate and maintain the cathode spot. However, this assumption has a critical limitation as it does not include the self-generated metal vapour from the cathode spot, which plays a dominant role in sustaining the cathode spot. In this work, the contribution of the self-generated metal vapour on the development of an individual cathode spot is investigated, by studying the effect of back ions. Based on a self-consistent cathode spot model developed by the Molecular Dynamics method, comparisons are made among different cases where the contributions of leftover plasma ions and back ions are controlled. This work models the self-sustaining cathode spot without continuous input of leftover plasma ions for the first time. Simulation results show that the leftover plasma ions are necessary to initiate a cathode spot, while the self-generated metal vapour is sufficient to sustain the development of the individual cathode spot. The simulation results are validated by the comparable erosion speed of the crater depth to the experimental values. Keywords: Cathode Spot · Molecular Dynamic Simulation · Metal Vapour · Contact Erosion

1 Introduction Under the requirements of the smart grid, the development of vacuum circuit breakers (VCB) into higher voltage levels becomes of great significance [1]. At present, VCBs are mostly applied in medium voltage levels less than 145 kV, while for high voltage © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 248–255, 2024. https://doi.org/10.1007/978-981-97-1072-0_26

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levels above 200 kV, SF6 circuit breakers dominate the applications. However, SF6 is a greenhouse gas and its usage is forbidden in the net-zero future. VCB is a promising technique to replace the application of SF6 circuit breakers at the high voltage level. There are two main factors that limit the development of VCBs into higher voltage levels: the post-arc recovery of the vacuum gap which limits the insulation degree of the vacuum medium, and the lifetime or maintenance cost of the VCB contacts due to contact erosion. From the microscopic point of view, these two problems are related to the plasma-surface interactions on the contact surface, more specifically, the behaviours of the cathode spots [2]. Therefore, investigations into the mechanisms of cathode spot dynamics are of great importance to the advancement of the VCBs application. Cathode spots have been observed from experiments, with a lifetime of several tens of nanoseconds, and a spatial size of several micrometres [3]. On a clean cathode surface, new cathode spots were always found near the old cathode spots [4]. Therefore, it was perceived that the plasma generated from the previous cathode spots is the source to ignite the next ones. There are multiple interacting effects during the cathode spot processes. The leftover plasma ions obtain a high kinetic velocity from the acceleration through the cathode sheath, with the sheath voltage found a constant related to the cathode materials (for copper, the sheath voltage is 15V) [5]. Under the bombardment of the leftover plasma ions, the cathode spot will be initiated, which was shown by either a luminous spot during the arcing process or a surface crater after the arcing process [2]. Electron emission and atom emission take place on the heated cathode surface, the area of which gradually expands due to heat conduction. In addition, the generated metal vapour is ionised by emitted electrons. Part of the generated ions travel to the plasma side, while the rest generated ions return back to the cathode surface and are named as back ions. The extinguishment of a cathode spot was hypothesised to be the result of the untenable surface temperature, due to the insufficient density of plasma ions above the cathode spot [6]. However, this process has not been fully verified by far. Because the processes of cathode spots are super quick temporally and super tiny spatially, the present experimental techniques are unable to observe the dynamics of an individual cathode spot. Simulations of cathode spot dynamics are of interest in recent years. Some models are based on the hydrodynamics method to analyse the formation of an individual cathode spot [7, 8]. Also, a model based on molecular dynamics was built to present more practical results [9]. From these simulations, the evolution of the cathode craters has been studied. The previous cathode spot simulations commonly adopted an assumption of a constant density of leftover plasma ions, which functions as the input, igniting and maintaining the development of the cathode spots. However, this assumption lacks support from both experimental results and cathode spot theory. The vacuum arc or vacuum plasma is distinguished from the gas plasma as they highly rely on the metal vapour generated from the cathode surface. There should not be a high-density cloud of external plasma ions existing throughout the whole lifetime of a new cathode spot. Under this assumption, the cathode spot will soon die out without the leftover plasma ions, while the contribution of the self-generated metal vapour is neglected. This paper investigates the contribution of the self-generated metal vapour to the development of the cathode spot, based on a self-consistent MD model of an individual

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cathode spot in our previous work [9]. Multiple effects are coupled together, including the leftover plasma ions, surface electron emission, surface atom emission, back ions, Nottingham effect, Joule heating, as well as heat conduction. For the transition from surface-emitted atoms to the back ions, assumptions according to the cathode spot theory is adopted. The erosion behaviours such as the number of surface emitted atoms and the evolution of the crater depth are taken as simulation results. Three different simulation sets are conducted: #1 with constant leftover plasma ions and without the contribution of back ions, #2 with constant leftover plasma ions and with the contribution of back ions, and #3 with limited leftover plasma ions and with the contribution of back ions. By the comparison of these three simulations, the contribution of the self-generated metal vapour to the development of the cathode spot is discussed. This work, for the first time, simulates the self-sustained cathode spot without constant leftover plasma ions and highlights the importance of the self-generated metal vapour on the cathode spot development. The simulation results are compared with the erosion behaviours measured from the experiments to validate the simulations. This work helps understand the mechanisms of cathode spots and provides guidance on managing the contact erosion of VCBs.

2 Model Based on the cathode spot model established by the Molecular Dynamics method in [9], an advanced model is built to involve all the effects contributing to the formation of an individual cathode spot in LAMMPS [10]. The model consists of two parts, a lower part which is a copper substrate, and an upper part which is an empty headroom for inserting the leftover plasma ions and recording the surface atom emission. An example of the model is shown in Fig. 1. The size of the copper substrate is 22.4 × 22.4 × 11.2 nm. A thermostat layer with a constant temperature of 300K surrounds the copper substrate, while a fixed layer is attached at the bottom. A combined potential of the Embedded Atom Method (EAM) and ZBL is adopted to calculate the interatomic forces [11]. The timestep of the simulation is 1 fs, and the total simulation time is around 100 ps. As for the multiple effects involved in the cathode spot processes, they are all coupled in this model. The effect of the leftover plasma ions is presented by the ion bombardment, the effect of surface atom emission is realized by the atoms leaving the cathode surface when they possess sufficient axial velocities. The surface electron emission is calculated based on the surface temperature and ion density, according to the T-F emission theory [5]. For all the emitted atoms travelling out of the ballistic layer but staying within the bombardment area, they will be transferred to be back ions with a certain axial velocity. On the contrary, the rest emitted atoms are regarded as either not being ionised or not returning back as ions. This assumption is similar to the assumption commonly taken in previous cathode spot simulations [7-9] and is advanced by the geometrical consideration. In addition, the Nottingham heat and the Joule heat are calculated for each atom and are reduced or added to each atom after each timestep. By coupling all of these effects, a self-consistent model of cathode spot is built.

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Fig. 1. Cross-section of the MD simulation box: (a) the copper substrate, the thermostat layer, the fixed layer, and the headroom. (b) the leftover plasma ions, the evaporated atoms, and the back ions. The arrows in (b) represent the directions of the velocity.

The practical cathode spots are with a radius of 5–10 µm, while the radial size of the copper substrate in Molecular Dynamics is only around 10 nm. Therefore, this work does not model the whole cathode spot. Instead, only the central region with a radius of 10 nm is modelled. From the previous cathode spot simulations either by HD [7, 8] or by MD [9], the peak density of the leftover plasma ions is commonly located at the centre of the modelled cathode surface. As a result, a cathode crater with the same centre was obtained, with the maximum temperature, maximum electron current density, and maximum atom evaporation occurring at the centre. In other words, the centre of the cathode spot is the place where the erosion is most intense. Therefore, in this work, by simulating the central region of the practical cathode spot, the most intense erosion behaviours on an individual cathode spot will be obtained, which can represent the intensity of the contact erosion in the whole cathode spot.

3 Results Table 1 shows the settings of the three simulation sets. In all three simulations, the leftover plasma ions are set as the input to initiate the formation of the cathode spot. However, only in #1 and #2 are the leftover plasma ions maintained throughout the whole simulation period. Moreover, in #1 all the emitted atoms leave the copper substrate without any back ion, representing a similar case as the previous cathode spot simulations [7-9]. In comparison, in #2 the contribution of the back ions is coupled according to the description in Sect. 2. In addition, in #3, the effect of the back ions is coupled, while the input of leftover plasma ions only lasts for the first 50 ps and is stopped afterwards. The simulation set #3 represents the development of the cathode spot under the contribution of the self-generated metal vapour. Focusing on the erosion behaviours, the evolutions of the number of the total emitted atoms and the crater depth are taken as the simulation results. First, the simulation results of cases #1 and #2 are compared, as shown in Fig. 2. Figure 2(a) presents the evolution of the number of the total emitted atoms within 70 ps, while Fig. 2(b) presents the evolution

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of the crater depth within 70 ps. From Fig. 2(a), the surface atom emission is not obvious in the beginning but gradually becomes intense as the development of the cathode spot. Compared to case #1 without back ions, a greater surface atom emission is observed in case #2 with back ions. Moreover, the difference between the two cases becomes larger with time. Table 1. Simulation settings. Set number

Leftover plasma ions

Back ions

1

Constant for 100 ps

No back ions

2

Constant for 100 ps

With back ions

3

Constant for 50 ps

With back ions

Fig. 2. The erosion behaviours of simulation set #1 (no back) and #2 (partly back): (a) the total number of surface-emitted atoms, (b) the crater depth.

In Fig. 2(b), the cathode surface first swelled up since the surface temperature increased and the interatomic distances became larger. Combined with Fig. 2(a), it can be found that the erosion behaviours are very slight during this period. However, after 20 ps the surface started to sink inwards. The time of the appearance of the sunken crater is similar for the two cases because the effects of leftover plasma are the same. However,

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the evolution of the crater depth in case #2 is faster than in case #1. A deeper crater is formed with the existence of the back ions. At 70 ps, the crater depth in case #1 is about 3 nm, while that in case #2 is already 5 nm. The greater erosion behaviours of case #2 exhibit the fact that with the contribution of the self-generated metal vapour, the development of the cathode spot is faster, and the contact erosion is more severe. The reason for this difference is the positive feedback established in case #2. When the emitted atoms are transitioned to back ions, they will bombard the cathode surface afterwards. As a result, the surface temperature increases faster. Also, according to the sputtering theory of ion bombardment [12], for a certain ion energy and a certain surface temperature, the sputtering yield should be constant. Therefore, with more ions bombarding the surface, more atoms will be emitted, either by evaporation or by sputtering. This positive feedback leads to a much faster development of the cathode spot, and more intense contact erosion. Next, the evolutions of the crater depth of case #2 and case #3 within 100 ps are presented in Fig. 3. During the first 50 ps, the crater depths were the same in the two cases. However, after 50 ps, the erosion speed of #2 did not change, while the erosion speed of #3 decreased. This result is as expected, since in #3 the input of the leftover plasma ions was stopped. However, compared to the previous cathode spot simulations it is unexpected that the erosion speed was still maintained in #3 after 50 ps.

Fig. 3. The evolution of crater depth of simulation set #2 (constant leftover ions) and #3 (limited leftover ions).

In previous cathode spot simulations, the kinetic effect of ion bombardment was ignored. Instead, the calculated energy flux density and pressure were set as boundary conditions on the cathode surface. Also, the surface atom emission cannot be observed, which was assumed as the saturated evaporation. Therefore, the contribution of the selfgenerated metal vapour to the cathode spot development was ignored, and the cathode spot would stop growing when the input of leftover plasma ions was stopped, which is not reasonable. However, in this MD model, by simulating the kinetic effect of ion bombardment directly, intense sputtering is observed, which leads to greater surface atom emissions than those assumed in previous simulations. As a result, the contribution of self-generated metal vapour is found non-negligible. As shown in Fig. 3, even when the

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input of leftover plasma is stopped, the development of the cathode spot and the erosion behaviours are maintained by the back ions at a considerable rate. From the experimental results of the cathode spot, the crater depth is 2–3 µm after the lifetime of tens of nanoseconds [3, 4]. From our simulation, the erosion speeds of both case #2 and case #3 are around 0.05–0.1 µm/ns. Direct comparison cannot be made as erosion speed could not be measured by experiments by far. However, by estimating the practical erosion speed by the crater depth and the lifetime of the cathode spot, the simulated range of erosion speed is comparable to the experimental values. Therefore, from our simulation, even though the input of leftover plasma ions is stopped, the self-generated metal vapour can still maintain the development of the cathode spot.

4 Conclusion In this work, the contribution of self-generated metal vapour to the development of a cathode spot is investigated, using a self-consistent model of an individual cathode spot developed in Molecular Dynamics. Leftover plasma ions with a constant density are assumed to initiate the cathode spot. The evolutions of surface atom emission and the crater depth are taken to indicate the intensity of contact erosion. By comparisons of three simulation sets with different combinations of leftover plasma ions and back ions, it is found that the surface atom emission becomes more intense when considering the effect of back ions. In addition, even though the input of leftover plasma ions is stopped, the cathode spot still continues to grow at a comparable rate to the experimental values. This finding aligns more with the cathode spot theory, in short, the leftover plasma ions are necessary to initiate the cathode spot, however, the back ions produced by the self-generated metal vapour are able to maintain the development of the cathode spot. Acknowledgements. This work was supported by the State Grid Corporation of China Science and Technology project 5108-202218280A-2-77-XG.

References 1. Yifei, W., Xin, L., Jianyuan, X., Wei, L.: Research on motor drive technology for an operating device of 126kV vacuum circuit breaker. IEEE Trans. Elect. Electron. Eng. 18, 970–979 (2023) 2. Slade, P.G.: The Vacuum Interrupter Theory, Design, and Application, 2nd edn. CRC Press, Boca Raton (2018) 3. Juttner, B.: Erosion craters and arc cathode spots in vacuum. Contrib. Plasma Phys. 19, 25–48 (2010) 4. Juttner, B.: Cathode spots of electric arcs. J. Phys. D Appl. Phys. 34, 103–123 (2001) 5. Boxman, R.L., Sanders, D., Martin, P.J.: Handbook of Vacuum Arc Science Technology Fundamentals and Applications, 1st edn. Noyes Publications, New Jesery (1996) 6. Yun, G., Jinlong, D., Xinggui, C.: Three-phase modeling of 40.5kV vacuum circuit breaker switching off shunt reactors and overvoltage suppression measure analysis. Electric Power Syst. Res. (194), 107058 (2021) 7. Lijun, W., Xiao, Z., Jiagang, L.: Model of cathode spots crater formation and deuterium desorption process on zirconium deuterium electrode. IEEE Trans. Plasma Sci. 49, 401–413 (2021)

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8. Lijun, W., Xiao, Z., Jiagang, L.: Study of cathode spot crater and droplet formation in a vacuum arc. J. Phys. D: Appl. Phys. (54), 215202 (2021) 9. Haonan, Y., Shuhang, S., Zhongdong, W.: Molecular dynamics simulation of cathode crater formation in the cathode spot of vacuum arc. J. Phys. D: Appl. Physics (56), 375023 (2023) 10. Thompson, A.P., et al.: LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. (271), 108171 (2021) 11. Deluigi, O.R., Pasianot, R.C., Valencia, F.J., Simulations of primary damage in a high entropy alloy: probing enhanced radiation resistance. Acta Materialia (213), 116951 (2021) 12. Anton, V.N., Andery, D.Z., Alexey, E.I.: On the angular distributions of atoms sputtered by gas cluster ion beam. Vacuum (212), 112061 (2023)

Study on Electromagnetic Radiation Phenomenon in Electrical Wire Explosion Ruoyu Han1,2

, Menglei Wang1 , Wei Yuan1 , Juan Wu1 , Manyu Wang1 , Pengfei Li1 , and Xi Chen1(B)

1 State Key Laboratory of Mechatronics Engineering and Control,

Beijing Institute of Technology, Beijing 100081, China [email protected] 2 State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Abstract. High-voltage pulsed discharges come with strong transient electromagnetic field due to the fast release of electric energy. Electrical explosion, as a special kind of pulsed discharge, exhibits more interesting electro-physical features than ordinary gas breakdown manner. In this study, we measured the electromagnetic field in the vicinity of an exploding Cu wire load. Meanwhile, the discharge waveforms and high-speed images were captured synchronously. The results revealed that there existed several electromagnetic radiation bursts within a single shot of wire explosion. Further analysis ascertained those radiations were closely related to the current variation through the wire load. In the frequency domain, the spectrum appeared wideband feature, and the majority of the energy is within 200 MHz. In addition, changing the discharge parameters can significantly alter the strength and frequency characteristics of the electromagnetic field and wave. Keywords: Electromagnetic Radiation · Pulsed Discharge · Electrical Explosion

1 Introduction Wideband electromagnetic wave (EMW) pulses can be a harmful interference source for electronic devices and communication systems [1–3]. Gas discharges, as the oldest approach to generate wideband EMW from Hertz (1893) [4], still remain active in power systems for the potential fault location [5–7]. Although the progress in semiconductors promotes the generation of wideband EMW in a more efficient and controllable manner, the methodology based on gas discharge should not be overlooked. On the one hand, gas discharges can easily achieve much stronger radio emissions, especially with pulsed power circuits [8]. On the other hand, it can simulate various wideband EMW, such as lightning, complex electromagnetic environment, electrostatic discharge (ESD), etc. [9– 11], and thus becomes an indispensable tool for testing the electromagnetic interference for electron devices [12, 13]. The investigation on discharge-related electromagnetic radiation has been conducted for many years, especially in the fields of power systems, electronics, geophysical © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 256–263, 2024. https://doi.org/10.1007/978-981-97-1072-0_27

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research, etc. [7, 14, 15] Theoretically, the electromagnetic radiation or saying the EMW emission mechanism of an electrical gas discharge system can be attributed to two aspects, circuit current and plasma radiation. Therein, the discharge channel can be regarded as an electric dipole source [16]. Zhang et al. measured the current and electromagnetic signals in Trichel pulse (negative corona discharge), and obvious correlations in time and frequency domain were verified [17]. In a larger scale, lightning discharge can also be regarded as a very long discharge channel with time-varying current. However, the long-distance breakdown is extremely difficult and brings new physics or phenomena, such as leader, return stroke, etc. The related processes of charge movement would be rather complicated. As a result, a wide spectrum of electromagnetic radiation from radio to x-ray/γ-ray regime [18]. Recently, Fan et al. captured the pulse train of magnetic field of “stepwise” propagating of upward positive leader [19]. Clearly, besides the radiation mechanism of electric dipole of pulsed current channel, the detected EMW may also come from the plasma-related processes. The electrical explosion refers to a special kind of pulsed discharge [20]. When placing a fine metal wire/foil between the gap of the gas discharge system, one may obtain an electrical explosion of the wire/foil. Different from an ordinary gas discharge, the electrical explosion exhibits more complex electromagnetic, thermodynamic, and mechanical effects [21]. Therein, the conductor is heated by the applied pulsed current, finishing a series of phase transitions and ionization to plasma state in a very short period. The conductivity of the load varies in several orders of magnetite during the discharge, which significantly changed the circuit behaviors as a non-linear resistor [22]. As a result, the time-varying resistance brings time-varying electric and magnetic field in the vicinity of the load, radiating EMWs. Different from a gas discharge with monotone decrease of resistance after breakdown, the current and voltage can exhibit obviously different features under several discharge modes [23]. In addition to this, the plasma in electrical explosion evolves from warm-dense-matter to arc-like regime, with a high expansion speed [24–26]. It is therefore anticipated that the complex, non-ideal plasma will bring more interesting results in radio-frequency EMW. After all, the higher energy emission of x-ray and optical light of wire explosion has been widely investigated [27– 29]. A recent study has phenomenally reported the electromagnetic signals captured in small-scale electrical explosion (with weak plasma process) [30], which has shown obviously different frequency spectrum than a gas breakdown [31]. Thus, the electrical explosion has attractive potential to be a wide-band electromagnetic radiation source, and more systematic and insightful work should be conducted. In this study, an experimental investigation is performed on exploring electromagnetic radiation characteristics and EMW emission mechanisms of an electrical wire explosion under different discharge conditions. The main issues examined are as follows. Firstly, the atmospheric electrical explosion is achieved and main processes are depicted. Secondly, electromagnetic radiation signals are demonstrated and correlation analyses are made. Finally, frequency domain analyses are made to find out more details for different electromagnetic radiation bursts in a single electrical wire explosion event.

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2 Experimental Setup 2.1 Pulsed Discharge Facility A simple micro-second timescale pulsed power source is adopted to achieve electrical wire explosions, as shown in Fig. 1. In the system, the pulse capacitor (6 μF capacitance) was charged to 7.1 kV voltage, at about 150 J stored energy. Then, close the switch (a trigger spark gap here), the capacitor will be shorted and pulsed current will pass through a coaxial cable to the wire holder and initiate wire explosion via Joule heating mechanism. Thus, the discharge process can be regarded as an RLC circuit. The exploding wire mainly plays a dynamic resistor and inductor in this process. Note that the resistance may vary in several orders of magnitude, while the inductance is less so. Under this arrangement of devices, the puled current can reach 10 kA level in about 4–5 μs (with fake load). More information on experimental devices can be found in the reference [32]. In the experiment, we control the length of the Cu wire to 4 cm and the diameter of the Cu wire to 50 mm.

Fig. 1. Experimental platform.

The voltage and current were obtained with PVM-5 high-voltage probe (bandwidth of 80 MHz) and Pearson 101 Coil (bandwidth of 4 MHz). The resistive load voltage could be roughly estimated as UR (t) = U (t) − L

di(t) dt

(1)

where U R is the resistive voltage drop of the wire load and U is the measured voltage. L refers to the inductance of the load and its holder. The plasma dynamics were monitored by a high-speed camera with a sampling speed up to 310,000 fps.The electromagnetic radiation was measured by a spiral antenna, placing 1 m away from the wire load, as shown in Fig. 2.

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Fig. 2. Schematic of the field measurement and characteristics of the antenna.

3 Results and Discussion 3.1 Main Process of the Electrical Explosion In order to study the characteristics of electromagnetic radiation in electrical wire explosion, it is necessary to have a clear diagnosis of the main process of the exploding wire. The high-speed camera synchronized with the discharge signal provides the reference. Fig. 3 show the electrical signal and high-speed backlight image under the specific conditions (7.1 kV-charging voltage, 4 cm-copper wire length and 50 mm-diameter).

Fig. 3. Typical discharge signal (a) and high-speed backlight image.

It can be clearly seen that the discharge mode has obvious current pause and secondary breakdown from Fig 3 (a). During the first current pulse, the exploding wire completed the phase transitions from solid to liquid and then to gas. Over-voltage occurred at this stage due to the rapid change in the resistance of the exploding wire during the phase transition process. The corresponding high-speed image is Frame #1, the exploding wire showed significant volume expansion and phase transition. Subsequently, due to the insufficient residual voltage between the electrodes to complete the breakdown of the explosive products, the current pause occurred. At this stage, the explosive products continue to expand, the current is maintained at tens of amperes, and the voltage continues to leak. Until the diffused explosive products can be broken down by residual voltage, secondary breakdown occurred. The discharge plasma channel (DPC) formed by breakdown is accompanied by strong light emission, as shown in Frame #3. Then, the remaining energy gradually dissipates in the DPC, manifested as the oscillation attenuation of the current. Of course, the diameter of the plasma column would gradually decrease over time. Around 300 μs, the light emission of the plasma gradually disappears. However, the thermal radiation of vapor can last for a longer time, approximately a few milliseconds.

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3.2 Electromagnetic Radiation Behaviors Based on the clear understanding of the main process of electric explosion, the behavior of electromagnetic radiation is the focus of our attention. The typical waveform of discharge electromagnetic radiation signal is shown in Fig. 4. In order to understand the temporal correlation between electromagnetic radiation and discharge processes, the current and the rate of current change are also presented in Fig. 4. From Fig. 4, electromagnetic radiation can be divided into three stages, corresponding to the ➀, ➁ and ➂ in the figure. The first stage corresponds to the Joule heating initiation stage of the wire. At this time, the pulse current has just been applied to the wire, and the wire was equivalent to a microwave antenna, radiating electromagnetic signals into space under the excitation of strong pulsed currents. The second stage corresponds to the moment when the electrical wire explosion occurs. The phase transition of the wire from the vapor to the low ionized plasma is accompanied by over-voltage and the rapid cutoff of the current. Strong electromagnetic radiation intensity is the main characteristic of this stage. The third stage corresponds to the generation of the high ionized plasma during secondary breakdown. The rapid movement of plasma generates electromagnetic radiation with higher frequency and longer duration. However, compared to the previous two stages, the electromagnetic radiation intensity in this stage is relatively weak.

Fig. 4. Typical electromagnetic radiation signal of electrical wire explosion.

3.3 Time and Frequency Domain Analysis In addition, perform fast Fourier transform (FFT) on the three zones mentioned in the previous section to study the frequency characteristics of electromagnetic radiation. The relevant results are shown in Fig. 5. For the stage 1, the dominant frequency appears at 8, 100 and 180 MHz. Compared to the frequency of stage 1, the frequency of stage 2 has a similar dominant frequency. However, the amplitudes of the two exhibit different behaviors. For the stage 2, the low-frequency part has a higher amplitude, while the high-frequency part has a lower

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amplitude. The similarity between the two indicates that there is a certain commonality between the electromagnetic radiation caused by the application of pulse current and the electromagnetic radiation caused by current cutoff of electrical wire explosion. Essentially, both are emissions of strong electromagnetic radiation caused by sudden changes in current. However, the plasma electromagnetic radiation corresponding to stage 3 is different. In the experiment, we only observed the low-frequency plasma radiation at around 25 MHz. This may come from the alternating current in the DPC. However, due to the limited detection spectrum of the antenna, the high-frequency electromagnetic radiation caused by bremsstrahlung has not been fully demonstrated. In addition, escaping electrons may also generate higher frequency radio radiation, which is worth further exploration.

Fig. 5. Frequency analysis of different stages

4 Conclusion In this paper, the electromagnetic radiation phenomenon was studied and mechanism explored. Due to the strong non-linear behavior of the resistance of the metallic wire load from solid to plasma state, the electric and magnetic field show unique variations as a function of time, which is distinctively different from that of a gas breakdown or pulsed discharge. Phenomenally, several electromagnetic radiation bursts were detected within the discharge process, mainly corresponding to the mutation of the discharge current. Specifically, the metal-insulator transition of the wire throttles the circuit current and brings the strongest radiation pulse. In addition, each of the current’s zero-crossing point will also generate electromagnetic pulses, implying the breakup and re-ignition of the current during the oscillation. More information could be obtained from the frequency domain analysis of the signals by using the Fast Fourier Transform. The overall spectrum shows that the radiation in radio-frequency domain could be close to 200 MHz, with typical continuous spectrum and strip regions.

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Measurement and Analysis of Multiple Parameters of Enhanced Accelerator Zihao Tian, Lihua Zhu(B) , Jianying Hao, and Ping Liu Tianjin Key Laboratory of New Energy Power Conversion, Transmission and Intelligent Control, Tianjin University of Technology, Tianjin 300382, China [email protected]

Abstract. The armature velocity, electromagnetic field, and spatiotemporal distribution of rail stress are important parameters of enhanced accelerators. It is extremely difficult to obtain dynamic parameters under extreme conditions. In order to obtain them, a multi-parameter measurement platform of enhanced accelerator is designed in this paper. The velocity of the armature and the magnetic field curve at a specific point are obtained by using a B probe, the spatiotemporal distribution characteristics of rail vibration displacement are obtained by using a laser micro displacement measurement device. Finally, the armature velocity, magnetic induction intensity B at a certain point in space, and the vibration changes of the rail at different times during the launch process are obtained through experiments. This work provides experimental basis for numerical calculation of multi field coupling and improving the service life of accelerators. Keywords: Enhanced Accelerator · B probe · Vibration

1 Introduction Electromagnetic acceleration technology has become a hot spot in the research of new concept weapons [1, 2]. When the armature slides at high speed, its working environment is extremely bad. Therefore, it is important to mastere the velocity of armature, the electromagnetic field of the accelerator and the spatial and temporal distribution characteristics of the vibration displacement of electromagnetic accelerator. In the literature, the current density distribution, temperature field [3–5], numerical calculation of electromagnetic field [6, 7], structure design of armature [8, 9] and rail have been studied extensively. In [10], the electromechanical coupling launch dynamics model of electromagnetic railgun by modeling methods have been established. The motion of the armature and the electromagnetic force have been studied. In [11], the magnetic field characteristic analysis model of electromagnetic railgun based on CST software have been established. The changes of transient magnetic field is studied. In [12], the sliding electric contact between the armature and rails have been studied. The experimental results of armatures in different positions are analysed. In [13], the accelerator is simplified as an infinite Bernoulli-Euler beam fixed on an elastic support. A multi-physical coupling dynamic model of electromagnetic-structure-motion is established by using a mixed finite element/boundary method to study the contact pressure © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 264–272, 2024. https://doi.org/10.1007/978-981-97-1072-0_28

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and strain distribution. The above research results focus on simulation analysis and single parameter measurement, and there is less research about the multi-parameters measurement of the enhanced accelerator. Our research focuses on the multi-parameters dynamic measurement of the electromagnetic accelerator. The velocity and displacement of the armature, the trends of magnetic field, and the changing trend of the rail vibration displacement is measured by experimental equipment. On the basis of the experimental data, the changing processes of armature and rail during electromagnetic launch is analyzed.

2 Principle of Accelerator

Fig. 1. Schematic diagram of the enhanced Accelerator

A schematic of the enhanced accelerator is shown in Fig. 1. The enhanced accelerator is made of four rails. The yellow material is copper, the green material is epoxy resin, the gray material is wear-resistant steel, and the silver-white material is aluminum alloy. The rails is connected by the copper plate on the side. Current flows in from one rail, flows through the armature and flows out from the other rail. Magnetic field is generated in the loop. The armature is moved forward by Lorentz force. If the current in the loop is respectively i1 , i2 , i3 , …, the inductance gradient of the main rail is L’1 , and the mutual inductance gradient between the lead rail and the auxiliary rail is M’12 , M’13 …. The force F of the armature is [14]: 2i2 1 2i3 (L1  + (1) M12  + M13  + ...) i12 2 i1 i1 Because the current of each loop in the enhanced accelerator is the same, the above formula is simplified as: F=

F=

1 (L1  + 2 M12  + 2 M13  + ...) i12 2

(2)

3 Measurement Method and Principle 3.1 The Measurement Principle of B Probe A diagram of the placement of B probes is shown in Fig. 2. a is the distance between the inner rails. c is the distance between the probes. l is the length of the rail. x(t) is the distance of the armature movement. I(t) is the size of the pulse current. When the armature passes through the B probes successively, the peak time of the induced voltage is denoted as t 1 , … t n .

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Fig. 2. B probe placement diagram

The speed at which the armature reaches the middle point of the two adjacent B probes is denoted as follows: v=

c c = t tn − tn−1

(3)

As the pulse current passes through the rails, magnetic field will change in the surrounding space. According to the law of electromagnetic induction, in a loop with a resistance R in series, the changing flux m creates an induced electromotive force ϕ. The induced electromotive force ϕ is proportional to the rate of change with time of the magnetic flux m passing through the closed loop, that is denoted as follows [15]:  d s B · ds d m ϕ=− =− (4) dt dt where ϕ is the induced voltage, m is the flux, B is the magnetic induction intensity, s is the coil area, ds is the element area, and t is the time. When the number of turns of the coil is N and the area ds is certain, the formula for calculating the magnetic field strength is:  t2 t ϕdt (5) B= 1 Nds 3.2 The Principle of Speed Measurement with Light Curtain Target

Fig. 3. Light screen target velocity measurement system diagram

A schematic diagram of the velocity measurement system of the light curtain target is shown in Fig. 3. It is composed of two laser transmitting and receiving devices. When the armature passes, the laser at the transmitting end is blocked, and the voltage signal is output at the receiving end. The time when the armature passes through the front end light curtain target is denoted t f , and the time when the armature passes through the rear end light curtain

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target is denoted t r . The distance between the two devices is denoted x. Muzzle speed is: v=

x tr − tf

(6)

3.3 The Principle of Laser Micro-displacement Measurement There are many commonly used laser measurement methods. Different laser measurement principles correspond to different usage scenarios. The main body of the laser micro-displacement measurement system is the LV-S01 single point laser vibrometer. It is a laser echo vibrometer using the Doppler principle. Its principle is: when the rail moves towards the laser vibrometer, the receiving frequency becomes higher. When the rail moves away from the laser vibrometer, the receiving frequency becomes lower. If λ is expressed as the wavelength of the original wave source, μ is expressed as the wave speed, f is expressed as the frequency of the wave source, and v is expressed as the moving speed of the observer. The formula for calculating the wave source frequency is: f =

μ2 λ(μ ± v)

(7)

The collected experimental data of wave source frequency is output to digital signal by data processing equipment. The non-contact advantages of the laser vibrometer solve the disadvantages of high temperature and strong magnetic interference in the actual measurement.

4 Construction of Experimental Platform 4.1 Construction of Enhanced Accelerator Platform The experimental platform of the enhanced accelerator is shown in Fig. 4. The main body of the enhanced accelerator is shown on the left. The charge and discharge control of the pulse capacitor is realized by collecting the optical fiber signal of the system. The intermediate device in Fig. 4 is a light curtain target. The sandbox on the right of Fig. 4 is used to collect the armature is launched.

Fig. 4. Experimental platform of enhanced Accelerator

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Fig. 5. Physical drawing of measuring device

4.2 Construction of Speed Measurement Platform 1) B probe velocity measurement platform was built The position, number of turns and winding mode of B probe is shown in Fig. 5 (a). The distance between the first B probe and the second B probe is 400 mm. The second, third, fourth, and fifth B probes are 500 mm apart in turn. The first B probe is isolated. The second and third B probes are connected in series by positive and negative winding. The fourth and fifth B probes are the same as above. The 5 B probes are divided into 3 parts and output 3 voltage signals through the pico device. 2) Construction of velocity measurement platform of light curtain target The muzzle velocity measurement system of the light curtain target is shown in Fig. 5 (b). The role of the XGK-GMB-DY power supply is to provide power for the laser velocity measurement device. It also can collect data on the time when the armature passes through. The distance between the front plate and the back plate of the laser measuring device is 505 mm. 3) Construction of magnetic induction intensity measurement platform The magnetic induction intensity measurement platform is the same as the B probe velocity measurement platform. The change of magnetic induction intensity is obtained by processing the induced voltage when the armature passes through the B probe with matlab software. 4.3 Construction of Laser Micro-displacement Measurement Platform The laser micro-displacement measurement system is shown in Fig. 5 (c). It is composed of laser instrument, signal receiving and processing device and software. The vibration of the rail in the horizontal direction is obtained by influencing the wavelength received by the laser through the slight displacement of the rail in the horizontal direction.

5 Analysis of Experimental Results 5.1 Experiment Parameter The experimental parameters mainly include material parameters, size parameters, pulse current parameters and so on. The details are shown in Table 1 below.

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Table 1. Transmitter basic parameter Transmitter basic parameter

Data

The form of the launcher

Enhanced Accelerator

The effective length of the rail

2100 mm

The width of the rail

30 mm

The material of the rail

Red copper

The material of the armature

Aluminium alloy

Electric current density

>108 A/m2

Insulating board material

Epoxy board

Fig. 6. Schematic diagram of pulsed current

5.2 Pulse Current Curve Analysis The pulse current curves at 3.5 kV, 4 kV and 5 kV voltage levels are shown in Fig. 6. It can be seen from the curve that the pulse currents of the three levels reaches the maximum value around 0.3 ms. The peak pulse current of 3.5 kV, 4 kV and 5 kV is about 173 kA, 198 kA and 246 kA, respectively. The inflection point of the falling part of the curve is caused by the armature exit. After the armature is out of the muzzle, the current does not decrease to 0 instantaneously because the strong current breaks through the air. 5.3 Experimental Results of Velocity Measurement

Fig. 7. Experimental curve of velocity measurement

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1) B probe data analysis The B probe data in the experiment is shown in Fig. 7 (a). Since the B1 signal is a separate B probe, there is only one peak. The first upward trend of B1 signal is because the rail and armature are energized, and the starting position of the armature is very close to the B1 probe, so it causes the change of the spatial magnetic field around the B1 probe. The second upward trend in the B1 signal is due to a larger change in the spatial magnetic field around the B1 probe as the armature passes through the B1 probe. After the armature passes through the B1 probe, the B1 signal will appear negative due to the action of eddy current. Therefore, the peak time of the B1 probe is equivalent to the time when the armature reaches the B1 probe. Because the B2 probe and B3 probe are connected in series, the output B2 voltage signal has positive and negative two peaks. The negative peak of the B2 signal is equivalent to the time when the armature reaches the B2 probe, and the positive peak of the B2 signal is equivalent to the time when the armature reaches the B3 probe. The same is true for B3 signals. By observing the signals of B1, B2 and B3, the effect of the space magnetic field change caused by the energized rail can be eliminated by winding the two B probes in series. 2) Light curtain target data analysis The experimental data of the light curtain target at a voltage level of 4 kV is shown in Fig. 7 (b). The negative voltage at the initial moment in the figure is due to the influence of arc light on the acquisition system. Because the experiment is carried out in a confined space, the effect of air resistance on the armature speed is ignored. The velocity obtained by the analysis of the light curtain target is equivalent to the muzzle velocity of the armature. 3) Velocity curve analysis The displacement and velocity-time curve of the armature fitted by the above experimental data at the voltage level of 4 kV is shown in Fig. 7 (c). The acceleration of the armature is represented by the slope of the velocity-time curve in the figure. The magnitude of the acceleration reflects the magnitude of the resultant force exerted on the armature. The resultant force is affected by many factors such as current. The slope of the armature displacement-time curve in the figure shows that the armature movement speed in the chamber has been increasing. The maximum speed is gained by the armature when the armature is out of the muzzle. 5.4 Curve Analysis of Magnetic Induction Intensity The change curves of magnetic induction intensity of B1 probe and B2 probe obtained through data processing are shown in Fig. 8. When the pulse current reaches the maximum value at 0.3 ms, because the armature is closest to the B1 probe, the magnetic induction intensity of the B1 probe is greater than B2 probe. Because the velocity of armature passing through B1 probe is smaller than that of B2 probe, the change rate of magnetic induction intensity of B2 probe is higher than B1 probe.

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Fig. 8. Curve of magnetic induction intensity

5.5 Vibration Curve Analysis of Lower Inner Track The vibration displacement-time curve of the rail at 4 kV voltage is shown in Fig. 9. It can be seen from the figure that within a few seconds, the vibration displacement of the rail first increases and then decreases and the final becomes stable. Because the launch test is carried out in a closed space, and the pressure in the air at the exit of the armature changes dramatically, which causes the laser micro-displacement measuring device to deviate from the zero point at last.

Fig. 9. Vibration displacement-time curve

A partial curve of the rail vibration displacement-time curve at 4 kV voltage is shown Fig. 9 (a). The peak of the curve in Fig. 9 (c) is to determine the time when the armature reaches the vibration measurement point. It can be seen from Fig. 9 (a) that the vibration displacement of the rail changes irregularly at the initial time, and when the armature passes through the measuring point, and the vibration displacement of the track increases rapidly, and the maximum value is about 0.001 mm.

6 Conclusion In this paper, the measuring principles of the measuring devices are introduced. And the measurement methods of each parameter of the enhanced accelerator are provided. According to the experimental data, the main conclusions are: When the armature is out of the muzzle, the current drops dramatically, but the current does not decrease to 0 instantaneously. That is because the strong current breaks through the air and the loop is created. The method of connecting two reverse-wound B probe in serie can eliminate the error of space magnetic field variation caused by energizing the enhanced accelerator.

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The spatial magnetic field distribution changes with the change of pulse current and the movement of armature. The vibration displacemen changes irregularly at the initial time. When the armature passes through the measuring point, and the vibration displacement of the rail increases rapidly, and the maximum value is about 0.001 mm. Acknowledgments. This research is supported by National Natural Science Foundation of China (No.92066206).

References 1. Ma, W., Lu, J.: Research status and challenges of electromagnetic emission technology. Trans. China Electrotech. Soc. 38, 1–17 (2023). (in Chinese) 2. Xu, W., Ye, W.: Current situation and development trend of augmented electromagnetic launching technology. High Volt. Eng. 49(2), 871–884 (2023). (in Chinese) 3. Wu, X., Lu, J., Li, Y., et al.: Experimental study on temporal and spatial distribution of rails temperature in electromagnetic launch. Gaodianya Jishu/High Volt. Eng. 44(6), 1982–1987 (2018). https://doi.org/10.13336/j.1003-6520.hve.20180529034 4. Yifan, G., Shihong, Q.: Transient electromagnetic thermal coupling field of electromagnetic launch rail section. J. Wuhan Inst. Technol. 44(03), 331–335 (2022). (in Chinese) 5. Yao, J., Chen, L., Xia, S., et al.: The effect of current and speed on melt erosion at rail-armature contact in railgun. IEEE Trans. Plasma Sci. PP(99), 1–7 (2019). https://doi.org/10.1109/TPS. 2018.2888595 6. Li, T., Feng, G.: Analysis of electromagnetic characteristics of orbits of series-enhanced four-rail accelerator. Fire Control Command Control 46(09), 56–61 (2021). (in Chinese) 7. Zhang, B., Kou, Y., Jin, K., et al.: A multi-field coupling model for the magnetic-thermalstructural analysis in the electromagnetic rail launch. J. Magn. Magn. Mater. 519, 167495 (2021). https://doi.org/10.1016/j.jmmm.2020.167495 8. Chen, S., Chen, W.: Stress analysis of the armature tail corner in electromagnetic rail launch after taking joule heating into consideration. High Volt. Eng. 48(7), 2762–2769 (2022). (in Chinese) 9. Fan, W., Su, Z.: Geometry design and contact force analysis of c-shaped monolithic armature. Acta Armamentarii 40(10), 1969–1976 (2019). (in Chinese) 10. Jin, Z., Yang, F.: Modeling and simulation of electromagnetic railgun launch dynamics. J. Nav. Univ. Eng. 35(03), 43–49 (2023). (in Chinese) 11. Zhang, B., Meng, X.: Analysis of system transient magnetic field radiative characteristics during electromagnetic railgun launch. J. Gun Launch Control 43(04), 33–37 (2022). (in Chinese) 12. Bandini, G., Marracci, M.: Detection of armature-rail contact instabilities in accelerators. IEEE Trans. Instrum. Meas. 71(10), 1–8 (2022) 13. Zhang, Y., Lu, J.: Analysis of dynamic response characteristics of interior ballistics process in electromagnetic rail launcher. J. Natl. Univ. Def. Technol. 41(4), 18–24 (2019). (in Chinese) 14. Xu, R., Yuan, W.: Simulation and analysis of electromagnetic field for augmented railgun. High Volt. Eng. 40(4), 1065–1070 (2014) 15. Feng, C., Ma, X.: Introduction to Engineering Electromagnetic Fields, pp. 146–148. Higher Education Press, Beijing (2000). (in Chinese)

Mathematical Modeling of Electrical Energy Storage System and Off-Grid Wind Turbine System Based on Load Demand Response Haseeb Shams(B) and Jie Yu(B) School of Electrical Engineering, Southeast University, Nanjing, China [email protected]

Abstract. Regarding the significance of providing electricity to areas that are so remote from power networks, this study focused on the analysis and modeling of an independent micro grid. A Load demand response is a major part of this system to fulfill the electrical energy requirement on consumer end. An energy storage-based control system requires the design and implementation of a power conversion system. Energy storage systems can be used to mitigate the fluctuations from intermittent renewable energy sources. This paper proposes a design of the 8.5 kW wind turbine which incorporates the energy storage system to diminish the fluctuations. The proposed system consists of double conversion, i.e. AC-DC and DC to AC. AC -DC conversion is done by the rectifier and the output is connected to a common DC bus at which the controller and the energy storage system are connected. The controller conditional base algorithm checks the battery parameters, load, and dump load conditions. The SOC of the battery is set at 0.6 and 0.8, so dc bus bar line sets to be reference voltage to avoid the harmonics on output according to the requirement of the load. To achieve the reference voltage from the wind source and battery source then design a controller for the PWM inverter that observes the ac output of the inverter and its control for fluctuations then feeds back to the inverter in the form of gate pulses for smooth output. Keywords: Wind turbine · Energy Storage · PWM inverter · SOC · Storage Controller

Nomenclature vavg α vs Vo IGBT MOS PWM HAWT VAWT CP

Average output voltage (V) Duty cycle Source voltage (V) Output voltage (V) Insulated gate bipolar transistor Metal oxide semiconductor Pulse width modulation Horizontal axis wind turbine Vertical axis wind turbine Turbine performance coefficient

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 273–286, 2024. https://doi.org/10.1007/978-981-97-1072-0_29

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λ β R V ρair cm Q Tmec ir qr ψr is qs ψs ωs Lm SCIG Ls Rs ωr ψ fr fr Kt CP PMPPT ωm−opt

Speed ratio of tip Pitch angle of blades (degrees) Radius of rotor (m) Wind Speed (m/s) Air density Torque coefficient Capacity of battery (Ah) Mechanical torque of turbine Rotor current (A) Rotor voltage (V) Rotor flux (Wb) Stator current (A) Stator voltage (V) Stator flux (Wb) Angular velocity (m/s) Mutual inductance (H) Squirrel cage induction generator Generator inductance (H) Stator resistance (ohm) Generator rotor speed (m/s) Magnetic flux (Wb) Frequency for switching of filter (Hz) Fundamental frequency for filter (Hz) Optimal coefficient of turbine Turbine performance coefficient for wind Power curve of MPPT (W) Wind turbine rotational speed (rd/s)

Is PMSG Rpm TSR D Tmec Tm MPPT Tb Tref Idref Vd

Source current (A) Permanent magnet synchronous generator Revolution per minute Tip speed ratio Rotor diameter of turbine (m) Mechanical torque (Nm) Actual mechanical torque (Nm) Maximum power point track Base torque (Nm) Reference torque (Nm) Reference dc current (A) Reference dc voltage (V)

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1 Introduction Meanwhile the presence of the human being on earth, energy has been a necessary requirement for humans. In the early stages, the rubbing of stones is the basic phenomenon from which they get energy, burning the leaves and wood. With the passage of time improvement in the living life and smartness in industry, sustainable energy is an important part of life. Energy needs in agriculture, industry, transport, commercial and domestic sectors have been met by reducing fossil fuels which are not available on large scale all over world and countries has to pay heavy amounts for the import of oil for producing energy. Now various renewable energy resources have been identified and related technology for each renewable energy resource has been established and is under further development stages. Most wind energies are identified sources of renewable energies but wind energy is not always reliable so our need is to smooth the structure of the output. Energy storage and its integration with wind sources is the best solution for this. A typical BESS contains an IGBT-based DC to AC power exchange system attached to a utility system. A power conversion system converts the utility AC power supply to the DC supply for the battery energy storage system and vice versa to release energy from the battery for the utility system [1]. These systems are typically used in remote locations or areas where grid access is limited or unreliable. The main components of a standalone energy storage system typically include the energy source (such as solar panels or wind turbines), a battery or other storage device, a charge controller to regulate the flow of energy to and from the battery, and an inverter to convert the stored energy into usable AC power. Standalone energy storage systems have many benefits, including reducing reliance on fossil fuels, increasing energy security, and providing access to electricity in remote areas. Consider a stand-alone wind turbine system which is mathematical modeled by using Matlab software and integrated with energy storage system, a conditional base algorithm controller is designed for this purpose to mitigate with the fluctuations and load demand response. In which considered different load conditions which will be observed in results portion. In all micro grid system there are use of system consists of double conversion, i.e. AC-DC and DC to AC. AC -DC conversion is done by the rectifier and the output is connected to a common DC bus at which the controller and the energy storage system are connected. Filters is also designed for the rectification which is used for a smooth output and generate the pulses according load side requirements, a buck-boost converter is also designed for the flow of energy in the forward and backward manners. Matlab Simulator software is used for this modeling and simulation of micro-grid.

2 Model of Proposed System This is the proposed model of system in which energy is first stored in the battery at a nominal value. As energy is needed then battery discharge occurs, when the battery’s charge drops to the bare minimum, battery charging occurs by the help of wind energy. In order to achieve this, we created a controller that analyses all the phenomena covered in the methodology part. I create a PMSG-based 8.5 KW wind turbine as a renewable energy source that can produce the variable power according to different time period. We

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investigate it using the MPPT control approach. In order to achieve reliable system output voltages and current, we merged the battery storage and wind turbine. The proposed system is given below in Fig. 1. A power conversion system consists of the chopper, DC bus, inverter, and AC filter. These all components make a sustainable energy conversion system. The main components of an PCS typically include power converters, inverters, transformers, and control systems. The power converters are used to convert the incoming power to a form that can be processed by the other components. The inverters are used to convert DC power to AC power, or to adjust the AC voltage level to match the requirements of the load. A wind turbine is a mechanical energy generator that captures kinetic energy. The two main sources of wind energy are wind turbines and wind mills.. On small scale, they are used for battery charging, etc. but on a large scale, They serve as the source of domestic power. There are three different kinds of wind turbines: the Giro-mill wind turbine, the Horizontal Axis Wind Turbine (HAWT), and the Vertical Axis Wind Turbine (VAWT). The most typical application for wind turbines is HAWT. VAWT and HAWT are two popular wind turbines that are used all around the world. The most popular wind turbine is the HAWT model [2].

3 Modeling Techniques for Components In this paper, used the mathematical modeling of all the grid components including wind turbine, energy storage system, converters, inverters, bus lines and loads. The mechanical components of the generator are mounted on a three-bladed rotor type HAWT that is extensively used in large-scale wind turbines. “The blades of some large-scale WTs can reach up to 140 m in diameter with a rotational speed between 5 and 25 rpm” [3]. The following equations can be used to determine wind power and mechanical power.

Fig. 1. Proposed model of the wind/energy storage system based on load demand

PM = CP (λ, β)pw

(3.1)

Mathematical Modeling of Electrical Energy Storage System

pw =

1 2 3 πR v ρair 2

(3.2)

CP λ

(3.3)

cm = Tmec =

277

1 3 πR .cm .v2 ρair 2 dids + Ls ωr iqs dt

(3.5)

diqs + Ls ωr ids + ωr ψ dt

(3.6)

Vds = −Rs Ids − Ls Vds = −Rs Ids − Ls Te =

(3.4)

3 pψiqs 2

ωm−opt =

vλopt R

(3.7) (3.8)

PMPPT = Kω3 m−opt

(3.9)

PMPPT = Kω3 m−opt

(3.10)

PMPPT = Kω2 m−opt

(3.11)

R K = 0.5 × ρACp [ ] λ

(3.12)

R K = 0.5 × ρACp [ ] λ

(3.13)

If λ= 8.1 and β = 0 and then CP is at its value of maximization [4]. Synchronous Generator The PMSG (permanent magnet synchronous generator) modeling is represent by Eqs.3.5 to 3.7. The electromagnetic torque Te is calculated by Like DFIG and SCIG, a slow rotating turbine rotor couples with the generator. It has a medium speed single stage gearbox and a high speed multiple stage gearbox. A permanent magnet is the basis of a direct-drive generator, which does not require a gearbox. 3.1 Maximum Power Point Tracking (MPPT) Control Algorithm MPPT works by continuously adjusting the load on the wind turbine to maintain the optimal operating point. This is done by measuring the output voltage and current of the wind turbine and using this information to calculate the power output. The MPPT controller then adjusts the load on the panel to maintain the maximum power point, even

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as the conditions change. MPPT controllers can be designed using a variety of techniques, including analog circuits, digital signal processing, and artificial intelligence algorithms. The choice of technique depends on the specific requirements of the application, such as the desired accuracy and response time. Wind turbine ideal rotational speed can be estimated from a given wind speed using Maximum power from a wind turbine is determined from Eq. (3.1), while mechanical power is calculated from Eq. (3.2). By controlling the wind turbine at various wind speeds and using an MPPT control method, maximum power is achieved as shown in 3. Optimal power is shown by the MPPT power curve and accompanying torque related as a function of ωm−opt and speed on the gearbox side. When wind speed is at its nominal value, the pitch angle controller must lower the power coefficient. The power controller is required when wind speed is at high power levels. When output power increases, the blade pitch turns slightly against the wind while the power maintains the rotor’s rated speed and wind speed. [5].

4 Mathematical Modeling of Micro-grid System 4.1 Renewable Source (Wind Turbine) I designed the 8.5 KW PMSG-based wind turbine with variable speed through the use of a controller. Variable-speed wind turbines are commonly used because we get maximum output power using the MPPT algorithm to improve efficiency [6] which is further defined in subsection. In the present environment, DFIG is mostly used as a variable speed wind turbine system but the reliability of variable speed wind turbine is achieved using direct drive base PMSG. In model of wind turbine from which we control the wind speed, generator speed and pitch angle [7, 8]. The wind mechanical power is 8.5 KW and base wind speed is 12 m/s. To find its RPM rpm =

60 × vs × TSR Pi × D

(4.1)

Tmec = Tm × Tb Tb =

Mechanical Power rpm

Idref = E = E0 − K

(4.2)

Tref × ωm vd

Q  + Aexp(−B Q − idt

(4.3) (4.4)  idt)

Vbat = E − RIbat Lf =

vo vo fr vdc 1 [k {1 + 4π2 ( )2 k }] 2 Io fs vo,av fs vo,av vdc Cf = k Lf fs 2 vo,av

(4.5) (4.6) (4.7) (4.8)

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A diode rectifier is used for current flowing in the forwarding direction. A boost converter is used to step up the voltage level. A load-side inverter with an LC filter is also used for load voltage but I use the rectifier for DC control of the battery according to my proposed topology. When the wind turbine AC power is rectified and converted to DC voltage and DC current, they can be considered as dc components imposed to harmonics. Due to these harmonics present in dc current, the lifetime of turbine shaft will reduce because electrical torque of generator will oscillate. Therefore an active filter is designed for this purpose [9] (Tables 1 and 2) Table 1. Wind Turbine Parameters Density of Air

1.225 kg/meter cube

Pitch Angle

45 degree

Diameter of Turbine

9m

Wind speed

12 m/s

Tip Speed Ratio

6

No. of Poles

40

Base Torque

55.5 Nm

RPM

152.89

Pitch Angle

45 degree

Power

8.5 KW

4.2 Battery Storage Storage is the basic part of this research because we stable our load and voltage through energy storage compensation. I use the battery model in which SOC as a state variable in order to avoid the algebraic loop problems and the battery is NIMH. A 300 v with 6.5 Ah battery is used. For modeling use the equation given below [10]. Table 2. Battery Storage Parameters Nominal Voltage

300 V

Cut-off Voltage

225 V

Rated Capacity

6.5 Ah

Fully Charged Volt

353.38

Initial and Maximum SOC

60% and 80%

Maximum Capacity

7 Ah

4.3 Storage Controller This controller is designed for the battery charging and discharging operation and control of the battery for overcharging at a specific point. The battery is connected through a buck-boost converter to dc-link which is bidirectional in operation for charging and discharging a battery. Battery voltage set lower than DC reference voltage which we consider 640 V. In this system, the battery is at 300 V through a series cell connection and at the initial level battery consider at 60% SOC. Assume a 2 KW load compensating battery work for one hour and is not less than 30% for caring purposes even wind

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power is zero [11]. A control scheme for this purpose the battery can either source or sink. From reference and actual DC voltage we take the reference current by use of PI controller and then compare the battery actual current and reference current for the operation of charging and discharging purposes. If the battery’s actual current is less than the reference current then the buck converter switch ON according to the reference of SOC which is less than 80% means if the actual SOC of the battery 0 is the ratio of the phase shift time to Ths. D > 0 in Fig. 2 is the power forward transmission mode. The switching frequency fs = 1/Ts is defined in the DAB converter.

S1S4 S2S3

D

T

D

D

S5S8 S6S7 Uab Ucd iL t0 t1 t2

t3 t4 t5 t

t6

Fig. 2. Single phase-shift modulation voltage-current waveforms.

4 A Model Predictive Control Approach for Reconfigurable Battery Energy Storage Systems From the model analysis in the previous section, it can be seen that the dual active bridge converter selected in the energy storage system has four modes in one cycle under the single phase shift regime, and the differential equations for the four modes are expressed as: ⎧ −n 1 ⎪ ⎪ ⎪ C2 iL − −RC2 Udc2 t ∈ [0, DThs ) ⎪ ⎪ ⎪ ⎪ ⎪ n 1 ⎪ ⎪ iL − Udc2 t ∈ [DThs , Ths ) ⎨ dUdc2 C2 −RC2 = (1) n 1 ⎪ dt ⎪ ⎪ iL − Udc2 t ∈ [Ths , (1 + D)Ths ) ⎪ ⎪ C2 −RC2 ⎪ ⎪ ⎪ ⎪ −n 1 ⎪ ⎩ iL − Udc2 t ∈ [(1 + D)Ths , 2Ths ] C2 −RC2 In Eq. (1), R is the secondary output resistance, C2 is the secondary output capacitance, and Udc2 is the instantaneous output voltage; The differential equations of the four modes can be obtained by averaging the equivalent treatment: n(D − D2 ) 1 d Udc2  Udc2 + = Udc dt −RC2 Lk fs C2

(2)

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Equation (2) where < Udc2 > is the average value of output voltage per cycle, Lk is the primary-side output equivalent inductance, and fs is the switching frequency of the secondary-side H-bridge switching tube. A discretization of the above equation yields: Udc2 (k + 1) = −

Udc2 (k) n(D − D2 ) + Udc + Udc2 (k) Rfs C2 Lk fs C2

(3)

In its (3), Uoref is the reference value of the secondary output voltage. In the first case, the phase shift duty cycle D ∈ [0,0.5], so the range of D can be divided into a finite number of copies (e.g., 100), and this finite number of D is brought into the discrete equation to obtain different cost equations, respectively, and it is worthwhile to make D(j) be the current moment that makes the cost equation the minimum of the phase shift duty cycle, and at this time, the derivative of the cost equation, d(gout(D(j)))/dD = 0, the output voltage of the predicted value is closest to the reference value. The derivative of the cost equation is a nonlinear equation about D. The equation can be solved by Newton’s method. This nonlinear equation is written as:  io (k) n(D − D2 ) 4nUdc d (gout (D)) U = + − Udc f (D) = oref dD Lk fs2 C2 fs C2 Lk fs2 C2 (4) −Udc2 (k)D) If the phase shift duty cycle D = Dn for the nth iteration, then Dn + 1 for the n + 1st iteration is: Dn+1 = Dn −

f (Dn ) f  (Dn )

(5)

The above analysis shows that the model predictive control is an active control strategy suitable for nonlinear control. It derives the predicted value for the next moment based on the circuit parameters and the sampled electrical quantity information at the current moment, and in this section, the optimal phase-shift duty cycle Dopt is obtained by deriving the cost equation, so that the output capacitor voltage has the minimum deviation from the reference value. Compared with some literature on DAB phase-shift predictive control such as the look-up table method and full-range discrete prediction, the computational amount can be greatly reduced. Compared with PI control, there is no need to calculate the control parameters, the program is simple to write, and there is no integration link, the dynamic response and calculation speed is faster.

5 System Simulation and Experiment In order to verify the correctness and effectiveness of the proposed model predictive control method for reconfigurable battery energy storage system, a simulation model is constructed using Matlab/Simulink software and the circuit parameters are shown in Table 1.

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Table 1. Simulation Parameters. Parameter

Value

Input voltage Udc1(V)

100

Square wave frequency (fs)

10000

Primary Inductance L1 (H)

5e-5

Load resistance R ()

20

Side capacitance C(F)

3e-5

5.1 Steady-State Simulation As shown in Fig. 3, when the input voltage of the battery storage system is stabilized at 100V, it can be seen that the output voltage u1 of the model predictive control method rises rapidly and stabilizes at 100V within 0.001s, and the subsequent fluctuation is small. On the other hand, the output voltage u2 of the traditional control method rises slowly until it stabilizes at 100V around 0.015s, and the fluctuation is bigger.

Fig. 3. Single phase-shift modulation voltage-current waveforms.

5.2 Transient Simulation As shown in Fig. 4, when the input voltage of the battery energy storage system is 100V, the load is suddenly reduced by 10 within 0.02s, it can be found that the output voltage u1 of the model predictive control method can quickly regulate the small fluctuation, so that the output voltage continues to be stabilized at 100V, while the output voltage u2 of the traditional control method can not respond quickly, has a certain degree of hysteresis, and the adjustment time is longer, so it affects the stable operation of the system. Stable operation of the system.. As shown in Fig. 5, when the input voltage of the battery energy storage system is 100 V, the input voltage suddenly decreases by 10 V at 0.02 s. As shown in Fig. 6, after the voltage is reduced by 10 V, the voltage u1 with the model predictive control method can quickly regulate the small fluctuations shown in the figure so that the output voltage continues to be stabilized at 100 V, whereas the

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Fig. 4. Voltage output waveforms of two control methods during sudden load change.

Fig. 5. Voltage input waveform during transient operation

output voltage u2 with the traditional control method, returns to 100 V only after 0.005 s with significant fluctuations. The effectiveness of the model predictive control method for energy storage systems proposed in this paper is demonstrated through simulation.

Fig. 6. Voltage output waveforms for both control methods for sudden input changes.

6 Conclusion Energy storage systems, which can be reconfigured to model predictive control methods for battery energy storage systems. Using the battery switch-bypass type topology, separate isolation of faulty and dangerous batteries can be achieved to ensure that the whole system can continue to operate after the system battery failure, which improves its flexibility and utilization. Meanwhile, the model predictive control of the DAB converter in the energy storage system solves the problems of unstable steady-state operation and

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untimely response to sudden load and input changes in the traditional control methods, and improves the stability and safety of the system. The reliability of the proposed model predictive control method for reconfigurable battery energy storage system is also verified by simulation. Acknowledgment. This paper is supported by State Grid Jiangsu Electric Power Company Limited Science and Technology Project J2022159.

References 1. Ding, M., Chen, Z., Su, J.H., et al.: A review of battery energy storage systems in renewable energy generation. Power Syst. Autom. 37(1), 19–25, 102 (2013). (in chinese) 2. Ci, S., Zhou, Y.L., Wang, H.J., et al.: Modeling and operation control of digital energy storage system based on reconfigurable battery network: a case study of base station energy storage application. Global Energy Internet 4(5), 427–435 (2021). (in chinese) 3. Xu, G.N., Du, X.W., LI, Z.J.: Reliability design of battery management system for power battery. Microelectron. Reliability 2018, 88–90: 1286–1292 (2021) 4. Zhao, H., Zhang, X., Liu, H., et al.: Research on reconfiguration of battery network of energy storage system based on the weights of charge state diagram. Electrotechnology 30(1), 13–18 (2023). (in chinese) 5. Liu, H.R., Zhang, Z.H.: Charge-discharge equalizer and equalization strategy for lithium-ion battery pack. J. Electrotechnol. 30(8), 186–192 (2015). (in chinese) 6. Zhang C J, S M D, Xu C, et al.: Intrinsic safety mechanism and example analysis of energy storage system based on dynamic reconfigurable battery network. Energy Storage Sci. Technol. 11(8), 2442–2451 (2022). (in chinese) 7. Shan, Z., Jatskevich, J., Iu, H.H.C., et al.: Simplified load-feedforward control design for dual- active-bridge converters with current-mode modulation. IEEE J. Emerging Sel. Top. Power Electron., IEEE 6(4), 2073–2085 (2018) 8. Ma, X.H., Chen, S.P., Ren, Y.P., et al.: LNG vehicle gas cylinders. Gas Heat 31(9), 14–18 (2011). (in chinese) 9. Sun, K., Chen, H., Wu, H.F.: A review of analysis methods and control techniques of isolated bi-directional DC-DC converter for energy storage system applications. New Technol. Electr. Power 38(08), 1–9 (2019). (in chinese) 10. Koch, G.G., Queiroz, S.S., Rech, C., et al.: Design of a robust PI controller for a dual active bridge converter. In: 12th IEEE International Conference on Industry Applications (INDUSCON), pp. 1–6. IEEE, New York (2016) 11. Nguyen, D.D., Nguyen, D.H., Funabashi, T., et al.: Sensorless control of dual-active-bridge converter with reduced-order proportional-integral observer. Energies 11(4), 1–18 (2018)

Stability Analysis on Large-Scale Adiabatic Compressed Air Energy Storage System Connected with Power Grid Chengqian Xiao1 , Yanbing Zhang1 , Shu Zhang1 , Xiaoya Zhen1 , Zihao Jia1 , and Jiaxin Ding2(B) 1 State Grid Pingdingshan Electric Power Supply Company, Pingdingshan 467000 , China 2 School of Information Engineering, Nanchang University, Nanchang 330031, China

[email protected]

Abstract. In this paper, the stability of adiabatic compressed air energy storage (ACAES) system connected with power grid is studied. First, the thermodynamic process of energy storage and power generation of ACAES system is analyzed. Then, the stability analysis model for stability analysis, which takes both ACAES and permanent magnet synchronous motor/generator into consideration, is built. According to the stability analysis model, the stability of grid connected ACAES is mainly influenced by structure parameters and coefficients of the control systems. A grid connected ACAES station, which is being built in Henan Province, China, is selected as the research case for the stability analysis. Influence of structure parameters and control coefficients on the system stability are studied in details. According to the analysis results, the equivalent resistance of ACAES system and the proportional coefficient of controller shows obvious influence on the capability of the grid connected system. The proposed stability analysis model and analysis results in this paper contributes to the stability analysis of large-scale grid connected ACAES system and providing advises for the parameter design process. Keywords: Adiabatic compressed air energy storage · Stability analysis of grid connected energy storage system · Large-scale energy storage system · Stability analysis model

1 Introduction In order to achieve the goal of “peak carbon dioxide emissions by 2030 and achieve carbon neutrality by 2060”, China has formulated a series of policies to active the commercial use of renewable energy technologies [1]. By 2022, the proportion of non-fossil energy in primary energy consumption in China is 17.5%, and it is expected to be 25% by 2030, becoming the main source of energy supply in China. In 2060, it is expected that non-fossil energy will occupy more than 80% of primary energy consumption [2– 4]. Renewable energy sources, such as wind energy and solar energy, are accelerating the low-carbon transition in China. However, due to the intermittence and instability of © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 308–322, 2024. https://doi.org/10.1007/978-981-97-1072-0_32

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renewable energy generations, energy storage is necessary to ensure the stable operation of modern power systems integrated with large-scale of renewable energy generations [5]. Nowadays, the most widely used energy storage systems include pumped storage, compressed air storage, high temperature molten salt heat storage and electrochemical energy storage, etc. al. Pumped storage systems show merits of low cost and high efficiency. By the end of September 2022, installed pumped storage capacity accounts for 85.6% of the total installed energy storage capacity in China. However, the development of pumped storage station is limited by the requirement of special geographical conditions and low energy density of the system [6]. The high temperature molten salt heat storage technology has advantages of low cost and high energy storage density, and is widely used in the flexible transformation of solar thermal power generation and thermal power plants. However, the efficiency in the energy conversion process is relatively low. In [7], Hanbin Diao established a unified model of electric/thermal energy storage as well as an optimal scheduling model from the perspective of complementary and coordinated operation of multi-energy storage, and analyzed it as an example of a coupled thermal network system, which realizes the advantages of complementarity on multienergy storage. Although electrochemical energy storage technology shows advantages in high energy density and high efficiency, the electrochemical energy systems suffer from the high cost of lithium-ion batteries and safety problems. Compressed air energy storage (CAES) systems show merits of large capacity, long lifecycle, high efficiency, low cost, high safety, low cost, etc. Thus, CAES can be adopted for large-scale energy storge stations [8]. By compressing the air and storing the air during low electric consumption period, excess electrical energy can be stored in the station. By releasing the high-pressure air during the high electric consumption period, CAES generates electric power and supports the power grid. CAES systems had been proved to improve the stability and reliability of the power grid [9–11]. The early CAES systems rely on gas turbines and the system efficiency is improved by additional fossil fuel secondary combustion [12]. With the development of CAES, in order to improve the energy conversion efficiency and overcome the shortcomings of carbon emission generated by additional fossil fuels, adiabatic compressed air energy storage (ACAES) system is proposed, in which thermal energy loss during both compression process and expansion process is reduced [13, 14]. Permanent magnet synchronous motor is widely used in various fields because of its light weight, small size, simple structure and high power density [15, 16]. In [17], Xiping Liu used the chaotic variable mirror particle swarm optimization algorithm with initial parameter optimization to accurately identify parameters such as stator winding resistance and permanent magnet flux linkage at the same time, so the permanent magnet synchronous motor was selected as the motor in the system studied in this paper. By analyzing the thermodynamic process of energy storage and power generation process of ACAES system, the mathematical model of the compressed air energy storage system is established. Then, ACAES system is connected to power grid through permanent magnet synchronous motor/generator (PMSM/G). The influence of system equivalent impendence and control parameters on the system stability are analyzed in details. The rest part of this paper is organized as following. In Sect. 2, basic principle of

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AACAES is given, by which the mathematic model is built for AACAES in Sect. 3. In Sect. 4, AACAES is connected to power grid through PMSM/G and the analysis model of the total system is proposed. In Sect. 5, stability of the grid connected AACAES station is analyzed, in which a AACAES station being built in Henan Province, China is employed as a research study. Finally, this paper is concluded in Sect. 6.

2 Basic Principle of ACAES System ACAES is composed of air compressor, gas storage chamber, expansion machine, heat exchange device, throttle valve, electronic control device, etc. Compared with traditional CAES system, ACAES system recovers heat generated in the compression process and thus saves fossil energy cost in the expansion process. Since both excessively high compression and excessively high expansion ratio reduce system efficiency, multi-stage compression units and multi-stage expansion units are combined with inter-stage colling units and inter-stage reheating units. Typical ACAES system usually consists of a threestage compressor and a three-stage expander, the structure of which is shown as Fig. 1. Motor M

Compressors C-1

C-2

HX-1

Expanders

C-3

HX-2

T-1

HX-4

HX-3

T-2

HX-5

T-3

generator G

HX-6

Heat exchanger Hot tank

Cold tank

Air reservoir

Fig. 1. Structure of typical ACAES system.

When the ACAES system operates in the energy storage mode, PMSM/G operates as PMSM and absorbs active power from power grid. Then, the low-pressure air is compressed into the air reservoir by the compressor. Since the air temperature rises sharply in the compression process, the high-temperature air is cooled by the interstage heat exchange unit. The recovered heat in the compression process is then stored in the hot tank. When the ACAES system operates in generator mode, the air is reheated by the heat exchange unit and then expanded in the turbine to drive PMSG, by which the ACAES supports the power grid.

3 Thermodynamic Process in ACAES System According to the system structure shown in Fig. 1, the mathematic model of ACAES system can be built by establishing the mathematic model of the compressor, turbine, heat exchanger, heat storage tank and air reservoir separately. To simplify the discussion, both fluid leakage and pressure loss in the compression/expansion process are not considered in this paper. Also, the ACAES system will not operate concurrently in energy storage mode and generating mode.

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3.1 Thermodynamic in Compressor In ideal ACAES system, air is adiabatically compressed by compressors at each stage. For air compressors with a certain boost ratio, pressure at the output port of compressor can be expressed as CA = βiCA · piICA pi0

(1)

piICA

CA piO

where is the air pressure at the input port of the ith compressor; is the air CA pressure at the output port of the ith compressor; βi is the compression ratio of the ith compressor. Energy absorbed to compress unit mass of air can be expressed as    κ−1 κ 1 C.s CA CA κ βi Rg TiI wi = C.s −1 (2) ηi κ − 1 where Rg is the gas coefficient; ηiC.s is the isentropic efficiency of compressor; TiICA is the temperature of air at the input port of ith compressor; κ is the isentropic index (specific heat capacity ratio, usually is 1.4). Actually, the actual ACAES system cannot avoid heat exchange with the external environment. Take both entropy increase and heat loss into consideration, (2) can be rewritten as    n−1 n 1 C,n CA CA n βi Rg TiI −1 (3) wi = C,n η n−1 i

where wiC,n is the ratio of power consumption in the ith compressor; ηiC,n is the polytropic efficiency of ith compressor, which can be expressed as ηiC,n = 0.91 −

βiCA − 1 300

(4)

where n is the index and n = κ = 1.4 , so the electric energy power consumed by each compressor is: PiC,n = Gin wiC,n =

   n−1 n air CA n β G R T − 1 in g i i ηC,s n − 1 1

(5)

i

= k3 Gin Tiair where Gin is the mass air flow in the ith compressor. For multi-stage compressors, the total absorbed electric power from power grid can be expressed as N PiC (6) Pc = i=1

where N represents the number of compressors. Considering that the gas temperature will rise during the compression process, according to the laws of thermodynamics, temperature at the output port of ith compressor is CA = TiICA ( TiO

CA PiO

PiICA

)

n−1 n

= TiICA (βiCA )

n−1 n

(7)

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3.2 Expansion Process in Turbine The thermodynamic principle of expansion process in turbines is similar to principle of compression in the compressor and can be expressed as TA pj0 =

pjITA

(8)

βjTA

where βjTA is the expansion ratio of the jth turbine; pjITA is the pressure at the input port TA of jth turbine; pjo is the pressure at the output port of jth turbine. According to state equation for air, the decrement of temperature expander is closely related to the expansion ratio. Therefore, temperature at the output port of jth compressor is: TA TjO = TjITA (

TA PjO

PjITA

)

n−1 n

= TjITA (βjTA )−

n−1 n

(9)

TA is the pressure at the input port of where βjTA is the expansion ratio of jth turbine, PjO TA jth turbine. PjI is pressure at the output port of jth turbine. The output power of each turbine is:

PjT ,n = Gin wjT ,n =

   n−1 n n Gin ηjT ,n Rg TjITA βjTA −1 n−1

(10)

where wjT is the specific power of jth turbine. For a multistage (L-class) ACAES, the total output power is PT =

L 

PjT

(11)

j=1

3.3 Principle of Heat Exchanger In order to improve the efficiency of ACAES system, heat generated in the compression process is absorbed by heat exchangers, which are named as HX-1, HX-2 and HX-3, and stored in the hot tank. The air temperature after heat exchange is:   HA (12) = TiIHA + E TiIHF − TiIHA TiO where E is the efficiency of heat exchange; TiIHF is the temperature of medium at the HA is the air temperature at the output port of ith input port of ith heat exchanger; TiO HA heat exchanger; TiI is the air temperature at the input port of ith heat exchanger. The heat-flux of the heat exchanger is:   A HA HA (13) δqiH = dmHA i cP TiI − TiO

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where δqiH is the heat-flux in the ith heat exchanger; dmHA i is the mass air flow in the ith heat exchanger; CPA is the mass heat capacity at constant pressure. Thus, the heat medium flow required by the heat exchange unit is: dmHF = i

δqH  HF i HF  cpF Ti0l − Td

(14)

where cpF is the mass heat capacity of heat medium. When the ACAES system operates in expansion and generating mode, air is released from air reservoir for expansion. When the heat medium heats air through heat units, which are named as HX-4, HX-5 and HX-6 in Fig. 1, the thermodynamic process is similar to the heat storage process. 3.4 Basic Equations in Heat Storage Tank In the compression process, the heat medium flows out of the low-temperature tank, cools the hot air, and stores heat in the high-temperature tank. In the expansion process, the heat medium flows out of the high-temperature tank and heats the air in expander. Take the high temperature heat storage tank as an example, the mass balance equation can be expressed as L N dMhSF dmHF − dmHF = i j i=1 j=1 dt

(15)

HF is the total mass of the heat medium flows into the high-temperature where N i=1 dmi heat storage tank within unit time; MhSF is the total mass of heat medium in high HF is the total mass of the heat medium flows out of the temperature tank; N j=1 dmj high-temperature tank within unit time. Since ACAES will not absorbs electric power from power grid and generates power to support power grid at the same time, heat release process Nand heat storageHFprocess HF in (15) is 0. The dm or dm will not occur simultaneously. Thus, either N i=1 j=1 i j energy balance can be expressed as MhSF · cpF ·

N L dThSF SF = δqiSF − δqjSF − δqhl i=1 j=1 dt

(16)

SF where N i=1 δqi is the total energy stored in the high-temperature heat storage tank within unit time; ThSF is the temperature of heat medium in high-temperature tank; N SF is the total energy flows out of the high-temperature tank within unit j=1 δqj SF is the decrement of total energy in high-temperature tank within unit time. time; δqhl According to the basis of mass conservation, dMhSF dMcSF = dt dt where McSF is the total mass of heat medium in the low-temperature tank.

(17)

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3.5 Basic Equations in Air Reservoir The air reservoir can be regarded as the energy storage unit in ACAES system. Since the volume of air reservoir is certain, we can have following expression according to the law of mass conservation dmac (18) = Gin − Gout dt where mac is the mass of air compressed into the air reservoir; Gin is the mass flow into the air reservoir; Gout is the mass flow out of the air reservoir. According to the first law of thermodynamics d (mu) = Gc hc − Ge he − Uac Aac (Tac − Tenv ) (19) dt where u is the internal energy of air; h is the specific enthalpy of air; Uac is the heat transfer coefficient between external environment and stored high-pressure air; Aac is the contact area between external environment and air reservoir; Tenν is the ambient temperature. The equation of state of ideal air is expressed as dT dm dp dV + − − =0 p V T m

(20)

The air reservoir is assumed to be adiabat and no heat exchange with the external environment, so the convective heat transfer coefficient is zero, and formula (20) is simplified as

  cp cp dTac 1 G G Tac = T + 1 − − G in in out in dt mac cv cv (21) Rg cp dpac dt = Vcv (Gin Tin − Gout Tac ) where Tac is the air temperature in the air reservoir; pac is the pressure in the air reservoir; T in is the temperature of air compressed into air reservoir; V is the volume of the air reservoir. Assuming that the intake air flow is constant and there is no heat exchange, mathematic model of air reservoir can be transformed as follows mac (t) = m0 + ∫t0 Gin dt Tac (t) = 1.4Tin −

k1 2t Gin m0 + Gin

(22) (23)

where pac can be solved by the ideal equation of state of air, T in is the air temperature at the input port of air reservoir, and k1 is constant. So, the Laplacian form of the transfer function of ACAES in energy storage mode can be expressed as G1 (s) =

C1 (s + C2 ) s(s + C3 )

(24)

0) where C1 = k2rkω1m , C2 = 1.4Tink(1+m , C3 = 1.4Tkin1 m0 , k2 is ratio between the rotor speed 1 of PMSM and air inflow. According to analysis above, simulation model of ACAES in energy storage mode is built as Fig. 2.

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Fig. 2. Model of ACAES system in energy storage mode.

4 Grid Connected ACAES System The structure of grid connected ACAES system is shown as Fig. 3. The ACAES system is connected to power grid through PMSM/G. During the low electricity consumption period, compressor is driven by PMSM and pumps air to the air reservoir for energy storage; during the peak electricity consumption period, PMSG is driven by the turbine and supports the power grid. Since frequency of power system is related active power flow in the grid, connected ACAES system can be applied to help frequency regulation in the power system.

Compressor

Grid-connected switch

Power grid

PMSM/G

Transformer for grid connection

Air reservoir

Turbine generator

Fig. 3. Sketch of grid connected ACAES system

Figure 4 shows the basic structure of PMSM/G converter with current source inverter, where U dc is DC side voltage; E a 、E b 、E c are three-phase power grid voltage respectively; T k ,T k  (wherek = a、b、c) are the power switch tube of the three-phase bridge circuit; M is the PMSM/G. 4.1 Mathematical Model of PMSM/G Control After transforming the dq axis of the energy storage converter model, a coupling term appears between the alternating and direct axes. Current of the dq axis of the energy storage converter is not only affected by the voltage control quantity, but also affected by the grid voltage ed , eq , and the coupling term -ωLiq of the current id and iq . The amplitude of this value is equal to that of the current coupling term, but the direction is opposite. The feedforward decoupling control method of the current source inverter is shown in Fig. 5.

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R

L

Ta

Tb

Tc

Ta1

Tb1

Tc1

Ea Udc1 Eb

PMSM/G

Ec Ta’

Tb’

Tc’

Ta1’

Tb1’

Tc1’

Fig. 4. AA-CAES structure

Fig. 5. Converter feedforward decoupling control

Assuming the DC voltage is constant, following expression can be obtained. ⎧   ⎨ L did + Rid = (i∗ − id ) K p + Ki d dt s   ⎩ L diq + Riq = (i∗ − iq ) K p + Ki q dt s

(25)

where L is the equivalent reactance value of the grid side; K p is the proportional coefficient of the current inner loop PI controller; R is the equivalent impedance of the circuit; id∗ , iq∗ are reference current on d axis and q axis, respectively; Ki is the integral coefficient of the current inner loop PI controller. By comparing the actual output current with the reference current, the controller adjusts required voltage through PI. Then, after decoupling and space vector pulse width modulation, the driving signals for each IGBT is thus generated. Considering the time delay of converter system, the control time delay and current sampling time delay are necessary. So, the equivalent control transfer function of the inner loop of the current control is expressed as follows: G2 ( s) =

Kpwm (Kp s + Ki ) s( 1 + 1.5Ts)(R + Ls)

(26)

where Kpwm is the equivalent gain coefficient of the converter; T is the switching period of the control system,

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In practical applications, in order to achieve good dynamic response, the damping ratio of energy storage converter is generally 0.707. Thus, the proportional coefficient and integral coefficient of PI controller can be calculated by  Kp = 3TKL pwm (27) Ki = 3TKR pwm

4.2

Mathematical Model of PMSM/G

PMSM/G is one of the key components in ACAES system, dynamic equation under rotating coordinates can be expressed as ⎧ did ⎪ + Rs id − np ωLq iq ⎨ ud = Ld dt (28) ⎪ ⎩ u = L diq + R i + n ωL i + n ωψ q q s q p p d d f dt where np is the pole number of the motor; ω is the angular velocity of the machine; Ld is the stator inductance on d axis; Lq is the stator inductance on q axis; id , iq , ud , uq are the current and voltage under the rotating coordinates; Rs is the stator resistance; ψf is the flux-linkage in the machine. The torque equation of permanent magnet synchronous motor is as follows Te = np [(Ld − Lq )id iq + ψf iq ]

(29)

The motion equation of PMSM/G can be obtained J

dω = Te − TL − Bω dt

(30)

where T L is the load torque; T e is the electromagnetic torque of PMSM/G; B is the friction coefficient; J is the rotational inertia of synchronous motor. Meanwhile, the torque of PMSM/G is Te =

3 np ψf iq 2

(31)

Thus, the motion equation can be thus expressed by 1 dω = (Te − TL ) dt J 1 3 = ( np ψf iq − Bw − TL ) J 2

(32)

According to above analysis, the transfer function of PMSM/G is G3 (s) =

ωr (s) K = = iq Te (s) Js + B

(33)

Combining inverter, PMSM/G and ACAES, the block diagram of grid connected ACAES system can be built as following (Fig. 6).

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1 Js+B

C1(s+C2) s(s+C3)

1 Ks+M

Fig. 6. Diagram of grid connected ACAES system

5 Stability Analysis on Grid Connected ACAES An ACAES station being built in Henan Province, China is taken as a research study. Key parameters of the studied ACAES station are shown in Table 1. Table 1. Main parameters of AA-CAES Parameter (unit)

Value

1

Release time (h)

8

2

Storage duration (h)

10

3

Maximum intake rate of single stage compressor (Kg/s)

194

4

Number of Compressor

3

5

Single-stage compressor compression ratio

5

6

Isentropic efficiency of compressor

0.85

7

Maximum output rate of single stage turbine (Kg/s)

227.66

8

Number of turbines

3

9

Expansion ratio of a single stage turbine

3.2

10

Isentropic efficiency of turbine

0.85

11

Cold fluid initial temperature (K)

293

12

Efficiency of heat exchanger

0.85

13

Ambient temperature (K)

293

14

Minimum pressure of gas reservoir (MPa)

3

15

Maximum pressure of gas reservoir (MPa)

18

16

Gas storage chamber outlet throttle Outlet Constant pressure (MPa)

3

17

Gas reservoir volume (m3 )

50000

18

Initial gas reservoir temperature (K)

293

5.1 Effect of Equivalent Inductance on Stability Setting Kpwm = 0.85, R = 0.01 and damping ratio, Kp = 1.22586, Ki = 12.2586 the Bode diagram of the system under L = 0.1 mH, L = 1 mH and L = 10 mH is shown in Fig. 7(a), Fig. 7(b) and Fig. 7(c), respectively.

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Fig. 7. Bode diagram under different equivalent inductances. (a) L = 1 mH. (b) L = 0.1 mH. (c) L = 10 mH.

As shown in Fig. 7, when the equivalent reactance is 1mH, the cut-off frequency of the system is 151 Hz and the phase margin is 65.5°. When the equivalent reactance is 0.1 mH, the system cut-off frequency is 74.3 Hz, and the phase margin is 15.3°. When the equivalent reactance is 10 mH, the system cutoff frequency is 233 Hz, and the phase margin is 8.09°. That is, when the equivalent reactance L changes between 0.1 and 10mH, phase margin changes of grid-connected ACAES system varies within the range from 8.09° to 65.5°, and the system can be steady. 5.2 Effect of Equivalent Resistance on System Stability Setting Kpwm = 0.85, Kp = 1.22586, Ki = 12.2586, system equivalent inductance L = 1mH. The Bode diagram of studied grid-connected ACAES system under R = 0.001 and R = 0.1 is shown in Fig. 8(a) and Fig. 8(b), respectively. As can be seen in the figure, when the equivalent resistance R is 0.001 , the cutoff frequency of the system is 155 Hz, and the phase margin is 68.8°; when the equivalent resistance R is 0.1 , the cutoff frequency of the system is 154 Hz, and the phase margin P is 61.6°. When the equivalent resistance varies from 0.001 to 0.1 , the phase margin of the studied system varies within the range from 61.6° to 68.8°.

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Fig. 8. Bode diagram under different equivalent resistance. (a) R = 0.001 . (b) R = 0.1 .

5.3 Effect of Propitiation Coefficient on System Stability Setting Kpwm = 0.85, Ki = 12.2586, R = 0.01 , L = 1 mH, Fig. 9 shows the comparison when Kp is 0.613 and 1.83879 respectively. As shown in the comparison, when Kp = 0.613, the cutoff frequency is 80.6 Hz and the phase margin is 75.2°; when Kp = 1.83879 = 1.83879, the cutoff frequency is 210 Hz and the phase margin is 57.8°. Therefore, when Kp = 1.83879 changes from 0.613° to 1.83879, the phase margin varies within the range from 57.8° and 75.2°, and the system maintains steady.

Fig. 9. Bode diagram under different Propitiation coefficient. (a) K p = 0.613. (b) K p = 1.83879.

5.4 Effect of Integral Coefficient on System Stability Setting Kpwm = 0.85, Kp = 1.22586, R = 0.01 , L = 1 mH, Fig. 10 shows the comparison between Ki = 6.13 and Ki = 18.83879. As shown in Fig. 10(a), when Ki = 6.13, the cut-off frequency is 151 Hz and the phase margin is 65.8°; as shown in Fig. 10(b), when Ki = 18.83879, the cut-off frequency is 151 Hz and the phase margin is 65.2°. As Ki changes from 6.13 to 18.83879, the phase margin of the system varies from 65.2° to 65.8°. According to the above results, the system shows high robustness.

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Fig. 10. Bode diagram under different integral coefficient. (a) K i = 6.13. (b) K i = 18.83879.

6 Conclusion In this paper, the stability of grid-connected ACAES system is studied. Mathematic model of ACAES system is built by analyzing the thermodynamic process of compression process and expansion process in ACAES. Then, the transfer function of gridconnected function of grid-connected ACAES system is built by combining the model of ACAES and model of PMSM/G, according to which the stability analysis model can be thus established. A being built ACAES station in Henan Province, China is employed for research study. Influence of structure parameters and control parameters on the system stability on system stability is studied in details. Main contribution of this paper is listed in the following. (1) The thermodynamic process of compression process and expansion process in ACAES system is analyzed, and the stability analysis model of grid-connected ACAES system is established. (2) For engineering applications, relationship between structure parameters and the stability of grid-connected ACAES system is studied. Through comparative analysis, it can be seen that the change of equivalent inductance shows larger influence on the system stability. When the system impendence changes, control coefficients in PI controller should be adjusted to ensure the system stability. (3) Referring to controller parameters, the analysis results show that the change of proportional coefficients has larger influence on the system stability. (4) Analysis results provide design range for structure parameters design and control coefficient adjustment for the being built grid-connected ACAES station.

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Handwritten Table Recognition Method Based on Multi-head Attention Mechanism and Knowledge Graph Chao Tong1 , Jijing Yan2 , Ziwei Zhu2(B) , Fan Li1 , Xing Zhang1,2 , Hua Hua1 , Yucong Mei1 , and An Hu1 1 State Grid Jiangxi Electric Power Co., Ltd. Electric Power Research Institute, Nanchang,

China 2 Nanchang University, China Resources Digital Technology Co., Ltd., Nanchang, China

[email protected]

Abstract. With the development of smart grid, the use of digital to reduce the burden of the basic level is the efficiency of the development of power grid. However, most of the data of operation and maintenance are stored in paper reports, which cannot be extracted quickly. Among them, it is difficult to identify the handwritten form data and cannot accurately extract the knowledge logic. This paper presents a handwritten table identification method based on multi-head attention mechanism and knowledge graph, aiming to improve the efficiency and accuracy of automated processing of tabular data. In the table generation stage, we use the extracted semantic and structural information to generate accurate and consistent table results. Through experimental evaluation, we verify the table based on long attention mechanism and knowledge graph recognition and generation method identification result logic is very strong, can match the identification results of the new template, its accuracy is above 95%, the method can effectively deal with different types and complex structure of the table data, and provides strong support for subsequent table data processing task. Keywords: Multi-head attention mechanism · knowledge graph · table identification · table generation · natural language processing

1 Introduction At present, most of the operation and maintenance data of the power grid is stored in paper reports, which plays a huge role in the intelligent analysis of equipment. With the advent of the digital age, a large amount of structured data exists in the form of tables, and the automatic identification and generation of handwritten forms has become an important direction in the research field. However, the recognition of handwritten forms still has great challenges in the accuracy of handwritten words and the logical establishment of tables.

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 323–333, 2024. https://doi.org/10.1007/978-981-97-1072-0_33

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In terms of handwriting recognition, different algorithms have been proposed in the literature. The SegLink algorithm [1] adds rotation angle learning to the SSD algorithm but doesn’t perform well on widely spaced or curved text. The progressive extension algorithm [2] separates closely located instances for text localization. Shape perception embedding [3] separates adjacent text examples and solves the problem of long text lines. The CRAFT algorithm [4] accurately locates each character and connects them into a complete text line but requires precise data annotation and struggles with adhesion fonts. In terms of table processing, different approaches have been proposed in the literature. Document [5] proposed an automatic feature target identification table for complete assessment form recognition by detecting the area of interest. However, these systems are limited to specific or similar table formats and use template matching by extracting table lines. Literature [6] presents a method for classifying and identifying tables based on predefined models. Furthermore, literature [7] proposes a table detection algorithm based on Faster-RCNN (Area Generation Network) for extracting table information from documents. However, there is no related research on table knowledge logic extraction and matching different templates.

2 Handwritten Text Extraction This paper proposes a recognition method combining multiple attention mechanism and CRNN for its low accuracy, such as fuzzy, overlapping or missing CRNN [8]. This method can effectively help the model to better understand and recognize the handwritten text, and improve the accuracy and robustness of the handwritten text recognition system. 2.1 Multi-head Attention It is most commonly used in the field of natural language processing, especially in Transformer models in machine translation tasks. The multi-head attention mechanism expands the ability to express attention by introducing multiple attention heads (attention head). Mul-Head Aenon Linear

Concat

Scaled Dot-Product Aenon

Linear

Linear

Linear

V

Q

K

h

Fig. 1. Structure diagram of the multi-head attention mechanism

the calculation formula is: Qi = XWq

(1)

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Ki = XWk

(1)

Vi = XWv

(3)

headi = Soft max(αQi KiT )Vi (i = 1, 2, . . . , h)

(4)

Youtput = concat(head1 , . . . , headh )Wo

(5)

2.2 Time Sequence Convolution is Combined with the Long-Head Attention Mechanism One approach to effectively integrate temporal convolution and multi-head attention mechanisms in handwritten table recognition is as follows [9]. This integration of temporal convolution and multi-head attention can enhance the performance of handwritten table recognition. For the n th temporal convolutional subnetwork, the convolution operation of the m th convolutional layer can be expressed as: Cef = f (X ∗ We + be )

(6)

Specifically, first, for each convolution output in each temporal convolution subnetwork, it is used as an input to the query matrix Q, key matrix K, and value matrix V: Qe,f = Cef We

(7)

Ke,f = Cef Weκ

(8)

Ve,f = Cef Weν

(9) Q

K and W V Weight matriSecond, for the i-th head, the weight matrix is set Wi,e , Wi,e i,e ces corresponding to the i-th head and the n-th temporal convolution subnetworks, respectively.First calculate Qef , Kef and Vef . 

Qi,ef = Qef Wi,e

(10)

Ki,ef = Kef W κi,e

(11)

Vi,ef = Vef W νi,e

(12)

The n th temporal convolutional subnetwork, and the i th head of the m th convolution is Attentioni,ef (Qi,ef , Ki,ef , Vi,ef ) As shown in the Eq. (12):   T Qi,ef Ki,ef Attentioni,ef (Qi,ef , Ki,ef , Vi,ef ) = soft max (13) Vi,ef √ dk

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Finally the output of h heads are concatenated and passed by the output weight matrix WeO Linear transformation was performed,To obtain the multi-head attention output of the f-th convolutional layer of the final e-th temporal convolutional subnetwork MHef , ,As shown in the formula for (14):   (14) MHnm = Concat Attention1,ef , · · · , Attentionh,ef Wefo Formula (14) can be simplified to: MHf = MultiHead(Cef , Cef , Cef )

(15)

2.3 Handwritten Text Recognition Model Through the multi-head attention mechanism, the model can simultaneously pay attention to the different text areas and structural information in the table, and learn the correlation between various features, which further improves the ability to extract and understand the text features in the table. The flow chart is shown in the figure:

Fig. 2. Flow chart of handwritten text recognition based on the multi-head attention mechanism

By thresholding the image after binarization. The segmentation is followed by expansion operations, dealing with some interference, such as the connection of horizontal lines, the connection between text and text. The processed images were contour to initially detect the position of the word. At this point, after the line slice is completed, the column slices are checked, find the words in advance, input the words into the CNN model for detection, and further identify the currently extracted text. The recognition effect is shown in the figure:

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Fig. 3. Identify the renderings

3 Table Content Logical Structure Construction Adding a knowledge graph model in the process of table content identification can solve the above problems well. Knowledge graph can well transform the data with complex structure in operation and maintenance, which can not only efficiently mine text data, but also have good advantages in terms of interpretability. 3.1 The Construction of the Electric Power Knowledge Graph Knowledge graph is a graph structure representing entities and relationships and can be used to enhance [10] understanding and representation of table structure and semantics. The construction process of the electric power knowledge graph is shown in Fig. 4 below:

Fig. 4. Construction process of electric power knowledge graph

3.2 PowerRoberta Layer In order to extract the information of electric text words in model training, Roberta pre-training language model. Roberta The whole word mask strategy is used to fully obtain the information of words in Chinese electric power text, improve the modeling ability of coarse-grained semantics of electric power text, and thus significantly improve the model performance [11]. By constantly adapting to the changing mask strategy, it can learn the characteristics of the power corpus more flexibly, and is more suitable for the entity relationship extraction task in the Chinese power field. Because power

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usually exist more dense distribution in the text of professional vocabulary, so this paper use GB/T50297-2018 power engineering basic term standard, GB/T2900.1-2008 electrical term basic terms, the power equipment operation procedures and management regulations of power text trained the Roberta module, build the exclusive PowerRoberta model in the field of electric power, model architecture and input expression as shown in the Fig. 4. For the input power text sequence X = {x1 , x2 , x3 , . . . , xn }, N is the number of words, each word is expressed by the single heat vector (one-hot), set the dimension to k, then the embedding matrix corresponding to the input sequence is The input of the multi-head attention layer is matrix An, and the input of the Roberta self-attention layer are calculated according to the following formula: Q = An × W Q , K = An × W K , V = An × W V In the formula, W Q , W K , W V are the weight matrix. The self-attention layer output formula is:   QK T V Aattention (Q, K, V ) = Ssoftmax √ dk

(16)

(17)

3.3 BiLSTM Layer The BiLSTM model controls the flow and computational processing of information through the three gates, the forgetting gate and the output gate. The PowerRoberta layer converts the power text into an embedding vector, so a sequence of a word can be represented as X , = [x1, , x1, , . . . xη, ], xt, ∈ Rd is the d-dimensional word vector corresponding to the t-word in a sentence processed by the PowerRoberta layer, with η representing the length of a given sentence. 3.4 Visualization of the Electric Power Knowledge Graph In this study, a knowledge graph that can accurately reflect the physical properties and correlation information of DC resistance is constructed, and the construction effect of the final knowledge graph is shown in Fig. 5

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Fig. 5. Part of the knowledge map effect diagram

4 Handwritten form Identification Traditional methods of handwritten form recognition usually rely on rules and templates, and their performance is limited by changes in handwriting style, noise interference, and complex table structure. To address this problem, deep learning-based methods have made remarkable progress in the field of table processing. In particular, the introduction of the multi-head attention mechanism and the knowledge graph provides a more powerful model and semantic understanding ability for table recognition and generation. 4.1 Form Preprocessing Morphological operations, including erosion and dilation, were used to remove noise from the image. Edge detection and contour approximation techniques were employed to identify the edge lines of the table. The rotation angle of the table was determined through calculations or fitting of the minimum bounding rectangle. After denoising and angle correction, the corrected image was compared to the original image.

Fig. 6. Angle correction processed the images.

The obtained gr-scale images were binarized for later detection with frame line extraction [12]. By using the multi-threshold binarization method, the handwritten text image can be divided into multiple binary images according to the different local features and gray scale distribution of the image, so as to enhance the contrast between text and background and contribute to the subsequent text recognition process.

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Fig. 7. Binarized processing of the images

4.2 Cell detection and Extraction During the extraction of table cells, the corrosion and expansion operations in mathematical morphology are used to detect the table lines. Other parts of the table image can be removed by corrosion operation and then expansion operation.This keeps the cells and their boxed lines to extracts the frames of the table. The processed images are shown in Fig. 8.

Fig. 8. The ame line detects processing images

4.3 Handwritten Table Recognition Based on the Knowledge Graph This paper aims to propose a method of table identification and generation based on multi-head attention mechanism and knowledge graph, and apply it to the basic network structure CRNN. The application of knowledge graph can enhance the understanding and representation of the structure and content of tables, so as to improve the accuracy and robustness of table identification and generation. The flow chart is shown below:

Fig. 9. Flow chart of handwritten chart recognition based on the knowledge graph

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5 Case Analysis This paper tries to verify the accuracy and logic of different methods for table identification by testing three methods. The three methods are set up as follows: Method 1: Using the traditional handwritten writing method for recognition (CRNN + CTC);Method 2: add the long-head attention mechanism (CRNN + multi-head attention + CTC) on the basis of method 1;Method 3: Add the knowledge graph model on the basis of method 2 (CRNN + multi-head attention + Knowledge Graph + CTC); 5.1 Interpretation

Table 1. Experimental results were analyzed and compared Method

Accuracy rate

Logicality

Method 1

93.48%

Bad

Method 2

95.86%

Bad

Method 3

95.88%

Good

The results of this experiment are shown in the figure below: Method 1: The handwritten experimental data is shown in Fig. 10. The output accuracy after recognition is low, and the logic is not high; Method two: The recognition of the output result accuracy is high, and the logic is not high; Method 3: The accuracy of the output results after recognition is also very good, so as to match the identified results with the new experimental report. The identification results and the new template matching results are shown in Fig. 11.

Fig. 10. Handwritten experimental data

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Fig. 11. Method 3 identifies the results and New template to match the result

6 Conclusion In order to improve the logical relationship of table content, this paper designs a method based on multi-head attention mechanism and knowledge graph. By introducing the multi-head attention mechanism and the knowledge graph, the accuracy and logic of handwritten form recognition can be improved. As can be seen from the experimental results, this paper processes and identifies the handwritten forms in the experimental report, and obtains the corresponding data files. For the characters without adhesion, the recognition rate is more than 95%, which can meet the needs of general practical application. Moreover, the logical recognition results of this method are very good, and the matching rate of the new template is also very high. The next step is how to improve the accuracy of the segmentation algorithm and the reliability of the identification model.

References 1. Shi, B., Bai, X., Belongie, S.: Detecting Oriented Text in Natural Images by Linking Segments. IEEE Computer Society (2017) 2. Wang, W., Xie, E., Li, X., et al.: Shape robust text detection with progressive scale expansion network. IEEE (2019) 3. Tian, Z., Shu, M., Lyu, P., et al.: Learning shape-aware embedding for scene text detection. In: 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE (2020) 4. Baek, Y., Lee, B., Han, D., et al.: Character Region Awareness for Text Detection. IEEE (2019) 5. Bin, L., Lianjun, Z., Shuai, L.: Research on object recognition technology for tabular image features. Technol. Vision 23, 105–106 (2016). (in Chinese) 6. Coüasnon, B.: LEMAITRE A.Handbook of document image processing&recognition [M] .Berlin: Springer (2014) 7. Ma, Z., Yu, S.: Research on the table detection algorithm based on the Faster-RCNN network. Intell. Comput. Appl. 12(10), 24–27,31 (2020). (in Chinese) 8. Shiwen, Z.: Research on handwriting recognition in primary school english test papers based on deep learning. Nanjing University of Posts and Telecommunications (2021). https://doi. org/10.27251/d.cnki.gnjdc.2021.000874.(inChinese) 9. Ming, W.: Intrusion detection of multi-head attention timing convolution based on metalearning. Network security and Data Governance 42(07), 49–54 (2023). https://doi.org/10. 19358/j.issn.2097-1788.2023.07.008.(inChinese) 10. Qi, X., Zhi, M.: Summary of attention mechanisms in image processing [J / OL]. Computer Science and Exploration, 1–20 [2023–08–06]. http://kns.cnki.net/kcms/detail/11.5602. TP.20230629.1447.002.html (in Chinese)

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11. Shu, J., Yang, T., Geng, Y., et al.: Joint extraction method for power knowledge graph construction [J / OL]. High voltage technology, 1–11 [2023–08–10]. https://doi.org/10.13336/j. 1003-6520.hve.20230772(in Chinese) 12. CAI became poor, Long, W., Luo, X., et al.: Multi-threshold binarization algorithm based on block processing. Mining Res. Dev. 40(12), 153–157 (2020). https://doi.org/10.13827/j.cnki. kyyk. 2020.12.029. (in Chinese)

Research on the Planning Method for EV Charger Allocation in Highway Network Hengjie Li and Tianyi Liu(B) School of Electrical Engineering and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected]

Abstract. In response to the charging challenges faced by electric vehicles (EVs) operating on highway networks, a guidance framework tailored for charging systems within these networks is proposed. By real-time analysis of data from EVs and charging stations, this framework provides EV users with rational trip planning and charging reservation services. Additionally, a planning model addressing the capacity determination of charging stations in highway networks has been introduced. This model, aiming to minimize investment costs, takes into account constraints such as user waiting times and equitably allocates the number of chargers within the stations. This not only improves charger utilization but also reduces both investment and operational costs. Lastly, the proposed method was simulated and validated on a highway network consisting of 20 charging stations. The simulation results demonstrate that this capacity planning method not only reduces investment and operating costs for charging stations but also enhances the convenience of EV users’ charging experience. Keywords: Highway network · Electric vehicle · Charging station planning · charging guidance

1 Introduction In recent years, with the sustained economic growth, car ownership has been steadily increasing, bringing both convenience to people and environmental pollution challenges. The development of electric vehicles (EVs) can expedite the substitution of gasoline vehicles, and consequently, the advancement of EVs has received significant support from governments around the world [1]. Charging stations for electric vehicles are essential infrastructure for their regular commuting on highway networks. Rational planning and allocation of these stations can not only reduce the investment costs for investors but also make the charging process more convenient for users. Thus, the strategic planning of charging stations holds great significance and practical value [2]. There have been considerable research efforts both domestically and internationally addressing the charging concerns of EVs. Literature [3] considered traffic factors, defined a vehicle-hour variable, and applied graph theory to construct a road network © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 334–341, 2024. https://doi.org/10.1007/978-981-97-1072-0_34

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model, aiming for the lowest investment cost to derive the optimal charging station planning. Literature [4], to address the non-charging needs of EVs on highways, introduced an orderly charging strategy based on a new pricing mechanism that incentivizes users to adjust their charging times. Conclusions highlighted that orderly charging not only reduces users’ charging costs and waiting times but also boosts the utilization of charging facilities and minimizes impacts on highway traffic. Literature [5] investigated the charging demand distribution of EVs on highway networks and employed a two-stage method for station planning. By considering factors like distance from highway exits and vehicle range, potential station locations were identified. Further, by considering charging demand and aiming to minimize construction costs, grid connection costs, and maintenance costs, the optimal location and capacity for stations were established. Several planning solutions emerged from the consideration of multiple factors. Literature [6], recognizing the unique traffic and mobile load characteristics of EVs, proposed a spatiotemporal distribution prediction method for EV charging load based on dynamic traffic information. Depending on the scale of the network, the corresponding trafficdistribution grid interaction model was established. Furthermore, by introducing the OD matrix analysis method and real-time Dijkstra dynamic path search, EVs were allocated start and end nodes, simulating their dynamic travel and charging behaviors. Literature [7] determined charging load distribution through OD analysis to inform station location and capacity planning. Literature [8–10], based on various analytical methods, established dual-layer planning and two-stage planning models for charging station location and capacity determination. Building upon these studies, this paper presents a charging guidance system framework tailored to the driving characteristics of EVs on highway networks. Considering the charging load, and aiming to minimize the investment and operational costs of charging stations while accounting for user waiting times and other constraints, a method for charger allocation in highway networks is proposed. The effectiveness of this method is further verified through simulation.

2 Charging System Guidance Framework for Highway Networks In 2022, China’s sales of new energy vehicles reached 6.887 million units, marking a year-over-year increase of 93.4% and accounting for 61.2% of global sales. Notably, the sales of new energy vehicles represented 25.6% of the total new car sales, achieving the planned target for 2025 three years ahead of schedule [11]. With the advancements in network communication technology and navigation systems, the real-time information exchange between electric vehicles and charging stations has become increasingly sophisticated. Additionally, features based on navigation systems, such as route guidance and real-time positioning, effectively help avoid congested areas while choosing the most optimal routes. Therefore, navigation systems are widely utilized in electric vehicle travel scenarios, especially when driving long distances on highways where they are heavily relied upon by drivers. Given the current technological conditions, a charging guidance system framework for electric vehicles on highway networks is proposed, as shown in Fig. 1. As shown in Fig. 1, the charging guidance system is based on existing digital map platforms, navigation technology, and network communication technology. Electric vehicles

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Fig. 1. Highway network electric vehicle charging guidance system

and charging stations form the physical connection layer, communicating through the network to a cloud-based decision platform. Electric vehicles upload real-time information to the cloud, such as destination, travel time, remaining battery charge, and current latitude and longitude. Meanwhile, charging stations upload real-time information to the cloud about the usage of charging piles within the station and charging reservation status. The cloud decision platform and the digital map platform serve as the information exchange layer. The cloud decision platform, through the digital map platform, integrates and decides on the information such as the latitude and longitude of the electric vehicles and charging stations, subsequently planning the journey for the electric vehicles.

3 EV Charging Behavior in Highway Networks 3.1 Model Description and Assumption Conditions In the process of planning charging stations within the expressway network, numerous factors come into play. To ensure the universality of the model constructed in this paper, and to take a comprehensive approach to the charging stations on expressways, the following assumptions are made: (1) Electric vehicles on expressways always travel to their destination following the shortest path. Compared to urban roads, expressways experience less congestion. It’s assumed that electric vehicles travel at an average speed of V. At present, service areas are typically set up approximately every 50 km on highways, providing facilities for passengers and drivers, such as parking lots, public restrooms, gas stations, vehicle repair shops, dining areas, and convenience stores. Based on this premise, it’s assumed that the integrated photovoltaic storage and charging stations are built within these existing service areas, and land acquisition costs are not taken into account. (2) To ensure the sustainability of the electric vehicle’s battery and to prevent the vehicle from breaking down due to insufficient charge during its journey, it is assumed that the electric vehicle’s battery level remains above the critical level throughout the trip. (3) In the highway network, vehicles travel in one direction and the traffic flow of twoway lanes does not affect each other. The subject of this study is solely the charging station on the same side of the one-way traffic.

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3.2 Waiting Time for Charging Behavior in Electric Vehicle Charging Stations Based on the habits of electric vehicle users, it is assumed that electric vehicle users issue a charging request when the battery level reaches β. Let this moment be T . At this time, the total distance DjT traveled by electric vehicle j in the highway network is represented as shown in Eq. (1).   C I     T 0 c c Dj = V × T − Tj − Kij Ti,j,O − Ti,j,I (1) i=1 c=1

In Eq. (1), T represents the time when the electric vehicle issues a charging request. C is the number of times the electric vehicle j has been charged. Kij is a binary variable, where Kij is 1 if electric vehicle j charges at charging station i, and 0 otherwise. c , Tc Ti,j,O i,j,I respectively represent the exit (out) and entry (in) times of electric vehicle j during its c time of charging at station i. The charging guidance system plans the charging behavior of the electric vehicle. During the entire travel process, the time taken by the electric vehicle j from sending a charging request to arriving at the selected charging station is denoted as T as shown in Eq. (2). T =

Di,j −DjT

(2) V Di,j is the distance traveled by the electric vehicle j from the starting point to the charging station i within time T after sending a charging request. W for the electric vehicle j to charge at the station i is: The queuing time Ti,j ⎧ CL m ⎪ ⎨ Ti,j − (T + T ), Yj ≥ ni W FL m (3) Ti,j = Ti,j − (T + T ), Yj = ni ⎪ ⎩ m 0, Yj ≤ ni CL and T FL respectively represent the time when the electric vehicle arrives at the Ti,j i,j designated charging station, and the time when the c vehicle inside the station completes its first charging action. The charging process of electric vehicles typically involves first charging at high power until the battery reaches 80% of its rated capacity. After that, it charges with lower power to its rated capacity in order to slow down the battery capacity degradation. In this paper, it is set that the charger charges the electric vehicle at a constant power of 120kW, and the charging target for the electric vehicle is 80%. Therefore, the charging C for the electric vehicle is: time Ti,j C Ti,j =

0 )C (80% − Cj,soc j,soc + ξj Di,j C Pi,j

(4)

0 In formula (4), Cj,soc represents the SOC (State of Charge) of electric vehicle j at the end of its last charging session. ξj and Cj,soc respectively represent the rated battery C capacity and the electricity consumption per unit mileage of the electric vehicle j. Pi,j is the constant charging power set in this paper.

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4 Model for Charging Station Quantity Allocation in Highway Networks 4.1 Charger Configuration Model To address the capacity planning issue of photovoltaic storage charging stations on highways, this study establishes a capacity planning model that balances the economic interests of investors and the satisfaction of electric vehicle users with charging services. The model aims to minimize the construction and maintenance costs of the charging stations. At the same time, it considers the constraints of equipment within the charging stations and the capacity of the power grid in determining the capacity of charging stations on highways. Additionally, a convenience model for the charging behavior of electric vehicle users is developed. The key convenience indicator is minimizing the maximum waiting time for electric vehicles queuing at each charging station within the road network. With the aim to minimize investment costs of the charging station, this study simplifies the model by using the number of chargers as a substitute. The objective function and its constraints are as follows: min

I 

ni

(5)

i=1

The objective function is represented by Eq. (5), the variable ni represents the number of chargers configured within each charging station. max nmin ≤ nm i i ≤ ni I 

Pi ≤ Pmax

(6)

(7)

i=1 I 

λi,j = 1

(8)

i=1

In the above formula, the terms respectively represent the constraints on the number of chargers within the charging station, the capacity constraints for accessing the charging station, and the uniqueness of the charging station chosen by the electric vehicle user for a single charging action. Pi and Pmax respectively represent the active power of the charging station and the maximum charging power of its corresponding distribution network node. Waiting time, or the delay in receiving services, has been a significant concern for service providers. Previous studies have extensively shown that waiting time has a negative impact on consumer satisfaction. The satisfaction with waiting time serves as a complete mediating variable in the link between perceived waiting time and overall service satisfaction. On one hand, prolonged waiting times can cause service providers to lose business; on the other hand, consumers perceive extended waiting times as a

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sacrifice they make to receive the service [12]. Based on this, the paper considers the waiting time of user charging behavior and proposes the following constraint: Ti,j ≤ max Ti,j

(9)

Ti,j represents the waiting time inside charging station i after the j electric vehicle user arrives.

5 Case Study Setup and Analysis 5.1 Case Study Setup The numerical example in this paper uses the highway network structure and typical daily EV traffic flow characteristics and EV origin-destination distribution information as shown in Fig. 2. The length of road segment 1 to road segment 10 is 100, 120, 120, 80, 120, 80, 110, 145, 100, 100 km, respectively, and it is assumed that electric vehicle users always choose the shortest path between the starting point and the destination when traveling. The various parameters for electric vehicles traveling on the highway network are set as: Departure time range: 0:00–24:00, battery capacity: 40–80 kW/h, energy consumption per 100 km: 0–15 kW·h/100 km, initial State of Charge (SOC): 0.3–1, and driving speed range: 90–30 km/h.

Fig. 2. Highway network road network structure, characteristics of typical daily electric vehicle traffic flow and distribution information of electric vehicle origin-destination

5.2 Analysis of Case Through the simulation of the case study in this paper, the configuration quantity of chargers in each charging station in the highway network and the maximum queue waiting time for electric vehicle charging behavior at each charging station before and after optimization are shown in Fig. 3. In this paper, the pre-optimization charger configuration scheme distributes all chargers evenly among the charging stations. While the maximum queue waiting time for charging at other photovoltaic storage charging stations has slightly increased, the maximum queue waiting time at the high-load node’s photovoltaic storage charging station has been significantly reduced. Under the same investment level, a limited number of chargers can be used more reasonably, reducing congestion inside the station during electric vehicle charging, making the charging behavior of electric vehicle users more convenient. This verifies the effectiveness of the strategy proposed in this paper.

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Fig. 3. The configuration number of chargers in each charging station and the maximum queue waiting time of EV charging behavior in the station before and after optimization

6 Conclusion This paper mainly focuses on the study of the rational configuration of charger quantities within charging stations in the high-speed road network. Firstly, concerning the issue of electric vehicle charging station selection on highways, a charging guidance framework is proposed. Subsequently, for the problem of charger quantity configuration in the highway network, a planning strategy based on minimal investment costs, while also considering constraints like the maximum waiting time in queues for users, is introduced. Case study results indicate that the strategy proposed in this paper makes the charging behavior of EV users more convenient under the same investment level. Acknowledgments. This work was supported by the Gansu Province Science and Technology Plan Project, grant number 22CX8GA127.

References 1. Wu, L., Bo, Z.: Overview of static wireless charging technology for electric vehicles: Part I. Trans. China Electrotech. Soc. 35(6), 1153–1165 (2020) 2. Yang, J., Li, A., Liao, K.: Capacity planning of light storage charging station for intercity highways based on charging guidance. Power Grid Technol. 44(03), 934–943 (2020). (in Chinese) 3. Jia, L., Hu, Z., Song, Y., et al.: Optimal siting and sizing of electric vehicle charging stations. In: 2012 IEEE International Electric Vehicle Conference. IEEE, pp. 1–6 (2012) 4. Chen, L., Huang, X.: Ordered charging strategy of electric vehicles at charging station on highway. Electric Power Autom. Equipment 39(01), 112–117+126 (2019). https://doi.org/ 10.16081/j.issn.1006-6047.2019.01.017. (in Chinese) 5. Jia, L., Hu, Z., Song, Y., et al.: Planning of electric vehicle charging stations in highway network. Autom. Electric Power Syst. 39(15), 82–89+102 (2015). (in Chinese) 6. Li, X., Li, L., Liu, W., et al.: Spatial-temporal distribution prediction of charging load for electric vehicles based on dynamic traffic information. Protection Control Electric Power Syst. 48(01), 117–125 (2020). https://doi.org/10.19783/j.cnki.p(inChinese) 7. Dong, X., Mu, Y., Jia, H., et al.: Planning of fast EV charging stations on a round freeway. IEEE Trans. Sustainable Energy, 1 (2016) 8. He, C., Wei, G., Zhu, L., et al.: Locating and sizing of electric vehicle charging-swappingdischarging-storage integration station. Proc. CSEE 39(2), 167–177, 333 (2019). (in Chinese)

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9. Yang, Q., Sun, S., Deng, S., et al.: Optimal sizing of PEV fast charging stations with Markoviandemand characterization. IEEE Trans. Smart Grid 10(4), 4457–4466 (2018) 10. Sun, S., Yang, Q., Yan, W.: Hierarchical optimal planning approach for plug-in electric vehicle fast charging stations based on temporal-SoC charging demand characterisation. IET Gener. Transm. Distrib.Gener. Transm. Distrib. 12(20), 4388–4395 (2018) 11. Liu, Y.: How can fully marketized new energy vehicles move towards high-quality development?. Science and Technology Daily, 2023-04-03(003). (in Chinese) 12. Bielen, F., Demoulin, N.: Waiting time influence on the satisfaction-loyalty relationship in services. Managing Serv. Quality: Int. J. 17(2), 174–193 (2007)

Multi-fidelity Data Fusion for Electromagnetic Field Prediction of Electromagnetic Railgun Field Liang Jin1,2(B) , Shuo Shi1,2 , Juheng Song1,2 , and Chenyuan Zhang1,2 1 State Key Laboratory of Reliability and Intelligence of Electrical Equipment,

Hebei University of Technology, Tianjin 300401, China [email protected] 2 Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability in Hebei Province, Hebei University of Technology, Tianjin 300401, China

Abstract. High-fidelity (HF) numerical simulations play a crucial role in realizing the fine design of armature and track structures for electromagnetic railguns, but are limited by the high cost. In contrast, low-fidelity (LF) numerical simulation serves as an important alternative paradigm that also reflects the flow of electromagnetic fields, but is less accurate compared to experiment. By fusing high-fidelity and LF electromagnetic field data, accurate prediction of electromagnetic field can be realized at a low computational cost. In this paper, a multi-fidelity convolutional long- and short-term memory neural network, in which both HF and LF data are introduced into the loss function with appropriate weighting factors to balance the overall accuracy, is developed for predicting the electromagnetic field distribution in the orbit of an electromagnetic railgun. The results show that the proposed method can accurately predict the electromagnetic fields distribution in an electromagnetic railgun track using an appropriate amount of LF data and a small amount of HF data. The performance of the proposed method in this paper is superior compared to the convolutional long- and short-term memory neural network method that only works from either high or low fidelity. Keywords: Electromagnetic railgun · electromagnetic field distribution · deep learning · data fusion

1 Introduction During electromagnetic launching, the distribution characteristics of the electromagnetic field play a crucial role in optimizing and improving track and armature design. This analysis is an important basis for the study of track control, armature temperature rise, and armature turning, and has a profound impact on the reliability design of electromagnetic railguns [1, 2]. However, in practice, the various physical fields of an electromagnetic railgun are dynamically varying, and therefore, numerical simulation methods are needed to obtain the spatial and temporal distribution characteristics of the fields.

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 342–350, 2024. https://doi.org/10.1007/978-981-97-1072-0_35

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Some of the literature did not consider the effect of the armature motion velocity, but used software such as ANSYS and COMSOL to analyze the electromagnetic railgun with multi-physics field coupling when the armature is stationary [3–5]. The other part of the studies used software such as MEGA and COMSOL to investigate the electromagnetic field distribution characteristics of the two-dimensional electromagnetic railgun model considering the effect of the armature motion velocity [6, 7]. Based on these studies, some researchers have developed the EMAP3D software based on the Lagrangian description, which is able to realize the dynamic multi-physics field numerical simulation of the armature of a three-dimensional electromagnetic railgun up to 500 m/s [8, 9]. In addition, some researchers have used the COMSOL finite element simulation platform based on the Laplacian equation mapping for dynamic mesh shifting method to realize the numerical simulation of the dynamic launching process at a maximum speed of 450 m/s [10]. Another researcher used LS-DYNA software to numerically simulate the electromagnetic field of the armature motion and analyzed the characteristics of the armature motion in different cases [11]. Artificial neural networks, known for their ability to handle high-dimensional problems, have been overwhelmingly successful in computational science and engineering [12, 13]. In particular, convolutional long short-term memory (ConvLSTM) networks have proven to be effective in time series analysis [14]. ConvLSTM network has powerful function of spatiotemporal sequence analysis, so it is a natural and promising choice to embed ConvLSTM cells into multi-fidelity (MF) models to solve the problem of spatiotemporal parameter correlation. Low fidelity (LF) data lacks accuracy and reliability for numerical discretization. To solve these problems, the researchers developed a MF proxy modeling method. These methods effectively obtain accurate and reliable results by integrating different information sources, while avoiding excessive computational costs. Specifically, multi-fidelity models based on deep neural networks have been developed to make accurate aerodynamic predictions by integrating experimental and computational aerodynamic data [15– 17]. Calculating high-fidelity (HF) electromagnetic fields for electromagnetic railguns is very computational, and LF calculations often lack the required accuracy. Therefore, a multi-fidelity neural network (MFNN) using ConvLSTM network and multi-fidelity data fusion method is proposed to efficiently integrate LF and HF data. This approach significantly reduces computing resource consumption while maintaining simulation accuracy, thereby improving overall simulation efficiency.

2 Finite Element Calculation Model 2.1 Mechanism Considering the effect of armature motion velocity, the electromagnetic field control equations of the electromagnetic railgun obtained under the Eulerian coordinate system description are: ⎧ ∂A ⎪ ⎪ + ∇φ − v × (∇ × A)] = μJs ⎨ ∇ × ∇ × A − ∇(∇ · A) + μσ [ ∂t   (1) ∂A ⎪ ⎪ + ∇φ − (∇ × A)] = 0 ⎩ ∇ · −σ [ ∂t

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where A is the vector magnetic potential; ϕ is the scalar potential; and μ is the relative permeability; σ is the conductivity; J s is the source current density; v is the armature motion speed. The frictional resistance of the armature rail and the air resistance are considered during the armature motion. Influence, the thrust of the armature in the direction of motion is: F = Fem − Ff − Fair

(2)

⎧ ∂A ⎪ Fem = J × B = σ [v × (∇ × A) − − ∇φ] × (∇ × A) ⎪ ⎪ ⎪ ∂t ⎨ Ff = μf (FN ,em + FN ,p ) ⎪ ⎪ ⎪ Cf Lv2 x γ +1 ⎪ ⎩ ρ0 (Sv2 + Sxa + ) Fair = 2 2

(3)

included among these:

where F em is the armature electromagnetic thrust, the size of the current density J and flux density B; F f is the armature track frictional resistance, the size of the friction coefficient μf , armature electromagnetic contact pressure F N,em , armature mechanical preload pressure F N ,p ; Fair is the air resistance, the size of the armature motion parameters and the aerodynamic shape; γ is the specific heat ratio of the air; ρ 0 is the initial air density; S is the armature cross-sectional area; L is the perimeter of the armature cross-section; C f is the viscous friction coefficient. S is the armature cross-sectional area; L is the armature cross-sectional circumference; C f is the coefficient of viscous friction. The armature mass ma is known, and the armature acceleration, velocity and displacement are respectively: ⎧ a(t) = F/ma ⎪ ⎪ ⎪  t ⎪ ⎪ ⎨ v(t) = a(τ ) d τ (4) 0 ⎪  ⎪ t ⎪ ⎪ ⎪ ⎩ x(t) = v(τ ) d τ 0

The typical C-shaped armature and rectangular caliber electromagnetic railgun were used as the research object. The electromagnetic railgun is simulated and analyzed by finite element simulation software. The model parameters of pivot rail are shown in Table 1. According to the central orbit parameters in Table 1, the geometrical model of the electromagnetic railgun is constructed, as shown in Fig. 1. Among them, the air domain and part of the orbit region are not drawn. After the excitation force is loaded, the excitation wave appeared and then transmitted to the other side of the wire system. The maximum amplitude of each point is 0.2 m and the vibration characteristics of each point are very similar. After 1.25 s, the oscillation starts at the mid-span of the line. The time for the excitation wave to travel back and forth is about 2.5 s, which is consistent with the second natural period. Due to damping, the amplitude of the overhead line conductor vibration decreases with time.

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Table 1. Parameters of armature and rail model. Model parameter

Numerical value

Track length l/mm

2500.00

Track width h/mm

31.75

Rail thickness w/mm

6.35

Track spacing s/mm

25.00

Orbital conductivity σ /(S/m)

5.80e7

Orbital relative permeability μ

1.00

Armature length l a /mm

28.59

Armature width ha /mm

25.00

Armature conductivity σ a /(S/m)

1.86e7

Armature relative permeability μa

1.00

Armature mass ma /g

100.00

Fig. 1. Electromagnetic railgun geometry model.

3 ConvLSTM Theory and Multi-fidelity Modeling of Electromagnetic Field distributIons 3.1 ConvLSTM Convolution operation can extract the spatial features of the electromagnetic cloud image well, and LSTM can deal with the temporal correlation of the electromagnetic cloud image. Therefore, ConvLSTM has the advantages of both CNN and LSTM. By capturing the spatial correlation and spatial characteristics of electromagnetic field cloud image, the time series modeling of electromagnetic field cloud image during the whole launching process can be carried out to characterize its spatial characteristics. Its structure is shown in Fig. 2. 3.2 Construction of the Loss Function The difference between the network output and the available data yi is measured by the Mean Squared Error (MSE) loss function and minimized to determine all trainable

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parameters of the network model. The difference between the model prediction and the true value is reflected by the loss function, which determines the goal of model training. Given input x i and output yi , choose the following mean squared error (MSE) loss function: 1 ∧ MSE = ( y −yi )2 n i n

(5)

i=1

The MSE loss function is modified to give multiple fidelity levels to the dataset. The goal of the current work is to impose such constraints on the LF data as a priori information in a flexible manner, appropriately penalizing the ConvLSTM approximation of the MSE loss function, which consists of both LF and HF data, and also avoiding overfitting. Therefore, the modified mean square error loss function is defined as: Loss =

∧ 1 ∧ HF 2 1 ( y −yi ) + k ∗ ( y −yjLF )2 n m i j n

m

i=1

j=1

(6)

where n and m are the number of HF and LF samples, respectively; k defines coefficient of the LF data, whose selection will be described in detail below. This is the main contribution and the key strategy used in the current work. In addition, it is noteworthy that the proposed approach is also able to be used for problems with multiple fidelities, more than two fidelities. 3.3 Multi-fidelity Electromagnetic Field Distributions Modeling The model architecture consists of 40 hidden neurons and 4 hidden layers, which have been selected based on prior research and empirical evidence to be effective in similar applications. The modeling procedure can be summarized as follows: 1) The finite element simulation software was used to simulate and analyze the type c armature rectangular caliber electromagnetic railgun. The software can provide detailed information about the railgun track field distribution; 2) Both HF and LF data of the electromagnetic fields on the railgun track are obtained. The LF data is generated through a coarse numerical discretization process, while the

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HF data is obtained with higher precision. This division of data into different fidelity levels enables the incorporation of both accurate but computationally expensive HF data and a large volume of easily accessible LF data; 3) To train the model, the HF data is further split into training and validation samples. Approximately 80% of the HF data is used for training the model parameters, while the remaining 20% is used for validating the model during the training process. Adjust the hyperparameter k by verifying the model; 4) In the training process, Adam optimization is used to update the model parameters to ensure convergence and regularization. Once the model is trained, it is evaluated using test samples. The performance of the model is evaluated using MSE to measure its ability to accurately predict the distribution of electromagnetic fields.

4 Data Sets 4.1 Modeling The 40 mm × 50 mm medium aperture orbit launcher developed by South Korea’s Agency for Defense Development is the research object. The armature mass is 300 g, the armature accelerates from 0 ms to 3 ms. Regardless of the influence of armature motion speed and resistance, this paper first establishes a finite element simulation model and selects an appropriate viewing Angle, as shown in Fig. 3. For the stable stage, the mapping relationship between time and electromagnetic field distribution is obtained.

Fig. 3. Observation angle.

Set the time step to 0.0015ms to get sufficient sample data. In the constant current stage, 600 sets of electromagnetic field sample data can be obtained for stable numerical simulation, and each set of samples contains a current field distribution and a magnetic field distribution. 4.2 Fidelity Division Both the HF and LF models are constructed through the numerical approximation of using the COMSOL. The two fidelity levels are distinguished by the mesh sizes, whose structure are shown in Fig. 4. On the left is the meshing diagram of the LF model, and on the right is the meshing diagram of the HF model. For the LF model, the maximum

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mesh size is 41.8 mm, the minimum mesh size is 8.8 mm, the maximum cell growth rate is 1.7, the curvature factor is 0.8, and the narrow region resolution is 0.3, so the total number of cells in the model is 3278; For the HF model, the maximum mesh size is 4.4 mm, the minimum mesh size is 0.044 mm, the maximum cell growth rate is 1.3, the curvature factor is 0.2, and the narrow region resolution is 1. The total number of cells in the model is 779403. The HF and LF models of the same electromagnetic railgun are constructed by using the above two meshing methods with different precision.

Fig. 4. Grid diagram of electromagnetic railgun.

5 Results To assess the predictive capacity of the ConvLSTM model, the initial 500 samples were employed for training. Subsequently, the final 100 samples served as the test dataset. Three model variations were evaluated: one utilizing only HF data, another with solely LF data, and the last leveraging MF data with hyperparameter k = 0.1. Evaluation metrics included MSE and mean absolute percentage error (MAPE), with results for magnetic and current fields tabulated in Tables 2 and 3, respectively.

∧

n 100%

yi −yi

(7) MAPE =



yi

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Table 2. Comparison of Prediction Results of Magnetic Field. Model

MSE

MAPE(%)

Time consumption(h)

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0.005

0.79

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2.67

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45

The MF model has the best effect, reducing the time consumption while maintaining a high precision. A set of predicted results are selected from the test data set, and the

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Table 3. Comparison of Prediction Results of Current Field. Model

MSE

MAPE(%)

Time consumption(h)

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0.003

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0.013

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0.004

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Fig. 5. The predicted results of MCNN.

current field and magnetic field predicted by the MF model are compared with the finite element analysis (FEA) results. The comparison results are shown in Fig. 5. The prediction and distribution characteristics of electromagnetic field cloud map solve the problem of large calculation amount and slow speed of numerical simulation of electromagnetic rail gun launch, provide a basis for the layout and protection of launching components, and contribute to the fine design of electromagnetic rail gun structure.

6 Conclusion In this study, a modified ConvLSTM-based MCNN model is proposed for predicting electromagnetic field distributions using a combination of LF and HF data. The model incorporates a re-weighted loss function to effectively fuse data of different fidelity levels. The model is validated using data from numerical simulations of an electromagnetic railgun, where HF data is obtained from detailed simulations and LF data from coarser discretization models. The results show that compared with the single fidelity model, the proposed MCNN model also shows reasonable prediction in the case of limited high frequency training data. Acknowledgments. This work was funded by the Major Research Program of National Natural Science Foundation of China Grant 92066206; National Natural Science Foundation of China Grant 51977148; Central Leading Local Science and Technology Development Special Free Exploration Project 226Z4503G.

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References 1. Ma, W., Junyong, L.: Thinking and study of electromagnetic launch technology. IEEE Trans. Plasma Sci. 45(7), 1071–1077 (2017). (in Chinese) 2. Li, B., Lin, Q.: Analysis and discussion on launching mechanism and tactical electromagnetic railgun technology. Defence Technol. 14(5), 484–495 (2018). (in Chinese) 3. Chen, L., He, J., Xia, S., et al.: Influence of rail resistivity and rail height on armature edge erosion at current ramp-up in solid armature railgun. High Vol. Eng. 40(04), 1071–1076 (2014). (in Chinese) 4. Gang, G., Lizhou, W., Hao, G., et al.: Simulation and analysis of rail cooling based on electromagnetic and fluid field coupling. Trans. China Electrotechn. Soc. 35(17), 3601–3608 (2020). (in Chinese) 5. Tian, Z., An, X.: Multiphysical field coupling analysis of composite electromagnetic track. J. Gun Launch Control 38(03), 1–6 (2017). (in Chinese) 6. Tang, L., Li, H.: Simulation analysis of railgun in-bore high magnetic field. Comput. Simul. 31(11), 1–5 (2014). (in Chinese) 7. Yin, Q., Zhang, H., Li, H.: Analysis of in-bore magnetic and electric fields in electromagnetic railgun under dynamic condition. Acta Armamentarii 38(06), 1059–1066 (2017). (in Chinese) 8. Hsieh, K.: A Lagrangian formulation for mechanically, thermally coupled electromagnetic diffusive processes with moving conductors. IEEE Trans. Magn. 31(1), 604–609 (1995) 9. Hsieh, K.: Hybrid FE/BE implementation on electromechanical systems with moving conductors. IEEE Trans. Magn. 43(3), 1131–1133 (2007) 10. Yang, F., Zhai, X., Zhang, X., et al.: Dynamic multiphasic coupling analysis of electromagnetic orbit launcher. J. Projectiles Rockets Missiles Guidance 41(02), 20–24 (2021). (in Chinese) 11. Li, C., Chen, L., Wang, Z., et al.: Influence of armature movement velocity on the magnetic field distribution and current density distribution in railgun. IEEE Trans. Plasma Sci. 48(6), 2308–2315 (2020). (in Chinese) 12. Han, J., Jentzen, A.: Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci. 115(34), 8505–8510 (2018) 13. Beck, C., Jentzen, A.: Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. J. Nonlinear Sci. 29(4), 1563–1619 (2019) 14. Shi, X., Chen, Z., Wang, H.: Convolutional LSTM network: A machine learning approach for precipitation nowcasting. In: Proceedings of the Computer Vision and Pattern Recognition (2015) 15. Fernández-Godino, M.G., Park, C., Kim, N. H., Haftka, R.T.: Issues in deciding whether to use multifidelity surrogates. AIAA J. 57(5), 2039–2054 (2019). https://doi.org/10.2514/1.J05 7750 16. Li, K., Kou, J., Zhang, W.: Deep Learning for multi-fidelity aerodynamic distribution modeling from experimental and simulation data. arXiv e-prints (2021) 17. Leifsson, L., Koziel, S.: Multi-fidelity design optimization of transonic airfoils using physicsbased surrogate modeling and shape-preserving response prediction. J. Comput. Sci. 1(2), 98–106 (2010). https://doi.org/10.1016/j.jocs.2010.03.007

An Online Battery Electrochemical Impedance Spectroscopy Measuring Method Yu Zhang1 , Haojing Wang1 , Cheng Peng2(B) , Xinyue Liu2 , and Rui Li2 1 Electric Power Research Institute, State Grid Shanghai Municipal Electric Power Company,

China Electric Power Research Institute, Shanghai 200240, China 2 School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University,

Shanghai 200240, China {DrVegapunk,lxy999,liruiqd}@sjtu.edu.cn

Abstract. The safety of battery energy storage systems is becoming increasingly important in the context of the rapid development of renewable energy. In order to address that issue, the identification of battery state is crucial. At present, methods for estimating battery states using electrochemical impedance spectroscopy (EIS) are widely studied, and existing research results indicate that EIS can estimate battery state of charge (SOC), state of health (SOH) and even state of safety (SOS). Therefore, achieving online measurement of EIS has become a hotspot. At present, the vast majority of EIS online measurement methods focus mainly on measuring the full frequency band and require injecting current disturbances of different frequencies, resulting in low testing efficiency and insufficient utilization of the current during system operation. This article analyzes the most valuable EIS frequency range for achieving state estimation, and proposes an EIS online measurement system and corresponding measurement method. Relevant verification has been completed using a publicly available dataset. The proposed method exhibits good performance for measuring within the specified frequency range. Keywords: Configurable battery energy storage system · Equivalent circuit model · Electrochemical impedance spectroscopy

1 Introduction With the establishment of carbon peak and carbon neutrality target, more and more renewable energy will be grid-connected to replace traditional thermal power generation [1]. However, due to the intermittent nature of renewable energy sources, the stability of the grid will be deteriorated. To suppress the power fluctuations of renewable energy, energy storage systems are introduced into the power system [2]. Among all kinds of energy storage systems, battery energy storage system is an excellent candidate due to the flexibility of the placement location and the rapidity of power input and output [3]. As is expected by the research company BloombergNEF (BNEF), battery energy storage installations around the world will be 1095GW/2850GWh by 2040 [4]. However, safety has always been one of the key issues that troubles the large-scale application of battery energy storage systems. According to the database collected by © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 351–358, 2024. https://doi.org/10.1007/978-981-97-1072-0_36

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Electric Power Research Institute, over 50 battery energy storage systems (BESSs) failure has been reported during the past five years [5]. Therefore, to enhance the safety of the battery energy storage system is top priority. There are many causes that lead to battery failure [6]. Since the design aspect can only be further improved by manufactures, safety can only be improved by preventing battery abuse. In stationary battery energy storage system, mechanical abuse can rarely happen due to the fixed installation position of the batteries; thermal abuse can be settled by using proper thermal management method; only electric abuse can be hard to eradicate. Electric abuse includes external short circuit, internal short circuit, overcharge and overdischarge and so on. Short circuit can be detected by testing the battery impedance; overcharge and over-discharge can be avoided by accurate state estimation and proper power control.

Electrochemical Impedance Spectroscopy (EIS)

Understand degradation

Characterize performance

Validate model

Degradation mechanism

Growth pattern of solid electrolyte interphase

Equivalent circuit model

Factors affecting degradation

Conductivity of materials

Physics-based model

Estimate state State of charge State of health Temperature

Ion migration rate of materials

Fig. 1. The Application of Electrochemical Impedance Spectroscopy

In recent years, research has found that electrochemical impedance spectroscopy of batteries can be applied to multiple types of applications [7], including typical applications related to battery safety, as is shown in Fig. 1. As a result, the method of measuring EIS has become a popular topic of research. In [8], an impedance-based battery management system is proposed, which has the ability to measure battery impedance between 1–1000 Hz. In [9], a method for online monitoring of battery SOC using EIS techniques is proposed. The above methods both achieve impedance measurement by injecting current disturbances of different frequencies. The advantage of this method is that the meaning of the measurement quantity is clear and the accuracy is high. However, when measuring the low-frequency impedance, this method is time-consuming. Sometimes, it is not necessary to measure a very accurate electrochemical impedance value across the entire frequency band, thus simplifying the electrochemical impedance measuring method. In this paper, an online battery electrochemical impedance measuring method in reconfigurable battery system is provided, and its application in SOC estimation is verified. This paper is organized as follows: In Sect. 2, the system configuration is provided and the corresponding EIS measuring method is introduced. In Sect. 3, the proposed method is validated on public datasets, and remaining issues and future work is discussed. Section 4 concluded this paper.

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2 System Configuration and EIS Measuring Method To enhance the safety of BESSs, more and more configurable BESS topologies are proposed. Several typical configurable BESS topologies are shown in Fig. 2.

Fig. 2. Typical configurable BESS topologies: (a) AC side parallel-connected, (b) DC side parallel-connected, (c) AC side cascaded.

To realize active configuration, each battery module should be connected with two active switches, which can bypass or insert the battery module into the main circuit. When the cluster converter works at chopping mode and the battery module is inserted in the main circuit, the current flowing through the battery can be regarded as pulse current. Besides, by controlling the active switches, the pulse length of the current flowing through the batteries can be controlled. In this way, a relatively easy way to measure battery EIS can be conducted. Typical EIS Nyquist plot is shown in Fig. 3. Usually, in the high-frequency band, inductive behavior will be observed due to the stray inductance in the testing circuit and cell windings. Therefore, the mapping effect between the EIS high-frequency band and the internal state of the battery is not as good as the low-frequency band. In [10], researchers found that the state of the battery is mainly related to the low-frequency band EIS, which means the EIS measuring method only needs to reflect the low-frequency band exactly (for example, 0.01 Hz–100 Hz). In this way, battery equivalent circuit model (ECM) can be used to fit EIS curve. Since the batteries have multiple ECMs, a more ECM for parameter identification can be selected as the benchmark, and the battery voltage response triggered by the current pulse can be used to determine the parameters of the battery ECM. Two selected ECMs of the battery are shown as follows: (a) second-order RC model; (b) second-order RQ model. These two models are shown in Fig. 4. In the ECMs, Rdc , R1 and R2 represent dc resistance, charge transfer resistance and diffusion resistance respectively. C1 (Q1 ) and C2 (Q2 ) model the double layer effects and diffusion process respectively. Q1 and Q2 are constant phase elements (CPEs), which can be regarded as generalized capacitance that can reflect the non-linear effect in the circuit. Secondorder RC model is easy to implement, while second-order RQ model has higher fitting

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-Zimag (Ω) Frequency decrease O

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accuracy. In practice, it is preferable to determine which equivalent circuit model to use based on the processor’s operating speed.

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Take the second-order RQ model for example. The EIS online measure method using ECM can be calculated by the following steps. When the configurable system is working in stable state, the current flow through each cluster can be regarded as a constant value. Then, if a battery module needs to realize SOC correction, by switching the “bypass” and “insert” state of it can generate a current pulse, as is shown in Fig. 5. The testing time t1 , t2 and t3 can be adjusted according to the operating conditions of the system. It will be a good practice to keep t1 and t3 longer while keep t2 less than 10s, since longer t2 will cause greater change in battery SOC. When the typical testing waveform is realized, the parameters of the ECM can be calculated as follows: V2 − V1 I  α1   α2  t t v(t) = −vp1 · Eα1, 1 − − vp2 · Eα2, 1 − + V1 τ1 τ2 Rdc =

(1) (2)

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In (2), vp1 is the residual voltage on the R1 //Q1 ; vp2 is the residual voltage on R2 //Q2; α1 and α2 reflect the τ1 and τ2 are time constants of R1 //Q1 and R2 //Q2 respectively;  α1 α2 Q1 and R2 //Q2 respectively; Eα1, 1 − tτ1 and Eα2, 1 − tτ2 are Mittag-Leffler functions. The definition of Mittag-Leffler function is shown as follows: Eα, 1 (z) =

∞

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where  (x) =

+∞

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0

(x) is a gamma function that can be calculated using existing code, and the MittagLeffler function can also be calculated using similar methods. In special circumstances, α in (7) equals to 1, and the Mittag-Leffler function will become the exponential function, which can greatly simplify calculation. At this time, the second-order RQ model is reduced to the second-order RC model. By fitting formula (2) with the actual voltage waveform curve in Fig. 5, vp1 , vp2 , τ1 , τ2 , α1 and α2 can be obtained. The solutions for R1 , R2 , Q1 and Q2 can then be derived from (3) to (6).

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After get the value of R1 , R2 , Q1 and Q2 , the EIS can be obtained using the following formula: Z(ω) = Rdc +

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Need EIS measurement?

No

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Bypass the module for t1

Insert the module for t2

Bypass the module for t3

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Fig. 6. Online EIS measurement method flowchart.

Therefore, the overall process of the EIS online measurement method is shown in Fig. 6. When the cluster level control converter has current control function, this method will be more convenient to implement.

3 Method Validation and Discussion To check the fitting ability of the selected ECM model, testing data based on the Panasonic 18650PF Li-ion Battery Data [11] is used. As can be seen from Fig. 7, when choosing second-order RQ ECM model, the fitting result can reach a satisfactory level within the required frequency band (0.01 Hz–100 Hz), which indicates that this EIS fitting method has some practicality. To further examine the practicality of the method, an experimental platform is constructed, as illustrated in Fig. 8(a). The host computer simulates battery insertion and bypass by programming the current waveform of the power supply. Since cells in the battery module are typically connected in a series, the technique’s simulation effect is viable if the battery module is not performing state balancing. In Fig. 8(b), HIOKI BT4560 battery impedance meter is used for offline measurement of battery EIS as a reference for the measured results. Future research will explore the adjustment of the current amplitude, t1, t2, and t3 parameters used for measurement, as well as the conduction of EIS measurements using the indicated system.

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Fig. 8. EIS testing platform: (a) Online EIS testing platform; (b) EIS checking platform.

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4 Conclusion This article presents a method for measuring EIS online and proposes several structures for battery energy storage systems that are suitable for this method. Firstly, the system’s stable operation mode is determined. After that, the battery module to be measured is inserted and bypassed through a control switch to achieve pulse excitation. Moreover, the formula is used to fit the response voltage, and the second-order equivalent circuit model parameters of the battery are ultimately obtained. Finally, the EIS is acquired. The validity of the results was confirmed using online datasets. In addition, an experimental platform was developed for EIS testing. Acknowledgements. This work is supported by Science and Technology Project from the State Grid Shanghai Municipal Electric Power Company “Preliminary research on large-scale reconfigurable battery energy storage technology” project.

References 1. Rouholamini, M., Wang, C., Nehrir, H., et al.: A review of modeling, management, and applications of grid connected li ion battery storage systems. IEEE Trans. Smart Grid 13(6), 4505–4524 (2022) 2. Calero, F., Cañizares, C.A., Bhattacharya, K., et al.: A review of modeling and applications of energy storage systems in power grids. Proc. IEEE, 1–26 (2016) 3. Gutsch, M., Leker, J.: Global warming potential of lithium-ion battery energy storage systems: A review. J. Energy Storage 52, 105030 (2022) 4. BloombergNEF: Energy Storage Investments Boom As Battery Costs Halve in the Next Decade. https://about.bnef.com/blog/energy-storage-investments-boom-battery-costs-halvenext-decade. Accessed 8 Aug 2023 5. Electric Power Research Institute: BESS Failure Event Database. https://storagewiki.epri. com/index.php/BESS_Failure_Event_Database. Accessed 8 Aug 2023 6. Yang, Y., Wang, R., Shen, Z., et al.: Towards a safer lithium-ion batteries: A critical review on cause, characteristics, warning and disposal strategy for thermal runaway. Adv. Appl. Energy 11, 100146 (2023) 7. Meddings, N., Heinrich, M., Overney, F., et al.: Application of electrochemical impedance spectroscopy to commercial Li-ion cells: A review. J. Power Sources 480, 228742 (2020) 8. Carkhuff, B.G., Demirev, P.A., Srinivasan, R.: Impedance-based battery management system for safety monitoring of lithium-ion batteries. IEEE Trans. Indust. Electron. 65(8), 6497–6504 (2018). https://doi.org/10.1109/TIE.2017.2786199 9. Gadoue, S., Chen, K.-W., Mitcheson, P., Yufit, V., Brandon, N.: Electrochemical impedance spectroscopy state of charge measurement for batteries using power converter modulation. In: 9th International Renewable Energy Congress, pp. 1–5. Hammamet, Tunisia (2018) 10. Wang, X., Wei, X., Dai, H., et al.: State estimation of lithium ion battery based on electrochemical impedance spectroscopy with on-board impedance measurement system, In: Vehicle Power & Propulsion Conference IEEE (2015) 11. University of Wisconsin-Madison: Panasonic 18650PF Li-ion Battery Data. https://data.men deley.com/datasets/wykht8y7tg/1. Accessed 8 Aug 2023

Research on Location Determination and Capacity Optimization Method for Large-Scale Energy Storage Station in Regional Power Grid Liming Zhai(B) , Chengqian Xiao, Xiaohang Li, and Yanbing Zhang State Grid Pingdingshan Electric Power Company, Pingdingshan 467000, China [email protected]

Abstract. In this paper, an optimization method is proposed to optimize the location and capacity of large-scale energy storage station in regional power gird. First, according to the requirement of power system, a multi-objective function is built for performance evaluation, which includes node voltage fluctuation, load fluctuation and investment of energy storage station. Then, an improved particle swarm algorithm (PSA) is proposed for location and capacity optimization. Since traditional PSA is easy to get stuck on locally optimal value, weight coefficients with nonlinear adjustment functions and cross-compilation processes in the genetic algorithm are employed to avoid the local optimal results. In the end, the regional power grid in Pingdingshan, Henan Province is taken as a case study to evaluate the effectiveness of the proposed optimization method. The proposed optimization result shows that the proposed method shows quickness and accuracy in location and capacity optimization for large-scale energy storage station. Keywords: Large-scale Energy Storage Plant · Improved Particle Swarm Algorithm · Regional Power Grids · Site Selection and Capacity Determination

1 Introductory With the rapid increase of installed renewable energy capacity, energy storage systems have become one of the effective solutions to ensure the stable operation of modern power system[1, 2]. Considering the requirement of the power system and geographical limitations, the determination of the location and capacity of the energy storage station is important for power system planning. Thus, site selection and capacity determination are multi-objective and complex optimization problems [3, 4]. First, proper location and capacity are necessary for system reliability considering both the fluctuation of load and renewable energy generations; second, the system should be properly designed considering the investment costs [5]. According to published literature, scholars have focused on the design optimization of battery energy storage systems for peak regulation in power system. In [6], an optimization method aiming at peak load shifting, which was combined with a genetic © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 359–369, 2024. https://doi.org/10.1007/978-981-97-1072-0_37

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algorithm and quadratic programming, was proposed for the determination of the location and capacity of distributed energy storage systems in the distributed power grid. In [7], the particle swarm algorithm was employed for capacity optimization of the energy storage system, in which network loss was considered as the optimization objective. In [8], scholars focused on economic evaluation and pollution gas, according to which the location and capacity of energy storage systems in the distribution network were optimized. In [9], a multi-objective evaluation function, which taken both load fluctuation and power quality into consideration, was built for energy storage system distribution in the active distribution network. In [10], the capacity planning and investment benefits of energy storage systems in micro-energy systems were investigated by modeling photovoltaic power generation and energy storage systems. In [11], the total investment of the energy storage system and operating cost in a single day were considered as optimization objectives to determine the location and capacity of the battery energy storage system. Intelligent algorithms have been proven to be an effective way to solve related multiobjective problems. Reported intelligent algorithms in published literature include particle swarm optimization, genetic algorithm and simulated annealing algorithm, etc. al [12, 13]. These algorithms are able to find optimized solutions among a range of non-inferior solutions to satisfy multi-objectives. However, traditional multi-objective optimization algorithms are easy to strike into local optima and thus should be modified according to characteristics of actual application objects [14, 15]. To overcome the above issues, an improved particle swarm optimization algorithm (IPSA) is proposed for location determination and capacity optimization for large-scale energy storage stations connected to the regional power grid. The multi-objective function is built, which takes node voltage fluctuation, load fluctuation and investment of energy storage station into consideration. The constraint condition for each decision variable is given according to the basic principles of the energy storage system in the power system. In the end, the regional power grid in Pingdingshan, Henan Province, China is taken as a case study. The optimization result of the case study demonstrates the quickness and accuracy of the proposed solution in solving the multi-objective optimization problem.

2 Mathematic Model for Location Determination and Capacity Optimization 2.1 Multi-objective Functions Since the performance of large-scale energy storage stations is influenced by many factors, location determination and capacity optimization of energy storage station are a complex multi-objective problem. Although grid-connected energy storage system contributes to improving the load fluctuation and power balance problems in modern power system, energy storage station requires high investment in all life cycle. Thus, it is very important to determine the location and capacity of the energy storage station in the early plan and design process. Considering the requirement of the power system and construction cost of energy storage station, fluctuation of node voltage, fluctuation of load, and capacity of energy storage station are considered as optimizing objectives.

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(1) Fluctuation of node voltage. Voltage should be strictly limited within a certain range to ensure the safe and stable operation of the power system. The node voltage fluctuation can be expressed as f1 =

N T bur  

  Vij − V i 

(1)

i=1 j=1

where V ij is the voltage value at time j of node I; N bur is the number of nodes in the system; V i is the average voltage of node i in the daily hour time; T stands for the current moment. (2) Fluctuation of load. Load is becoming pluralistic in the modern power system. Besides traditional load in distributed networks, distributed sources, such as renewable power generations, and random loads, such as charging electric vehicles, will intensify load fluctuation. One of the most important functions of energy storage system is to suppress the load fluctuation. The node load fluctuation can be expressed as T   2 Ps (i) − P f2 =

(2)

i=1

where P(i) is the input power of the grid at time i; P is the average power input during the concerned period. (3) Capacity of energy storage system. It’s clear that both the fluctuation of node voltage and the fluctuation of load will be better stabilized under a larger capacity of energy storage system. However, referring to the energy storage station, the larger the capacity is, the larger the investment will be. Thus, the capacity of the energy storage system should be properly optimized to balance the investment and system performance. Since the capacity of the energy storage system relies on the energy stored in the station and energy generated by the station, the capacity of the energy storage system can be expressed as f3 =

+nt N store t0 j=1

Pstorej (i) · t

(3)

i=t0

where Pstorej (i) is the charge/discharge power at moment i of the number jth energy storage unit; t is the time interval between adjacent sampling moments; t 0 + nt is the switching moment between charging and discharging mode; N store is the number of energy storage unit; t 0 indicates the start moment of each mode. Taking node voltage fluctuation f 1 , load fluctuation f 2 , and energy storage system capacity f 3 into consideration, the optimization function is built as   min F = λ1 f1 + λ2 f2 + λ3 f3 (4) where λ1 , λ2 , λ3 are the weights coefficient of the function f 1 、f 2 、f 3 .

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2.2 Constraints Both location and capacity of energy storage station should be optimized under certain constraints, including node voltage constraint, transient power balance of energy storage station and energy balance in the energy storage station. (1) Node voltage constraint. The node voltage in power system should never exceed the limitation and the node voltage constraint is expressed as following Vmin ≤ Vij ≤ Vmax

(5)

where V min and V max are the lower limit and upper limit of the system node voltage, respectively. (2) Transient power balance. The input power of the network should always be equal to the load of the system network. The energy storage station can operate as either load (Pstorek > 0) or source (Pstorek < 0) to help the power balance. Therefore, the constraint power balance constraint can be expressed as Ps =

Nbus 

Ploadi −

i=1

N DG  j=1

PDGj −

N store

Pstorek

(6)

k=1

where N DG is the number of distributed power supplies (including power supplied by thermal units); Ploadi is the load power of node I at a certain time; PDGj is the output of the number of j power supply at a certain time; Ps is the input power of the grid; Pstorek is the output of the number of k energy storage power at a certain time and is positive when the energy storage is discharged. (3) In order to prevent from overload in energy storage station, transient power should also satisfy Pstoremin ≤ Pstore ≤ Pstoremax

(7)

where Pstoremin and Pstoremax are the upper and lower limits of the energy storage system power, respectively. (4) The energy storage station should always satisfy the energy balance equation in a single day and the energy balance constraint is expressed as T 

Pstore (i) · t = 0

(8)

i=1

3 Improved Particle Swarm Algorithm for Multi-objective Optimization 3.1 Traditional Particle Swarm Algorithm Particle swarm Algorithm (PSA) is an optimal algorithm applied to solve complex optimization problems. The algorithm simulates the flight behavior of birds and searches the optimal solution in concerned space of the problem with multiple individuals (particles) and outputs optimized decision variables. However, the traditional PSA is easy to struck into local optimal during the process of location and capacity optimization of energy storage power station. To overcome such issue, an improved PSA (IPSA) is proposed in this section.

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3.2 Improved Particle Swarm Algorithm for Optimization 3.2.1 Adaptive Inertia Weight In this paper, the value of w is determined according to the difference between the difference between the particle and the optimal particle of the population, named as X, and is adaptively adjusted according to the performance of the particle and the search process. The difference between w and X is shown in Fig. 1. The difference between the number i particle at time K and the overall optimal solution x i (k) is obtained from the following equation: D  1   (k) 1 (k)  = gd − xid  xmax − xmin D d =1 2  (k) = wstart − (wstart − wend ) Xi − 1

(k) Xi (k)

wi

(9) (10)

where W start , W end refer to the initial and final values of w respectively; wi (k) stands the inertial weight of the number i particle at time k; X max , X min stand for the variables of the maximum and minimum particle positions respectively; D is the solution space dimension. In this paper, the simulation inertia weight coefficient is 0.4 for W start and 0.9 for W end .

wstart

wend 0

0.2

0.4 0.6 0.8 Difference X

1

Fig. 1. Inertia weight curve

3.2.2 Crossover and Mutation Since traditional PSA is easy to struck into local optimal, the PSA optimization process is combined with the crossover and mutation process of genetic algorithm in this paper. The crossover and mutation process is shown as Fig. 2 and the cross rate is calculated according to the difference between current optimal solution and vector of particle position. In Fig. 2, pc is the crossover rate; pm is the variation rate; Xmin is the threshold for the difference X; and rid is the random number of i particles selected in each dimension. Its flow chart is shown in Fig. 2. 3.3 Flow Chart of Location Determination and Capacity Optimization The aim of proposed IPSA in this paper is to determine location and optimize the capacity of large-scale energy storage station in the regional power grid. The multiobjective evaluation function is established according to (1)–(4). The decision variables

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Fig. 2. Flow chart of crossover and mutation process

are energy storage location and capacity, the value range of energy storage location is node 1 to node 48, and the energy storage capacity is 10 MW–100 MW. The conclusion condition is whether there is an optimal solution in Pareto solution set at the end of 50 iterations. By combining adaptive inertia weight coefficients and cross mutation process, the flow chart of IPSA is shown as Fig. 3.

4 Case Study In order to further verify the proposed IPSA, regional power grid in Pingdingshan, Henan Province, China is taken as a case study. The node model of studied power grid is shown as Fig. 4. The rated voltage of the studied power grid is 220 kV and the key parameters of the studied power grid is shown as Table 1. The daily load curve of the studied power grid is shown in Fig. 5. As shown in the figure, the daily load curve shows two peak power consumption periods: from 10:00 to14:00 first peak power consumption appears and the second peak power consumption

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Start Initialize population position variable x and velocity variable y Calculate the multi-objective evaluation result of each particle and set into the set of non-inferior solutions Determine the historical optimal solution p of each particle and the current optimal solution g of all population Calculate the difference between each particle and the optimal particle, named as X Update the inertia weights for each particle Update the velocity component and position component of each particle Crossover and mutation operations on each particle Evaluating and refreshing the optimal solution p and forming a new set of non-inferior solutions Refreshing non-inferior solution sets Select global optimal solution g N End? Y Output the optimal solution End

Fig. 3. Flow chart of IPSA for location determination and capacity optimization of large-scale energy storage system in regional power grid

period lasts from 18:00 to 22:00. The second peak power consumption period is higher than the first peak power consumption period. After optimization by IPSA, the Pareto solution is shown in Fig. 6. As shown in the figure, the solution set presents a diversity distribution so that the accuracy of IPSA is ensured. According to the optimized result, the energy station should be built at node 48 in Fig. 4 and the installed capacity is 20 MW.

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Fig. 4. Node model of 220 kV regional power grid in Pingdingshan, Henan Province, China.

Table 1. Key parameters of studied regional power grid Pingdingshan regional power grid system parameters total load

5558MW+1859.4Mvar

nominal voltage

220 kV

Range of node voltage fluctuation

0.9–1.05 p.u

Fig. 5. Pindingshan Daily Load Curve

Figure 7 shows the comparison of node voltage fluctuation between power grid with energy storage station and power grid without energy storage station. As shown in the figure, the node voltage fluctuation can be effectively reduced with the program optimized by the proposed IPSA and the node voltage fluctuation is reduced by 43.6%. Figure 8 shows the comparison on daily load curve between power grid with energy storage station and power grid without energy storage station. As can be seen from the comparison, load fluctuation can be effectively reduced with the programme optimized by proposed IPSA and the load fluctuation is reduced by 26.7%.

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Fig. 6. Distribution of Pareto solution sets

Fig. 7. Comparison on node voltage fluctuation

Fig. 8. Comparison of daily load profile before and after optimization

5 Conclusion In this paper, an optimized method is proposed for location determination and capacity optimization of large-scale energy storage station connected with regional power grid. In order to achieve multi-objective optimization, a multi-objective evaluation function, which takes voltage fluctuation, load fluctuation and capacity of energy storage station

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into consideration, is established for global evaluation. Then, referring to actual application, serval constraints, including node voltage balance, transient power balance and energy balance, are listed for the optimization process. In order to avoid local optimal, traditional PSA is improved according to the characteristics of power system. In the proposed IPSA, the adaptive inertia weight coefficient is designed and cross mutation process is added in traditional PSA. In the end, regional power grid of Pingdingshan, Henan Province, China is taken as a case study to validate the effectiveness of proposed method. According to optimized results, the proposed method shows good accuracy and robust in the optimization process. Work in this paper contributes in determining the location and capacity of large-scale energy storage station in regional power grid in the early design stage.

References 1. Zhu, J.: Capacity optimization method of electrochemical energy storage system based on demand side response improved particle swarm optimization algorithm. J. Phys. Conf. Ser. 2418(1), 012099 (2023). https://doi.org/10.1088/1742-6596/2418/1/012099 2. Zhang, Y., Liu, X., Yan, Z., Zhang, P.: Decomposition-coordination based optimization for PVBESS-CHP integrated energy systems. Trans. China Electrotechn. Soc. 35(11), 2372–2386 (2022). (in Chinese) 3. Zheng, Z., Miao, S., Li, C., Zhang, D., Han, J.: Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy internet. Trans. China Electrotechn. Soc. 37(1), 192–207 (2022). (in Chinese) 4. Li, J., Kang, J., Cui, Y.: Research review on optimal location and capacity of energy storage power station. Electric Age 06, 34–37 (2022). (in Chinese) 5. Yan, S., Maoyi, H.: Distribution network distributed energy storage configuration optimization method considering variance of network loss sensitivity. J. Phys. Conf. Series 2404(1) (2022) 6. Jianwei, G., Yaping, W., Ningbo, H., et al.: Optimal site selection study of wind-photovoltaicshared energy storage power stations based on GIS and multi-criteria decision making: A two-stage framework. Renewable Energy 201(P1) (2022) 7. Wenwei, L., Long, Z.: Multi-objective optimization method for hybrid energy storage capacity of wind farm based on source-load interaction. J. Phys. Conf. Series 2418(1) (2023) 8. Yi, Y., Dong, L., Qing, Z., et al.: Multi-objective optimal placement of energy storage systems in an active distribution network. Autom. Electric Power Syst. 38(18), 46–52 (2014). (in Chinese) 9. Hu, T.: Research on Energy Storage Planning of Microgrid Considering the Fluctuation of Wind Power. North China Electric Power University (2019). (in Chinese) 10. Li, J., Niu, M., Zhou, X., Xiu, X., Zhou, J.: Energy storage capacity planning and investment benefit analysis of micro-energy system in energy interconnection. Trans. China Electrotechn. Soc. 35(4), 874–884 (2020). (in Chinese) 11. Xiaogang, W., Zong-qi, L., Li-Ting, T., et al.: Energy storage device locating and sizing for distribution network based on improved multi-objective particle swarm optimizer. Power Grid Technol. 38(12), 3405–3411 (2014). (in Chinese) 12. Yang, R., Zhang, Y.: Title multi-objective reactive power optimization of distribution network based on lmproved particle swarm optimization algorithm. J. Anhui Eng. Univ. 37(06), 42–50 (2022).(in Chinese) 13. Gao, C., Wang, H., Zhu, S.: Optimal siting and sizing of distributed energy storage based on voltage stability 23(07), 2884–2891 (2023). (in Chinese)

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14. Xiaoming, L., Zhi, D., Ming, G., et al.: Grid planning model of medium and low voltage distribution network based on particle swarm algorithm. Electric. Autom. 45(02), 58–60 (2023). (in Chinese) 15. Wang, L.: Research on Optimal Configuration of Energy Storage System Based on Improved PSA. China mining university (2021). (in Chinese)

Research on the Transient Temperature Field of the High-Speed Permanent-Magnet Motor for Dragging Pulsed Alternator Yuan Wan1(B)

, Xu Zhang1 , Yuqi Jia2 , Jian Guo1 , and Wenlong Li1

1 School of Automation, Nanjing University of Science and Technology, Nanjing 10094, China

[email protected] 2 Aviation Key Laboratory of Science and Technology on Aero Electromechanical System

Integration, AVIC Nanjing Engineering Institute of Aircraft System, Nanjing 211102, China

Abstract. For dragging the pulsed alternator, the high-speed permanent-magnet synchronous motor (HSPMSM) is required with a high-power density. Considering the specific working condition that the speed and load both change with time, the steady-state thermal analysis is not applicable to check the effectiveness of thermal design for the dragging motor. This paper studies the characteristics of the losses of a 300 kW, 12000 rpm dragging motor with the variation of time. Then based on the fluid-solid coupling analysis method, the transient temperature field analysis was then carried out. The variation of temperature field distribution over the time and the influence of discharging times are both discussed. With the pulsed alternator discharging 20 bursts continuously, that is 60 shorts, the temperature rise of the dragging motor is 60.9% of that of the steady-state with the highest speed and maximum power. This paper lays the foundation for the later design and optimization of the dragging motor. Keywords: High-speed Permanent Magnet Motor · Transient Temperature Field · Fluid-solid Coupling · High-frequency Loss · Pulsed Alternator

1 Introduction Pulse alternator is thought as a promising pulsed power for driving electromagnetic railguns [1, 2]. It needs a high-speed dragging motor to accelerate its rotor to desired rotating speed to store the mechanical energy [3]. Considering that strict requirements of railguns on the volume and weight of the pulsed power, the dragging motor should be designed to work under the thermal limit, in order to maximize the power density. The dragging motor in this paper employs the toroidal windings and surface-mounted permanent-magnet rotor configuration, as shown in Fig. 1 [4, 5]. Its losses mainly include the copper loss, iron loss, rotor eddy- current loss and air frictional loss [6, 7]. Due to the that the speed and load both change with time, all the losses will change with the time. The distribution of fluid is quite complicated inside of the HSPMSM [8, 9]. And the flow regime and velocity are closely related with the rotor speed, so the air frictional © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 370–378, 2024. https://doi.org/10.1007/978-981-97-1072-0_38

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loss and heat transfer coefficient of the surfaces, such as the end-windings, stator end, rotor end, will be also changed with the speed. Besides, the running time of the dragging motor is generally not long enough to reach the steady-state temperature field. Therefore, the thermal limit design of the motor cannot be acquired based on the steady-state temperature field at the highest speed and maximum load. Otherwise it will cause an excessive safety margin. Computational fluid dynamics (CFD) is widely used in the thermal analysis of HSPMSM, with which the heat transfer coefficient can be calculated according to the distribution of fluid, without relying on traditional empirical formulas [10, 11]. In [12], CFD was used to investigate the transient temperature rise during the starting process of an asynchronous motors with different loads. And the maximum load capacity of the motor originally designed for duty type S1 was also predicted if it used at duty type S2. This paper studies the transient temperature field of the dragging HSPMSM with CFD. The specific working condition was first analyzed, then the variation of the losses with time was calculated. Finally, the CFD model of transient thermal analysis model was built, and the characteristics of transient temperature field with time and the influence of discharging times were given.

Fig. 1. Configuration of the dragging HSPMSM.

2 Description of Specific Working Condition The pulsed power, used for driving an electromagnetic railgun mounted on the fighting vehicles, is made up by two counter-rotating pulse alternators. The total mechanical energy storage is 100 MJ and the highest rotational speed of the system is 12000 rpm. With railgun firing one burst of 3-short shells, the speed of the pulsed alternators would drop to 9295 rpm herein to release the mechanical energy in a few milliseconds. The average firing frequency is 2shells per minute. The motor drags the pulsed alternator with constant torque to store the mechanical energy. Once reaching the desired speed, the electricity of the motor will be cut off. Then the pulsed alternator begins the wait for instructions to discharge. After discharging, the electricity will be recovered and the motor redragged the pulsed alternator to desired speed with constant torque. The specific working condition of the motor was given in

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Fig. 2. It can be seen that the motor alternates between constant torque and no load. And the speed ranges from 9295 rpm to 12000 rpm. That is, the speed and load are changed with time. The cycle time is 90 s, and the dragging time is 75 s.

Fig. 2. Specific working condition of the dragging motor.

3 Calculation of the Losses Under Specific Working Condition 3.1 Copper Loss Due to the high frequency, the additional copper loss caused by the skin and proximity effect can’t be ignored for the dragging motor. Considering that the magnetic flux density of the end winding is different from that of the winding in the slots, the loss of different parts was modeled and calculated by finite element method, respectively. Figure 3 shows the distributions of magnetic flux density and current density of the windings in the slot and the end windings. It can be seen that the distribution of the current density is not uniform for the windings in the slot, and the value becomes larger at the position closer to the notch, while the current density of the end winding is basically uniform.

Fig. 3. Influence of skin and proximity effects on the distribution of current density of the windings in the slot and the end windings.

According to the specific working condition of the motor, the curves of the copper loss with time is given, as shown in Fig. 4(a). It can be seen that the copper loss changes

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periodically with time after the end of the initial discharge. When the motor drags the pulse alternator with constant torque for energy storage, the copper loss is large and increases with speed slightly. The copper loss increases by 2.47% with the speed of 12000 rpm than 9295 rpm. The reason can be attributed to the increase of the highfrequency AC loss. The average copper loss of one cycle is 82.2% of the value at 12000 rpm with constant torque. 1800 1500

1500

Iron loss (W)

Copper loss (W)

2000

1000 500 0 0

300 600 900 1200 1500 1800 Time (ms)

Rotor eddy-current loss (W)

(a) Curve of the copper loss with time. 800

1200 900 600 300 0

0

300 600 900 1200 1500 1800 Time(ms)

(b) Curve of the iron loss with time. Magnets sleeve

600 400 200 0

0

300

600

900 1200 1500 1800 Time(ms) (c) Curves of rotor eddy-current loss with time.

Fig. 4. Variation of the losses under the specific working condition.

3.2 Iron loss The iron loss is calculated based on Bertotti’s classical iron loss separation model. Considering the specific working condition of the motor, the iron loss with time was calculated, shown in Fig. 4(b). The iron loss increases rapidly with the speed during acceleration time. It will decrease slightly due to the removement of the armature magnetic field during the waiting time for discharge, and then decease 28.9% rapidly when discharging. The average loss of one period is 85.2% of value of 12000 rpm with constant torque. 3.3 Rotor Eddy-Current Loss Due to the high-frequency harmonics of the magnetic field in the air gap, the eddycurrent loss induced in the sleeve and magnets must be considered. The conductivity of the carbon-fiber sleeve and permanent magnets are 33000 S and 62500 S, respectively.

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Based on the finite-element analysis, the eddy-current loss of the sleeve and magnets with time are calculated and provide in Fig. 4(c). As can be seen, the loss of the sleeve is much higher than that of the magnets. The total eddy-current loss of the sleeve and magnets increase 61.6% at 12000 rpm with constant torque than that of 9295 rpm. Besides, the eddy-current loss decreases largely after the electricity power is cut off. It is because the armature magnetic field harmonics in the airgap caused by the spatial distribution of windings is eliminated. The average of the magnets and sleeve loss are 74.9%, 72.3% of that at12000 rpm with constant torque.

4 Numerical Calculation of the Transient Temperature Field 4.1 Modeling of 3-d Transient Temperature Field The 3-d fluid and solid coupling model was established to calculate the transient temperature field of dragging motor based on CFD. In order to reduce the computing time, one tooth-pitch physical model was analyzed according to symmetry of the geometric structure and heat transferring of the motor, shown in Fig. 5. According to the loss results of Figs. 4, 5 and 6, the loss curve was discretized into six segments during the initial energy storage. The average loss and speed for each segment was calculated and applied to the fluid and solid coupling model. In the cycle of restoring energy storage and discharge, the average loss is implemented as the heat source. Consider the speed varies periodically between 9295–12000 rpm, each cycle is discretized into 7 equal segments and the average speed is applied to each segment.

Fig. 5. The fluid and solid coupling model based on CFD.

4.2 Variation of the Transient Temperature Field Based on the above CFD model, the analysis of transient temperature field was implemented for the dragging motor. Figure 6(a) shows the distribution of temperature field at 20th burst of discharge. It can be seen that the hot spot is at the sleeve. The highest temperature rise of each key component was shown in Fig. 6(b). It can be seen that all the temperature rises increase rapidly with time during the initial energy

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storage stage (0–330 s). Besides, the temperature rise of the sleeve increases the fastest, followed by the stator, permanent magnets and windings. Moreover, the hot spot is at the windings between 0-200 s. The reason is that the speed during starting is very low, resulting in the lower rotor eddy-current loss and air frictional loss. And the copper loss contributes the most to the total loss of the motor at this time, so the temperature rise of the windings is the highest. After that, the rotor eddy-current loss and air frictional loss become prominent with the further increase of speed, so the temperature rise of the rotor increase faster. And that explains why the hot spot of the motor appears in the rotor sleeve at the end of the initial energy storage.

Temperature rise (K)

Windings 120

Stator

Magnets

Sleeve

100 80 60 Initial energy storage stage 40 20 0

0

500



1000 1500 Time (ms)

2000

(a) Distribution of the temperature field at 20th burst of discharge. (b) Variation of transient temperature rise with time.



Fig. 6. Analysis of the transient temperature rise for the dragging motor.

In the cycle of restoring energy storage and discharge, all of the highest temperature rise of each key component continues to increase with time. The increase rates of the highest temperature of windings, stator and sleeve are close, while the increase rate of magnets is much higher. From 1800 s, the temperature rise of magnets becomes to be higher than that of windings and stator. In addition, at the end of each burst of discharge, the temperature rise of the sleeve reaches the highest value and then decreases slightly. The reason is the decrease of speed after discharge, leading to the decrease of rotor eddy-current loss and air frictional loss. 4.3 Distribution of Temperature Field with Different Bursts of Discharge The distribution of temperature field at the end of the 1st , 5th , 10th and 15th bursts of discharge are given in Fig. 7, respectively. It can be seen that hot spot is always at the sleeve. Besides, the end of rotor has higher temperature than the middle of the rotor in the 1st and 5th bursts of discharge. With increase of the burst of discharge, the temperature rises of the magnets and sleeve both increase rapidly. Consequently, the temperature at the middle of the rotor is gradually higher than that of the rotor end. 4.4 Comparison with the Steady-State Temperature Field The highest temperature of each key components of the motor at the 1st , 5th , 10th , 15th and 20th bursts of discharge were compared with the steady-state temperature with

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(b)Temperature field at 5th burst of discharge.

(a)Temperature field at1st burst of discharge.

(c)Temperature field at 10th burst of discharge. (d)Temperature field at 15th burst of discharge.

Fig. 7. Distribution of temperature field with different bursts of discharge.

highest speed and maximum load, shown in Fig. 8. It can be calculated that the highest temperature of the winding, stator core, permanent magnet and sleeve at the 20th bursts is only 68.1%, 67.3%, 52.8% and 60.9% of the steady-state temperature with highest speed and maximum load. And based on the results, the design of the dragging motor should be optimized in the future. 1st

5th

10th

15th

20th

steady-state

Temperature(℃)

200 150 100 50 0

Winding

Stator

Magnet

Sleeve

Fig. 8. Comparisons of temperature of each key component with that of steady state.

5 Conclusions This paper studies the transient temperature field of the HSPMSM for dragging the pulsed alternators. The conclusions are as follows:

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(1) The dragging motor alternates between constant torque and no load, and the average copper loss, iron loss, sleeve and magnet eddy-current loss are 82.9%, 85.2%, 74.9% and 72.3% of that at the highest speed and maximum power, respectively. (2) During the initial energy storage, the highest temperature of the motor is in the windings, but it gradually appears in the middle of the sleeve with the increase of the speed. (3) The end of rotor first has higher temperature than the middle, but it becomes to be lower than that of the middle of the rotor with increase of the burst of discharge. (4) With continuous discharge of 20 bursts, the highest temperature of the winding, stator, magnet and sleeve are only 68.1%, 67.3%, 52.8%, 60.9% of the steady-state temperature with highest speed and maximum load. Acknowledgement. This research is supported by Harbin Institute of Technology State Key Laboratory of Advanced Welding and Joining (Grant No. AWJ-23M27), and China Postdoctoral Science Foundation (Grant No. 2023M740618).

References 1. McNab, I.R.: Large-scale pulsed power opportunities and challenges. IEEE Trans. Plasma Sci. 42(5), 1118–1127 (2014) 2. Yu, K., et al.: Loss analysis of air-core pulsed alternator driving an ideal electromagnetic railgun. IEEE Trans. Transport. Electrific. 7(3), 1589–1599 (2021). https://doi.org/10.1109/ TTE.2021.3051630 3. Wu, S., Dou, C., Du, B., Yu, J.: Analysis of discharge impulsive torque control of pulsed alternator based on genetic algorithms. In: 2023 IEEE International Conference on Predictive Control of Electrical Drives and Power Electronics (PRECEDE), pp.1–5. IEEE, Wuhan (2023) 4. Wang, T., Wen, F., Zhang, F.: Analysis of multi-field coupling strength for mw high-speed permanent magnet machine. Trans. China Electrotechn. Soc. 33(19), 4508–4516 (2018). (in Chinese) 5. Wan, Y., Li, Q., Guo, J., Cui, S.: Thermal analysis of a Gramme-ring-winding high-speed permanent-magnet motor for pulsed alternator using CFD. IET Electric Power Appl. 14(11), 2202–2211 (2020). https://doi.org/10.1049/iet-epa.2020.0086 6. Du, G., Xu, W., Zhu, J., Huang, N.: Power loss and thermal analysis for high-power highspeed permanent magnet machines. IEEE Trans. Indust. Electron. 67(4), 2722–2733 (2020). https://doi.org/10.1109/TIE.2019.2908594 7. Gao, Q., Wang, X., Gu, C., Liu, S., Li, D.: Design of ultra high speed micro permanent magnet motor with integrated support type based on multi coupling characteristics. Trans. China Electrotechn. Soc. 67(4), 2989–2999 (2021). (in Chinese) 8. Qi, Z., Zhang, Y., Zhang, H., Wang, X., Wang, H., He, L.: Thermal and stress analysis for a high-speed permanent magnet motor with solid rotor. In: 2021 IEEE 4th Student Conference on Electric Machines and Systems (SCEMS), pp. 1–5. IEEE, Huzhou (2021) 9. Wang, X., Yu, T., Li, N., Xu, Y.: Eddy current loss reduction and thermal analysis of ultrahigh-speed bearingless permanent magnet synchronous motor. In: 2022 25th International Conference on Electrical Machines and Systems (ICEMS), pp. 1–6.IEEE, Chiang Mai (2022) 10. Ding, S., Shen, S., Yang, Z., Chen, S., Dai, Y.: Fluid-solid coupling simulation and performance analysis of high-speed permanent magnet synchronous motor. Electric Mach. Control 25(10), 112–121 (2021). (in Chinese)

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11. Qin, X., Shen, J.: Multi-physics design of high-speed large-power permanent magnet synchronous motor. In: 2020 Fifteenth International Conference on Ecological Vehicles and Renewable Energies (EVER), pp. 1–5. IEEE, Monte-Carlo (2020) 12. Xia, Y., Xu, Y., Ai, M., Liu, J.: Temperature calculation of an induction motor in the starting process. IEEE Trans. Appl. Superconduct.y 29(2), 1–4 (2019). https://doi.org/10.1109/TASC. 2019.2895313

Effect of Pre-qualification Test on Properties of Semi-conductive Shielding of High Voltage XLPE AC Cable Xueqi Huang1 , Man Xu1(B) , Hengyi Liu2 , Fa Xie1 , Ruofei Wang1 , Shuai Hou3 , and Yunpeng Zhan3 1 State Key Laboratory of Electrical Insulation of Power Equipment, Xi’an Jiaotong University,

Xi’an 710049, China [email protected] 2 Ningbo Power Supply Company, State Grid Zhejiang Electric Power Co, Ningbo 315000, China 3 Electric Power Research Institute, China Southern Power Grid, Guangzhou 510663, China

Abstract. To evaluate the performance stability and reliability of a domestic 220-kV cable shielding material, shielding samples cut from 220-kV high voltage cables that have passed the pre-qualification (PQ) test were examined, including a domestic shielding material and two imported shielding materials. The changes in electrical and mechanical properties of the material samples were investigated using the volume resistivity test and tensile test before and after the PQ test. Further, the influences of the PQ test on the structure of semi-conductive composite matrix resin and conductive carbon black were analyzed at the microscopic level using the gel content test, X-ray diffraction (XRD) analysis, differential scanning calorimetric (DSC) analysis, scanning electron microscopy (SEM) analysis and Raman spectroscopy analysis. The results show that before the PQ test, the degree of cross-linking in the domestic cable shield was low, the mechanical properties were poor, but the electrical properties were stable. After the PQ test, the electrical and mechanical properties of the three types of cable semi-conductive shielding layer still met the requirements of the national standard, which ensured the stable operation of the cable system. However, the material properties changed. The resistivity of the three shielding layers increased but its stability deteriorated. The elongation at break and fracture energy decreased, and the tensile strength increased after the PQ test. The reason for the deterioration of the electrical and mechanical properties of the composite materials was the re-aggregation of carbon black caused by high temperature during the PQ test and the decrease in material polarity, which led to diminished dispersion of carbon black in the system, and affected the formation of conductive network and the interface combination of carbon black and resin. Keywords: Semi-conductive shielding · pre-qualification (PQ) test · degree of cross-linking · dispersion of carbon black

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 379–397, 2024. https://doi.org/10.1007/978-981-97-1072-0_39

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1 Introduction China is the world’s largest cable manufacturer and user. It currently has the ability to manufacture high-voltage AC and DC cables suitable for voltage levels of 500 kV. However, the performance of domestic XLPE cable materials lags behind the advanced international standards. Furthermore, a complete production system from base materials to high-voltage XLPE cable insulation and shielding materials and cable products has not been established [1]. For the manufacturing of high-voltage cable materials (220 kV and above), China has long relied on imported materials, including Nordic Chemicals, Dow of the United States. Not only are the prices of these products high, but there are also risks of unstable supply. The annual cost of importing high-voltage cable semiconductive shielding materials is 300–400 million yuan, which is a pressing issue that needs to be addressed [2]. Compared to other countries, the development of high-voltage cable insulation and shielding materials in China started late, only in the 1990s, and research on semiconductive shielding materials even later [3]. In recent years, several domestic research teams have carried out a large amount of basic research on raw material ratios, new conductive fillers and overall performance improvement [4]. Domestic and foreign researchers have conducted basic research on filled semiconductive polymers. He, Y et al. [5] found that the differences in the carbon black particle size and structure have an impact on the thermal conductivity and tensile strength of natural rubber filled with carbon black. Song, JP [6] found that acetylene black makes a significant contribution to the thermal conductivity of composites, and a small load significantly improves the thermal conductivity of rubber. The content of conductive fillers in shielding materials affects the mechanical properties and smoothness of the entire system. Therefore, many researchers have tried to improve the performance of high-voltage semi-conductive shielding materials by adding conductive fillers, developing new conductive fillers and processing aids and improving critical resin properties. Dai, HB et al. [7] studied the influence of the amount of conductive carbon black on the volume resistivity and mechanical properties of shielding materials and determined that the optimal amount of conductive carbon black is 30wt% to achieve a comparable surface smoothness and high-temperature stability as imported products. Shen, ZH et al. [8] found that a composite of carbon nanotubes and carbon black can significantly reduce the volume resistivity of shielding materials and the number of conductive systems in the entire formulation. Li, GC et al. [9] observed that graphene-modified semi-conductor layers can effectively reduce charge accumulation in the insulation layer and inhibit the positive temperature coefficient (PTC) effect by replacing a suitable amount of carbon black. Xu, S et al. [10] proposed that the polarity or ester content of the material is a key parameter reflecting the properties of the base resin in semi-conductive shielding materials, confirming the key role of base resin in semi-conductive shielding materials. In recent years, there have been significant domestic breakthroughs in the development of insulation and semi-conductive shielding materials for high-voltage cables. In 2021, Wanma Polymer independently developed domestic 220-kV high-voltage cable

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materials. At the end of that year, the first domestic 220-kV insulation cable demonstration project was carried out in Shenzhen, and a domestic 220-kV cross-linked polyethylene AC cable passed the PQ test [11]. In China, before a cable system made of domestic materials can be industrially adopted, a PQ test must be conducted to prove that the complete cable system has satisfactory long-term operational performance. There have been studies on the impact of PQ experiments on the characteristics of cable insulation layers [12], but there are fewer reports on the shielding materials. To further compare the long-term performance of cable shielding materials, samples of three domestic cables subjected to PQ tests were dissected, and the outer shielding layers were cut for material performance analysis tests. The focus is on studying the impact of PQ tests on the electrical and mechanical properties of high-voltage cable shielding, establishing a connection between the dispersibility of carbon black, degree of cross-linking, aggregation state structure and polarity of the matrix and changes in macroscopic shielding performance, to provide a basis for the development of semi-conductive shielding for higher voltages.

2 Sample Preparation 2.1 Cable Material Sample Information Both domestic and imported shielding materials were examined in this study. We only examined the outer shielding layer that can be sampled. The numbering and description of the materials of the outer shielding layer are listed in Table 1. Table 1. Cable shield layer samples Sample number before PQ test

Sample number after PQ test

Source

Shielding thickness/mm

#1

#1’

Import 1

1.2

#2

#2’

Import 2

1.4

#3

#3’

Domestic

1.4

2.2 Pre-identification Test and Sampling of Cable Outer Shielding Layer For each type of cable, two cables from the same batch were selected, with one cable used for PQ tests and the other stored as an untested backup. The PQ test for the three cables was conducted in a series circuit for 9,000 h according to the requirements of GB/T18890.1-2015. The test conditions are shown in Table 2. 2.3 Sampling of Cable Outer Shielding Layer For the material performance tests of cable outer shielding described in this paper, each cable segment was cut into 100-mm sheet samples. The obtained samples were sheared into a size of 75 × 100 × 0.4 mm (see Fig. 2) (Fig. 1).

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National standard

Testing voltage

1.7U 0 (216 kV)

1.7U 0 (216 kV)

Thermal cycling conditions

Heating for 8 h to 90°C, maintaining for 2 h, cooling for 16 h

Heating for 8 h to 90°C, maintaining for 2 h

Number of cycles

186

At least 180

Fig. 1. Schematic diagram of cable sample ring cutting

(a) Cable cross-section

(b) Shield sample after cutting

Fig. 2. Cable segment and shielding sample cutting for testing

3 Testing Methods 3.1 Gel Content Test ACS reagent-grade xylene was selected in accordance with the JB/T10437–2004 requirements. A 40 × 40-mm square pocket was cut from stainless steel mesh with an aperture of 120 and weighed (W 1 ). A 0.5-g sample was cut into small pieces and placed in the pocket and the entire weight was measured (W 2 ). Then, the prepared sample was placed in a grinding bottle to which xylene was added and left in an air oven at 110 °C for 24 h. Then, xylene was filtered out, and the sample was washed with alcohol and dried at 110 °C for 24 h. The sample was then again weighed (W 3 ).

Effect of Pre-qualification Test on Properties of Semi-conductive Shielding

The gel content was calculated as follows:   W3 − W1 × 100% gel = W2 − W1

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(1)

where W 1 is the net weight of the filter (g), W 2 is the total weight of the sample and filter bag (g), and W 3 is the total weight of the extracted and dried sample and filter (g). 3.2 Scanning Electron Microscopy (SEM) A GeminiSEM500 field emission scanning electron microscope was used to observe the dispersion of carbon black in the resin by fracturing the shielding layer sample in liquid nitrogen and gold-spraying the fractured surface. The acceleration voltage was 30 kV and the magnification was 30K. 3.3 Differential Scanning Calorimetry (DSC) The thermal properties of the shielding layer were characterized using a DSC822E differential scanning calorimeter. The following program was adopted: 1) Heating from 30 °C to 200 °C at a rate of 10 °C/min and then holding at 200 °C for 3 min to eliminate thermal history. 2) Cooling from 200 °C to 30 °C at the same rate and then holding at 30 °C for 3 min. 3) Heating from 30 °C to 200 °C at a rate of 10 °C/min to obtain the second heating data. The crystallinity was calculated as follows: Xm =

Hm H0

(2)

where H m is the melting enthalpy (J·g−1 ), and H 0 is the melting enthalpy of 100% crystallized polyethylene, which is 293 J·g−1 [13]. 3.4 X-Ray Diffraction (XRD) Test A D8ADVANCEA25 X-ray diffractometer was used with a CuKα target. The X-ray wavelength was λ = 0.154nm, while the scanning ranges 2θ were from 10° to 50° in 0.01° steps at 0.2s/step. The acceleration voltage was 40 kV and the current was 40 mA. 3.5 Thermogravimetric Analysis (TGA) The TGA was performed using a TGA/SDTA851 thermogravimetric analyzer with a ceramic crucible. The experiment was conducted in a nitrogen atmosphere with a flow rate of 10 L/min, with the temperature programmed to increase from 50 °C to 600 °C at a rate of 10 °C/min.

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3.6 Raman Spectroscopy Raman spectroscopy was performed using a Renishaw Invia Raman spectrometer to analyze the orderliness of carbon black in the shielding layer. The sample was a 0.4 mm sheet sample and the laser source was 633 nm. The wavenumber range was 100–3200 cm−1 and the exposure time was 15 s with a laser intensity of 10%. 3.7 Volume Resistivity Test The temperature-volume resistivity test was carried out according to the national standard GB/T3048.3-2007, using a BD400H semi-conductor rubber resistivity tester. The sample size was 110 × 50 × 0.4 mm. The volume resistivities of the samples were measured at temperatures of 20 °C, 40 °C, 60 °C and 90 °C in an oven for at least 15 min at each test temperature. Each sample was tested three times and the average values were calculated. 3.8 Mechanical Tensile Test According to the national standard GB/T13022-91, the sample was a standard dumbbell shape with dimensions of 4 × 75 mm. The test was conducted using an electronic universal testing machine CMT4505 (5 kN) at a test speed of 250 mm/min and a gauge length of 200 mm. Each testing sample group comprised at least five samples and the average values were adopted.

4 Results and Discussion 4.1 Physical and Chemical Properties of Shielding Layer The gel content is an indicator of the cross-linking structure of cable insulation. The degree of cross-linking is an important physicochemical property of polyolefin resins, reflecting the long-term stability of cables. The gel content results of the shielding layer samples taken from the cables are listed in Table 3, while Table 4 shows the gel content of the same shielding materials pelletized and cured in a plate vulcanizer. From Table 3, it can be deduced that before the PQ test, the gel content of the outer shielding layer of cables #1 and #2 was 87.55% and 82.43% respectively, which was close to the gel content of the pelletized shielding materials, indicating the formation of a good cross-linking network [14]. The degree of cross-linking in the domestic shielding material #3 was only 75.45%, i.e., much lower than in the corresponding pelletized shielding material sample of 82.48%, indicating that the cross-linking reaction in the domestic shielding material during cable production was insufficient, resulting in an imperfect cross-linking structure. After the PQ test, the gel content in shielding material #3 increased slightly from 75.45% to 83.34%, indicating an improvement in the crosslinking structure of the shielding layer during the high-temperature PQ test. The reason for this phenomenon may be the different adaptability of the cable processing technology to different materials. The differences in cross-linking characteristics between domestic and imported shielding materials need to be minimized by adjusting the cable extrusion and vulcanization processes.

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Table 3. Gel content results of cable samples Sample number

W 1 (g)

W 2 (g)

W 3 (g)

gel (%)

#1

1.378

1.873

1.811

87.55

#2

1.518

2.020

1.932

82.43

#3

1.461

1.947

1.827

75.45

#1’

1.409

1.898

1.845

88.95

#2’

1.509

2.013

1.934

84.29

#3’

1.441

1.942

1.853

83.34

Table 4. Gel content results of pellet pressed tablet samples Sample

gel (%)

Import 1

90.00

Import 2

82.65

Domestic

82.48

4.2 Microstructural Changes in Shielding Layer Figure 3 shows the SEM images of the cross-sections of the shielding layers before and after the PQ test, which directly reveal the changes in the dispersion of carbon black in the shielding materials and facilitate analyzing their impact on the macroscopic properties. In Figs. 3(a, c) and (e), it can be observed that the carbon black dispersion in the shielding materials was uniform before the pre-appraisal test, forming dense and connected conductive paths. After the PQ test, there was a certain amount of carbon black agglomeration in the shielding materials. This indicates that in the high-temperature stage of aging, the molecular chain thermal activity increased, causing the displacement and re-aggregation of the conductive carbon black [15], affecting the formation of the conductive network and increasing the volume resistivity of the shielding layer. As shown in Fig. 3(b), the aggregation and voids in carbon black in imported shielding #1 layer after the pre-appraisal test significantly increased, resulting in a marked increase in volume resistivity and the most notable decrease in elongation at break. 4.3 Analysis of Aggregation State Structure of Shielding Layer Matrix 4.3.1 Influence of PQ Test on Crystallization Behavior of Shielding Layer To study the changes in the aggregation state structure of the shielding materials before and after the PQ test, DSC tests were conducted on the shielding layers. The melting curves of each sample were plotted based on the DSC experimental data, as shown in Fig. 4, and the melting parameters and crystallinity were calculated and listed in Table 5. Due to the presence of two peaks in the domestic sample data,

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(a) #1

(b) #1’

(c) #2

(d) #2’

(e) #3

(f) #3’

Fig. 3. SEM photos of shielded brittle section (×30K)

peak separation was performed to obtain the peak curve of shielding #3 layer, as shown in Fig. 5(a) and (b). The imported shielding #1 and #2 layers had a single melting peak, with peak temperatures around 90 °C. On the other hand, domestic shielding #3 layer had two melting peaks, indicating the presence of two resins with different melting points. The exothermic peak at 90 °C was the main melting peak of the matrix resin, while the endothermic peak at 102 °C corresponded to a high-melting-point resin.

Fig. 4. DSC melting curves of shieldings before and after PQ test

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(a) Sub-peak curves of sample #3

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(b) Peak 1 and peak 2 curves of sample #3

Fig. 5. Melting curves of shielding #3

Before the PQ test, the melting peak temperature (T m ) of shielding #1 layer was 87.2 °C, i.e., about 2–3 °C lower than those of the other samples. At the same time, the melting range of shielding #1 layer was smaller. It is generally believed that more complete crystals usually melt at higher temperatures. This led to the conclusion that the shielding #1 layer contained a larger number of small spherulites and the completeness of the internal crystals was similar. The crystallinities of the shielding layers was calculated and listed in Table 5. The results show that before the PQ test, the crystallinities of imported shielding #1 and #2 layers were similar, at 10.72% and 10.96%, respectively, indicating similar crosslinking characteristics of their matrix resins with a high degree of cross-linking and low crystallinity. The crystallinity of the domestic shielding #3 layer was higher, reaching 15.73%, and it had two melting peaks, indicating a different crystallization characteristics from the imported shielding layers. In the cable production process, due to the hightemperature cross-linking followed by cooling and crystallization, the grain size and distribution will be affected by the cross-linking structure. The study demonstrated that the integrity of the crystal structure and crystallinity of the shielding material showed an upward trend followed by a downward trend during the aging test [16]. During the pre-appraisal test, a recrystallization process occurs, increasing the regularity and arrangement of molecular chains in crystals, but when the crystals remain in a heated state for a long time, the integrity of their structure is destroyed and crystallinity decreases. After the pre-appraisal test, the melting peak temperature (T m ) and crystallinity of the shielding samples changed differently. The T m of the shielding #1 layer increased by 1.7 °C and the crystallinity slightly increased. The T m of the shielding #2 and #3 layers decreased and their crystallinities decreased. The T m of the shielding #2 layer decreased by 1.1 °C, while the crystallinity of the domestic shielding #3 layer decreased significantly to 14.47%. 4.3.2 XRD Testing and Radial Distribution Function Analysis In amorphous structures, the arrangement of atoms is irregular on a large scale, but regular in the nearest neighbor, known as short-range order [17]. Generally, amorphous materials have short-range orders within 10 Å.

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Sample

Melt

Crystal

T m /°C

H m /(J/g)

X m /%

T cry /°C

T cry /°C

#1

87.2

31.4

10.72

75.9

11.1

#2

90.4

31.5

10.96

77.1

22.5

#3

89.7\102.7

34.1\12.0

11.63\4.10

79.2\92.0

29.2\17.4

#1’

89.0

32.4

11.28

78.2

10.5

#2’

89.3

31.2

10.86

78.4

20.6

#3’

89.5\102.3

30.0\11.7

10.42\4.05

78.7\91.5

28.9\17.3

The XRD diffraction patterns of the shielding samples before and after the preappraisal test are shown in Fig. 7.

Fig. 7. XRD pattern of each shielding layer

The diffraction peaks at 2θ angles of 21.6° and 23.7° correspond to the orthorhombic crystal planes (110) and (200) of the methylene polymer, respectively. The shielding #1 layer exhibited additional characteristic peaks at 25.7° and 43°, corresponding to the graphite (002) and (100) crystal planes, respectively, indicating a higher degree of graphiteization in the shielding #1 layer. A further analysis of the short-range ordered structure of the matrix material required a radial distribution function analysis [18, 19], using three main types of radial distribution functions: Radial distribution function (RDF):  2 ∞ s[I (s) − 1] sin srds (3) RDF(r) = 4π r 2 ρ0 + π 0 Reduced radial distribution function:  2 ∞ G(r) = s[I (s) − 1] sin srds π 0

(4)

Effect of Pre-qualification Test on Properties of Semi-conductive Shielding

Pair Distribution Function: g(r) = 1 +

1 2π r 2 ρ0

(a) G(r) curve of each shielding layer



∞

s[I (s) − 1] sin srds

389

(5)

0

(b) g(r) curve of each shielding layer

Fig. 8. G(r) and g(r) curves of each shield

In Fig. 10, it can be seen that the reduced radial distribution function G(r) represented the nearest neighbor distance r 1 , the second nearest neighbor atomic distance r 2 , and the third nearest neighbor atomic distance r 3 , which were characterized by the first, second and third peak of the function. The calculation results are listed in Table 6. Table 6. Atomic nearest neighbor distances of each shielding layer Sample

r 1 /Å

r 2 /Å

r 3 /Å

#1

1.51

3.06

4.61

#2

1.50

3.06

4.61

#3

1.50

3.06

4.61

#1’

1.50

3.06

4.61

#2’

1.52

3.07

4.62

#3’

1.52

3.08

4.62

From the plot of G(r) in Fig. 8, it can be concluded that the nearest neighbor distance (r 1 ) for all four shielding layers was around 1.5 Å, reflecting the bond length of the main chain C-C single bond. As the atomic distance (r) increased, the peak width of G(r) gradually rose, indicating increased uncertainty in the positions of atoms in the coordination shell [20].

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An analysis of g(r) revealed that as the atomic distance (r) increased, g(r) approached 1, indicating a completely disordered long-range structure for all three shielding materials. The size of the ordered domain for all three shielding layers was around 10 Å, indicating that the short-range order range was similar for all shielding layers. The polarities of the imported and domestic shielding layers were not significantly different. After the PQ test, the r 1 -r 3 values of the shielding #2 and #3 layers slightly increased, while shielding #1 showed no significant changes, indicating a slight decrease in polarity of the shielding #2 and #3 layers due to aging. This indicates that the high-temperature processing during the pre-appraisal test not only caused carbon black aggregation due to the thermal motions of polymer chains but also resulted in the detachment of polar groups [21]. 4.4 Influence of PQ on Orderliness of Carbon Black in Shielding Layer Figure 9 shows the Raman spectra of the shielding layers before and after the preappraisal experiment. The spectra were processed to identify peaks, where the blue curves represent the D peak near 1,350 cm−1 , which corresponds to the breathing vibration of sp2 -hybridized carbon atoms in disordered carbon structures. The red curves represent the G peak near 1,580 cm−1 , which corresponds to the stretching vibration of sp2 -hybridized carbon atoms in ordered graphite structures [22, 23]. The green curves represent the G’ peak at 2,700 cm−1 , which reflects the stacking arrangement of carbon atoms and indicates the presence of graphene-like structures. In Fig. 9, it can be observed that the Raman spectra of the shielding #1 layer had sharp and narrow peaks, including one at 2,700 cm−1 . The Raman spectra of the shielding #2 and #3 layers were similar, with only D and G peaks present. The PQ test had little influence on the Raman spectra of the shielding samples. From Table 7, it can be concluded that before the PQ test, shielding #1 had the lowest FWHM(Full-width at the half of the maximum) of the G peak (92.33) and the lowest I D /I G value of 1.59, which was significantly lower than those of shieldings #2 and #3. This indicates that shielding #1 exhibited the highest orderliness of carbon black and the lowest defect density in the graphite microcrystals. After the PQ test, the I D /I G value of shielding #1 remained essentially unchanged, while the half-width of the G peak decreased, indicating a further reduction in the defect density of carbon black. The I D /I G values of shieldings #2 and #3 slightly increased, but this had little effect on the structure of the carbon black particles or the integrity of the conductive network. This was because the temperature experienced by the cable during the pre-appraisal test was much lower than the structural transformation temperature of carbon black. 4.5 Influence of PQ Test on Thermal Stability of Shielding Layer To characterize the influence of the PQ test on the thermal stability of the shielding samples, the TGA was performed on the samples (Fig. 10).

Effect of Pre-qualification Test on Properties of Semi-conductive Shielding

(a) #1

(b) #1’

(c) #2

(d) #2’

(e) #3

(f) #3’

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Fig. 9. Raman spectra of each shield before and after pre-identification test

Table 7. Peaks D and G and peak intensity ratios before and after pre-identification test Sample

Area of peak D

Area of peak G

I D /I G

#1

1.30 × 105

8.14 × 104

FMHW of peak G

1.59

92.33

#2

2.34 × 105

9.67 × 104

2.42

117.59

#3

2.38 × 105

8.54 × 104

2.79

115.01

#1’

1.30 × 105

8.14 × 104

1.59

81.11

#2’

2.19 × 105

8.95 × 104

2.45

115.00

#3’

3.23 × 105

1.15 × 104

2.81

115.90

The thermal decomposition parameters of the shielding materials were obtained from the thermogravimetric curves shown in Fig. 10 and are listed in Table 8. The thermogravimetric curves of the three shielding samples exhibited first-order weight

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Fig. 10. Thermogravimetric curves before and after pre-identification test Table 8. TGA results of each shielding sample Sample

T 5%

T 50%

T max

Carbon residue/%

#1

421.7

482.7

477.7

34.7

#2

415.2

485.5

480.2

37.7

#3

421.6

486.8

482.3

35.5

#1’

422.1

482.7

477.7

34.7

#2’

417.2

485.3

480.2

37.7

#3’

419.5

486.6

482.3

36.0

loss, with the initial decomposition temperature around 420°C. According to the DSC curves discussed above, the domestic sample contained two types of matrix resins, but still had a first-order weight loss curve, indicating that the thermal decomposition characteristics of the two resins were similar. Furthermore, the thermogravimetric curves of the samples before and after the PQ test were almost identical, indicating that the main chain structure of the matrix material remained unchanged during aging. Table 8 demonstrates that the residual carbon content differed among the three shielding materials, with the shielding #1 sample having the lowest value of 34.7%. This may be because the shielding #1 sample had the best conductivity and required less carbon black content, which was also beneficial for other mechanical properties, while maintaining the electrical performance of the shielding material. After the PQ test, the residual carbon content of the shielding samples did not change significantly, indicating that the thermal stability of the various shielding materials was good. 4.6 Changes in Macroscopic Performance of Shielding Layer 4.6.1 Electrical Performance Changes of Shielding Layer To verify the stability of volume resistivity of the shielding layer after the pre-appraisal test, the volume resistivity at different temperatures was measured and the results are listed in Table 9 (Table 10).

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Table 9. Resistivity of shieling samples before and after pre-identification test Sample

20 °C

40 °C

60 °C

90 °C

#1

18.5

21.2

29.9

60.9

#2

12.7

15.0

19.2

136.7

#3

5.8

6.2

5.9

13.6

#1’

36.7

39.1

43.8

178.9

#2’

14.7

16.0

20.0

280.8

#3’

5.3

5.3

6.7

22.0

Table 10. Temperature coefficients of resistivity of each shielding layer Sample

20 °C–60 °C

20 °C–90 °C

60 °C–90 °C

#1

0.015

0.033

0.035

#2

0.013

0.139

0.204

#3

0.001

0.019

0.044

#1’

0.005

0.055

0.103

#2’

0.009

0.259

0.435

#3’

0.007

0.045

0.076

Based on the results included in Table 9, the volume resistivity of each shielding layer before the PQ test increased nonlinearly with temperature, with minimal changes from room temperature to 60 °C, but a significant increase at 90 °C. Before the pre-appraisal test, according to the standard GB/T 18890.2–2015, all three shielding layers met the requirements of volume resistivity not exceeding 100 ·cm at room temperature and 350 ·cm at 90 °C.

Fig. 11. Sample volume resistivity variations with temperature

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In actual operational conditions, the fluctuations in volume resistivity of a cable at different temperatures should also be considered. The smaller the change in resistivity with temperature, the more stable the electrical performance of a semi-conductive shielding layer. Therefore, the temperature coefficient of resistivity was selected for evaluating the electrothermal stability of the semi-conductive shielding layer. The temperature coefficient of resistivity, α (1/°C), is defined as follows: α=

ρ − ρ0 ρ0 (t − t0 )

(6)

where ρ and ρ 0 are the resistivities at temperatures t and t 0 (·cm), respectively. Before the PQ test, the shielding #1 layer had a lower resistivity and a better hightemperature stability due to the low amount of carbon black added, which resulted in a dense conductive network. The shielding #2 layer had the highest amount of carbon black added, resulting in a low resistivity below 60 °C, which, however, rapidly increased to 136.7 ·cm at 90 °C, indicating a poor high-temperature stability. The shielding #3 layer exhibited the lowest temperature coefficient of resistivity, indicating the best stability, with a volume resistivity of only 13.6 ·cm at 90 °C. After the PQ test, the volume resistivity of the shielding layers increased and the hightemperature stability decreased, but they still met the national standard requirements. This was mainly because during the high-temperature processing, the molecular chains in the polymer matrix were subjected to increased thermal motions, leading to the aggregation of conductive carbon black. At the same time, the degree of cross-linking within the semi-conductive material increased during long-term aging, and a cross-linking network formed during the cross-linking process hindered the connection between carbon black particles, which to some extent arrested the formation of the conductive network. After the PQ test, the trends of changes in resistivity were similar for all shielding layers, but there were some differences, nevertheless. The shielding #1 layer showed more obvious carbon black agglomeration, which resulted in a significant increase in resistivity, indicating a poorer stability. The domestic shielding #3 layer still had low resistivity and a low temperature coefficient, which may be due to its melting peak at 102 °C, which allowed for the presence of crystals at the high temperature of 90 °C during the PQ test, preventing the agglomeration of carbon black and ensuring good electrical performance stability. 4.6.2 Mechanical Performance Changes of Different Shielding Layers In the analysis of mechanical performance, the tensile test data of each shielding layer were analyzed and parameters such as tensile strength, elongation at break, fracture energy and elastic modulus were obtained. The results are listed in Table 11. The semi-conductive shielding before the PQ test met the requirements of tensile strength of at least 12.0 MPa and elongation at break exceeding 150% stipulated in the standard GB/T 18890.2-2015. Before the PQ test, the shielding #1 and #2 layers had similar characteristics of the matrix resin, with higher tensile strength and elongation at break. The shielding #1 layer had the lowest amount of carbon black added, resulting in the highest elongation at break of 220.5%. The domestic shielding #3 layer had the lowest tensile strength and elongation at break of 17.59 MPa and 157.07%, respectively,

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Table 11. Tensile test data of shielding layers before and after pre-identification test Sample Tensile strength/MPa Elongation at break/% Breaking Elasticity modulus/MPa energy/J #1

20.11

220.50

0.95

360.75

#2

21.44

179.15

0.85

356.69

#3

17.59

157.07

0.78

423.11

#1’

20.12

170.48

0.69

371.15

#2’

21.68

172.80

0.83

368.49

#3’

20.52

160.54

0.81

472.17

with a larger elastic modulus and lower fracture energy. The mechanical performance of the domestic shielding layer differed significantly from the imported ones, possibly due to differences in the structure of the matrix resin. The matrix of the shielding #3 layer was a two-phase system, with larger interfaces between the resin and carbon black.

(a) Tensile strength

(b) Elongation at break

Fig. 12. Changes in mechanical properties before and after pre-identification test

As shown in Fig. 12, after the PQ test, the mechanical performance of each shielding layer changed less than 25%, thus, still meeting the operational requirements. The tensile strength and elastic modulus of the two imported shielding layers increased slightly, whereas the tensile strength of the domestic shielding #3 layer increased significantly from 17.5 MPa to 20.52 MPa. This was due to the formation of a strong cross-linking network during the PQ test, which facilitated the orientation of the molecular chains and improved the tensile strength and elastic modulus of the material. After the PQ test, the elongation at break and fracture energy of the imported shielding #1 and #2 layers decreased. This was related to the observed agglomeration of larger diameter carbon black particles in the SEM images after the PQ test, which easily formed stress concentration points and reduced the elongation at break. The elongation at break of the shielding #2 layer slightly decreased, mainly due to the decrease in polarity of the resin, which hindered the interface bonding between carbon black and the resin

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and affected the distribution of carbon black. The elongation at break of shielding #3 slightly increased, possibly due to the significant increase in cross-linking during the preappraisal test, the formation of covalent bonds between cross-linking sites and the twophase interfaces, and an improvement in the interface bonding strength, which increased the elongation at break. The results revealed that after the pre-appraisal experiment, the degradation of the mechanical properties of the shielding samples was mainly due to the increased thermal motions and entanglement of the molecular chains within the matrix resin caused by long-term aging and high temperature, resulting in a decrease in polarity, reduced dispersion of internal carbon black and hardening of the semiconductive shielding material, leading to a decrease in elongation at break.

5 Conclusions In this study, a comparison of the performance of domestic and imported shielding materials before and after the PQ test was conducted. The effects of the PQ aging test on the electrical and mechanical performance of the semi-conductive shielding layer were analyzed. The key factors influencing the performance of the composite materials during the PQ test were identified by linking microscopic parameters with macroscopic performance. The main observations, conclusions and recommendations are as detailed below. Before the PQ test, the low degree of cross-linking in the domestic shielding #3 layer affected the crystalline characteristics of the material. This may be due to the significant differences in cross-linking characteristics between domestic and imported resins and a poor matching between the cable production technology and the formulation of the domestic shielding material. The cable extrusion and vulcanization processes need to be adjusted to the cross-linking characteristics of the domestic material. Before the PQ test, the imported shielding layers exhibited a better mechanical performance, with a higher tensile strength, higher elongation at break and lower elastic modulus. However, the domestic shielding layer had a better electrical performance. After the pre-appraisal experiment, the volume resistivity of the three semi-conductive shielding materials increased slightly, and although the mechanical performance changed, it still met the requirements of long-term operation. After the PQ test, the degradation of the macroscopic performance of the shielding samples was mainly due to the change in the aggregation and distribution of carbon black caused by the molecular thermal motions within the matrix resin. The decrease in carbon black orderliness had little effect. The shielding #1 layer had a higher degree of aggregation of carbon black after aging, resulting in a significant deterioration in its macroscopic performance. After PQ test, the main reason for the agglomeration of carbon black in the shielding layer was the thermal motions of the polymer chains promoted by high temperature and leading to carbon black re-aggregation. At the same time, some polar functional groups within the resin detached, reducing the polarity of the matrix and hindering the dispersion of carbon black within the resin.

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References 1. Li, S., Wang, S, Yang, L., Li, J., Zhao, J., Jing, Z.: Key properties and basic problems of crosslinked polyethylene insulation for high voltage cables. Proc. CSEE 42(11), 4247–4255 (2022) 2. Shengtao, L., Shihang, W., Jianying, L.: Research progress and path analysis of insulating materials used in HVDC cable. High Voltage Eng. 44(5), 139–1411 (2018) 3. Fu, M., Hou, S., et al.: Research progress and Key technology analysis of semi-conductive shielding materials for High voltage cables. J. Mater. 2023(21), 1–14 (2023) 4. Li, G., Wei, Y., Lei, Q., et al.: Key problems and research progress of semiconducting shielding materials for high-voltage cables. Chin. J. Electric. Eng. 42(04), 1271–1285 (2022) 5. He, Y., Yin, Z., Ma, L.X., et al.: Research of thermal conductivity and tensile strength of carbon black-filled nature rubber. Adv. Mater. Res. 87–88, 86–91 (2010) 6. Song, J.P., Ma, L.X.: Contribution of carbon black to thermal conductivity of natural rubber 561, 158 (2013) 7. Dai Hongbing, T., Bidong, L.W., et al.: Preparation and properties of semi-conductive shielding material for 220kV cable. Wire Cable 05, 32–34 (2017) 8. Zhihua, S.: Application of carbon nanotubes in semi-conductive shielding materials. Wire Cable 06, 18–20 (2017) 9. Li, G.C., Li, X.J., Zhang, F., et al.: Effect of graphene modified semi-conductive shielding layer on space charge accumulation in insulation layer for high-voltage direct current cables. High Voltage 7(3), 545–552 (2022) 10. Xu, S., Zhang, B., Hu, C., et al.: Research on key properties of XLPE insulating high voltage cable shielding material resin. Insul. Mater. 56(02), 91–95 (2023) 11. Du, B., Han, C., Li, J., et al.: Research status of polyethylene insulation materials for highvoltage DC cables. J. Electric. Technol. 34(01), 179–191 (2019) 12. Yaojun, S., Zhenxin, C., Shuhui, Y., et al.: Effect of pre-qualification Test on insulation conductance Characteristics of HVDC cable. Insul. Mater. 51(09), 61–69 (2018) 13. Xuelei, D., Dongxue, R., Yafei, L., et al.: Structure and properties of LDPE for cable insulation. Mod. Plastics Process. Appl. 33(06), 5–8 (2021) 14. Hu, C.: Study on Key performance parameters of shielding material for high voltage AC cable and electrical matching between insulation and shielding. Xi‘an Jiaotong University (2022) 15. Fang, Y.: Preparation and properties of new medium and high voltage semi-conductive shielding materials. Beijing University of Chemical Technology (2012) 16. Luo, P., Ren, Z., Xu, Y., et al.: Aging State analysis of decommissioned high voltage crosslinked polyethylene cable insulation. Trans. China Electrotechn. Soc. 28(10), 41–46 (2013) 17. Li, S.: Experimental methods for X-ray diffraction. Metallurgical Industry Press, Beijing (2000) 18. Mo, Z., Zhang, H.: Structure and X-ray Diffraction of Crystalline polymers. Science Press, Beijing (2003) 19. Simard, G.L., Warren, B.E.: X-ray study of amorphous rubber. Rubber Chem. Technol. 9(3), 417–421 (1936) 20. Guo, L., Han, F., Cheng, Z.: Two-phase separation of semi-crystalline polyesters and its reliability analysis. J. Phys. Chem. 2002(04), 372–376 (2002) 21. Mao, B., Chen, S., Xu, H., et al.: Study on the structure and properties of EVA/LDPE/CB conductive composites. Plastics Sci. Technol. 40(03), 51–55 (2012) 22. Yang, X.-G.: Analysis and Application of Raman Spectroscopy, p. 11. National Defense Industry Press, Beijing (2008) 23. Dewa, K., Ono, K., Matsukawa, Y., et al.: Determining the structure of carbon black using Raman spectroscopy and X-ray diffraction. Carbon 100(114), 749 (2017)

Study on Noise Characteristics of Scaled Capacitor Stacks Li Long1(B)

, Xiaoyan Lei2 , Lingyu Zhu1 , and Jinyu Li2

1 State Key Laboratory of Electrical Insulation for Electrical Equipment, Xi’an Jiaotong

University, Xi’an 710049, China [email protected] 2 China Electric Power Research Institute, Wuhan 430074, China

Abstract. As one of the main noise sources of the converter station, capacitor stacks have the most significant impact on the noise around the converter station. In order to accurately master the noise characteristics of capacitor stacks and eliminate the interference of other sound sources during field measurement, a scale capacitor device is made up of a scale capacitor unit and the noise is measured in a semi-anechoic chamber. The spectral characteristics and the spatial distribution of the noise are discussed. It could be found that the noise radiation of the scaled capacitor stacks is directional and symmetrical. In addition, the sound field distribution of the device is obtained by simulation. With the increase of frequency, the interference becomes more obvious. Above can provide basic data support for the noise evaluation and reduction design. Keywords: Scaled capacitor stacks · noise characteristics · noise evaluation · spectral characteristic

1 Introduction In recent years, with the large-scale construction and operation of UHVDC transmission projects in China, the problem of noise pollution in converter stations has become increasingly prominent and needs to be solved urgently. Among them, the filter capacitor device has become one of the main noise sources of the converter station because of its high harmonic content, a large number of capacitors, large area and close to the factory boundary [1, 2]. Mastering the noise characteristics of the main noise sources is the premise of noise control, so it is necessary to evaluate the noise characteristics of the filter capacitor device. The filter capacitor device is composed of a large number of filter capacitor units in series and parallel. Many scholars have systematically and fully studied the generation mechanism and noise characteristics of the capacitor unit [3–7]. However, in the actual operation of the capacitor device, the noise emitted by each capacitor is not independent, but associated. The noise characteristic of the device is obviously different from that of the unit [8]. The field measurement is the most direct means to obtain the noise characteristics of the device. Wang ZM set up a measuring point every 1 m around the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 398–406, 2024. https://doi.org/10.1007/978-981-97-1072-0_40

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AC filter fence with a height of 1.5 m, and carried out sound pressure measurement and characteristic frequency narrow band spectrum testing in order to determine the surrounding sound pressure and spectrum characteristics [9]. Because the position of the filter equipment in the fence is close and there is acoustic interference with each other, it is impossible to measure the sound pressure of a single sound source. In addition, the field measurements are carried out under the operating conditions at that time, and the noise characteristics of the filter devices are closely related to the operating conditions and layout, so the data obtained by them can only reflect the noise characteristics at that time. Statistics are relatively lacking. Jan Smede et al. of ABB company established a physical model of capacitor device reduced according to 1:4 ratio for the first time to measure its noise distribution. The results show that the noise levels of capacitor devices are quite different in different directions, which confirms the directionality of noise radiation of capacitor devices [10]. The deficiency is that there is less analysis of influencing factors. What’s more, simulation is another way to analyze the noise characteristics and influencing factors of the filter capacitor device. By establishing the noise simulation model of multiple capacitors, the scholars analyze the noise characteristics of the filter capacitor device, and make use of the coherent characteristics of the capacitor sound source to optimize the sound field of the device by adjusting the arrangement of the capacitor unit [8, 11]. In this paper, the scaled capacitor unit is used to simulate the typical array arrangement. The sound field distribution of the scale capacitor is measured in the semi-anechoic room, and its noise characteristics are analyzed by simulation, which provides basic data support for the noise reduction design and sound field optimization of the capacitor device.

2 Noise Measurement Experiment Platform 2.1 Mechanism The test object of this paper is the scale capacitor device, which is placed in the ground center of the semi-anechoic chamber. Figure 1 shows the casing side direction and noncasing side direction of the device. The device consists of four tower frames. Pillar insulators are used as structural support and electrical isolation between the towers frames. Eight capacitors are placed on each tower, which are arranged symmetrically in two rows. The bottom is opposite, and the sleeve points to the outside of the tower. The capacitor units are arranged vertically. The bottom spacing lfloor of the capacitor units arranged in the same layer is 286 mm, and the side spacing lside of the adjacent capacitor units is 110 mm. Typical arrangement of the filter capacitor units in the converter station is simulated. The electrical connection of 32 capacitor units is 4 series and 8 parallel, each series branch flows through 20 A, 50 Hz current superimposed 20 A, 550 Hz current. The purpose is to make the noise emitted by the capacitor unit the strongest under the condition of harmonic current loading but not overload, convenient to measure and analyze the noise characteristics of the device at the same time.

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(a) Casing side direction.

(b) Non-casing side direction.

Fig. 1. Vertical layout diagram of scaled capacitor stacks.

2.2 Arrangement of Measuring Points The scale capacitor device is regarded as a parallel hexahedral structure, and a microphone array around it. The overall layout of the measuring point is shown in Fig. 2. Each red four-pointed star represents a measuring point. A microphone is placed at each measuring point, and its sensitivity is about 50 mV/Pa. In order to ensure the accuracy of noise measurement, a calibrator has been used to calibrate the sensitivity of the microphone before the experiment. The testing time of each measuring point is 20 s, and the axis of the microphone points vertically to the measuring surface. Figure 2 only shows the arrangement of measuring points in two planes, the xz plane arranges the measuring points according to 6 rows and 6 columns, the yz plane arranges the measuring points in 6 rows and 4 columns, and the measuring points in the other two planes are symmetrical with respect to the center of the capacitor device. Considering the coincidence of the positive and negative measuring points with the side measuring points and the limitation of the number of microphones, in the field test, 24 measuring points can be arranged one by one in the way of 6 rows and 4 columns to measure the sound pressure level. The layout diagrams of the measuring points on the reverse side and the flank side are shown in Fig. 3, respectively. The measuring points are numbered from right to left by the capacitor device, numbering from bottom to top. A (a‘) represents the horizontal distance of the adjacent measuring points in the same layer; b represents the vertical distance between the adjacent layers; c represents the distance from the positive and negative sides of the measuring point to the top terminal of the capacitor; d represents the distance from the side of the measuring point to the end face of the insulator side of the capacitor tower; and e forms the distance from the first layer of the measuring point to the ground. A (a‘) and b can be calculated from the geometric parameters of the capacitor device and the arrangement of measuring points, a is about 1.16 m, a‘ is about 1.56 m, b is 0.4 m, d is 1.5 m, and e is 0.8 m.

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b

y x

Fig. 2. Diagram of measuring points layout

b y

y

x

x

(a) Front plane.

(b) Flank plane.

Fig. 3. Diagram of measuring points layout.

Fig. 4. Scene diagram of measuring points layout.

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In the field experiment, an adjustable bracket system is used to fix the microphone in a preset position to complete the measurement. The actual layout of the site is shown in Fig. 4.

3 Sound Field Distribution Characteristics 3.1 Horizontal Distribution Characteristics By comparing the noise sound pressure level of each measuring point at the same measuring height, the noise distribution characteristics of the filter capacitor device in the horizontal direction can be analyzed. Taking the measuring height of 1.6 m as an example, the measuring point 9 to 12 are selected, and the noise level distribution at its main frequency are shown in Fig. 5. The sound pressure level data have been weighted by A. The following conclusions can be drawn. • The sound pressure level of 100 Hz noise is generally small, and there is no obvious distribution in the horizontal direction below 50 dB, because the 100 Hz sound wave length is about 3.4 m, and the horizontal distance has little influence on the sound path difference from each sound source. The noise distribution is similar as a whole. • For 500 Hz and 600 Hz noise, the sound pressure level of the middle two rows in the direction of the casing of the capacitor device is large, about 70 dB, and the sound pressure level of the next two columns is small, about 60 dB. The noise level of the non-sleeve side of the device is obviously lower than that of the casing side. • Distribution characteristics of 1100 Hz noise become irregular, because the acoustic wavelength decreases with the increase of frequency. The interference phenomenon of the same frequency noise is more prominent, and the corresponding noise distribution will change dramatically.

3.2 Vertical Distribution Characteristics By comparing the noise sound pressure level of each measuring point at different plane height, the noise distribution characteristics of the filter capacitor device in the vertical direction can be analyzed. In order to facilitate the mapping and analysis, the sound pressure levels of four measuring points at the same height are averaged, and then the vertical distribution of noise at the main frequency are shown in Fig. 6. The sound pressure level data have been weighted by A. • The average sound pressure level of 100 Hz noise at different heights is generally low, below 50 dB. Because the ground acts as the reflector of noise, the average sound pressure level of the measuring point with lower height is higher. With the increase of the height of the measuring point, the average sound pressure level of noise decreases at first and then increases. • For 500 Hz and 600 Hz noise, the average sound pressure level of noise at different vertical heights is similar, and the ground reflection effect is weak. The noise level on the non-casing side of the capacitor device is obviously lower than that on the casing side.

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(a) 100Hz.

(b) 500Hz.

(c) 600Hz.

(d) 1100Hz.

403

Fig. 5. Horizontal noise distribution characteristics at different frequencies. (From point NO.9 to point NO.12 are four measuring points in the horizontal direction at a height of 1.6 m)

• The variation law of noise in the vertical direction on the positive and negative sides of the casing of the condenser device at each frequency is basically similar. The noise radiation of the capacitor device is symmetrical obviously.

4 Sound Field Simulation Analysis There are a number of capacitor units in the capacitor device, each unit will produce vibration and noise under electrical excitation. Noise will superimpose and shadow each other, which makes the sound field distribution of the capacitor tower more complex. The measured method can only obtain the sound pressure data of a few measuring points in the spatial domain, and the understanding of the overall sound field distribution of the device is limited. For this reason, the measured vibration velocity of each point on the surface of the capacitor can be used as the boundary condition, and the boundary element square method can be used to simulate the sound field.

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(a) 100Hz.

(b) 500Hz.

(c) 600Hz.

(d) 1100Hz.

Fig. 6. Vertical noise distribution characteristics at different frequencies (The A-weighted sound pressure levels of four measuring points at the same height have been averaged).

The simulation model sets the ground as the total reflector, and ignores the influence of the capacitor tower frame on the sound field distribution, and makes the cloud pictures of the sound pressure level distribution on the front of the measuring points under the vibration frequencies of 100 Hz, 500 Hz, 600 Hz and 1100 Hz respectively as shown in Fig. 7. Under the condition of symmetrical arrangement of capacitors and symmetrical loading, the distribution of sound field is symmetrical as a whole, which is in good agreement with the measured results. With the increase of vibration frequency, the interference phenomenon of sound field becomes more and more obvious, and the interference fringes increase gradually. At the same time, the overall noise directivity will change obviously with the frequency. This shows that the high-frequency sound pressure level data is very sensitive to the position, which is easy to cause measurement errors, and change noise distribution dramatically.

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(a) 100Hz.

(b) 500H].

(c) 600Hz.

(d) 1100H].

405

Fig. 7. The sound pressure level distribution cloud map of front plane at different frequencies.

5 Conclusions (1) The noise radiation of the scale capacitor device has obvious directionality and symmetry, and its sum frequency and difference frequency noise are dominant. The sound pressure level of frequency doubling noise is generally small, and the distribution characteristic is not obvious. (2) The reflection of the ground has a great influence on the low-frequency noise, and the average sound pressure level with different vertical height is similar. (3) With the increase of vibration frequency, the interference phenomenon of sound field becomes more and more obvious, and the interference fringes increase gradually. At the same time, the overall noise directivity will change obviously with frequency. Acknowledgments. This work was funded by Project of National Natural Science Foundation, China (No. 51877168).

References 1. CIGRE. No.202 W.G 14.26. HVDC stations audible noise (2002) 2. Ji, S.C., Li, J.Y., Wu, X.S., et al.: Review of vibration and audible noise of ac filter capacitors in converter stations. High Voltage Eng. 42(04), 1159–1167 (2016). (in Chinese) 3. Cao, T., Ji, S.C., Wu, P., et al.: Vibration and noise characteristics for capacitor in HVDC converter station. Trans. China Electrotechn. Soc. 25(10), 87–93+100 (2010). (in Chinese)

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4. Zhu, L.Y., Gao, L., Li, J.Y., et al.: Mass tuning reduction method for vibration and audible noise of HVDC filter capacitors. IEEE Trans. Power Delivery 35(6), 2583–2590 (2020) 5. Li, J.Y., Lei, X.Y., Zuo, Z.Q., Xiong, Y.: Vibration Model of a Power Capacitor Core under Various Harmonic Electrical Excitations. Energies 15(5), 1848 (2022) 6. Zhang, Y., Xie, L.K., Zang, Y.W., Guo, Z.F.: Computer Simulation Analysis and Control of Vibration and Noise in UHVDC Converter Station. J. Phys. Conf. Series 1648(3), 032185 (2020) 7. Li, J.Y., Zhu, L.Y., Xiong, Y., et al.: Mechanism model of multi-times-frequency spectrum of filter capacitor vibration and audible noise. High Voltage Eng. 44(06), 2081–2088 (2018). (in Chinese) 8. Jiang, Z.T., Cui, H.T., Zhu, L.M., et al.: Study on noise reduction measures of capacitor based on central symmetrical arrangement. Power Capac. React. Power Compen. 39(05), 7–12 (2018). (in Chinese) 9. Wang, Z.M., Xu, M.L., Wang, X., et al.: Field test and characteristic analysis on noise of AC filter capacitor. Power Capac. React. Power Compen. 38(04), 17–23+46 (2017). (in Chinese) 10. Smede, J., Johansson, C.G., Winroth, O., et al.: Design of HVDC converter stations with respect to audible noise requirements. IEEE Trans. Power Delivery 10(2), 747–758 (1995) 11. Xiong, Y., Li, J.Y., Lei, X.Y., et al.: Noise interaction between capacitor units and sound field optimization measures. Power Capac. React. Power Compen. 43(04), 1–8 (2022). (in Chinese)

Insulator Defects Detection and Classification Method Based on YOLOV5 Yingbin Gu, Peifeng Huang, Juan Wang, Lize Tang, Jia Weng, and Xiaofeng Wang(B) Chaozhou Power Supply Bureau Guangdong Power Grid Co. LTD, Chaozhou, China [email protected]

Abstract. With the expansion of high-voltage transmission line construction, UAVs(Unmanned Aerial Vehicles) have been widely adopted in line inspection. The issue of self-explosion in glass insulators has attracted significant attention. In this study, we propose a method for self-explosion defect recognition based on YOLOv5 and incorporate various data augmentation techniques to enhance adaptability to complex environmental factors. Experimental results demonstrate the method’s remarkable performance in defect detection, achieving an average precision (mAP) of 95.8% that satisfies practical detection requirements. Furthermore, for the detected self-explosion defects, the glass insulators are further classified into upper, middle, and lower defects based on the explosion location. Experimental findings indicate that this method effectively classifies self-explosion defects in glass insulators, holding significant implications for analyzing self-explosion patterns. Keywords: defects detection · YOLOv5 · classification

1 Introduction China has developed rapidly in recent years, and the need for high-voltage transmission lines is expanding to meet the growing demand. In overhead transmission systems, glass insulators play a vital role as essential components for electrical insulation and mechanical support. However, Insulators are often exposed to the outdoors Consequently, glass insulators in high-voltage lines are susceptible to breakage or explosion due to extreme natural environments, such as corrosive effects of rainwater and lightning strikes. These incidents significantly impact the safety and stability of the power grid operation [1–3]. Therefore, conducting regular inspections on insulators is crucial to maintain the reliable functioning of overhead transmission lines [4]. The current methods for inspecting overhead transmission lines primarily include manual inspections, helicopter inspections, and unmanned aerial vehicle (UAV) inspections. Manual inspection is difficult and inefficient due to the limitations imposed by the distribution scope and environment of the overhead transmission lines, while helicopter inspection is expensive and poses high risks. With the development of UAV inspection technology, the use of drones to automatically detect transmission line faults from aerial images or videos has become increasingly popular. Faced with a large number of inspection images captured by UAVs, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 407–414, 2024. https://doi.org/10.1007/978-981-97-1072-0_41

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there are two main methods for insulator defect detection. One is to use traditional image processing methods for defect detection, and the other is to use deep learning algorithms for defect detection. Early methods for insulator defect detection primarily relied on conventional image processing techniques, such as threshold segmentation, morphological operations, and edge detection. However, With the swift progress of deep learning methods, they have gradually emerged as the predominant research approach in the field of insulator defect detection. By leveraging neural network algorithms and extensive training data, deep learning methods demonstrate the capability of rapidly and accurately detecting defects, along with robustness and generalizability. Object detectors based on deep learning including single-stage and two-stage detectors. Single-stage detectors are characterized by their simplicity and high efficiency. In the literature [5], A CSP-ResNeSt backbone network was put forward, which was coupled with a new multi-scale bi-directional feature pyramid network (Bi-SimAM-FPN) with simple attention mechanisms to resolve difficulties detecting small scale insulator defects in aviation images while retaining the ability to overcome the interference caused by complex backgrounds. In the literature [6], The SSD model was improved to detect infrared image anomalies in power equipment, which involved the ability to automatically detect multiple power equipment and accurately locate abnormal heat zones in real-time. However, this method was limited to detecting hot-spot anomalies in infrared images. In the literature [7], The lightweight Ghost module and CBAM attention mechanism were introduced to enhance the YOLOv5 model for detecting insulator defects. This approach aimed to raise the accuracy and efficiency of detection in insulators. In the literature [8], The USRNet was incorporated into the YOLOv5x detection model to improve the detection accuracy of small faults in intricate background associated with power line patrol images. The overall model performance was further optimized using an effective intersection over union loss function (EIou_lOss). Based on a two-stage detector, In the literature [9], The authors used a Faster RCNN to detect faults in high-voltage lines, which can locate damaged insulators and nests. However, this method does not provide real-time detection. In the literature[10], Cascade R-CNN is introduced as a cascaded detection architecture that addresses the issue of overfitting and performance degradation caused by high detection thresholds in object detection. By progressively improving hypothesis quality and reducing overfitting, Cascade R-CNN performs well on several different public datasets. Furthermore, it has been extended and improved for instance segmentation. In brief, the detection of insulator defects in UAV images with complex backgrounds is a highly challenging task. Moreover, most insulator defect detection models are trained using only a single kind of insulator, which breaks the overall robustness of the model. The strings of insulators present in the entire image often occupy large areas, whereas glass insulator defects are typically small targets. This necessitates the detector to precisely fuse multi-scale features to detect the defect area more accurately. Additionally, insulator self-explosion defects are often not classified in detail in most studies. To address these issues, this paper put forward a glass insulator self-explosion detection algorithm, basing on YOLOv5s, which can classify identified glass insulator selfexplosion defects further. The Main purpose of this study is to introduce a precise and

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efficient technique for detecting and categorizing glass insulator self-explosion defects in overhead power line systems.

2 Related Work 2.1 YOLOv5 The Network architecture of YOLOv5 can be found in Fig. 1

1_1

1_3

1_3

2_1

608*608*3

2_1 2_1

76*76*255

2_1 38*38*255

2_1

1_

19*19*255

2_ 2*

Fig. 1. Network architecture of YOLOv5.

YOLOv5 employs CSPDarknet53 as its backbone network architecture, which is constructed by combining convolution, cross-stage partial (CSP), and spatial pyramid pooling (SPP) modules. The Conv module serves as the standard building block, while the C3 module increases the network’s depth and receptive field, enhancing feature extraction capabilities. The SPP module performs pooling using receptive fields of different scales, allowing the capture of multi-scale features. In the neck section, the FPN (Feature Pyramid Networks) and PAN (Pyramid Attention Network) structures are utilized to enhance the feature extraction capability by utilizing the information extracted from the backbone part. For target detection in the head section of YOLOv5, multiple feature layers are extracted. These feature layers, with respective shapes of (19, 19, 255), (38, 38, 255), and (76, 76, 255), contribute to the overall detection process. In the prediction stage, YOLOv5 utilizes the CIOU (Complete Intersection Over Union) loss function as the feature points regressor while employing cross-entropy loss as the classifier to identify and localize objects. Details of the CIOU loss function are presented in the following definition: CIOU = IoU −

ρ 2 (b, bgt ) − αv c2

(1)

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4 wgt w (arctan − arctan )2 2 gt π h h  0, ifIoU < 0.5, α= V , (1−IoU )+V ifIoU ≥ 0.5.

V =

(2) (3)

ρ 2 (b, bgt ) + αv (4) c2 The variable IoU (Intersection over Union) signifies the extent of overlap existing between the predicted and actualized bounding boxes. Notably, the symbols ‘b’ and each denote the centers of these bounding boxes, with the distance between the two calculated using the Euclidean distance. Remarkably, the symbol ‘c’ denotes the diagonal length of the tightest enclosing rectangle or the mini-mum bounding box. LCIoU = 1 − IoU +

2.2 Evaluation Indicators To compare the detection accuracy of various object detection models against insulator self-explosion defects, the average precision (AP) is selected as the indicator for evaluating the performance accuracy of the models. The AP is calculated based on the precision (P) and recall (R), where P and R are computed using the following equations: TP (5) TP + FP TP (6) R= TP + FN In this context, within the framework, the metric TP (True Positive) denotes the count of accurately identified positive samples, while FP (False Positive) quantifies the instances of misclassifying negative samples as positive. Conversely, FN (False Negative) characterizes the number of positive samples that are either overlooked or erroneously labeled as negative. The precision and recall values, which are calculated based on these metrics, are used to plot the P-R curve. The area under this curve represents the AP value, which is calculated using the formula:  1 AP = P(R)dR (7) P=

0

3 Methodology 3.1 Data Set Labelling Insulator images were annotated using the labelimg tool. In view of the fact that the dominant insulators featured in the dataset are glass and composite insula-tors, with selfexplosion defects being the main types of defects observed, three distinct labels: “glass insulator”, “detect”, and “insulator”, were employed during the annotation process. The annotation requirement differed depending on the condition of the glass insulator: only the position of the glass insulator needs to be marked where the glass insulator is intact, whereas both the position of the glass insulator and the defective part need to be marked where a self-explosion defect has occurred.

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3.2 Data Set Augmentation In order to prevent overfitting and improve the generalization ability of the model, this study uses the data enhancement method to process the pictures. Environmental factors, such as lens shake during shooting that causes image blurring, electro-magnetic interference during transmission that introduces noise, and uneven lighting which results in exposure inconsistencies, pose significant challenges to image detection. The authors addressed these issues by implementing a range of data augmentation methods on the dataset, such as the addition of Gaussian noise, random pixel dropout, blurring, altering brightness, increasing the number of masks, and rotating images. The application of these methods has proved effective in enhancing the model’s performance and ensuring its reliability in practical settings. 3.3 Improved YOLOv5 The original dataset is first subjected to data augmentation, and the augmented data is then used for object detection using YOLOv5. The detected bounding boxes for the defects and insulators are obtained, and the number of defect-insulator pairs are counted. By utilizing the central point of the defect’s bounding box, the defect types are determined and categorized into upper, middle, and lower defects represented by “upper”, “in”, and “lower”, respectively. The bounding box is shown in Fig. 2.

Fig. 2. Bounding boxes

4 Experiments 4.1 Datasets In this study, a total of 1,122 insulator images were selected from UAV inspection photos of power transmission lines provided by a company in Guangzhou, China, after removal of duplicate samples, those without insulators, and low-quality samples. The dataset mainly comprised glass and composite insulators. Given the scarcity of insulator defect images in real-world scenarios, image-based methods were employed to capture 133 glass insulator self-explosion images, while the remaining 989 images depicted intact insulators, thereby establishing a dataset of insulator images based on UAV inspection photos. To increase the diversity of the experimental dataset and prevent overfitting during the training phase, the insulator dataset was subjected to data augmentation

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techniques. Specifically, the original images were processed using techniques such as Gaussian noise addition, random pixel activation, blurring, brightness adjustment, mask addition, and rotation to modify their appearance. The results of data augmentation can be found in Fig. 3. The final insulator dataset comprised a total of 4,488 images, including 3,956 normal insulator images and 532 images of insulator defects, which were randomly divided into training and validation sets. The training set contained 3,590 images, whereas the validation set comprised 898 images, with both sets being divided in a 4:1 ratio.

Fig. 3. Several Kinds of Data Augmentation.

4.2 Experimental Setup The experiment was conducted using the PyTorch framework. The GPU is NVIDIA GeForce GTX 2080 Ti, Training parameter setting are shown in Table 1. Table 1. Training parameter setting. Parameter name

Value

Initial learning rate

0.01

momentum

0.937

Image size

640 × 640

Batch size

16

Weight decay

0.0005

Epochs

200

4.3 Experimental Results The overall training situation is illustrated in Fig. 4.The graph indicates that both the training loss and validation loss converge effectively. The trained model achieves a map value of 95.8%.

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Fig. 4. The results of Yolov5 training.

Image detection results: The complete image inspection results are shown in Fig. 5.The presented figure displays the outcomes of our pro-posed algorithm. The algorithm effectively detects the positions of insulators in (a), (b), and (c) without identifying regions beyond the insulator border. Notably, the detection category is precise, indicating the reliability and robustness of the algorithm. Further, in (d), (e), and (f), the algorithm accurately distinguishes be-tween upper, middle, and lower insulator defects, as indicated by the labeling scheme “upper,” “in,” and “lower.” The classification allows for better characterization of insulator defects by providing additional information regarding the defect location and may aid in understanding the spontaneous self-explosion patterns of glass insulators. Our proposed methodology shows promising potential for detecting and classifying glass insulator spontaneous self-explosion defects accurately. It may provide valuable assistance to maintenance personnel responsible for monitoring overhead power line systems.

Fig. 5. A Few Detection Results.

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5 Conclusion This study presents a novel approach for identifying glass insulator self-explosion defects using YOLOv5. To alleviate the negative impact of complex environments on image detection, the study proposes different data augmentation techniques. The experimental evaluations reveal that the proposed method achieves a high detection accuracy, with the mAP of 95.8%, which successfully meets the practical requirements. Moreover, this approach further addresses the issue of detecting and classifying insulator self-explosion defects into upper, middle, and lower parts based on the explosion position. This classification strategy holds great significance in exploring the self-explosion patterns of glass insulators.

References 1. She, L., Fan, Y., Wang, J., et al.: Insulator surface breakage recognition based on multiscale residual neural network. IEEE Trans. Instrument. Measure. 70, 1–9 (2021) 2. Park, K.-C., Motai, Y., Yoon, J.R.: Acoustic fault detection technique for high-power insulators. IEEE Trans. Indust. Electron. 64(12), 9699–9708 (2017). https://doi.org/10.1109/TIE. 2017.2716862 3. Qiu, Z., Zhu, X., Liao, C., et al.: Detection of transmission line insulator defects based on an improved lightweight YOLOv4 model. Appl. Sci. 64(12), 12(3), 1207 (2022) 4. Ling, Z.N., Zhang, D.X., Qiu, R.C.: An accurate and re-al-time method of self-blast glass insulator location based on faster R-CNN and U-net with aerial images. CSEE J. Power Energy Syst. 5(4), 474–482 (2019) 5. Hao, K., Chen, G., Zhao, L., Li, Z., Liu, Y., Wang, C.: An insulator defect detection model in aerial images based on multiscale feature pyramid network. IEEE Trans. Instrument. Measure. 71, 1–12 (2022) 6. Wang, X., Li, H., Fan, S., et al.: Infrared image anomaly automatic detection method for power equipment based on improved single shot multi box detection. Trans. Electrotechn. Soc. 35(S1), 302–310 (2020) 7. Lan, Y., Xu, W.X.: Insulator defect detection algorithm based on a lightweight network. J. Phys. Conf. Ser. 2181(1) (2022) 8. Huang, Y., Liu, H., Chen, Q., et al.: Churui. Transmission line insulator fault detection method based on USRNet and improved YOLOv5x. High Voltage Eng. 48(09), 3437–3446 (2022) 9. Lei, X., Sui, Z.: Intelligent fault detection of high voltage line based on the Faster R-CNN. Measurement 138, 379–385 (2019) 10. Cai, Z., Vasconcelos, N.: Cascade R-CNN: high quality object detection and instance segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 43(5), 1483–1498 (2021)

Design and Implementation of Indirect Lightning Protection for Airborne Electronic Equipment Zhifei He(B) , Xinyao Li, and Kai Dong Aeronautics Computing Technology Research Institute, Xian 710076, China [email protected]

Abstract. Airborne electronic devices are susceptible to lightning attacks during aerial operation, which can affect signal transmission and collection, and even lead to damage to airborne electronic devices, affecting flight safety. In response to the issue of airborne electronic equipment being susceptible to indirect lightning interference or even damage, indirect lightning protection is designed and implemented at the corresponding lightning test level. The protection objects include the chassis, power supply, and various interface signals. The focus is on analyzing the methods of selecting different transient suppression diodes based on the characteristics of various interface signals, aiming to improve the reliability of airborne electronic equipment. After experimental verification, a design method for indirect lightning protection of airborne electronic devices has passed rigorous lightning tests and meets the requirements of lightning protection. It can effectively protect the back-end circuit and provide reference for indirect lightning protection design of other airborne electronic devices. Keywords: Lightning Protection · Airborne Electronic Equipment · Indirect Effect of Lightning · TVS · Interface Signal

1 Overview The current indirect lightning protection test for airborne electronic equipment is mainly carried out in accordance with the lightning protection test requirements in the "RTCA DO-160G-2010 Environmental Conditions [1] and Test Procedures for Airborne Equipment" standard. Lightning protection tests are mainly divided into pin tests, single and multiple return stroke tests, and multiple pulse group tests [2]. This article takes the strict requirements for B3, J3, and L3 test levels as an example to design and implement indirect lightning protection, where the pin test waveform is B and the test voltage level is level 3; The waveform of single and multiple return stroke tests for cable bundles is J, and the test voltage level is level 3; The waveform of the multi pulse group test is L, and the test level is level 3. The test level reference is shown in the table below [3] (Tables 1, 2 and 3). This article takes a certain type of airborne electronic equipment as an example and mainly designs corresponding lightning protection for indirect lightning strikes. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 415–422, 2024. https://doi.org/10.1007/978-981-97-1072-0_42

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The lightning protection objects include the chassis, power supply, and various external interface circuits. The main measure for indirect lightning protection of interface circuits is to connect devices that can quickly absorb high-energy surges in parallel on electronic circuits, discharge energy surges to the ground [4], and clamp the voltage on electronic circuits within a safe range, thereby protecting onboard electronic equipment.

2 Indirect Lightning Protection Design 2.1 Lightning Protection Methods for Chassis The chassis is made of aluminum alloy conductive material, and the overall chassis is an electromagnetic sealed box structure. The components of the chassis are connected with low impedance, and a low impedance grounding wire grounding terminal is set on the chassis [5]. Through the grounding wire, a good discharge circuit is formed between the hardware platform and the system ground, enabling the timely and effective release of high-energy lightning induced on the cables and chassis, avoiding external lightning strikes affecting the internal functional circuit of the chassis. Equipment can be effectively shielded and protected through shielding layers and well grounded shielding grounding protection. To effectively prevent indirect lightning from having adverse effects on the internal circuits and interface signals of the hardware platform, and even affecting their normal operation, the following protective measures are carried out on the signal transmission cables. 1) All differential signal lines are connected using twisted pair shielded wires; 2) The connection between the cable shielding layer and the connector adopts shielded accessories to ensure that the signal line does not produce electromagnetic leakage at the connection point. 2.2 External Interface Signal Protection Methods Due to the fact that the debugging interface of airborne electronic equipment does not affect the normal working status of airborne electronic equipment in the flight environment, the ground debugging and maintenance interface is designed with a cover protection for indirect lightning shielding. Classify external interface signals in airborne electronic equipment, except for debugging interfaces. The interface signals to be tested for indirect lightning effects include power supply signals, RS422 bus signals, ARINC429 bus signals, discrete input/output signals, and other signals. The interface signal classification, signal type, signal description, and signal level are shown in Table 4. 2.2.1 Lightning Protection Methods for Power Signal The power interface is connected in series with the back end of the filter, and the corresponding lightning protection design is processed in the filter. The circuit schematic diagram is shown in Fig. 1.

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Table 1. Pin test voltage level. Voltage level

Wave Form 3/3(VOC /ISC )

5A/5A(VOC /ISC )

3

600/24

300/300

Note: The ratio of VOC to ISC is the source impedance of the transient pulse source used for calibration

Table 2. Single and multiple rebound test voltagel levels. Voltage level

3

Wave Form 2/1 (VL /IT )

2/1 (VT /IL )

3/3 (VT /IL )

4/1 (VT /IL )

4/5 A (VT /IL )

Single return stroke

300/600

300/600

600/120

300/600

300/1000

Multiple counterattacks

First counterattack

300/300

300/300

600/120

150/300

120/400

First counterattack

150/150

150/150

300/60

75/150

60/200

Note: VL represents the test voltage level, IT represents the test current level, and VL and IL represent the limit level

Table 3. Single and multiple return stroke test voltage levelsl. Voltage level 3

Wave Form 3

Wave Form 6

VL /IT

VL /IT

360/6

600/30

Due to the low impedance of the power interface of airborne electronic devices, the power signal is more susceptible to large surges during lightning strikes [6]. Therefore, it is necessary to use protective devices with high current capacity for the power signal protection. When designing indirect lightning protection for power signals, a total of 9 TVS tubes are connected in parallel in the filter to achieve indirect lightning protection, including 115 V three to shell ground, 28 V positive and negative to shell ground, and AAP signal to shell ground. 2.2.2 Lightning Protection Methods for Power Signal For airborne electronic devices, the most direct lightning protection method is to add protective devices to their external interface signals for lightning protection. The principle is to absorb the instantaneous large energy such as surge voltage and current pulses applied to the airborne electronic devices through lightning protection devices [7], and limit the

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Signal Type

Signal Description

Power Supply

28 V Power Supply

Input

18 V–32 V

Power Supply

115 V Power Supply

Input

AC 115 V

Power Supply

AAP

Input

28V Ground

Differential Output

0–5 V

Differential Input

0–5 V

ARINC429 Bus

Differential Output

0–10 V

Differential Input

0–10 V

Discrete Input

Input

0–28 V

Discrete Output

Output

0–28 V

Input

0–28 V

RS422 Bus

Other Signals

Ground Signal, etc

Direction

Signal Level

Fig. 1. Lightning protection methods for power signal.

voltage below the design value, thereby protecting the airborne electronic devices from damage. This article selects TVS tubes for indirect lightning protection design of interface signal circuits. The basic principle of indirect lightning protection circuit design is that the transient voltage suppression tube acts on the front end of the interface signal, used to release the instantaneous surge voltage and surge current passing through the interface signal line to the ground, thereby protecting the interface signal. In the protection circuit of interface signals, TVS tubes are usually connected in parallel with the protected signal circuit [8]. When the instantaneous voltage introduced by indirect lightning exceeds the

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normal working voltage of the signal circuit, the TVS transistor will provide a path with ultra-low resistance for the instantaneous current. The TVS transistor will divert the instantaneous voltage and clamp the voltage at both ends of the signal circuit to the predetermined clamping voltage value of the TVS transistor, thereby avoiding the instantaneous energy introduced by indirect lightning from the protected circuit and effectively protecting the interface circuit.

3 Design of TVS Selection The parameters of the selected TVS tube vary for different airborne equipment, interface types, and protection levels. After determining the parameters of TVS tubes through calculation, it can provide a basis for device selection. The calculation formulas are shown in Eqs. (1) to (3). ZS = VOC ÷ ISC

(1)

IP = (VOC − VC ) ÷ ZS

(2)

P = IP × VC × βt

(3)

In the formula, ZS is the source impedance, VOC is the open circuit voltage, ISC is the short-circuit current, IP is the peak current, VC is the clamping voltage, βt is the ratio of the rated power of the TVS tube at room temperature to the rated power of the TVS tube at actual operating temperature, and P is the rated power of the selected TVS tube. By summarizing the types of external interface signals, they can be mainly divided into the following 5 types of circuits: 1) 2) 3) 4)

Discrete input output (28V) interface circuit; RS422 level interface circuit; ARINC429 level interface circuit; Other interface (video/infrared) circuits.

According to formulas (1)–(3) [9], the selection list of TVS tubes for each interface circuit is shown in Table 5. After adding lightning protection circuits to the high-frequency signals of airborne electronic devices, they are susceptible to interference and signal distortion, which affects the normal communication of the bus. When using TVS tubes for lightning protection of high-frequency signal lines, the smaller the junction capacitance, the weaker the attenuation of high-frequency signals. Therefore, for interface signals, especially highfrequency interface signals, when selecting TVS tubes, it is necessary to fully consider the junction capacitance parameters of TVS tubes to ensure signal integrity. The RS422 bus communication rate is 11.25 kb/s. To avoid the impact of TVS tube on data transmission and ensure normal data communication, the TVS tube model (G) SMDJ7.0CA-HR is selected. The junction capacitance of the TVS transistor is about 10nf, and the normal working voltage is 5 V, which meets the requirements of indirect lightning protection while also reducing the signal attenuation.

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Serial Interface Number

Model

Minimum Maximum Maximum Maximum Peak Breakdown Breakdown Clamping Peak Power Voltage Voltage Voltage Current

1

Discrete quantity

(G)SY469CA

31.1 V

2

RS422 Interface

(G)SMDJ7.0CA-HR 7.78 V

3

ARINC429 (G)SMDJ12CA-HR Interface

4

Other interfaces

(G)SY469CA

34.4 V

45.4 V

110 A

5000 W

8.6 V

12 V

250 A

3000 W

13.3 V

14.7 V

19.9 V

150.8 A

3000 W

31.1 V

34.4 V

45.4 V

110 A

5000 W

The ARINC 429 signal is a differential signal, with a normal working voltage of plus or minus 10 V and a breakdown voltage of around 13 V. The TVS transistor with model (G) SMDJ12CA-HR can be selected. The clamping voltage VC of the TVS tube is 19.9 V, and the rated power is 3000 W, which can meet the design requirements. Due to the fact that pin testing is mainly used to verify the ultimate withstand voltage capability of airborne electronic devices and their external interface circuits, the selection of TVS tubes for airborne electronic devices is based on the pin injection test level. The peak power calculation of each interface circuit is shown in Table 6. Table 6. Peak power of interface circuit. Interface Type

Zs

Voc

Isc

VC

IP

P

Discrete quantity

25

600

24

45.4

22.184

1007.1536

Interface

1

300

300

45.4

246.7

11200.18

RS422

25

600

24

12

23.52

282.24

Interface

1

300

300

12

288

3456

ARINC429

25

600

24

19.9

23.204

461.76

Interface

1

300

300

19.9

280.1

5573.99

Other interfaces

25

600

24

45.4

22.184

1007.1536

1

300

300

45.4

246.7

11200.18

In Table 4, the peak power is the maximum peak power within a single cycle. Typically, the peak power of lightning protection devices (such as 1500 W, 3000 W, 5000 W, etc.) is the peak power of the device under standard pulse time conditions of 10/1000 microseconds [10]. In actual indirect lightning effect tests, the pulse time applied to the lightning protection device will be much smaller than the standard pulse time, The maximum peak power of the device will significantly increase with the shortening of pulse time.

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According to the inherent characteristics of lightning protection devices, the lightning protection devices (G) SMDJ7.0CA-HR, (G) SMDJ12CA-HR selected in the experiment have a peak power of 3000 W under standard pulse time of 10/1000 microseconds [11], and a peak power of 5000 W under standard pulse time of 10/1000 microseconds for (G) SY469CA. According to calculations, under the 5 A/5 A waveform, the peak pulse power of the selected lightning protection devices (G) SMDJ7.0CA-HR and (G) SMDJ12CA-HR is 6600 W, and the peak pulse power of (G) SY469CA is 11650 W. According to calculations, under the 3/3 waveform, the peak pulse power of the selected lightning protection devices (G) SMDJ7.0CA-HR and (G) SMDJ12CA-HR is 33900 W, and the peak pulse power of (G) SY469CA is 56500 W [12]. After calculation, the selected lightning protection devices (G) SMDJ7.0CA-HR, (G) SMDJ12CA-HR, and (G) SY469CA can meet the indirect lightning protection test requirements of grades B3, J3, and L3.

4 Test Verification The pin injection test applies waveform 3 (1 MHz) and waveform 5 A to the tested airborne electronic equipment, and the test level requirement is level 3. Apply 10 independent transient signals to each test pin, with a time interval of 10 s between each applied transient signal. The pin injection test waveform of waveform 5 A is shown in Fig. 2.

(a) The 5A Waveform(VOC+)

(b) The 5A Waveform(ISC+)

Fig. 2. Waveform 5 A pin injection test waveform diagram.

In the cable bundle test, waveform 1 and waveform 3 are applied for single and multiple impact tests, and waveform 3 is applied for multiple pulse group tests. The test level requirement is level 3. The single return stroke test waveform with a test level of level 3 and waveform 3 is shown in Fig. 3. Through experimental verification, the tested airborne electronic equipment functions normally and performs stably during the indirect lightning test process, meeting the requirements of B3, J3, and L3 lightning test levels, meeting the requirements of indirect lightning protection, and effectively protecting the back-end circuit. The indirect lightning protection method designed and implemented in this article can effectively

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(a) The 3 Waveform(+, 1MHz)

(b) The 3 Waveform(+, 10MHz)

Fig. 3. Waveform 3 Single Impact Test Waveform.

protect the back-end interface circuit of airborne electronic devices, and can also serve as a reference for the indirect lightning protection design of other airborne electronic devices.

References 1. RTCA/DO-160G-2010. Environmental Conditions and Test Procedures for Airborne Equipment. USA: RCTA. Inc (2004) 2. Liting, Z., Xijun, Z., Min, Z.: Suppressing characteristics of TVS device under electromagnetic pulse. In: 2017 International Applied Computational Electromagnetics Society Symposium (ACES), pp. 1–2. IEEE (2017) 3. Yang, Q., Zhang, D., Zhu, E., et al.: Lighting protection design for airborne electronic based on TVS devices. Aeron. Comput. Techn. 50(6), 96–100 (2020). (in Chinese) 4. Yang, Z., Wang, L., Xiao, C., et al.: A review of transient voltage suppression diodes. Electron. Des. Eng. 24(24), 108–112 (2016). (in Chinese) 5. Kraemer, J.G.: Circuit simulator based analysis for cable induced lightning effects. In: 2020 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI), pp. 312–317. Reno, NV, USA (2020) 6. Clark, M.: Lighting Protection for Aircraft Electrical, Power and Data Communication Systems. Micro semi Technical Note 127 (2004) 7. Cao, M., Wei, L.: Lightning protection design of the interface module of avionics. In: Proceedings of the 2018(7th) Civil Aircraft Avionics International Forum, pp. 311–316. CSAA, China Aviation Academy, Beijing (2018). (in Chinese) 8. Dong, C.: Design and Optimization of Single-Chip Lightning Protection Circuit, pp. 11–13. School of Electronic Science and Engineering, Chengdu (2021). (in Chinese) 9. Xi, L., Yan, L., Yin, X.: Lightning protection design for data interface transfer signal of aircraft avionics based on TVS devices. Avionics Technol. 4(45), 10–14 (2014). (in Chinese) 10. Liang, L.: Optimal Design of a Low-Capacitance Transient Voltage Suppressor Protection Device, pp. 1–4. School of Electronic Science and Engineering, Chengdu (2021). (in Chinese) 11. Attila, G., Kiss, I.: High Reliability Preventive Lightning Protection, pp. 12–16 (2022) 12. Swanson, A.: High Frequency Current Distribution in a Structure With Application to Lightning Protection Systems, pp. 25–30 (2022)

Optimization of Non-Destructive Testing of Power Equipment Based on X-ray Backscattered Imaging Zihao Cao1 , Ruohan Wu1 , Weiping Zhu2 , Peng Gu2 , Yong Yang1 , and Zhengzheng Liu1(B) 1 School of Electrical and Electronic Engineering,

Huazhong University of Science and Technology, Wuhan, China [email protected] 2 iRay Imaging Technology Chengdu Co., Limited, Chengdu, China

Abstract. Unlike conventional X-ray transmission imaging, X-ray backscattered imaging, which is based on the Compton effect, offers the advantage of imaging on the same side as the source-detector setups. This characteristic proves to be highly advantageous in specific applications, such as handheld security inspection. Which usually fixes a universal energy and flying-spot scanning method. To extend its innovative application to other fields, such as portable non-destructive testing of power equipment, we have utilized Monte Carlo simulation to establish a fundamental parameter model for X-ray backscattered imaging of defects. This model has enabled us to systematically investigate the impact of X-ray energy on backscattered resolution and imaging quality. Experimental tests were also implemented to verify the feasibility of same-side imaging for power equipment and confirm the optimal energy selection. Keywords: X-ray Backscattered Imaging · Power Equipment · Non-destructive Testing · Monte Carlo

1 Introduction X-ray backscattered imaging is an X-ray imaging technique based on Compton scattering, which is an incoherent process. The technique detects X-rays scattered from an object in a backscattered direction. The backscattered imaging technique has been widely used in various non-destructive testing (NDT) fields, including aircraft components [1], security checks [2], historical exploration [3], and concrete structures [4], and others. These applications are mainly stimulated by two attractive properties of the backscatter technique, compared to the common X-ray transmission method. The X-ray transmission method typically involves placing the X-ray source on one side of the object being inspected and the X-ray transmission detector on the other side. In contrast, the Compton scattering method involves placing the X-ray source and backscatter detector on the same side of the object [5]. This is particularly useful for © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 423–432, 2024. https://doi.org/10.1007/978-981-97-1072-0_43

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inspecting large area structures and for access from only one side. Another appealing feature of Compton scattering is that it can more effectively detect density variations in low-density materials than the transmission method [6]. Some research organizations have already applied X-ray transmission imaging to the nondestructive testing of power equipment. Zhong [7] investigates the feasibility of XDR imaging technology in identifying cracks and air gap defects in basin insulators. The research utilizes orthogonal test methods to determine the optimal parameter settings for X-rays, including tube voltage, tube current, exposure time, and angle. Darian, L. A. [8] tests high-voltage oil and SF6 circuit breakers and evaluates the impact of X-ray spectral energy characteristics on the image information. However, transmission imaging needs to ensure enough space on both sides of the power equipment to place the ray source and detector, and it takes a long time to set up the equipment, which is not applicable to the inspection of ductile objects. Therefore, this paper investigates the use of X-ray backscattered imaging in power equipment. This paper provides an introduction to the theoretical principles of backscatter imaging. It employs Monte Carlo simulation to systematically investigate the impact of different photon energies and fluxes on the imaging contrast and signal-to-noise ratios. The study focuses on simple defects, such as air-gap cracks in insulators, and extends to more complex equipment, such as the wires of electric meters. Additionally, preliminary validation experiments using X-rays of various energies are performed.

2 Theoretical Background Compton scattering involves the transfer of energy from photons to electrons, which results in a change of direction of the photons and their conversion into scattered photons. The equation below provides an interpretation of the energy variation of the photons caused by the Compton effect [9] E=

E0 1 + α(1 − cos θ )

(1)

where E 0 is the incident photon energy and E is the scattered energy, θ is the scattering angle relative to the incident photon direction, and α = E 0 /m0 c2 , m0 c2 is the rest mass energy of the electron (511 keV). Remarkably, the scattered energy of photons remains unaffected by the material being irradiated, and is only determined by the photon energy and the scattering angle. The number of scattered photons detected varies de-pending on the scattering angle and energy. The Klein–Nishina cross-section formula describes the relationship between the angular distribution and photon energy [10]    2  r02 E 2 E 1 E0 d σKN (θ ) 2 2 = − sin θ = r0 + d 2 E02 E0 E 1 + α(1 − cos θ )     1 + cos2 θ α 2 (1 − cos θ )2

(2) 1+ 2 1 + cos2 θ [1 + α(1 − cos θ )]

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where r 0 is the classical electron radius (2.82 × 10–15 m). It shows the odds that the scattered photon will be emitted from within a unit solid angle () in the direction of a certain scattering angle. A brief sketch of X-ray Compton scattering is illustrated in Fig. 1. A well-collimated X-ray source directs a beam of incident photons onto the test material, with the scattered photons being recorded by a detector, which is located on the same side of the material and at a certain scattering angle. This intersection of the incident beam and the detector’s solid angle defines the scattering or sensitive volume.

Fig. 1. Schematic illustration of Compton scattering

The scattered photons recorded by the detector attenuate in the incident path, get scattered in the scattering volume and are also attenuated in the scattering path. The count of scattered photons reaching the detector is given by the relation [11]:   dσ ρe dVd k S = 0 exp − μ1 (x)dx − μ2 (x)dx (3) d  x1 x2 where 0 is the incident photon flux (photons · m−2 · s−1 ), x 1 is the incident path from the source to the scattering volume, x 2 is the scattering path from the scattering volume to the detector, μ1 and μ2 are the linear attenuation coefficients in the paths x 1 and x 2 respectively, ρ e is the average electron density inside the scattering volume, dV is the scattering volume, d  is the solid angle and k is the detection efficiency of the detector. The electron density ρ e is derived by applying the following equation: ZNA (4) A where ρ is the physical density of the test material, Z is the atomic number, N A is Avogadro’s number and A is the material atomic mass of the test material. The property of the material determines the electron density. To some extent, the electron density within the scattering volume affects the number of scattered photons received by the detector according to (3). The scattering intensity (S) reflects the physical density of the test material. By recording all relevant scattering data, information concerning each specific voxel along the designated path of the incident beam may be obtained. The scattering volume dV is determined by the size of the collimator aperture, and it in turn determines the spatial resolution. Based on the method above, an X-ray scattering image is obtained. ρe = ρ

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3 Geant4 Simulation The study of backscattered imaging often involves several simplifications when employing the analytical approach, such as the use of the Klein-Nishina (K-N) formula, the failure to account for multiple scattering, and the neglect of the detector and ray source setups. Consequently, it is necessary to develop more precise models by utilizing Monte Carlo simulations. This section uses the simulations to verify the feasibility of defect detection, explore the theoretical signal-to-noise ratio, optimize energy selection. The systematic simulations were conducted on basin insulators and electricity meters used in power equipment. 3.1 Insulator Defect Model 3.1.1 Modelling Basin insulators, a critical role in Gas Insulated Switchgear (GIS), are composite materials manufactured through a vacuum casting process, primarily using modified epoxy resin infused with alumina particles. The survey revealed that 29% of faults were caused by air gap defects, while 71% were attributed to particles and foreign matter. The subsequent discussion will concentrate on air gap defects. Figure 2 illustrates the schematic diagram for detecting air gap defects in basin insulators using the backscattering technique. In this method, the source emits photons in the forward direction along the Z-axis, and the detector captures the backscattered photons on the same side of the object at a scattering angle of 180°. The basin insulator is composed of epoxy resin with a molecular formula of (C11 H12 O3 )n , a density of 1.2 g/cm3 , and a thickness of 5 cm. The air gap dimensions can be seen in Fig. 2(b).

(a)

(b)

Fig. 2. Schematic illustration of backscattering detection of basin insulator

In order to simulate the X-ray backscatter detection system, Geant4 simulation software was used, which is an object-oriented program for particle transport simulation developed by the CERN [12]. The prominent effects of X-rays on matter include photoelectric effect, Compton scattering, coherent scattering, and electron pair effect. X-ray

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backscattered imaging, which typically operates within the 10–300 keV energy range, is mainly impacted by photoelectric effect and Compton scattering, while the effects of coherent scattering and electron pair effect are negligible. Compton scattering is the predominant effect considered in the simulation. It is worth mentioning that the PhysicsList used in the simulation is G4EmLivermorePhysics, which adopts the LivermoreCompton model and the LivermorePhElectric model below 1 GeV. The cut values for gamma and electron are 3000 nm and 500 nm, respectively. 3.1.2 Simulation Results The result of the number of scattered photons received by the detector is depicted in Fig. 3 as the source is translated along the X-axis at 100 keV. A notable decline in photon count occurs between -1 and 1 mm, indicating the presence of a 2 mm air gap defect. Beyond X > 1 mm, an elevation in the quantity of scattered photons is observed, attributed to the beam spot’s dimensions. The introduction of an air gap evidently leads to a roughly 5% reduction in photon count, enabling its differentiation in backscattered signal intensity or imagery.

Fig. 3. Result of simulation of air gap defect detection in basin insulators

3.2 Electricity Meter Simulations The previous example involved a simple material composition and defects. However, this section shifts focus to a device with a more intricate internal structure: an electricity meter. Typically affixed to a wall while in use, the suitability of X-ray backscatter imaging over transmission imaging in this scenario becomes evident. There are occasional cases where users illegally modify the electricity meters through rewiring the meters. If this phenomenon can be observed, one can check the electricity meter without risking opening it or interfering with its operation. Figure 4 displays the schematic diagram of the backscatter configuration of the electricity meter. The simplified electricity meter comprises several components: a 4 mm plastic shell, a copper wire with a diameter of

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2 mm (including a 1 mm thick outer layer), and a double-layered 3.2 mm PCB. The plastic shell is constructed from polycarbonate, a high polymer with a density of 1.221 g/cm3 . Positioned 5 cm behind the plastic shell, the copper wire is surrounded by a PVC outer layer. The PCB material of choice is FR-4, characterized by a density of 1.86 g/cm3 .

Fig. 4. The schematic of the electricity meter model

3.2.1 Energy Optimization The incident photon energy plays a crucial role in determining the quality of the imaging process. Figure 5(a) illustrates the variation in the number of scattered photons received by the detector for scenarios both with and without copper wires, while Fig. 5(b) presents the corresponding contrast variations. The incident photons remain constant at 108 . N s and N b represent the detected scattered photons with and without the copper wire, respectively. The contrasts are calculated by the following formula: C=

Ns − Nb Ns

(5)

In both cases, the number of scattered photons decreases as photon energy increases. This phenomenon occurs because higher energy levels correspond to lower scattering probabilities within the simulation. The presence of copper wires, however, leads to an increase in the number of scattered photons. The contrast exhibits an upward trend in correlation with increasing energy, albeit at a gradual pace for energy levels surpassing 140 keV. Therefore, an incident energy of 140 keV proves to be a suitable choice, offering superior contrast and reduced radiation dosage.

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(b)

Fig. 5. Result of simulation of changes of photon energies

3.2.2 Intensity The number of photons collected to form every pixel is a crucial determinant of the backscatter image quality. Figure 6 illustrates the simulation result from a variation in the incident photon count from 107 to 108 . N s and N b are the scattered photons detected with and without the copper wire, maintaining a constant photon energy level of 140 keV. The noise fluctuation σ of the scattered photons with a copper wire is (N s )1/2 , and the difference in X-ray intensity with and without a copper wire is N = N s -N b . Therefore, the detection criterion for the copper wire should follow as proposed in [13]: N = K × σ where K represents the signal-to-noise ratio of detection.

Fig. 6. Result of simulation of change of the number of incident photons

(6)

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As observed in Fig. 6, the increments in N s and N b correspond proportionally to the increase in the incident photon count. With the incident photon count ranging from 107 to 108 , the value of K escalates from 16.8 to 30.7. To achieve a high SNR in practice settings, one can utilize a higher flux source (which relates to the source voltage and current) or lengthen the data collection period to accumulate a greater number of photons.

4 Experiment and Results An experiment on the electricity meter is conducted with the assistance of iRay Imaging Technology Chengdu Co., Limited, utilizing the X-ray backscatter flying spot imaging system. The physical picture of an electricity meter is presented in Fig. 7(a). The system scans at 1 cm/s speed. At an incident energy of 140 keV, the energy meter backscattered imaging result is shown in Fig. 7(b). The components and copper wire behind the plastic shell can be seen clearly.

(a) electricity meter

(b) backscattered image

Fig. 7. An electricity meter experiment

Figure 8 illustrates the imaging outcomes within the region of interest for various photon energies. The X-ray tube energies range from 90 keV to 140 keV, while the tube current remains constant. It is apparent that higher photon energy levels improve the sharpness of image edges and reveal finer details. Additionally, Fig. 8 demonstrates the alteration in contrast, with gray values normalized for the aforementioned three energies. The contrast value increases from 18.2 to 30.1, aligning with the changes observed in the simulation (Fig. 9).

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Fig. 8. Backscattered images of the electricity meter under different energies

Fig. 9. Contrasts under different energies

5 Conclusion X-ray backscattered imaging is a promising non-destructive testing method with unilateral access. But few people systematically study the parameter optimization and application in the power industry. This study aims to demonstrate the feasibility of using X-ray backscattered imaging to inspect power equipment, specifically examining air gap defects in basin insulators and detecting illegal rewiring in electricity meters. To simulate the interaction of photons with the power equipment, a Monte Carlo model is proposed in this paper. The simulation results validate the practicality of this technique in detecting air gap defects in basin insulators. Additionally, the simulation of the electricity meter reveals that an incident photon energy of 140 keV offers the better contrast and lower radiation dosage. Furthermore, increasing the number of incident photons can enhance the SNR by boosting the photon flux or extending the irradiation time. The experimental results of backscattered images captured for different energies on the electricity meter align with the simulations. Future research will focus on optimizing system parameters to enhance resolution and investigating other non-destructive testing applications using X-ray backscattered imaging.

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References 1. Kolkoori, S., Wrobel, N., Zscherpel, U., Ewert, U.: A new X-ray backscatter imaging technique for non-destructive testing of aerospace materials. NDT and E Int. 70, 41–52 (2015) 2. Dinca, D.C., Schubert, J.R., Callerame, J.: X-ray backscatter imaging. In: Optics and Photonics in Global Homeland Security IV, vol. 6945, pp. 283–295. SPIE, Florida (2008) 3. Harding, G., Harding, E.: Compton scatter imaging: A tool for historical exploration. Appl. Radiat. Isot. 68(6), 993–1005 (2010) 4. Amana, M.S., Aldhuhaibat, M.J.R., Salim, A.A.: Evaluation of the absorption, scattering and overall probability of gamma rays in lead and concrete interactions. SCIOL Biomed. 4, 191–199 (2021) 5. Callerame, J.: X-ray backscatter imaging: photography through barriers. Powder Diffr. 21(2), 132–135 (2006) 6. Huang, S., Wang, X., Chen, Y., Xu, J., Mu, B.: Simulation on x-rays backscatter imaging based on Monte Carlo methods for security inspection. In: Counterterrorism. Crime Fighting, Forensics, and Surveillance Technologies II 10802, pp. 7–14. SPIE, Berlin (2018) 7. Zhong, F., et al.: The X-DR imaging detection of simulation defect in GIS basin-type insulator. Nondestruct. Test. 40(1), 45–49 (2018). (in Chinese) 8. Darian, L.A., et al.: X-ray testing of high voltage oil-filled electrical equipment: Physical background and technical requirements. IEEE Trans. Dielectr. Electr. Insul. 27(1), 172–180 (2020) 9. Qiao, C., Wei, J., Chen, L.: An overview of the compton scattering calculation. Crystals 11(5), 525 (2021) 10. Wang, X.J., et al.: On the relativistic impulse approximation for the calculation of Compton scattering cross sections and photon interaction coefficients used in kV dosimetry. Phys. Med. Biol. 65(12), 125010 (2020) 11. Scannavino, F.A., Jr., Cruvinel, P.E.: A graphical tool for an analytical approach of scattering photons by the Compton effect. Nucl. Instrum. Methods Phys. Res., Sect. A 674, 28–38 (2012) 12. Agostinelli, S., et al.: GEANT4—a simulation toolkit. Nucl. Instrum. Methods Phys. Res. Sect. A 506(3), 250–303 (2003) 13. Wei, A., Chang, B., Xue, B., Peng, G., Du, D., Han, Z.: Research on the weld position detection method for sandwich structures from Face-Panel side based on backscattered X-ray. Sensors 19(14), 3198 (2019)

Visual Positioning Method for Unmanned Aerial Vehicle Charging Platform Using Cooperative Target Jiahao Lu1(B) , Wei Yang2 , Hengxing Zhou2 , Shaoqi Ma1 , Yuanshang Fan1 , Zhongbiao Ling1 , Jianwen Zhong1 , and Ruifeng Chen1 1 Foshan Power Supply Bureau of Guangdong Power Grid Co, Ltd., Foshan, China

[email protected] 2 Guangdong Polytechnic of Environmental Protection Engineering, Foshan, China

Abstract. This paper proposes a precise landing visual positioning scheme for an unmanned aerial vehicle (UAV) charging platform. By using a two-level cooperative target and feature segmentation method, the perimeter and area of the connected domain are calculated for preliminary fast rough segmentation, and then precise segmentation is performed based on the geometric features of the connected domains, and the goal of quickly filtering a large number of connected domains is achieved. Through real-time testing with an airborne pixel camera, the average processing speed reaches 35.3 ms, the problems of high-precision positioning and real-time performance in the process of UAV automatic landing have been solved. Experiments have shown that proposed visual positioning scheme can improve the efficiency of UAV automatic landing, and provide the good practical value for the application and promotion of fully automatic UAV inspection. Keywords: Charging platform · unmanned aerial vehicle · visual positioning · cooperative target

1 Introduction Unmanned aerial vehicles (UAVs) are with the advantages of high efficiency, low cost, and strong flexibility, and are widely used in tasks such as power facility inspection and monitoring [1–3]. At present, UAVs are limited by their endurance and inevitably require ground charging, and hence automated charging is particularly necessary. To achieve automatic landing charging, the accuracy of UAV landing is crucial for the docking of the charging interface. The single point positioning accuracy of global position system (GPS) or other navigation systems is above the meter level, which cannot meet the requirements of automatic landing charging of UAV [4, 5]. The real-time kinematic (RTK) positioning system can achieve positioning accuracy above the centimeter level, but the cost of the RTK system is high, and the positioning accuracy also cannot meet the accuracy requirements of the charging interface [6]. Machine vision systems have the advantages of low cost, higher © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 433–439, 2024. https://doi.org/10.1007/978-981-97-1072-0_44

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flexibility, and ease of installation, making them suitable for application in the recognition and positioning of unmanned aerial vehicle charging platforms. Authors in [7] use three black and white concentric circles as cooperative targets, and the UAV localization is achieved through edge detection and geometric matching. Authors in [8] have achieved high recognition frame rates by using target tracking algorithms that modify the tracking learning detection framework to locate composite rectangles, but the target graphics of these studies cannot provide directional information for UAVs. Authors in [9] used a combination of circular and square images with red and green direction guidance, providing ideas for UAV attitude positioning. However, the color guidance band occupied too small an area of the graph, and its robustness was not strong enough. Moreover, this study was only simulation, and the real-time performance was uncertain. Authors in [10] used a combination of concentric black and white triangles, and a oneway FLANN matching algorithm for feature point matching, which can provide strong position and direction information, but the real-time performance is not strong enough. This paper proposes a precise visual positioning scheme for a fast unmanned aerial vehicle charging platform to address issues such as positioning accuracy, speed, and cost of icon recognition during UAV landing. Using a landmark composed of two-level cooperative target graphics and a two-step feature segmentation method, the perimeter and area information of the connected domain in the image is utilized for preliminary fast coarse segmentation, followed by precise segmentation based on geometric features, and the goal of quickly filtering a large number of connected domains and achieving good real-time performance is achieved.

2 Cooperative Target Graph UAV’s electrodes are divided into positive and negative poles, and directional landmark graphs are required to assist in adjusting the UAV’s posture during landing, and docking with the correct electrodes of the charging platform. The landmark graph of the charging platform is shown in Fig. 1, consisting of red and blue directional arrow graphs. The red arrow graph has a large area and is used for rough positioning targets when UAV is at high altitude. The blue arrow graph has a small area and is used for precise positioning targets when UAV is near to ground.

Fig. 1. Landmark graph of the charging platform

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3 Target Detection The process of target detection mainly includes image pre-processing and target segmentation. 3.1 Image Pre-processing The process of image pre-processing is mainly aimed at reducing the interference of environmental noise. Gaussian filtering is widely used in image denoising, which can effectively eliminate Gaussian noise, and perform moderate smoothing on images. The noise of the target scene in this article is mainly Gaussian noise. Gaussian filtering is used in the image pre-processing process to smooth the RGB image and eliminate certain noise interference. 3.2 Target Segmentation 3.2.1 Color Segmentation The target graphics are mainly composed of red and blue, which have obvious color characteristics. The red and blue connected domains of the image can be segmented by color segmentation. Color segmentation is usually used in the HSV color space. The RGB space of the image is converted to the HSV space, and the values of H component are converted to (0, 180), while the values of S and V components are converted to (0, 255). The original image of target is shown in Fig. 2, and the red and blue components of the original image are shown in Figs. 3 and 4.

Fig. 2. Original image of target

3.2.2 Connected Domain Segmentation After color segmentation, the red and blue components of image are obtained. There will inevitably be some small connected domains in the two component images, such as the red interference in the upper left corner of Fig. 3 and the black stripe interference on the right, corresponding to the interference connected domain appearing in the upper left

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Fig. 3. Red components

Fig. 4. Blue components

corner of Fig. 4 and the stripe interference connected domain appearing on the right side. The generation of these small connected domains is due to the inevitable presence of targets in the environment that are similar in color to the target shape. During the color segmentation process, they are segmented together with the target shape, and further processing is necessary. In order to eliminate these small connected domains, reducing the computational complexity of subsequent processes, and improve detection speed, in the connected domain segmentation process, all connected domains in the component image are first detected and their areas are calculated. If the area is less than the threshold, no subsequent processing is performed. The experiment shows that when the size of landmark image is 800 mm * 800 mm, it is better to set the area threshold around 200 in the image obtained by the UAV at a distance of 10 m from the ground. 3.2.3 Feature Segmentation In order to quickly screen targets, this paper proposes a two-step feature segmentation method, which is divided into two parts: rough segmentation and precise segmentation. Rough segmentation performs preliminary and rapid screening based on the perimeter and area of the connected domain. Further, precise segmentation is performed, and final screening is performed based on the geometric features of the connected domain contour. This process can quickly filter a large number of connected domains and calculate target contour feature information.

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4 Target Location 4.1 Position Location In order to better guide the landing of UAVs, it is necessary to convert the pixel coordinate system into a world coordinate system with the UAV as the origin. Camera depth calibration can be achieved by recording the camera height H and the pixel area S of the target image multiple times to obtain a series of (H, S) data pairs and fitting the camera height function H (S). When the pixel area of the target image is detected, the fitted camera height function H (S) is substituted to obtain the camera height. Combined with the camera calibration data, the real 3D world coordinates are obtained. 4.2 Direction Determination By using vertex coordinates, the maximum two cosine angles composed of its four elements can be calculated to obtain their corresponding vertices, namely points A and D or points B and C in Fig. 1. The attitude direction of the target is taken as the direction of the vector AD (high altitude) or BC (near ground).

5 Experiments Firstly, experiments debugging in the laboratory are conducted to achieve the required accuracy, and then actual experiments outdoors are conducted. The experiment shows that in outdoor, due to the influence of outdoor lighting conditions and complex surrounding environment, it is not possible to recognize landmark graphics at a long distance. When the UAV flies near the landmark, it can accurately recognize the landmark graphics. However, due to the influence of outdoor wind, the UAV can only achieve centimeter level landing accuracy. 5.1 Experiments in Laboratory The experimental platform is the Raspberry Pi 4 Model B Rev development board. Through real-time testing with an airborne 640 * 480 pixel camera, the charging platform landmark graphics are obtained, and the coordinates, direction, and height of the landmark graphics are detected in real-time. The results are shown in Fig. 5. Image processing can obtain local positioning results with pixel level accuracy. The real-time performance of the algorithm is shown in Table 1, with an average time consumption of 35.3 ms per frame, approximately 28 frames per second, which is fully meeting the requirements of airborne real-time detection, and is roughly the same as the real-time performance of literature [7, 8].

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Fig. 5. Experimental results in laboratory. Table 1. Real-time performances of algorithm experiment number

1

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average value

time

40.4 ms

36.2 ms

29.5 ms

34.5 ms

35.7 ms

35.3 ms

5.2 Experiments in Outdoor Condition The UAV needs to recognize and locate the landmark graphics of the charging platform in the distance, flying directly above the landmark graphics, and then slowly landing. In outdoor experiments, as shown in Fig. 6, due to the influence of camera perspective, outdoor lighting conditions, and complex surrounding environment, it was found that it is impossible to recognize landmark graphics at a long distance. When the UAV flies near the landmark, it can accurately recognize the landmark graphics. However, due to the influence of outdoor wind, the UAV can only achieve centimeter level landing accuracy.

Fig. 6. Experimental results in outdoor condition.

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6 Conclusions The operation environment of distribution network line is complex, and the inspection workload is large. The automatic landing charging platform system proposed in this paper has the following advantages: effectively solving the visual problem of high-precision positioning during UAV landing; helping to achieve automatic UAV inspection, which will greatly improve work efficiency. The landmark composed of secondary cooperative target graphics used in this study can provide directionality and is suitable for scenarios with directional landing requirements. The system has been tested in real-time with an airborne 640 * 480 pixel camera, and the actual landing accuracy has reached centimeter level, which indicates that the scheme is feasible and has strong real-time performance, fully meeting the requirements of airborne real-time detection. It realizes the automatic landing and charging of UAVs, solves the problem of manual assistance required for UAV charging, and has important practical significance, which is conducive to the development of fully automatic UAV inspection. Acknowledgment. This work was supported by the Guangdong Power Grid Co., Ltd under Grant GDKJXM20180091.

References 1. Wu, S., Cai, C., Chen, Y., Chai, W., Yang, S.: Research progress and development trend of multi-rotor unmanned aerial vehicles wireless charging technology. Trans. China Electrotechn. Soc. 37(3), 555–565 (2022). (in Chinese) 2. Zhong, L., Hu, X., Liu, K.: Power tower anomaly detection from unmanned aerial vehicles inspection images based on improved generative adversarial network. Trans. China Electrotechn. Soc. 37(9), 2230–2240 (2022). (in Chinese) 3. Du, Q., Dong, W., Su, W., Wang, Q.: UAV inspection technology and application of transmission line. In: 2022 IEEE 5th International Conference on Information Systems and Computer Aided Education (ICISCAE), pp. 594–597. Dalian, China (2022) 4. Guan, J., et al.: Autonomous patrol technology and system on leapfrog-type charging uav automatic charging control based on machine vision. In: 2023 6th International Conference on Energy, Electrical and Power Engineering (CEEPE), pp. 412–417. Guangzhou, China (2023) 5. Lu, J., et al.: Autonomous patrol technology and system on leapfrog-type charging UAV automatic positioning of UAV based on GPS/RTK. In: 2023 6th International Conference on Energy, Electrical and Power Engineering (CEEPE), Guangzhou, China, pp. 844–848 (2023) 6. Umut, G., Mertcan, N.: Consistency analysis of RTK and Non-RTK UAV DSMs in vegetated areas. IEEE J. Select. Top. Appl. Earth Observ. Remote Sens. 16, 5759–5768 (2023) 7. Su, Y., Wang, T., Yao, C., Shao, S., Wang, Z.: A Target tracking method of UAV based on cooperative target. ROBOT 41(4), 425–432 (2019). (in Chinese) 8. Chen, F., Yue, W., Rao, Y., Xing, J., Ma, X.: Autonomous precision landing of drone based on improved TLD algorithm. Comput. Eng. Appl. 56(7), 247–254 (2020). (in Chinese) 9. Suo, W., Hu, W., Ban, L., Lin, Y., Qian, L.: Research on flight control of quad-rotor UAV based on visual image. Laser Technol. 44(4), 451–458 (2020). (in Chinese) 10. Jiang, Q., Wei, H., Zhang, K.: Research on inspection method of UAV photovoltaic based on markers 2020(1), 161–164 (2020). (in Chinese)

Statistical Distribution Law of CVT Test Data in Guangzhou Power Grid Hongling Zhou(B) , Shengya Qiao, Guocheng Li, Wangwei Ji, Sen Yang, Guangmao Li, Jun Xiong, and Feng Luo CSG Guangdong Guangzhou Power Supply Bureau, Guangdong 510620, China [email protected], [email protected]

Abstract. This paper analyzes the distribution law of dielectric loss and capacitance change rate of capacitor voltage transformer (CVT) in Guangzhou power grid since 2010, and analyzes the 90% and 95% quantile values. The results show that the dielectric loss and capacitance change rate conform to the approximate lognormal distribution and approximate normal distribution respectively, and the 95% quantile values are 0.187% and 1.68% respectively. At the same time, the influence of operating years and voltage level is discussed, and the influence of operating years on the 95% quantile value of normal CVT is negligible. For the influence of voltage level, the 95% quantile value of 500 kV CVT is less than other voltage. The 95% quantile values of dielectric loss of 110 kV, 220 kV and 500 kV CVT are 0.191%, 0.186% and 0.14%, respectively, and the absolute values of capacitance change rate are 1.77%, 1.71% and 1.19%, respectively. Through the above data statistics, it provides operation and maintenance ideas for the safe operation of CVT. Keywords: 95% quantile value · Operating years · Normal distribution

1 Introduction CVT is an important measurement and protection equipment in power system, which is widely used in the protection and measurement of 110 kV and above lines [1–3]. In the process of CVT operation, due to the influence of overvoltage and moisture, the capacitance deviates from the initial value, the dielectric loss increases, and the longterm operation leads to capacitor cell breakdown, which eventually leads to equipment damage and outage [4–6]. Therefore, through the test of CVT electrical parameters, defects in the early development stage can be found in advance [7, 8]. Take Guangzhou Power Grid as an example, for CVT, at present, it is mainly based on DL/T 596–2021 “preventive test code for electric power equipment” and Q/CSG 1206007–2017 “ test code for maintenance of power equipment” requirements: compared with the initial value, when the capacitance value exceeds ±2%, it is necessary to shorten the test period, and when the dielectric loss value exceeds 0.2%, the relationship between dielectric loss and voltage should be analyzed and the cause should be found out. During the actual operation process, in order to ensure the reliability and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 440–447, 2024. https://doi.org/10.1007/978-981-97-1072-0_45

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safety of the power grid operation, when the capacitance or dielectric loss exceeds the above allowable value, it is considered that the CVT has serious defect and does not have normal running conditions. However, at present, there is only an allowable value for CVT, and there is a lack of early warning value, so as to warn the development trend of equipment failure in advance and find potential hidden danger. This paper mainly analyzes the distribution form of CVT historical normal test data, obtains 90% and 95% quantile values, then puts forward the early warning values of dielectric loss and capacitance change rate, and analyzes the influence of operating years and voltage level, so as to provide reference for CVT differential maintenance [9, 10].

2 Analysis Method By 2023, Guangzhou Power Grid has a total of 1388 110 kV and above voltage transformers in operation, of which 110 kV,220 kV, 500 kV voltage transformers are 766,449,173 respectively. According to the statistics of CVT defects in the past 10 years, there are about 25 defects of dielectric loss or capacitance. The CVT dielectric loss and capacitance test data currently in operation of Guangzhou Bureau are selected, and the dielectric loss and capacitance exceeding the allowable value are eliminated as abnormal data, and a total of 9787 groups of normal data of dielectric loss and capacitance are obtained. Combined with the characteristics of data distribution, normal distribution and lognormal distribution are selected to fit, and the optimal fitting distribution is selected. Because the lognormal distribution requires that the data is not 0, the capacitance change rate is only fitted by normal distribution, and its probability density function is [11, 12]: f (x) = √

1 2π σ

e

− (x−u) 2

2

2σ

2 1 − (ln x−u) e 2σ 2 f (x) = √ 2π xσ

(1) (2)

Equation (1) is the probability density function of the Normal distribution, where μ is the average value, σ is the variance. Equation (2) is the probability density function of the Lognormal distribution, where μ is the average of the logarithms and σ is the variance of the logarithms.

3 Data Analysis 3.1 Global Analysis The dielectric loss and the capacitance change rate are fitted respectively, and the histogram and the fitted probability density function diagram are obtained as shown in Figs. 1–2. Where P1 is the expected cumulative probability, P2 is the actual cumulative probability, and P is the deviation from the fitted distribution form.

442

H. Zhou et al. 0.15

0.08

Proportion

0.06

Proportion

Basic data Normal

Basic data Normal Lognormal

0.04

0.1

0.05

0.02

0

0

0.05

0.1 0.15 Dielectric loss/%

(a) Dielectric loss

0.2

0

-2

-1 0 1 Capacitance change rate/%

2

(b) Capacitance change rate Fig. 1. Distribution histogram

(a) Dielectric loss

(b) Capacitance change rate Fig. 2. P1 −P2 curve and P- P2 error curve

In Fig. 1, it can be seen that for dielectric loss, it is closer to the lognormal distribution, while for capacitance change rate, the frequency distribution histogram fits well with

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the normal distribution. In Fig. 2(a), for dielectric loss, the data points are distributed near the oblique line, and the maximum error P is 6%, in Fig. 2(b), the capacitance change rate data are basically distributed on the oblique line, and the maximum error P is −4%. Statistics of the dielectric loss and capacitance change rate of 90% and 95% quantile values are shown in Table 1. Table 1. Eigenvalue value (%) Parameter

μ

σ

90% quantile fitting value

95% quantile 90% quantile fitting value actual value

95% quantile actual value

Dielectric loss

−2.49

0.56

0.17

0.208

0.174

0.187

Capacitance change rate

0.66

0.4

−0.69–1.49

−0.9–1.69

−0.73–1.48

−1.06–1.68

In Table 1, for 90% and 95% quantile values, the actual values of the dielectric loss are 0.174% and 0.187% respectively, and the deviation between the calculated value and the actual value is 2.3% and 11.2% respectively. For the capacitance change rate, the maximum absolute values of the actual values are 1.48% and 1.68% respectively, and the deviation between the calculated value and the actual value is 0.7% and 0.6%, respectively, indicating that the capacitance change rate fits well with the normal distribution. Correspondingly, the early warning values of dielectric loss and capacitance change rate can be set to 0.19% and ± 1.8%, respectively. 3.2 Influence of Operating Years This section analyzes the influence of different operating years on dielectric loss and capacitance change rate, and draws the frequency distribution histogram as shown in Fig. 3. The quantile values of 90% and 95% under different operating years are calculated to get Table 2. It can be seen from Fig. 3 that the histogram distribution of dielectric loss and capacitance change rate under different operating years is similar. Combined with Table 2, for different operating years, the 95% quantile value varies between 0.186% and 0.189% for dielectric loss, and the maximum absolute value for the capacitance change rate of 95% quantile varies between 0.163% and 0.172%. It can be considered that for good capacitive units, the dielectric loss and capacitance change rate are basically not affected by the operating years. 3.3 Influence of Voltage Level The influence of voltage level on dielectric loss and capacitance change rate is analyzed, and the cumulative distribution function is drawn according to 110 kV, 220 kV, 500 kV, the cumulative distribution function (CDF) is shown in Fig. 4, and the 90% and 95% quantile values under different voltage level are calculated to get Table 3.

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(a) Dielectric loss histogram

(b) Capacitance change rate histogram Fig. 3. Dielectric loss and capacitance distribution histogram

In Fig. 4, whether it is dielectric loss or capacitance change rate, the 500 kV CDF curve is closest to the left, and 220 kV CDF curve is close to 110 kV CDF curve. In Table 3, the 95% quantile value of dielectric loss of 110 kV, 220 kV and 500 kV are 0.191%, 0.186% and 0.14%, respectively, while the maximum absolute values of capacitance change rate are 1.77%, 1.71% and 1.19%, respectively. It means that the higher the voltage, the smaller the 95% quantile value is. The 110 kV value is close to the 220 kV value, mainly because the 220 kV CVT is composed of two capacitor units, and the voltage of each capacitor unit is the same as that of the 110 kV CVT.

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Table 2. Eigenvalue result of different operating years (%) Operating years

dielectric loss Mean value

95% quantile value

95% quantile value

capacitance change rate Mean value

90% quantile value

95% quantile value

0–5 years

0.094

0.172

0.186

0.33

−0.72–1.49

−1.11–1.68

6–10 years

0.091

0.171

0.186

0.45

−0.75–1.51

−1.12–1.72

11–15 years

0.101

0.179

0.187

0.46

−0.7–1.45

−0.91–1.63

16–20 years

0.106

0.174

0.189

0.31

−0.77–1.38

−1.04–1.64

100

CDF/%

80 110kV 220kV 500kV

60 40 20 0

0

0.05

0.1

0.15

0.2

Dielectric loss/%

(a) Dielectric loss curve 100

CDF/%

80

110kV 220kV 500kV

60 40 20 0 -2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Capacitance change rate/%

(b) Capacitance change rate curve Fig. 4. The CDF of capacitance and dielectric loss change rate

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H. Zhou et al. Table 3. Eigenvalue result of different voltage level (%)

Voltage Dielectric loss Capacitance change rate level Mean value 95% quantile 95% quantile Mean value 90% quantile 95% quantile value value value value 110 kV 0.107

0.183

0.191

0.57

−0.58–1.64

−0.96–1.77

220 kV 0.101

0.175

0.186

0.36

−0.9–1.49

−1.19–1.71

500 kV 0.068

0.105

0.14

0.22

−0.67–1.06

−0.81–1.19

4 Conclusion This paper mainly analyzes the distribution form and 95% quantile values of CVT dielectric loss and capacitance change rate normal data, and discusses the influence of operating years and voltage level. The main conclusions are as follows: 1) The dielectric loss and capacitance change rate accord with approximate lognormal distribution and approximate normal distribution respectively, and the 95% quantile values are 0.187% and 1.68%, respectively. And early warning values of dielectric loss and capacitance change rate can be set to 0.19% and ± 1.8%, respectively. 2) For normal CVT, the influence of operating years on dielectric loss and capacitance change rate is negligible. 3) The dielectric loss and capacitance change rate of 500 kV CVT are significantly less than 110 kV and 220 kV CVT. The 95% quantile values of dielectric loss of 110 kV, 220 kV and 500 kV CVT are 0.191%, 0.186% and 0.14%, respectively, and the absolute values of capacitance change rate are 1.77%, 1.71% and 1.19%, respectively. Acknowledgments. This research was funded by the China Southern Power Grid Co., Ltd. Science and Technology Project (GDKJXM20220079/ 030111KK52220002).

References 1. Han, H.N., Xiang, X., Wang, H.N., et al.: Study on temperature characteristic of capacitor voltage transformer. High Volt. Apparatus, 57(05), 123–129 (2021). (in Chinese) 2. Tong, T., Xu, B.C., Yuan, S.F., et al.: A CVT secondary voltage abnormal accident. Insulators Surge Arresters 306(02), 98–104 (2022). (in Chinese) 3. Zhou, X., Zhang, Q., Niu, B., et al.: Analysis on low secondary voltage of a 220kV bus CVT. In: 6th Asia Conference on Power and Electrical Engineering (ACPEE), pp. 1499–1503. IEEE (2021) 4. Zhou, F., Zhao, P., Lei, M., et al.: Capacitive voltage transformer measurement error prediction by improved long short-term memory neural network. Energy Rep. 8, 1011–1021 (2022) 5. Zhang, C., Ding, X.Z., Wang, B., et al.: Analysis and suppression of ferro-resonance of capacitive voltage transformer based on time domain analytical method. Guangdong Electr. Power 35(10), 56–64 (2022). (in Chinese)

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6. Chen, M.W., Li, D., Ji, Z.N., et al.: Analysis of an on-line monitoring insulation case of capacitor voltage transformer. High Volt. Apparatus 48(05), 99–104 (2012). (in Chinese) 7. Yin, D., Yu, W., Li, Q., et al.: Experimental study on transient overvoltage measurement based on capacitive voltage transformer. In: 4th International Conference on Power and Energy Technology (ICPET), pp. 222–227. IEEE (2022) 8. Costa, F., Mingotti, A., Peretto, L., et al.: Combined effect of temperature and humidity on distorted currents measured by Rogowski coils. In: 20th International Conference on Harmonics & Quality of Power (ICHQP), pp. 1–6. IEEE(2022) 9. Xiong, J., Lu, G.J., Wang, Y., et al.: HV switchgears state judging and operation and maintenance strategy based on empirical cumulative distribution characteristics of TEV PD Levels. Southern Power Syst. Technol. 10(02), 38–43 (2016). (in Chinese) 10. Zhao, C., Li, D., Bai, H., et al.: The statistical distribution of the DGA data of transformers and its application. In: IEEE International Conference on Dielectrics (ICD), vol. 1, pp. 497–500. IEEE (2016) 11. Li, G.M., Zhao, L., Cheng, Y.C.: Analysis on off-line detection results of 110 kV ZnO arrester. Insulators Surge Arresters 294(02), 111–118 (2020). (in Chinese) 12. Zhao, C.Z., Bai, H.Y., Cheng, Y.C., et al.: Statistic distribution of the chromatographic data of running transformer oil. High Voltage Apparatus 54(12), 180–187 (2018). (in Chinese)

A Transformer Insulation Life Assessment Method Considering Variational Annual Load Coefficient Chenying Yi1 , Qianyi Chen1,2(B) , Qingfa Chen1 , Dechao Li3 , and Chen Wang3 1 Electric Power Research Institute of Guangxi Power Grid Co., Ltd, Nanning 530023, China

[email protected]

2 Guangxi Power Grid Equipment Monitoring and Diagnosis Engineering Technology Research

Center, Nanning 530023, China 3 Hechi Power Supply Bureau of Guangxi Power Grid Co., Ltd, 547000 Hechi, China

Abstract. The transformer insulation life determines the operating state and useful life of the transformer, and accurately predicting the remaining useful life can effectively improve the transformer maintenance efficiency. A10 kV oil-immersed stereo roll core amorphous metal transformer is taken as the research object in this paper, based on the calculation of hot spot temperature, the transformer insulation life loss under variable load coefficient was studied, and the remaining insulation and useful life of transformer were predicted. The results show that the proposed method can improve the practicability of transformer insulation life assessment in the actual operation and maintenance of transformers. Keywords: oil-immersed power transformer · hot spot temperature · load coefficient · insulation life · useful life

1 Introduction The electrical and mechanical characteristics of the transformer insulation structure are difficult to measure, while the researches of thermal characteristics are relatively simple, and early researchers took thermal characteristics as the main factor affecting the deterioration of transformer insulation, so transformer insulation life evaluation is associated with the hot spot temperature research. Since the transformer hot spot temperature usually appears on the transformer winding, the insulation life of the transformer winding is one of the main factors that determine the operating state and transformer useful life. With the increase of the transformer operating life, CO and CO2 gas will be generated in the transformer insulation aging oil, and the CO and CO2 gas concentration are strongly correlated with the operating life [1, 2], so the degree of transformer insulation aging can be evaluated according to the CO and CO2 concentration. In addition, the concentration of dissolved gases in the transformer, including carbon dioxide, ethane, ethylene, etc., these gases can also be analyzed by dissolved gas analysis (DGA) [3, 4] to evaluate transformer insulation life. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 448–456, 2024. https://doi.org/10.1007/978-981-97-1072-0_46

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Cheng et al. [5] used the Weibull distribution and Arrhenius reaction law to establish a static aging failure model based on the hot spot temperature, and the winding hot spot temperature was obtained. Then the gray target theory was used to dynamically correct the model, and the dissolved gas analysis (DGA) data in power transformer oil was combined to dynamically correct the life expectancy calculated by the model. Based on fluid-thermal field calculation, Deng et al. [6] proposed a feature set of HST on the transformer core shell, which was taken as the input parameters of a support vector regression (SVR) machine learning model, thus to predict the HST. Thango et al. [7, 8] presented a feed-forward artificial neural network (FFANN) for predicting the degree of polymerization (DP) and life loss in oil-submerged transformers based on the 2-Furaldehyde (2FAL) concentration. This paper took the 10 kV oil-immersed stereo roll core amorphous metal transformer as the research object, based on the HST calculation results, the transformer insulation life loss under the condition of variational annual load coefficient was considered, and the remaining insulation and useful life of the transformer were predicted.

2 Transformer Hot Spot Temperature Calculation Method 2.1 Multiphysics Simulation Computational Models A 10 kV oil-immersed stereo roll core amorphous metal transformer is taken as the research object, which is shown in the following (Fig. 1).

(a)

(b)

Fig. 1. Multiphysics simulation model. (a) transformer actual structure; (b) transformer model.

2.2 Empirical Formula for Transformer Transient Hot Spot Temperature Calculation A hot spot temperature estimation formula is given in the IEEE standard, namely:  θh = θa + θoi + θor ×



1 + RK 2 1+R

x

 − θoi

× f1 (t) + θhi

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C. Yi et al.   + Hgr K y − θhi × f2 (t)  x 1 + RK 2 θh = θa + θor × + {θoi − θor 1+R x   1 + RK 2 × f3 (t) + Hgr K y × 1+R

(1)

(2)

f1 (t) = 1 − e−t/(k11 ×τo )   f2 (t) = k21 × 1 − e−t/(k22 ×τw ) − (k21 − 1) × 1 − e−t/(τo /k22 )

(4)

f3 (t) = e−t/(k11 ×τo )

(5)

(3)

where θ h is the transformer hot spot temperature; θ a is the ambient temperature; θ or is the top oil temperature rise under rated loss; θ oi is the top oil temperature rise before the load change; θ hi is the initial gradient of hot spot temperature to top oil temperature; R is the ratio of load loss and no-load loss at rated current; K is the operating load coefficient; x is the transformer oil index; H gr is the temperature difference between the hot spot and the top oil of the winding, and y is the winding index. The constants K 11 , K 21 , K 22 , τ o and τ w are the characteristic parameters of the transformer; τ o is the transformer average oil time; τ w is the transformer winding time. The transient changes in transformer hot spot temperature under rated condition is obtained through numerical calculations,and the Levenberg-Marquardt method (LM) [9] combined with the universal global optimization (UGO) [10] were used to determine the time constant (τo and τw). The results are shown in Table 1. Table 1. Transformer winding and oil time constants for different fitting methods. Parameters

LM + UGO

transformer oil time constant

161.79

winding time constant

13.72

Thus the transient hot spot temperature calculation formula can be further expressed as: θh = 89.89−33.3 × e−t/161.79 −31.6 × e−t/27.44

(6)

3 Insulation Life Assessment of Oil-Immersed Transformers 3.1 Insulation Aging Calculation Method For the thermally modified paper used in oil-immersed transformers, when only considering the influence of hot spot temperature on its insulation life, the insulation aging rate at the transformer hot spot temperature of 110 °C is used as the reference value. Then the insulation relative aging rate and insulation life loss are calculated respectively 

V =e

15000 15000 383 − θh +273



(7)

A Transformer Insulation Life Assessment Method

L=

t2

Vdt ≈

N

t1

n=1

Vn × tn

451

(8)

where θ h is the transformer hot spot temperature; L is the insulation life loss of oilimmersed transformer in the time period t 1 to t 2 ; N is the number of time intervals in this time period; V n and t n are the insulation relative aging rate in the nth time interval and time, respectively. If the annual life loss of the transformer is estimated at one minute interval, the hot spot temperature and insulation life loss of the transformer must be calculated according to the load coefficient and ambient temperature of the transformer within one minute. Then the transformer insulation life loss in one hour, one day, one month, and up to one year is iteratively calculated. When the transformer is in operation to the k-th year, its annual insulation life loss and remaining insulation life expression is Lrk = Ln −

k 

Lk

(9)

n=1 N 12 N 30 N 24 N 60

Lk =

Vn × tn

n=1 n=1 n=1 n=1 N 12 N 30 N 24 N 60

(10) tn

n=1 n=1 n=1 n=1

where t n is the 1-min interval; V n is the n-th interval; N 12 , N 30 , N 24 , and N 60 are the months, days, hours, and minutes of the k-th year, respectively; L rk is the remaining insulation life after the transformer runs for k years; L n is the transformer insulation useful life. The experimental value of the insulation useful life of the distribution transformer is 20.55 years. 3.2 Insulation Life Loss Calculation In order to accurately analyze the influence of transformer load coefficient (LC) on insulation life loss, the time interval of load coefficient in insulation life calculation is taken as one hour, and the load coefficient of the transformer is considered to be constant in this time period. Combined with the measurement data of the top oil temperature of the transformer, the temperature gradient of the hot spot temperature to the top oil temperature and the ambient temperature (AT), the hot spot temperature (HST) variation curve of the transformer in one day can be calculated and plotted, as shown in Fig. 2. The insulation relative aging rate of oil-immersed transformer corresponding to the hot spot temperature variation curve in Fig. 3 and the insulation life loss curve over time in a single day is shown in Fig. 4. The final calculation is that the insulation life loss of the transformer in this day is 0.0093 days. According to the calculation principle, the annual insulation life loss curve of the oil-immersed transformer can be plotted, so as to calculate the annual insulation life loss of the transformer. This paper is mainly concerned with the influence of variational annual load coefficient on insulation life loss, and the variational annual load coefficient

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Fig. 2. Transformer hot spot temperature variation curve under a given load curve.

Fig. 3. Transformer insulation life loss variation curve under a given load curve.

is mainly reflected in the daily variational load coefficient, so the calculation process of annual insulation life loss can not be solved. The proportion of transformer insulation life loss in one day is equivalent to the annual insulation life loss coefficient, that is, the transformer annual insulation life loss at the end of the first year is considered to be 0.0093 years.

4 Transformer Remaining Life Prediction Considering Variational Annual Load Coefficient In the actual operation process, the load coefficient of the transformer continues to increase with the economic development of the transformer installation area, resulting in its load coefficient and annual insulation life loss gradually increasing, but the specific impact of variational annual load coefficient on insulation life loss is often ignored in transformer insulation life assessment. Therefore, this paper introduces the annual load coefficient in the transformer insulation life evaluation, and realizes the evaluation and prediction of the remaining insulation life and remaining useful life of the transformer by the collection and prediction of the transformer annual load coefficient historical data.

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4.1 Transformer Remaining Insulation and Useful Life Prediction Method Based on the calculation method of insulation aging and insulation life loss of oilimmersed transformers, when the transformer continues to operate until the kth year, the specific realization process of the remaining insulation life calculation and remaining useful life prediction mainly includes the following four steps: (1) Take the first year of operation data as the reference value to understand the change of transformer variation curve and the variation of annual load coefficient from the first year to the k-th year; (2) According to the load curve and ambient temperature, the annual insulation life loss of the transformer is calculated, and the remaining insulation life of the transformer is corrected and updated; (3) According to the variation of the annual load coefficient of the transformer in k years, the Levenberg-Marquardt method was used to predict the annual load coefficient of the transformer in the k + 1 year, and the annual insulation life loss in the k + 1 year was calculated. (4) Based on the calculated value of the remaining insulation life after the k-th year of operation and the predicted value of the annual insulation life loss in the k + 1 year, the remaining service life of the transformer is calculated as follows Lrk = Lrk /Lk+1

(11)

where L rk and L’rk are the remaining insulation and useful life of the transformer after the k-th year, respectively, and L k+1 is the predicted annual insulation life loss in the k + 1 year. 4.2 Transformer Remaining Insulation and Useful Life Prediction Applications Taking the first year load coefficient as a reference value, it is assumed that with the increase of regional economic development and population density, the variational annual load coefficient of the oil-immersed transformer is shown in Table 2. In the table, the operating life of the transformer increases, the annual load coefficient gradually increases, and with the increase of the operating life of the transformer, the annual load coefficient increases and shows a trend of gradual saturation. Considering that the annual load coefficient of transformer is mainly reflected in the variation of daily load curve in different years, the proportional coefficient of the transformer’s annual load coefficient is equivalent to the growth coefficient of the daily load curve in this paper. That is, its daily load curve is the product of the annual load coefficient and the daily load curve in Fig. 4 after k years of operation. In Fig. 4, the hot spot temperature of the transformer gradually increases with the increase of operating life, and with the saturation of the annual load coefficient, the trend of hot spot temperature increase is gradually slowing down. Corresponding to the hot spot temperature curve of the oil-immersed transformer in Fig. 5, when the transformer is operated to the fourth year, its insulation life loss increases significantly, mainly because the transformer hot spot temperature is in a state of exceeding the temperature limit for a long time. Moreover, the annual insulation life

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C. Yi et al. Table 2. Variation law of oil-immersed transformer annual load coefficient.

Transformer operating life

Annual load coefficient

1

1.0

2

1.20

3

1.35

4

1.45

5

1.50

6

1.53

Fig. 4. Relationship between hot spot temperature and annual load coefficient of oil-immersed transformer.

loss and the variational annual load coefficient are not simple linear relationships, that is, the annual insulation life loss in the k-th year must be calculated according to the influence of the annual load coefficient reflected on the hot spot temperature.

Fig. 5. Relationship between hot spot temperature and annual load coefficient of oil-immersed transformer.

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According to the variation of the annual load coefficient of the transformer in Table 3, the Levenberg-Marquardt method was used to predict the annual load coefficient of the transformer in the seventh year, and the predicted value was 1.552. According to the calculation process of annual insulation life loss, the annual insulation life loss in the seventh year is calculated to be 1.6856 years, and the remaining insulation and useful life prediction values of the oil-immersed transformer are shown in Table 4. Table 3. Remaining insulation and useful life prediction values of oil-immersed transformers. Transformer operating life

Annual load coefficient

Insulation life loss (y)

Remaining insulation life (y)

Remaining useful life (y)

1

1.0

0.0093

20.5407

344.6426(e)

2

1.20

0.0596

20.4812

82.2869(e)

3

1.35

0.2489

20.2322

31.1936(e)

4

1.45

0.6486

19.5837

18.7189(e)

5

1.50

1.0462

18.5375

13.3067(e)

6

1.53

1.3931

17.1444

10.1711(e)

1 Superscript (e) indicates the predicted value

According to the prediction results of Table 4, the remaining insulation life and useful life of the transformer in the same year are very different. Where the remaining useful life of the transformer represents its remaining useful life under the condition of variational load, and the insulation life of the transformer is mainly used to express the effective life of its insulation. Since the hot spot temperature of the transformer is not maintained at 110 °C for a whole year, it is not equivalent to the actual operating life of the transformer. Therefore, the proposal and calculation prediction of the remaining useful life of the transformer have more reference significance for its operation and maintenance.

5 Conclusions In this paper, a 10 kV oil-immersed stereo roll core amorphous metal transformer is used as the research object. The transient changes in transformer hot spot temperature under rated condition is obtained through numerical calculations,and the LevenbergMarquardt method (LM) combined with the universal global optimization (UGO) were used to determine the time constant. Then, taking the transformer hot spot temperature as the reference value, combined with the historical data of the transformer’s annual load coefficient, the LM algorithm was used to evaluate and predict the remaining insulation life and remaining useful life of the transformer. The results show that the proposed method can effectively evaluate the insulation life of transformers, and has reference significance for the daily operation and maintenance of transformers.

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Acknowledgments. This work was supported the Science and Technology project of Guangxi Power Grid Company under Grant GXKJXM20220126.

References 1. Yang, X., Chen, W., Li, A., Yang, C., Xie, Z., Dong, H.: BA-PNN-based methods for power transformer fault diagnosis. Adv. Eng. Inform. 39, 178–185 (2019) 2. Saha, T.K.: Review of time-domain polarization measurements for assessing insulation condition in aged transformers. IEEE Trans. Power Deliv. 18, 1293–1301 (2003) 3. Jia, J., Tao, F., Zhang, G., Shao, J., Zhang, X., Wang, B.: Validity evaluation of transformer DGA online monitoring data in grid edge systems. IEEE Access 8, 60759–60768 (2020) 4. Wang, L., Littler, T., Liu, X.: Gaussian Process multi-class classification for transformer fault diagnosis using dissolved gas analysis. IEEE Trans. Dielectr. Electr. Insul. 28, 1703–1712 (2021) 5. Cheng, L., Yu, T., Wang, G., Yang, B., Zhou, L.: Hot spot temperature and grey target theory-based dynamic modelling for reliability assessment of transformer oil-paper insulation systems: a practical case study. Energies 11, 249 (2018) 6. Deng, Y., et al.: A method for hot spot temperature prediction of a 10 kV oil-immersed transformer. IEEE Access 7, 107380–107388 (2019) 7. Thango, B.A.: Feedforward artificial neural network (FFANN) application in solid insulation evaluation methods for the prediction of loss of life in oil-submerged transformers. Energies 15, 8548 (2022) 8. Thango, B.A., Bokoro, P.N.: Prediction of the degree of polymerization in transformer cellulose insulation using the feedforward backpropagation artificial neural network. Energies 15, 4209 (2022) 9. Ranganathan, A.: The levenberg-marquardt algorithm. Tutoral LM Algorithm 11, 101–110 (2004) 10. Shiyou, Y., Guangzheng, N., Yan, L., Baoxia, T., Ronglin, L.: A universal tabu search algorithm for global optimization of multimodal functions with continuous variables in electromagnetics. IEEE Trans. Magn. 34, 2901–2904 (1998)

Die Matching Performance of Ultra-Thin Titanium Sheet Driven by Polyurethane During Electromagnetic Forming Runze Liu1,2 , Xiaotao Han1,2 , Pengxin Dong1,2 , and Zelin Wu1,2,3(B) 1 National Pulsed High Magnetic Field Science Center, Huazhong University of Science and

Technology, Wuhan 430074, China [email protected] 2 State Key Laboratory of High Power Electromagnetic Engineering and New Technology, Huazhong University of Science and Technology, Wuhan 430074, China 3 Shenzhen Interdisciplinary Research Center for High Magnetic Field Physics, Shenzhen University, Shenzhen 518000, China

Abstract. Electromagnetic forming of ultra-thin titanium plates requires high conductivity drive plates, resulting in low die matching rates. Rubber is expected to improve the die matching performance because of large deformation characteristics. This paper takes polyurethane and TA1 pure titanium as research objects, and carries out electromagnetic V-bending experiments under different driving modes to explore the influence of polyurethane on die matching performance. The results show that polyurethane can effectively inhibit the rebound of the workpiece while improving the forming uniformity, the average rebound angle is reduced from 14.5° to 9°, and the die matching rate is increased by 37.9%. Electromagnetic V-bending finite element model is established to analyze the mechanism of polyurethane. The results show that polyurethane maintains good contact with the workpiece during the forming period, can provide a longer contact force when colliding with die, and oscillation deformation occurs after collision with die, and the workpiece is subjected to high-frequency oscillating impact force, which effectively suppresses the rebound of the workpiece and improves die matching performance, and springback is reduced nearly 5 times. Keywords: Thin titanium electromagnetic forming · V bending · polyurethane · springback inhibit

1 Introduction Because of low density and high specific strength, titanium is considered as high quality matrix of hydrogen fuel cell bipolar plates. However, the high strength, low elongation, ultra-thin and high aspect ratio of microchannel make it have poor die matching rate and rebound phenomenon in forming process, resulting in low dimensional accuracy and affecting the assembly and battery efficiency. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 457–465, 2024. https://doi.org/10.1007/978-981-97-1072-0_47

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Electromagnetic forming is a high energy rate forming technology, the workpiece deformation speed reaches 100−300 m/s. According to research [1–7], electromagnetic forming has the following advantages: (1) increase forming limit, (2) inhibit wrinkling of the workpiece, (3) reduce rebound. Therefore it has a unique advantage in forming bipolar plates. For low conductivity metals such as titanium, high conductivity metal is usually used as driving plate. Li [8] from studied the influence of driving plate material, thickness, acceleration distance and discharge parameters on the forming of titanium bipolar plate based on the uniform pressure actuator. Under the conditions of 150 µF capacitance, 12 kV discharge voltage and 4 mm acceleration distance, a bipolar plate with channel depth of 0.4 mm was obtained, and the final die matching rate reached more than 90%. Wu [9] proposed a new type of uniform pressure actuator, and based on this, the maximum channel depth of 0.34mm and channel fluctuation of 3.75% were achieved in titanium bipolar plates forming under discharge energy of 7.5 kJ. Although the current die matching rate of titanium bipolar plates has reached 90%, there are still great challenges in high precision titanium bipolar plates forming. In rubber stamping, Liu [10] analyzed two modes of medium steel die. The results show that for concave die, the thinning range of workpiece increases with the decrease of channel width, making forming more difficult; for convex molds, with the reduction of the channel width, the workpiece forming becomes easier. Jin [11] studied the influence of soft die on forming quality. The result shows that the thicker the rubber soft die and the lower the hardness, the more beneficial to improve the formability. Shang [12] used drive plate and soft die to drive 0.1 mm stainless steel, achieving the forming of bipolar plates at a speed of several meters per second, and prepared a bipolar plate with a depth of 0.26 mm. In a similar way, Wang [13] achieved the preparation of stainless steel bipolar plates with a depth of 0.44 mm and a filling rate of 88.9%. Cai [14] studied the effect of soft die on uniform impact force in electrohydraulic forming of metal bipolar plate, the results show that the soft die making the force more uniform. The above researches show that rubber can uniform force and improve the formability, however, the mechanism of improving the formability and inhibiting the springback of rubber under high-speed forming is rarely studied. Therefore, this paper takes polyurethane rubber and TA1 titanium as research objects, V-bending experiments under different driving modes were carried out to verifies the effect of rubber. A finite element simulation model was established to analyze the deformation process, contact force and velocity of the workpiece, and the mechanism of polyurethane to improve the die matching performance and restrain the rebound was revealed.

2 Electromagnetic V Bending Experiment 2.1 Experimental Setup In this paper, AA1060 aluminum plate with the size of 135 mm × 20 mm × 1 mm is used as the driving plate; polyurethane rubber with the size of 35 mm × 15 mm × 1 mm is used as the elastic medium; and TA1 titanium plate with the size of 35 mm × 15 mm

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× 0.1 mm is used as the V bending workpiece. The size of the die is 45 mm × 25 mm × 15 mm, and the angle is 120°. In traditional electromagnetic forming, the titanium plate is placed on the aluminum driving plate, and the aluminum plate drives the titanium plate to collide with die at high speed after discharge; while in polyurethane electromagnetic forming, a layer of polyurethane rubber is placed between the titanium plate and the aluminum driving plate, and the aluminum plate drives the polyurethane rubber to collide with die at high speed together with the titanium plate after discharge. The whole device is placed in a vacuum chamber to conduct experiments in a low vacuum environment. Figure 1 shows the experimental setup.

Fig. 1. Experimental setup

2.2 Result Experiments were conducted under the experimental conditions of air pressure of 10 kPa, acceleration distance of 6 mm, crimping torque of 14 N-M, capacitance of 320 µF, and discharge voltage of 3 kV to 4.5 kV with an interval of 0.5 kV. It was finally found that the aluminum plate drive workpiece was most closely fitted to die at a discharge voltage of 4 kV, and the experiments were conducted at a voltage of 4 kV. The experimental results are shown in Fig. 2, and the measured and calculated results are shown in Table 1.

3 Finite Element and Performance Analysis 3.1 Simulation Model A 2D finite element simulation model of V-bending driven by different media was established based on ABAQUS, and the mesh of rubber model is shown in Fig. 3(a), while the aluminum model is the same as it except for the missing rubber part. The load is calculated by COMSOL electromagnetic model shown in Fig. 3(b). The coil current is measured in experiment to improve the accuracy of the model, and the results are shown in Fig. 5. The calculated electromagnetic force is applied to the driver plate in ABAQUS model through the body load.

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Fig. 2. V-bending results: (a) driven by aluminum (b) driven by rubber

Table 1. Experimental results of V-bending under different driving modes Diving mode

Angle(°)

Rebound(°)

Average(°)

aluminum sheet

102

18

14.5

aluminum sheet

109

11

titanium plate

109

11

titanium plate

113

7

rebound inhibition

/

/

9 5.5(37.9%)

The deformation behavior of workpiece was calculated using Explicit/Dynamic for 400 µs. All the parts except the workpiece were set as rigid bodies. AA1060 aluminum and TA1 titanium properties were defined by using the Johnson-Cook (J-C) model, and J-C parameters of TA1 titanium are: A = 182.55E6Pa, B = 441.1E6Pa, n = 0.5343, C = 0.0343, J-C parameters of AA1060 aluminum are: A = 76.19E6Pa, B = 49.2E6Pa, n = 0.4522, C = 0.4522. 0.4522, C = 0.022, the parameters are from previous work [15]. Rubber properties were defined by the Mooney-Rivlin model, whose parameters were obtained by fitting the results of stretching 1 mm thick rubber. The multiple contact pairs present in the model are set as face-to-face contacts, the rubber surface is set as self-contact. The material parameters are shown in Table 2 (Fig. 4). 3.2 Deformation Process The deformation process of the workpiece driven by different media is shown in Fig. 5. From Fig. 5(a), the workpiece driven by the aluminum is in contact with the die at 142 µs, the subsequent forming process of the driver plate and the workpiece separate from the side to the center; at 176 µs when the center area and the die contact, the workpiece can’t completely reach the bottom of the die, resulting a large gap, at this time the side wall of drive plate and the workpiece has long been separated; finally at 400 µs, the drive plate and the workpiece are completely separated, and there is a gap between workpiece and die at the sidewall.

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d

(a) V-bending finite element simulation model

(b) Electromagnetic finite element model

Fig. 3. Finite element model N

N

Coil current(A)

N

N

N

Electromagnetic force(N)

coil current emulate current emulate force

N





 



Time( s)

Fig. 4. Electromagnetic model simulation results Table 2. Finite element model material parameters Material

Parameter

Value

TA1 titanium

Young’s modulus

105.88 GPa

Poisson’s ratio

0.33

AA1060 aluminum

Rubber

Densities

4510 kg/m3

Conductivity

2.08 × 106 S/m

Young’s modulus

68 GPa

Poisson’s ratio

0.33

Densities

2700 kg/m3

Conductivity

2.05 × 107 S/m

Densities

1100 kg/m3

Mooney-Rivlin

C10 = 0.388, C01 = 1.159

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From Fig. 5(b), the rubber-driven workpiece is not yet in contact with die at 142 µs, and the rubber maintains good contact with the workpiece during the forming process, the center area is in contact with die at 192 µs and the workpiece almost reaches the bottom of the die, the rubber and the workpiece remain in contact with the die sidewall up to 400 µs. The final contours of the workpieces driven by different media are shown in Fig. 6. The contour of the workpieces driven by rubber almost completely wraps the contour of the workpieces driven by aluminum, the sidewalls are more expanded, the angle is closer to 120°, which is consistent with the experimental results. 10

Height(mm)

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Fig. 5. Deformation process: (a) driven by aluminum plate (b) driven by rubber

Fig. 6. Simulation results of workpiece contour under different driving modes

3.3 Contact Force and Velocity Analysis The central node of the workpiece is selected for analysis, and the results of the contact force given by rubber and aluminum and the velocity in the deformation process of different driving modes are shown in Fig. 7. From Fig. 7, when driven only by aluminum, the central point of the workpiece collides with die at about 170 µs. Before collision, the contact force between the driving plate and workpiece is messy, and there is a zero-value time exists, so more than one separation and re-collision phenomenon occurs between the driving plate and workpiece, which results in a part of the energy was wasted. After the collision, the zero contact force means there is no contact between the driving plate and workpiece, resulting in the V-shaped feature at the bottom of the workpiece is not obvious enough, and it is not possible to match the die. By adding the rubber, the moment of collision is around 190 µs. Before the collision, the contact force between the rubber and workpiece is almost no obvious fluctuation, so the workpiece and rubber maintain good contact. Unlike the workpiece driven by aluminum, after the collision the contact force between the workpiece and rubber still exists for a certain period of time, so the workpiece has more energy to flow and deform, the bottom V-shaped feature is obvious, which fits the die better. In addition, at the time

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of collision, the rubber acts on the workpiece for a longer period of time and with a greater force, which leads to a greater forming depth and improves formability. From the velocity curve, the velocity of workpiece driven by aluminum rises faster than driven by rubber, and the moment of collision is more advanced. After the collision, the speed of the workpiece decreases rapidly, but the aluminum-driven workpiece has greater fluctuation and the rebound speed is great, while the aluminum was unable to inhibit the rebound, resulting in the bottom not matching the die. 8 1.0

-200

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-7 -8 -9

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Time ( s)

Fig. 7. Contact force and velocity of the central node of the workpiece

Fig. 8. Springback results :(a) driven by aluminum (b) driven by rubber

The center node of the side wall of workpiece is selected for analysis, and the contact force of different driving methods is shown in Fig. 9. Similar to the central region, when driven by aluminum, the driving plate separates from the workpiece several times before collision, then completely separates from the workpiece after giving a large and short impact force at the moment of collision. In the case of rubber, the rubber maintains good contact with the workpiece before collision, and gives an impact force of relatively low amplitude and long duration at the moment of collision. Unlike the central node, after the collision the rubber itself undergoes a continuous process of conversion between elastic deformation energy and kinetic energy, which in turn leads to a prolonged, high-frequency oscillatory contact with the workpiece, ultimately resulting in a better matching performance on the sidewalls. Comparing the amplitude of the contact force given to the center and sidewalls, the impact force on different areas is very heterogeneous when driven by aluminum and

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Time( s)

Fig. 9. Contact force of the central node of the workpiece sidewall

the contact force on the sidewalls is greater, which increases the rebound, whereas the rubber has a more homogeneous impact force on the different areas of the workpiece, which leads to a smaller rebound. The uneven contact force may be one of the reasons for the impact on formability. 3.4 Springback Analysis The springback simulation of workpiece after forming was carried out to analyze the effect of polyurethane on the springback. The simulation results with different driving methods are shown in Fig. 8. From Fig. 8, the amount of springback of the polyurethane-driven workpiece is nearly 5 times less than that of the aluminum plate-driven one, which represents better formability and lower springback. The reason may be that the polyurethane has a long time high-frequency oscillatory contact with the workpiece after the collision, which converts more elastic strain into plastic strain, reduces the residual stress of the workpiece, and ultimately reduces the springback of the workpiece.

4 Conclusions (1) In this paper, electromagnetic forming V bending experiments were carried out under different driving modes, and the results show that the rubber makes the rebound of the workpiece reduced, the rebound is suppressed, and the forming performance is improved. The average rebound angle of the workpiece was reduced from 14.5° to 9°, and the rebound suppression effect reached 37.9%. The addition of rubber improves the forming uniformity of the workpiece, and the difference in the rebound angle between the two sides of the workpiece is reduced from 7° to 4°. (2) The simulation results show that there is separation and re-contact phenomenon when driven by aluminum, and there is no contact between workpiece and aluminum after collision with die, therefore the rebound of the workpiece cannot be suppressed. Workpiece driven by rubber and rubber remain good contact, high-speed deformation of rubber occurs after collision with die, and high-speed shock contact with

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the workpiece improves formability and die matching performance and effectively suppresses rebound. (3) The springback analysis shows that the high-speed shock collision of rubber on the workpiece effectively reduces the amount of springback, and the final springback is reduced by nearly five times, which improves the die matching performance. Acknowledgments. This work was funded by National Natural Science Foundation of China (No. 52077092); Key R&D Program of Hubei Province, China (No. 2021BAA174); China Postdoctoral Science Foundation (No. 2023M732346).

References 1. Takahashi, M., Murakoshi, Y., Terasaki, M., et al.: Study on electromagnetic forming. V. Free bulging of high-strength-metal plates. II. J. Mech. Eng. Lab. (Jpn.) 42(1), 1–8 (1988) 2. Li, F.Q., Zhao, J., Mo, J.H., et al.: Comparative study of the microstructure of Ti-6Al-4V titanium alloy sheets under quasi-static and high-velocity bulging. J. Mech. Sci. Technol. 31(3), 1349–1356 (2017) 3. Balanethiram, V.S.: Hyperlasticity: Enhanced Formability of Sheet Metals at High Workpiece Velocity. The Ohio State University (1996) 4. Li, C.F., Yu, H.P.: Progress in the theoretical study of electromagnetic molding technology. J. Plasticity Eng. 05, 1–7 (2005). (in Chinese) 5. Meng, Z.H., Huang, S.Y.: Influence factors of material formability in high rate molding. Forging Press. Technol. 04, 1–6 (2007). (in Chinese) 6. Jin, Y.Y., Yu, H.P.: Research progress of electromagnetic molding technology for plates. Prec. Molding Eng. 13(05), 1–9 (2021). (in Chinese) 7. Liu, W., Meng, Z.H., Huang, S.Y.: Research progress of electromagnetic forming process and theory of aluminum alloy sheet. Prec. Molding Eng. 13(05), 22–29 (2021). (in Chinese) 8. Li, Z.Z.: Research on the method and process of uniform pressure electromagnetic molding of titanium bipolar plates for hydrogen fuel cells. Huazhong University of Science and Technology (2020). (in Chinese) 9. Wu, Z.L.: Electromagnetic molding of thin-walled plates based on internal field uniform pressure actuator. Huazhong University of Science and Technology (2021). (in Chinese) 10. Liu, Y., Hua, L., Lan, J., et al.: Studies of the deformation styles of the rubber-pad forming process used for manufacturing metallic bipolar plates. J. Power Sour. 195(24), 8177–8184 (2010) 11. Jeong, M.G., Jin, C.K., Hwang, G.W., et al.: Formability evaluation of stainless steel bipolar plate considering draft angle of die and process parameters by rubber forming. Int. J. Precis. Eng. Manuf. 15(5), 913–919 (2014) 12. Shang, J., Wilkerson, L., Hatkevich, S., et al.: Commercialization of fuel cell bipolar plate manufacturing by electromagnetic forming. In: 4th International Conference on High Speed Forming—ICHSF. Columbus: American Institute of Physics, pp. 47–56 (2010) 13. Wang, L.: Research on Magnetic Pulse Molding of PEMFC Bipolar Plates. Harbin Institute of Technology (2011). (in Chinese) 14. Cai, X.H.: Electro-hydraulic molding process of 304 stainless steel bipolar plates for fuel cells. Harbin Institute of Technology (2020). (in Chinese) 15. Huang, Y.F., Dong, P.X., Wu, Z.L., et al.: Research on J-C constitutive and failure models for TAl pure titanium sheet under high strain rate. Forging Stamping Technol. 48(3), 236–243 (2023). (in Chinese)

Analysis of the End Electric Field of 66 kV Dry Transformer in Offshore Wind Power Ke Xu1 , Xinhan Qiao2,3(B)

, Wei Li4 , Jiliang Yi3 , Xia Li3 , Xiaoquan Zhang3 , and Wenfeng Chen3

1 State Key Laboratory of Environmental Adaptability for Industrial Products, China National

Electric Apparatus Research Institute Co., Ltd., Guangzhou 510663, China 2 School of Electrical Engineering, China University of Mining and Technology,

Xuzhou 221116, China [email protected] 3 Sunten Electric Equipment Co., Ltd., Foshan 528300, China 4 Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China

Abstract. With the continuous increase in the capacity and scale of offshore wind power units, 66 kV has more technological and economic advantages compared to 35 kV AC power collection schemes. However, the end electric field of high voltage level dry transformers faces more severe tests. Therefore, this article constructs a 1/2 cross-section geometric model of the transformer, which considers the structure of iron yokes and pads that have a significant impact on the end electric field. The distribution characteristics of the electric field at the end of the dry-type transformer were calculated and obtained through finite element analysis. The locations with higher field strength are concentrated in the insulation of the high-voltage winding end. The surface electric field strength at the contact position between the coil and the pad and the internal electric field strength of the coil can reach 2.63 kV/cm and 6.85 kV/cm, respectively. Finally, the structure of the high-voltage coil pad under the optimal electric field was analyzed, and the research results have important guiding significance for the development of 66 kV dry-type transformers. Keywords: 66 kV Dry Transformer · Electric Field · Insulating Pad

1 Introduction Dry-type transformer is the key equipment of distribution system [1–4]. Dry type transformers, due to their advantages of explosion-proof and high reliability, are used inside wind turbine towers for offshore wind power. With the continuous increase in the capacity and scale of offshore wind power units, 66 kV has more technological and economic advantages compared to 35 kV AC power collection schemes. But the high voltage level dry transformer end electric field faces more severe tests. Therefore, studying the electric field distribution of dry-type transformers is crucial, and some literature has studied the electric field distribution of dry-type transformers [5– 10]. For example, a model for analysis of the electric fields at winding ends of dry-type © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 466–473, 2024. https://doi.org/10.1007/978-981-97-1072-0_48

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transformer was established in [9]. Based on the model, several top maximum electric intensity values and their positions are given. A design of the insulating support that can help to reduce its length without increasing the possibility of breakdown is discussed in [6]. In [7] the electric field of air channel were further optimized by increasing air channels and adjusting winding arrangement, so as to make the insulation design safer and more reliable. The above research has found that the structure of dry-type transformers can be optimized through electric field simulation calculation. However, there is currently no research on 66 kV dry-type transformers. Therefore, this article establishes a 1/2 cross-section geometric model of the transformer, which considers the structure where the iron yoke and pad have a significant impact on the end electric field. The distribution characteristics of the electric field at the end of the dry type transformer were calculated and obtained through finite element analysis. The research results have important guiding significance for the development of 66 kV dry-type transformers.

2 Simulation Methods In order to simplify the research, this chapter makes the following assumptions about the model: 1) Neglecting the influence of wiring arrangement on the electric field at the end of the transformer; 2) Consider the iron yoke as an infinite flat plate perpendicular to the iron core; 3) Neglecting the inter turn insulation of the transformer winding and treating a section of the coil as a conductor; 4) No longer considering the insulation cylinder in the main air duct; 5) The model only establishes the upper iron yoke and upper cushion blocks; 6) The voltage applied to the winding conductor is fixed and unchanging. Based on the above assumptions, the established model is shown in the following figure, and the relative dielectric constant of the material is shown in the table below (Fig. 1). The voltage of the coil closest to the upper end of the high-voltage winding is set to √ 66/ 3 kV, and the remaining coils continue to be distributed according to the number of turns of the coil. The voltage of the low-voltage winding conductor is still set at 1.14 kV. The grid division at the end of the transformer model is shown in Fig. 2. In areas where components such as high-voltage windings are relatively small and require precise analysis, the grid is densely divided, while in areas such as external air and iron yokes, the grid is relatively sparse.

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Fig. 1. The model of transformer

Fig. 2. Mesh partitioning at the end of the model

3 Results and Analysis 3.1 Electric Field Distribution at the End of the Transformer The electric field distribution at the end of the transformer obtained through finite element calculation is shown in Fig. 3. From the figure, it can be seen that the locations with high electric field intensity are concentrated at the end of the coil conductor in the high-voltage winding and the air near it, with a maximum electric field intensity of 6.84582 kV/cm. Below, this paper studies the distribution of the end electric field by making several representative cross-sections (Fig. 4). Compared to the electric field intensity along Sect. 1, there is a significant decrease in the electric field intensity along Sect. 2. In the electric field along Sect. 2, the distribution of electric field strength is relatively uniform in both air and epoxy resin media, and the electric field strength in air is even higher than that in epoxy resin.

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Fig. 3. Electric field at the end of the transformer

There is a certain degree of distortion in the electric field near the rectangular dielectric interface, but overall, the closer it is to the high-voltage winding, the greater the electric field strength. 3.2 Influence of Insulating Pad on the Electric Field at the End of Transformer The models and calculation results of the three types of insulation pads are shown in Figs. 5 and 6, respectively. The maximum electric field strength of the pad 2 model is 6.66805 kV/cm, which is slightly reduced compared to the electric field of the model using pad 1. The maximum electric field strength at the end of the transformer when using pad 3 is 7.12777 kV/cm, which is significantly increased compared to pad 2. Further analysis of the maximum and average electric fields on different crosssections yields Tables 2, 3 and 4 (Table 1). Overall, Block 2 has significantly more advantages compared to Block 1. It can not only suppress the occurrence of surface discharge on the cushion block, but also effectively reduce the electric field strength at the end of the high-voltage winding and its surrounding area. In addition, although the field strength of pad 3 is lower near the low-voltage winding, the field strength of pad 2 is lower near the high-voltage winding, and from the maximum and average values of field strength, it is lower for pad 2. It is still considered that the insulation near the high-voltage winding is relatively weaker, so pad 2 is better than pad 3.

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Analysis of the End Electric Field of 66 kV Dry Transformer

(a)Type 2

(b)Type 3

Fig. 6. Electric field at the end of the transformer

Table 1. The relative permittivities of materials in the transformer Medium material

Relative permittivity

Iron

8000

Copper

8000

Insulating cylinder

4.5

Epoxy

3.5

Air

1.0

Table 2. Electric field strength on the surface of the pads Pad type

Maximum field strength (kV/cm)

Average field strength (kV/cm)

Pad 1

2.6295

1.0816

Pad 2

2.0239

0.9383

Pad 3

2.1945

0.9473

Table 3. Electric field strength of the line 1 Pad type

Maximum field strength (kV/cm)

Average field strength (kV/cm)

Pad 1

6.8458

1.6058

Pad 2

6.6680

1.5612

Pad 3

7.1278

1.6084

471

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Pad type

Maximum field strength (kV/cm)

Average field strength (kV/cm)

Pad 1

2.1811

1.2330

Pad 2

2.0153

1.2002

Pad 3

2.1102

1.2391

4 Conclusions This article constructs a 1/2 cross-section model of the transformer, which incorporates structures such as iron yokes and pads that have a significant impact on the end electric field. Based on this model, this chapter introduces the distribution characteristics of the electric field at the end of the transformer. The positions with higher field strength are concentrated in the end insulation of the high-voltage winding. The surface electric field strength at the contact position between the coil and the pad and the internal electric field strength of the coil can reach 2.63 kV/cm and 6.85 kV/cm, respectively. Afterwards, this chapter discussed the advantages and disadvantages of three types of insulation pads, and finally selected pad 2 as the type of pad, which has certain guiding significance for engineering applications. Acknowledgement. Project funded by China Postdoctoral Science Foundation (2023M732412).

References 1. Chen, Y., Yang, Q., Zhang, C., Li, Y., Li, X.: Thermal network model of high-power dry-type transformer coupled with electromagnetic loss. IEEE Trans. Magn. 58(11), 1–5 (2022) 2. Ou, F., Huang, J., Chen, B., Liu, Y.: Numerical study on thermal characteristics of cabinmounted dry-type transformers. In: Proc. 2022 2nd International Conference on Electrical Engineering and Mechatronics Technology (ICEEMT), pp.129–133 (2022) 3. Wang, Z., Liu, S., Zhang, L.: Analysis of vibration characteristics of dry-type transformer iron core and windings based on multi physical field. In: Proceedings 2022 12th International Conference on Power and Energy Systems (ICPES), pp. 52–56 (2022) 4. Yangjue, H., et al.: Design of 10 kV dry transformer monitoring and control system. In: Proceedings of 2021 3rd Asia Energy and Electrical Engineering Symposium (AEEES), pp.85–88 (2021) 5. Saberi, S., Bigdeli, M., Azizian, D.: Insulation system optimization in dry-type transformer using finite element method. In: Proceedings of 2022 30th International Conference on Electrical Engineering (ICEE), pp. 518–523 (2022) 6. González, V.E., Gómez, P., Espino-Cortés, F.P.: Design of the insulating supports in medium voltage dry-type transformers. In: Proceedings of 2011 Electrical Insulation Conference (EIC), pp. 45–48 (2011) 7. Hu, R., et al.: Electric field optimization of cast resin dry-type transformer under lightning impulse. In: Proceedings of 2019 IEEE Conference on Electrical Insulation and Dielectric Phenomena (CEIDP), pp. 556–559 (2019)

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8. Jaafar, M.J., Muhamad, N.A., Jamil, M.K.M., Rosle, N.: Electric field and potential changes studies on cast-resin dry-type power transformer having misalignment. In: Proceedings of 2021 IEEE International Conference on the Properties and Applications of Dielectric Materials (ICPADM), pp.37–40 (2021) 9. Jin, H., Lin, H., Xu, Z.: Three-dimensional finite element analysis of electric fields at winding ends of dry-type transformer. In: Proceedings of 2005 International Conference on Electrical Machines and Systems, vol. 2133, pp. 2136–2139 (2005) 10. Ning, W., Ding, X.: Three-dimensional finite element analysis on fluid thermal field of dry-type transformer. In: Proceedings of 2012 Second International Conference on Instrumentation, Measurement, Computer, Communication and Control, pp. 516–519 (2012)

Research Status and Development Trend of Gravity Energy Storage Technology Chen Qimei1,2(B)

, Gou Yurong1,2 , and Wang Tangrong1,2

1 National Science Library, Chinese Academy of Sciences, Beijing 100190, China

[email protected], {gouyurong22, wangtangrong}@mails.ucas.ac.cn 2 University of Chinese Academy of Sciences, No. 19(A) Yuquan Road, Shijingshan District, Beijing 100049, People’s Republic of China

Abstract. Gravity energy storage is a new type of physical energy storage system that can effectively solve the problem of new energy consumption. This article examines the application of bibliometric, social network analysis, and information visualization technology to investigate topic discovery and clustering, utilizing the Web of Science database (SCI-Expanded and Derwent Innovation Index) as a basis for analysis. These are searched for literatures related to gravity energy storage technology. The objective is to uncover the evolving trends in gravity energy storage technology and offer valuable insights for guiding technical planning and tracking current areas of focus. The results of paper analysis show that the global output of gravity energy storage technology patents and papers continues to grow steadily, which is at the initial stage of commercialization, still needs technological breakthroughs. The topic clustering analysis show that the gravity energy storage technology research has focuses on techno-economic analysis, system modeling and simulation, renewable energy power generation coupled with gravity energy storage, energy management and operational control methods for gravity energy storage, hybrid energy storage system and gravity energy storage technology routes. The results of patent analysis show that more and more new renewable energy generation systems based on gravity energy storage systems have emerged in recent years. The most widely used scenario of gravity energy storage technology is wind power generation system, followed by solar power generation system and ocean power generation system. In addition, there are geothermal, hydro-energy, bioenergy and hydrogen generation system. Keywords: Gravity Energy Storage · Renewable Energy · Domain Development trend

1 Introduction As the grid system continues to integrate a multitude of new energy sources, their intermittent and fluctuating nature disrupts the balance of the grid “source follows load”, making it difficult for the traditional grid system to cope with the load pressure brought by new energy generation. The bi-directional charging and discharging functionality © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 474–481, 2024. https://doi.org/10.1007/978-981-97-1072-0_49

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of energy storage systems can effectively solve the problem of new energy consumption. Gravity energy storage (GES) is a kind of physical energy storage technology that is environmentally friendly and economically competitive. Gravity energy storage has received increasing attention in recent years, with simple principles, low technical thresholds, energy storage efficiencies of up to 85%, fast start-up and long service life. Gravity energy storage refers to the storage of energy by the potential energy caused by gravity. Gravity energy storage technology depends on the vertical movement of a heavy object in a gravitational field to store or release electricity [1]. The specific principle is to lift a heavy object to a high place through electricity, increase its gravitational potential energy, complete the energy storage, and then convert the gravitational potential energy into kinetic energy and then into electricity through the process of falling of the heavy object. At present, the new gravity energy storage is in the early stage of industry development, but experts from all walks of life are very optimistic about gravity energy storage technology, that the new gravity energy storage is more flexible than pumped storage site, more electrochemical energy storage safety, adjustable frequency, although it is still in the “prototype” stage, but in the foreseeable future, this technology will bring the development of the energy storage industry This technology will provide an immeasurable boost to the development of the energy storage industry in the foreseeable future. The new gravity energy storage will be realized through a variety of paths, currently there are different paths based on pumped storage, based on the height difference of the structure, based on the fall of the mountain, based on underground shafts and other projects, forming a variety of technologies such as mountain gravity energy storage, suspended gravity energy storage, piston gravity energy storage system, tower crane gravity energy storage, railway track gravity energy storage, underground gravity energy storage [2, 9].

2 Data and Method Two important records of scientific research achievement are papers and patents. The scientific papers serve as a record of the most recent advancements in research and technological innovation, making them a crucial source of data for gaining insights into technological progress. The patents constitute an important information resource that integrates information on technology, law, and economics. The patents reflect the current development level of a specific technology, the potential technology market, and the economic sphere [10]. The patent data used in this study is sourced from the Derwent Innovation Index (DII) patent database, which encompasses over 40 authorized patent offices and comprises fundamental inventions. The paper data utilized in this research was extracted from the Clarivate Analytics company’s WoS Core Collection database (SCI-Expanded). The search strategy was based on the association of keywords related to gravity energy storage. By June 2023, 1166 patents and 82 SCI papers were retrieved. Based on the literature data, by utilizing bibliometric and social network analysis approaches, this research performed a bibliometric network analysis and generated a domain knowledge map in order to elucidate the status, progress, and trends of research

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and application, of gravity energy storage technology. In this paper, social network analysis techniques were employed to construct network representations using document knowledge units, and the VOSviewer software tool, known for its visualization capabilities, was employed for knowledge map analysis. It is important to note that VOSviewer is a freely available software tool.

3 Development Trend of Gravity Energy Storage Technology 3.1 Analysis of Time Trend The trend in outputs for papers and patents can provide insight into research and development within particular fields to a certain extent, while also capturing the shifting focus of research and application over time at a macro level. The first patent application for gravity energy storage technology was filed by Tah Sun Lin in the USA in 1974, providing a device for harnessing wave energy and storing the energy in the form of potential energy for subsequent use in driving various machines. Since then, gravity energy storage has gone through three stages of development, as shown in Fig. 1(a). The first stage was between 1974 and 2000, when patent output was low and the technology was in its infancy. The second stage was between 2001 and 2019, when patents maintained slow growth and entered the growth period of the technology. The third stage was after 2020, when the number of patents grew rapidly and the technology entered a period of rapid development. It can be seen that the number of gravity energy storage patents has shown an obvious increasing in the past five years, and showing a sustained growth trend.

(a)

(b)

Fig. 1. The yearly production of patents and papers associated with GES technology

Figure 1(b). Shows that the yearly paper output concerning gravity energy storage technology can be categorized into two distinct periods. The first stage, from 2004 to 2014, belongs to the incubation period, with only a few papers appearing. The second stage, after 2014, enters the early stage of development, and the number of papers published fluctuates and rises slightly. Overall, the number of papers produced in the field of gravity energy storage is still at a low level, and the number of papers published has not yet entered a period of rapid growth, but has shown a trend of sustained growth.

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3.2 Analysis of Countries and Regions Through an analysis of patent applications in specific fields across various countries and regions, we identified significant target markets for technology applications. There are 45 countries and regions around the world have accepted gravity energy storage technology patents. The main countries and regions of patents that accepted gravity energy storage technology patents are shown in Fig. 2(a). The figure clearly illustrates, China is the most important target market for gravity energy storage technology, accounting for 60% of the total number of the global gravity energy storage technology patents. This is followed by the USA, Japan, Korea and Germany.

(a)

(b)

Fig. 2. The literature number of main countries and regions related to GES technology

Through an examination of paper counts across various countries and regions, we gained insights into the primary nations and regions where research on gravity energy storage technology has been undertaken. Research papers on gravity energy storage have been authored by scholars from 31 different countries and regions, with Fig. 2(b) depicting the ten nations responsible for the highest paper yields. China is the country with the highest number of publications in the field of gravity energy storage, with 19 papers published, accounting for about 23% of the total number of papers worldwide, followed by Morocco, India, Austria, South Africa, the USA and other countries. 3.3 Analysis of Technology Research Trend 1For this research, we utilized VOSviewer, a scientific visualization tool, to construct a knowledge map (network) using a word co-occurrence matrix. Figure 3 showcases the resultant map, where each node corresponds to a keyword, with larger nodes denoting higher frequency keywords, and distinct colors representing different topic clusters. The topic clustering analysis of SCI paper keywords in the gravity energy storage field shows that gravity energy storage technology research focuses on six research categories, i.e., Techno-economic Analysis and Management, System Modelling and Simulation, New Energy Generation Systems coupled with Gravity Energy Storage, Gravity Energy Storage Systems and their Control Methods, Composite Energy Storage Technologies, and Gravity Energy Storage Technology Solutions.

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Fig. 3. Research topics of gravity energy storage papers.

In Table 1, the primary classifications (#1, #2, #3, #4, #5, #6) for each technology concentration area are outlined in detail. The six research themes can be broadly divided into two directions, economic efficiency and technical performance. The economic benefit direction is concentrated in cluster #1, including cost-benefit analysis, techno-economic assessment, smart grid management, etc. The technical performance direction is distributed in clusters #2 to #6, focusing on the gravity storage technology itself and the coupled power generation system from models, algorithms, strategies, etc. 3.4 Analysis of Technology Application Trend Through the analysis of patent texts, it is found that more and more new renewable energy power generation systems based on gravity energy storage system have emerged in recent years. The most widely usage scenario of GES technology is wind power generation system, followed by solar power generation system and ocean power generation system. In addition, there are geothermal, hydro-energy, bioenergy and hydrogen generation system. Table 2 shows the application and proportion of gravity energy storage in various renewable energy power systems. Application technologies of gravity energy storage system in wind power generation systems include the gravity storage type wind power generation tower frame [11], the gravity energy storage type double-wind wheel wind driven generator [12], the marine wind power generation system based on gravity energy storage technology [13] and the vertical gravitational potential energy storage double-layer paddle push-pull drive wind generating set [14], etc. By integrating gravity energy storage technology, the wind

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Table 1. Appearance properties of accepted manuscripts. Number Research Theme

Keywords

#1

Techno-economic Analysis and Management

cost-benefit analysis; electricity; electricity storage; energy in islands; grid management; levelized cost of energy; smart grid management; technoeconomic assessment;

#2

System Modelling and Simulation

CAES; controller; efficiency; hydraulic modeling; implementation; integration; mathematical modeling; predictive control; simulation; simulink model;

#3

New Energy Generation Systems coupled renewable energy; solar photovoltaic with Gravity Energy Storage system; solar; PV; biomass; electricity cost minimization; energy management system; feasibility; microgrid; model; power-generation; artificial neural-networks;

#4

Gravity Energy Storage Systems and their control strategy; arbitrage; economics; Control Methods modeling; operation; plants; risk; sizing; algorithm;

#5

Composite Energy Storage Technologies

hybrid excavator; hydraulic accumulator; hydraulic excavator; energy saving; recovery-system; wind turbine;

#6

Gravity Energy Storage Technology Solutions

levelized cost of storage; linear electric machines; poles and towers; renewable energy sources; technologies;

power generation system can work in a wider wind speed range [15], or it can be stored when the wind is sufficient or the electricity is low, to ensure a stable power supply [16]. In the solar power generation system, the redundant energy generated by photovoltaic panels can be used to transport water, sand, earth and other media in gravity energy storage to the appropriate location [17], improving the geographical location adaptability of energy storage technology while reducing the overall cost. In the wind-light complementary system, the gravity energy storage system can be used to absorb the redundant power generated by wind power, photovoltaic, etc., to assist the optimal allocation of the capacity requirements of the power system for peak regulation [18]. Furthermore, it can also use gravity energy storage systems to store and reuse surplus wind and wave energy to realize frequency modulation and phase modulation, and suppress the fluctuations in the grid-connected power of traditional renewable energy generation [19].

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Usage scenario of GES technology

Proportion(%)

Wind Power Generation System

Onshore wind power generation

44.86

Offshore wind power generation

11.21

Onshore or/and Offshore

1.87

Photovoltaic power generation (PV)

22.43

Concentrating solar power (CSP)

8.41

PV or/and CSP

6.54

Wave power generation

18.69

Tidal power generation

13.08

Wave or/and Tidal

0.93

Solar Power Generation System

Ocean Energy Power Generation System

Other Renewable Energy Generation Systems

Geothermal power generation

5.61

Hydroelectric power generation

3.74

Biomass power generation

2.80

Hydrogen power generation

1.87

57.94

36.45

28.04

14.95

4 Conclusion Technological breakthroughs are still required for gravity energy storage technology, which is currently in its early stage of commercialization. Firstly, the efficiency of gravity energy storage mainly depends on the energy loss in the energy storage and release process. In order to reduce the energy loss, many energy saving measures are adopted, such as optimizing the design and using efficient materials. Secondly, the precision technologies, such as precise control algorithms of gravity blocks, are required to ensure the safe and stable operation of gravity energy storage system. The mutual cooperation of all links of gravity energy storage system is a large consumption of manpower and computing power. Furthermore, in addition to the system itself, gravity blocks are also an important component of gravity energy storage system. In the future, if new breakthroughs are found for the preparation of gravity blocks and effective utilization of materials, the power generation cost of gravity energy storage system will be greatly reduced.

References 1. Tong, W., et al.: Solid gravity energy storage: a review. J. Energy Res. 53, 105226 (2022) 2. Hunt, J.D., Zakeri, B., Falchetta, G., et al.: Mountain gravity energy storage: a new solution for closing the gap between existing short- and long-term storage technologies. Energy 190, 116419 (2020) 3. Gao, X.Z., Hou, Z.X., Guo, Z., Fan, R.F., Chen, X.Q.: The equivalence of gravitational potential and rechargeable battery for high-altitude long-endurance solar-powered aircraft on energy storage. Energy Convers. Manag. 76, 986–995 (2013)

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4. Fraenkel, P., Wright, M: Apparatus and Method for Electrical Energy Storage. In: UK Patent (2013) 5. Berrada, A., Loudiyi, K., Zorkani, I: Sizing and economic analysis of gravity storage. J. Renew. Sustai. Energy 8(2), 024101 (2016) 6. Emrani, A., Berrada, A., Bakhouya, M.: Modeling and performance evaluation of the dynamic behavior of gravity energy storage with a wire rope hoisting system. J. Energy Stor. 33, 102154 (2021) 7. Moore, S.K.: The ups and downs of gravity energy storage: startups are pioneering a radical new alternative to batteries for grid storage. IEEE Spectr. 58(1), 38–39 (2020) 8. Moazzami, M., Moradi, J., Shahinzadeh, H., et al.: Optimal economic operation of microgrids integrating wind farms and advanced rail energy storage system. Int. J. Renew. Energy Res. 8(2), 1155–1164 (2018) 9. Cava, F., Kelly, J., Peitzke, W., et al.: Advanced rail energy storage: green energy storage for green energy. In: Letcher, T.M., (ed.) Storing Energy. Amsterdam: Elsevier, pp. 69–86 (2016) 10. Chen, Q., Wang, Y., Zhang, J., Wang, Z.: The knowledge mapping of concentrating solar power development based on literature analysis technology. Energies 13, 1988 (2020) 11. I.R.N., Liao, S.: Gravity storage type wind power generation tower frame used with sectional support mechanism, comprises tower frame that is placed on foundation bearing platform, and wind power generating set is installed on tower cylinder. In: Patent 2022A29652 (2022) 12. Xiao, Z.: Gravity energy storage type wind driven generator with double wind wheels, has gravity energy storage system that is provided for realizing peak-to-peak energy storage. In: Patent 202302004A (2023) 13. Wang, T., et al: Marine wind power generation system based on gravity energy storage technology, has energy storage power generation grid-connected switch and energy storage switch whose ends are connected to energy storage motor. In: Patent 202075931Y (2020) 14. Xu, J: Vertical gravitational potential energy storage double-layer paddle push-pull drive wind generating set, has fan provided with vertical gravitational potential energy storage device that is combined with control system. In: Patent 2009P78315 (2009) 15. Han, B.: Wind power generation system based on gravity energy storage system has control instruction generating module generating gravity energy storage device energy storage instruction and wind power generating set operation instruction, Univ Harbin Sci & Technology. In: Patent 2023169445 (2023) 16. Yan, J: Flow sand energy storage system for solar energy, wind energy and other energy generation using gravity energy storage, has air compressor that is driven to work, and convert electrical energy into air compression energy. In: Patent 2022D4172F (2022) 17. Wang, H: Gravity energy storage system for transporting sand by rail and cable car, has cable car carrying sand operated to bottom sand pit through bottom automatic loading and unloading system to unload sand into bottom pith. In: Patent 202214354R (2022) 18. Xia, F.: System for storing e.g. solar energy, in wind-light complementary system, has heavy object that is given by ejector at initial speed at highest position, where rope passes through pulley to drive roller to rotate to drive electric generator. In: Patent 202266089A (2022) 19. Wang, T.: Marine wind power generation system based on gravity energy storage technology, has energy storage power generation grid-connected switch and energy storage switch whose ends are connected to energy storage motor. In: Patent 202075931Y (2020)

Research on Control Strategy of Permanent Magnet Synchronous Motor Speed Sensorless System Based on New Wide Band Gap Devices Jun Jiang1,2(B) , Chengsheng Wang2 , Wei Duan2 , Zhiming Lan2 , Fan Li1 , and Qiongtao Yang2 1 Beijing Aritime Intelligent Control Co., Ltd., Beijing 100071, China

[email protected] 2 Metallurgical Automation Research and Design Institute, Beijing 100070, China

Abstract. A new type of wide band gap semiconductor device, represented by silicon carbide, has advantages such as high switching frequency and low losses, which can significantly improve the power density of converter and system efficiency. Synchronous motors have the advantages of high efficiency, large moment of inertia, and fast dynamic response. In recent years, sensorless control technology for permanent magnet synchronous motor (PMSM) has become a research hotspot, which can significantly enhance system anti-interference, reduce costs, and reduce volume. This article is based on a 50 kw converter mainly consisted of new wide band gap semiconductor SiC devices, with a focus on the speed sensorless initial positioning method of PMSM to detect accurate initial position. Simultaneously, it aims to achieve the stable switching and control from low to medium and high speeds of PMSM without speed sensors. By comparing with the measured values of the code disk, system experiments are conduct in the full speed domain to verify the accuracy and reliability of speed sensorless control, which has good theoretical significance and application prospects. Keywords: New Wide Band Gap Devices · Permanent Magnet Synchronous Motor · Speed Sensorless

1 Introduction At present, PWM converters generally use power devices based on silicon materials. The switching speed, forward conduction resistance, and blocking voltage of silicon power devices have approached theoretical limits, which restrict the further optimization of voltage stress, switching frequency, power density, and operation efficiency. The features of new wide band gap semiconductor devices can significantly improve the power density of converters and system performance [1]. For different application fields such as switching power supply, electric vehicles, new energy generation, rail transit, and smart grid, the application advantages of SiC power devices are obvious. Therefore, the converter system designed in this article uses SiC MOSFET. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 482–492, 2024. https://doi.org/10.1007/978-981-97-1072-0_50

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Permanent magnet synchronous motor (PMSM) has high power factor, relatively simple structure, small volume and weight, low losses, and reliable operation. At the same time, this type of motor has high utilization of converters, large rotational inertia, and fast dynamic response [2]. With the rapid development of modern control technology, the accuracy of control system continues to improve. PMSM has become mainstream in more and more application systems, and have obvious advantages in the field of high-power AC transmission [3]. Due to the fact that PMSM is a complex nonlinear system with strong coupling, its high-performance control depends on obtaining accurate rotor position information. Traditionally, mechanical sensors such as photoelectric encoders and rotary transformers are used to detect the position and speed of the rotor which may cause many problems, including installation issues, environmental impacts, operating costs, system robustness and other aspects. Therefore, in order to overcome the drawbacks, it is necessary to study control methods without speed sensors. Sensorless control technology means that appropriate methods are applied to estimate the position and speed of the rotor by using the relevant electrical signals to achieve closed-loop control of the motor. The AC transmission system without position sensors has become a research hotspot recently and has broad application prospects because of its reduced system cost and improved reliability.

2 Mathematical Model of PMSM PMSM can be regarded as a synchronous motor with constant excitation current [4], and the three-phase winding of the motor can be equivalent to a two-phase static AC winding or a two-phase rotating DC winding through coordinate transformation.

Fig. 1. PMSM coordinate system

In Fig. 1, θ represents the angle between the two-phase rotating coordinate system and the two-phase stationary coordinate system, Ñ represents the rotational speed of the two-phase rotating coordinate system, which is the rotational speed of the motor rotor. In the d-q coordinate system, the voltage equation of PMSM is: ud = Rid + pψd − ωψq = Rid + Ld pid − ωLq iq uq = Riq + pψq + ωψd = Riq + Lq piq + ωLd id + ωψf

(1)

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The magnetic flux equation of PMSM is: ψd = Ld id + ψf ψq = Lq iq

(2)

The electromagnetic torque equation of PMSM is: Te = Pn (iq ψd − id ψq ) = Pn iq ψf + Pn (Ld − Lq )id iq

(3)

The symbols in the equation above: ψ–flux linkage, R–stator resistance, p–differential operator, ψ f –rotor flux linkage, Pn –number of pole pairs.

3 Control Scheme for Speed Sensorless System 3.1 Initial Positioning PMSM can be mainly divided into three types: surface mounted, embedded, and built-in [5]. For embedded and built-in types, the magnetic circuit structures of the d-axis and q-axis are different, resulting in L d being smaller than L q and having a saliency effect. For surface mounted PMSM, the d-axis and q-axis magnetic circuits are symmetrical, but they are usually designed to be in a nearly magnetic saturation state to improve its utilization. When the air gap flux increases to a certain extent, the stator core becomes saturated, the d-axis inductance decreases, and saliency effect occurs. By utilizing this characteristic, it can be concluded that the larger the winding current, the deeper the saturation degree, and the smaller the d-axis inductance. Due to the small stator resistance, the resistance term shown in Eq. (1) can be ignored. Therefore, ensuring the rotor stationary and injecting the voltage vector ud into the d-axis, the rate of change of id is proportional to the amplitude of ud and inversely proportional to the inductance L d . When applying voltage vectors with the same amplitude but different angles to the stator winding, the d-axis N-pole inductance of the rotor is the smallest and the current change rate is the largest because of the inductance saturation effect. As a result, when the action period of each voltage vector is the same, and the angle of the voltage vector ud is consistent with the actual angle of the motor rotor, the inductance is the smallest and the id is the largest. If the voltage vector angle corresponding to the maximum current value is found, the initial angle of the motor rotor can be acquired. The principle of setting vector is to apply 12 voltage vectors U 1 -U 12 in sequence, with an electrical angle interval of 30° between each vector, and maintain the same action time. The vector angle U 1 starts from 0° (U 2 is labelled in the opposite direction of 180°). In anticlockwise order, the voltage vector corresponding to 30° is U 3 (U 4 is labelled in the opposite direction of 180°), and so on. The numerical sequence is the application step of voltage vector. Detect the current amplitude which is consequential to each vector through a current sensor. By comparison, we can obtain the maximum id value, and record its corresponding vector angle. Up and down at this angle, apply 6 voltage vectors (V 1 −V 6 are the second wave voltage vectors) with an interval of 15°, and find the vector angle corresponding to the maximum id value in these 6 records. After completing the 15° accuracy judgment, the 7.5° accuracy judgment begins similarly. Subdivide and judge in this order until the required accuracy is achieved. With the development of integrated circuit technology, multiple digital control chips can quickly complete relevant calculations and statistics. The schematic diagram is shown in Fig. 2.

Research on Control Strategy of PMSM Speed Sensorless System u

dq

Vector amplitude

u

SiC Inverter

SVPWM

Vector angle Initial angle selected

485

PMSM iabc

ˆ

0

i Data filtering

id

abc

dq

i

Fig. 2. Schematic diagram of initial angle detection

3.2 Improved High-Frequency Voltage Signal Injection Method at Low Speed When PMSM operates at low speed, there is a problem of inaccurate estimation of rotor position and speed due to the small values of detected voltage and current, as well as the potential impact of interference. Two scholars (M. L. Corley and R.D. Lorenz) from the University of Wisconsin in the United States proposed the method of highfrequency injection [6]. This article proposes an optimized observer based on the dual coordinate system decoupling algorithm, which can effectively separate the positive and negative sequence components of the high-frequency current vector, and extract rotor position information from the negative sequence component. It is effective to improve the accuracy and reliability of rotor position and speed estimation. Assuming the injection voltage’s frequency Ñi (with amplitude ui ) is much higher than the fundamental frequency Ñf of the motor. In two phases stationary α-β coordinate system, the total input voltage of PMSM is the sum of fundamental frequency voltage and high-frequency voltage, expressed as:         uαf + uαi cos ωf t cos ωi t uα = = uf + ui (4) uβ uβf + uβi sin ωf t sin ωi t Due to Ñi >> Ñf , Ñf is approximately treated as 0 and the resistance voltage division is ignored. The response voltage of the motor under high-frequency voltage excitation is approximately equal to the corresponding inductance multiplied by the derivative of the current [7]. Further simplifying the model above, the current response of PMSM corresponding to the high-frequency voltage excitation is:     ipi sin ωi t − ini sin(2θ − ωi t) iαi = (5) iβi −ipi cos ωi t + ini cos(2θ − ωi t) In the formula (5), ipi represents the amplitude of positive sequence component of the high-frequency current, ini represents the amplitude of the negative sequence component of the high-frequency current. From the high-frequency current response of PMSM, the motor rotor position is hidden in the negative sequence current component, while the positive sequence current component does not contain any information related to the rotor position [8]. It is necessary to use signal processing technology to filter out the positive sequence components in the current, extract the negative sequence components, and realize estimation

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of rotor position. Assuming that the current vector contains two components rotating with angular velocity of ωpi and ωni separately, (dq)pi and (dq)ni are the corresponding rotational coordinate systems. Then the current expression in d-q coordinate system can be expressed as:    pi      pi ˜ipi id id cos ϕpi pi d idq = pi = pi + pi = Ipi + ˜iq sin ϕpi iq iq (6)     cos[(ωni − ωpi )t] − sin[(ωni − ωpi )t] + Ini sin ϕni Ini cos ϕni sin[(ωni − ωpi )t] cos[(ωni − ωpi )t]    ni      ˜ini i ini cos ϕni ni + = dni = dni + ˜dni = Ini idq iq iq sin ϕni iq (7)     cos[(ωni − ωpi )t] sin[(ωni − ωpi )t] Ipi cos ϕpi + Ipi sin ϕpi − sin[(ωni − ωpi )t] cos[(ωni − ωpi )t] The current expression in the (dq)pi and (dq)ni coordinate systems are both composed of the DC and AC parts. In (dq)pi coordinate system, the DC part is determined by the current component of ωpi . The amplitude and angle of the AC part are related with the current component of ωni . The same law applies to the coordinate system (dq)ni . In order to eliminate the coupling between them and ideally extract current components of different frequencies, it is necessary to decouple them. The principle is shown in Fig. 3. idpi iqpi

LPF LPF

idopi iqopi

sin ni

pi

cos idni iqni

LPF

idoni iqoni

LPF

Fig. 3. The principle of improved decoupling algorithm

The decoupling effect depends on the estimated value of the DC component. In an ideal situation, the output after decoupling is the DC component in different coordinate systems. But in practical engineering, it often contains AC interference. This article optimizes and designs a low-pass filter which can filter the decoupled output to obtain the DC component. By setting ωpi = ωi = −ωni , ϕ pi = 0, ϕ ni = 2θ, a decoupling algorithm for PMSM’s induced current under high-frequency voltage injection can be obtained. Adding a voltage feedforward link into the double closed-loop structure to convert the current signals into voltage signals and obtain their d-q axis components [9]. The control diagram of improved high frequency injection method in dual synchronous coordinate system is shown in Fig. 4.

Research on Control Strategy of PMSM Speed Sensorless System id*

PI

uiD uiE

id dq

UMO

Z

*

PI

iq*

Tˆ

iD f iE f

DE dq

Zˆ

Tˆ

SVPWM

DE

PI

iq

487

ni ido ni iqo

dq

PMSM

iD abc iE

LPF DE

SiC

DE

iD i iE i BPF

Fig. 4. Control diagram of improved high frequency injection method

3.3 Optimized MRAS Algorithm at Medium to High Speeds Model reference adaptive system (MRAS) method is a type of adaptive control algorithm. It designs an adaptive rate to make the dynamic characteristics of the control object infinitely close to the dynamic characteristics of the reference model. Its adaptive mechanism is to make the performance index function very small and use a generalized error to correct system parameters or generate auxiliary signals. Therefore, minimizing the performance index function as much as possible is the standard for designing. A formula without unknown parameters is used as the expected model, and the formula with parameters to be identified is used as the adjustable model. These two models output physical quantities with consistent physical meanings. Use the difference between the outputs of two models to obtain relevant information about the electric motor through a reasonable adaptive rule. Ignoring the magnetic flux leakage of stator, the voltage model of PMSM’s flux linkage is abbreviated as:  1 ψα = (uα − Riα )dt= (uα − Riα ) s  (8) 1 ψβ = (uβ − Riβ )dt = (uβ − Riβ ) s The current model of PMSM’s flux linkage is represented as:: ψα = Lq iα + [(Ld − Lq )id + ψf ] cos θ ψβ = Lq iβ + [(Ld − Lq )id + ψf ] sin θ

(9)

The rotor position of motor θ is integral of the rotational speed ω. They are parameters to be estimated. According to equations above, there are no parameters to be estimated in the flux voltage model, while the flux current model contains parameters to be estimated. Therefore, the voltage model can be used as a reference model and the current model can be used as an adjustable model to construct a model reference adaptive system [10]. Taking Eq. (9) as a derivative of time, for the control strategy of PMSM with id = 0, it can be considered that the d-axis current is a constant value of 0, and its derivative is 0. The following matrix form expression can be deduced:        ψα 0 −ω ψα − Lq iα ψα − Lq iα  = =Aψs (10) = p pψs = p ψβ ψβ − Lq iβ ψβ − Lq iβ ω 0

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Similarly, the adjustable model is pψˆ s = Aψˆ s . Then the linear forward part and nonlinear time-varying feedback part of the adaptive system can be constructed: ⎫ e = ψs − ψˆ s ⎪ ⎬  ˆ (11) pe = Ae − I (A − A)ψs ⎪ ⎭ v = De In the Eq. (11), D is a compensator that corrects the linear forward link. When implementing the above method, for the voltage reference model, due to the fact that the stator flux is a pure integration link of the motor’s back electromotive force, it will generate cumulative errors during the initial estimation of the flux. Meanwhile, there will be DC bias during actual sampling, which can also cause saturation of the integrator [11]. Therefore, it is necessary to optimize this integrator. In this paper, a firstorder low-pass filter is used to replace the pure integrator. At the same time, considering that introducing a first-order low-pass filter will cause amplitude error and phase lag of the signal, a compensation link is introduced to achieve the final optimization effect. The optimized voltage model is as follows: ψα/β =

1 ωc (uα/β − Riα/β ) + Y s + ωc s + ωc

(12)

The principle of optimized MRAS algorithm is shown in Fig. 5, and the system control diagram of optimized MRAS at medium to high speeds is shown in Fig. 6.

Fig. 5. Optimized MRAS algorithm at medium to high speeds

4 Simulation and Experiment Based on the above theoretical analysis and research, a simulation model of PMSM speed sensorless control system is built on Matlab/Simulink platform to simulate the static and dynamic performance of the system. To verify the consistency, the parameters of PMSM are the same in simulation and experiment. The rated power is 7.5 kw, the rated voltage is 380 V, the rated current is 13 A, the rated frequency is 50 Hz, the rated speed is 1500 r/min, the d-axis/ q-axis inductances are 9/15 mH, stator resistance is 1.33 , and the pairs of poles is 2.

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Fig. 6. Optimized MRAS system diagram

For the power frequency of 50 Hz, 10 Hz is considered as the boundary point between low speed and medium to high speeds. An improved high-frequency voltage injection method in a dual synchronous coordinate system is used at low speed, while an optimized MRAS algorithm is adopted at medium to high speeds. This paper applies a two-level AC-DC-AC PWM converter based on a new wide bandgap semiconductor SiC device which includes a rectifier, an inverter, and an intermediate DC link connecting the two parts. The controller uses 28335DSP to achieve initial positioning of the PMSM, as well as operation control and smooth switching from low speed to high speed. 4.1 Verification of Initial Positioning Detection Method With the help of DSP’s powerful computing ability, conduct a transformation cycle with a precision of 15° during the experiment. Firstly, the average number of id under the action of each vector during every working period should be calculated. Then the changes of id under different vectors are summarized and compared to select the highest peak value. The actual controlled object is a PMSM with two pairs of poles. Consequently, there are four peaks in the change of id during one cycle. As shown in Fig. 7, the horizontal axis represents the voltage vector sequence number (starting from 0 degree numbered as 1, 15° numbered as 2, and so on, corresponding to the angle which equals to (sequence number −1) multiplied by 15°). The vertical axis represents the unit value of id based on the rated current. In Fig. 7, the highest peak is 240° which is considered as the estimated initial angle of the PMSM. The actual initial angle measured by the code disk is 238°, and these two results are basically consistent. This method has strong practicality. 4.2 Verification of Improved High-Frequency Voltage Signal Injection Method at Low Speed When PMSM operates at low speed, an improved high-frequency voltage signal injection method based on the dual synchronous coordinate system is selected. For a motor with a rated frequency of 50 Hz, less than or equals to 10 Hz (corresponding to 300 r/min or 62.8 rad/s), is considered as a low-speed state. To avoid overcurrent impact, the speed is given by a slope form. The simulation waveforms are shown in Fig. 8. The experimental waveform is shown in Fig. 9. The final speed of PMSM is 300 r/min, θ and ω are

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Fig. 7. Experimental test results of initial positioning angle

the actual measured values of code disk, while θˆ and ωˆ are the estimated value of the algorithm.

(a) Rotational angular velocity

of PMSM

(b) Electric angle of rotor of PMSM

Fig. 8. Simulation waveforms of actual and estimated rotor position from 0 to 300 r/min

Fig. 9. Experimental waveform of actual and estimated rotor position at 300 r/min

4.3 Verification of Optimized MRAS Algorithm at Medium to High Speeds When PMSM operates at medium to high speeds, the optimized MRAS method is used. In simulation, various processes are tested, such as acceleration, deceleration, and stable operation. The simulation waveform of the acceleration process from 900 to 1200 is shown in the Fig. 10. The simulation waveform of the deceleration process from 1200

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to 750 is shown in the Fig. 11. The experimental waveform at the speed of 1200 r/min is shown in Fig. 12.

(a) Rotational angular velocity

of PMSM

(b) Electric angle of rotor of PMSM

Fig. 10. Simulation waveform of actual and estimated rotor position from 900 to 1200 r/min

(a) Rotational angular velocity

of PMSM

(b) Electric angle of rotor of PMSM

Fig. 11. Simulation waveform of actual and estimated rotor position from 1200 to 750 r/min

Fig. 12. Experimental waveform of actual and estimated rotor position at 1200 r/min

5 Conclusion This article selects the highly representative new SiC MOSFET module as the main power device and develops a 50 kw high-power density AC-DC-AC converter prototype which meets the requirements of high-power variable frequency drive systems. Based

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on the above converter and PMSM, a complete system simulation platform has been built. This article focuses on the speed sensorless initial positioning method of PMSM to achieve accurate initial position detection. At the same time, the control algorithms of PMSM without speed sensors at low and medium to high speeds are optimized. And a high-performance digital processor is used to achieve their smooth switching. Full speed domain system experiments are conducted to verify the accuracy and reliability of the speed sensorless composite control strategy. The estimation results in each state are basically consistent with the measured values of the code disk, with a static speed accuracy of 0.1% which has good theoretical significance and application prospects.

References 1. Wang, L., Ma, H., Yuan, K., Liu, Z.: Modeling and influencing factor analysis of SiC MOSFET half-bridge circuit switching transient overcurrent and overvoltage. Trans. China Electrotechnical Soc. 35(17), 3652–3665 (2020). (in Chinese) 2. Li, C.: AC Synchronous Motor Speed Control System. Science Press, Bejing (2005). (in Chinese) 3. Gu, S., He, F., Tan, G., Ye, S.: The current status and development of sensorless control technology for permanent magnet synchronous motors. J. Electr. Technol. 24(11), 14–20 (2009). (in Chinese) 4. Chen, Z., Qu, W.: Model Predictive current control for permanent magnet synchronous motors based on PID-type cost function. Trans. China Electrotechnical Soc. 36(14), 2971–2978 (2021). (in Chinese) 5. Wu, L., Lyu, Z., Chen, Z., Liu, J.: An enhanced sensorless control scheme for pmsm drives considering self-inductance asymmetry. CES Trans. Electr. Mach. Syst. 6(4), 384–392 (2022). https://doi.org/10.30941/CESTEMS.2022.00050 6. Wang, G.: IPMSM position sensorless control strategy based on high-frequency signal injection. J. Electric Technol. 27(11), 62–68 (2012). (in Chinese) 7. Bianchi, N., Bolagnani, S., Sul, S.K.: Advantages of inset PM machines for zero-speed sensorless position detection. IEEE Trans. Ind. Appl. 44(4), 1190–1198 (2008) 8. Anbo, Y., Liu, L., Kan, Z., Zhang, C.: Initial position identification of PMSM with filterless high frequency pulse signal injection method. Trans. China Electrotechnical Soc. 36(4), 801– 809 (2021). (in Chinese) 9. Pang, B., Li, F., Dai, H.: High frequency resonance damping method for voltage source converter based on voltage feedforward control. Energies 13(7), 1–16 (2020) 10. Kivanc, O.C., Ozturk, S.B.: Sensorless PMSM drive based on stator feed forward voltage estimation improved with MRAS multiparameter estimation. IEEE/ASME Trans. Mechatron. 23(3), 1326–1337 (2018) 11. Zhou, K., Sun, Y.C., Wang, X.D., Yan, D.: Active disturbance rejection control of PMSM speed control system. Electr. Mach. Control 22(2), 57–63 (2018)

Submodule Capacitance Dimensioning for Cascaded H-bridge STATCOM with Film Capacitors Hengyi Wang(B) Shanghai University, Shanghai 200444, China [email protected]

Abstract. The capacitance value is designed in this paper to increase system’s power density while maintaining converter performance for cascaded H-bridge (CHB) STATCOM in delta connection. The capacitance design rules are proposed for power quality and system safety. With the application of trigonometric transformation, the capacitance design rules can be represented as a series of nonnegative univariate polynomials, whose coefficients are associated with the capacitance value. The sum of squares (SOS) program is applied to obtain the minimal required capacitance. Simulations and experiments are conducted to validate the optimal capacitance design strategy. Keywords: cascaded H-Bridge · STATCOM · capacitance · nonnegative polynomials

1 Introduction The cascaded H-bridge (CHB) multilevel converter in delta connection is one of the most popular power converter topologies using as static synchronous compensator (STATCOM) in medium voltage power systems for harmonic currents and reactive power compensation [1, 2]. This power converter topology has modular structure, therefore the maintenance is easy, and the weighty and bulky transformer can be eliminated. The dclink of submodules (SMs) is often fed by film capacitors [3] because of film capacitors’ great electrical performance. The operating mode of STATCOM depends on the load. If the loads have the inductive property such as electric motors, STATCOM works in the capacitive mode. In this mode, the capacitor voltage and the branch voltage are in phase with each other. A low capacitance CHB has been designed in [4, 5] by accepting a strongly fluctuating voltage at the double of the line frequency. When STATCOMs are operated with the inductive mode, the capacitor voltage is in opposite phase with the branch voltage. The capacitance has been designed in [6, 7] by taking the capacitive operation into consideration, but not the inductive mode. After the capacitance has been designed, the inductive operating capability is then analyzed. Sometimes, the STATCOM needs to compensate harmonic currents to assist passive filters. The capacitor sizing for the mode of reactive power and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 493–502, 2024. https://doi.org/10.1007/978-981-97-1072-0_51

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harmonic compensation has been seldom studied. Overall speaking, to the authors’ best knowledge, a generic capacitance design method for various operating modes such as the capacitive/inductive and harmonic modes is lacked. This paper is able to determine the minimum required capacitance of the SM capacitors for CHB STATCOM under various operation modes, including reactive power and harmonic compensation. Influencing factors for capacitance design include overmodulation avoidance, the maximum limit and the peak-peak ripple limitation for capacitor voltages. With the help of trigonometric transformation, capacitance design rules can be represented as a series of non-negative univariate polynomials and the minimal capacitance can be obtained by optimal solvers. This paper is arranged as follows. In Sect. 2, the branch voltages and capacitors are analyzed. In Sect. 3, the design rules have been proposed to assure power quality and some safety reasons and an optimal solver is used to obtain the capacitance value. The simulations in Sect. 4 and experiments in Sect. 5 validate the optimal capacitance strategy.

Fig. 1. Delta-connected CHB-based STATCOM to the grid

2 Analytical Expression of Capacitor Voltages and Branch Voltages As shown in Fig. 1, the CHB STATCOM in delta connection is connected to the grid. Each CHB branch consists of N SMs and each SM dc-link capacitor has the same capacitance C. The equivalent branch inductor is L. A circulating current i0 flows inside the delta configuration. ia,b,c is the terminal current. iab,bc,bc is the branch current. uab,bc,bc is the SM branch voltage generated by the series of SMs. Denoting ucapijk , as the kth SM capacitor

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voltage in the ij(ij = ab, bc, ca) branch, the SM capacitor sum voltage is ucapij =

N 

SM

ucapijk

(1)

k=1

2.1 Time Expression of Branch Voltages and Capacitor Voltages with Sines and Cosines Expression of Branch Voltages. With the highest considered frequency order H, and we take branch-ab as an example. Branch voltage uab has the following expression in terms of sines and cosines. uab = ucapdc

H 

(asn sin(nωt) + acn cos(nωt))

(2)

n=1

where asn and acn are the nth Fourier coefficients. Expression of Capacitor Voltages. Capacitor voltages ucapij is composed of a dc and an ac component, denoted as ucapij and u˜ capij respectively. Assuming a known ucapij , defining Csum = C/N , the quantification of u˜ capij is based on pij =

ducapij d u˜ capij dEij = Csum ucapij = Csum ucapij dt dt dt

(3)

Given known pij , it is difficult to directly calculate u˜ capij because of the harmonic interaction between u˜ capij and its derivative. Traditionally, an approximate ac component, denoted as u˜ capij,tr , is calculated using pij = Csum ucapdc

d u˜ capij,tr dt

(4)

The ac component in ucapab,tr has expression in terms of sines and cosines as follows. u˜ capab,tr

2H ucapdc  = (bsn sin(nωt) + bcn cos(nωt)) Csum

(5)

n=2

where bsn and bcn are the n th Fourier coefficients. Moreover, ucapij can be obtained as follows  2 ucapij = ucapdc + 2ucapdc u˜ capij,tr

(6)

It should be noticed that the relationship between pij and ucapij is nonlinear (see Eq. (3)) while pij and ucapij,tr being linear (see Eq. (4)). As a result, pij contains the same harmonic orders with ucapij,tr , but different with ucapij .

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2.2 Time Expression of Branch Voltages and Capacitor Voltages with the Tangent Function Expression of Branch Voltages and Capacitor Voltages when Reactive Power Compensation. The branch voltage uab,bc,ca contained in uabc contains only the fundamental frequency, i.e., H = 1 in Eq. (2). Applying Eq. (7) in the branch voltage uab for the half-cycle, 1 tan(ωt) , cos(ωt) =  sin(ωt) =  2 1 + tan (ωt) 1 + tan2 (ωt)

(7)

so that the branch-ab voltage can be rewritten as as1 tan(ωt) ac1 uab = ucapdc (  + ) 2 1 + tan (ωt) 1 + tan2 (ωt) Similarly, the actual capacitor voltage in branch-ab can be expressed as  2 + 2ucapdc u˜ capab,tr ucapab = ucapdc  2 2ucapdc bc2 (1 − tan2 (ωt)) 2bs2 tan(ωt) 2 + ) = ucapdc + ( Csum 1 + tan2 (ωt) 1 + tan2 (ωt)

(8)

(9)

Expression of Branch Voltages and Capacitor Voltages when Reactive Power and Harmonic Compensation. The highest harmonic order in the branch voltages, H, is odd and H > 1. Using Eqs. (G.1) and (G.2) in the Appendix iteratively, any sine and cosine function, sin(nωt) and cos(nωt), can be rewritten as algebraic polynomials in the variable x, where x = tan(ωt) x ∈ (−∞, +∞). For example, sin(4ωt) =

4x(1 − x2 ) 1 − 6x2 + x4 , cos(4ωt) = (1 + x2 )2 (1 + x2 )2

(10)

Applying Eqs. (G.3) and (G.4) in the Appendix, branch voltages and capacitor voltages in branch-bc,ca can also be expressed as algebraic polynomials in x.

3 Proposed Synthesis of SM Capacitance To select the right capacitor, the following conditions must be checked. 1. The STATCOM must work in the linear modulation area.   ucapij > uij , (ij = ab, bc, ca)

(11)

The peak capacitor voltage shall not exceed the rated DC voltage of the capacitor, denoted as UNDC . ucapij ≤ UNDC , (ij = ab, bc, ca)

(12)

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3. The peak-peak ripple voltage upp shall not be greater than the rated AC voltage of the capacitor, denoted as εUNDC , where ε is the ripple ratio. ucapij,max − ucapij,min ≤ εUNDC

(13)

We still take branch-ab as an example. Put the branch voltage of Eq. (8) and the capacitor voltage of Eq. (9) into Eq. (11), the following inequality can be obtained, 2 ucapdc +

2 2 2 x 2 + a 2 + 2a a x) (as1 2ucapdc ucapdc s1 c1 2bs2 x bc2 (1 − x2 ) c1 ( + ) − >0 2 2 2 Csum 1 + x 1+x 1+x (14)

which can be rewritten as 2 2 f1 (x) = [(1 − as1 )Csum − 2bc2 ] · x2 + (−2as1 ac1 Csum + 4bs2 ) · x + [(1 − ac1 )Csum + 2bc2 ] > 0

(15)

Put the branch-ab capacitor voltage of Eq. (9) into Eq. (12), square both sides, and reorganize the inequality, we get f2 (x) = [(

2 UNDC 2 ucapdc

− 1)Csum + 2bc2 ] · x2 − 4bs2 · x + [(

2 UNDC 2 ucapdc

− 1)Csum − 2bc2 ] ≥ 0 (16)

Equation (13) is equal to the following ucapij ≤

ε UNDC + ucapdc 2

ε − UNDC + ucapdc ≤ ucapij 2

(17a) (17b)

The above analysis illustrates that when STATCOM operates for reactive power compensation, the right capacitance value Csum must guarantee non-negativity of these second-order polynomials fm (x), ∀m ∈ (1, 2, 3, 4), see Eqs. (15), (16), (17a) and (17b). The proper capacitance can be obtained by using solvers SOSTOOLS [8] and SeDuMi [9].

4 Simulations and Experiments The capacitive, inductive and harmonic modes have been simulated to evaluate the research. The parameters of the simulated system are listed in Table 1. The main simulation setup is taken from the delta-connected CHB STATCOM installed at a 11 kV distribution system in Kikiwa, New Zeeland [10]. The measurable PCC voltages (in kV) are assumed as follows, √ ⎧ usa = 11 2 sin(ωt) ⎪ ⎪ ⎪ ⎪ √ ⎨ 2π ) usb = 11 2 sin(ωt − (18) 3 ⎪ ⎪ ⎪ √ ⎪ ⎩ usc = 11 2 sin(ωt + 2π ) 3

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Item Amplitude of PCC line-line voltages (vsij )

Value √ √ 11 × 2 × 3 kV

Rated line frequency (ω/2π)

50 Hz

Sampling time (Ts )

5 × 10−6 s

Carrier frequency for PSPWM (fcr )

250 Hz

Branch inductor (L)

40 mH

Number of SMIs in each branch (N )

22

Rated DC capacitor voltage (UNDC )

52.36 kV

Ripple ratio limitation of film capacitor (ε)

28%

dc component of capacitor sum voltage (ucapdc )

42.9 kV

capacitance for the capacitive, inductive and harmonic mode (Csum,min ) 17 µF, 14 µF, 25 µF

Also, experimental validation is provided. The source voltage and branch current in experiments are respectively 0.1% and 1% of those in simulations, resulting in the equivalent Csum,min used in experiments for validation is 10 times in simulations. Case A – Capacitive Operation Mode. The load currents (Eq. (19) in kA) are lagging behind the PCC voltages as Eq. (18). The polynomials are of degree two. ⎧ π ⎪ iLa = 2 sin(ωt − ) ⎪ ⎪ 18 ⎪ ⎪ ⎨ 13π iLb = 2 sin(ωt − ) (19) ⎪ 18 ⎪ ⎪ ⎪ ⎪ ⎩ iLc = 2 sin(ωt + 11π ) 18 Figure 2(a) gives the simulated waveforms of steady-state capacitor voltages and branch voltages with Csum,min = 17μF (left subplot), as well as their frequency spectra (right subplot). Figure 2(a) shows that all the constraints for capacitance sizing are satisfied. The STATCOM operates in the linear modulation area. The positive peak of the capacitor voltage is less than 52.36 kV. The maximum and the minimum value of ucapca are indeed unsymmetrical to ucapca (42.9 kV). More specifically, the negative peak is 36.2 kV, 0.128 UNDC less than ucapca while the positive peak is 49.1 kV, 0.118 UNDC larger than ucapca . The slight asymmetry is due to the presence of multiple harmonics in capacitor voltages, other than the 2nd order. The experiment result as in Fig. 2(b) also validates the result. .. .. Case B – Inductive Operation Mode. Shown in Eq. (20), the load currents (in kA) lead the PCC voltages. In this case, the branch currents and voltages contain the +1st frequency order, therefore the powers, the harmonic interaction from the branch currents

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(a) (simulation) with C sum , min

17 F

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(b) (experiment) with .

Fig. 2. Case A – Simulation and experimental results for the capacitive mode

(a) (simulation) with C sum , min

14 F

(b)

(experiment) with C sum , min

140 F

Fig. 3. Case B – Simulation and experimental results for the inductive mode

and voltages, contain the −2nd frequency order. The polynomials for capacitance sizing are of degree two. ⎧ π ⎪ iLa = 2 sin(ωt + ) ⎪ ⎪ 18 ⎪ ⎪ ⎨ 11π iLb = 2 sin(ωt − ) (20) ⎪ 18 ⎪ ⎪ ⎪ ⎪ ⎩ iLc = 2 sin(ωt + 13π ) 18 The minimum capacitance is Csum,min = 14 µF. The simulated waveforms of steady state capacitor voltages and branch voltages are given in Fig. 3(a), showing that the negative peak capacitor voltage is 36.2 kV, 0.12 UNDC less than ucapdc while the positive peak is 49.1 kV, 0.118 UNDC larger than ucapdc , indicating that the positive and the

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(a) (simulation) with C sum , min

25 F

(b) (experiment) with C sum , min

250 F

Fig. 4. Case C – Simulation and experimental results for the harmonic mode

negative peak is asymmetric about ucapdc .The peak-peak voltage ripple is about 0.25 UNDC . The experiment result as in Fig. 3(b) also validates the result. Case C – Reactive Power and Harmonic Compensation. The load cur-rents (in kA) in Eq. (21) contain the +1st and the −5th frequency orders. The polynomials for capacitance sizing are of degree ten. The resulting minimum capacitance is Csum,min = 25 µF. ⎧ π π ⎪ ⎪ ⎪ iLa = 2 sin(ωt + 18 ) + 0.4sin(5ωt + 18 ) ⎪ ⎪ ⎨ 13π 11π iLb = 2 sin(ωt − ) + 0.4sin(ωt + ) (21) ⎪ 18 18 ⎪ ⎪ ⎪ ⎪ ⎩ iLc = 2 sin(ωt + 13π ) + 0.4sin(ωt − 11π ) 18 18 Figure 4(a) shows the simulated waveforms of capacitor voltages and branch voltages at the steady state. The left subplot shows that the negative peak of ucapdc is 37.3 kV, 0.107 UNDC less than ucapdc while the positive peak is 50.1 kV, 0.138 UNDC larger than ucapdc , i.e., the positive and the negative peaks are obviously unsymmetrical to ucapdc . The experiment result as in Fig. 4(b) also validates the result.

5 Conclusion This paper has proposed the minimization of capacitance for delta-connected CHBbased STATCOM but limited by some factors such as overmodulation avoidance, the peak and the peak-peak capacitor voltages not exceeding the defined boundaries. This is a generic method for capacitance sizing, so that the optimal capacitance value under various operating modes can be obtained. Especially for the operating mode of reactive and harmonic compensation, because branch voltages and capacitor voltages contain multiple frequency components, it is difficult to design capacitance, however, this paper is still able to deal with this operating mode.

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The converter cost and volume are impacted by the capacitance value. If an allowable minimum capacitance is selected, the cost and volume can be reduced, therefore the capacitance sizing method has practical value. The presented method can also be used in other power-electronic-based systems, especially for the applications where the lowfrequency capacitor voltage harmonics should be an important consideration. Acknowledgement. This work was supported by the National Natural Science Foundation of China under Grant 52007111, and grants from the Delta Power Electronics Science and Education Development Program of the Delta Group.

Appendix sin((n + 1)ωt) = sin(nωt) cos(ωt) + cos(nωt) sin(ωt)

(G.1)

cos((n + 1)ωt) = cos(nωt) cos(ωt) − sin(nωt) sin(ωt)

(G.2)

sin(nωt ±

2π 2π 2π ) = sin(nωt) cos( ) ± cos(nωt) sin 3 3 3

(G.3)

cos(nωt ±

2π 2π 2π ) = cos(nωt) cos( ) ∓ sin(nωt) sin 3 3 3

(G.4)

References 1. Wang, H., Wang, F., Gao, F., Cheng, J.: Submodule capacitor sizing for cascaded H-bridge STATCOM with sum of squares formulation. In: 2022 International Power Electronics Conference (IPEC-Himeji 2022-ECCE Asia), pp. 2412–2417. Himeji, Japan (2022) 2. Wang, H., Liu, S.: Harmonic interaction analysis of delta-connected cascaded H-bridge-based shunt active power filter. IEEE J. Emerg. Sel. Top. Power Electron. 8(3), 2445–2460 (2020) 3. Cupertino, A.F., Pereira, H.A., Seleme, S.I., Teodorescu, R.: On inherent redundancy of MMC-based STATCOMs in the overmodulation region. IEEE Trans. Power Delivery 35(3), 1169–1179 (2020) 4. Rodriguez, E., et al.: Enhancing inductive operation of low-capacitance cascaded h-bridge statcoms using optimal third-harmonic circulating current. IEEE Trans. Power Electron. 36(9), 10788–10800 (2021) 5. Cheng, X., Lu, D., Hu, H.: The low DC-link capacitance design consideration for cascaded H-bridge STATCOM. In: IECON 2018 – 44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, USA, pp. 4338–4343 (2018) 6. Farivar, G., Townsend, C.D., Hredzak, B., Pou, J., Agelidis, V.G.: Low-capacitance cascaded H-bridge multilevel statcom. IEEE Trans. Power Electron. 32(3), 1744–1754 (2017) 7. Rodriguez Ramos, E., Leyva, R., Farivar, G.G., Townsend, C.D., Pou, J.: Operating limits for low-capacitance cascaded H-bridge static compensators. IEEE Trans. Power Electron. 37(3), 3421–3433 (2022) 8. Prajna, S., Papachristodoulou, A., Parrilo, P.: Introducing SOSTOOLS: a general purpose sum of squares programming solver. In: Proceedings of the 41st IEEE Conference on Decision and Control, vol. 1, pp. 741–746 (2002)

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9. Labit, Y., Peaucelle, D., Henrion, D.: SeDuMi interface 1.02: a tool for solving LMI problems with SeDuMi. In: Proceedings of the IEEE International Symposium on Computer Aided Control System Design, pp. 272–277 (2002) 10. Pereira, M., Retzmann, D., Lottes, J., Wiesinger, M., Wong, G.: SVC PLUS:An MMC STATCOM for network and grid access applications. In: 2011 IEEE Trondheim Power Tech, pp. 1–5 (2011)

Design of Electromagnetic Detection System for Underground Cultural Relics Protection Based on Spread Spectrum Coding Shiqiang Li1,2,3 , Guoqiang Liu1,2,3(B) , Wenwei Zhang1 , Zhiguang Lv1 , and Lijuan Guo4 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

[email protected]

2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology,

Qilu Zhongke, Jinan 25000, China 4 Beijing Eagle Lion Technology Co., Ltd., Beijing 102600, China

Abstract. Illegal theft of underground cultural relics is currently a difficulty in the field of cultural relics protection. The use of underground theft caves for cultural relics theft is a common form of theft. Traditional underground detection technology is difficult to apply due to the fact that the protected cultural relics are located in densely populated areas such as cities, and the cultural and electromagnetic environment is too complex. This article proposes an electromagnetic detection method based on spread spectrum coding combined with correlation identification to address the above issues. The method uses the good autocorrelation and cross correlation characteristics of spread spectrum coding to remove external interference and achieve the reconstruction of resistivity distribution images of underground thief tunnels. Under the guidance of the theory of spread spectrum encoding detection, an electromagnetic detection system for underground cultural relics protection based on spread spectrum encoding was designed, and detection experiments were conducted in the field for self-digging stolen caves. The detection and inversion image results can reflect the location and distribution of underground stolen caves. The experimental results prove that the electromagnetic detection system for underground cultural relics protection based on spread spectrum coding can be applied to detect underground stolen caves. This study provides a new technical protection method for underground cultural relics protection work, and has important scientific significance for maintaining China’s cultural heritage and strengthening cultural confidence. Keywords: Cultural relics protection · Underground thief cave · Spread spectrum encoding · Electromagnetic detection · Resistivity

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 503–509, 2024. https://doi.org/10.1007/978-981-97-1072-0_52

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1 Introduction China’s traditional culture is vast and profound, with a long history. In the process of development, a large number of historical relics have emerged. Among them, a large portion belong to ancient architectural relics located underground, such as palaces, government offices, and temples [1]. Due to their enormous cultural and historical value, and the special nature of underground space makes maintenance and protection of the cultural relics very difficult. The criminal phenomenon of underground cultural relic’s illegal theft has been repeatedly prohibited, bringing great economic and cultural property losses to the national cultural relics protection work [2–4]. How to effectively prevent theft of underground cultural relics and protect the safety of underground cultural relics is an urgent issue faced by cultural relic protection workers [5, 6]. The main form of underground cultural relics illegal theft is excavation of underground tunnels [7, 8]. Due to the complex geographical and spatial environment in which underground cultural relics are located, coupled with severe human and electromagnetic interference, traditional geophysical methods are difficult to apply [9–11]. For the anti-theft needs of underground cultural relics, this article proposes an electromagnetic detection method based on spread spectrum coding combined with correlation identification. The method uses the good autocorrelation and cross correlation characteristics of spread spectrum coding to remove external interference [12]. Field experiments were conducted using the independently developed spread spectrum coding electromagnetic detection system in the laboratory, and good detection results were achieved.

2 Technical Principles The principle of the spread spectrum encoding electromagnetic detection method is shown in Fig. 1. Using the system identification theory in the field of communication, consider underground theft tunnels as response systems. The excitation signal is modulated by spread spectrum coding and fed into the earth system. The ground synchronous detection signal includes the response of the underground tunnel stealing system and strong external electromagnetic and human interference signals. By performing correlation identification operations between the detection signal and the transmitted spread spectrum encoded signal, utilizing the good correlation of the spread spectrum encoded signal to remove irrelevant interference noise, the abnormal response of the theft tunnels is obtained, and combined with the excitation detection parameters of the detection system, the earth’s resistivity information is obtained.

Fig. 1. The principle of spread spectrum encoding electromagnetic detection method

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According to the principle of spread spectrum encoding electromagnetic detection, the detection signal includes two parts: the response of the theft tunnel system and external interference, which can be expressed as: r(t) = u(t) + n(t) = I (t) ∗ h(t) + n(t)

(1)

By performing correlation identification operations between the detection signal r(t) and the spread spectrum encoded signal m(t), it can be concluded that: Rrm(t)=r(t) ∗ m(t) = RIm(t) ∗ h(t) + Rnm(t)

(2)

In formula (2), the electromagnetic emission signal is self-correlation with the spread spectrum encoding sequence, while there is no correlation between external interference noise and the spread spectrum encoding sequence. So cross correlation function Rnm(t) is 0. This can effectively extract abnormal information for detecting theft tunnels from detection signals containing a large amount of interference.

3 Design of Electromagnetic Detection System As shown in Fig. 2, the electromagnetic detection system for underground cultural relics protection based on spread spectrum encoding mainly includes a spread spectrum encoding electromagnetic signal transmission unit, a multi-sensor rotation unit, a spread spectrum encoding correlation identification signal detection unit, and a theft tunnels resistivity inversion imaging unit.

Fig. 2. Schematic diagram of the electromagnetic detection system for underground cultural relics protection

The spread spectrum encoding electromagnetic signal transmission unit uses FPGA to generate excitation spread spectrum encoding signals, which are transmitted to the high-voltage inverter module after the solation drive module to generate high-voltage spread spectrum encoding excitation. The multi-sensor rotation unit realizes the rotation excitation of high-voltage spread spectrum excitation signals and the rotation detection of ground response signals under the control of rotation commands. The spread spectrum encoding correlation identification signal detection unit performs correlation identification and other processing on the synchronously collected excitation and detection signals, and then transmits them to the theft tunnels resistivity inversion imaging unit for theft tunnels image inversion and recognition. The schematic diagrams of the designed spread spectrum encoding electromagnetic signal transmission unit, multi-sensor rotation unit,

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(a) Design of spread spectrum encoding electromagnetic signal transmission unit

(b) Design of multi-sensor rotation unit

(c) Design of spread spectrum encoding correlation identification signal detection unit Fig. 3. Design of the electromagnetic detection system

and spread spectrum encoding correlation identification signal detection unit are shown in Fig. 3 (a), (b), and (c). The resistivity inversion imaging unit of underground theft tunnels constructs an inversion objective function containing spatiotemporal information, combines it with a forward electromagnetic field model, and uses least squares iteration to reconstruct

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the resistivity distribution image of underground theft tunnels. The inversion calculation formula is shown in Eq. (3), and the operation process of the designed resistivity inversion imaging algorithm is shown in Fig. 4. (JkT Jk + λWmT Wm + αWtT Wt )−1 mk+1 = −(JkT d + λWtT Wt mk )

(3)

In the formula, k is the k-th iteration. J is the sensitivity matrix. Wm , Wt are the smooth filtering matrix of space and time. λ, α are the Lagrangian space and time factors. m is the reconstruction parameter, m is the step size of the reconstruction parameter change, and d is the error between the calculated value and the measured value.

, ,

,

Fig. 4. The operation process of the designed resistivity inversion imaging algorithm

4 System Experiments The designed electromagnetic detection system for underground cultural relics protection based on spread spectrum encoding is shown in Fig. 5.

Fig. 5. The host and operation interface of the electromagnetic detection system

A detection experiment was conducted on a cultural relic protection site in Shaanxi using the developed spread spectrum encoding electromagnetic detection system. The detection object is a digging theft tunnel. The width of the thief tunnel is about 1 m, and the measurement height is about 0.96 m. The distance from the top of the thief hole to the measurement surface is about 6 m, and the size of the thief hole extending inward from the opening is about 4.5 m. The specific testing environment is shown in Fig. 6.

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Fig. 6. The internal dimension measurement of the thief tunnel

Fig. 7. The resistivity distribution of the underground thief tunnel

Using a 10th order spread spectrum encoded signal for detection, electrodes are used as detection sensors, with a spacing of 1 m between electrodes. The number of electrodes is 48, and the obtained distribution image of underground thief tunnel is shown in Fig. 7. In Fig. 7x represents the layout direction of the ground electrode sensor, and z represents the underground depth direction. From Fig. 7, it can be seen that there is an underground anomaly body about 6 m away from the ground, with a size of about 1.5 m. The location and size of the underground thief tunnel can be found from the inversion and reconstruction of the underground medium resistivity distribution image. The resolution of the resistivity distribution image obtained from underground electromagnetic exploration inversion is closely related to factors such as detection sensor system parameters, sensor layout, detection depth, geological conditions, and external interference. In this study, although the spread spectrum coding related identification technology was used to suppress the interference of external noise to a certain extent, due to the small size of the detection volume and the deep distance from the ground, the resolution of the inverted image in detecting thief tunnel was affected, and some artifacts appeared at the bottom of the inverted image. This is also the next step that needs to be improved in the electromagnetic detection system for underground cultural relics protection based on spread spectrum coding.

5 Conclusion Illegal theft of underground cultural relics is currently a difficulty in the field of cultural relics protection. The use of underground thief tunnels for cultural relics theft is a common form. Traditional underground detection technology is difficult to apply due to the fact that the protected cultural relics are located in densely populated areas such as cities, and the cultural and electromagnetic environment is too complex. The

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electromagnetic detection method proposed in this article based on spread spectrum coding combined with correlation identification technology can effectively remove irrelevant human and electromagnetic interference signals from the outside and obtain reliable underground detection information. The detection results of the self-developed spread spectrum encoding electromagnetic detection system for underground thief tunnels demonstrate that this technology can be used for detecting underground thief tunnels, distinguishing underground anomalies, and achieving the localization of thief tunnels. The research in this article is the preliminary research result of electromagnetic anti-theft technology for underground cultural relics. Further research is needed on the detection of underground thief tunnels in complex environments. Acknowledgement. Thanks to the National Natural Science Foundation of China (52077210), the Major Project of Cultural Relics Protection Science and Technology in Shaanxi Province.

References 1. Tian, X., Hu, J.: The temporal–spatial distribution of key cultural relics protection sites in China and tourism response. Prof. Geogr. 74(2), 327–339 (2022). https://doi.org/10.1080/003 30124.2021.2000447 2. Institute of cultural relics and Archaeology of Zhengzhou University (Luoyang), Luoyang Institute of cultural relics and archaeology. Excavation Bulletin of East area of Xuyang cemetery in Yichuan, Henan Province from 2015 to 2016. Chin. Archaeol. 2020(3), 23-40, 110. (in Chinese) 3. Zheng, Y.: Reconciliation and conflict: a study on the development path of unmovable surface cultural relics protection in Beijing. Chin. Stud. 12, 219–241 (2023) 4. Upadhyay, N.K., Rathee, M.: Protection Of cultural property under International Humanitarian Law: emerging trends. Centro de Ensino Unificado de Brasilia 2021(3) 5. Li, L.: On the importance of archaeological exploration for the protection of underground cultural relics. Chin. J. Sci. Technol. Database Soc. Sci. 4, 0057–0060 (2023). (in Chinese) 6. Wang, B., Zhai, X., Wei, X., et al.: A self-powered and concealed sensor based on triboelectric nanogenerators for cultural-relic anti-theft systems. Nano Res. 15(9), 8435–8441 (2022) 7. Zhou, P., Zhou, X., Xia, C., et al.: Environmental risk assessment at the Shangfang Eastern Wu Tomb in Nanjing based on environmental monitoring. Sci. Conserv. Archaeol. 35(2), 97–105 (2023). (in Chinese) 8. Make. Research on the current situation and prevention and Control Countermeasures of the crime of robbing and excavating ancient cultural sites and ancient tombs in S Province. Northwest University (2019). (in Chinese) 9. Zhao, X.: Analysis on the application of geophysical prospecting technology in Archaeology and cultural relic protection. Identification and appreciation of cultural relic (2020), 000 (003): 164, Feng 3. (in Chinese) 10. Shao, D., Li, R., Guo, Y., et al.: Application of high density electrical method in underground cavern detection. West. Resour. 97(04), 179–181 (2020). (in Chinese) 11. Dong, Y., He, P.: A 6LowPan based underground cultural relic anti-theft monitoring terminal and method: CN201910601373.7. CN110415471A. (in Chinese) 12. Shi, C., Zhai, H.: The application of digital panoramic borehole camera technique to the protection engineering of cultural relics sites. Geophys. Geochem. Exploration 4(06), 234– 238 (2020). (in Chinese) 13. Zhang, L., Li, S., Liu, G., et al.: Research on electromagnetic detection system for spread spectrum code. Trans. China Electrotech. Soc. 33(S2), 263–269 (2018). (in Chinese)

Electric Field Analysis and Research of 1000 kV AC Transformers High Voltage Direct Type Exit Device Xiangjun Li(B) , Yanyan Hou, Xiaoyang Zhang, Yuzhe Lu, Penghong Guo, and Xinbing Wang Shangdong Power Equipment Co., Ltd., Jinan 250022, China [email protected]

Abstract. At present, two kinds of high voltage exit devices are used in 1000 kV transformer products, direct exit and indirect exit devices. The structure of the high voltage exit devices must have reliable insulation. Two kinds of structures of the exit devices of UHV transformer are presented and analysed with ElecNet electric field analysis softwares by the authors in this paper. The global two-dimensional and three-dimensional electric field analysis is carried out for the high voltage horizontal and vertical lead pipe to exit device. Because of the complexity and importance of the exit device, it is necessary to design the shape and size of the insulator reasonably. The creepage analysis of the support insulation structure of the exit device is carried out by using the commercial software and self-developed creepage analysis software respectively. Also provides economic comparison of two ways. The indirect exit device has certain advantages in economy, technology and design simplification. It will be widely used in power grid construction. Keywords: Ultra-high-voltage (UHV) performance · electromagnetic field · exit device · insulation · creepage stress · 3D finite element method (FEM) · secondary development program

1 Introduction The development of UHV [1] transmission is an inevitable trend in the development of power grid in China. UHV transmission energy can also meet the basic requirements of large capacity, long distance, high efficiency, low loss and low cost transmission, and can effectively solve the problems of low transmission capacity, poor safety and stability, and poor economic benefits in the current 500 kV ultra-high voltage power grid [2, 3]. A full set of high-quality UHV equipment is a necessary prerequisite for the establishment of UHV system, and UHV transformer is one of its important components. In the UHV transformer, the 1000 kV exit device undertakes the function of drawing the 1000 kV high voltage from the coil, passing through the box and connecting with the bushing. The device needs to withstand extremely high voltage in a finite scale, requiring not only reliable insulation, but also to meet the needs of repeated disassembly and assembly to ensure long-term reliable operation. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 510–522, 2024. https://doi.org/10.1007/978-981-97-1072-0_53

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The UHV exit device is a multi-medium and complex shape important part composed of paper and paper insulation, metal electrode and supporting parts. In view of the importance of the exit device, under the planning and guidance of the State Grid Corporation, the domestic China electric power research institutes [4, 5] and major transformer manufacturers such as TBEA [6], Baoding Tianwei [7], Xian XD [8] etc. [9–11]have carried out the domestic development and test of the 1000 kV exit devices. At present, the high voltage of UHV transformer use the indirect exit type (as shown in Fig. 1), and this structure runs reliably. The HV winding line lead connect to the bushing through the exit device which mounted in “L” shaped bushing turret. Because the exit device mostly adopts complete sets of imported shaped insulation parts, the cost is high and complicated to install. Our company’s indirect exit device structure UHV transformer has years of reliable operating performance. In recent years, our company began to carry out the research and development of UHV high-voltage direct exit device (hereinafter referred to as direct exit), the characteristics of this method (as shown in Fig. 2) are: after the high-voltage exit comes out of the middle of the coil, it is not led out through the “L” shaped bushing turret, but directly leads out to the bushing through the internal exit device in the same tank, which has high reliability, simple structure and convenient installation (especially on-site installation). Our company developed this type of UHV 1000 kV direct exit device transformer this year, and the products have passed all type tests smoothly.

Fig. 1. Arrangement and structure of indirect exit device

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Fig. 2. Arrangement and structure of direct exit device

2 Basic Parameter The development of UHV transmission is an inevitable trend in the development of power grid in China. UHV transmission energy can also meet the basic requirements of large capacity, Model: ODFPS-1000000/1000 Rated power: 1000/1000/334MVA √ √ Rated voltage: 1050/ 3/525/ 3 ± 4 × 1.25%/110 kV Frequency: 50 Hz Maximum service voltage: 1100 kV Connection: YNa0d11 (three-phase). Insulation level: HV: LI2250AC1100 (5 min)-LI750AC275.

3 Modeling and Evaluation Principle of Insulation Safety Margin 3.1 Mathematical Model The electric field has the basic characteristics of scattered and non-curling, and Maxwell’s equations reveal the law of the electric field [12–16]: D = εE

(1)

divD = 0

(2)

E = −grad φ

(3)

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Equation (1) is the differential form of Ohm’s law in an electric field; Equation (2) is the differential equation of Kirchhoff’s first law derived from the continuity of the current; Equation (3) is derived from the rotationality of the electric field. Where, D is electric current density, E is field strength, ε is The dielectric constant of the insulating medium in the field, ϕ is The potential at a point in the field under study. From Eqs. (1), (2), and (3), the two-dimensional and three-dimensional plane Laplace equations calculated by the potentiometric function can be derived. ∂ ∂φ ∂ ∂φ ε + ε =0 ∂x ∂x ∂y ∂y

(4)

∂ ∂φ ∂ ∂φ ∂ ∂φ ε + ε + ε =0 ∂x ∂x ∂y ∂y ∂z ∂z

(5)

For an axisymmetric field, it can be reduced to:     1 ∂ ∂φ ∂ ∂φ εr + ε =0 r ∂r ∂r ∂z ∂z

(6)

Equations (4), (5) and (6) is a second-order partial differential equation that can be solved directly by analytical and analog methods, but these methods are not accurate enough or even can’t be solved when encountering complex electric fields. A more precise solution can be obtained by using the finite element method (FEM). Since the electric field calculation is generally a static electric field problem based on Laplace equation, and the boundary problem is often the first type, that is, the Dirichlet problem, it means that each boundary of the region has its potential value, and in the whole calculation process it is a constant. 3.2 Establishment of Insulation Model In the AC withstand voltage test, the analysis of the AC electric field [17], due to its capacitance, its electric field distribution depends on the dielectric constant values of different materials in the composite insulation structure. The relative permittivity of oil εO = 2.2, and the relative permittivity of paper εp = 4.0, The magnitude of the electric field strength in different insulating materials is inversely proportional to the dielectric constant of the insulating material, so the electric field strength in transformer oil with lower dielectric constant is relatively high, while the AC field strength in pressboard is low. When analyzing and calculating the alternating current electric field, we focus on the distribution of the electric field in the oil gap. The failure of the insulation structure of the AC transformer mainly depends on the maximum field strength in the oil gap. Therefore, the author conducts comprehensive electric field stress calculation and verification analysis according to several high field stress areas, such as equalizing pressure ball, shielded copper tube to ground, and lead to coil as the key parts of insulation.

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3.3 Software Verification In the electric field model area, the coil, the line lead and equipotential shielding for bushing, are applied the test voltage, and the rising seat and the tank housing part are grounded, both of which belong to the first type of boundary conditions, and the rest are the second type of boundary conditions. We use ElecNet software in Canada and Telax software in Ukraine for electric field analysis. The test voltage at the line end is 1100 kV (5 min), which is converted to 1200 kV (1 min) according to the volt-second characteristics. 3.4 Evaluation Principle of Insulation Safety Margin Since oil is the weakest area in the transformer oil-paper insulation system, its allowable electric field strength greatly affects the reliability level of the entire insulation system. The factors affecting the allowable electric field strength of transformers mainly include: oil gap length, insulation test type, whether there is insulation on the electrode surface and insulation thickness, and the oil gap position. This analysis uses the Weidmann formula for the relationship between the partial discharge starting voltage and the oil gap length of the transformer insulation model. Ep = A × d −0.37

(7)

where, A is the coefficient related to the gas content and oil gap position in the transformer oil, for the withstand voltage test of power frequency 50 Hz and 1 min, A = 21.5 is taken between degassing oil and pressboard. d is the length of the oil gap along the direction of the electric field line, mm. Ep is the allowable value of the field stress of the initial partial discharge in uniform electric field, kV/mm. The relationship between the allowable field stresss value Ep and the oil gap length d is shown in Fig. 3. The safety margin (safety factor) can be calculated by the following formula. Sm =

Ep Em

(8)

where, Sm is safety margin, Em is the mean value of the field stress in oil gap in uniform electric field, kV/mm.

4 Software Verification in Direct Exit The mesh generation diagram after modeling is shown in Fig. 4. The analyzed electric field distribution is shown in Fig. 5. The four key areas highlighted in Fig. 5 are analyzed below.

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Fig. 3. The relation between Ep and d

Fig. 4. Model mesh generation of direct exit device (tank hidden)

4.1 The Electric Field Analysis Between High voltage Direct Exit Device and Turret Wall of Bushing The analyzed electric field distribution is shown in Fig. 6, and the safety margin distribution is shown in Table 1. From the analysis results, it can be seen that the safety margin distribution in the oil gaps is uniform and reasonable. The minimum safety margin is in the fourth oil gap on the bushing side, and the minimum safety margin is 1.15. The safety margin of the remaining parts is greater than this value.

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Fig. 5. The electric field distribution of direct exit device

Fig. 6. The distribution of the electric field between direct exit device and turret wall

4.2 Electric Field Analysis Between High Voltage Horizontal Lead and Side Yoke and Tank The analyzed electric field distribution is shown in Fig. 7, and the safety margin distribution is shown in Table 2. From the analysis results, it can be seen that the safety margin is the smallest in the oil gap between the outermost corner ring of the horizontal outlet and the outermost pressboard of the side yoke, and the minimum safety margin is 1.15. The safety margin of the remaining parts is greater than this value.

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Table 1. The oil gap electric field safety margin Oil gap

Margin

1

1.19

2

1.27

3

1.21

4

1.15

5

1.30

6

1.37

7

3.92

8

4.08

9

3.53

Fig. 7. The distribution of the electric field between high voltage horizontal leads and side yoke and tank Table 2. Key area electric field safety margin place

Margin

The oil gap between the outermost corner ring of the horizontal lead and the outermost pressboard of the side yoke

1.15

The oil gap between the outermost corner ring of the horizontal lead and the outermost pressboard of the tank

1.21

4.3 Electric Field Analysis Between high Voltage Exit Device and Side Yoke and Tank The analyzed electric field distribution is shown in Fig. 8, and the safety margin distribution is shown in Table 3. From the analysis results, it can be seen that the minimum

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safety margin is 1.16 in the oil gap between the outermost corner ring of the equalizing pressure ball and the outermost pressboard of tank. The safety margin of the remaining parts is greater than this value.

Fig. 8. The distribution of the electric field between high voltage direct type exit device and side yoke and tank

Table 3. Key area electric field safety margin place

Margin

The oil gap between the outermost corner ring of the equalization ball and the outermost pressboard of the side yoke

1.29

The oil gap between the outermost corner ring of the equalization ball and the outermost pressboard of tank

1.16

4.4 Analysis of the Electric Field at the Elbow of the Exit Device The analyzed electric field distribution is shown in Fig. 9. From the analysis results, it can be seen that the minimum safety margin is in the oil gap between the outermost corner ring of the turning point (elbow, point A) of the exit device and the outermost pressboard of the tank, and the minimum margin is 1.18. The insulation margin of the remaining parts is greater than this value. 4.5 Electric Field Analysis at the Turn of the Exit Device The clamping part of the outlet device adopts the Weidmann standardized structure, as shown in Fig. 10. In order to evaluate the insulation structure, the creepage field strength of the horizontal lead and supporting frame is analyzed by finite element method(FEM) software,

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Fig. 9. The distribution of the electric field of elbow of high voltage leads

Fig. 10. The clamping structure of the high voltage exit device

and the creepage (tangential) field stress of the analyzed oil-paper interface is shown in Fig. 11. The minimum creepage safety margin along the surface of the support is 1.28, and the value is qualified. After applying the secondary development creepage program “Program of Creepage Stress(Et_X2015)” based on Weidemann’s algorithm [18], the creepage (tangential) field

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Fig. 11. Tangential stress of horizontal leads along supporting frame using FEM software

stress of the oil-paper interface is shown in Fig. 12. The minimum creepage safety margin along the surface of the supporting frame is 2.01, and the value is qualified.

Fig. 12. Tangential stress of horizontal leads along supporting frame using secondary development software(Program of Creepage Stress(Et_X2015))

5 Conclusion This year, our company’s UHV high voltage direct exit device transformer have passed all type tests smoothly, which proves that the insulation structure is reasonable, safe and reliable. Since then, our company has formed two mature structures: UHV high voltage direct exit transformer and indirect exit AC transformer. At the same time, it should be seen that the direct exit device transformer has several advantages compared with the indirect exit device transformer: First of all, the former is economical, reducing two insulating paper basins, simplifying the overall insulation structure, reducing the purchasing cost, and eliminating the L-shaped bushing turret, thereby reducing the amount of steel and transformer oil;

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Secondly, the installation processability is good, which reduces the complex process of connecting the exit device and the transformer active part, which facilitates product manufacturing, especially on-site installation; Thirdly, the overall layout of the product is more reasonable, which can improve the layout of the transformer conservator, simplify the design of the transformer foundation, and reduce the overall size of the transformer. Finally, UHV direct exit transformers have good promotion prospects in the power grid.

References 1. Kong, Q., Feng, Z.: A Chinese-English Glossary of Transformer Technology, 1st edn. China Electric Power Press, Beijing (2008). (in Chinese) 2. Lu, C.: Power Transformer Insulation Technology, 1st edn. Harbin Institute of Technology Press, Harbin (1997). (in Chinese) 3. Zhu, D., Yan, Z.: High Voltage Insulation, 1st edn. Tsinghua University Press, Beijing (1992). (in Chinese) 4. Xiong, H., Sun, J., et al.: Design and study of insulation margin test system for direct-type lead exit of ultra-high voltage transformer. In: 22nd International Conference on Electrical Machines and Systems (ICEMS). Harbin, China(2019) 5. Sun, J.T., Zhang, H.J., Li, J.Z., et. al.: Insulation design and performance analysis for directtype lead exit of UHV transformer. In: 20th International Conference on Electrical Machine and System. Sydney, Australia (2017) 6. Liu, K., Tang, T., Li, J.: Research and Trial Production of Net Side Outlet Device for UHV Converter Transformer. Transformers 58(2), 19–23 (2021) (in Chinese) 7. Wang, K., Zhang, X., Zhang, D., Ran, Q.: AC 1000 kV analysis of insulation structure of transformer outlet device. Transformers 53(7), 52–54 (2016). (in Chinese) 8. Mi, C., Xie, Q., et al.: Design and application of exits insulation structure for EHV and UHV AC transformers. High Voltage Eng. 36(1), 122–128 (2010). (in Chinese) 9. Yang, Y., Yang, H., Yao, Q.: Structure and fault analysis and defect treatment of UHV transformer outlet device. Transformers 57(12), 32–35 (2020). (in Chinese) 10. Zeng, L., Xiao, P., et al.: Analysis of electric field of HV lead in Ultrahigh Voltage Power Transformer. IEEE (2020) 11. Liu, H., Huang, T., Qin, F.: Research on a new high outlet device for 1000 kV UHV AC transformer. Transformers 59(11), 47–50, 55 (2022). (in Chinese) 12. Ni, G.: Principle of Engineering Electromagnetic field, 1st edn. Higher Education Press, Beijing (2009). (in Chinese) 13. Tan, K., Xue, J.: Numerical Calculation of High Voltage Electrostatic Field, 1st edn. Water Conservancy and Electric Power Press, Beijing (1990). (in Chinese) 14. Phaengkieo, et al.: Transformer Design by Finite Element Method with DOE Algorithm. In: International Conference on Electrical Machines and Systems, 1st edn. Busan, Korea (2013) 15. Kulkarni, S.V., Khaparde, S.A.: Transformer Engineering Design & Practice, 1st edn. Marcel Dekker Inc, New York (2004)

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16. Dasgupta, I.: Design of Transformers, 1st edn. Tata Mcgraw-Hill Publishing Co., Ltd., New Delhi (2002) 17. Design and optimization of inter-coil insulation system of a Cast resin transformer using FEM. In: International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), pp. 2887–2890. IEEE (2016) 18. Li, X., Feng, L., Luan, L., Zhang, K.: Program development of creepage stress evaluation and the application of this program in the analysis on creepage stress in UHV transformer. Transformers 54(4), 7–13 (2017). (in Chinese)

Analysis of Current and Voltage Characteristics of 500 kV Noninverting Parallel Cable Zhifang Zhu, Dongmei Fan, Jingjing Huang(B) , and Weiwei Liu Guangzhou Power Supply, Bureau of Guangdong Power Grid Co., Ltd., Guangzhou, China [email protected] Abstract. The normal operating current of power cables is an important basis for the development of their protection devices. In order to analyze the operating current and voltage characteristics of parallel cable lines, firstly, the parameter model of non-phase parallel cable routes is established according to the Carson analysis method, the metal sheath is regarded as a general line, and its self-inductance and mutual inductance with the core circuit are considered, and the influence of the sheath circulation is equivalent to the phase impedance matrix of the line through Kron simplification in this process. At the same time, the calculation method of line sequence parameters is explained by phase domain analysis. Establish the -type equivalent circuit of the cable line, and calculate the operating parameters of the noninverting parallel cable. The concept of cable route imbalance is introduced, and the operating characteristics of noninverting parallel cables under different arrangement, different loads and core temperatures are compared and analyzed. Keywords: In-phase parallel cable · line parameters · operating parameters · laying method · imbalance

1 Introduction At present, it is imperative to change urban high-voltage and ultra-high-voltage overhead line transmission lines to cable transmission lines, but the transmission capacity of threephase single-core AC cables is obviously insufficient. If the 500 kV cable adopts ordinary wrinkled aluminum sheathed cable with a maximum ampacity carrying capacity of 1800 A and a transmission capacity of 1500 MW, even if the ampacity enhancement technology such as smooth aluminum sheathed cable, enameled insulated wire and good ventilation and heat dissipation is used, the maximum current carrying capacity is within 2200 A, and the transmission capacity is up to 1900 MW. However, the current transmission capacity of urban overhead hub lines is 3600 MW, and the 500 kV cable with 2500 mm2 section cannot meet the load demand. The expansion of 500 kV cable line mainly includes methods such as increasing the cross-sectional area of the cable and connecting multiple cycles in phase. The former increases the transmission capacity by reducing the cable resistance and heat generation, but the expansion capacity is limited; at present, the latter mostly adopts non-inverting parallel double-loop cables, which can not only effectively increase cable capacity, but also maximize the use of cable tunnel space, which has gradually become the focus of research. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 523–544, 2024. https://doi.org/10.1007/978-981-97-1072-0_54

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Due to the strong electromagnetic coupling relationship between the phases, the noninverting parallel double-loop cable produces a large unbalanced current [1–3], which makes the traditional single-loop cable route parameter calculation and operation characteristics analysis methods no longer applicable. The power frequency phase, sequence parameters and electrical quantity operation characteristics of the cable are the basis for the design, operation and calculation of relay protection tuning of the power system [4–6]. Therefore, it is of great significance to study the parameter calculation method and operation characteristic analysis suitable for noninverting parallel double-loop cable. At present, the research on non-inverting parallel cables is mostly based on the research basis of the same rod parallel double loop. Literature [7] studies double-loop overhead lines, and proposes that parameter asymmetry caused by different spacing of parallel lines is the main source of current imbalance. In actual engineering, overhead lines are usually transposed to reduce the imbalance of line parameters, while cable routes are not transposed, so there are differences in research between the two. For the parallel operation of cables, scholars have done relevant research. Literature [8] uses the cable support program in EMTP-RV to calculate the phase parameters of the unit length of the cable line, and analyzes the current imbalance of the cable under different arrangements. The results of literature [8, 9] explain the calculation method of sequential impedance parameters of multi-loop parallel cable lines, and analyze the symmetry of double-loop cable routes under uneven arrangement, and the results of literature [8, 9] show that the symmetry of fret arranged cables is better than other arrangements. In addition to the arrangement, the phase sequence of the cable is also an important factor affecting its symmetry, and the best phase sequence of parallel cables is given in the standard proposed by the International Electrotechnical Commission (IEC) [10], which will not be repeated in this article. In fact, most of the above research on parallel cables is based on transmission systems of 220 kV and below, or for submarine cables. The research on 500 kV noninverting parallel cables is not perfect. In addition, in the past, most of the calculation of the operating parameters of parallel cable systems ignored the cable-to-ground capacitance. Compared with overhead lines, the cable is closer to the ground and the capacitance is larger, which should not be ignored in the actual analysis. Based on this form, this paper adopts a combination of theory and simulation, and first establishes the impedance parameter matrix and admittance parameter matrix of 500 kV inverting parallel cable based on Carson analysis method. According to the Kron simplification principle, the two matrices are simplified, and the above phase parameters are converted into sequence parameters by phase domain analysis, which provides data support for the calculation of subsequent sequence currents. Due to the influence of the cable on the ground capacitance, the -type equivalent circuit of the cable line is established, the size of the line phase current and phase voltage is calculated based on the phase impedance matrix and the phase admittance matrix, and the size of the sequence current is calculated based on the sequence impedance and sequence admittance parameters. Then, the equivalent circuit model of the cross-interconnection of the sheath of the noninverting parallel cable is established to solve the sheath current and sheath voltage. Finally, a 500 kV in-phase parallel cable route model is established by PSCAD/EMTDC to verify the correctness of the mathematical model by case study,

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and the operating characteristics of cable routes under different arrangements, different loads and different temperatures are analyzed.

2 Basic Cable Parameters 2.1 Phase Impedance Parameter Calculation In the analysis of the operating current of the cable, its self-impedance and mutual impedance should be taken into account. Since there is an unbalanced current when the cable is running, the geodetic loop is also taken into account. For noninverting parallel cables, an equivalent circuit model is established, and its core and sheath form a loop with the earth. From this, a noninverting parallel cable route model including sheath is established, as shown in Fig. 1.

n

ĂĂ ĂĂ

11

22

2

1 yabc 2

1 yabc 2

Fig. 1. Noninverting parallel cable route model

Referring to the Carson analysis method, suppose that the Earth is an infinitely homogeneous solid with a uniform surface and constant resistivity. By using the conductor mirror method, the self-impedance of the cable route and the degree of mutual impedance between the cables can be obtained (Fig. 2). Core – Earth loop self-impedance (/km): Zcc = rc + re + j0.1445 log

De dGMRc

(1)

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nn

Fig. 2. Conductors and mirrors

Sheath – Earth loop self-impedance (/km): De

Zss = rs + re + j0.1445 log

dGMRs

(2)

When the core and sheath are in the same phase, the mutual impedance between the ’core wire-earth’ loop and the ’sheath-earth’ loop (/km): Zsc = re + j0.1445 log

De dGMRs

(3)

When the core wire and the sheath are not in phase, the mutual impedance between the ’core wire-earth’ loop and the ’sheath-earth’ loop (/km): Zsc = re + j0.1445 log

De D

(4)

Between the two core-earth circuits and the two sheath-earth circuits,there is a mutual impedance that is shown above. In the formula above, re is the earth-equivalent resistance, rc is the AC resistance per unit length of the wire core, and rs is the AC resistance per unit length of the sheath: re = π2 f × 10−4 = 0.0493 /km;  When the earth serves as the circuit, De is the depth of the comparable loop. De = ρe /f ; The geometric mean distance of the core is denoted by dGMRc , the geometric radius of the sheath by dGMRs , and each phase’s wire spacing by D. During the actual operation of the cable, the resistance of the wire core is affected by the temperature and its calculation formula is as follows. R = R (1 + YS + YP )

(5)

where YS is the cable skin effect factor, R’ is the DC resistance at conductor operating temperature, and YP is the proximity effect factor between cables.

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According to IEC-60287, the formula for calculating the ampacity of the cable at different temperatures can be obtained [10]: 

θ − Wd [0.5T1 + n(T2 + T3 + T4 )] I= RT1 + nR(1 + λ1 )T2 + nR(1 + λ1 + λ2 )(T3 + T4 )

0.5 (6)

where: I is the current flowing in the conductor of the core (A); θ is the conductor temperature rise (K) above the ambient temperature; R is the AC resistance per unit length of the conductor at the maximum operating temperature (/m), and Wd is the insulation dielectric loss around the conductor per unit length (W/m); T1 is the thermal resistance per unit length (K.m/w) between the wire core conductor and the metal sheath; T2 is the unit length thermal resistance of the lining layer between the metal sleeve and the armor (K.m/w); T3 is the unit length thermal resistance of the outer sheath of the cable (K.m/w); T4 is the unit length thermal resistance (K.m/w) between the cable surface and the surrounding medium; n is the number of conductors carrying the load in the cable (conductors of equal cross-section and carrying the same load); λ1 is the ratio of cable sheath loss to total loss of all conductors; λ2 is the ratio of cable armor loss to total loss of all conductors. Considering the influence of the sheath, an initial impedance matrix can be established: ⎤ ⎡ Za1a1 Za1b1 Za1c1 · · · Za1aw2 Za1bw2 Za1cw2 ⎥ ⎢ Z ⎢ b1a1 Zb1b1 Zb1c1 · · · Zb1aw2 Zb1bw2 Zb1cw2 ⎥ ⎥ ⎢ ⎢ Zc1a1 Zc1b1 Zc1c1 · · · Zc1aw2 Zc1bw2 Zc1cw2 ⎥ ⎥ ⎢ . .. .. .. .. .. .. ⎥ (7) Z =⎢ . . . . . . ⎥ ⎢ .. ⎥ ⎢ ⎢ Zaw2a1 Zaw2b1 Zaw2c1 · · · Zaw2aw2 Zaw2bw2 Zaw2cw2 ⎥ ⎥ ⎢ ⎣ Zbw2a1 Zbw2b1 Zbw2c1 · · · Zbw2aw2 Zbw2bw2 Zbw2cw2 ⎦ Zcw2a1 Zcw2b1 Zcw2c1 · · · Zcw2aw2 Zcw2bw2 Zcw2cw2 Write it in the form of a chunked matrix:  [Z ] Z =  ii Zji

  Zij Zjj

(8)

where each parameter in [Zii ] represents the self-impedance and mutual impedance between the “core-earth” circuit; Each parameter in [Zij ] and [Zji ] represents the mutual impedance between the “core-earth” circuit and the “sheath-earth” circuit; Each parameter in [Zjj ] represents the self-impedance between the sheath-earth circuits.

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Assuming that the double split cable uses cross-interconnect grounding, KVL is used for the above circuit: ⎡ ⎡ ⎤ ⎡ ⎤ ⎤ Va1n Ia1 Va1m ⎢I ⎥ ⎢V ⎥ ⎢ ⎥ ⎢ b1 ⎥ ⎢ b1m ⎥ ⎢ Vb1n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ Ic1 ⎥ ⎢ Vc1m ⎥ ⎢ Vc1n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢I ⎥ ⎢V ⎥ ⎢ ⎥ ⎢ a2 ⎥ ⎢ a2m ⎥ ⎢ Va2n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ Ib2 ⎥ ⎢ Vb2m ⎥ ⎢ Vb2n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥  ⎥  ⎢ ⎢V ⎥ ⎢ ⎥ ⎥ Zii Zij ⎢ Ic2 ⎥ ⎢ c2m ⎥ ⎢ Vc2n ⎥ (9) ·⎢ ⎢ ⎥=⎢ ⎥+ ⎥ ⎢ Vaw1m ⎥ ⎢ Vaw1n ⎥ Zji Zjj ⎢ Iaw1 ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢I ⎥ ⎢V ⎥ ⎢ ⎥ ⎢ bw1 ⎥ ⎢ bw1m ⎥ ⎢ Vbw1n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ Icw1 ⎥ ⎢ Vcw1m ⎥ ⎢ Vcw1n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢I ⎥ ⎢V ⎥ ⎢ ⎥ ⎢ aw2 ⎥ ⎢ aw2m ⎥ ⎢ Vaw2n ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ ⎥ ⎣ Ibw2 ⎦ ⎣ Vbw2m ⎦ ⎣ Vbw1n ⎦ Vcw2m

Vcw2n

Icw2

Also write the form of a block matrix:

        Vabc Iabc [Vabc ] ] [Z Z ii ij =   +   · Zji Zjj Iabcw [Vabcw ] Vabcw

(10)

Since the sheath crosses interconnect grounding, the voltages [Vabcw ] and [V’abcw ] are equal to 0. This can be solved  −1  Iabcw = − Zjj · Zij · Iabc (11) So that it can be obtained in the end  −1  Iabcw = − Zjj · Zij · Iabc

(12)

2.2 Phase Impedance Parameter Calculation In addition to the impedance parameters of the cable, its admittance parameters are also an integral part of the analysis of operating currents. Since it is complicated to analyze the admittance of shielded cables used in engineering separately, we start with the analysis of common coaxial cables. Figure 3 shows a basic neutral coaxial cable with a core conductor that is a phase conductor and is replaced by a series of wires at a distance of Rb from the center conductor. To calculate the capacitance of the core conductor to ground, you can calculate the potential difference between the core and a neutral line. Since the neutral wire is grounded, the potential is 0 and equal, so only one neutral wire needs to be calculated.

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12 b 12

d

d

Fig. 3. Basic neutral coaxial cable

Considering the role of all neutral wires and core conductors, the following equation is written:    qp Rb k · RDs 1 (13) ln ln Vp1 = − 2π ε RDc k Rb where qp is the charge density on the phase conductor; ε is the permittivity of the phase conductor; Rb is the distance between the surrounding conductor and the center conductor; RDc is the radius of the phase conductor; k is the number of neutral lines; RDs are the radius of the neutral line. Since the neutral point is grounded, the capacitance between the phase and ground of a neutral coaxial cable can be obtained according to the above formula: Cpg =

qp 2π ε = Vp1 ln(Rb /RDc ) − (1/k) ln(k · RDs /Rb )

(14)

Thus, the admittance of the cable can be obtained: yag = Cpg = 0 + j

2π ε ln(Rb /RDc ) − (1/k) ln(k · RDs /Rb )

(15)

For shielded cables, the structure is shown in Fig. 4: Because its structure contains a shield, the electric field is as limited as that of a coaxial cable, so that it can be regarded as a special neutral coaxial cable, the number of neutral lines k is regarded as infinity, and the second term of the denominator in the admittance calculation formula tends to 0. Therefore, the formula for calculating the parallel admittance of the shielded cable can be obtained: yag = 0 + j

2π ε ln(Rb /RDc )

where Rb is the distance from the wire core to the sheath; RDc core radius.

(16)

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b

Fig. 4. Diagram of the actual structure of the cables

Similarly, according to the calculation method of cable line impedance parameters, a matrix of admittance parameters is established: ⎤ ⎡ ya1a1 ya1b1 ya1c1 · · · ya1aw2 ya1bw2 ya1cw2 ⎥ ⎢ y ⎢ b1a1 yb1b1 yb1c1 · · · yb1aw2 yb1bw2 yb1cw2 ⎥ ⎥ ⎢ ⎢ yc1a1 yc1b1 yc1c1 · · · yc1aw2 yc1bw2 yc1cw2 ⎥ ⎥ ⎢ . .. .. . . .. .. .. ⎥ (17) Y =⎢ . . . . . . ⎥ ⎢ .. ⎥ ⎢ ⎢ yaw2a1 yaw2b1 yaw2c1 · · · yaw2aw2 yaw2bw2 yaw2cw2 ⎥ ⎥ ⎢ ⎣ ybwwa1 ybw2b1 ybw2c1 · · · ybw2aw2 ybw2bw2 ybw2cw2 ⎦ ycw2a1 ycw2b1 ycw2c1 · · · ycw2aw2 ycw2bw2 ycw2cw2 Refer to the treatment of the impedance matrix, which is simplified to the phase admittance matrix Yabc . Due to the presence of a shield, the electric field generated by the conductor of the core is not associated with the adjacent conductor, so only diagonal elements are present in its phase admittance matrix, and the rest are 0. 2.3 Phase Impedance Parameter Calculation In fact, when analyzing the normal operating current asymmetry and fault current of the cable line, the size of the cable sequence impedance parameter needs to be used, so it is necessary to calculate it. Commonly used methods for solving sequential impedance matrices generally include phase domain analysis and symmetric component methods. Because the 500 kV single-phase double-split cable route does not undergo phase transformation, its phaseto-phase coupling is not equal, so the non-diagonal elements of the sequential impedance matrix are not equal to zero, so the phase domain analysis method is selected for parameter solving.

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The function that defines the core phase voltage-sequence voltage is as follows: ⎡ ⎤ ⎡ ⎤ ⎡ V1(0) ⎤ Va1 1 1 1 ⎢V ⎥ ⎢ ⎥ ⎢ V1(1) ⎥ ⎢ b1 ⎥ ⎢ 1 a2 a ⎥ ⎥ ⎢ ⎢ ⎢ ⎥ ⎢ ⎥ ⎢V ⎥ ⎢ Vc1 ⎥ ⎢ 1 a a2 ⎥ ⎢ 1(2) ⎥ ⎢ ⎥ ⎥ (18) ⎥· ⎢V ⎥ = ⎢ 1 1 1 ⎥ ⎢ V2(0) ⎥ ⎢ ⎢ a2 ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ 1 a2 a ⎦ ⎢ ⎣ V2(1) ⎦ ⎣ Vb2 ⎦ ⎣ 1 a a2 V V c2

2(2)

Write it as a simplified form: [Vabc ] = [A] · [V012 ] There into

⎡ ⎢ ⎢ ⎢ ⎢ A=⎢ ⎢ ⎢ ⎣

1 1 1 1 a2 a 1 a a2

(19) ⎤

⎥ ⎥ ⎥ ⎥ ⎥ 1 1 1 ⎥ ⎥ 1 a2 a ⎦ 1 a a2

(20)

Similarly, the core phase current is defined as follows [Iabc ] = [A] · [I012 ]

(21)

Multiply both sides of Eq. (19) by [A]-1 and substitute Eq. (21) to get: [V012 ]n = [A]−1 · [Vabc ]n = [A]−1 · [Vabc ]m + [A]−1 · [Zabc ] · [A] · [I012 ] = [V012 ]m + [Z012 ] · [I012 ]

(22)

[Z012 ] = [A]−1 · [Zabc ] · [A]

(23)

Thereinto:

By analogy with the analysis process of sequential impedance parameters, without going into detail here, it can be deduced that the sequence admittance matrix is:   (24) y012 = [A]−1 · yabc · [A]

3 Basic Cable Parameters 3.1 Phase Impedance Parameter Calculation Usually 500 kV cable is within 30 km, so the  model is used for equivalence, as shown in Fig. 5, establish a -type equivalent circuit of 500 kV in-phase parallel cable line,

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I1 V1

n

I1

V1 Y1 2

n

I2 V2

n

IY1

I1

n

n

IY1 m

Y1 2

I2

V2 Y2 2

IY 2

I2

n

IY2 m

m

V1

m

V2

m

m

Y2 2

Fig. 5. Pi equivalent circuit of noninverting parallel cable line

According to the -type circuit, the line currents of the two circuits can be written to solve the equation:

     [V1 ]n [I1 ] [I1 ]n 1 [Y11 ] 0 · − · (25) = 0 [Y22 ] 2 [I2 ] [I2 ]n [V2 ]n Among them, Y11 and Y22 represent the 3 × 3-dimensional admittance parameter matrix of the two lines, and Y12 and Y21 represent the 3 × 3-dimensional mutual admittance parameter matrix of the two lines, and the parameters in the matrix are obtained from Eq. (18). Write the above form in short [I ] = [I ]n −

1 · [Y ] · [V ]n 2

(26)

For the receiving voltage:   

  [I1 ] [V1 ]n [V1 ]m [Z11 ] [Z12 ] · = − [Z21 ] [Z22 ] [I2 ] [V2 ]m [V2 ]n

(27)

Similarly, Z11 , Z22 , Z12 , and Z21 are all phase impedance matrices simplified by Kron. Shorten the above equation to write: [V ]m = [V ]n − [Z] · [I ]

(28)

Substituting Eq. (26) into Eq. (28) yields:

    [V1 ]m [V1 ]n [Z11 ] [Z12 ] · = − [Z21 ] [Z22 ] [V2 ]m [V2 ]n       V1 [I1 ] 1 [Y11 ] 0 − · · 0 [Y22 ] 2 V2 [I2 ] n

n

(29)

Analysis of Current and Voltage Characteristics of 500 kV

Finishing, get:    

   [E] [V1 ]m [V1 ]n 1 [Z11 ] [Z12 ] [Y11 ] 0 = + · 0 [Y22 ] [Z21 ] [Z22 ] 2 [E] [V2 ]m [V2 ]n

   [I1 ]n [Z11 ] [Z12 ] · − [Z21 ] [Z22 ] [I2 ]n Equation (30) can be written as   1 [V ]m = [E] + · [Z] · [Y ] · [V ]n − [Z] · [I ]n 2

533

(30)

(31)

Equation (31) can be written as [V ]m = a · [V ]n + b · [I ]n

(32)

1 · [Z] · [Y ] 2

(33)

thereinto [a] = [E] + [b] = −[Z] The receiving current is:

     [V1 ]m [I1 ]m [I1 ] 1 [Y11 ] 0 · = − · 0 [Y22 ] 2 [I2 ] [I2 ]m [V2 ]m

(34)

Shorten the above equation to write: 1 [I ]m = [I ] − [Y ] · [Vm ] 2

(35)

Substituting Eqs. (26) and (32) into Eq. (35) yields: 1 1 · [Y ] · [V ]n − · [Y ]· 2 2 ([a] · [V ]n + [b] · [I ]n )

[I ]m = [I ]n −

(36)

Tidying up, gotta 1 [I ]m = − · ([Y ] + [Y ] · [a]) · [V ]n 2   1 + [E] − · [Y ] · [b] · [I ]n 2

(37)

Formula (37) can be written [I ]m = [c] · [V ]n + [d ] · [I ]n

(38)

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thereinto 1 1 [c] = − · ([Y ] + [Y ] · [a]) = −[Y ] − · [Y ] · [Z] · [Y ] 2 4 1 1 [d ] = [E] − · [Y ] · [b] = [E] + · [Y ] · [Z] 2 2 From this, the final current equation can be written:     

  [I1 ]m [V1 ]n [I1 ]n [c11 ] [c12 ] [d11 ] [d12 ] = + · · [c21 ] [c22 ] [d21 ] [d22 ] [I2 ]m [V2 ]n [I2 ]n

(39)

(40)

The [a], [b], [c], [d] obtained in the above derivation process are all 6 × 6-dimensional matrices. It includes the self-impedance of two parallel lines and the mutual impedance between them. According to Eq. (40), the current size of each line of the 500 kV singlephase double-split cable line can be calculated, and subsequent analysis can be carried out. 3.2 Mathematical Model of Sequence Voltage and Sequence Current In the previous analysis process, the sequence impedance matrix and sequential admittance matrix of 500 kV parallel cable route have been calculated by Eqs. (12) and (17). The sequence impedance matrix Z012 and the sequential admittance matrix Y012 can be substituted for the phase impedance matrix and the phase admittance matrix in Eq. (31) to obtain a mathematical model of the sequence voltage:   1 [V ]m012 = [E] + · [Z]012 · [Y ]012 · [V ]n 2 (41) −[Z]012 · [I ]n Write it down [V ]m012 = a012 · [V ]n + b012 · [I ]n

(42)

1 · [Z]012 · [Y ]012 2

(43)

thereinto [a]012 = [E] +

[b]012 = −[Z]012 Similarly, a mathematical model of sequence current can be obtained by replacing the phase impedance matrix and the phase admittance matrix in Eq. (40) with the phase impedance matrix in Eq. (40) of the sequence impedance matrix Z012 and the sequential admittance matrix Y012: 1 [I ]m012 = − · ([Y ]012 + [Y ]012 · [a]012 ) · [V ]n   2 1 + [E]012 − · [Y ]012 · [b]012 · [I ]n 2

(44)

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Write it down [I ]m012 = [c]012 · [V ]n + [d ]012 · [I ]n

(45)

thereinto [c]012 = −[Y ]012 − [d ]012

1 · [Y ]012 · [Z]012 · [Y ]012 4

1 = [E] + · [Y ]012 · [Z]012 2

The final mathematical model of sequential current is:

 

  [V1 ]n [I1 ]m [c11 ] [c12 ] = · [c21 ] [c22 ] 012 [I2 ]m [V2 ]n 012

   [I1 ]n [d11 ] [d12 ] + · [d21 ] [d22 ] 012 [I2 ]n

(46)

(47)

3.3 Phase Impedance Parameter Calculation Voltage deviation is one of the important factors affecting the power quality of noninverting parallel cables. For noninverting parallel cables, the voltage deviation during normal operation is defined as the relative value of the deviation of its actual operating voltage to the nominal voltage of the system, and its calculation formula is as follows: δU =

Ure − UN × 100% UN

(48)

where is the voltage deviation, % is the actual operating voltage of the system, kV, UN is the rated voltage of the system, kV. According to the national standard GB/T 12325-2008, the sum of the absolute values of the positive and negative deviations of the power supply voltage of the 500 kV voltage level cable does not exceed 10% of the nominal voltage. 3.4 Unbalanced Due to the asymmetry of cable parameters and the influence of factors such as arrangement mode, the voltage and current between parallel cable lines will be unbalanced. The current imbalance of the three-phase parallel line A, B, and C is defined as:  6  1 6  j=1  6 i=1 Ii − Ij  M0 = (49) 6 i=1 Ii In the above formula, the denominator part represents the sum of the currents of each phase of the parallel line, and the numerator part represents the sum of the average

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current values of each phase and the absolute value of the difference between the currents of each phase. The imbalance of each line is:    1 6   6 i=1 Ii − Ij  (50) Mj = 1 6 i=1 Ii 6 MJ represents the current imbalance of one of the phases in a noninverting parallel cable route.

4 Basic Cable Parameters The cable model used in the study is ZB-YJLW02-Z 290/500 1 × 2500 mm2 , and its main parameters are shown in Table 1. Table 1. Basic parameters of ZB-YJLW02-Z 290/500 cable Parameter Conductor nominal outer diameter

61.0 mm

DC resistance at 20 °C

0.0072 /km

AC resistance at 90 °C

0.0108 /km

The pin-shaped laying inductor

0.399 mH/km

Planar routing inductor

0.555 mH/km

Core capacitance

0.192 μF/km

There are many arrangement methods of cables in the project, including threephase horizontal independent arrangement, three-phase horizontal cross arrangement, three-phase vertical arrangement, horizontal arrangement of “product” and vertical arrangement of “product” shape, as shown in Fig. 6. For different arrangements, the distance between cables will be different, which will lead to differences in self-inductance and mutual inductance between cables, so the obtained impedance matrix per unit length is not the same, affecting the imbalance of the cable route. In order to verify the theoretical analysis, first take the vertical arrangement of the “product” shape as an example, take the spacing d = 0.4 m, the full length of the line is 3 km, and the metal sheath grounding method is directly grounded at both ends of the cross-interconnection, which is divided into six sections, each section is 500 m long, the voltage is set to 500 kV, and the line is no-load. Firstly, the unit length impedance matrix and unit length admittance matrix are calculated according to Eq. (14) and Eq. (18), and then the current magnitude is calculated according to Eq. (41), and the specific calculation results and simulation results are shown in the following Tables 2 and 3.

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d

(a) The three phases are arranged horizontally independently

d

h (b) Three-phase vertical arrangement

d

(c) The "product" glyph is arranged horizontally

h

(d) The "product" glyph is arranged vertically Fig. 6. Several typical laying methods

Table 2. The theoretical and calculated values of the phase parameters under the vertical arrangement of the “product” font Phase current

Phase voltage

Calculate the value

436

419

428

451

418

410

406.213

405.167

407.563

Calculate the value

442

425

437

456

420

418

408.121

407.936

408.057

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Table 3. The theoretical and calculated values of the lower order parameters are arranged vertically in the “product” font Sequence current Calculate the value

299

8.7

7.2

299

8.7

7.2

Calculate the value

306

9.3

7.6

306

9.3

7.1

Since the change of core temperature is not taken into account in the theoretical calculation process, there is a slight difference between the calculated value and the simulated value. Change the load size of the cable route, and establish the current curve of each phase of the noninverting parallel cable under different arrangements, as shown in the Fig. 7 below.The load size in the figure is 0 MW, 600 MW, 1200 MW, 1800 MW, 2400 MW, and 3000 MW. According to the definition of unbalance, the current imbalance of each arrangement can be obtained when different loads can be obtained in the substitution of each current in Fig. 7 (49) and (50) as shown in Tables 4, 5, 6 and 7, according to the phase current curve under different load arrangements in the figure, it can be seen that as the load increases, the degree of current imbalance gradually decreases. Among the four selected permutations, the difference in current between the phases of the horizontal arrangement of the “frets” is smaller than that of the other arrangements, that is, its degree of imbalance is minimal. In the other three arrangements, the difference in current between the phases arranged vertically in the three phases is less than that of the other two. Combined with Tables 4, 5, 6 and 7, the imbalance of the horizontal arrangement of the “product” is less than that of the other three arrangements, followed by the three-phase vertical arrangement. The unbalance under each arrangement also decreases with increasing load. This is because the mutual inductance and self-inductance between parallel cable lines are very small, and with the increase of load, the line operating current increases, and the influence of line parameters on the operating current is limited. The following table shows the sequential current magnitude of each arrangement under different loads (Tables 8–11): It can be seen from the table that with the gradual increase of the load size, the negative sequence and zero sequence currents of the three-phase independent arrangement and the three-phase vertical arrangement increase significantly, while the negative sequence and zero sequence currents arranged vertically in the “product” shape and the horizontal arrangement of the “product” shape increase, but the increase is very small. Among them, the zero-sequence current under the horizontal arrangement of the “product” shape is slightly larger than the vertical arrangement of the “product” shape, while the negative sequence current is slightly smaller than the vertical arrangement of the “product” shape. In the actual operation of the power grid, the negative sequence component has a greater impact on the normal operation of the cable than the zero sequence component, so the horizontal arrangement of the “product” zigzag is optimal.

Analysis of Current and Voltage Characteristics of 500 kV

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Fig. 7. Current curves of each phase under different arrangements Table 4. Current imbalance of each phase under different loads under the independent horizontal arrangement of three phases A1

A2

B1

B2

C1

C2

M0

0

0.0124

0.0124

0.0422

0.0422

0.0298

0.0298

0.0281

600

0.0144

0.0144

0.0192

0.0192

0.0048

0.0048

0.0128

1200

0.0127

0.0127

0.0153

0.0153

0.0027

0.0027

0.0102

1800

0.0163

0.0163

0.0093

0.0093

0.0070

0.0070

0.0109

2400

0.0167

0.0167

0.0083

0.0083

0.0083

0.0083

0.0111

3000

0.0168

0.0168

0.0068

0.0068

0.0099

0.0099

0.0112

3600

0.0171

0.0171

0.0063

0.0063

0.0108

0.0108

0.0114

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Table 5. Current imbalance of each phase under different loads under three-phase vertical arrangement. A1

A2

B1

B2

C1

C2

M0

0

0.0012

0.0037

0.0331

0.0307

0.0307

0.0307

0.0217

600

0.001

0.0034

0.0134

0.0134

0.0106

0.0118

0.0089

1200

0.0019

0.0039

0.0061

0.0054

0.0019

0.0039

0.0039

1800

0.0022

0.004

0.0028

0.0028

0.0014

0.0008

0.0023

2400

0.0027

0.0041

0.0018

0.0018

0.0028

0.0004

0.0023

3000

0.0025

0.0039

0.0003

0.0003

0.0042

0.0017

0.0022

3600

0.0031

0.0043

0.0001

0.0001

0.0051

0.0025

0.0025

Table 6. The current imbalance of each phase when different loads are arranged vertically under the word “product” A1

A2

B1

B2

C1

C2

M0

0

0.0069

0.0078

0.0372

0.0372

0.0413

0.0339

0.0274

600

0.0084

0.0072

0.0179

0.0203

0.0215

0.0156

0.0152

1200

0.0091

0.0062

0.0095

0.0128

0.0124

0.0071

0.0095

1800

0.0096

0.0059

0.0068

0.0105

0.0091

0.0046

0.0078

2400

0.0095

0.0064

0.005

0.0092

0.0081

0.0029

0.0069

3000

0.0097

0.006

0.0041

0.0077

0.0063

0.0018

0.0059

3600

0.0102

0.0056

0.0037

0.0077

0.0055

0.0013

0.0057

Table 7. The current imbalance of each phase when different loads are arranged horizontally under the word “product” A1

A2

B1

B2

C1

C2

M0

0

0.0008

0.0008

0.0327

0.0327

0.0335

0.0335

0.0223

600

0

0

0.0132

0.0132

0.0132

0.0132

0.0088

1200

0.0002

0.0002

0.0051

0.0051

0.0049

0.0049

0.0034

1800

0.0003

0.0003

0.0024

0.0024

0.0021

0.0021

0.0016

2400

0.0002

0.0002

0.0012

0.0012

0.0009

0.0009

0.0008

3000

0.0005

0.0005

0.0002

0.0002

0.0007

0.0007

0.0005

3600

0.0009

0.0009

0.0005

0.0005

0.0014

0.0014

0.0009

Analysis of Current and Voltage Characteristics of 500 kV

541

Table 8. The size of the downstream current in different arrangements when the load is 300 MW I1 +

I1-

I10

I2 +

I2-

I20

A

0.386

0.003

0.003

0.386

0.003

0.003

B

0.388

0.002

0.002

0.387

0.001

0.001

C

0.386

0.002

0.001

0.389

0.002

0.001

D

0.387

0

0.001

0.387

0

0.001

Table 9. When the load is 1500 MW, the “different arrangement of the downsequence current.” I1 +

I1-

I10

I2 +

I2-

I20

A

1.308

0.012

0.012

1.308

0.012

0.012

B

1.309

0.006

0.005

1.308

0.005

0.005

C

1.304

0.005

0.003

1.314

0.005

0.003

D

1.309

0.002

0.005

1.309

0.002

0.005

Table 10. The size of the downstream current in different arrangements when the load is 2100 MW I1 +

I1-

I10

I2 +

I2-

I20

A

1.797

0.016

0.017

1.797

0.016

0.017

B

1.799

0.008

0.008

1.799

0.008

0.008

C

1.791

0.007

0.005

1.806

0.007

0.005

D

1.798

0.002

0.007

1.798

0.002

0.007

Table 11. When the load is 2700 MW, the downsequence current is divided into different arrangements I1 +

I1-

I10

I2 +

I2-

I20

A

2.283

0.02

0.022

2.283

0.02

0.022

B

2.285

0.01

0.01

2.282

0.008

0.009

C

2.275

0.009

0.006

2.294

0.01

0.006

D

2.284

0.003

0.009

2.284

0.003

0.009

From the above analysis of the phase current and sequence current under each arrangement under different load conditions, it can be seen that under normal operating conditions, the degree of imbalance of the horizontal arrangement of the “product”

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shape is less than that of other arrangements, because the phase cables arranged horizontally in the “product” shape are the most symmetrical in spatial position, so the mutual inductance is the smallest, and the degree of imbalance is the smallest. For 500 kV transmission lines, the line impedance and admittance are very small, so the mutual inductance generated under different arrangements has little effect on the voltage, so the voltage characteristics under different arrangements are basically the same. Figure 8 shows the voltage and voltage deviation curves of a 500 kV noninverting parallel cable under different load conditions.

Fig. 8. Voltage and voltage deviation curves under different loads

It can be seen from the figure that under different loads, the size of the voltage deviation for each arrangement is less than 10% as specified by the national standard. As the load increases, the line voltage decreases linearly, and the voltage deviation decreases linearly.

5 Conclusion In order to analyze the voltage and current characteristics of 500 kV noninverting parallel cable, this paper first establishes the line parameter model according to the Carson analysis method, and then establishes the calculation method of the line operation parameters by establishing the -type equivalent circuit, and then analyzes and verifies through simulation, and obtains the main conclusions as follows: 1) For 500 kV in-phase parallel cable lines, the symmetry of the “product” shape arrangement is better than other arrangements, among which the vertical arrangement of the “product” character is the best; Among the other arrangements, the symmetry of the three-phase independent horizontal arrangement was better than that of the threephase vertical arrangement and the three-phase cross horizontal arrangement, and the symmetry of the three-phase cross horizontal arrangement was the worst. The voltage deviation under each arrangement is in line with the national standard, and the influence of different arrangement on the voltage deviation is negligible.

Analysis of Current and Voltage Characteristics of 500 kV

543

2) When the load of the cable line gradually increases from no load to rated load, the corresponding core temperature increases, the symmetry of the cable under different arrangement changes poorly, and its change trend is linear. When the line is overloaded for a short time, the symmetry does not change much. The voltage deviation under each load case is within the specified range, and it decreases linearly with the increase of the load. 3) When the “product” is arranged horizontally, the distribution of the sheath circulation is the most uniform, but the voltage of the sheath is the smallest when the “pin” is arranged vertically. The sheath circulation and sheath voltage for each arrangement comply with the regulations. Acknowledgments. Large-capacity long-distance high-voltage bifurcated c able parallel technology research topic 2: 500 kV singlephase bifurcated parallel cable technology analysis and protection research. (GDKJXM20220292(030140KK5222 0001)).

References 1. Li, Z., et al.: Study on sheath grounding mode and reasonable arrangement of return line for parallel cables. In: The 16th IET International Conference on AC and DC Power Transmission (ACDC 2020), Online Conference, pp. 2248–2252 (2020). https://doi.org/10.1049/icp.2020. 0336 2. Liu, G., Zhou, T., Zhao, Y., Yao, D., Bao, W., Wei, Y.: Parallel operation analysis and optimization of cables in urban DC distribution system. In: 2020 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), pp. 213-220. Weihai, China (2020).https://doi. org/10.1109/ICPSAsia48933.2020.9208565 3. Guo, Y., Zhou, M., Zheng, S., Cai, L., Wang, J., Fan, Y.: Study on the induction coupling response characteristics of parallel cables. In: 2020 IEEE 4th Conference on Energy Internet and Energy System Integration (EI2), pp. 1158–1160. Wuhan, China (2020). https://doi.org/ 10.1109/EI250167.2020.9346625 4. Li, Z., et al.: Steady and transient characteristics analysis for parallel cables. In: The 16th IET International Conference on AC and DC Power Transmission (ACDC 2020), Online Conference, pp. 2015–2020 (2020). https://doi.org/10.1049/icp.2020.0029 5. Jiménez, V.J.H., Castronuovo, E.D., Sánchez, I.: Optimal statistical calculation of power cables disposition in tunnels, for reducing magnetic fields and costs. Int. J. Electr. Power Energy Syst. 103, 360–368 (2018). https://doi.org/10.1016/j.ijepes.2018.05.038 6. Jiménez, V.J.H., Castronuovo, E.D., Rodríguez-Morcillo, I.S.: Optimal statistical calculation of underground cable bundles positions for time-varying currents. Int. J. Electr. Power Energy Syst. 95, 26–35 (2018). https://doi.org/10.1016/j.ijepes.2017.08.003 7. Chatzipetros, D., Pilgrim, J.A.: Impact of proximity effects on sheath losses in trefoil cable arrangements. IEEE Trans. Power Delivery 35(2), 455–463 (2020). https://doi.org/10.1109/ TPWRD.2019.2896490

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8. Wang, X., Xiang, Z., Ban, L., et al.: Calculation and analysis of power frequency parameters of 500 kV cable line. Power Syst. Technol. 37(08), 2310–2315 (2013). https://doi.org/10. 13335/j.1000-3673.pst.2013.08.040 9. Deng, X., Meng, S., Yin, X., et al.: Asymmetry analysis of multiple parallel cable route parameters. High Voltage Eng. 36(12), 3119–3124 (2010). https://doi.org/10.13336/j.10036520.hve.2010.12.037 10. IEC Standard-Electric Cables-Calculation of the current rating-part 2-1: Thermal resistancecalculation of thermal resistance , IEC Standard 60287-2-1 (2006)

Characteristic of the Power-Frequency Induced Current and the Corresponding Power Loss on the OPGW of 220 kV Overhead Line Qi Wei1 , Guangxiang Jin1 , Yong Wei2 , Jinxin Cao3(B) , Xianchun Wang4 , Wenhao Zhang3 , Yufei Chen3 , and Jianguo Wang3 1 State Grid Economic and Technological Research Institute Co. Ltd., Beijing 102209, China

[email protected]

2 State Grid Hebei Information & Telecommunication Branch, Shijiazhuang 050000, China 3 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

4 State Grid Hengshui Electric Power Supply Company, Hengshui 053000, China

[email protected]

Abstract. 220 kV overhead transmission line is one of the longest high-voltage transmission line systems in China, and the insulating modification of its widely used tower-by-tower grounded optical fiber composite ground wire (OPGW) will have critical prospects and potential for energy saving and power-transmission efficiency. At present, there are relatively few studies on the power-frequency induced current and power loss in the tower-by-tower grounding mode of OPGW for 220 kV overhead transmission lines, the results of which are an important prerequisite for the feasibility analysis of OPGW insulation technology. Based on the modeling and numerical simulation of the ATP-EMTP software platform, this paper investigates the OPGW power-frequency induced current and the corresponding power loss characteristics for 220 kV overhead lines with the recommended double-circuit towers and lines according to the standard design files. The characteristics of induced current and power loss influenced by different standard towers, line heights, DC resistance of the OPGW, tower span, and phase sequence are and analyzed and summarized with well sensitivity analysis. The present study is of great significance for guiding the comprehensive evaluation of the technical feasibility and economic performance of OPGW insulation retrofit. Keywords: 220 kV transmission line · Optical fiber composite overhead ground wire (OPGW) · Tower-to-tower grounding · Power-frequency induced current

1 Introduction The optical fiber composite overhead ground wire (OPGW), as a new lightning conductor, has lightning stroke, short-circuit fault discharge performance, and lightning shielding electrical performance. Currently, it has been widely used in high-voltage transmission lines of 110 kV and above in China. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 545–554, 2024. https://doi.org/10.1007/978-981-97-1072-0_55

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The main grounding methods for Optical Fiber Composite Ground Wire (OPGW) are “all grounding” and “single-point grounding after segmented insulation”. The former provides a more favorable pathway for lightning strikes and fault current discharge, which is beneficial for protecting OPGW and its internal optical fibers. As a result, “all grounding” is currently the more widely adopted grounding method for OPGW in high-voltage transmission lines in China [1–4]. However, there are issues related to electromagnetic and electrostatic induction between the overhead ground wire and the live conductors [5]. The imbalance in electromagnetic induction electromotive forces generated by individual phase conductors in the ground wire can create alternating current loops through the ground wire, tower, and the Earth, leading to power frequency electromagnetic induction current and subsequently causing power frequency induction energy loss in OPGW [6–13]. This paper conducts research on the power frequency electromagnetic induction currents and energy loss characteristics of OPGW for 220 kV overhead lines. The study is based on modeling and numerical simulation using the ATP-EMTP software platform. It considers various factors such as different standard tower types recommended in the “Typical Design of State Grid Corporation of China’s Transmission and Transformation Projects,” different tower heights, different ground wire DC resistances, different spans, different phase sequences, and operating conditions. The research results will provide guidance on the feasibility and economic assessment of insulating modifications for 220 kV lines.

2 Calculation Model and Line Parameters 2.1 Typical Line Parameters and Model A transmission line model was established in ATP-EMTP. The transmission line uses the PI-type circuit of the LCC module for calculations, and the impedance parameters of the line are determined using a simplified low-frequency version of the Carson model. The entire line was modeled with 40 towers, and the span distance was set to the reference value of 350 m. The OPGW was adopted all grounding. For line model, the both ends are substations and the load of each circuit line is taken as a reference value of 500A.The model of the 220 kV overhead transmission system has been constructed in ATP-EMTP software. By numerical calculation with this model, the induced voltage, induced current among the ground wire, and the induced current when the tower enters the ground can be obtained. The total of the energy loss by the power frequency electromagnetic induction in OPGW can be obtained by the following formula:   I (l)2 ρ(l)dldt (1) Pl = I (l) is the effective value of the induced current along OPGW considering that the lengths of the lines corresponding to the span of the two base towers are equal and determined. ρ(l) represents the low frequency resistance value per kilometer of OPGW. Furthermore, using Ii to represent the effective value of the induced current for the i-th

Characteristic of the Power-Frequency Induced Current

547

section of the line, the formula for calculating OPGW’s power loss due to electromagnetic induction at power frequency is transformed into: P1 =

n 

I1i2 ρi li · T

(2)

I2i2 ρi li · T

(3)

i=1

P2 =

n  i=1

where subscripts 1 and 2 represent the calculated losses for the OPGW on both sides of the line, li represents the length of that section of the line (in kilometers), and n represents the total number of spans in the line. On the other hand, the calculation of energy loss caused by the current into the earth at the tower is as follows: P3 =

n+1 

I3j2 Rj · T

(4)

j=1

where I3j represents the effective value of the current into the earth for the j-th tower, and Rj is the power frequency ground resistance of that tower. Thus, the total induced electrical energy loss in the grounded OPGW due to power frequency electromagnetic induction is calculated as follows: Pt = P1 + P2 + P3

(5)

2.2 Typical Tower Parameters According to the 2011 edition of the “State Grid Corporation of China’s Transmission and Transformation Projects Typical Design for 220 kV Transmission Lines,” and taking into consideration meteorological conditions, engineering requirements, and the suitability of calculations, four representative models from double-circuit lines were selected for simulation calculations. The tower models and parameters are shown in Table 1, and the parameters for the conductors and OPGW used are shown in Table 2. Table 1. 750 kV typical tower. Type

Feature

Wire

Span (m)

Height (m)

2D1-SZ1

double-circuit

2 × LGJ-300/40

350

27

2E1-SZ1

double-circuit

2 × LGJ-400/35

350

30

2E9-SZ1

double-circuit

2 × LGJ-400/50

350

30, 36

2F1-SZ1

double-circuit

2 × LGJ-630/45

350

27

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Q. Wei et al. Table 2. Conductors and ground wires.

Type

Calculation inside diameter (mm)

Calculation outside diameter (mm)

20°C direct current resistance (Ω/km)

2 × LGJ-300/40

7.04

23.94

0.09641

2 × LGJ-400/35

6.61

26.82

0.07389

2 × LGJ-400/50

8.12

27.63

0.07232

2 × LGJ-630/45

7.41

33.6

0.04633

OPGW (0/143-162.1)

\

16

0.306

OPGW (0/175-351.3)

\

17.75

0.251

OPGW (0/110-89.4)

\

13.9

0.428

2.3 Line Operation Parameters The operational parameters discussed in this paper include: 1) Ground wire DC resistance, which refers to the direct current resistance of the OPGW used, measured in /km. 2) Span, which means the distance between adjacent towers. In typical designs, recommended span values are provided, but in practice, span design may be adjusted based on actual conditions. 3) Phase sequence. In theory, the conductor phase sequence for dual-circuit transmission lines is typically arranged in the order of A, B, C. However, different phase sequence arrangements can also be chosen.

3 Analysis of Line Induced Current and Energy Loss This chapter analyzes the induced current along OPGW, current into the earth, and the corresponding energy losses for a 220 kV line. It investigates the impact of tower height, ground wire DC resistance, tower spacing, different tower types for dual-circuit lines, and phase sequence, as well as other line and operational parameters. 3.1 Induced Current Distribution Characteristics The four types of towers mentioned in Table 1 were subjected to simulation and analysis calculations for induced current along the OPGW and current into the earth. Figure 1 shows the distribution of the effective value of induced current along the OPGW and current into the earth for four typical double-circuit line towers. Based on the statistical analysis of the distribution results, it can be concluded that the induced current along the OPGW has a higher magnitude in the middle. When the line is loaded with 500 A, the highest induced current along the OPGW can reach 54 A (for the 2D1-SZ1 type tower). The amplitude of the induced current gradually decreases towards both ends of the line, with the induced current at the ends of the 2D1-SZ1 tower attenuating to approximately 37 A, which is only about 68.5% of the highest amplitude at the middle position.

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Upon comparison, it is found that the distribution trend of the current into the earth is opposite to the distribution characteristics of the induced current along the line. The current into the earth is relatively small in the middle of the line, approaching zero, and relatively larger on both sides, but the amplitude does not exceed 7 A, which is much smaller than the amplitude of the induced current along the line under the same conditions. The trend of these two currents is related to the symmetry of the tower-ground wire-tower-earth loop current formed by every two adjacent towers. The symmetry is higher at the towers in the middle, where the loop currents passing through the towers on both sides have opposite directions and similar amplitudes, thus canceling each other out, resulting in an effective current that approaches 0. As the process continues towards both sides, the symmetry of the loop currents decreases, leading to an increase in the current into the earth caused by the asymmetry. Therefore, the overall distribution trend of the current into the earth is “small in the middle, large on both sides”.

Fig. 1. The power-frequency induced current along the OPGW and the current into the ground with different tower types (a) 2D1-SZ1, (b) 2E1-SZ1, (c) 2E9-SZ1, (d) 2F1-SZ1.

Additionally, a comparison of the induced current calculation results for different typical towers shown in different subplots of Fig. 1 reveals that, although the distribution characteristics of induced current along the OPGW for different typical towers are highly similar, the amplitudes fluctuate within the range of 38 to 54 A. Analysis suggests that the differences in calculation results are related to the OPGW-conductor spatial positions and spacing in the designs of different tower types, which directly affect the strength of the power-frequency electromagnetic coupling effect and vector superposition effect [2].

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3.2 Impact of the OPGW DC Resistance This section further discusses the impact of OPGW DC resistance on the induced currents along the OPGW and the current into the earth. In the simulation and modeling, three different OPGW cables were used with DC resistances of 0.251 , 0.306 , and 0.428 , respectively. The tower type chosen for the calculations is the double-circuit line 2D1SZ1. The simulation results are shown in Fig. 2.

Fig. 2. The influence of ground wire DC resistance (a) Induced current along OPGW, (b) Current into the earth.

From Fig. 2, it can be observed that the DC resistance of the ground wire has a noticeable impact on the magnitude of the induced current along the OPGW. A change in DC resistance from 0.251 /km to 0.428 /km leads to a 16.7% variation in magnitude. At the same time, the magnitude of the current into the earth also experiences some degree of change, although its variation is less affected by the DC resistance. Table 3. The induced annual energy loss with different DC resistance of the OPGW. OPGW DC resistance (/km)

Induced loss on OPGW (kWh/a.km)

Tower grounding loss (kWh/a.km)

Total loss (kWh/a.km)

0.306

12560.56

1076.298

13636.85

0.251

13124.98

1157.597

14282.58

0.428

16203.56

902.4277

17105.98

Table 3 provides the annual energy losses corresponding to the induced current along the OPGW for different OPGW DC resistance values. It’s worth noting that the total energy loss is determined by both the energy loss due to induced current along the OPGW and the energy loss due to current into the earth. The data in the table show that the OPGW with the lowest induced current (0.428 /km) actually has the highest overall losses, while the OPGW with the highest induced current (0.251 /km) falls in the middle range of losses. This is because the increase in induced current along the ground wire in the ground-tower-ground loop caused by a decrease in DC resistance (0.251 /km) is not in a linear proportionate trend. Therefore, even though the induced current is highest under this condition, the reduction in resistance results in it falling in the

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middle range of energy losses. When the DC resistance is at its maximum (0.428 /km), the decrease in current is less than the increase in resistance, and according to the energy loss calculation formula, it still results in a relatively higher energy loss. 3.3 Impact of Span This section further discusses the impact of span on the induced current along the OPGW and the current into the earth. Conductor spacing represents the distance between adjacent towers, which affects physical parameters like tension, sag, and other aspects of the conductor. Additionally, conductor spacing determines the distance between grounding points along the line, which can alter the overall impedance of the circuit and, consequently, affect induced currents and current into the earth, further influencing the magnitude and distribution of current losses. In practical situations, span is determined based on various factors, including geographical constraints. Therefore, it may not always conform to standard spacing values. In this study, simulations were conducted for three common conductor spacings of 350 m, 480 m, and 850 m on a 220 kV transmission line for comparative analysis. The simulation results are depicted in Fig. 3.

Fig. 3. The influence of span (a) Induced current along OPGW, (b) Current into the earth.

As evident from the figure, the conductor spacing has a noticeable impact on the distribution characteristics of the induced current along the OPGW and the current into the earth. With increasing conductor spacing, the magnitude of the OPGW-induced current along the OPGW slightly decreases in the central tower section while slightly increasing on both sides of the towers. Simultaneously, the current into the earth experiences a slight decrease in the central section and a slight increase on both sides of the towers. Table 4 provides the annual electrical energy losses under different span. It can be observed that with increasing conductor spacing, the losses due to induced currents gradually increase, although the increase is not substantial. On the other hand, the losses due to current into the earth decrease progressively, and this reduction is relatively significant. This is related to the reduction in the number of towers per unit length, which corresponds to a decrease in grounding point density. In terms of total losses, increasing the spacing from 350 m to 850 m results in a mere 0.05% increase in losses, indicating virtually no change.

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Span (m)

Induced loss on OPGW (kWh/a.km)

Tower grounding loss (kWh/a.km)

Total loss (kWh/a.km)

350

12560.56

1076.30

13636.85

480

12990.28

651.63

13641.91

850

13250.08

394.15

13644.23

3.4 Impact of Phase Sequence In the reference case, the phase sequence of both the two circuit lines has been fixed to ABC. In the investigation of the phase sequence, there are six possible arrangements for the two circuits: ABC-ABC (in-phase arrangement), ABC-CBA (out-of-phase arrangement), ABC-ACB, ABC-BCA, ABC-BAC, and ABC-CAB. The distribution of induced currents along the OPGW and currents into the earth under different phase sequences is shown in Fig. 4. It is observed that the phase sequence has a significant impact on the distribution of both the induced currents along the OPGW and currents into the earth.

Fig. 4. The influence of phase sequence (a) Induced current along OPGW1, (b) Induced current along OPGW2, (c) Current into the earth.

From Fig. 4, it can be observed that in the case of the same phase sequence (ABCABC), both the induced currents along OPGW and the earthward currents are relatively high. However, when the phase sequence is reversed (ABC-CBA), both the induced

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currents along OPGW and the earthward currents are at their lowest or lower levels. The situations for the other four phase sequence arrangements are in intermediate states. Table 5. The induced annual energy loss with different phase sequences of the second circuit. Phase sequence of the second circuit

Induced loss on OPGW (kWh/a.km)

Tower grounding loss (kWh/a.km)

Total loss (kWh/a.km)

A-B-C

12560.56

1076.30

13636.85

C-B-A

10969.73

35.89

11005.63

A-C-B

13522.20

504.37

14026.57

B-C-A

11827.97

223.21

12051.18

B-A-C

12068.55

809.26

12877.82

C-A-B

11827.97

223.21

12051.18

Table 5 provides the annual energy losses along OPGW for different phase sequences. The data shows that among the six different phase sequence conditions, the arrangement of ABC-ABC (same phase sequence) results in the highest tower grounding loss and higher total losses. Conversely, the ABC-CBA (opposite phase sequence) arrangement leads to the lowest total losses, with the least induced current losses along the OPGW and tower grounding loss losses. The ABC-ACB arrangement has the highest total losses and also the highest induced current losses on OPGW. The remaining scenarios fall within intermediate values. In all six scenarios, except for the ABC-ACB arrangement, the other phase sequences contribute to reducing the total current losses, with the ABC-CBA (opposite phase sequence) arrangement having the most significant reduction effect. Overall, considering the goal of minimizing OPGW total energy losses, it is recommended to avoid using the ABC-ACB phase sequence arrangement during the process of changing the sequence for double-circuit lines.

4 Conclusion This study established a model of a 220 kV single-circuit transmission line with two OPGW installed on typical towers. The analysis focused on the distribution of induced currents along the line under the condition of all grounding, as well as the impact of OPGW DC resistance, span, phase sequence on induced currents. The simulation results indicate that OPGW DC resistance significantly affects induced currents and annual energy losses. A higher resistance value leads to greater energy losses, with the highest reaching 17105.98 kWh/km. While different conductor spacings for the same tower type do influence the amplitude and distribution characteristics of induced currents to some extent, they have only a minimal impact of 0.05% on the total annual energy losses of the line. With the exception of the ABC-ACB phase arrangement, all other arrangement methods have the effect of reducing the total current

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loss. Among them, the reverse phase sequence (ABC-CBA) has the most significant effect on reducing OPGW’s power frequency induction energy loss. The research results reveal the distribution characteristics of power frequency electromagnetic induction currents and energy loss characteristics of 220 kV transmission lines under different line and operating conditions. This has guidance significance for the feasibility and economic evaluation of OPGW insulation transformation technology. Acknowledgment. This work was supported by the Science and Technology Project of State Grid Limited Headquarters (Project 5108-202218280A-2-418-XG).

References 1. Hu, Y., Liu, K.: Analysis and Research on the Grounding Method of OPGW in Transmission Lines. High Voltage Eng. 34(9), 1885–1888 (2008). https://doi.org/10.13336/j.1003-6520. hve.2008.09.018 2. Wang, Y., Wang, J., Peng, X., et al.: Induced current and energy loss of overhead ground wire in 220 kV double-circuit transmission lines on the same tower. High Voltage Apparatus 49(05), 31–38 (2013) 3. Xu, X., Mao, X., Wang, Y., et al.: Influence of conductor arrangement on induced current of overhead ground wire in double-circuit transmission lines on the same tower. South. Power Syst. Technol. 7(04), 60–66 (2013) 4. Peng, X., Mao, X., Hu, W., et al.: Energy-saving grounding technology for overhead ground wire in transmission lines. Electr. Power Constr. 35(08), 84–90 (2014) 5. Chen, Y., et al.: Characteristic of power-transmission-induced current and power loss on the OPGW of 750 kV transmission line system. Electr. Power Syst. Res. 229, 110130 (2024). https://doi.org/10.1016/j.epsr.2024.110130 6. Chen, Y., et al.: Analysis of induced voltage of optical fiber composite ground wire in 35 kV overhead distribution lines. IEEE Trans. Electromagn. Compat. 66(1), 313–323 (2024). https://doi.org/10.1109/TEMC.2023.3319052 7. Wang, J., Wang, Y., Peng, X., Li, X., Xu, X., Mao, X.: Induced voltage of overhead ground wires in 500-kV single-circuit transmission lines. IEEE Trans. Power Delivery 29(3), 1054– 1062 (2014) 8. Sun, Y., et al.: Analysis of Induced Voltage of Ground Wires in 1000 kV transmission lines. In: 2022 IEEE International Conference on High Voltage Engineering and Applications (ICHVE), pp. 1–4. Chongqing, China (2022) 9. Fu, Z.-X, Guo, J.-M., Li, Y.-G.: Calculation of line parameters in different grounding modes of double earth wire. In: 2016 International Symposium on Computer, Consumer and Control (IS3C), pp. 148–151 (2016) 10. Yuqun, F., Liqun, Q., Taishan, H., Bo, Z., et al.: Analysis of the effect on induced voltage initiate by insulated ground wire transposition in double-circuit transmission line on the same tower. In: 2016 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1–8. Chengdu, China (2016) 11. Zhang, D.-s.: Design handbook for high voltage power supply circuit of electric power engineering. China Electr. Power Press 156–161 (1999) 12. National Energy Administration, China Electricity Council. 2021 National Electricity Reliability Annual Report, p. 162 (2022) 13. Liu, Z.: Typical design of state grid corporation’s transmission and transformation projects: 220 kV transmission lines. China Electr. Power Press (2011)

Construction and Application of Knowledge Graph in Electric Power Field Huapeng Chen1(B) , Shuo Yu1 , Tian Cao2 , and Xinyu Cao1 1 School of Electrical Engineering, China University of Mining and Technology,

Xuzhou 221116, China [email protected] 2 School of Electrical Engineering, Sichuan University, Chengdu 610065, China

Abstract. In the process of the gradual deepening of the electric power system informatization construction, a large amount of electric power data is accumulated in the electric power field (EPF). In order to effectively organize, manage and utilize the knowledge of large amounts of power data, knowledge graph (KG) technology is introduced into the field of electric power system. Firstly, the concept, classification and construction method of KG in EPF are introduced, and the key technology and difficult problems are elaborated in detail. Secondly, the typical application of KG in EPF is analyzed from three aspects: health management of electric power equipment, fault handling of power distribution network, and supervision and transaction of electric power market. Finally, the application prospect of KG in EPF is discussed, which provides the reference for further in-depth research on the application of KG technology in EPF. Keywords: Knowledge Graph · Electric Power Field · Information Processing

1 Introduction As an important support of the national economy, the electric power system is of great significance to the supply of energy and the sustainable development of energy. However, with the dramatic increase in the amount of data in EPF, traditional data management and analysis are no longer sufficient to meet the demand. KG, as a way to be able to transform data into knowledge, offer a new solution for EPF. KG is a graphical model for representing and reasoning about knowledge. By modeling the entities, attributes and relations of the real world in the form of graphs, it can integrate and connect scattered knowledge to form the structured knowledge network [1]. As an important branch of artificial intelligence, KG is already researched in several fields, but it is still in its infancy in EPF. In order to be used for fault defect information retrieval, the electric power dictionary is utilized to extract defect information entities and construct the KG of power equipment defects [2]. By integrating and mining data from multiple low-voltage (LV) distribution network information systems, a KG construction method for LV distribution network topology is proposed, which realizes the identification of household-variable relationships of LV distribution networks within the system © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 555–561, 2024. https://doi.org/10.1007/978-981-97-1072-0_56

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[3]. Oriented to the intelligent scheduling of power grid, the KG construction method in this field is proposed, which is mainly applied to the scenarios such as fault disposal [4]. The application scenarios of KG in the health management of electric power equipment are analyzed, and the application prospects are outlooked [5]. The KG based analytical framework is proposed to sort out the core frontiers of electricity market development in the last decade from the time dimension [6]. Based on the results of existing research, the concept of KG is introduced, the construction technology of KG in EPF is analyzed, and three major categories of application scenarios, such as health management of electric power equipment, fault handling of power distribution network, and the supervision and transaction of electric power market, are summarized in this paper. At the same time, the future development prospects of KG in EPF are analyzed and possible directions are provided for the development of digitization, informatization, and intelligentization of the new electric power system.

2 Conceptualization and Construction of KG 2.1 The Concept of KG for Electric Power According to the coverage and domain of knowledge, the KG can be divided into general KG and domain KG. The general KG covers a wide range of content and usually serves the structured encyclopedic knowledge base in the general domain, which is not required to be accurate in practical application. The domain KG can be regarded as a branch of the KG. Different from the general KG, it focuses on the specific domain and usually provides business functions or solves specific problems in response to the needs and characteristics of the domain. Therefore, the depth and accuracy of its knowledge in the field is highly required. KG of electric power is a form of technology that applies KG technology to the EPF, which belongs to the domain KG. Its typical application scenarios include health management of electric power equipment, fault handling of distribution network and supervision and transaction of electric power market. The KG of electric power can be categorized according to the kind of electric power knowledge entities stored, such as textual KG, image KG, and multi-modal KG. In addition, based on the storage method of entity data, the KG of electric power can be categorized into single-sample-based KG and sample-set-based KG. Moreover, it can be divided according to the way of storage and expression of entity data in the graph, including different types of KG such as KG of resource description framework databases and KG of graph databases [7]. 2.2 The Construction of KG for Electric Power At present, the construction of KG in EPF is relatively scarce. Along with the continuous advancement of the digitization process of electric power business, a large amount of EPF knowledge is latent in the unstructured text data, semi-structured tabular data, and the databases of the internal management system of electric power enterprises. How to build a KG with in-depth knowledge of EPF from scratch is a difficult task for experts and engineers related to the electric power industry.

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Domain KG ontology construction methods mainly include knowledge-driven topdown, data-driven bottom-up and a combination of both. The bottom-up construction method is to extract entities, concepts, relationships, attributes and other information from the existing unstructured data to be added to the data layer, and then analyze and summarize these knowledge elements layer by layer to finally form the schema layer, as shown in Fig. 1. The top-down construction method is to create the schema layer based on the existing structured data and expert knowledge base construction, form the corresponding conceptual model and rule relationships based on the ontologies and their interrelationships in the schema layer, and then construct the data layer based on this schema by obtaining the structural information of the knowledge entities in EPF from the data source, as shown in Fig. 2.

Fig. 1. Bottom-up Construction Method of KG.

Fig. 2. Top-down Construction Method of KG.

There are wide range of data source in EPF. On the one hand, the existing structured data, such as the expert experience knowledge base, can be directly used to guide the topdown construction of the KG. On the other hand, various electric text data in EPF, as well as semi-structured and unstructured data such as subjective experiences of experts and technicians, also contain rich electric power industry knowledge. Through the technology of knowledge extraction and knowledge fusion, these knowledge of electric power are formed into abstract concepts and mapped or supplemented into the KG of EPF, thus realizing the bottom-up construction of the ontology. Therefore, the combination of topdown and bottom-up method is usually used to improve the quality and coverage of the KG when actually constructing the KG in EPF, as shown in Fig. 3.

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Fig. 3. Construction Method of KG.

Multiple aspects of information processing technology need to be applied to the construction of KG. Analyzing the existing studies, it can be seen that the technical architectures proposed by different scholars for the construction of domain KG are slightly different, but the core modules include knowledge extraction, knowledge fusion, intellectual inference and other parts. The knowledge extraction extracts information such as entities, relationships and attributes from the source data and converts this information into structured data. The knowledge extraction is mainly divided into two aspects: named entity recognition and entity relationship extraction. The common entity recognition techniques include BI-LSTM-CRF model [8] and LSTM-CNNs-CRF model [9]. The commonly used methods for relation extraction include the pipeline method based on Att-RCNN model [10] and the joint extraction method based on Bert + BI-LSTM model [11]. The knowledge fusion is the process of eliminating, processing and integrating heterogeneous and diversified knowledge from different data sources under the same framework so as to achieve the fusion of data and information from multiple perspectives. Knowledge inference is to infer unknown fact or relationship based on a large number of existing fact or relationship in the KG, to achieve the purpose of expanding, perfecting and enriching the knowledge base, and then to ensure the diversity and completeness of the KG.

3 Application of KG in EPF 3.1 Health Management of Electric Power Equipment Currently, in the health management of power equipment, continuous online monitoring data are mainly used for fault classification and diagnosis. However, a large corpus of power text is generated during daily inspections, and the relevant knowledge it contains is underdeveloped and underutilized. It is crucial for health management of power equipment to mine the knowledge in the power text corpus. The application of KG technology in the health management of power equipment can effectively cope with the rapid growth of power equipment data and meet the needs of knowledge management. It combines the inherent characteristics of devices and human empirical knowledge, and utilizes the technology of knowledge graph to process and manage massive multi-source heterogeneous data. Through the stages of question and answer generation, search matching,

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and decision strategy generation and recommendation, the knowledge graph for health management of power equipment can provide interpretability and personalization for assisted decision making. This method not only improves the efficiency and accuracy of health management of power equipment, but also provides guidance for developing unique inspection and operation and maintenance method for power system. 3.2 Fault Handling of Power Distribution Network The power distribution network is an important part of urban power supply. However, due to its large scale and difficulty in realizing refined analysis, fault handling often takes a lot of time and manpower. Traditional troubleshooting methods often rely on manual experience, which is inefficient and error-prone. To solve this problem, a knowledge graph-based assisted decision-making method was proposed by the researchers. A fault handling knowledge graph is constructed using grid scheduling rules, fault profiles, which contains fault handling knowledge, business process knowledge, and manual experience knowledge. It provides regulators with fast, intelligent and accurate auxiliary decision support. When the fault occurs, the processing computation module searches for matching knowledge paths in the fault field KG of the distribution network, and then queries the lower levels for concepts and equipment entities that are closely related to the fault. After gaining relevant knowledge, the information analysis module, fault judgment module and fault disposal module are used for research and judgment, and the type of fault and disposal suggestions are given. During the disposal process, it is necessary for the machine to provide the dispatcher with filtered primary information, implied knowledge, operating principles and special requirements. At the end of the fault disposal process, the structured knowledge of the intelligently extracted fault events is taken and remitted to the case knowledge base, as well as being used for subsequent case recording, access and reasoning. This assisted decision-making method based on KG not only improves the efficiency of fault handling, but also reduces problems such as human misjudgment and delay. 3.3 The Supervision and Transaction of Electric Power Market The electricity market is currently facing a number of challenges, including insufficient market competition, difficulty in achieving a balance between electricity supply and demand, and inefficient energy consumption. To address these challenges, the researchers proposed a methodology for constructing the KG of electric power market. On the one hand, the KG can help the power market to establish a more accurate market model, including information about each participating subject, market rules, supply and demand relationships in the power market. By structuring the representation of this information, market participants can be provided with more comprehensive market information, which promotes the full realization of market competition and thus enhances market competitiveness. On the other hand, the KG can integrate a variety of powerrelated data, including the status of power generation equipment, the topology of the power network, customer demand and other information. By correlating and analyzing this information, it is possible to establish a model for the balance of power supply and demand, and provide corresponding forecasting and scheduling strategies, thus realizing

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the balance of power supply and demand. In addition, the knowledge graph can help the electricity market establish a more comprehensive and accurate energy consumption model. By analyzing information such as changes in various energy efficiencies and influencing factors, potential problems in energy consumption can be identified and corresponding optimization strategies can be provided to improve the efficiency of energy consumption.

4 Perspectives of KG in Electric Power Field 4.1 Data Quality Data quality is a critical issue in the construction of KG in EPF. Data inaccuracies, inconsistencies, incompleteness and unreliability are current data quality problems. To address these issues, data sources must be evaluated and validated to ensure their accuracy and reliability. Therefore, improving data quality in the electric power field is a key area for future research. 4.2 Knowledge Inference Knowledge inference is the process of inferring unknown fact or relationship based on a large number of existing fact or relationship in the KG, thereby complementing the KG. Existing knowledge reasoning is mainly based on logic rules, distributed feature representation, neural networks and reinforcement learning. However, when these methods are applied to the KG of EPF, the accuracy is still limited. On the one hand, the power system generates new data continuously, whereas traditional inference techniques based on static graph struggle to incorporate time-series information as well as perform dynamic modeling in power scenarios. On the other hand, researchers can use accumulated knowledge and a small number of cases to reason effectively, but it is difficult for machine to do this often. The current numerous methods of knowledge inference are difficult to obtain higher-order rules as well as knowledge information in small samples, thus leading to poor inference effects. Therefore, further research is needed on how to incorporate time series information into knowledge inference techniques and to combine small-sample learning with knowledge inference. 4.3 Cross-Domain Knowledge Fusion The KG in EPF can be fused with the KG in other domains to realize cross-domain knowledge sharing and interaction. On the basis of constructing the KG in EPF, the KG in transportation field and the KG in charging service field are constructed. Realtime road traffic data, environmental data, and historical data can be fed into the KG of transportation field. Real-time charging data, environmental data, and historical data can be fed into the KG of charging service field. Then, knowledge fusion techniques are used to obtain the correlation between the power network-charging service networktransportation network. Through this synchronous prediction and correlation relationship between multi-domain KG, it is possible to realize autonomous assessment of the

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matching degree of traffic, charging service and power relationship and rolling planning of charging facilities, so as to create the new ecology of intelligent new energy vehicle service.

5 Conclusion In this paper, the concept and framework of the KG in EPF are elaborated in detail. Then the typical applications of KG in EPF are analyzed. Finally, the application of KG in EPF is prospectively analyzed by combining the characteristics of EPF itself with the current relevant research. In the future, the application of KG can be further deepened to enhance the intelligence of the electric power system and promote the development of EPF.

References 1. Wang, N., Haihong, E., Song, M., et al.: Construction method of domain knowledge graph based on big data-driven. In: 5th International Conference on Information Management, pp. 165–172. IEEE, Cambridge (2019) 2. Liu, Z., Wang, H.: Retrieval method for defect records of power equipment based on knowledge graph technology. Autom. Electr. Power Syst. 42(14), 158–164 (2018). (in Chinese) 3. Gao, Z., Zhao, Y., Yu, Y., et al.: Low-voltage distribution network topology identification method based on knowledge graph. Power Syst. Protect. Control 48(2), 34–43 (2020). (in Chinese) 4. Yu, J., Wang, X., Zhang, Y., et al.: Construction and application of knowledge graph for intelligent dispatching and control. Power Syst. Protect. Control 48(3), 29–35 (2020). (in Chinese) 5. Li, G., Li, Y., Wang, H., et al.: Knowledge graph of power equipment health management: basic concepts, key technologies and research progress. Autom. Electr. Power Syst. 46(3), 1–13 (2022). (in Chinese) 6. Bian, X., Zhang, L., Zhou, B., et al.: Review on domestic and international electricity market research based on knowledge graph. Trans. China Electrotech. Soc. 37(11), 2777–2788 (2022). (in Chinese) 7. Wang, R., Yuan, Y., Yuan, X.: Study on the construction of Chinese knowledge graph based on deep learning and graph database. Library Inform. 1, 110–117 (2016). (in Chinese) 8. Meng, L., Qi, W., Zhou, Y., et al.: News text named entity recognition based on BI-LSTM-CRF model. In: 41th Chinese Control Conference, pp. 7217–7222. IEEE. Hefei (2022) 9. Miwa, M., Bansal, M.: End-to-end relation extraction using LSTMs on sequences and tree structures. In: 54th Annual Meeting of the Association for Computational Linguistics, pp. 1105–1116. Association for Computational Linguistics, Berlin (2016) 10. Guo, X., Zhang, H., Yang, H., et al.: A single attention-based combination of CNN and RNN for relation classification. Access 7, 12467–12475 (2019) 11. Wang, C., Li, A., Tu, H., et al.: An advanced BERT-based decomposition method for joint extraction of entities and relations. In: 5th International Conference on Data Science in Cyberspace, pp. 82–88. IEEE, Hong Kong (2020)

Study on Characteristic and Optimization of Eddy Current Damper Under Impact Load Chao Zhang1 , Xin-ke Ma1 , Xiao-ming Han2(B) , and Qiang Li2 1 The 713 Research Institute of CSSC Zheng, Zhou 450015, China 2 College of Mechatronic Engineering, North University of China, Taiyuan 030051, China

[email protected]

Abstract. To investigate the damping force characteristics of an eddy current damper under the impact load, a permanent magnet eddy current damper model is proposed, and a dynamic model of the moving part under the impact load is created. Furthermore, the finite element approach is used to analyze the dynamic properties of damping force under different structural parameters. Taking the minimum fluctuation of damping force and the minimum volume of damper as the optimization objectives, the objective function is established and the boundary conditions are determined. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is utilized to maximize the research during the procedure. The results demonstrate that structural elements such as the pair equivalent air gap thickness and conductivity of the conductor tube have significant effects on the damping force. After optimization, the volume of the damper is noticeably lower, the regular curve of the resistance under the impact load is smoother and flatter, and the control effect of the damping force is obvious, which can effectively avoid the saddle-shaped curve of the traditional damper. The research findings contain specified reference values for better damping force control under high impact loads and boosting equipment performance. Keywords: Eddy current damper · Impact load · Damping characteristics · Optimization study

1 Introduction The performance of the damper, being the main component of the impact vibration equipment, directly affects the performance of the equipment. Due to the hypothesis and process factors, the regular curve of resistance in the buffer shows large fluctuations at the initial and final stages of the buffer, and the performance of the damper will decline dramatically when the liquid leaks and deteriorates [1]. Eddy current damper, without liquid, has the advantages of simple maintenance and less influence by the environment [2, 3]. It can effectively avoid the drawbacks of liquid dampers and improve the equipment performance, which has piqued the interest of many academics. Qiang Jia [4] explored the characteristics of eddy current buffering technology for buffering and braking of high-speed moving bodies. By controlling the thickness of © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 562–571, 2024. https://doi.org/10.1007/978-981-97-1072-0_57

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inner cylinder, Zixuan Li et al. [5, 6] investigated to lessen the effect of demagnetization effect on electromagnetic damping force. Jun Xiong Ye [7] studied the characteristics of hybrid excitation eddy current damper under impact load. The buffer energy recovery and reciprocating motion under impact load were investigated by Tong Huang [8] and Chenglong Luan [9]. Yanping Shen et al. [10] analyzed the dynamic properties of eddy current dampers under impact loading. Kara koc et al. [11] dedicated to braking torque of an eddy current damper in time-varying magnetic field. Zhou et al. [12] studied the demagnetization effect caused by eddy current as well as the effect of temperature on the braking torque of an eddy current damper. Sainjargal et al. [13] specializes in the effect of permanent magnet arrangement on the magnetic flux distribution and braking power characteristics of an eddy current damper. Based on the research of the aforementioned scholars, the author aims at the minimum fluctuation of damping force and the smallest volume of damper, and conducts the research on the features and optimization of an eddy current damper under impact loading.

2 Structural Principle of Eddy Current Damper As a new principle and new structural damper, the structural principle of eddy current damper is presented in Fig. 1 below.

Fig. 1. The structure diagram of an eddy current damper

The permanent magnet eddy current damper is mainly composed of primary and secondary components. The primary component consists of permanent magnets, a connecting rod, and a magnetic shoe, whereas the secondary component consists of a conductor tube and a magnetic tube. When the primary and secondary parts are subjected to impact load, relative motion occurs, and the secondary portion produces induced eddy current. When the secondary part’s eddy current is impacted by the working magnetic field, a damping force is generated to consume the impact vibration energy.

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3 Kinetic Model 3.1 Eddy Current Damping Force Model According to Maxwell’s electromagnetic field theory and Faraday’s law of electromagnetic induction, taking into account the “skin effect” of eddy current, which generated by the secondary part, the eddy current damping force Fwe generated by the eddy current damper under the impact load can be expressed as: Fwe = 4π(2N − 1)σ

τ − τ2m

rdo

τm 2

rdi

∫ v ∫ Br2 e

−(rd 0 −rdi ) δdp

drdz

(1)

In the above formula: N is the number of permanent magnets; σ is the conductivity of a conductor tube; τm is the magnetization thickness of permanent magnets; τ magnetic pole thickness; v is the relative velocity between the primary and the secondary; rdo is the outer diameter of the conductor tube; rdi is the inner diameter of the conductor tube; Br is the working magnetic field strength; δdp is the penetration depth of the surface of the conductor tube. 3.2 Dynamic Model of Motion Part In this paper, the motion part of the buffered device is used as the subject of study; the coordinate system is formed along the direction of motion, and combined with Newton’s second law, the dynamic model of the buffer process under impact load can be shown as follows: mht

d 2 xw = Fhpt − Fwe − Ffj − Fy − FTf + mh g ∗ sin(ϕj ) dt 2

(2)

In the above formula: mht is the mass of the buffer motion part; xw is buffer stroke; Fhpt represents the impact load force; Ffj represents the counter-recoil force; FTf represents the friction force of guide rail; Fy represents the friction force of the sealing guide device; ϕj represents the inclination angle of the moving parts. The dynamic model in the reentry process is as follows: mht

d 2x = Ffj − Fwe − Fy − FTf − mht g ∗ sin(ϕj ) dt 2

(3)

In the formula: x is the re-entry displacement.

4 Dynamic Characteristics Analysis of the Eddy Current Damper The dynamic features of the eddy current damper are investigated from the typical structural factors, including the material of conductor tube, thickness and air gap.

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Fig. 2. The effect of conductivity of a conductor tube on the eddy current damping force at constant velocity

4.1 Effect of Conductor Tube Material on the Eddy Current Damping Force Under the condition of constant velocity motion and other structural parameters unchanged, the effect of the conductivity of the conductor tube on the eddy current damping force can be seen in Fig. 2 below. Figure 2 shows that when the speed is less than 5 m/s, the eddy current damping force rises with increasing conductivity; when the speed is greater than 5 m/s, the eddy current damping force increases first and subsequently declines with increasing conductivity. When the conductivity is less than 2*10^7 S/M , the eddy current damping force grows as the speed increases. When the conductivity is greater than 2*10^7 S/M , the eddy current damping force increases first and then declines as the speed increases. The effect of the conductivity of the conductor cylinder on the eddy current damping force under impact load is demonstrated in Fig. 3 when all other structural parameters stay constant.

Fig. 3. The effect of conductor tube material on the eddy current damping force under impact

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The “demagnetization” effect is visible under the impact in the usage of copper or aluminum alloy, and the eddy current damping force changes greatly, as shown in Fig. 3. It also shows a certain degree of “demagnetization” by using brass, but the damping force fluctuates less, and has a good “platform effect” in the later stage of braking. Although there is no damping force fluctuation caused by high-speed “demagnetization” in the use of copper alloy, there is no good “platform effect” of damping force in the later stage of braking. 4.2 The Effect of the Conductor Tube Thickness on Eddy Current Damping Force Figure 4 illustrates the effect of conductor tube thickness on eddy current damping force when all other structural parameters are held constant and the primary and secondary sections have a constant relative motion velocity.

Fig. 4. The effect of the conductor tube thickness on the eddy current damping force at a constant speed

Figure 4 shows that when the speed is less than 8 m/s, the eddy current damping force increases with the increase of the conductor tube thickness. When the speed exceeds 8 m/s, the eddy current damping force increases, then reduces as the conductor tube thickness increases. When the conductor tube thickness is less than 4 mm, the eddy current damping force increases with the increase of velocity. When the thickness of the conductor tube exceeds 4 mm, the eddy current damping force increases initially and then reduces as velocity increases. When the other structural parameters remain unchanged, the influence of the thickness of the conductor tube on the eddy current damping force under the impact load can be seen in Fig. 5. As shown in Fig. 5, as the thickness of the conductor tube grows from 1 mm to 3 mm, the eddy current damping force increases dramatically. When the conductor tube thickness grows from 3 mm to 5 mm, the peak force changes slightly, and the “platform effect” of damping force appears. When the thickness exceeds 4 mm, the “demagnetization effect” of the recoil brake is clearly visible, and the curve of eddy current damping force fluctuates greatly.

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Fig. 5. The effect of the conductor tube thickness on the eddy current damping force under impact

4.3 The Effect of the Air Gap on the Eddy Current Damping Force The air gap, being the most critical structural parameter of an eddy current damper, has a direct impact on the distribution of the working magnetic field and the eddy current field. It also has an impact on the output rule and buffering effectiveness of the eddy current damping force. The effect of the air gap thickness on the eddy current damping force at constant speed is shown in Fig. 6.

Fig. 6. The impact of the air gap on eddy current damping force at steady speed

Figure 6 shows that the eddy current damping force falls exponentially with increasing air gap at constant speed. When the air gap is within 1.8 mm ~ 2.0 mm, the eddy current damping force has dropped to a state which is close to 0. When the buffer speed is in the range of 0 ~ 5 m/s, the eddy current damping force increases as the speed increases. When the speed is greater than 5 m/s, the eddy current damping force drops exponentially with the increase of speed.

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With all other structural parameters unchanged, the impact of air gap thickness on the eddy current damping force under the impact is shown in Fig. 7.

Fig. 7. The effect of the air gap on the eddy current damping force in the state of impact

Figure 7 shows that as the air gap increases from 0.1 mm to 0.7 mm, the eddy current damping force decreases greatly. The reason is that as the air gap spacing grows, so does the magnetic circuit reluctance, the magnetic field intensity decreases, and the eddy current damping force decreases.

5 Optimization Research on the Eddy Current Damper The minimum fluctuation of damping force and the minimum volume of damper under impact load are the optimization goals in this research. The structural parameters that minimize the volume of damper without increasing resistance fluctuation are investigated. The fluctuation of damping force can be described as the formula: n (Fwe − FRL )2 (4) FR = i=0 n In the above formula: FR is the undulating quantity of resistive force; FRL represents the ideal damping force. The volume of damper can be listed as follows. 2 L VZ = π rzn

(5)

In the above formula: rzn represents the radius of the damper cylinder; L represents the length of the outer damper cylinder. According to previous analysis in this paper, the conductivity of and the thickness of conductor tubes, the air gap, and the thickness of the magnetizer cylinder all had a significant impact on the braking force. The variables listed above are used as optimization variables, which are recorded as xyc1 …xyc4 ; the value range of xyc1 …xyc4 ; is displayed in the Table 1 below.

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Table 1. Optimization variable value range table Parameters

Lower limit

Upper limit

xyc1

1 ∗ 106 S/m

5.8 ∗ 107 S/m

xyc2

1.0 mm

5 mm

xyc3

0.3 mm

1.8 mm

xyc4

5 mm

18 mm

The structural strength and the related process of the damper are employed as constraint conditions, and the algorithm NSGA-II is used for optimization. Taking both actual the engineering application and the optimization objectives into consideration, a set of optimization parameters are chosen in the pareto as indicated in Table 2 below. Table 2. Optimized structural parameter table Parameters

Before optimization

Optimized

xyc1

1.5 ∗ 107 S/m

1.35 ∗ 107 S/m

xyc2

2.0 mm

4.5 mm

xyc3

0.5 mm

0.66 mm

xyc4

5 mm

18 mm

According to the above optimized damper parameters, it can be found that the volume of the damper changes from 0.375 m3 (before optimization) to 0.315 m3 (after optimization), and the volume is effectively reduced. After optimization, the variation rule of damping force of eddy current damper under impact load and the variation rule of traditional liquid damping force are shown in Fig. 8. The damping force of the damper has a faster response speed and can achieve the “platform resistance” at a faster speed after optimization, as shown in Fig. 8. The curve of damping force becomes smoother and flatter, the fluctuation of damping force is small, and the peak value of damping force is considerably reduced. Compared with the traditional hydraulic damper, the eddy current damper significantly reduces the peak resistance of the buffer’s beginning and final stages, and the damping force control effect is remarkable. Thus, the eddy current damper has certain technical advantages over the traditional damper.

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Fig. 8. Damping force curve

6 Conclusion Based on the eddy current buffer theory, this research proposes a permanent magnet eddy current damper model. Besides, analytical and finite element methods are used to study and optimize the dynamic properties of an eddy current damper under impact load. The results reveal that the eddy current damper, as a liquid-free device, can can match the criteria of efficient and stable buffer braking of the equipment. The the eddy current damper’s damping force characteristics are sensitive to the conductivity and the thickness of the conductor tube, the air gap and the thickness of the magnetic tube. The damping force curve is smoother and closer to the ideal state after optimization. It efficiently avoids the typical damper’s peak damping force, and the control effect is visible. The optimized damper not only decreases the fluctuation of damping force, but also significantly reduces its volume, resulting in a more balanced construction and performance that better meets the needs of use.

References 1. Yang, Y., Zhang, P., Fu, J., Zhang, X., Wang, C.: Performance analysis of recoil mechanism of gun considering liquid cavitation. J. Vibrat. Shock 31(20), 94–98 (2012). (in Chinese) 2. Jin, Y.: Research on hybrid excitation linear eddy current device. Harbin Institute of Technology (2012). (in Chinese) 3. Kou, B.-q., Jin, Y.-x., Zhang, L., et al.: Characteristic analysis and control of a hybrid excitation linear eddy current brake. Energies 8(7), 7441–7464 (2015). https://doi.org/10.3390/en8 07744 4. Qiang, J., Gao, Y., Tong, Y., Zhao, P.: Research on the design of linear eddy current buffer. Chinese J. Eng. Desi. 18(03), 209–213 (2011). (in Chinese) 5. Li, Z., Yang, G., Sun, Q., Wang, L., Yu, Q.: Research on resistance characteristics and optimization of permanent magnet eddy current damper under strong impact load. Acta Armamentarii 39(04), 664–671 (2018). (in Chinese) 6. Li, Z., Yang, G., Liu, N.: Finite element simulation model of electromagnetic buffer under strong impact load. Acta Armamentarii 42(05), 913–923 (2021). (in Chinese)

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7. Ye, J.: Analysis and design of hybrid excitation gun recoil mechanism, p. 4. The North University of China (2020). (in Chinese) 8. Huang, T., Guo, B., Zhang, T., Mao, H., Ding, N.: Study on dynamic characteristics of eddy current device under impact load. Sci. Technol. Eng. 18(32), 174–178 (2018). 4. (in Chinese) 9. Luan, C., Huang, T., Pan, Y., Guo, B., Zhu, J.: Analysis of the effect of a new electromagnetic recoil mechanism on the recoil motion of artillery. J. Gun Launch and Control 41(01), 18–22 (2020). (in Chinese) 10. Shen, Y., Liu, N., Xie, Z., et al.: Research on magnetic circuit simulation of permanent magnet eddy current recoil machine. J. Vibrat. Shock 41(06), 8–14 (2022). in Chinese) https://doi. org/10.13465/j.cnki.jvs.2022.06.002 11. Karakoc, K., Suleman, A., Park, E.J.: Analytical modeling of eddy current brakes with the application of time varying magnetic fields. Appl. Math. Model. 40(2), 1168–1179 (2016). https://doi.org/10.1016/j.apm.2015.07.006 12. Zhou, Q., Guo, X.-x., Tan, G.-f., et al.: Parameter analysis on torque stabilization for the eddy current brake: a developed model, simulation, and sensitive analysis. Math. Prob. Eng. 436721(10) (2015). https://doi.org/10.1155/2015/436721 13. Sainjargal, S., Byun, J.-k.: Analysis and case study of permanent magnet arrays for eddy current brake systems with a new performance index. J. Magnet. 18(3), 276–282 (2013). https://doi.org/10.4283/JMAG.2013.18.3.276

SOH Prediction for Lithium-Ion Batteries Based on SSABP-MLR Xueqin Zheng(B) , Ning Su, and Weibiao Huang School of Electrical Engineering and Automation, Xiamen University of Technology, Xiamen 361024, China [email protected]

Abstract. Accurate prediction of the state of health (SOH) is important for ensuring the safe operation of lithium-ion batteries and minimizing maintenance expenses. In practical applications, direct measurement of SOH is challenging. In the paper, the NASA lithium-ion battery capacity decay dataset is used. The multidimensional health indicators (HI) for charging and discharging as model inputs are selected. The Sparrow Search Algorithm (SSA) optimized backpropagation neural network (BPNN) combined with the Multiple Linear Regression Model (MLR) as a combined learning model (SSABP-MLR) for prediction is proposed. The results show that RMSE and MAE are below 0.60% and 0.51%, respectively. The generalization error (GE) remains below 0.23% in the model of the generalization test. Compared with the traditional models such as BPNN, MLR, and SSA-BP, the SSABP-MLR model demonstrates superior prediction accuracy, minimal error, and outstanding generalization performance. This demonstrates the capability of the proposed method in the paper to meet the demand for SOH prediction in lithium-ion batteries. Keywords: Lithium-ion batteries · Health indicators · Combined learning model

1 Introduction Lithium-ion batteries, as exemplary energy storage devices, have extensive applications in new energy vehicles and other domains. The reliability plays an important role in sustaining the stability of energy storage systems [1]. Its continuous charging and discharging of batteries result in performance degradation, which can be quantified by SOH [2, 3]. Currently, With the rapid development of machine learning and big data technology, data-driven algorithms for predicting SOH have been widely applied. In [4], Park et al. established a multi Auto-Regressive (AR) model to estimate SOC and SOH of the battery. The combination of double-extended Kalman filtering and AR can compensate for the scarcity of experimental data. In [5], battery parameters were extracted from differential thermovoltaic curves to estimate battery SOH using a Gaussian Process Regression (GPR) model. In [6], Fan et al. introduced an approach based on the Gated Recurrent Unit-Convolutional Neural Network (GRU-CNN) for battery SOH estimation. This approach involves training with voltage, current, and temperature data during © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 572–581, 2024. https://doi.org/10.1007/978-981-97-1072-0_58

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the charging process. In [7], Khumprom et al. achieved precise predictions for both SOH and Remaining Useful Life (RUL) in Lithium-ion batteries using the Deep Neural Network (DNN) method. In [8], Li et al. introduced a bidirectional Long and Short-Term Memory (LSTM) neural network algorithm for SOH estimation and RUL prediction. This algorithm enhances the ability of the information processing of LSTM, which can sift the favorable information and improve the estimation accuracy and effectiveness. In [9], Wu et al. introduced an online neural network-based approach for estimating the Remaining Useful Life (RUL) of lithium-ion batteries. The connection between charge profiles and RUL was modeled by the Feed Forward Neural Network (FFNN). In [10], Kai et al. explored the historical performance of a proton exchange membrane fuel cell employing a Back-Propagation Neural Network (BPNN) and an adaptive neuro-fuzzy inference system. The investigation assessed how the operational modes affected future performance. Reliable prediction outcomes were achieved. Nevertheless, DNN has multiple hidden layers, computational complexity, and extensive inference processing time during operation [7]. FFNN lacks the ability to store and utilize past information, resulting in a decrease in the accuracy of prediction results [9]. Comparatively, BPNN has high computational efficiency, error backpropagation ability, and the ability to refine parameters through error, which can improve the accuracy of estimation results. These attributes render BPNN well-suited for nonlinear problems like SOH prediction in lithium-ion batteries. However, BPNN is not exempt from its own set of issues, including parameter initialization and overfitting. In view of the above issues, this paper proposes an initial optimization process for the BPNN using the SSA [11], namely SSA-BP. This optimization focuses on determining the optimal values for parameters such as the number of hidden layers (NL), the number of neurons (NN) within each layer, and the L2 regularization coefficient weight (Lambda). During the testing of the model generalization, as the training sample size decreases, the BP neural network is susceptible to overfitting issues, resulting in suboptimal predictive performance. Establish a combined learning model SSABPMLR by combining multiple linear regression (MLR) models that are more suitable for small sample prediction. Regarding HI extraction, multidimensional HI parameters are selected during the battery charging and discharging processes, including voltage, current, time, and voltage drop slope. The Spearman correlation coefficient is adopted to analyze the relationship between HI and battery capacity. HI parameters highly correlated with capacity are chosen as inputs for the battery SOH prediction model.

2 Battery HI Extraction 2.1 Battery Data Analysis Data from NASA Ames Prognostics Center of Excellence, the batter dataset of B5, B6, B7, and B18 are selected. This dataset provides comprehensive information on battery degradation, including cycle count, voltage, current, temperature, and other relevant factors, which facilitates the construction of predictive models for SOH. Table 1 displays the battery parameters.

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The curve in Fig. 1 depicts the change in NASA battery capacity with the number of charging and discharging cycles. It shows that the battery capacity does not exhibit continuous decline but rather demonstrates capacity self-recovery. Table 1. NASA battery parameters. Battery Number

Parameters

Value

B5,B6,B7,B18

Rated capacity/Ah

2

Charging current/A

1.5

Discharging current/A

2

Charging cut-off voltage/V

4.2

End-off voltage/V

2.5–2.7

Fig. 1. NASA Battery Capacity Degradation Curve

2.2 HI Selection Based on Charging Curves Based on the charging and discharging conditions depicted in Fig. 2 (a), the battery charging HI extraction method illustrated in Fig. 2 (b), three indicators to record the degradation data during the charging process is selected. The selection process is as follows: HI1 corresponds to the duration required to reach the charging cut-off voltage of 4.2V during constant current charging. HI2 corresponds to the voltage values at 250s, 1000s, and 2500s during constant current charging. HI3 corresponds to the current variations during the initial 1000s, 2000s, and 3000s of constant voltage charging. These representations are depicted in Eqs. (1). ⎧ ⎪ ⎨ HI 1 = t4.2v = [ti |V (ti ) = 4.2v], i = 1, 2, ..., T HI 2(250s,1000s,2500s) = V (t = 250s, 1000s, 2500s) (1) ⎪ ⎩ HI 3(1000s,2000s,3000s) = Ii = 1.5 − I (t = 1000s, 2000s, 3000s) where, T is the number of cycle periods, t 4.2v is the bottom cutoff voltage time, and I is the current change difference.

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2.3 HI Selection Based on Discharging Curves The discharge voltage curves are displayed in Fig. 2(c), in conjunction with the voltage dip and time variation curves, opt for the ratio k to represent the voltage drop rate between 3.2V and 3.8V points in different cycles, as HI4. In Fig. 2 (d), HI5 is defined as t maxTemp , denoting the moment when the battery temperature attains its maximum value throughout the discharge process. These expressions are illustrated in Eqs. (2).  HI 4 = ki , i = 1, 2, 3, ..., T (2) HI 5 = tmax Temp = [ti |Temperature = max], i = 1, 2, 3, ..., T

(a)

(c)

(b)

(d)

Fig. 2. Charging and discharging extraction diagram (a) Charging and discharging voltage-current curves, (b) Charging voltage-current HI extraction, (c) Discharge slope HI extraction, (d) Discharge temperature HI extraction.

2.4 HI Correlation Coefficient Evaluation and Selection Spearman’s correlation coefficient has analyzed the relationship between battery capacity and HI. The corresponding equations are presented as Eq. (3). Where, x i ’ is the ranked position of HI, yi ’ is the ranked position of battery capacity, ω is the sample size, d i is the difference in ranked position, and r xy is the value of

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Spearman’s correlation coefficient. di = x i − yi ; rxy = 1 −

 6 × ωi=1 di2  ω × ω2 − 1

(3)

Table 2. Spearman’s correlation coefficient analysis HI HI1

B5

B6

B7

B18

0.9966

0.9975

0.9739

0.9954

HI2(250s)

−0.8835

−0.9647

−0.3175

−0.6369

HI2(1000s)

−0.9753

−0.9729

−0.6293

−0.9325

HI2(2500s)

−0.9610

−0.9518

−0.8132

−0.9112

HI3(1000s)

−0.9843

−0.9940

−0.9651

−0.7321

HI3(2000s)

−0.9868

−0.9955

−0.9819

−0.8442

HI3(3000s)

−0.9920

−0.9966

−0.9864

−0.9281

HI4

0.9568

0.9998

0.9991

0.9168

HI5

0.9988

0.9814

0.9332

0.9994

The absolute values of Spearman correlation coefficients closer to 1 indicate stronger correlations. As shown in Table 2, most of the correlation coefficients between the extracted HI and battery capacity are above 0.9, which indicates a strong correlation between the extracted HI and battery capacity. The top 3 HI parameters with the highest correlation coefficients are selected to prevent dimensional disasters caused by excessive input features from affecting prediction performance.

3 Combined Learning Model (SSABP-MLR) An SSABP-MLR model for predicting the SOH is proposed in the paper. SSABPMLR is a multi-model integrated learning method. The method contains two prediction algorithm models with SSA-BP and MLR. In the training set, the traditional BPNN model is optimized with network hyperparameters through the SSA to establish the SSA-BP model. In combination with the MLR model, the relative difference of error is used to compare with the mean absolute error (MAE) of the two model validation sets. The weight calculation is used to assign the two model weights for test set prediction. Figure 3 shows the flowchart of the SSABP-MLR combined learning optimization strategy. The fitness function is defined as shown in Eq. (4). N y (P (i) == validy (i)) (4) FitnessValue = 1 − I =1 valid N where, N represents the number of samples in the validation set, the formula Py valid (i) = = valid y (i) determines whether the predicted value Py valid in the validation set is equal to the true value valid y , and if it is equal, it outputs 1, and vice versa it outputs 0, and then it makes a difference with 1 to get the fitness function.

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Data analysis and feature extraction

Battery dataset

Correlation analysis and HI extraction

Training set

Validation set

Test set ˄Ypre˅

MAESSA-BP MAEMLR

SOH prodiction

Sparrow Search Algorithm ˄SSA˅

Sample set

Performance evaluation

Is it within the error relative difference within the threshold?

Optimising hyperparameters ˄NN,NL,Lambda˅

N

Selection of model with small error rounding error large

Y BPNN

Combinational model weights calculation and assignment

MLR

SSBP-MLR

Fig. 3. Combined learning strategy flowchart.

4 Simulation Results and Analysis To verify the accuracy and reliability of the proposed method, the prediction and generalization performance SOH of the four models are tested. The performance evaluation of BPNN, MLR, SSA-BP, and SSABP-MLR is achieved through the utilization of Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Generalization Error (GE), as defined in Eqs. (5). ⎧ n  ⎪ n ∧ 2 ⎪

  ⎪ i=1 yi − yi ∧ ⎪ MAE = 1  ⎪ yi − yi ; RMSE = ⎪ ⎪ n n ⎪ ⎪ i=1 ⎪ ⎪ ⎫ ⎪ ⎨ L ⎪ 1

⎪ (5) (h) = (yi , h(xi )) ⎪ E ⎪ train ⎪ ⎪ ⎬ L ⎪ ⎪ i=1 ⎪ ⎪ GE = |Etest − Etrain | ⎪ ⎪ M ⎪ ⎪

⎪ ⎪ 1 ⎪ ⎪ E (h) = ⎪ (yi , h(xi ))⎪ ⎪ ⎪ ⎭ ⎩ test M i=1

where, yi, and yi ^ are the actual and predicted value of SOH, respectively, and n is the number of cycle times. GE is expressed as the absolute value of the difference between the training set error E train and the test set error E test for model h. L, M are the number of samples in the training set and test set respectively,  is the loss function.

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(B5)

(B6)

(B7)

(B18) Fig. 4. Different model predictions for B5, B6, B7, B18.

4.1 SOH Prediction Results and Analysis Figure 4 presents a comparative analysis of prediction outcomes achieved by various models at the Start Prediction Point (SP) of 60%. The outcomes indicate that as the cycle progresses, the predictions of the conventional BPNN gradually diverge from the actual values during the later stages of forecasting. Sharp fluctuations appear in the MLR predictions within the B7 model dataset. In contrast, both SSABP-MLR and SSA-BP consistently demonstrate superior tracking of the subsequent SOH trend within all four model datasets. The prediction outcomes of the B5 model dataset are shown in Table 3, the results indicate that the RMSE and MAE values of the BPNN, MLR, and SSA-BP models are (2.26%, 1.95%), (1.02%, 1.01%), and (0.37%, 0.26%) respectively. The SSABPMLR model exhibits lower errors, with an RMSE of 0.27% and an MAE of 0.22%, which surpasses the performance of other models. This trend continues in the remaining datasets. Table 4 displays the optimized hyperparameter values. 4.2 Generalization Testing The B5 battery dataset is adopted to conduct testing at varying SP of 50%, 40%, and 30%. Table 5 presents the generalization performance metrics. The outcomes indicate that SSABP-MLR exhibits the smallest prediction error. As the training sample size decreases, SSABP-MLR consistently maintains RMSE

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Table 3. SOH prediction outcomes Battery Number

Model

RMSE(%)

MAE(%)

B5

BPNN

2.26

1.95

MLR

1.02

1.01

SSA-BP

0.37

0.26

B6

B7

B18

SSABP-MLR

0.27

0.22

BPNN

1.89

1.54

MLR

0.34

0.30

SSA-BP

0.44

0.36

SSABP-MLR

0.33

0.30

BPNN

1.10

0.90

MLR

2.62

2.39

SSA-BP

0.52

0.51

SSABP-MLR

0.34

0.27

BPNN

0.83

0.74

MLR

0.63

0.55

SSA-BP

0.71

0.55

SSABP-MLR

0.60

0.51

Table 4. Optimizing hyperparameter values Battery

NL

NN

Lambda

Weight

Fitnessvalue

B5

[5 13]

2

0.0012

[0.49 0.51]

0.022

B6

[4 2]

2

0.001

[1 0]

0.024

B7

[2]

1

0.001

[0 1]

0.051

B18

[3 7]

2

0.0013

[0.43 0.57]

0.064

and MAE levels below 0.60% and 0.51%, with minimum values reaching 0.27% and 0.22%respectively. In comparison to other models, the conventional BPNN exhibits inferior predictive performance. As the sample size decreases, RMSE and MAE errors surge to over 4%. SSA-BP performs exceptionally at SP = 50% and 40%, achieving minimum errors of 0.49% and 0.42% respectively. However, the predictive accuracy diminishes at SP = 30%, resulting in errors of 3.46% and 3.07%. Conversely, MLR has the unsatisfactory predictions at SP = 50% and 40%. Nonetheless, at SP = 30%, it achieves the prediction errors of 0.42% and 0.31%. The generalization error histogram presented in Fig. 6 (h), it is evident that the SSABP-MLR model consistently maintains a GE below 0.23% across different SP points, which surpasses the performance of the other three

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SP

Model

RMSE(%)

MAE(%)

GE(%)

50%

BPNN

2.15

1.82

1.74

MLR

2.81

2.71

2.36

SSA-BP

0.49

0.42

0.21

40%

30%

SSABP-MLR

0.24

0.17

0.06

BPNN

3.04

2.64

2.65

MLR

2.94

2.76

2.37

SSA-BP

0.81

0.74

0.52

SSABP-MLR

0.50

0.46

0.23

BPNN

4.51

3.98

3.85

MLR

0.42

0.31

0.20

SSA-BP

3.46

3.07

2.81

SSABP-MLR

0.43

0.31

0.11

models. In summary, the proposed model of the paper has superior prediction accuracy and a higher level of model generalization at the various SP points. 4.3 Conclusion An SSABP-MLR model for predicting the SOH of lithium-ion batteries is proposed in the paper. Initially, the NASA lithium-ion battery capacity decay dataset is performed to extract the easily measurable HI data from the battery charging and discharging processes. The correlation between HI and battery capacity is evaluated using Spearman’s correlation coefficient. The HI with the highest correlation coefficient is selected as the model input. Subsequently, the SSA optimized BPNN combined with MLR as SSABP-MLR for prediction is proposed. During the SOH prediction experiments, RMSE and MAE values below 0.6% and 0.51% are achieved respectively in the model. In the generalization test, the GE remains below 0.23%, which is better than the other three models in terms of prediction accuracy, error reduction, and generalization performance. These results demonstrate that the model proposed in the paper can satisfy the requirements for SOH prediction of the lithium battery. Acknowledgments. This work was funded by Science and Technology Guiding Project of Fujian Province, China (No. 2022H0056).

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References 1. Zheng, Y., Jiao, C., Yaxar, T., Zhao, L.: Research on grid-forming coordinated energy storage control strategy based on converter-interfaced generation. High Voltage Apparatus 46(03), 128–133 (2023). (in Chinese) 2. Liao, L., Xiao, T., Wu, T., Jiang, J.: SOH and RUL prediction for lithium batteries based on fusion of multiple health features. Chinese J. Power Sourc. 47(02), 193–198 (2033). (in Chinese) 3. Zhu, Z., Gao, D.: Lithium-ion batteries state of health detection method based on CNNBiLSTM network. Electr. Measure. Technol. 46(03), 128–133 (2023). (in Chinese) 4. Park, J., Lee, M., Kim, G., Park, S., Kim, J.: Integrated approach based on dual extended Kalman filter and multivariate autoregressive model for predicting battery capacity using health indicator and SOC/SOH. Energies 13(9), 1–20 (2020) 5. Wang, Z., Yuan, C., Li, X.: Lithium battery state-of-health estimation via differential thermal voltammetry with Gaussian process regression. IEEE Trans. Transport. Electrific. 7(1), 16–25 (2020) 6. Fan, Y., Xiao, F., Li, C., et al.: A novel deep learning framework for state of health estimation of lithium-ion battery. Journal of Energy Storage 6(6), 1–9 (2020) 7. Khumprom, P., Yodo, N.: A data-driven predictive prognostic model for lithium-ion batteries based on a deep learning algorithm. Energies 12(4), 1–21 (2019) 8. Li, P., Zhang, Z., Xiong, Q., et al.: State-of-health estimation and remaining useful life prediction for the lithium-ion battery based on a variant long short term memory neural network. J. Power Sources 55(15), 1–12 (2020) 9. Wu, J., Zhang, C., Chen, Z.: An online method for lithium-ion battery remaining useful life estimation using importance sampling and neural networks. Appl. Energy 42(13), 134–140 (2016) 10. He, K., Zhang, C., He, Q., et al.: Effectiveness of PEMFC historical state and operating mode in PEMFC prognosis. Int. J. Hydr. Ener. 45(56), 32355–32366 (2020) 11. Lyu, X., Mu, X., Zhang, J., Wang, Z.: Chaos sparrow search optimization algorithm. J. Beijing Univ. Aeronaut. Astronaut. 47(08), 1712–1720 (2021). (in Chinese)

Integrated Design and Optimization of SSPC Current Measurement Module Based on AMR Feiran Xu1 , Li Wang1(B) , and Kaijun Wang2 1 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics,

Nanjing 210016, China {xufeiran,liwang}@nuaa.edu.cn 2 Powerland Technology Inc., Nanjing 210016, China

Abstract. With the development of aircraft power supply and distribution system to high power density, it is urgent for its core component, solid state power controller (SSPC), to realize current measurement integration to ensure reliable current monitoring and fault protection of high-power DC SSPC integrated modules. However, a large amount of losses and heat caused by the traditional current detection method based on shunts will reduce efficiency and reliability of SSPC with high current. To address the issue, this paper proposes a high-precision, highlinearity, fast-response, wide-range, and compact anisotropic magnetoresistance (AMR) current detection component integrated in the SSPC module. In order to eliminate the electromagnetic interference caused by other current paths of SSPC integrated module, a magnetic shield is proposed, and its feasibility and effectiveness are verified by electromagnetic simulation. The performance of the detection component was verified on a SSPC module prototype with a direct current rating of 540V /200A, showing detection accuracy of less than 1% and excellent linearity and response speed. Keywords: Integration · Current Measurement · Electromagnetic Shielding · Solid State Power Controller (SSPC) · Anisotropic Magnetoresistance (AMR)

1 Introduction As the core component of aviation intelligent power distribution system, solid state power controller (SSPC) depends on accurate and fast current detection for its current monitoring, inverse time overcurrent protection and short circuit protection [1–3]. The trend of aircraft multi-electrification and full-electrification [1, 2] makes it develop in the direction of high power, high power density and integration with the aircraft power supply and distribution system [3], so it is urgent to realize current detection on high-power integrated DC SSPC module. Magnetoresistance sensors, with their high sensitivity, high bandwidth, and low delay characteristics [4, 5], are commonly used for current detection in power modules, whether AC or DC. Reference [6] introduces an anisotropic magnetoresistance (AMR) sensor integrated in the control circuit of a DC/DC converter. References [7, 8] integrate tunnel © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 582–589, 2024. https://doi.org/10.1007/978-981-97-1072-0_59

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magnetoresistance (TMR) current sensors on the terminals of commercial power modules to achieve accurate and fast fault current detection for short circuit and overcurrent protection. Reference [9] designs a point field detector (PFD) bridge based on giant magnetoresistance (GMR) sensors for high-bandwidth current detection in IGBT modules. Among the three types of MR sensors, AMR current sensors have a wide detection range of up to kA and can meet the detection requirements of high-power SSPC up to 1000A. In addition, the small temperature drift [10] make small temperature drift suitable for high-power SSPC with the high operating temperature and high heat generation. Therefore, AMR current sensors can help achieve high-precision, wide detection range, and fast current detection in high-power integrated SSPC modules. However, the complex electromagnetic environment inside compact power modules is a significant factor affecting the accuracy of current sensors based on magnetic field detection. Researchers have proposed various methods to suppress electromagnetic interference. Reference [11] proposed using multiple GMR PFD bridges to decouple the interference magnetic field from the measured magnetic field to achieve accurate highfrequency current detection. However, the required number of bridges is relatively large, which is not conducive to integration. References [7, 8] used electromagnetic simulation and algorithm optimization to determine the optimal location for integrating sensors on the power terminal, but did not eliminate the influence of adjacent terminals on current detection accuracy. Reference [12] designed a magnetic shielding cage for TMR current sensors to suppress the impact of electromagnetic noise, but did not verify its shielding effect. Building upon the research discussed above, to achieve precise and fast current sensing in high power integrated SSPC module, a novel AMR-based current detection component for SSPC integrated modules is proposed and optimization for electromagnetic problems caused by integration is carried out. The feasibility and effectiveness are verified by simulation and experiments both independently and on 540V/200A DC integrated SSPC prototype. The proposed AMR current detection component can provide technical support for real-time current monitoring and fast, accurate protection of SSPC integrated module, which is beneficial for further improving the power density of SSPC modules.

2 Principle of SSPC Current Detection Based on AMR Current Sensor The resistance of AMR materials depends on the angle between the current direction and the magnetization direction of its internal magnetic domains [13] and 45° is the linear range. The simplified block diagram of the internal conditioning circuitry of the AMR sensor used in this paper is shown in Fig. 1. The AMR sensor is only sensitive to the X-direction magnetic field gradient, while the Y-direction magnetic field is used to provide a stabilizing field to avoid the flipping error. In order to ensure the accuracy and linearity of the sensor output, it is required that the X-direction magnetic field gradient be 1920 ± 190 A/m and the Y-direction magnetic field be 0 ± 500 A/m at 1/3 detection range.

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HX

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Fig. 1. Simplified block diagram of conditioning circuit in AMR sensor [14].

The gradient of the magnetic field intensity H X generated by the primary current is the input to the sensor, and I OUT is the current output of the sensor. The sensor output voltage signal I OUT -FB can be obtained through the external resistor RM . The input-output relationship of the system is given by IOUT − FB = RM ·

1 SSENS · G1 · HX = RM · S · HX FCC RSENSE − SSENS · G1 · FCOMP

(1)

where S is the sensitivity of the AMR sensor. According to the datasheet, the sensitivity of the AMR sensor can be calculated as S = 1.51e-3mA/(A/m). Obviously, the output voltage I OUT -FB can be linearly represented by the field difference in X-direction generated by the primary current.

3 Integrated Design of SSPC Current Detection SSPC integrated module contains the main switching circuit, the drain circuit, and the pre-charge circuit (as shown in Fig. 2(a)). The layout and connections of the power circuit are realized using bonding wires and the upper copper layer of the direct-bond copper (DBC), which the thickness is 0.3mm. In order to integrate the current detection into the SSPC power module, the design and integration position of the measured conductor are the primary issues. Due to the nonlinearity introduced by the traditional straight-shaped current conductor, a U-shaped current conductor is adopted to provide a magnetic field gradient in the MR-areas to correct the nonlinearity error of the current sensor. In order to achieve wide-range current detection (0 ~ 1000A), quantitative analysis of magnetic field intensity variation of the AMR induction region under different U-shaped conductor structure parameters was carried out with ANSYS Maxwell. An iterative simulation design was performed with control variate method to meet the magnetic field gradient requirements with a smaller size U-shaped current guide. The size parameters of each part are shown in Table 1, corresponded to Fig. 2(b). The power density of the current detection component consisting of the U-shaped conductor with the dimensions specified in Table 1 is 62.4 W/cm3 , while the power density of the detection resistor used for the same range of detection is only 15 W/cm3 . The X-direction magnetic field intensity gradient of the AMR-area at 1/3 detection range is 2085.1 A/m, and the Y-direction magnetic field intensity is no more than 418.6 A/m, which satisfies the magnetic field requirements of the sensor. By realizing high power

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Fig. 2. Schematic diagram of SSPC module (a) layout and current flow, (b) the U-shaped conductor. Table 1. Parameters of current detection conductor in SSPC integrated module. Parameter

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density current detection components, the accuracy and linearity of current detection results are ensured, which is beneficial for integration into the SSPC multi-circuit power layout. The layout of the SSPC integration module is compact, with a power density of several hundred watts per cubic centimeter at a rated current of 200A. When the current detection component is integrated into SSPC integrated module, other high-current paths in the module will interfere with the magnetic field of the U-shaped conductor for current detection, affecting the accuracy of current detection. The U-shaped conductor is placed as shown in Fig. 2. The current direction of the X-direction U-shaped conductor is opposite to that of the Q2 region, and the magnetic field cancels out each other, which can eliminate the influence of the Q2 region on the magnetic field intensity of the AMR induction region. Thus, part of the electromagnetic interference is eliminated through the circuit layout of the integrated module.

4 Electromagnetic Problems for Integrated Optimization of SSPC Current Detection Although the magnetic field generated by some circuits in SSPC integrated module is counteracted by the reverse current layout in Sect. 3, there are still non-negligible magnetic field interference in the AMR induction region caused by other flow paths in SSPC integrated module. To eliminate electromagnetic interference, static magnetic shield is the most effective method for DC applications. According to the minimum reluctance principle, most of the magnetic induction lines of an external magnetic field enter the ferromagnetic material

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with high magnetic permeability, effectively shielding external interference. Permalloy has a relative magnetic permeability of up to 80,000 and is often used as a static magnetic shield material. Based on the electromagnetic effects discussed earlier and considering the problem of the inability to perforate the insulating ceramic layer of DBC, a shield structure as shown in Fig. 3 is proposed.

Fig. 3. Magnetic shield structure of current measurement in SSPC integrated module.

The magnetic field strengths in the MR induction zone when the U-shaped conductor and other current paths are separately flowing under the magnetic shield are shown in Table 2. The shield can effectively attenuate the external magnetic field strength to within 1.5 A/m. Table 2. Magnetic field strengths in MR-areas with shield. Flow Region

Average of HX (A/m)

Average of HY (A/m)

U-shaped

284

−20.5

Other

−0.28

1.43

When the current detection module with the only shield is integrated into SSPC integrated module, the X-direction magnetic field intensity gradient difference in the MRarea under different currents is simulated by MAXWELL. When the external resistance RM = 300, the relationship between the sensor output voltage and the measured current is given by (2). I OUT − FB = 0.738 × I − 0.091(mV )

(2)

The magnetic field distribution inside the SSPC integrated module without and with the only shield is shown in Fig. 4. It can be seen that the shield has almost no effect on the magnetic field in the main switching area, but the magnetic field in the current detection area of the SSPC integrated module with the shield is significantly enhanced, and the coupling effect between the magnetic field in the detection area and the external magnetic field is significantly reduced, indicating the effectiveness of the shield in eliminating external magnetic field interference.

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Fig. 4. Magnetic field distribution of SSPC integrated module (a) Without magnetic shield, (b) With magnetic shield.

5 Validation in SSPC Integrated Module Prototype A prototype of DC 540V/200A SSPC integrated module, which includes the current detection component, is shown in Fig. 5. The U-shaped conductor is surrounded by a 0.3mm thick permalloy alloy to form the upper shield, which is secured in place with electronic RTV silicone gel.

Fig. 5. Test platform of high power DC SSPC integrated module prototype.

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Fig. 6. Linear fitting curve of current detection output in SSPC integrated module.

Static characteristic testing was performed on the current detection component of the integrated module prototype under the load current of 0–375 A, and the test results are shown in Fig. 6. The current value was measured using a current probe TCP0150,

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and the measured current value was used as the reference. The current accuracy of the current detection component uploaded to the software within the 0–375 A range is 0.76%. Considering the accuracy of the current probe, the accuracy of the current detection component proposed in this paper is considered to be 1%. The output of the current detection component was linearly fitted in MATLAB with a determination coefficient of 0.9998, indicating excellent linearity. The linear fitting expression is as follow: IOUT − FB = 0.7859I − 5.808(mV )

(3)

The sensitivity of the current detection component is 0.7859 mV/A, and the zerovoltage drift is −5.808 mV. Compared with the electromagnetic simulation results and (2), the error between the measured data and the simulation calculation data is between −7.5% and + 5.21%, which indicates that the physical integrated module is basically consistent with the simulation design. The dynamic test results of the current sensing component are shown in Fig. 7. Compared with the Tektronix current probe TCP0150, the waveform detected by the current sensing component is basically consistent and the response speed is comparable. When the SSPC integrated module is connected to a purely resistive load, the output waveform of the current detection component has good tracking consistency with the load voltage waveform.

Fig. 7. The dynamic test results (a) Comparison between current measurement module and current probe, (b) Follow-up test of current measurement module.

6 Conclusion This paper presents a study on the integration method of a high-precision, high-linearity, and fast wide-range current detection method in a high-power SSPC integrated module. A current detection component with a maximum current detection range of 1000A, a highest detection accuracy of 1%, and a small size is proposed. To avoid the nonlinear error of the sensor, based on the circuit layout characteristics, the parameters of the Ushaped conductor are designed with an iterative simulation and the integration position is determined to eliminate part of the electromagnetic interference. In order to address the issue of electromagnetic interference between the current sensing components and the surrounding circuits in the integrated module, a shield is proposed, ensuring the linearity

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and accuracy of the detection. With the experimental platform based on a prototype of a DC 540V/200A SSPC integrated module, the static and dynamic characteristics of the current detection component were tested. The result shows the detection accuracy of less than 1% and good linearity and response speed, validating the feasibility of this method. This current detection method is advantageous for real-time current monitoring and fast, accurate protection function implementation in SSPC, and also holds application value for other types of high-power modules. Acknowledgments. This work is supported by National Natural Science Foundation of China (52277187) and Postgraduate Research & Practice Innovation Program of Nanjing University of Aeronautics and Astronautics (xcxjh20220309).

References 1. Barzkar, A., Ghassemi, M.: Electric power systems in more and all electric aircraft: A review. IEEE Access 8, 169314–169332 (2020) 2. Benzaquen, J., He, J.B., Mirafzal, B.: Toward more electric powertrains in aircraft: technical challenges and advancements. CES Trans. Electr. Mach. Sys. 5(3), 177–193 (2021) 3. Zhao, R., Wang, L., Huang, R.: Cascode GaN HEMT switching process oscillation in DC solid state power controller. Trans. China Electrotech. Soc. 37(S1), 67–276 (2022). (in Chinese) 4. Xin, Z., et al.: A review of megahertz current sensors for megahertz power converters. IEEE Trans. Power Electron. 37(6), 6720–6738 (2021) 5. Slatter, R., Brusius, M., Knoll, H.: Development of high bandwidth current sensors based on the magnetoresistive effect. In: 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), pp. 1–10 (2016) 6. Slatter, R., Brusius, M., Knoll, H.: Magnetoresistive current sensors as an enabling technology for ultra-high power density electric drives. In: CIPS 2016; 9th International Conference on Integrated Power Electronics Systems, pp. 1–7 (2016) 7. Shao, S., et al.: Tunnel magnetoresistance-based short-circuit and over-current protection for IGBT module. IEEE Trans. Power Electron. 35(10), 10930–10944 (2020) 8. Feng, Y., et al.: Short-circuit and over-current fault detection for SiC MOSFET modules based on tunnel magnetoresistance with predictive capabilities. IEEE Trans. Power Electron. 37(4), 3719–3723 (2022) 9. Schneider, P.E., Horio, M., Lorenz, R.D.: Integrating GMR field detectors for high-bandwidth current sensing in power electronic modules. IEEE Trans. Ind. Appl. 48(4), 1432–1439 (2012) 10. Ripka, P., Janosek, M.: Advances in magnetic field sensors. IEEE Sens. J. 10(6), 1108–1116 (2010) 11. Brauhn, T.J., et al.: Module-integrated GMR-based current sensing for closed-loop control of a motor drive. IEEE Trans. Ind. Appl. 53(1), 222–231 (2016) 12. Chen, X., et al.: Research on anti-interference technology of complex electromagnetic environment of TMR current sensor. Instr. Techniq. Sensor 1, 13–16 (2020). (in Chinese) 13. Fullerton, E.E., Childress, J.R.: Spintronics, magnetoresistive heads, and the emergence of the digital world. Proc. IEEE 104(10), 1787–1795 (2016) 14. SENSITEC CFS1000, https://www.sensitec.com/products-solutions/current-measurement/ cfs1000, last accessed 16 August 2023

Multi-Vibration Sensor Fusion of Flexible DC Converter Transformer Based on Adaptive Extended Kalman Filter Dong Xie1(B) , Hong Zheng1 , Meijun Bao1 , Guowei Zhou2 , and Jiangyang Zhan2 1 Hangzhou KeLin Electric Co., Ltd., Hangzhou 310000, China

[email protected] 2 State Grid ZheJiang Electric Power Co., Ltd., Hangzhou 310000, China

Abstract. Mechanical stability is a crucial aspect influencing the rheological properties of flexible direct converters. Monitoring mechanical stress can efficiently enhance the operational capacity of these converters. To increase sensing accuracy and stability for roadside sensors, an adaptive extended Kalman filter (AEKF)-based-sensor fusion method is proposed, which accounts for measurement noise. Employing the sensing results from MEMS vibration sensors, this approach achieves data fusion at the target level for heterogeneous sensors. A method is available online to assess sensor stability and generate adaptive correction coefficients for measurement noise.Practical tests have shown that the multisensor fusion method compares to a single sensor and improves lateral distance estimation accuracy by 9.7%. Keywords: Sensor Fusion · High Voltage Transformer · Neural Network · Weighted Fusion

1 Introduction Ultra-high voltage (UHV) converter transformers serve as the power voltage conversion hub in power grids. Ensuring their safe and stable operation is crucial for maintaining normal industrial manufacturing, residential life, and social order. The timely detection of potential issues in converter transformers through state online monitoring and evaluation is essential to prevent sudden failures that might adversely impact social life [1]. In converter mechanical stress monitoring, the operating environment can affect sensor accuracy, leading to poor sensing stability and flexible measurement noise. Traditional extended Kalman filter (EKF) [2] and unscented Kalman filter (UKF) algorithms [3] utilize a constant measurement noise covariance matrix, making it difficult for the fusion results to dynamically adapt to sensor changes. To address this issue, [4] proposed an adaptive Kalman filtering algorithm. By simultaneously considering the Kalman filtering results of two different steps, the measurement noise covariance matrix is adaptively adjusted, reducing accuracy loss due to imprecise measurement noise [5]. However, adjusting the measurement noise remains a challenge in different application contexts [6–8]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 590–597, 2024. https://doi.org/10.1007/978-981-97-1072-0_60

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To address the difficulty of obtaining and describing sensor error characteristics dynamically and quantitatively during roadside multi-sensor fusion, this study proposes an adaptive extended Kalman based on filtering multi-sensor fusion method for roadside applications. Polynomial fitting is used to obtain the residual error of each sensor’s measured value sequence, generating initial measurement noise through variance functions. By detecting sensor measurement value stability, the measurement noise correction coefficient is generated and adaptively adjusted. The extended Kalman filter algorithm fuses multi-sensor information. Tests on a high voltage transformer test platform validate the proposed method’s effectiveness. The accurate and reliable condition monitoring of converter transformers is critical for preventing catastrophic failures in the power grid. However, the harsh electrical environments and weather conditions in which these transformers operate can significantly affect the stability and accuracy of condition monitoring sensors. The proposed adaptive extended Kalman filter approach provides an elegant solution to maintain robust state estimation and sensor fusion in spite of dynamically changing sensor noise and environmental interference. By modeling the measurement noise as a polynomial function of the sensor residuals, the method captures noise characteristics without requiring extensive models of the sensors themselves. The noise correction coefficient further tunes the noise estimates based on real-time stability assessments, allowing adaptive response to changing conditions. This enables the extended Kalman filter to maintain optimal performance even with fluctuating measurement uncertainty. The implementation on a physical converter transformer test platform demonstrates that the approach can work effectively in practice. The results highlight the power of adaptive state estimation techniques for critical infrastructure monitoring applications, where maintaining situational awareness is paramount. As power systems continue to operate under increasing stresses, condition monitoring and predictive maintenance will become ever more vital. This work provides a valuable framework for enhancing the reliability and fault tolerance of such monitoring systems in adverse real-world environments. The adaptive noise modeling concept could potentially be applied to state estimation challenges in a wide range of other domains as well. There are several promising directions for further research and development. Expanding the method to handle nonlinear system models could increase applicability. Algorithms for online optimization of the noise correction parameters could improve performance. And testing across broader operational scenarios could further validate robustness. Overall, the study provides an important advance towards smarter condition monitoring for smarter power grids. With further maturation, techniques like this that fuse data from multiple imperfect sensors could unlock new levels of grid resilience.

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2 First Section The sensor fusion framework is shown in Fig. 1. Due to the different starting time and data update frequency of each sensor, it is necessary to synchronize the sensor information before fusion. Assuming linear change of the target motion attribute over a period, time synchronization is achieved through linear interpolation. This involves calculating the equivalent data of a specific moment by interpolating between the data of the sensor at two consecutive moments. The target-level data from all sensors have been converted to the UTM coordinate system in space. The target-level data after spatiotemporal synchronization is transmitted to the edge cloud information fusion platform, and then the multi-sensor information is fused through the adaptive extended Kalman filter algorithm proposed in this paper.

Fig. 1. The sensor fusion framework

The adaptive extended Kalman filter aims to approximate nonlinear models using Taylor expansion.The prediction formula of EKF can be set as xt = g(ut , xt−1 ) + εt zt = h(xt ) + δt

(1)

Since the measurement noise of the sensor will change dynamically with the position and state of the moving target, the fixed noise value is easy to cause the filter to be unstable or even divergent. Therefore, based on the extended Kalman filter, The utilization of the correction coefficient in the adaptive adjustment of the measurement noise covariance matrix allows for the refinement of the EKF algorithm’s estimation and prediction capabilities. By continuously updating the covariance matrix based on the observed measurements and the correction coefficient, the AEKF fusion algorithm achieves improved accuracy and stability in estimating the target’s state. This iterative process enhances the algorithm’s ability to handle uncertainties and variations in the measurement noise, resulting in more reliable and robust estimation results.The correction coefficient is used to dynamically adjust the measurement noise covariance matrix in order to optimize the performance of the Extended Kalman Filter (EKF) algorithm. The flow of the AEKF fusion algorithm is as follows.

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1) The CTRA model is utilized to establish the equation for system state transition. Benxiton derived the state transition equation through a first-order Taylor expansion x(t) = Gt · x(t − 1) + g(u(t − 1)) + ε(t − 1) y(t) = Ht · x(t) + δ(t)

(2)

The Jacobi matrix Fk of the state equation is further solved. 2) During the time update phase, the predicted target state xk and the state covariance matrix Pk are calculated using the Jacobi matrix Fk , which is obtained in the first step. 3) Determine the observation matrix. 4) Solving measurement noise. In this paper, The measurement noise is addressed by processing the sensor measurements in a given time series. The fitting terms for the various measurements from different sensors are obtained by fitting the sensor measurements of a specific time series. zˆik = fitf(zik , k)

(3)

Within the given context, zik represents the measurement sequence of the ith component of the measurement vector z at time k. ik denotes the fitting term associated with the measurement sequence of the ith component of the measurement vector z at time k. The fitting term is calculated using the fitting function fitf(·). The residual error for the measurement sequence of the ith component of the measurement vector z at time k represents the difference between the observed measurement and the predicted measurement. zik = zik − zˆik

(4)

The variance function is utilized to calculate the measurement noise of the sensor. Specifically, it computes the initial measurement noise for the ith component at time k. R0k = [R01k , R02k , ..., R021k ]T

(5)

R0k will continue to converge and stabilize as time increases. 5) Adaptive adjustment of the measurement noise is necessary in estimation algorithms to accommodate variations in the target’s motion state and the dynamic characteristics of the sensor. The measurement noise in the system is not static and can change over time due to unpredictable factors or external influences. To ensure the stability and accuracy of the estimation process, it is important to dynamically adjust the measurement noise using a correction coefficient. The correction coefficient, denoted as u, is a parameter that determines the adjustment of the measurement noise. Its value is determined through stability detection of the sensor measurement. This involves monitoring and analyzing the stability of the sensor’s measurements over a certain period of time or by applying statistical techniques. In order to account for the uncertainty in the target’s motion state and the dynamic sensing characteristics of the sensor, an adaptive adjustment of the measurement noise is considered. The measurement noise in the system is known to change over time, and to maintain the stability of the filter, a correction coefficient u is defined to dynamically adjust the measurement noise. The generation of the correction coefficient involves stability detection

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of the sensor measurement. The correction coefficient of the ith measurement component at time k is  |zki −ˆzki | , |zki − zˆki | > δi ; δ (6) uki = 1, |zki − zˆki | ≤ δi . In the context mentioned, zik represents the measurement value of the ith measurement component at time k. ki denotes the fitting value associated with the ith measurement component at time k. δ i represents the threshold value for the ith measurement component. It is important to note that the fluctuation of the measured value can either be a constant or a time-varying function. However, in this paper, the measured value’s fluctuation is constrained within a fixed value, hence the use of a constant δ i . If the residual zik -ki of the ith measured value at time k is less than or equal to δ i , indicating that the sensor measurement is stable, the correction coefficient uki for the ith measured component is set to be equal to 1; if the residual zik -ki of the measured value at time k is greater than δ i , indicating that the sensor measurement is unstable, then uki is set to a value greater than 1 to amplify the noise variance of the measured component.In order to limit the fluctuation of the measured value of the sensor within a specific range, this paper employs a constant threshold value, δ i . The determination of δ i , involves considering the percentiles of the absolute values of zik , where zik represents the difference or deviation between consecutive measurement values of the ith component over a certain time period. To determine the appropriate value of δ i , the absolute values of zik are arranged in ascending order. By selecting an applicable percentile from this sorted list, δ i , can be set to constrain the fluctuation of the measured value of the sensor within a smaller range. This percentile-based approach allows for a flexible and adaptable way to adjust the threshold value, taking into account the characteristics of the sensor and the specific requirements of the application. The measurement noise correction matrix is constructed to account for the estimation error caused by measurement noise: Nk = diag(uk1 , uk2 , ..., uk21 )

(7)

The adaptive adjustment of the initial measurement noise matrix, denoted as R0k , is achieved using Nk . By applying Nk to R0k , a new measurement noise matrix is obtained. The process can be described as follows: Rk = Nk R0k

(8)

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3 Verification This paper presents the use of a MEMS-based vibration acceleration sensor to monitor the vibration signal of a transformer. The monitoring of the transformer operating current is achieved using a high-voltage transformer, and the recording of the operating current is done using a waveform recorder. Set up the converter transformer test system as shown in Fig. 1, the installation position of the vibration voiceprint sensor in the system is shown in Fig. 2. By changing the load current of the converter transformer, test the converter transformer installed with the vibration voiceprint sensor and synchronously record the load and vibration voiceprint test data. It is worth noting that the power grid for this test is dedicated to the test area power supply, which is independently powered by the 110 kV substation. When a short-circuit current of 560 A is applied, mechanical instability occurs in the left winding of the transformer, showing an abnormal mechanical vibration of 0.25 Hz. The output signal of the proposed method is shown in Fig. 3. Compared with traditional EKF method, the accuracy of the proposed method has improved 9.7%. Detailed experiment process and more results will be given in the final paper.

Fig. 2. Set up the converter transformer test system

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Fig. 3. The experimental result comparison

4 Conclusion In multi-sensor fusion processes, obtaining sensor error characteristics online and providing a dynamic quantitative description is challenging. This paper proposes an online measurement noise acquisition method using the measured values from different sensors within a specific time series. By applying polynomial fitting to the measured value sequence, the residual is obtained and the variance function generates the initial measurement noise. Furthermore, an adaptive extended Kalman filter (AEKF)-based multisensor fusion method is introduced for fusing multi-source heterogeneous information. By detecting the stability of a sensor’s measured values, the measurement noise matrix is adaptively adjusted using a correction coefficient, reducing the noise’s impact on system estimation. Compared to single-sensor measurements, the adaptive adjustment fusion based on the measurement noise enhances accuracy by 9.7%, improving estimation and reducing noise interference. Acknowledgments. This project was supported by the Science and Technology Projects of Zhejiang Electric Power (B311MR220003).

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References 1. Key, S., Kang, S.-H., Lee, N.-H., Nam, S.-R.: Bayesian deep neural network to compensate for current transformer saturation. IEEE Access 9, 154731–154739 (2021) 2. Zhang, Y., Yang, S., Hao, Z., Lin, Z., Liu, Z.: A hybrid model-driven and data-driven approach for saturation correction of current transformer. IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5 (2021) 3. Jin, N., et al.: Research on protection tripping scheme of multiple criteria with high reliability for HV transmission lines. In: 2021 IEEE 4th International Electrical and Energy Conference (CIEEC), pp. 1–4 (2021) 4. Li, Z., Xiao, S., Yue, Q., Wang, T.: Electrical capacitance tomography sensor with house structure for assisting recognition of objects. IEEE Sens. J. 22(5), 4534–4544 (2022) 5. Bahari, S., Hasani, T., Sevedi, H.: A new stabilizing method of differential protection against current transformer saturation using current derivatives. In: 2020 14th International Conference on Protection and Automation of Power Systems (IPAPS), pp. 33–38 (2019) 6. Xue, T., Wang, W., Ma, J., Liu, W., Pan, Z., Han, M.: Progress and prospects of multimodal fusion methods in physical human-robot interaction: a review. IEEE Sens. J. 20(18), 10355– 10370 (2020) 7. Kapourchali, M.H., Banerjee, B.: State Estimation via Communication for Monitoring. IEEE Trans. Emerg. Top. Computat. Intell. 4(6), 786–793 (2020) 8. Schettino, B.M., Duque, C.A., Silveira, P.M.: Current-transformer saturation detection using savitzky-golay filter. IEEE Trans. Power Delivery 31(3), 1400–1401 (2016) 9. Yao, C., et al.: Detection of internal winding faults in power transformers based on graphical characteristics of voltage and current. In: 2014 ICHVE International Conference on High Voltage Engineering and Application, Poznan, pp. 1–4 (2014) 10. Yu, H., Kong, L.: Research on modal parameter identification method of power transformer winding. In: 37th Chinese Control Conference (CCC), pp. 5681–5686. Wuhan, China (2018) 11. Attiyah, B.A., Alnujaimi, A.A., Alghamdi, M.A.:Reliability enhancement of high voltage power transformer using online oil dehydration. In: Modern Electric Power Systems (MEPS), pp. 1-4. Wroclaw, Poland (2019) 12. Chen, Y., Mao, H., Yan, Z., Li, P., Liu, C.: Development of transformer winding fault monitoring system based on vibration analysis. In: International Conference on Advanced Electrical Equipment and Reliable Operation (AEERO). Beijing, China (2021)

Parameter Identification of Retired Batteries Based on Improved Adaptive Particle Swarm Optimization Liang Li1(B) , Jingyun Chen1 , Shiqi Nie1 , Yuan Li1 , Yanwei Li1 , and Jialing Li2 1 State Grid Zhejiang Electric Vehicle Service Co., Ltd., Hangzhou 310000, China

[email protected] 2 Zhejiang Huadian Equipment Testing and Research Institute Co., Ltd., Hangzhou 310000,

China

Abstract. To address the issue of traditional Particle swarm optimization algorithms easily falling into local extremes and exhibiting low identification accuracy when identifying parameters in decommissioned batteries, an improved adaptive Particle swarm optimization algorithm-based parameter identification model is proposed. This model is developed by analyzing the five-parameter model of decommissioned batteries. The adaptive strategy adjusts the inertia weight factor within the conventional Particle swarm optimization algorithm. Additionally, an asynchronous learning factor is introduced to balance the search relationship between global and local extremes. The constructed adaptive Particle swarm optimization model is then employed to identify parameters in three distinct types of decommissioned batteries and compared with the traditional Particle swarm parameter identification method. Results demonstrate that the improved adaptive Particle swarm optimization algorithm exhibits higher accuracy in parameter identification, with average relative errors ranging from 0.975% and 5.975% and an overall error below 6%. These findings validate the feasibility and effectiveness of the proposed adaptive Particle swarm optimization algorithm in identifying parameters for retired batteries. Keywords: Parameter Identification · Retired Batteries · Particle Swarm Optimization

1 Introduction Currently, the identification of parameters for retired batteries primarily relies on the saltwater immersion discharge method. This approach necessitates extended discharge times and yields low efficiency. The immersion process can cause heavy metals in the battery to leak into the saltwater, leading to environmental contamination. Further, retired batteries are often crushed uniformly, which hinders the tiered utilization based on performance levels. Additionally, the data supplied by manufacturers does not directly offer solutions for all five unknown parameters of the retired battery model, making research on identifying these parameters an area of widespread interest. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 598–605, 2024. https://doi.org/10.1007/978-981-97-1072-0_61

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The primary methods for identifying retired battery parameters encompass analytical methods, numerical calculation methods, and intelligent algorithms. In one approach, researchers [1] utilized manufacturer-provided data and simplified analytical expressions to achieve parameter identification for retired batteries. Another study [2] determined the remaining four parameter values by using current and voltage temperature coefficients found in the manufacturer’s data, assuming a pre-established constant ideal resistance factor. Researchers in another instance [3] employed the Gaussian Iterative method to solve retired battery parameters. Additionally, study in [4] established an algebraic equation set for the five unknown parameters, drawing from the Lambert W function’s explicit method. Lastly, experiment-based testing was employed by [5] to provide parameter identification results for retired batteries, although this method is comparatively more cumbersome to implement. Compared to the parameter approximation method, intelligent optimization algorithms offer higher identification accuracy and faster optimization speeds. These algorithms have been utilized to some extent to solve retired battery parameters [6]. A parameterless meta-heuristic JAYA optimization algorithm proposed by [7] can address constrained optimization problems. By incorporating the concept of Particle Swarm Optimization (PSO) for individual updates, an improved Ant Lion optimization algorithm used by [8] to identify retired battery model parameters shortened optimization times. Researchers [9] enhanced the accuracy and speed of parameter identification by integrating chaos algorithms and PSO into the SA CPSO particle swarm algorithm. As suggested by [10], different algorithms perform variably in their respective fields, signifying the importance of evaluating advantages, drawbacks, and applicability in specific research contexts. Considering the traditional PSO algorithm’s limitations in convergence and optimization speed, this digest employs an improved adaptive PSO algorithm to identify retired battery model parameters. By introducing an adaptive strategy to modify the weight factor and asynchronous learning factor, the algorithm’s search accuracy and rate of convergence are balanced. The final paper will further improve the reliability and accuracy of parameter identification and will verify the identification results for various types of retired batteries.

2 Battery Model and Its Parameter Identification 2.1 Retired Power Battery Model The Thevenin equivalent circuit model can simultaneously reflect the characteristics of both capacitance and resistance of retired power lithium batteries, and can also well reflect the dynamic and static characteristics of retired power lithium batteries, and is easy to identify parameters. Therefore, this digest will use a second-order Thevenin equivalent circuit model to model retired power batteries, in order to estimate their SOC. The circuit model is shown in Fig. 1.

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From Fig. 1, the voltage source UOC, ohmic internal resistance R and two parallel RC circuit constitute the second-order RC equivalent circuit model of retired power lithium batteries in series. UOC is related to the SOC of retired power lithium batteries, indicating their open circuit voltage; R0 represents the Ohmic internal resistance of retired power lithium batteries; Two parallel RC circuits can simulate the voltage change process after the discharge of retired power lithium batteries, representing their internal polarization reaction. R1 and R2 represent the polarization resistance of the retired batteries, and C1 and C2 represent the polarization capacitance of the retired batteries; Ut represents the terminal voltage of retired power batteries; I(t) represents the current flowing inside the retired power battery. 1

2

1

2

0

Fig. 1. Thevenin equivalent circuit model

2.2 Model Parameters Identification This digest uses the recursive least squares method to identify the parameters of the equivalent circuit model of retired power lithium batteries established in the previous section under constant current pulse charging and discharging experiments. Fully charge the retired battery and let it stand still, reducing the SOC from 80% to 0. Cycle charging and discharging every 5% to identify its parameters. The specific pulse process is shown in Fig. 2. Using experimental data and Matlab, the SOC - OCV curve was fitted using an 8th degree polynomial. The fitted SOC - OCV curve is shown in Fig. 3. The corresponding form of the fitting function is Uoc = aSOC4 + bSOC3 + cSOC2 + d SOC + e

(1)

The parameters that need to be identified for this equivalent circuit model include R0 , R1 , C 1 , R2 , C 2 . Among them, the ohmic internal resistance R0 is caused by the voltage difference that momentarily drops. Using the battery charging and discharging current data, the voltage jump value at the time of current input or disconnection is found, and the average value of the voltage jump voltage difference is taken to calculate R0. The calculation formula is as follows: R0 =

U1 + U2 2I (t)

(2)

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Voltage(V)

5

4

-20

3.8

4.5 -30 4 -40 3.5 -50

3 2.5 2

4.2

-10

OCV/V

Voltage Current

Current(A)

6 5.5

0

5

5

10

601

3.6 3.4 3.2

-60

3

-70 15

2.8

t/(x10 s)

Fig. 2. Constant current pulse discharge process

Real Value Fitting Value 0

20

40

SOC/%

60

80

100

Fig. 3. Curve fitting of SOC-OCV

In the formula, I(t) is the discharge current. After the end of pulse discharge, the terminal voltage slowly returns to a stable value. This process curve can show the discharge process of polarization capacitors C 1 and C 2 towards polarization resistors R1 and R2 through their respective resistive and capacitive circuits. The zero input response equation can be written from the resistive and capacitive circuits of this segment: t−t t−t     − 0 − 0 U t = Uoc t0 − U1 (t0 )e τ1 − U2 (t0 )e τ2

(3)

3 Particle Swarm Optimization Algorithm for Model Parameter Identification 3.1 Particle Swarm Optimization Algorithm for Model Parameter Identification The Particle swarm optimization (PSO) algorithm requires fewer adjustment parameters, has a fast Rate of convergence and is easy to implement. It needs to consider the two attributes of Particle speed and position for iterative optimization. Each Particle in the PSO represents a possible solution to the parameter identification of the photovoltaic cell model. The updated formula during Particle work is     vin = uvin−1 + c1 r1 pin − xin + c2 r2 g n − xin (4) xin+1 = xin + vin

(5)

where vni is the velocity of Particle i at the nth iteration, X ni is the position of Particle i at the nth iteration, w is inertia weight, C1 and C2 are the individual learning factor, and group learning factor, respectively. r1 and r2 are random numbers from 0 to 1, pni is the optimal position of Particle i at the nth iteration, gn - the best position for all Particle s to stop at the nth iteration. The fitness value of Particle s is determined by the optimized function, following the current optimal Particle to search in the solution space. In the iteration, the Particle continuously updates itself by tracking two extreme values, namely the individual extreme value p and the population extreme value g. p is the optimal solution found by the Particle itself, and g is the current optimal solution found by the entire population.

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In traditional PSO, the values of inertia weight and learning factor are fixed, which cannot be adjusted according to requirements throughout the entire optimization process, and the convergence and optimization speed are slow, affecting the speed of parameter identification. 3.2 Improved Adaptive Particle Swarm Optimization Algorithm By introducing adaptive weight factors and asynchronous learning factors, the inertia weight and learning factor no longer maintain linear changes during Particle iteration, but are adjusted in a timely manner based on the Particle optimization situation. In the speed term of the PSO algorithm, the dynamic inertia weight w is introduced, which represents the ability of the Particle s to inherit the previous speed. A larger weight inertia is conducive to the algorithm jumping out of the local optimal solution, improving the global optimization ability, and a smaller weight is conducive to the local search, accelerating the rate of convergence. Traditional methods often use linearly decreasing inertia weights to better balance the global and local search capabilities of algorithms will be w = wmax − (wmax − wmin )(nmax − n)/nmax

(6)

where wmax is the initial inertia weight, wmin is the iterative final inertia weight, N max is the maximum number of iterations, and N is the current number of iterations. In (6), it indicates that global optimization is the main focus at the beginning of the iteration, and the inertia weight takes the maximum value. As the iteration progresses, the inertia weight decreases linearly, and the local search ability gradually improves. Linear decreasing inertia weight is an empirical method, and the Particle swarm algorithm performs best when the inertia weight wmax = 0.9 and wmin = 0.4. On this basis, the APSO algorithm adds an adaptive adjustment strategy to update the inertia weight during the iteration process, and the update formula is c1 = c1max −

n(c1min − c1max ) nmax

(7)

c1 = c1max −

n(c1min − c1max ) nmax

(8)

Based on the number of unknown parameters of retired batteries, it can be determined that the dimension space of the APSO algorithm is 5, that is, the Particle variable is a 5-dimensional vector. The position vectors of Particle s represent possible solutions, so the identification results of photovoltaic cell parameters can be regarded as five position vectors at the same time. Let the independent variable X = (R0 , R1 , C 1 , R2 , C 2 ) in the fitness function, and combine it with the error equation to determine the fitness function of the algorithm   n  (9) f (X ) =  (Ic − It )2 i=1

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where I c is the current value obtained by substituting the identification result into (5), and I t is measured current data. The APSO algorithm sets n to 500 and the population size to 50. The specific parameter identification process is shown in Fig. 4. From Table 2, the average relative error of traditional Particle swarm optimization algorithm in parameter recognition is between 6.324% and 9.736%, while the average relative error of improved AP - SO optimization algorithm is between 0.975% and 5.975%, with overall errors below 6%. It is demonstrated that the improved APSO algorithm proposed in the digest can improve the accuracy of parameter calculation (Table 1).

,

1, 2

p

g

o

p

oup g

Fig. 4. The process of the APSO

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SOC/%

R0 /

Ri /m

R/m

C i /F

C J /F

80

3.82

1.46

4.63

13684.83

108305.75

60

3.64

1.89

0.95

22360.81

861528.76

40

3.55

1.56

2.30

37880.47

679832.85

20

3.59

2.71

8.78

21260.77

242305.46

Table 2. Comparison of the relative error between PSO and APSO (%) SOC/%

Method

R0 /

Ri /m

R/m

C i /F

C J /F

80

PSO

8.174

9.058

9.134

6.324

9.649

APSO

1.271

0.975

2.785

5.496

5.975

60

PSO

0.971

9.572

8.013

9.157

9.595

APSO

1.576

4.584

0.142

4.218

4.922

40

PSO

6.557

9.341

7.577

7.432

6.555

APSO

3.057

4.891

3.787

3.922

1.172

PSO

7.293

9.627

9.736

8.648

8.537

APSO

1.273

2.398

3.492

2.812

1.475

20

4 Conclusion This digest constructed an improved adaptive Particle swarm optimization algorithm model for parameter recognition of retired batteries. On the basis of the traditional Particle swarm optimization algorithm, linear weight and asynchronous learning factor are introduced, and an improved adaptive Particle swarm optimization algorithm is given in this digest. The experimental results show that the average relative error of the improved APSO algorithm in the parameter identification process is 1.109% ~ 2.505%, and the overall error is below 3%, with higher search accuracy. Acknowledgments. Discovery by Guo.com Zhejiang Electric Power Co., Ltd. Science and Technology Project "Research on Key Performance Detection and Full Life cycle Status Evaluation Method of Energy Storage Class Battery" (Project Number: 2023FD03).

References 1. Xuan, L., Lixin, W., Chao, L., Junfu, L.: Modeling and parameter identification of lithium ion batteries. Journal of Power Supply 16(01), 145–150 (2018) 2. Liaw, B.Y., Nagasubramanian, G., Jungst, R.G., et al.: Modeling of lithium ion cells—A simple equivalent-circuit model approach. Solid State Ionics 175(1–4), 835–839 (2004)

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3. Deng, Z., Yang, L., Cai, Y., et al.: Online available capacity prediction and state of charge estimation based on advanced data-driven algorithms for lithium iron phosphate battery. Energy 112(oct. 1), 469–480 (2016) 4. Hung, M.H., Lin, C.H., Lee, L.C., et al.: State-of-charge and state-of-health estimation for lithium-ion batteries based on dynamic impedance technique. J. Power Sour. 268(dec. 5), 861–873 (2014) 5. Chun, H., et al.: Capacity estimation of lithium-ion batteries for various aging states through knowledge transfer. IEEE Trans. Transport. Electrific. 8(2), 1758–1768 (2022) 6. Kim, J., et al.: Parameter identification of lithium-ion battery pseudo-2-dimensional models using genetic algorithm and neural network cooperative optimization. Journal of Energy Storage 45 (2022) 7. Andrew, H., et al.: Searching for MobileNetV3. In: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pp. 1314–1324 (2019) 8. Mark, S., et al.: MobileNetV2: inverted residuals and linear bottlenecks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4510–4520 (2018) 9. Chun, H., et al.: Parameter identification of an electrochemical lithium-ion battery model with convolutional neural network. IFACPapersOnLine 52(4), 129–134 (2019) 10. Bogno, B., et al.: Improvement of safety longevity and performance of lead acid battery in off-grid PV systems. Int. J. Hydrog. Energy 42(5), 3466–3478 (2017)

A Bidirectional DC-DC Converter and Fast-GMPPT Algorithm for Photovoltaic Cells Lianggang Xu(B) , Baoxian Ji, Lijuan Lu, and Wenming Liu Guizhou Puyuantong Technology Co., Ltd., Guizhou, China [email protected]

Abstract. Aiming at the laser wireless power transfer (LWPT) system powered by photovoltaic (PV) cells for batteries at receiver, this paper proposes a new type of cascaded bidirectional DC-DC converter, which is convenient for energy transfer between PV cells and energy storage batteries. This DC-DC converter improves efficiency by providing an auxiliary current path which can reduce output current ripple. In addition, aiming at the energy distribution law of Gaussian laser irradiation, this paper summarizes the unique law of the output characteristics of PV arrays under Gaussian laser irradiation, and proposes a global maximum power point tracking (GMPPT) algorithm for PV arrays under Gaussian laser irradiation, which can be used for the proposed cascaded bidirectional DC-DC converter, and is faster than the existing traditional GMPPT algorithm that is generally applicable to uneven sunlight, which further improves the energy utilization. The experimental platform of the proposed converter and GMPPT algorithm is built to verify their effectiveness, and the results show that the proposed converter has better performance, and the GMPPT algorithm used can quickly and effectively track the global maximum power point compared with the traditional GMPPT algorithm. Keywords: LWPT · Photovoltaic (PV) · DC–DC Converter · GMPPT

1 Introduction The structure of the LWPT system is shown in Fig. 1, which is divided into a transmitter and a receiver, and there is a PV converter with GMPPT function on the receiving side. However, when the PV cell at the receiver needs to power the energy storage batteries, the photovoltaic converter needs to use a bidirectional buck–boost converter for the following reasons: 1) The battery cells frequently discharge and charge, which causes an enormous alternation in voltage [2, 3]. 2) The PV module’s voltage varies significantly depending on the solar irradiation and the module’s temperature [4]. Thus, the ranges of the input voltage and output voltage can overlap. Cascaded buckboost (CBB) converter shown in Fig. 2 can meets the requirement of overlapping input © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 606–619, 2024. https://doi.org/10.1007/978-981-97-1072-0_62

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Fig. 1. Structure diagram for LWPT system

and output voltages [5]. However, operating in DCM raises L’s current ripple, which impacts the output current ripple and raises the output voltage ripple. In this paper, an improved CBB converter aimed at a PV smart grid system is suggested to increase the performance of the traditional CBB converter.

Fig. 2. Circuit topology of CBB convert

Moreover, in the instance of a smart grid powered by photovoltaic (PV) cells, the diminished overall efficiency, primarily attributed to uneven laser irradiance on the PV array, constrains the adoption of high-intensity laser power beam (HILPB) systems. Due to the nonuniform laser irradiance, the power-voltage (P-V) curve of the PV array exhibits multiple peaks, necessitating the development of a Global Maximum Power Point Tracking (GMPPT) method to precisely locate the global maximum power point (GMPP) under Gaussian laser beam conditions (GLBC). Nevertheless, existing GMPPT techniques are primarily tailored for en-tirely disordered partially shaded conditions (PSC), making it challenging to achieve rapid tracking while maintaining tracking accuracy. It’s worth noting that GLBC represents a specific scenario within PSC where the laser irradiance distri-bution, although non-uniform, still exhibits some degree of regularity. In this article, mathematical expressions for per-unit voltage, per-unit current, and per-unit power of local maximum power points (LMPPs) under GLBC are introduced, derived from extensive studies on the PV array’s output characteristics. Subse-quently, a GMPPT method optimized for GLBC, capitalizing on these equations, is proposed.

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2 Proposed PV DC-DC Converter 2.1 Circuit Structure The proposed enhanced CBB converter is shown in Fig. 3. Four switches are triggered in the ZVS state by working in DCM. By providing a current path, the auxiliary capacitor C a reduces output current ripple, whilst the capacitors can minimize output voltage ripple and noise (Table 1).

Fig. 3. Circuit structure of the proposed converter.

Table 1. Switch states under six different operating circumstances Six operating conditions

Switches

Directions of energy transfer

Type of the operation

S1

S2

S3

S4

V IN → V O

Buck

1-D

D

0

1

Buck-Boost

1-D

D

D

1-D

Boost

0

1

D

1-D

Buck

0

1

D

1-D

Buck-Boost

1-D

D

D

1-D

Boost

1-D

D

0

1

V O → V IN

2.2 Principle of Operation In LWPT systems, photovoltaic converters tend to operate in boost mode, so this section details the operation of the proposed converter in boost mode. The boost operating mode and key circuit waveforms are shown in Fig. 4 and Fig. 5, respectively. When t 0 ≤ t ≤ t 1 , shown in Fig. 4(a): when S 3 is turned ON, S 3 accomplishes ZVS switch ON at t = t 0 , so the iL is expressed as iL (t) =

VIN (t − t0 ) + iL (t0 ) L

(1)

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(a)

(b)

(c)

(d)

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Fig. 4. Circuit diagrams of boost. (a) Mode I. (b) Mode II. (c) Mode III. (d) Mode IV.

Fig. 5. Key waveforms of boost.

Since the current i3 of S 3 is the same as iL , so i3 is represented as i3 (t) = (t − t0 )

VIN +iL (t0 ) L

(2)

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Due to iO = − iCa = iCo + I O , and iCa = iCo ·C a /C O , iCa and iO are represented as ⎧ CO ⎪ ⎪ )IO ⎨ iCa (t) = −(1 − CO + Ca (3) CO ⎪ ⎪ ⎩ iO (t) = (1 − )IO CO + Ca The voltage vCa can be expressed as vCa (t) = VCa + vCa,AC(t)

(4)

Because V Ca > > vCa,AC , this expression can be approximated as vCa (t) ≈ VO − VIN

(5)

When t 1 ≤ t ≤ t 2 , shown in Fig. 4(b): when S 3 is switched OFF and S 4 keeps off. When t 2 ≤ t ≤ t 3 , shown in Fig. 4(c), the iL can be expressed as iL (t) =

VIN − VO (t − t2 ) + iL (t2 ) L

(6)

The current i4 of S 4 is equal to − iL , so i4 is obtained as i4 (t) =

VO − VIN (t − t2 ) − iL (t2 ) L

(7)

Due to iO = iL − iCa = iCo + I O , and iCa = − iCo ·C a /C O , iCa and iO are expressed as

⎧ ⎪ ⎪ ⎨ iCa (t) = (1 −

CO )[iL (t) − IO ] Ca + CO CO Ca ⎪ ⎪ ⎩ iO (t) = iL (t) + IO Ca + CO Ca + CO

(8)

When t 3 ≤ t ≤ t 4 , shown in Fig. 4(d): It is consistent with the above analysis, ΔiL for boost operation is obtained as iL (t) = iL (t2 ) − iL (t0 ) =

DTS VIN L

(9)

where DT S = t 2 − t 0 . Because < iL > = I IN and iL (t 0 ) = < iL > − ΔiL /2, iL (t 0 ) is expressed as DTS VIN 2L

(10)

DTS VIN + IIN 2L

(11)

iL (t0 ) = IIN − iL (t 2 ) = < iL > + ΔiL /2 is expressed as iL (t2 ) =

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According to the above analysis, it can be seen that when the circuit works in boost mode, Δvo is expressed as  tO t iCO (t)dt vO = 2 (12) CO For t 3 ≤ t ≤ t 4 , (6), (8), and (11): iCo (t) =

CO VIN − VO DTS VIN VIN − VO (IIN + t− t2 + − IO ) Ca + CO L L 2L

(13)

As shown in Fig. 5, according to (13), t c is obtained as tc = t2 +

(IIN − IO )L + VIN DTS /2 VO − VIN

(14)

Then, Δvo is obtained using (12)-(14) as vo =

[VIN DTS /2 + (IIN − IO )L]2 2L(VO − VIN )(Ca + CO )

(15)

3 Improved GMPPT Method Under GLBC 3.1 PV Array’s Output Characteristics Under GLBC In Fig. 6, you can observe the output characteristics and equivalent circuit of a photovoltaic (PV) cell. As depicted, the power-voltage (P-V) curve exhibits a single peak of power, known as the Maximum Power Point (MPP). The current at the MPP (I m ) and the voltage at the MPP (V m ) can be approximately described as [16] and [17]. I sc corresponds to PV cell’s current when circuit is short, while V oc represents the PV cell’s voltage when circuit is open. Im ≈ 0.9Isc

(16)

Vm ≈ 0.8Voc

(17)

In Fig. 7(a), we can observe a PV series consisting of two cells. Assuming that the cell above gets more irradiation. Specifically, the short-circuit (SC) current, the irradiance, the voltage and power at MPP of the PV above are designated as reference indicators, denoted as “1.“ Consequently, the indicators of the PV below are defined as “r.“ Fig. 7(b) shows the PV’s P-V curve. It’s evident that the plot of Current-Voltage (I-V) exhibits n distinct current steps, several power peaks appears in one P-V curve. The characteristics of such a PV string can be similarly inferred. GLBC (Gaussian Laser Beam Conditions) can be considered as a specific in-stance of Partially Shaded Conditions (PSC). In this scenario, the laser emits beams that closely analogous to a Gaussian profile. As a result, the irradiance on central part of the photovoltaic array is higher than that situated at the periphery. An irradiance profile, which

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Fig. 6. PV cell

1 1

1 (a)

2 (b)

Fig. 7. PV string with two cells under PSC

considers the physical location of each cell and the irradiance received across its entire surface area, has been raised in [9]. The PV array is conceptualized as a grid. Each pair of indices (i, j) corresponds to a specific photovoltaic cell, and the irradiation (Gi,j) on the PV cell is mathematically represented as [10].   2 · (Di,j )2 Gi,j = exp − (18) G0,0 w02 Here, G0,0 represents the irradiance at the network center, w0 stands for radius of the beam, and Di,j indicates the length of the origin (0, 0) to the position (i, j). Given that the irradiation in the middle of the network is the highest within the entire array, to maximize the utilization of laser power, the PV cell at the geometric center is designated as center. In this layout, the quantity of PV cells connected in series is an odd number. This configuration ensures that the irradiance received by two symmetrically arranged PV cells is identical. Additionally, it’s essential to ensure that the photovoltaic array’s length of the diagonal equals w0 , enabling all cells to be capable of photoelectric conversion. This symmetrical arrangement optimizes the utilization of laser irradiance in the PV array.

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In Fig. 8, you can see the PV string denoted as S0, which consists of (2m-1) PV cells connected as string. These cells experience m different levels of irradiance. In accordance with Eq. (18),per-cell’s irradiation is represented as Gi,j *.

j2 ∗ Gj = exp − (19) (m − 1)2

Fig. 8. Simplified laser irradiance distribution in S0

In this context, the current of the Local Maximum Power Point (LMPP) is denoted as LMPP1 (and subsequent LMPPs LMPP2, LMPP3, and so on. Therefore, the LMPPn’s current is represented as follows:

(n − 1)2 ∗ (20) = exp − Ipn (k − 1)2 The MPPs in the P-V curve are approximately located at 0.8 * V oc [11]. The voltage of LMPP1 is determined to be the reference value of 1. Consequently, the LMPPn’s voltage is represented using Eq. (21). ∗ = 2n − 1 Vpn

To calculate LMPPn’s power, you can multiply Eq. (20) and Eq. (21).

(n − 1)2 ∗ Ppn = (2n − 1) ∗ exp − (m − 1)2

(21)

(22)

As depicted in Fig. 9, when m is equal to 2, the differential calculus of Eq. (22) is consistently bigger than zero. This implies that Ppn * increases as n increases, therefore, LMPP2 becomes the Global Maximum Power Point (GMPP). However, when m > 2, the differential calculus of Eq. (22) initially shows a positive trend and subsequently becomes negative. This behavior indicates that Ppn * increases until it become GMPP, and then decreases. As a result, the GMPP is positioned in all MPPs. To locate the GMPP, you can set the derivative of Eq. (22) to 0,which yields Eqs. (23) and (24). √ 3 + 8m2 − 16m + 9 (23) n= 4

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N ≤n≤N +1

(24)

In Eqs. (20) to (24), where N > 0, the comparison between the power of LMPPN and LMPP(N + 1) can be used to determine the Global Maximum Power Point (GMPP). The GMPP is the one with higher power. These equations and their corresponding relationships are presented in Fig. 10 for clarity and visualization.

Fig. 9. Per-unit LMPP power Ppn * -n curve

Fig. 10. Per-unit output characteristics of PV string

In Fig. 11, you can observe the positions and the calculated normalized irradiation on each PV cell within a 3x3 and 5x5 PV array. PV cells with the same x coordinate are connected in series in every PV array to form a PV string denoted as Sx . Let’s consider the 3x3 PV array illustrated in Fig. 11 as an example. It’s evident that the irradiance received by S-1 and S1 is the same, resulting in identical output behavior for these two strings. Comparing S0 with S1 , the connection between G0,j and G1,j (where j takes values 0, 1, and 2) can be described by an expression: G1,j = G1,0 ∗ G0,j

(25)

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Based on Eq. (21), the voltage of LMPPn (where n can take values 1, 2, and 3) for the PV strings S-1 , S0, and S1 are all the same. Consequently, the power of LMPPn for S1 (PLMPP_S1 ) can be expressed as follows: PLMPP_S1 = G1,0 ∗ PLMPP_S0

(26)

It is plain that the region of monotonicity and the monotonic pattern of each Px-V curve are equivalent. Following the superposition theorem, the region of monotonicity and the monotonic pattern of the Power-Voltage (P-V) curve of the entire PV array are equivalent to those of each individual Px-V curve. This means that the collective P-V curve of the PV array inherits the monotonous characteristics observed in each component Px-V curve.

1 1, 1

0, 1

2, 1

1, 1

0, 1

1, 1

2, 1

2, 2

1, 2

0, 2

1, 2

2, 2

1, 1

(a) 3×3 PV array

(b) 5×5 PV array

Fig. 11. Irradiance profile model for the 3 × 3 and 5 × 5 PV array

3.2 Proposed GMPPT Method Under GLBC Figure 12 shows a method for finding the GMPP in a PV array. This method offers the advantage of calculating an approximate voltage for the Global Maximum Power Point (GMPP), significantly reducing the range of voltage that needs to be searched. As it’s only necessary to search in the vicinity of Vref , the search time is significantly reduced compared to global scanning methods. It’s important to note that this proposed method has only been evaluated assuming that the center of the PV array aligns with the focal point of the laser. If there are variations in laser irradiance, the Perturb and Observe method can be reapplied to ensure accurate GMPP tracking.

4 Experimental Results To demonstrate the effectiveness of this proposed method, an experimental setup, as illustrated in Fig. 13, was used. The parameters of the PV cell are detailed below: V oc = 5.6 V, I sc = 8.34 A, V m = 4.6 V, I m = 7.59 A. The values of the elements within the converter are listed in Table 2. Figure 14(a) and (b) display the Px-V and the P-V curves of a 3x3 and 5x5 PV array, respectively. Given the approximate consistency between the monotonic behavior of the

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a 1 2

k

k

m

* Ppm

Pp*( m

INT (

3

3

8k 2 16k 9 ) 4

(m 1) 2 (k 1) 2

(2m 1) * exp

1)

(2m 1) * exp

* Ppm

Pp*( m

m2 (k 1) 2

1)

DL

Vref

(2m 1) 0.8Voc

Vref

(2m 1) 0.8Voc

Vref

0 & & DR

0

3 0.8Voc

Fig. 12. Flowchart of the proposed method

Table 2. Values of components C in = C out

1000 µF

L

200 µH

RL

10 

fs

100 kHz

sampling interval t s

0.001 s

P-V curve of the PV array and each Px-V curve, the experiment was conducted on the PV string S0 within the 5x5 PV array under Gaussian Laser Beam Conditions (GLBC). This setup allowed for an effective evaluation of the proposed method’s performance. In order to conduct a fair comparison, a conventional global Incremental Conductance (C-GMPPT) method is employed as a control group to track the GMPP for the PV string under the same Gaussian Laser Beam Conditions (GLBC). The parameters used for this comparison, including f s , t s , and Dstep , are both the same. This standardization ensures a fair and meaningful comparison.

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Fig. 13. Experimental setup for the PV system

(a) 3×3 PV array

(b) 5×5 PV array

Fig. 14. Px-V curves and P-V curve of the PV array

Figure 15 presents the experimental results of the two methods for tracking the GMPP under the same Gaussian Laser Beam Conditions. The conventional C-GMPPT algorithm requires 0.85 s to find the GMPP, which has a voltage of 13.5 V and a power of 85.4 W. In contrast, the proposed approach ultimately acts on the second Local Maximum Power Point (LMPP), which has a voltage of 13.5 V and a power of 85.4 W. The entire tracking process with the proposed method takes 0.38 s. This indicates that the method proposed performs better than the conventional method.

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(a) C-GMPPT

(b) proposed method

Fig. 15. Tracking results under GLBC of S0 in 5 × 5 PV array

5 Conclusion In this paper, a novel bidirectional buck-boost converter and a high-speed GMPPT method under GLBC, utilizing fixed voltage control in conjunction with the conventional P&O method, have been introduced. The proposed converter effectively reduces output current ripple compared to the traditional bidirectional buck-boost (CBB) converter through offering an alternate route for the output current. This reduction in output current ripple leads to lower output voltage ripple and increased efficiency compared to conventional converters. In the proposed GMPPT method, the global scanning process has been replaced with only one local scanning, resulting in a substantial reduction in tracking time compared to conventional GMPPT methods that are designed for Partially Shaded Conditions (PSC). This approach is well-suited for PV arrays with long PV strings. Experimental results demonstrate that the proposed method accurately tracks the GMPP and enhances tracking speed without requiring additional circuits or sensors.

References 1. Jin, K., Zhou, W.: Wireless laser power transmission: a review of recent progress. IEEE Trans. Power Electron. 34(4), 3842–3859 (2019) 2. Tremblay, O., Dessaint, L., Dekkiche, A.: A generic battery model for the dynamic simulation of hybrid electric vehicles. In: Proc. IEEE Veh. Power Propulsion Conf., pp. 284–289 (2007) 3. Wang, H., Dusmez, S., Khaligh, A.: Design and analysis of a full bridge LLC based PEV charger optimized for wide battery voltage range. IEEE Trans. Veh. Technol. 63(4), 1603– 1613 (2014) 4. Paraskevadaki, E.V., Papathanassiou, S.A.: Evaluation of MPP voltage and power of mc-Si PV modules in partial shading conditions. IEEE Trans. Energy Convers. 26(3), 923–932 (2011) 5. Yari, K., Mojallali, H., Shahalami, S.H.: A New Coupled-Inductor-Based Buck–Boost DC– DC Converter for PV Applications. IEEE Transactions on Power Electronics (37–1) (2022) 6. Kermadi, M., Salam, Z., Ahmed, J., Berkouk, E.M.: A high performance global maximum power point tracker of PV system for rapidly changing partial shading. IEEE Trans. Ind. Electron. 68(3), 2236–2245 (2021)

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7. Huang, Y.-P., Huang, M.-Y., Ye, C.-E.: A fusion firefly algorithm with simplified propagation for photovoltaic MPPT under partial shading conditons. IEEE Trans. Sustain. Energy 11(4), 2641–2652 (2020) 8. Ali, A.I.M., et al.: An Enhanced P&O MPPT Algorithm With Concise Search Area for GridTied PV Systems. IEEE Access 11, 79408–79421 (2023). https://doi.org/10.1109/ACCESS. 2023.3298106 9. Zhou, W., Jin, K.: Optimal photovoltaic array configuration under Gaussian laser beam condition for wireless power transmission. IEEE Trans. Power Electron. 32(5), 3662–3672 (2017) 10. Daniel, E.B., Chiang, R., Keys, C.C., Lyjak, A.W., Nees, J.A.: Photovoltaic concentrator based power beaming for space elevator application. In Proc. AIP, 271–182 (2010) 11. Patel, H., Agarwal, V.: Maximum power point tracking scheme for PV systems operating under partially shaded conditions. IEEE Trans. Ind. Electron. 55(4), 1689–1698 (2008)

Power Analysis and Experimental Study of Vortex-Excited Vibrating Ocean Current Energy Generation Based on a Cylindrical Permanent Magnet Linear Motor Liguo Fan1,2 , Guoqiang Liu1 , Xianjin Song2 , Wenwei Zhang1 , Lipeng Wu2 , and Hui Xia1(B) 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

[email protected] 2 School of Electric Power and Architecture, Shanxi University, Taiyuan 030006, China

Abstract. In order to solve the problem of large mechanical loss and low energy conversion efficiency of traditional rotary motors in the vortex vibration ocean current energy generation system, this paper proposes a vortex vibration power generator based on cylindrical permanent magnet linear motor and conducts marine experiments. Firstly, Ansys software is used to analyze the influence of the magnetizing method, winding form and pole-slot combination on the air-gap magnetism and three-phase induced electromotive force of the linear motor; secondly, the optimization of the positioning force and the load characteristics are explored, and a cylindrical linear motor with radial magnetization, 9 poles and 10 slots combination is designed, which can reach a maximal power of 364 W; finally, the vortex vibration power generation system is constructed and tested on the Zhoushan Finally, a vortex-excited vibration power generation system is constructed and tested on the Zhoushan marine experimental platform, and the results show that the maximum power generation of 49.13 W is obtained when the current velocity is 0.45 m/s, and the energy conversion efficiency of the system is 38.1%. Keywords: Vortex-induced vibration current power generation system · cylindrical permanent magnet linear motor · finite element simulation analysis · marine experiment

1 Introduction As China’s “dual-carbon” program has entered a critical period, in order to achieve environmentally friendly development, the search for safe and reliable new clean energy has become the focus of many scholars [1]. China’s ocean current energy is rich in content, but limited by the flow rate of power generation efficiency is low. The research of new ocean current energy generation technology has a timely role. Prof. Bernitsas et al. at the University of Michigan were the first to propose an eddyexcited vibration aquatic clean energy device [2]. The device utilizes a gearing structure © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 620–627, 2024. https://doi.org/10.1007/978-981-97-1072-0_63

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to transmit vortex-excited vibration energy to a generator for power generation. 2022 Zhang et al. investigated the effect of high damping on the free surface of the converter [3]. Pool experiments are designed to test the vortex excitation response and energy conversion performance. 2022 Wu et al. explored the optimal parameters in terms of mass ratio and blunt body diameter, and proposed a three-stable vortex excitation vibration energy harvesting device [4]. The traditional vortex-excited vibration power generation system transmits energy to a rotating motor for power generation through an intermediate drive structure, which is susceptible to friction loss as well as interference from marine organisms. The use of linear motors can directly convert the current energy captured by the blunt body into electrical energy, and improve the efficiency of the utilization of ocean current energy. In this paper, firstly, a two-dimensional generator finite element model is constructed by Ansys software, and different magnetizing methods, winding forms and pole-slot combinations are discussed to illustrate the design method of vortex-excited vibration sea current energy power generation system based on a tubular permanent magnet linear generator(TPMLG); secondly, the positioning force of the motor is optimized and the load characteristics are analyzed, and it is verified that the motor can realize the rated power generation power of 150 W; finally, the marine experimental vortex-excited vibration power generation system is constructed to test the real sea conditions.

2 Working Principle of Vortex Vibration Current Energy Generation System The vortex-excited vibration current energy generation system works in two processes. The first is the low-flow current energy capture process, using the vortex-excited vibration effect, the blunt body array is placed in the low-flow current, when the fluid impacts the blunt body, it will produce periodic shedding vortices in the downstream, triggering the periodic vibration of the structure, and the fluid kinetic energy is converted into vibrational mechanical energy [5]. Next is the linear motor conversion of electrical energy process, the secondary permanent magnet is driven by the blunt body to do linear periodic motion, forming a traveling wave magnetic field in the air gap, cutting the primary coil to generate induction electromotive force, to realize the conversion of mechanical energy to electrical energy [6, 7] (Fig. 1).

Fig. 1. Vortex Vibration Current Energy Generation System.

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3 Cylindrical Permanent Magnet Linear Generator Finite Element Simulation 3.1 Three Different Magnetization Methods In order to observe the magnetic field in the primary core, finite element simulation is used to obtain the distribution of magnetic lines of force as shown in Fig. 2, where more magnetic lines in the air gap form a path through the primary coil [8].

(a) Axial magnetization.

(b) Radial magnetization.

(c) Halbach magnetization. Fig. 2. Distribution of magnetic lines of different magnetizing structures.

Fig. 3. Magnetic density curves of air gap with different magnetizing methods.

The magnitude and sinusoidality of the air gap magnetic field affect the linear motor performance. As can be seen from the curves in Fig. 3, the sinusoidality of the radial and Halbach magnetization curves is better, and the RMS values of the magnetic flux density are higher than those of the axial magnetization. However, the magnitude of radial magnetization air-gap magnetization is better than that of Halbach magnetization, which indicates that the radial magnetization method is more suitable for the structural parameters of this motor. 3.2 Winding Form Reasonable distribution of the winding form is conducive to the formation of sinusoidal and symmetrical three-phase induced electromotive force waveforms, and improves the

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efficiency of electrical energy output. Take 8 pole 12 slot motor as an example, analyze the three winding forms, the current commonly used winding forms are double layer winding, centralized winding and 120° phase band winding.

(a) Double layer winding.

(b) Centralized winding.

(c) 120° phase band windLQJ

Fig. 4. Three No-load induced electromotive force for each winding form.

From the simulation results in Fig. 4, it can be seen that the three-phase no-load induced electromotive force obtained with the double-layer winding has the best sinusoidal nature and the waveform distortion is small. The centralized winding produces the smallest electromotive force, with an amplitude of only 31.05 V. The 120° phase band winding cannot produce a symmetrical three-phase induced electromotive force waveform, with a large waveform aberration rate, and is not suitable for 8-pole, 12-slot motors. In summary, for the TPMLG with the same pole-slot combination corresponding to different winding forms, the induced electromotive force amplitude and waveform distortion rate are not the same, which indicates that it is necessary to calculate and analyze with the pole-slot combination to select the TPMLG structure with the optimal power generation performance. 3.3 Pole Slot Combination The pole-slot combinations of the cylindrical permanent magnet linear generator are more flexible, and 4-pole 6-slot, 8-pole 12-slot, and 9-pole 10-slot, which are more widely used, are selected for analysis [9]. The effective length, outer diameter and air gap width of the TPMLG structure with three different pole-slot combinations are kept constant.

(a) 4-pole, 16-slot.

(b) 8-pole, 12-slot.

(c) 9-pole, 10-slot.

Fig. 5. Winding form and pole-slot combination no-load induced electromotive force.

The 4-pole, 6-slot generator structure shown in Fig. 5(a) is unable to generate a symmetrical sinusoidal three-phase electromotive force. Figure 5(b) shows an 8-pole 12-slot generator combined with a double-layer winding with better sinusoidality of the electromotive force waveform and increased frequency of the no-load induced electromotive force. Figure 5(b) shows for the 9-pole, 10-slot motor combined with centralized

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winding is more advantageous to produce induced electromotive force waveforms with larger amplitude.

4 Positioning Force Optimization and Load Characterization 4.1 Linear Motor Positioning Force Optimization Positioning force is a non-negligible force that impedes the movement of the secondary permanent magnets of a linear motor. For linear motors operating at low frequencies, excessive positioning force leads to motor operation instability [10]. Edge-end force is the main cause of localization force, and the effect on the localization force by decreasing the radial length of the edge-end teeth is shown in Fig. 6(a). As the radial length of the edge end teeth decreases, the positioning force decreases linearly.

(a) Reduced radial length of side end teeth.

(b) Slot shoulder optimization.

Fig. 6. Positioning force optimization curve.

Considering the actual situation, the groove shoulder is designed as a parallel groove shoulder, and by changing the axial width of the groove shoulder, the primary teeth are enlarged to achieve the effect of reducing the tooth groove force. As shown in Fig. 6(b) at the slot shoulder width of 2.5 mm, the positioning force has a minimum value, the tooth groove force is effectively weakened, and the three-phase no-load induced electromotive force is also larger at this point. 4.2 Load Characterization Load characteristics indicate the ability of the motor to carry loads during operation, which is an important parameter to verify whether the motor meets the design requirements. The phase voltage magnitude, current magnitude and three-phase output power under load variation conditions are shown in Table 1. As the load resistance increases, the output voltage becomes larger and the output current decreases. When the load resistance is 50 , the maximum three-phase output power can reach 364.201 W.

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Table 1. A-phase voltage, current and three-phase output power at different loads. Load resistance ()

Output current amplitude (A)

Output voltage amplitude (V)

Three-phase output power (W)

10

3.253

32.528

182.499

30

2.86

85.784

345.38

50

2.321

116.04

364.201

100

1.463

146.343

278.676

5 Marine Experiment on Vortex Excitation Vibration Power Generation System The vortex-excited vibrating current energy generator for ocean test was machined based on the cylinder permanent magnet linear generator model obtained from the simulation design, as shown in Fig. 7. The test was accomplished in the sea area near West Flash Island, Zhoushan, Zhejiang Province.

Fig.7. Vortex Vibration Power Generation System Physical Drawing.

(a) Displacement Waveform.

(b) Combined waveforms.

Fig. 8. Vibration Characteristic Waveform.

Figure 8 shows the curves of the vibration displacement and the external force applied to the vibrator of the vortex-excited vibration power generator in a certain time interval. From Fig. 8(a), it can be seen that the maximum value of the vibration displacement is 513 mm and the minimum value is 225 mm, i.e., the peak value is 288 mm. According to the force curve shown in Fig. 8(b), the peak value of the force is about 200 N and the frequency is about 0.39 Hz.

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(a) Transient single-phase output voltage.

(b) Transient three-phase output voltage.

Fig. 9. Output Voltage Waveform.

Figures 9(a) and 9(b) reflect the single-phase instantaneous voltage waveforms and three-phase output voltage waveforms of the generator output during a certain period of time, which corresponds to an average value of the current velocity of 0.45 m/s. It is seen from the graphs that, in this 20 s period, the vortex-excited vibration of the oscillator drove the generators secondary motion, whose voltage amplitude was variable, while the frequency change was small. The peak value of the generator output voltage is 65.9 V, and the frequency is about 2.2 Hz. The three-phase output voltage curve contains a large harmonic component, which is mainly due to the double influence of the sea current and the power supply of the test system.

Fig.10. Transient power.

The instantaneous power during the 20 s time period is shown in Fig. 10. The maximum instantaneous power output from the generator during this trip reached 128.24 W. The average power within this trip was 49.13 W, and the energy conversion efficiency of the system was 38.1%. The feasibility and practicality of the vortex-excited vibration power generation system based on a cartridge-type permanent-magnet linear motor in the generation of ocean current energy are preliminarily verified through the ocean test.

6 Conclusion In this paper, a vortex-excited vibrating ocean current energy generation system based on a cylindrical permanent magnet linear generator is proposed and marine experiments are conducted, and the main conclusions include:

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(1) The radial magnetizing structure of the air gap magnetism is more amplitude and better sinusoidal compared to other ways, which is more suitable for this motor parameter. Secondly, the generator is optimized in terms of winding form, poleslot combination and positioning force, and the optimum motor design dimensions are obtained by analyzing the three-phase no-load induced electromotive force and positioning force. (2) By analyzing the generator load characteristics, the maximum three-phase output power of the generator is up to 364.201 W when a 50  resistive load is connected to the external circuit, which is in line with the expected rated power of 150 W motor. (3) A vortex-excited vibration ocean current energy generator based on a cartridge-type permanent magnet linear motor was designed and processed, and experiments were carried out on the Zhoushan ocean energy test platform, with the maximum power generation power of 49.13 W obtained at a current speed of 0.45 m/s, and the energy conversion efficiency of the system was 38.1%. The success of the ocean experiment verifies that the homemade vortex vibration power generation device can effectively convert ocean current energy into electricity. Acknowledgments. This work was funded by the Strategic Pioneer Science and Technology Special Project (Class A) of the Chinese Academy of Sciences (XDA22010401).

References 1. Curto, D., Franzitta, V., Guercio, A., et al.: An experimental comparison between an ironless and a traditional permanent magnet linear generator for wave energy conversion. 15(7) (2022) 2. Bernitsas, M.M., Raghavan, K., Ben-Simon, Y., et al.: VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A new concept in generation of clean and renewable energy from fluid flow. J. Offshore Mech. Arctic Eng. 130(4) (2008) 3. Zhang, B., Li, B., Fu, S., et al.: Experimental investigation of the effect of high damping on the VIV energy converter near the free surface. Energy 244, 122677 (2022) 4. Ziying, W., Yuchen, C., Wei, Z., et al.: Research on power generation performance of threestable electromagnetic vortex-induced vibration energy harvesting device. J. Vibr. Shock 41(13), 26–33 (2022). (in Chinese) 5. Wise, M., Albadri, M., Loeffler, B., et al.: A novel vertically oscillating hydrokinetic energy harvester. In: Proceedings of the 2021 IEEE Conference on Technologies for Sustainability (SusTech), F 22–24 April (2021) 6. Tao, X.: Research on optimization design and control of cylindrical linear motor for direct drive wave power generation. Southeast University (2019) (in Chinese) 7. Fuli, W.: Design and research of cylindrical permanent magnet linear generator for wave power generation. Guangdong University of Technology (2020). (in Chinese) 8. Gao, F., Qi, X., Li, X., Yuan, C., Zhuang, S.: Optimization design of partially-segmented Halbach permanent magnet synchronous motor. Trans. China Electrotech. Soc. 36(4), 787– 800 (2021). (in Chinese) 9. Rao, D.: Design of Cylindrical Permanent Magnet Linear Generator with Composite Transformer. Shenyang University of Technology (2020) (in Chinese) 10. Jiang, Q., Lu, Q., Li, Y.: Thrust ripple and depression method of dual three-phase permanent magnet linear synchronous motors. Trans. China Electrotech. Soc. 36(5), 883–892 (2021). (in Chinese)

Research Review of Non-invasive Load Monitoring Dan Chen1(B) , Wenxuan Liu2 , Sheng Ding3 , and Chen Zhang1 1 Economic and Technological Research Institute of State Grid Ningxia

Electric Power Co., Ltd., Ningxia, China [email protected] 2 State Grid Economic and Technological Research Institute Co., Ltd., Beijing, China 3 State Grid Ningxia Electric Power Co., Ltd., Ningxia, China

Abstract. Non-invasive load monitoring technique is to decompose the total load profile into the separate load profiles of each connected electrical equipment and to identify the operation status of each connected equipment.Then, the power consumption or supply of each equipment can be adjusted accordingly which enables the power system load-side demand response capability to alter the electricity consumption on time. Meanwhile, with the wide application of smart meters and machine learning algorithms, more attention has been paid to non-invasive load monitoring techniques in recent literature. Therefore, this paper presents a comprehensive review of non-invasive load monitoring techniques. Firstly, the basic framework of sub-intrusive load monitoring is presented and explained. Secondly, the equipment is classified in its operating state and the load characteristics of the connected equipment are listed and analyzed. Finally, existing research methods are summarized and discussed along with the monitoring difficulties in existing methods and the future research direction in non-invasive load monitoring techniques. Keywords: Non-invasive Load monitoring · Load Recognition · Load Decomposition · Deep Learning · Hidden Markov Model

1 Introduction Load monitoring techniques can be divided into invasive load monitoring techniques and non-invasive load monitoring techniques. Traditional invasive load monitoring methods require the use of sensors to be installed at each household load so that the energy consumption and operating status of each household load can be monitored. Although invasive load monitoring has high accuracy, it has suffered drawbacks such as high installation cost, high implementation difficulty, and is not easy to promote and deploy in a wide range, etc., which is not conducive to protecting user privacy, and users may have certain resistance. The work in the paper is sponsored by Science and Technology project of State Grid Ningxia Electric Power Co., LTD: Research on the planning design principle and typical application scheme of Ningxia distribution network control and protection system for novel power system (No. 5229JY22000M). © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 628–637, 2024. https://doi.org/10.1007/978-981-97-1072-0_64

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In the 1980s, a non-invasive load monitoring (NILM) technique is proposed by G. W. Hart for the first time [1]. NILM only installs a sensor at the entrance of the home bus, collecting the total voltage and current at each household, and then analyzing the energy consumption and running state of each load through load decomposition technology. Compared with the traditional intrusive load monitoring methods, NILM has the advantages of easy to operate, low installation cost, easy to popularize on a large scale, and protecting the user’s privacy, etc. Based on the above-mentioned benefits, non-invasive load monitoring is studied in this paper. The detailed energy consumption information provided by load monitoring can be used to guide power consumption behavior, as well as to promote power users to save electricity and to achieve the goal of energy saving and emission reduction. Non-invasive load monitoring techniques can provide power companies with detailed and in-depth data, provide a basis for their planning, operation, and management, and promote the development of smart grids.

2 Non-invasive Load Monitoring Framework Non-invasive load monitoring technique contained two main parts where the first part is load identification [2] and the second part is load decomposition [3]. Load identification can further be subdivided into event detection and load identification. The event detection method in nilm used by g. W. Hart is to judge the event based on the step change of power events [1]. Specifically, the power consumptions are divided into steady state or excessive state according to the rule. If the power change value is greater than the threshold value, the event is regarded as occurring. Meanwhile, load identification is to identify the specific load of the action based on judging the occurrence of the event. In load decomposition studies, the load was assumed to be switched between ON and OFF states [1, 4], and the operating power of each load was recorded in the database. Load decomposition methods were then used to decompose the total load of various electrical equipment under the time sequence into the load of a single electrical equipment. The information obtained from load monitoring methods is of great practical value to each power consumption participant. For ordinary users, if the equipment details obtained through load monitoring methods can be timely fed to the users, it can help guide the users to use electricity reasonably and save electricity costs. For power companies, it provides a basis for their operation and is conducive to the development of a smart grid. The essence of load identification is a classification problem, and its approximate steps are shown as follows: (1) Data collection: generally based on the specific area of the meter acquisition; (2) Data pre-processing: the collected data are processed by outlier processing, missing value interpolation, data denoising, data discretization, data normalization, and other pre-processing methods; (3) Feature extraction: New feature states can be obtained by analyzing some existing load feature states (4) Feature selection: such as steady-state feature, transient feature, etc. (5) Event detection: such as judging events based on the step change of power events, the power is divided into steady state or excessive state according to the rule, if the power change value is greater than the set threshold, it is regarded as an event [1].

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(6) Event detection: it can determine the time of event occurrence, to analyze the event data before and after the event; (7) Load recognition: the change of feature state before and after the event is compared and analyzed, and the state at the time of the event is put into the trained model for identification and comparison. However, some load recognition algorithms can complete the recognition without using an event detection algorithm in advance. The steps of load decomposition are similar to those of load identification, but event detection is generally not required. At the same time, the data set required for load decomposition includes the total power consumption data and the independent power consumption data of each equipment. The frame diagram of non-invasive load identification and decomposition is presented in Fig. 1.

,

Fig. 1. Non-invasive load identification and decomposition frame diagram.Load Equipment Analysis

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3 Load State Types Considering that there exists a massive difference in the circuit structure of each electrical equipment and the use modes of each device, it is important to study different running states and load characteristics in this equipment [5, 6]. The electrical appliances can be divided into the following four categories [7] as shown in Fig. 2: (1) Switch equipment: Switch-type equipment only has two states: ON and OFF such as On-Off oven, water pump, light bulb, and other equipment. (2) Multi-state equipment: this equipment has a limited number of limited operating states, such as electric fans, refrigerators, etc. (3) Continuous variable load: these equipment have variable power consumption and usually do not have a specific operating state and a periodic top power transition, such as air conditioning, water heater, or heat pump. (4) Permanent operation load: This equipment will generally run all the time, and will not stop, such as a router.

Fig. 2. Device running status type

These four kinds of loads make up most of the load in the system, and can be used for load decomposition and identification. 3.1 Type of Load Characteristics Load characteristic is an important index to judge the running state of equipment and is the key to realizing a non-invasive load monitoring technique, which is generally divided into traditional characteristics and other characteristics, as shown in Fig. 3. Traditional characteristics such as steady state characteristics and transient characteristics. Among them, the transient characteristics include current waveform, power change, voltage noise, duration, and so on. Steady-state characteristics include power, current, V-I curve, etc. Other features such as electromagnetic interference [8], and recursive graphs [9].

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Fig. 3. Device feature type

4 Existing Research Methods 4.1 Hidden Markov Model The hidden Markov model has gained a lot of attention in non-invasive load monitoring because of its ability to observe the difficult state when modeling time series [10–16]. In [10], a method that combines human behavior with a hidden Markov model was proposed, which forms a link between human behavior and electrical appliance usage to optimize its performance. In this method, the proposed time-varying state transition matrix and uncertainty regulator have shown a strong ability to identify periodic and aperiodic electrical appliances. A hidden Markov variant with a hierarchical structure was proposed in [11] to enhance the representation of Markov chain-based models. It can effectively deal with appliances with multi-state devices, and can achieve better represent conventional appliances, which has shown better results than the traditional hidden Markov model. In [12], a new power decomposition method based on hidden Markov and deep neural networks was proposed and explained which can extract multiple loads from the same aggregate signal by using multiple DNN-HMM networks to model the load. This method omits the event detection step and performs well on multistate devices. In [13], a framework based on the modified factor Hidden Markov model was proposed which applies the hidden Markov model to all electrical appliances as separate load models. The characteristic state of the electrical apparatus is obtained by K-means clustering. This method has shown improved solution accuracy and a reduction in time complexity. Literature [14] models a single device using its active power as a hidden Markov model. And a mobile phone application, through Bluetooth to obtain data from the database

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was developed, to realize the visualization of equipment energy consumption data. An event-based factor hidden Markov model, rather than a time-based factor Markov, was developed in [15] to reduce computational complexity by performing inference only when an event occurs and to improve accuracy by utilizing transient features extracted from event detection based on high-resolution data, thus ensuring accurate load decomposition in real-time. Based on the energy consumption data of the factory, a factor Hidden Markov model (FHMM) was applied in [16] to the load decomposition of five industrial equipment in the factory, and proved the effectiveness of the model to the industrial load decomposition. Because of its extensibility, the hidden Markov model can be applied to different environments and complex monitoring systems. Through model training and parameter adjustment, it can be applied to different load types. But the model performance is greatly affected by the choice of order, especially for the complex load data, it is not easy to choose the right parameters. 4.2 Graph Signal Processing Model Graph signal processing model can process graph, text and other data, and then represents different model data into structures, such as voltage, current, and power consumption of electrical equipment in power system applications. In the field of non-invasive load monitoring, the graph signal processing model based on the V-I trajectory has received more attention. Literature [17] presents a method based on the emerging graph signal processing concept which has shown good advantages in signal denoising, clustering, and classification for high-frequency data. Active power, current harmonics, reactive power, and V-I locus are used as load features, and a graph is constructed based on the extracted features, and then state transition events with similar features are grouped into decomposition results. In [18], an adaptive non-invasive load monitoring method based on feature fusion was proposed, which utilizes the information on harmonic current characteristics and voltage-current (V-I) trajectory characteristics. Two new features were proposed in [19] namely convex hull area and trajectory length, to improve the performance of the training process. When K-Nearest Neighbor (KNN) and Support Vector Machines (SVM) methods are used to classify existing data sets, the combination of old and new features is more effective than the old features in electrical appliance recognition ability. To solve the problem of low and inaccurate load data sampling rate, unsupervised learning and energy efficiency analysis and prediction are realized by integrating graph signals in [20]. A load decomposition prediction model based on graph signal processing was proposed in [21] for a better understanding of the power consumption in different periods. The V-I diagram is used to apply the neural network classification method to non-invasive load monitoring, and the KNN-based method provides the fastest and best accuracy. A graphics signal processing method is developed in [22] which combines low-level signal processing with application-driven data processing to improve the performance of various event-based NILM methods for different power load data sets. Some of the problems with event-based NILM methods were addressed in [23], such as measurement noise, difficult-to-distinguish load characteristics, and inaccurate power reconstruction. Based on the low sampling data, a least squares reconstruction

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method is also proposed in [23], which uses the signal smoothness and iterative least squares reconstruction algorithm to classify graphs. Based on the piecewise smoothness of power load signals, two kinds of graph signal processing methods are proposed in [24] for steady-state NILM, which are based on the total graph variation minimization and the total graph variation minimization. In [25], current harmonic characteristics are analyzed utilizing parallel passive filters installed at the source of residential buildings and adopting an intelligent recognition method based on fuzzy rules to detect and monitor different power loads. In general, graph signal processing performs well in processing multi-modal data. The correlation between data can be better analyzed through graph structure, to extract more efficient features. Moreover, data sparsity can be used for modeling, reducing complexity, and improving computational efficiency. However, data preprocessing is troublesome, especially for high-dimensional data, and graph signal processing may face the problem of computational complexity. 4.3 Deep Learning Model The deep learning model can achieve time series data processing, complex patterns, and feature learning between data, equipment state information, and feature information extraction between devices in non-invasive load monitoring. A learning model was proposed in [26] based on deep convolutional neural networks that perform well in continuous multivariable devices with multiple power states, complex state transitions, and multiple modes of operation. In [27], a neural network method in the NILM problem is trained by a data reduction process based on wavelet transform, which reduces and reconstructs the consuming time series and improves the prediction efficiency of the neural network. Two deep learning-based models were proposed in [28], namely, home energy decomposition based on convolutional neural networks and shared parameter learning based on gated recursive units. By using the entire context information in a sliding window over a given aggregation sequence to predict the energy of each device, it has been proven to be more efficient in decompressing the energy of nonlinear and multistate devices. An improved sequence-to-point load decomposition algorithm was proposed in [29], which combines sequence-to-point learning neural network with an attention mechanism to improve the performance of the algorithm. Based on the multi-channel convolutional neural network architecture, a deep learning model was proposed in [30] where the selected features include not only active power but also additional variables related to power consumption such as current and reactive power to improve the overall performance, robustness to noise and convergence time. A multiscale self-attention network that utilizes global time dependence and local sequence features was designed in [31] to more accurately decompose power consumption and ON/OFF states. Meanwhile, unlike traditional algorithms, event detection and device classification is carried out in [32] through the same process, allowing simultaneous detection and classification of events without having to perform dual processing. The calculation time is reduced and the operation efficiency is improved. A parallel bidirectional long and short-term memory model was developed and explained in [33], which can cope with multi-state devices and fast-changing devices well, and can recognize the state of multi-state devices well through a feature extractor module. By combining gated

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recurrent unit neurons, long and short-term memory neurons, and convolutional unit neurons, a non-invasive load decomposition model of layered hybrid recurrent neural network was constructed in [34], which can extract and utilize sequence information more effectively and improve the decomposition accuracy. Deep learning models can also process multi-modal load data, and can automatically learn the features between loads and capture the relationship between loads. However, the accuracy of the model depends on a large number of labeled load data, and the complexity of the model itself is high, which requires the storage space and computing power of the computer.

5 Summary and Prospect More and more attention has been paid to non-invasive load monitoring techniques, with research objects ranging from the original residence equipment to some research in industrial applications, and with research methods ranging from the original Markov model to the increasingly advanced neural network model. The accuracy of load monitoring is gradually enhanced, but the universality of the model still needs to be improved. Moreover, there are few researches on continuous multi-state devices, which may be due to the fact that their operating states are not definite and their features are difficult to extract. Future research can be considered from the following aspects: (1) To improve the universality and generalization of the model, for example, how to reduce costs and achieve applicability in different regions with the same application scenarios. Migration learning provides a way to solve this problem. (2) How to deal with the more difficult continuous multi-state measurement equipment. (3) Generally, only known equipment types can improve the accuracy of monitoring. How can less or even unlabeled equipment data be used to improve the applicability of monitoring. (4) How can different devices but similar operating states and the same equipment be accurately monitored.

References 1. Hart, G.W.: Nonintrusive appliance load monitoring. Proc. IEEE 80(12), 1870–1891 (1992) 2. Viana, F.A.C., Pan, Y., Bose, S.: Bayesian model selection and calibration applied to composite load identification. In: IEEE PES T&D Conference and Exposition, Chicago, IL, USA, pp. 1–5 (2014) 3. Ou, F., Liu, M., Zhao, Z.: Non-intrusive load decomposition based demand responsiveness assessment of regional residents. In: IEEE International Conference on Power Science and Technology (ICPST), Kunming, China, pp. 573–577 (2023) 4. Kundu, A., Juvekar, G.P., Davis, K.: Deep neural network based non-intrusive load status recognition. In: Clemson University Power Systems Conference (PSC), Charleston, SC, USA, pp. 1–6 (2018) 5. Liang, J., Ng, S.K.K., Kendall, G., Cheng, J.W.M.: Load signature study—part I: basic concept, structure, and methodology. IEEE Trans. Power Delivery 25(2), 551–560 (2010)

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6. Liang, J., Ng, S.K.K., Kendall, G., Cheng, J.W.M.: Load signature study—part II: disaggregation framework, simulation, and applications. IEEE Trans. Power Delivery 25(2), 561–569 (2010) 7. Zeifman, M., Roth, K.: Nonintrusive appliance load monitoring: review and outlook. IEEE Trans. Consum. Electron. 57(1), 76–84 (2011) 8. Guzel, T., Ustunel, E.: Principal components null space analysis based non-intrusive load monitoring. In: 2015 IEEE Electrical Power and Energy Conference (EPEC), London, ON, Canada, pp. 420–423 (2015) 9. Popescu, F., Enache, F., Vizitiu, I.-C., Ciotîrnae, P.: Recurrence plot analysis for characterization of appliance load signature. In: 10th International Conference on Communications (COMM), Bucharest, Romania, pp. 1–4 (2014) 10. Wang, X., Wang, J., Shi, D., Khodayar, M.E.: A factorial hidden Markov model for energy disaggregation based on human behavior analysis. In: IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, USA, pp. 1–5 (2018) 11. Kong, W., Dong, Z.Y., Hill, D.J., Ma, J., Zhao, J.H., Luo, F.J.: A hierarchical hidden Markov model framework for home appliance modeling. IEEE Trans. Smart Grid 9(4), 3079–3090 (2018) 12. Mauch, L., Yang, B.: A novel DNN-HMM-based approach for extracting single loads from aggregate power signals. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, pp. 2384–2388 (2016) 13. Kumar, P., Abhyankar, A.R.: A time efficient factorial hidden Markov model based approach for non-intrusive load monitoring. IEEE Trans. Smart Grid 14(5), 3627–3639 (2023) 14. Raiker, G.A., Reddy, S.B., Umanand, L., Yadav, A., Shaikh, M.M.: Approach to non-intrusive load monitoring using factorial hidden Markov model. In: IEEE 13th International Conference on Industrial and Information Systems (ICIIS), Rupnagar, India, pp. 381–386 (2018) 15. Yan, L., Tian, W., Han, J., Li, Z.: EFHMM: event-based factorial hidden Markov model for real-time load disaggregation. IEEE Trans. Smart Grid 13(5), 3844–3847 (2022) 16. Yang, F., et al.: FHMM based industrial load disaggregation. In: 6th Asia Conference on Power and Electrical Engineering (ACPEE), Chongqing, China, 330–334 (2021) 17. Li, X., Zhao, B., Luan, W., Liu, B.: A training-free non-intrusive load monitoring approach for high-frequency measurements based on graph signal processing. In: 7th Asia Conference on Power and Electrical Engineering (ACPEE), Hangzhou, China, pp. 859–863 (2022) 18. Kang, J.-S., Yu, M., Lu, L., Wang, B., Bao, Z.: Adaptive non-intrusive load monitoring based on feature fusion. IEEE Sens. J. 22(7), 6985–6994 (2022) 19. Chea, R., Thourn, K., Chhorn, S.: Improving V-I trajectory load signature in NILM approach. In: International Electrical Engineering Congress (iEECON), Khon Kaen, Thailand, pp. 1-4 (2022) 20. Yu, L., Jing, W., Lihui, W.: Nonintrusive load disaggregation method based on graph signal processing. In: IEEE 5th International Electrical and Energy Conference (CIEEC), Nangjing, China, pp. 2010–2013 (2022) 21. Vargic, R., Londák, J., Medvecký, M.: An approach to NILM using image-based features and transfer learning. In: 30th International Conference on Systems, Signals and Image Processing (IWSSIP), Ohrid, North Macedonia, pp. 1–5 (2023) 22. Zhao, B., He, K., Stankovic, L., Stankovic, V.: Improving event-based non-intrusive load monitoring using graph signal processing. IEEE Access 6, 53944–53959 (2018). https://doi. org/10.1109/ACCESS.2018.2871343 23. Zheng, D., Ma, X., Wang, Y., Wang, Y., Luo, H.: Non-intrusive load monitoring based on the graph least squares reconstruction method. IEEE Trans. Power Delivery 37(4), 2562–2570 (2022) 24. He, K., Stankovic, L., Liao, J., Stankovic, V.: Non-intrusive load disaggregation using graph signal processing. IEEE Trans. Smart Grid 9(3), 1739–1747 (2018)

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25. Ghosh, S., Chatterjee, A., Chatterjee, D.: An improved load feature extraction technique for smart homes using fuzzy-based NILM. IEEE Trans. Instrum. Meas. 70, 1–9, Art no. 2511209 (2021) 26. Kong, W., Dong, Z.Y., Wang, B., Zhao, J., Huang, J.: A practical solution for non-intrusive type II load monitoring based on deep learning and post-processing. IEEE Trans. Smart Grid 11(1), 148–160 (2020) 27. Santos, E.G., Ramos, G.S., Aquino, A.L.L.: An energy disaggregation approach based on deep neural network and wavelet transform. IEEE Trans. Industr. Inf. 18(10), 6789–6797 (2022) 28. Ayub, M., El-Alfy, E.-S.M.: Contextual sequence-to-point deep learning for household energy disaggregation. IEEE Access 11, 75599–75616 (2023) 29. Zhang, J., Sun, J., Gan, J., Liu, Q., Liu, X.: Improving domestic NILM using An attentionenabled Seq2Point learning approach. In: IEEE Intl Conf on Dependable, Autonomic and Secure Computing, Intl Conf on Pervasive Intelligence and Computing, Intl Conf on Cloud and Big Data Computing, Intl Conf on Cyber Science and Technology Congress (DASC/PiCom/CBDCom/CyberSciTech), AB, Canada, pp. 434–439 (2021) 30. Kaselimi, M., Protopapadakis, E., Voulodimos, A., Doulamis, N., Doulamis, A.: Multichannel recurrent convolutional neural networks for energy disaggregation. IEEE Access 7, 81047–81056 (2019) 31. Shan, Z., et al.: Multiscale self-attention architecture in temporal neural network for nonintrusive load monitoring. IEEE Trans. Instrum. Meas. 72, 1–12, Art no. 2512212 (2023) 32. Ciancetta, F., Bucci, G., Fiorucci, E., Mari, S., Fioravanti, A.: A new convolutional neural network-based system for NILM applications. IEEE Trans. Instrum. Meas. 70, 1–12, Art no. 1501112 (2021) 33. Andrean, V., Lian, K.L., Iqbal, I.M.: A parallel bidirectional long short-term memory model for energy disaggregation. IEEE Can. J. Electr. Comp. Eng. 45(2), 150–158 (2022) 34. Zhang, Z., Fan, C.: Non-intrusive load decomposition of stacked hybrid recurrent neural networks. In: IEEE 8th International Conference on Advanced Power System Automation and Protection (APAP), pp. 322–325, Xi’an, China (2019)

Harmonic Coordination Suppression Strategy of Hybrid Grid-Connected System in Complex Grid Scenarios Tailin Huang1(B) , Fei Rong1 , Xiaobin Mu2 , Guofu Chen2 , Xiang Wang2 , and Yalei Yuan2 1 College of Electric and Information Engineering, Hunan University, Hunan Province,

Changsha 410082, China [email protected] 2 State Key Laboratory of Advanced Power Transmission Technology State Grid Smart Grid, Research Institute Co. Ltd, Beijing 102209, China

Abstract. With the construction and development of new power system, currenttype grid-following inverters and voltage-type grid-forming inverters are widely accessed to distribution substations, but this hybrid grid-connected system will have power quality problems in complex grid scenarios where there are distortions in the grid voltage as well as access to nonlinear loads, which will seriously affect the quality of regional power supply. This paper firstly establishes a harmonic equivalent model of the hybrid control grid-connected system, analyzes the strong coupling relationship between grid voltage harmonics and grid current harmonics, and proposes a harmonic coordination suppression strategy, which realizes the effective coordination of grid harmonic voltage and current harmonics by controlling the output harmonic voltage of grid-forming inverter and reshaping the harmonic output impedance of grid-following inverter, and by adopting a method of selecting the standard value of the self-adaptive impedance and harmonic content. The effective coordinated management of grid-connected harmonic voltage and harmonic current is realized. Finally, the effectiveness and control robustness of the proposed strategy are verified by simulation. Keywords: Grid-following inverters · Grid-forming inverters · Hybrid grid-connected system · Complex grid scenarios · Power quality · Coordination suppression

1 Introduction With the construction and development of new power systems, grid-following (GFL) and grid-forming (GFM) inverters are widely connected to the distribution area [1], resulting in large background harmonics in the power grid. Under the influence of local nonlinear loads, the problem of harmonic pollution in the distribution area is becoming more and more serious [2]. Therefore, it does not meet the requirements of relevant national standards for PCC point voltage of new energy grid connection and total harmonic distortion (THD) of grid connection less than 5% [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 638–648, 2024. https://doi.org/10.1007/978-981-97-1072-0_65

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The traditional voltage and current harmonic suppression method is to connect power quality compensation equipment such as active power filter (APF) or static var compensation generator (SVG) in series or parallel in the line, and realize the effective control of system harmonics by outputting compensation components [4]. However, this method will undoubtedly increase the cost of system construction and operation and maintenance. In order to enable the grid-connected inverter to achieve active control of harmonic components, References [5] used various current harmonic component measurement methods to superimpose them on the current reference value to achieve harmonic suppression. However, this method is greatly affected by the accuracy of harmonic detection, and the harmonic compensation effect is not ideal when there is background harmonics in the power grid. In reference [6], the harmonic voltage feedforward compensation strategy is adopted to suppress the harmonic current by equivalently increasing the harmonic impedance of the grid side. For the suppression of voltage harmonics, Reference [7] realized harmonic voltage compensation by increasing the power virtual synchronization link of characteristic sub-harmonics, but the parameter design and control structure are more complicated, and the compensation effect is not good. In reference [8], the harmonic impedance of the inverter is equivalently reduced by using the virtual capacitive impedance to suppress the voltage harmonics at the PCC point. However, the above methods do not consider the applicability in the complex grid scenario where the grid harmonic voltage and the nonlinear load coexist. When the grid harmonic voltage is large, due to the coupling characteristics of the grid-connected voltage and the grid-connected current, the simultaneous suppression of the two will be contradictory. In view of the shortcomings of the existing research, this paper first takes the hybrid control grid-connected system composed of virtual synchronous generator grid-forming inventers (VSG-GFM) and phase-locked-loop grid-following inventers (PLL-GFL) as the research object, establishes its equivalent harmonic model for analysis, and proposes a harmonic coordination suppression strategy. By controlling the output harmonic voltage of grid-forming inventers and the harmonic output impedance of reshaping gridfollowing inventers, and adopting an adaptive impedance and harmonic content standard value selection method, the effective coordinated control of grid-connected harmonic voltage and grid-connected harmonic current is realized. Finally, the effectiveness and control robustness of the proposed strategy are verified by simulation.

2 Analysis of Main Topology and Harmonic Mechanism of Hybrid Control Grid-Connected System The main topology of the hybrid control grid-connected system studied in this paper is shown in Fig. 1. The two inverters adopt PLL-GFL and VSG-GFM control methods respectively. In the figure, U s is the grid power supply, U dc is the DC voltage source, L 1 and L 2 are the filter inductors, RC is the damping resistor, C 1 is the filter capacitor, Z g is the line impedance, U 01 and U 02 are the grid-connected voltages of PLL-GFL and VSG-GFM, I s1 and I s2 are the inverter output currents of PLL-GFL and VSG-GFM respectively, I 01 and I 02 are the actual output currents of PLL-GFL and VSG-GFM respectively, I g is the total grid-connected current of the grid-connected system, load 1 is

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a three-phase uncontrollable rectifier load, and load 2 is a three-phase linear symmetrical load. In order to simplify the analysis, this paper assumes that the DC side of the inverter is a constant, ignoring the influence of its dynamic characteristics [9]. PCC PLL-GFL Is1

Udc

L2

Io1 Uo1 Ig

Rc C1

New energy

Udc

L1

VSG-GFM Is2

L1

IL L2

Us Grid

Io2 Uo2

Rc C1

New energy

Zg

Load1

Load2

Fig. 1. Main topology structure of hybrid control grid-connected system.

Z GFL

U pcch I gh Z gh

Z GFM

I Lh

U sh

Fig. 2. Harmonic equivalent model.

Since the two control strategies are mainly aimed at the control of the fundamental frequency, the modulation signal mainly includes the fundamental signal. Therefore, in the harmonic frequency band, the controlled current source can be regarded as an open circuit, and the controlled voltage source can be regarded as a short circuit. Both inverters can be equivalent to output impedance. Finally, the harmonic equivalent model of the hybrid control grid-connected system is established as shown in Fig. 2. In the figure, U sh is the grid harmonic voltage, U pcch is the grid-connected harmonic voltage, I Lh is the nonlinear load harmonic current, I gh is the grid-connected harmonic current, Z PLL and Z VSG are the equivalent impedance of PLL-GFL and VSG-GFM, respectively. According to Fig. 2, the relationship can be obtained as shown in Eq. (1). It can be seen that the existence of nonlinear load and grid distortion voltage will seriously affect the harmonic content of U pcch and I gh , which does not meet the national power quality standard (THD ≤ 5%). At the same time, due to the coupling relationship between U pcch and I gh , when U sh is large, the harmonic suppression of U pcch and I gh is contradictory. Therefore, it is necessary to study the coordinated suppression strategy of grid-connected voltage and grid-connected current harmonics when the grid background harmonics are

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large, so as to improve the grid-connected power quality of the hybrid control gridconnected system. ⎧ (ZPLL //ZVSG )Zgh (ZPLL //ZVSG ) ⎪ ⎪ Upcch = ILh + Ush ⎪ ⎪ (ZPLL //ZVSG ) + Zgh (ZPLL //ZVSG ) + Zgh ⎪ ⎪ ⎪ ⎨ (ZPLL //ZVSG ) 1 Igh = ILh − Ush (1) ⎪ (ZPLL //ZVSG ) + Zgh (ZPLL //ZVSG ) + Zgh ⎪ ⎪ ⎪ ⎪ Upcch − Ush ⎪ ⎪ ⎩ = Igh Zgh

3 Coordinated Suppression Strategy of Voltage and Current Harmonics Based on MCCF 3.1 Harmonic Component Extraction Method Based on Multiple Complex Coefficient Filters In this paper, multiple complex coefficient filters (MCCF) are used to extract the harmonic components of voltage and current. It is composed of multiple CCF sub-modules, which has the advantages of simple digital implementation, less resource occupation and easy engineering implementation [10]. Taking the extraction of I g harmonic component as an example, the control structure is shown in Fig. 3.

Fig. 3. The implementation structure of MCCF.

3.2 Voltage and Current Harmonic Coordination Suppression Strategy The equivalent circuit structure of the voltage and current harmonic coordination suppression strategy based on MCCF proposed in this paper is shown in Fig. 4. By controlling the output harmonic voltage U VSGh of VSG-GFM and reshaping the harmonic output impedance Z PLL of PLL-GFL, the coordinated suppression between grid-connected voltage and grid-connected current is realized. The specific control structure is shown in Fig. 5.

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Fig. 4. The equivalent circuit structure of the proposed harmonic coordination suppression strategy.

Fig. 5. The inverter control structure of the proposed harmonic coordination suppression strategy.

In order to analyze the theoretical effectiveness of the proposed strategy, according to the superposition theorem, the harmonic mechanism analysis considering only the local nonlinear load harmonic current and only the grid background voltage harmonic is carried out respectively. When only the local nonlinear load harmonic current is considered, the harmonic equivalent circuit of the proposed method is shown in Fig. 6.

Fig. 6. The harmonic equivalent circuit only considers the local nonlinear load harmonic current.

According to Fig. 6, the expression of I oh is: Ioh =

− Upcch U∗ UVSGh − Upcch (k − 1)Upcch − kZIgh ≈ VSGh = ZVSG ZVSG ZVSG

(2)

Then Z VSG can be represented as: ZVSG =

(k − 1)Upcch Igh − kZ Ioh Ioh

(3)

At the same time, according to Fig. 6, the following formula can be obtained: Igh =

Upcch Upcch , Ioh = − Zg Zeq

(4)

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Combining Eq. (3) with Eq. (4), the equivalent impedance Z eq can be solved: Zeq =

ZVSG Zg (1 − k)Zg + kZ

(5)

Thus, the harmonic current I gh(1) can be obtained as shown in Eq. (6): Igh(1) =

Zeq //Z ZVSG Zg Z ILh = ILh (6) 2 Zeq //Z + Zg ZVSG Zg Z + ZVSG Zg + ZZg [(1 − k)Zg ] + kZ 2 Zg

According to the Eq. (6), when k = 1, we can get: Igh(1) =

ZVSG Zg Z ILh = ZVSG Zg Z + ZVSG Zg2 + Z 2 Zg 1+

1

I Z 2 +ZVSG Zg Lh ZVSG Z

(7)

When only the background harmonic voltage of the power grid is considered, the harmonic equivalent circuit of the proposed method is shown in Fig. 7.

Fig. 7. The harmonic equivalent circuit when only the background harmonic voltage of the grid is considered.

Similar analysis can be obtained, when k = 1, the harmonic current I gh(2) can be showed as follows: Igh(2) = −

1 Zg +

(ZVSG +Z)Z ZVSG

Ush = −

1 Zg + Z +

Z2 ZVSG

Ush

(8)

Finally, according to the superposition theorem, the total grid-connected harmonic current I gh can be obtained as shown in Eq. (9): Igh =

1

1+

I Z 2 +ZVSG Zg Lh ZVSG Z

−

1 Zg + Z +

Z2 ZVSG

Ush =

1 1 ILh − Ush m n

(9)

When the value of Z is very large, the derivation of Z for m and n can be obtained as shown in Eq. (10). The Eq. (10) shows that both m and n are increasing functions of Z. The larger the Z value, the larger the m and n, the smaller the harmonic current components generated by the nonlinear load and the background harmonics of the power grid, and the I Lh is generally larger than U sh , so that the I gh is smaller. Therefore, the inhibition of I gh can be achieved by controlling the size of Z. Zg Z 2 − Zg ZVSG 1 2Z dm dm dn dn = =1+ > − 2 = > 0, > 0, dZ ZVSG Z Z 2 ZVSG dZ ZVSG dZ dZ

(10)

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When U sh is large, according to Eq. (4), the smaller I gh is, the larger U pcch is. On the contrary, the larger I gh is, the smaller U pcch is. Therefore, the coordinated inhibition of U pcch and I gh can be achieved by controlling Z. Z = Rh + sLh ≈ Rh +

s Lh , Rh = 100Lh 0.0001s + 1

(11)

The value method of Z is shown in Eq. (11). In this paper, the first-order inertial expression is used to replace the differential link to avoid the influence of high-frequency harmonics. At the same time, this paper realizes the flexible value of Z by using the negative feedback control structure of voltage and current harmonic content double closed loop, as shown in Fig. 8.

Fig. 8. Hth voltage and current harmonic content negative feedback control structure.

In the Fig. 8, I g1 is the fundamental amplitude of current, I gh is the h-th harmonic amplitude of current, I* gh % is the reference value of h-th harmonic current content, U pcc1 and U pcch are the fundamental amplitude of voltage and h-th harmonic amplitude respectively, U* pcch % is the reference value of h-th harmonic voltage content. In order to realize the coordinated suppression of voltage and current harmonic content, it is necessary to select U* sh % reasonably. The specific selection method is shown in Fig. 9. Firstly, the harmonic distortion rate THD(I g ) and THD(U pcc ) of grid-connected current and grid-connected voltage are detected. When THD(I g ) > 5%, the algorithm runs. Then, the U* pcch % value is set to 4, so that I gh is suppressed to the greatest extent, and THD(I g ) and THD(U pcc ) are detected again. If THD(I g ) is still greater than 5% at this time, it is necessary to add a compensation device to achieve suppression, and the algorithm is over. If THD(I g ) ≤ 5%, I gh is effectively suppressed, and the distortion rate and x = THD(I g ) + THD(U pcc ) are calculated, and the algorithm continues to run. In the next step, the value of U* pcch % is continuously adjusted according to the suppression effect of THD(I g ) to continuously find the optimal value. Finally, the U* pcch % with the minimum distortion rate and x is output, and the algorithm ends.

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Fig. 9. Flow chart of algorithm for selecting reference value of voltage harmonic content.

4 Simulation Verification In order to verify the effectiveness of the harmonic coordination suppression strategy proposed in this paper, the main circuit simulation model shown in Fig. 1 is established based on Simulink for verification, the main circuit parameters are shown in Table 1. The simulation condition is set as follows: when the simulation time t = 0.4 s, the three-phase uncontrollable rectifier load is connected, the filter inductance is 0.6 mH, the resistance is 30 , and the grid voltage is superimposed with 5-th voltage harmonics of 5% U s and 7-th voltage harmonics of 3% U s . The effectiveness of the proposed strategy is verified by comparison. When the harmonic coordination suppression strategy proposed in this paper is not adopted, the simulation results are shown in Fig. 10(a) and Fig. 10(b). According to Fig. 10, it can be seen that after the nonlinear load is connected, the system reaches stability near 0.47 s. At this time, the harmonic distortion rate of the grid-connected voltage is 1.29%, and the harmonic content is much smaller than the threshold. The harmonic content of the grid-connected current is large, and the harmonic distortion rate is 6.67%, which does not meet the requirements of grid-connected power quality. When the proposed harmonic coordination suppression strategy is adopted, the simulation results are shown in Fig. 11(a) and Fig. 11(b). It can be seen from the diagram that the system reaches stability near 0.46 s. At this time, the harmonic distortion rate of the grid-connected voltage increases to 4.3%, but it is still less than 5%, while the harmonic distortion rate of the grid-connected current decreases to 3.66%. Both meet

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Parameter

Physical meaning Value

Parameter

Physical meaning Value

U dc /V

DC voltage

700

I 1q_ref /A

q-axis reference value

0

L 1 /mH

Inner filter inductor

3

Pset /kW

Given active power

20

L 2 /mH

Outer filter inductor

0.1

Qset /kW

Given reactive power

0

C 1 /µF

Smoothing capacitor

20

J/ (kg. m2 )

Factor of inertia

0.064

Rc /

Damping resistance

2

Dp

damping coefficient

10

Z g /

Line impedance

0.023 + j0.722

Kq

droop coefficient

0.001

S N /kW

Rated capacity

20

Rn /

Virtual resistance

0.1

I 1d_ref /A

d-axis reference value

42.8

L n /mH

Virtual inductor

2

the requirements of the national grid-connected harmonic content, and achieve effective coordinated suppression of voltage and current harmonics.

Fig. 10. Simulation results of power quality without the proposed strategy.

In order to analyze the control robustness of the proposed strategy, a 10 kW linear load is connected for research when the simulation time is 1 s. Figure 12 is the simulation results. From the diagram, the grid-connected voltage and grid-connected harmonic distortion rate are 4.83% and 3.84%, respectively, and both are still less than 5%, which meets the requirements of grid-connected harmonic content, indicating that the proposed strategy has better control robustness.

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Fig. 11. Simulation results of power quality using the proposed strategy.

Fig. 12. The simulation results of power quality after increasing the load.

5 Conclusion Aiming at the control problem of voltage and current harmonics of grid-connected system under the influence of grid background harmonics and nonlinear loads, a harmonic coordination suppression strategy is proposed. By controlling the output harmonic voltage of VSG-GFM and reshaping the harmonic output impedance of PLL-GFL, an adaptive impedance selection method is designed to realize the coordinated control of the two harmonics. The simulation verifies the effectiveness and good control robustness of the proposed strategy. Acknowledgment. This study is supported by the State Key Laboratory of Advanced Power Transmission Technology (Grant No. GEIRI-SKL-2022-010).

References 1. Li, W., Zhang, G., Zhong, H., et al.: A high frequency resolution harmonic and interharmonic analysis model. Tran. China Electrotech. Soc. 37(13), 3372–3379, 3403 (2022)

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2. Chen, J., Zhang, X., Yan, Z., et al.: Deadtime effect and background grid-voltage harmonic suppression methods for inverters with virtual impedance control. Trans. China Electrotech. Soc. 36(8), 1671–1680 (2021) 3. IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, pp. 519-1992. Institute of Electrical and Electronics Engineers [IEEE] (1992) 4. Jianzhong, Z, Zhi, G, Shuai, X, et al.: An improved adaptive harmonic detection algorithm for active power filter. Trans. China Electrotech. Soc. (2019) 5. Wei, J., Yongli, L., Lizhi, B., et al.: Research on multi-functional grid-connected inverters based on conservative power theory and repetitive control. Trans. China Electrotech. Soc. 33(18), 4345–4356 (2018) 6. Jian, X., Xin, C., Zhenyang, H., et al.: A harmonic current suppression method for virtual synchronous rectifier based on feedforward of grid harmonic voltage. Trans. China Electrotech. Soc. 37(8), 2018–2029 (2022) 7. Hirase, Y., Ohara, Y., Bevrani, H.: Virtual synchronous generator based frequency control in interconnected microgrids. Energy Rep. 6, 97–103 (2020) 8. Tu, C., Yang, Y., Xiao, F., et al.: The output side power quality control strategy for microgrid main inverter under nonlinear load. Trans China Electrotech. Soc. 33(11), 2486–2495 (2018) 9. Bidram, A., Davoudi, A., Lewis, F.L., et al.: Distributed cooperative secondary control of microgrids using feedback linearization. IEEE Trans. Power Syst. 28(3), 3462–3470 (2013) 10. Rajendran, K.P.A., Jayaprakash, P.: Multiple complex coefficient filter isogi-qsg based control for grid connected SPV system. In: 2019 International Conference on Power Electronics Applications and Technology in Present Energy Scenario (PETPES). IEEE (2020)

Study on Partial Discharge Characteristics of Epoxy Resin Under Bipolar High-Frequency Square Wave Voltage Yongsheng Xu1 , Bing Luo1 , Jiaju Lv2 , Qihang Jiang2 , and Weiwang Wang2(B) 1 State Key Laboratory of HVDC, Electric Power Research Institute (China Southern Power

Grid), Guangzhou, China 2 Xi’an Jiaotong University, Xi’an 710049, China

[email protected]

Abstract. One of the essential parts of the isolated DC-DC power converter is the high-frequency transformer (HFT). It typically functions with non-sinusoidal high-frequency excitation. Epoxy resin insulation is suffered from high dv/dt and high-frequency square voltage in HFT. Consequently, it is more vulnerable to cause degradation and failure. This study uses the Ultra-high frequency (UHF) antenna sensoring technique to examine the partial discharge (PD) characteristic parameters of 3 epoxy resin samples under high-frequency square wave voltage. PD characteristics and associated parameters are calculated and examined. Effects of frequency on discharge amplitude, discharge delay time etc. were discussed. They increase with the increase in frequency. It is noted that the coronal discharge is enhanced at high frequency. PD events at high frequency increases the discharge photon. This work is extremely important for the insulation design and optimization of HFT. Keywords: Epoxy resin · Partial discharge · UHF · Corona discharge · High-Frequency square wave voltage

1 Introduction Large-capacity power electronic transformer (PET) is promising equipment for smart grids with flexible functions of voltage change, isolate electrical systems, power flow control, power quality improvement, and real-time monitoring [1, 2]. It presents many advantages, such as small size, high flexibility and light weight [3, 4]. HFT is the key component that constitutes the isolated DC-DC converter [5, 6]. The design and reliability of high power HFT has been challenged in high power PET, especially for the structural optimization, heat dissipation and insulation. PD occurs in the insulation system [7, 8]. In the case of HFT, the insulation system undertake high frequency and rapidly changing repetitive pulse voltages. It is challenging to monitor the PD activities under high-frequency square-wave voltage due to the high dv/dt at rising edge, complex noise and effects of multi-harmonics. Liu et al. [9] studied the effect of pulse square wave voltage frequency on PD parameters and found © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 649–656, 2024. https://doi.org/10.1007/978-981-97-1072-0_66

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that the average discharge amount, maximum discharge amount and discharge energy increase with the increase in frequency. The number of discharges per unit cycle initially increases and then decreases with frequency. The partial discharge onset voltage (PDIV) slightly changes with frequency. It is interesting that and it the PDIV is similar between sinusoidal voltage and bipolar square-wave voltage. PD characteristics under pulsed square-wave voltage are influenced by the voltage rise time and the pulse duty ratio. The effect of rise time on partial discharge characteristics, especially PDIV is obvious. M KAUFHOLD et al. [10] found that the repetitive discharge initiation voltage (RPDIV) gradually decreases,and the insulation life decreases with the decrease in pulse voltage rise time or the increase in voltage drop time. However, H. HAYAKAWA et al. [11] found that when a continuous pulse voltage with a rise time of 60 ns to 3000 ns is applied to both ends of the twisted wire pair, the PDIV decreases with the increase in the rise time of pulsed voltage. Currently, PD characteristics are influenced by discharge models, voltage parameters, environmental temperature, etc. Due to different test methods, there are significant differences in the test results of different scholars. In the case of PD resistance of polymers under high-frequency square-wave voltage, it is still lacking of research on the variation of PD characteristics with the degree of damage. In this paper, PD parameters and the number of discharge photons of epoxy resin defects under different frequencies are investigated using a high frequency nonsinusoidal partial discharge platform. The PD parameters of 3 types of epoxy samples were investigated. It is of great importance in understanding high frequency insulation failure.

2 Experiments and Result 2.1 Sample Preparation In order to investigate the differences in electrical insulation performance between different base resins, three bisphenol A epoxy resins with different epoxy values (EV) were selected for this article, namely: epoxy resin DER-331 (EV = 0.525) produced by Dow Chemical in the United States, epoxy resin CYD-128 (EV = 0.532) produced by Yueyang Petrochemical, and epoxy resin HE-1080N (EV = 0.576) produced by Shanghai Xiongrun. The selected curing agent is methyl tetrahydrophthalic anhydride (JH-910, industrial grade) manufactured by Jiaxing Lianxing Company, and the accelerator is N, N-dimethylbenzylamine (BDMA, industrial grade) manufactured by McLean Company. 2.2 Experimental Platform Figure 1 shows the schematic diagram of the PD measurement system. The upper electrode is a cylindrical electrode with a diameter of 6 mm and a radius of curvature of 1 mm, and the lower electrode is a plate electrode with a diameter of 51 mm. The electrode is used to simulate the surface discharge model. An ultra-high frequency (UHF) antenna is used to detect the PD activities with a measurement frequency range of 300 MHz to 1500 MHz. A high-pass filter with a cut-off frequency of 400 MHz is connected between

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the UHF sensor and the oscilloscope to filter out interference pulses caused by interruptions in the power electronics. The PD signals and the voltage signal measured by the high-voltage probe are transferred in real time to a digital oscilloscope.

Fig. 1. Partial discharge testing platform under high-frequency square wave voltage.

3 High-Frequency Partial Discharge Detection and Signal Processing Unlike sinusoidal voltage, bipolar square wave voltage is generated by chopping power electronic devices, which requires frequent interruptions of the power electronic devices to achieve voltage polarity reversal. This inevitably leads to strong electromagnetic interference pulses on the rising and falling edges of the voltage. This interference is influenced by factors such as voltage rise time and voltage amplitude [14]. For the bipolar square-wave voltage source used in this article, its voltage rise time and fall time are stable in the range of 130–140 ns, so the influence of the rise time on the interference pulses is not considered. At the same time, the pressure method used to test the partial discharge characteristics in this article is consistent with the amplitude, so the influence of voltage on interference is also ignored. To effectively filter out spurious signals, it is necessary to compare and analyse the signals without and with partial discharge. Comparative analysis of signal spectra during partial discharge. Using a 20 kHz discharge signal as an example, Fig. 2 shows the time-frequency waveform of the 20 kHz noise signal and the partial discharge signal. Comparing the energy distribution before and after the discharge, it can be seen that the energy of the interference signals is mainly concentrated below 200 MHz, while the energy of the partial discharge is mainly concentrated in the frequency range from 400 MHz to 1.2 GHz. Based on this, a high-pass filter with a cut-off frequency of 400 MHz is selected to filter out the spurious signals. Figure 3 shows the time-frequency

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waveform of the filtered discharge signal. Comparing the time-frequency distribution of the discharge signal before and after filtering, it can be seen that the high-pass filter with a cut-off frequency of 400 MHz meets the filtering requirements.

Fig. 2. PD signal at 20 kHz without filtering.

Fig. 3. PD signal at 20 kHz with filtering.

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4 The Influence of Frequency on Partial Discharge Characteristics 4.1 Partial Discharge Phase Spectrum (PRPD) Taking the initial discharge stage of sample E1 as an example, the PRPD spectra at different frequencies were plotted as shown in Fig. 4. The rising and falling edges of the bipolar square wave voltage at different frequencies are around 130 ns, while the pressure amplitude remains constant. Therefore, the dv/dt of the bipolar square wave voltage remains unchanged. Taking the 90% range of the upper and lower polarity voltage amplitude, the dv/dt is calculated to be about 30 kV/s. Under bipolar square wave voltage, partial discharge occurs mainly at the moment of polarity reversal, while there is almost no discharge at other positions. And the distribution spectrum of partial discharge signals appearing on the rising and falling edges is symmetrical. From the time of partial discharge occurrence, it can be seen that the discharge starts when the voltage reaches PDIV, and the discharge is mainly concentrated at this time. However, when the voltage rises to a stable level, no discharge occurs.

(a)1 kHz rising period

(b)1 kHz falling period

Fig. 4. PRPD result of epoxy resin under 1 kHz square wave voltage

4.2 Partial Discharge Characteristic Parameters In order to further investigate the variation characteristics of the partial discharge with frequency, the characteristic parameters of the partial discharge at different frequencies were extracted from the PRPD spectrum. Due to the strong symmetry between the rising and falling edge PRPD spectra reflected in the previous test results, only the rising edge discharge characteristic parameters were investigated. These include discharge amplitude and discharge delay time. The discharge delay time represents the time interval between the partial discharge and the 0 potential at the next rising edge. Figure 5(a) shows the variation of the partial discharge amplitude with frequency for three types of epoxy samples. It can be seen that for the three types of epoxy samples, the discharge amplitude is smallest and the dispersion is smallest at 1 kHz. When the frequency is increased to 5 kHz, the discharge amplitude increases significantly. Overall, above 5 kHz, the

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discharge amplitudes of E1 epoxy samples are all above 100 mV, E2 samples are below 100 mV and E3 samples are distributed around 100 mV. Figure 5(b) shows the discharge delay time of three types of epoxy insulation at different frequencies. The discharge delay time shows a clear trend of increasing with increasing frequency. From 1 kHz to 20 kHz, the discharge delay time of the three types of epoxy increased by a total of about 14 ns, with the fastest increase occurring in the 1–5 kHz range. It increases slightly or even decreases in the range of 5 kHz to 20 kHz, which is similar to the relationship between PD amplitude and frequency. This may be because the longer delay time leads to a higher instantaneous voltage at the moment of discharge, thus increasing the discharge amplitude.

(a) Discharge amplitude

(b) discharge delay time

Fig. 5. PD parameters of epoxy resin VS frequency.

4.3 Number of Discharge Photons During the partial discharge test, it was observed that as the frequency gradually increased, a visible corona was generated at the contact between the column electrode and the sample, and the corona intensity increased as the frequency increased, as shown in Fig. 6. The appearance of the corona represents the generation of photons, which can be generated in two ways: 1) emission of photons during the transition of particles from high to low energy levels; 2) ions produced by ionisation recombining with heterocharges during migration and diffusion to produce photons. As the frequency increases, the number of partial discharges increases, resulting in more electrons and ions generated by ionisation, which increases the number of particle transitions and charge recombination, and a rapid increase in the number of photons, i.e. an increase in discharge intensity. To give a clearer picture of the number and distribution of photons during the discharge, a UV imager was used to measure the number of photons within a defined area around the discharge source, as shown in Fig. 7. It can be seen that as the frequency increases, the intensity of the partial discharge increases and the number of discharge photons increases. The white pixels in the figure are discharge photons. It can be seen that photons are emitted from the discharge source and then diffuse at different angles, and the denser the photons, the more charge they participate in the recombination process.

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a

1kHz

b

10kHz

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c 20kHz

Fig. 6. Corona discharge during PD measurement at different frequencies.

a

1kHz

b

10kHz

c

20kHz

Fig. 7. UV imaging of PD at different frequencies.

5 Conclusion In summary, this article mainly studies the partial discharge characteristics of three types of epoxy resin samples under high-frequency non-sinusoidal voltage at different frequencies, and compares the PDIV and partial discharge characteristic parameters of three types of epoxy resin samples at different frequencies. The experimental results show that as the frequency increases, the PDIV value, the discharge amplitude and the discharge delay time of the partial discharge all show an overall increasing trend with the increase in frequency. In the process, it was observed that the corona discharge phenomenon increased with increasing frequency, and the number of discharge photons gradually increased with increasing frequency. The reason for this phenomenon may be that the corona discharge accelerates the dissipation of space charges in the air gap while generating photons. The higher the frequency, the stronger the charge recombination effect, the smaller the number of space charges in the gap, the longer the partial discharge delay time and the larger the discharge amplitude. Acknowledgement. This work is supported by China Southern Power Grid Research Institute Co. LTD (1500002022030103GY00069).

References 1. Li, K., Zhao, Z., Yuan, L., et al.: Review of research on multiport power electronic transformers for AC/DC hybrid distribution systems. High Voltage Eng. 47(04), 1233–1250 (2021). (in Chinese)

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2. Wang, W., Liu, Y., He, J., et al.: Research status and development trends of high frequency transformers in high voltage and large capacity power electronic transformers. High Voltage Eng. 46(10), 3362–3373 (2020). (in Chinese) 3. Ronanki, D., Williamson, S.S.: Evolution of power converter topologies and technical considerations of power electronic transformer-based rolling stock architectures. IEEE Trans. Transportation Electrification 4(1), 211–219 (2017) 4. Lusaurdi, L., Cavallini, A., Degano, M.: The impact of impulsive voltage waveforms on the electrical insulation of actuators for more electrical aircraft (MEA). In: IECON 2017–43rd Annual Conference of the IEEE Industrial Electronics Society. IEEE, pp. 4414–4418 (2017) 5. Sun, K., Lu, S., Yi, Z., et al.: Overview of high capacity high frequency transformer technology for power electronic transformer applications. Trans. China Electrotechnical Society 41(24), 8531–8546 (2021). (in Chinese) 6. Gradinger, T.B., Drofenik, U., Alvarez, S.: Novel insulation concept for an MV dry-cast medium-frequency transformer. In: 2017 19th European Conference on Power Electronics and Applications (EPE’17 ECCE Europe). IEEE, p. 10 (2017) 7. Peiyi, L., Peng, W., Shijin, M., et al.: Study on the influence of repetitive pulse parameters on the signal to noise ratio of PDIV insulation testing for variable frequency motors. High Voltage Eng. 47(8), 2981–2990 (2021). (in Chinese) 8. Arumugam, S., Gorchakov, S., Schoenemann, T.: Dielectric and partial discharge investigations on high power insulated gate bipolar transistor modules. IEEE Trans. Dielectr. Electr. Insul. 22(4), 1997–2007 (2015) 9. Liu, X., Wu, G., Tong, L., et al.: Influence of impulse frequency on partial discharge under PWM. Conference Record of the 2006 IEEE International Symposium on Electrical Insulation. IEEE, pp. 241–244 (2006) 10. Kaufhold, M., Borner, G., Eberhardt, M., et al.: Failure mechanism of the interturn insulation of low voltage electric machines fed by pulse-controlled inverters. IEEE Electr. Insul. Mag. 12(5), 9–16 (1996) 11. Hayakawa, N., Shimizu, F., Peng, X., et al.: Partial discharge inception voltage for magnet wire of inverter-fed motors under surge voltage application. In: 2010 Annual Report Conference on Electrical Insulation and Dielectic Phenomena. IEEE, pp. 1–4 (2010)

Partial Discharge Pattern Recognition of High Voltage GIS Defects by Using GWO-SVM Method Tianbao Wu1 , Huan Bai1 , Jiayi Wang2 , Jianyang Huang3 , Yue Yu3 , and Weiwang Wang3(B) 1 Sichuan Shuneng Electric Power Co. Ltd., High-Tech Branch, Chengdu, China 2 State Grid Sichuan Electric Power Research Institute, Chengdu, China 3 Xi’an Jiaotong University, Xi’an, China

{1602959241,yuyue2022}@stu.xjtu.edu.cn, [email protected]

Abstract. This paper focuses on partial discharges (PD) pattern recognition of typical GIS defects by UHF sensor detection and intelligence fault algorithm. 4 typical PD defects, such as needle tip, air gap, particle, and suspension were simulated in the SF6 filled GIS chamber. The PD results indicated an obvious difference among the 4 PD defects. The corona discharge presented sharp discharge peaks during the 200–300°. According to the PRPD analysis, the eigenvalues of PD signals were calculated, including the skewness, the steepness, the local discharge factor, the cross-correlation coefficient, and the corrected cross-correlation coefficient etc. We employ a Grey Wolf Optimization algorithm (GWO) to optimize the parameter of kernel function in SVM algorithm. The proposed GWO-SVM method presents a better PD pattern recognition result. The predicted accuracy rate can be reached to 98.8%. This work can be used to guide GIS fault diagnosis. Keywords: Partial discharge · GIS · PRPD · Grey Wolf optimization algorithm · SVM

1 Introduction Gas insulated switchgear (GIS) is the key equipment of high voltage power transmission and distribution. Various defects inside GIS cause the insulation failure of the GIS equipment, and power loss [1, 2]. Partial discharge (PD) is an effective signal to provide the insulation defect information of GIS equipment [3]. Measurement and pattern recognition of complicated PD events have been investigated for many years. The arrival time difference (time difference of arrival, TDOA) method based on ultrahigh frequency sensor technique (UHF) is widely used in PD detection and fault location [4]. The PD characteristics of these defects are different and present significant variation with the applied field and conditions. Currently, PD data analysis mainly depends on time analysis mode (Time resolved partial discharge, TRPD) and phase analysis mode (Phase resolved partial discharge, PRPD). R BARTNIKAS [5] first involved the application of artificial intelligence (AI) algorithm in the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 657–664, 2024. https://doi.org/10.1007/978-981-97-1072-0_67

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pattern recognition of PD measurement techniques and detection methods. Researcher employs the PD pulse signal of the time domain in the generalized neural network, and partition setting method to identify PD patterns [6]. The ultrasonic PD signal in GIS was studied by TRPD analysis [7]. Five-time domain features and three frequency domain features were extracted for describing the PD feature of each defect well. The PD pattern recognition was conducted by the support vector machine (SVM) classifier [7]. Literature [8] compared the recognition effect of statistical feature parameters in PRPD mode and TRPD mode, which proved that the PD pattern recognition is more efficient. In addition, the gray scale image of the PDs and chaos analysis of PD defects were studied to achieve the purpose of defect identification [9–12]. SVM is a typical method, which is used in the field of pattern recognition and fault diagnosis in GIS. However, two problems exist of the system training method. On one hand, the radial basis kernel function significantly affects the determination of the spatial distribution parameters. On the other hand, the training error of the SVM is still large due to the limitation of parameter optimization. To improve the pattern recognition of PD events in GIS diagnosis, this paper propose an optimized SVM algorithm by Grey Wolf optimization algorithm (GWO). 4 PD defects in GIS equipment were constructed and measured by UHF sensor. Then the PD features of each defect were extracted by the PRPD analysis. Finally, the PD pattern recognition is investigated by the proposed GWO-SVM method.

2 PD Models and Experiments Common defects in GIS, such as needle tip, suspension, air gap and particles, were constructed in the laboratory, as shown in Fig. 1. Needle tip is simulated to the corona discharge; Air gap is used to simulate the air discharge; particles, particularly for the metal particle is used to simulate the induced discharge; if the suspension tip occurs, some interior discharges happen. Each PD defect is placed in the GIS chamber, which is filled with SF6 gas of 0.4 MPa. Figure 2 shows the measurement platform of PD events in the GIS chamber. UHF sensor is used to detect the PD signal. The operating frequency band ranges from 300 MHz to 3 GHz. The high-performance data acquisition card is used to capture the data.

(a) corona discharge

(b) air gap discharge (c) particle discharge (d) suspension discharge

Fig. 1. PD discharge models simulated in the GIS condition

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Fig. 2. PD measurement platform of PD events in the GIS chamber

3 PD Results and Signal Processing 3.1 PRPD Results 20 data samples of each PD models were detected at a determined voltage level. The measured data were analyzed by TRPD and PRPD method. After that we establish a database of PRPD signals with 4 typical PD defects. Figure 3 shows the typical maps of PRPD results (3D) of the 4 PD models. The results indicate an obvious difference among the 4 PD defects. The corona discharge from the needle tip shows sharp discharge peaks during the 200–300° (negative half-cycle) of the voltage wave (50 Hz). While the air gap discharge shows a low discharge peak both at positive and negative half-cycle of voltage. If the particle exists on the electrode surface, the PDs show several small peaks, which distributes along the whole phase with a few discharge events. The PD events concentrate near 80° and 200°, respectively, at the suspension PD defect. The PD amplitude is relatively large. Due to the complex PD signals and their statistical characteristic, it is necessary to extract the PD features by discussing the PRPD analysis. 3.2 PD Eigenvalues Extraction The PRPD results are statistically analyzed to obtain the distribution characteristics of the maximum discharge quantity qmax , average discharge quantity qave , discharge number n with phase ϕ, etc. In addition, the 2D distribution spectra such as qmax -ϕ, qave -ϕ, and n-ϕ are regarded as the probability density distribution in mathematical statistics. If the ϕ is a random variable, statistical features such as the kurtosis value S k , steepness value K u , the local discharge factor Q, the cross-correlation coefficient C c , and the modified crosscorrelation coefficient MC c (MC c = QC c ) can be calculated to form a multidimensional discharge feature vector [7]. Table 1 shows the feature parameters from PRPD analysis. The features can realize the distinction of PD events.

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(a) corona discharge

(b) air gap discharge

(c) particle discharge

(d) suspension discharge

Fig. 3. PRPD results of 4 PD defects

Table 1. PD feature parameters from PRPD analysis. Feature parameters

Corona (tip)

Air gap

Particle

Sk_max-

Suspension

−0.199

0.474

−0.056

Sk_max +

0.281

0.626

0.139

0.116

Sk_ave-

−0.008

0.332

−0.326

0.112

Sk_n +

0

0.535

−0.650

0.478

0.121

Ku_max-

−0.812

−0.264

−0.877

−1.209

Ku_max +

0

0.275

−1.381

−1.135

Ku_ave-

0

−1.033

−1.322

−1.242 (continued)

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Table 1. (continued) Feature parameters

Corona (tip)

Air gap

Particle

Suspension

Ku_n +

−1.122

Q

0

0.086

−0.780

−1.029

−0.162

−0.973

−0.587

Cc

0

0.777

0.219

−0.073

MCc

0

0.749

0.240

−0.075

q_max_average

13.66

7.69

2.91

44.57

4 PD Pattern Recognition 4.1 GWO Optimization Algorithm GWO algorithm is a swarm intelligence algorithm, which can optimize SVM parameters quickly with both better calculation accuracy and convergence speed. The grey Wolf population has a strict hierarchy, which ranks from high to low according to the relationship between domin and domin. Generally, four types of wolf: α, β, δ and γ are used in GWO structure. They are used to guide the optimization process in the GWO and lead the other wolves (W) towards the best area in the seeking area. During the processing, three wolves, α, β, and δ assess the possible region of the prey. The positions of wolves can be updated by a known process. During the iterative calculation process, we record the best individual as α, the second best individual as β, and the third best individual as δ. Now, we need to relocate the other wolves, referred to γ, based on the positions of. To achieve this, we utilize the following mathematical expresstions to update the positions of the γ. ⎧ ⎪ 1 Xα − X| ⎨ Dα = |C    (1) Dβ = C2 Xβ − X ⎪ ⎩ Dδ = |C3 Xδ − X| where, Xα Xβ and Xδ present the vector of α, β, and δ, respectively. C1, C2, C3 are the vectors with random distribution, X is the vector of current individual. The final results of the position can be given by: ⎧ ⎪ ⎨ X1 = Xα − A1 Dα X2 = Xβ − A2 Dβ (2) ⎪ ⎩ X3 = Xδ − A3 Dδ X(t + 1) =

X1 + X2 + X3 3

(3)

where, A1, A2, A3 are the vectors with random distribution, and t is the iteration number. There are 10 grey wolves in this model, which are used to adjust 3 parameters (penalty factor, kernel function coefficient, kernel function independent term).

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4.2 GWO-SVM Classification Algorithm Figure 4 is the flow chart of PD diagnosis algorithm optimized by GMO-SVM. The PD feature parameters from PRPD analysis are decomposed and denoised by VMD. Then, the reconstructed signal is extracted with eigenvalues and divided into training set and test set for fault simulation training. The training set uses the 80% of the data, while, the test set is 20% the data. The training samples are input to SVM classifier to solve convexity problem. The penalty coefficient and nuclear parameter in SVM were optimized by GWO algorithm. If the parameters are optimal, the SVM optimized classifier is used for pattern recognition, and the identification result is obtained. If the parameters are not optimal, you need to go back to the original SVM and iterate until the parameters are optimal.

Fig. 4. GWO-SVM algorithm flow of PD pattern recognition

4.3 Results and Analysis In the case of GWO algorithm, parameter of kernel function is set as gamma, C is the penalty factor. The result of the independent term of kernel function can be obtained as: ceof = [0.08558017, 0.0977352, 0.4590168]. During the PD pattern recognition algorithm, 80 data were divided into learning sets and test sets. According to the training model, which is obtained by the PD feature values, the test data is identified. Figure 5 exhibits the results of the PD pattern recognition algorithm. Compared with the SVM, a traditional diagnosis algorithm, the proposed GWO-SVM method presents

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a better PD pattern recognition result. The predicted accuracy rate is 98.7% for GWOSVM algorithm. However, the predicted accuracy rate is only 85% for SVM method. Particularly for the PD defects of needle-tip and air gap, the predicted results of SVM method indicates a large gap with the test results.

85

(a) SVM result

98.7

(b) GWO-SVM result

Fig. 5. Comparison of SVM and GWO-SVM results of PD events

5 Conclusion This paper measured PD results of 4 typical defects in GIS equipment and analyzed the PRPD information of the PD models. After that, the GWO-SVM pattern recognition of PD events in GIS diagnosis was proposed to improve the traditional SVM method. The results indicated an obvious difference among the 4 PD defects. The corona discharge presented sharp discharge peaks during the 200–300°. The PD events concentrate near 80° and 200°, respectively, at the suspension PD defect. The eigenvalues of PD signals were calculated by the PRPD analysis, including the skewness S k , the steepness K u , the local discharge factor Q, the cross-correlation coefficient C c , and the corrected crosscorrelation coefficient MC c (MC c = QC c ) etc. The parameter of kernel function was optimized by the GWO algorithm. The proposed GWO-SVM method presents a better PD pattern recognition result. The predicted accuracy rate can be reached to 98.8%. This work is useful to provide the guidance to the GIS fault diagnosis. Acknowledgments. The authors thank the support of State Grid Corporation Science and Technology project “Special Key technology and Research of Chuan Yu UHV Main Electric Equipment”.

References 1. Okabe, S., Kaneko, S., Yoshimura, M., et al.: Propagation characteristics of electromagnetic waves in three-phase-type tank from viewpoint of partial discharge diagnosis on gas insulated switchgear. IEEE Trans. Dielectr. Electr. Insul. 16(1), 199–205 (2009)

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2. Gao, W., Zhao, D., Ding, D., et al.: Investigation of frequency characteristics of typical PD and the propagation properties in GIS. IEEE Trans. Dielectr. Electr. Insul. 22(3), 1654–1662 (2015) 3. Hoshino, T., Maruyama, S., Ohtsuka, S., et al.: Sensitivity comparison of disc- and loop-type sensors using the UHF method to detect partial discharges in GIS. IEEE Trans. Dielectr. Electr. Insul. 19(3), 910–916 (2012) 4. Li, J., Han, X., Liu, Z., et al.: Review on partial discharge measurement technology of electrical equipment. High Voltage Eng. 41(8), 2583–2601 (2015). (in Chinese) 5. Bartnikas, R.: Partial discharges-Their mechanism, detection and measurement. IEEE Trans. Dielectr. Electr. Insul. 9(5), 763–808 (2002) 6. Ambikairajah, R., Phung, B.T., Ravishankar, J., et al.: Spectral features for the classification of partial discharge signals from selected insulation defect models. IET Sci. Meas. Technol. 7(2), 104–111 (2013) 7. Zhang, B.: Research on partial discharge pattern recogoniton of GIS based on ultrasonic detection. North China Electric Power University, Beijing (2015). (in Chinese) 8. Gulski, E., Kreuger, F.H.: Computer-aided recognition of discharge sources. IEEE Trans. Electr. Insul. 27(1), 82–92 (1992) 9. Wang, Y., Yan, J., Yang, Z., et al.: Gas-insulated switchgear insulation defect diagnosis via a novel domain adaptive graph convolutional network. IEEE Trans. Instru. Meas. 71, 110 (2022) 10. Koo, J.Y., Jung, S.Y., Ryu, C.H., et al.: Identification of insulation defects in gas-insulated switchgear by chaotic analysis of partial discharge. IET Sci. Meas. Technol. 4(3), 115–124 (2010) 11. Yan, J., Wang, Y.X., Liu, W.C., et al.: Partial discharge diagnosis via a novel federated metalearning in gas-insulated switchgear. Rev. Sci. Instrum.Instrum. 94(2), 024704 (2023) 12. Fang, W.X., Chen, G.J., Li, W.X., et al.: A PRPD-Based UHF Filtering and Noise Reduction Algorithm for GIS Partial Discharge 23(15), 6763 (2023)

Modeling High Concealment LR Attack Based on Linearization of Signal Space Projection Wengen Li1 , Lu Zhou2 , Xingyu Shi2(B) , Huan Guo2 , and Duange Guo2 1 Hunan Fullde Electric Co. Ltd., Yiyang 413400, Hunan, China

[email protected]

2 School of Electrical and Information Engineering, Changsha University of Science and

Technology, Changsha 410000, China [email protected]

Abstract. False data injection attack (FDIA) is a typical cyber-physical system attack in a smart grid, and its attack vector generation and system defense methods have attracted many scholars’ research. This paper profoundly studies the destructive impact of load redistribution (LR) attacks on power system operation and control. It establishes a basic bi-level optimization model of attacker-attack benefit maximization and responder-system economic operation. At the same time, to enhance the concealment of the attack, the two-norm inequality constraint considering the attack deviation is further added to the upper layer of the bi-level model, and the signal space projection algorithm is proposed to linearize the twonorm inequality constraint. The proposed algorithm is verified on IEEE 14 and IEEE 39 bus systems, and the results show that the attack vector generation has good concealment and ensures the attack effect, which provides a reference for the information security of power systems. Furthermore, using the signal space projection algorithm to linearize the two-norm constraint can avoid the direct expansion of the norm for solving, thereby accelerating the solving speed. Keywords: false data injection attack (FDIA) · load redistribution (LR) · bi-level optimization · two-norm constraint · signal space projection algorithm

1 Introduction With the integration of information and communication technologies, among other aspects of cyberspace, the power system is advancing toward a smart grid [1–4]. Due to the utilization of open standard communication networks and the increasing complexity of network operations, the entire power grid is becoming more susceptible to malicious cyber attacks [5]. As the information source of the control center, SCADA systems, once attacked, may affect the outcome of state estimation and further mislead the operation and control functions of the energy management system (EMS), possibly resulting in catastrophic consequences. A false data injection attack [6] is a cyber attack conducted through the SCADA system to manipulate state estimation. Attackers can evade the current bad data detectors within the power system, directly disrupting state estimation © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 665–673, 2024. https://doi.org/10.1007/978-981-97-1072-0_68

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results, influencing control signals, and potentially causing economic losses and security risks to the power system. The False Data Injection (FDI) attacks concept was initially introduced by Liu et al. [7, 8] in 2009. In order to quantify the potential threats faced by the power grid, Sandberg et al. [9] introduced two categories of security metrics that correspond to two types of FDI attacks: sparse and small-scale. In 2011, Yuan et al. [10, 11] introduced the concept of Load Redistribution (LR) attacks for the first time, categorizing them as a distinct type of False Data Injection (FDI) attack. Aiming at the concealment of false data injection attacks, reference [12] analyzed the relationship between normal data and false data and defined a highly concealed dummy data attack (DDA). Reference [13] establishes a high-stealth false data attack model suitable for multiple line overloads by minimizing the distance between the false data and the center point of normal data in the objective function. In this paper, based on the LR attack bi-level model [10], in order to enhance the concealment of the attack, the two-norm inequality constraint considering the attack deviation is added to the upper layer of the bi-level optimization model, and a novel high concealment load redistribution attack bilevel optimization model is established. Moreover, the signal space projection algorithm is proposed to linearize the two-norm inequality constraint.

2 Modeling and Signal Space Projection Algorithm 2.1 High Concealment LR Attack The objective of LR attacks is to maximize the operational cost of the system under resource constraints, and the underlying assumption is that the control center will implement corrective measures based on false state estimation results to minimize operational costs. Similar to the vulnerability analysis of power systems under most physical terrorist attacks, we utilize a DC load flow model to characterize network behavior. Reference [10] introduced the LR attack bi-level model. Formulas (1)-(7) stand for upper-level attackers and determine the attack vector D to be injected into the original meter measurement to maximize the system’s operating cost. Formulas (8)-(13) represent the response of the lower-level SCED to successfully manipulated false data states using the determined attack vector D. Max D

Ng 

cg Pg∗

csd Sd∗

(1)

d =1

g=1

s.t.

+

Nd 

Nd 

Dd = 0

(2)

d =1

PL = −SF · KD · D

(3)

−τ Dd ≤ Dd ≤ τ Dd ∀d

(4)

Dd = 0 ⇔ δD,d = 0 ∀d

(5)

Modeling High Concealment LR Attack Based on Linearization

PLl = 0 ⇔ δPL,l = 0 ∀l Nd 

δD,d + 2

d =1

Nt 

δPL,l ≤ b

(6)

(7)

t=1

⎧ ⎫ Ng Nd ⎨ ⎬     cg Pg + csd Sd Pg∗ , Sd∗ = arg Min ⎩ P,S ⎭ Ng  g=1

Pg =

Nd 

(8)

d =1

g=1

s.t.

667

(Dd − Sd )

(9)

d =1

PL = SF · KP · P − SF · KD · (D + D − Sd )

(10)

−PLmax ≤ PLl ≤ PLmax ∀l l l

(11)

Pgmin ≤ Pg ≤ Pgmax ∀g

(12)

0 ≤ Sd ≤ Dd + Dd ∀d

(13)

This paper introduces a novel and highly covert false data injection attack to address the challenge of false data with significantly detectable magnitude changes. This attack aims to conceal the manipulated data within the normal measurement values, preventing its identification as anomalous. In order to ensure the concealment of false data, the tampered data should be required to be hidden in the normal data as much as possible. By doing so, if the manipulated data is spatially close to the center point of normal data, referred to as the center data, its concealment can be effectively guaranteed. We describe this as a constraint involving the two-norm of signal offsets: Z − Z0 2 ≤ R

(14)

Z = [PL, KD · D]T

(15)

Z = Z0 + Z

(16)

Z0 represents the measurement vector and is also the center point of normal data, referred to as the center data. Z refers to the measurement vector of the system after being subjected to an attack, while R represents the precision of the signal offset. The above formulas are put into the upper layer of the two-layer model to form a complete high concealment LR attack model.

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2.2 Two-norm Linearization Based on Signal Space Projection Algorithm Referring to Formula 1, the Jacobian matrix H demonstrates orthogonality between its r-dimensional column space and the (m − r)-dimensional left null space. The column space (signal space) and the left null space (noise space) are spanned by the first r left singular unit vectors and the remaining m − r left singular unit vectors of matrix H . That is: Col(H ) = span{u1 , u2 , . . . , ur } Null(H T ) = span{ur+1 , ur+2 , . . . , um } The signal space projection algorithm involves projecting both Z and Z0 onto hyperplanes within the hypersphere formed by the two-norm inequality constraints, achieving the projection on each respective space; Subsequently, the projection vectors of Z and Z0 on the hyperplanes are further projected onto various singular unit vectors, completing the line projection. Thus, the high-dimensional vector two-norm constraint is simplified, and the solution of the two-norm constraint is accelerated. Linearization of Constraints in Column Space. After the successive plane projection and line projection of Z and Z0 , the linearization in the column space is: 1−

|Pi PZ0 | R R ≤ ≤1+ i ∈ {1, 2, . . . , r} |Pi PZ| |Pi PZ| |Pi PZ| P = H (H T WH )−1 H T W Pi =

ui uiT uiT ui

i ∈ {1, 2, . . . , r}

P is the projection matrix. If W = I , P = H (H T H )−1 H T . Pi is a line projection matrix. Determination of Noise Threshold in Left Null Space. Since the noise threshold is small, the modulus of the vector projected by the measurement vector on the noise space Null(H T ) is small, and Col(H )⊥Null(H T ), the measurement vector is close to the signal space(if no noise is present, the measurement vector falls in Col(H )). Therefore, the constraints in the left null space can be straightforwardly linearized as: |Pi KZ| ≤ r i ∈ {r + 1, r + 2, . . . , m} K =I −P Pi =

ui uiT uiT ui

i ∈ {r + 1, r + 2, . . . , m}

(I − P)Z represents the measurement residual. Pi is a line projection matrix.

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3 Simulation Verification 3.1 Concealment of False Data This section presents a case study based on the IEEE 14 bus system, with generator parameters presented in Table 1. The system undergoes comprehensive measurements with a total of m = 54 measurements. Measurements 1–20 represent power flows “from” buses, measurements 21–40 represent power flows “to” buses, and measurements 41–54 correspond to bus power injections. The range of load attack amount is τ = 50%, the attack resource limit is b = 20, and the offloading cost is cs = 100$/MWh. Table 1. Generator parameters of IEEE14 Gen.bus

P min (MW)

P max (MW)

c($/MWh)

1

0

300

20

2

0

50

30

3

0

30

40

6

0

50

50

8

0

20

35

In Case 1, we analyze the traditional LR attack model without considering the twonorm inequality constraint of signal offset. The transmission capacity is modified to simulate a scenario where the system operates close to its capacity limit, with a capacity limit of 160 MW for transmission line 1 and 60 MW for all other transmission lines. The most destructive case of traditional LR attack is shown in Table 2. Table 2. The comparison of the most destructive traditional LR attack and high concealment LR attack with R = 0.2 Meas.m

Meas

Attack value(MW) Traditional LR attack

High concealment LR attack with R = 0.2

1&21

PL12 &PL21

1.3993&−1.3993

−2.4438&2.4438

2&22

PL15 &PL51

−1.3993&1.3993

2.4438&−2.4438

3&23

PL23 &PL32

16.7348&−16.7348

4&24

PL24 &PL42

−2.2301&2.2301

5&25

PL25 &PL52

−2.2614&2.2614

3.9663&−3.9663

6&26

PL34 &PL43

−21.6699&21.6699

4.5773&−4.5773

7&27

PL45 &PL54

4.4350&−4.4350

−2.2132&2.2132 (continued)

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Meas.m

Meas

10&30

PL56 &PL65

Attack value(MW) Traditional LR attack

42 43 44 45 46

inj P2 inj P3 inj P4 inj P5 inj P6

High concealment LR attack with R = 0.2 0.3968&−0.3968

−10.8500(−50%)

−10.8500(−50%)

38.4047(40.77%)

−4.5773(−4.86%)

−23.9000(−50%)

11.2305(23.49%)

-3.6547(−48.09%)

3.8000(50%) 0.3968(3.54%)

In Case 2, we analyze the LR attack model with high concealment by adding the twonorm constraint of signal offset. We set the signal offset degree as 0.2 while maintaining the same transmission line capacity constraints as in Case 1. The most destructive case of the high concealment LR attack model with R = 0.2 is shown in Table 2. In this case, the load on bus four is subjected to the maximum attack, but the magnitude of the attack has been reduced by nearly half. Meanwhile, the attack values on the transmission lines and other loads are relatively small. Compared to Case 1, the magnitude of attacks in Case 2 has significantly decreased. The results obtained from the original SCED are set as the center data. Figure 1 compare the results Z with and without the two-norm constraint and the center data Z0 . Through comparison, it becomes evident that the results with the added two-norm constraint are closer to the center data, indicating a higher level of concealment.

Fig. 1. The comparison of the results Z with and without the two-norm constraint and the center data Z0

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Through the analysis of Fig. 1, it can be observed that the data for R = 0.2 and R = 0.45 are closer to the center data compared to the results without the added twonorm constraint. Indeed, the data with R = 0.2 is closer to the center data compared to the data with R = 0.45. A smaller signal offset magnitude results in a smaller attack amplitude. When R = 0.45, the signal offset magnitude is relatively large and approaching saturation, the attack amplitude becomes similar to that without the added two-norm constraint. The resulting data is very close to the data obtained without adding the two-norm constraint. 3.2 High-Speed Efficiency of Signal Space Projection Algorithm This section uses a case study based on the IEEE 39 bus system, with generator parameters shown in Table 3. The range of load attack is τ = 50%, the cost of load shedding is cs = 100$/MWh, and the attack resource is b = 50. Table 3. Generator parameters of IEEE39 Gen.bus

P min (MW)

P max (MW)

c($/MWh)

30

0

1040

20

31

0

646

30

32

0

725

40

33

0

652

50

34

0

508

35

35

0

687

20

36

0

580

30

37

0

564

40

38

0

865

50

39

0

1100

35

The linearization of the two-norm inequality constraint is achieved by employing the signal space projection algorithm, which significantly accelerates the solving process in contrast to the direct two-norm inequality constraint. Setting R to 2, 3, 4, 5, and 6 and adjusting the appropriate value for r, the comparison between the signal space projection algorithm and the traditional two-norm constraint is presented in Table 4. As R increases, indicating a higher signal offset, the total operating cost rises continuously. Indeed, the signal space projection algorithm is much faster than the direct two-norm constraint.

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Table 4. Comparison of direct two-norm constraint and signal space projection algorithm R

Direct two-norm constraint

Signal space projection algorithm

Operation cost

Operation cost

time(s)

(×102 $/MWh)

time(s)

r

(×102 $/MWh)

2

2079

150

2080

84

0.55

3

2099

201

2101

100

0.76

4

2132

1030

2131

98

0.97

5

2158

361

2158

132

1.20

6

2181

566

2180

395

1.42

4 Summary • This paper introduces a highly covert false data injection attack based on two-norm inequality constraints and establishes a two-layer optimization model with added signal offset two-norm constraints. The signal space projection algorithm is proposed to project two-norm inequality constraints onto the column space and left null space of the Jacobian matrix for linearization, which can avoid solving the expansion norm directly and thus speed up the solution.

References 1. Zhao, C., He, J., Cheng, P., Chen, J.: Consensus-based energy management in smart grid with transmission losses and directed communication. IEEE Trans. Smart Grid 8(5), 2049–2061 (2017). https://doi.org/10.1109/TSG.2015.2513772 2. Musleh, S., Chen, G., Dong, Z.Y., Wang, C., Chen, S.: Vulnerabilities, threats, and impacts of false data injection attacks in smart grids: an overview. In: 2020 International Conference on Smart Grids and Energy Systems (SGES), Perth, Australia, pp. 7782 (2020). https://doi. org/10.1109/SGES51519.2020.00021 3. Mahela, O.P., et al.: Comprehensive overview of multi-agent systems for controlling smart grids. CSEE J. Power and Energy Syst. 8(1), 115–131 (2022). https://doi.org/10.17775/CSE EJPES.2020.03390 4. Abir, S.M.A.A., Anwar, A., Choi, J., Kayes, A.S.M.: IoT-enabled smart energy grid: applications and challenges. IEEE Access 9, 50961–50981 (2021). https://doi.org/10.1109/ACC ESS.2021.3067331 5. Hu, J., Wang, Q., Meng, K., Meng, Y.: Analysis of cyber attacks in the new energy industry. Network Security Technology and Applications 02, 103–105 (2023). (in Chinese) 6. Wang, Y.: Detection and Defense Research on False Data Injection Attacks in Smart Grids. [Doctoral dissertation, North China Electric Power University (Beijing)]. https://doi.org/10. 27140/d.cnki.ghbbu.2020.000186 (2020). (in Chinese) 7. Liu, Y., Ning, P., Reiter, M.K.: False data injection attacks against state estimation in electric power grids. In: Proceedings 16th ACM Conference Computational Commun. Secur., pp. 21– 32 (2009)

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8. Liu, Y., Ning, P., Reiter, M.K.: False data injection attacks against state estimation in electric power grids. ACM Trans. Inf. Syst. Secur. 14(1), 21–32 (2011) 9. Sandberg, H., Teixeira, A., Johansson, K.: On security indices for state estimators in power networks. In: Proceedings Preprints 1st Workshop Secure Control Syst., CPSWEEK, pp. 1–6 (2010) 10. Yuan, Y., Li, Z., Ren, K.: Modeling load redistribution attacks in power systems. IEEE Trans. Smart Grid 2(2), 382–390 (2011) 11. Yuan, Y., Li, Z., Ren, K.: Quantitative analysis of load redistribution attacks in power systems. IEEE Trans. Parallel Distrib. Syst.Distrib. Syst. 23(9), 1731–1738 (2012) 12. Liu, X., Song, Y., Li, Z.: Dummy data attacks in power systems. IEEE Transactions on Smart Grid 11(2), 1792–1795 (2020). https://doi.org/10.1109/TSG.2019.2929702 13. Du, M., Wang, L., Zhou, Y.: High-stealth false data attacks on overloading multiple lines in power systems. IEEE Transactions on Smart Grid 14(2), 1321–1324 (2023). https://doi.org/ 10.1109/TSG.2022.3209524

Design and Analysis of a Novel Type of Double Stator Switched Reluctance Wind Turbine Generator Wenju Yan1,2 , Jiangpeng Hu2 , Wenwen Sun1 , Hailong Li2 , Hao Chen2(B) , and Hongwei Yang2 1 State Key Laboratory of Operation and Control of Renewable Energy and Storage Systems

(China Electric Power Research Institute), Beijing 100192, China [email protected] 2 School of Electric Engineering, China University of Mining and Technology, Xuzhou 221116, China {6288,ts22230021a31,ts21130145p31,hchen, ts22230175p31}@cumt.edu.cn

Abstract. Conventional switched reluctance wind turbine has the problem of low energy density and big torque pulsation, in order to solve this problem, a new type of dual-stator switched reluctance generator motor is designed and its working principle is introduced. The new dual-stator switched reluctance generator is divided into dual structures of inside stator and outside stator, and both of them adopt the U-shaped stator structure. Changing the polarity assignments of the magnetic fields of the inside and outside stator and optimizing positions of the excitation phases at the same time can uncouple the magnetic fields of the inside and outside stator and improve the flexibility of the control of the new generator. Through the finite element static and dynamic simulation of the machine, the magnetic flux, torque, voltage, and current characteristics are analyzed. Then the prototype and test platform are built, and the rationality of the structural design and the validity of the simulation analysis are verified by experiment. Keywords: double stator · switched reluctance generator · magnetic field analysis · phase current

1 Introduction With the continuous exploitation and utilization of non-renewable energy resources, the global resource reservation and environmental problems become more and more serious. As a new type of renewable resource, wind energy has the advantages of lower exploration cost, green environmental protection, and rich resource, so wind energy generation technique has become a hotspot of research in recent years. [1, 2]. In common terms, wind power systems can be categorized into three power classes, large-scale wind power systems, medium-sized wind power systems and small-scale wind power systems, which correspond to a power range of more than 1,000 kW, between 100 and 1,000 kW, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 674–683, 2024. https://doi.org/10.1007/978-981-97-1072-0_69

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and less than 100 kW. Small-scale wind power systems are characterized by simple structure, low cost and easy to control, which provides a set of cost-effective and efficient solutions for regions with underdeveloped power system or even not covered by the power grid [3, 4]. DC generators are simple and easy to control, but high maintenance costs were used in early power generation systems. Electrically excited synchronous generators need to install a separate excitation device and the motor size is large, mostly used in large power generation systems [5, 6]. Permanent magnet synchronous generators are the mainstream models for small-scale power generation systems, however, there are still some problems in practical applications. For example, the motor structure is complex, the manufacturing cost is high. And in some environmentally hostile places, due to the primary magnetic field is provided by perpetual magnets, which are not adjustable, and their end voltage will change with the load conditions. Compared with the above motors, switched reluctance generator is more practical with direct-drive small wind power generation system due to its simple manufacturing, flexible control and good fault tolerance. The motor serves as the central place for the conversion between mechanical and electrical energy in the power generation system, for improving the system performance and maximize the power generation, switched reluctance generators have various structures and flexible stator and rotor poles matching, switched reluctance generator ontology design includes two parts of the motor structural design and the optimization of motor geometric parameters. Ref. [7] gives a switched reluctance wind generator optimization design method using a combination of genetic algorithm and Latin hypercubic sampling, which improves the effectiveness and the size of the motor. Ref. [8] designed a 12/6-pole hybrid rotor structure bearingless switched reluctance generator whose rotor consists of six convex poles and a disc axially stacked, and analyzed its levitation principle and generator theory. Ref. [9] designed a new structure of switched reluctance generator consisting of C-structure stator poles and independent rotor poles, which diminishes the rotational inertia of the motor and enhances the low-speed performance of the motor, system efficiency and power density. Ref. [10] proposes a rotor yawing dual stator switched reluctance motor that utilizes a hydraulic console to control the rotor’s multidegree-of-freedom rotation to comply with the varying wind directions and to enhance the generator’s productivity and power intensity. Therefore,a stator chunking dual stator switched reluctance generator (DSSRG) is put forward by combining the chunking structure with the dual stator in order to promote the power intensity of the generator.The internal and external stator magnetic fields are decoupled through the polarity distribution of the magnetic field of the internal and external stator, so as to achieve the control of the internal and external stator separately to promote the generator’s generating performance.

2 New DSSRG Structure and Operation Principle The magnetic field decoupled DSSRG proposed in this paper significantly improves the power density of the generator compared with the conventional SRG. By intervening in the conduction phases of the internal and external stators, the magnetic fields of the internal and external stators are staggered at a definite physical angle without passing

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through the same part of the rotor yoke at the same time. In this way, when the internal and external stators are excited at the one time, the utilization of the rotor yoke portion is greatly increased due to the staggering of the magnetic fields of the internal and external stators, and consequently the power intensity of the generator is further increased. The mutual repulsion between the magnetic fields in the parallel magnetic circuit allows the magnetic fields generated by the inside and outside stators to be uncoupled from each other. In Furthermore, in order to optimize the torque and current fluctuation characteristics of the motor, the inside and outside teeth on the rotor of the motor are staggered at an angle to each other. As shown in Fig. 1, for the magnetic flux path of the outside stator portion of a U-shaped stator split block DSSRG, the stator magnetic flux path passes through four partially closed sections, which are the stator teeth, the adjacent rotor teeth, and the stator and rotor yoke sections. This special design allows for good independence of the magnetic paths, with both the inside and outside stator flux passing through four sections, distinguished by the inside and outside rotor teeth and the respective stator yoke sections.

Fig. 1. The flux path of U-shaped segment stator SRG

The power generation system constituted by the new DSSRG motor structure and its power converter is shown in Fig. 2, where the polarity of the inside stator winding is in the form of S-N-N-S-S-S-N-N-S-S-N-S; and the polarity of the outside stator winding is in the form of N-S-S-S-N-S-S-S-N-S-S-S-S-N. Take outer stator phase A winding for example, when the rotor rotates counterclockwise In a certain position, turn on the switch S i1 and S i2 near the aligned position of the phase inductance, so that the phase is conducted. According to the principle of minimum reluctance, the magnetic field is closed through the outside teeth, rotor yoke and outside stator teeth of the two neighboring rotors. Then, the rotation direction of the generator rotor is reversed to the electromagnetic force received, and the electromagnetic torque does negative work, converting most of the mechanical power driven by the wind turbine to magnetic energy stored in the phase winding. After a period of time, S i1 and S i2 are turn off before the rotor is turned to the unaligned position of phase inductance. At this moment, the magnetic field energy storage and the mechanical energy of the turbine are transformed into electrical energy through the continuous flow action of the diode in the AO phase loop. According to the change of rotor rotation angle, the external stator A, B, C and D windings are excited counterclockwise in the appropriate position. It is enough to complete the power generation process of the outside stator part of the DSSRG in a cycle. The inside stator is identical to the outside stator and operates relatively independently of the outside stator from each other. It will not be elaborated here.

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Fig. 2. Novel DSSRG power generation system

3 Finite Element Modeling and Simulation Analysis of DSSRG This section will employ finite element method-based simulation software FLUX to conduct finite element modeling and simulation of the novel DSSRG. The modeling and simulation process diagram is illustrated in Fig. 3. Table 1 presents the motor parameters calculated based on the design procedure described in [11], with graphical representations of these parameters depicted in Fig. 4.

Fig. 3. Modeling and simulation steps of FLUX software

The magnetic field distribution of DSSRG directly affects the motor performance, so it is necessary to analyze the static electromagnetic field of DSSRG two-dimensional finite element model. Figure 5 shows the magnetic field distributions of the DSSRG at the locations of minimal and maximal inductances in the inside and outside of the stator for an excitation current of 40 A. From Fig. 5, it can be observed that the proposed DSSRG exhibits favorable magnetic field decoupling characteristics. Additionally, the magnetic field produced by the inside stator uses a different rotor yoke than the magnetic field produced by the outside stator. This approach significantly mitigates issues related to magnetic field saturation, increases core utilization, and consequently enhances motor power density. Figure 6 gives the magnetic chain features of the motor with the inside stator excited separately, the outside stator excited separately and the inside and outside stator excited simultaneously. It can be realized that the magnetic chain of the inside stator and the

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Fig. 4. Geometric model of the DSSRG

Table 1. Geometric parameter of the DSSRG Parameter

Parameter Description

Value (mm)

Dout

Rotor Outside Diameter

175.0

Din

Rotor inside Diameter

127.2

Ds_out

Outside Stator Outside Diameter

220.0

Dsh

Shaft diameter

45.0

L

Stack length

70.0

bsy_out

Outside stator yoke thickness

bro

Rotor outside tooth width

bsi

inside stator tooth width

6.0

bso

Outside stator tooth width

9.2

bsy_in

Inside stator yoke thickness

7.0

hro

Rotor outside tooth length

7.0

bri

Rotor inside tooth width

8.8

bry

Rotor yoke thickness

hri

Rotor inside tooth length

9.0 10.7

10.0 7.2

outside stator excited separately add up to the magnetic chain in the case of simultaneous excitation of both of them. Figure 7 give the torque curves of the motor with the inside stator excited separately, the outside stator excited solely and the inside and outside stator excited together.It can be shown from the figures that the torque with the inside and outside stator excited together is the sum of the torque with the inside and outside stator excited separately. Figure 6 and Fig. 7 show that the magnetic chain and torque have strong decoupling characteristics between the magnetic fields of the inside and outside stator of the motor during one rotor period.

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(a) Minimum inductance of the inner stator

(c) Minimum inductance of the outer stator

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(b) Maximum inductance of the inner stator

(d) Maximum inductance of the outer stator

Fig. 5. Magnetic field distribution nephogram of the DSSRG

(a) Excitation of outer stator individually

(b) Excitation of inner stator individually.

(c) Simultaneous Excitation of double stators Fig. 6. Flux characteristics of the machine

In order to verify the viability and dynamic property of the DSSRG generator topology, simulations are carried out in this section using MATLAB/Simulink and finite element analysis software. First, the magnetic chain and torque features of the motor can be got through the finite element analysis software, and the data are imported into the motor model for simulation through the difference module in MATLAB/Simulink. The power conversion circuit is a common three-phase unsymmetrical half-bridge circuit.

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(a) 20A

(c) average torque

(b) 40A

Fig. 7. Comparison of torque at different phase current

(a) Inner stator phase current

(b) Outer stator phase current

(c) Output voltage on RL Fig. 8. Phase current and output voltage waveform of the RL

The phase current generation waveforms of the motor at 1500 r/min for the inside stator and outdide stator are given in Fig. 8(a) and Fig. 8(b), and the motor excitation voltage is 48 V, the turn-on angle of the inner stator is 6.5°, and the turn-off angle of the inner stator is 15.5°, while the turn-on angle of the outer stator is 5.5°, and the turn-off angle of the outer stator is 15°. Figure 8(c) gives the output motor after the load RL is stabilized by the capacitor, which is basically maintained at 73 V. It is shown that the motor has good power generation characteristics.

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4 Prototype Validation A 16/18/18/16 DSSRG prototype was machined and fabricated in this paper. A detailed photograph of the DSSRG experimental test platform is given in Fig. 9. The testbed is composed of a prototype, a transducer for torque, a magnetic particle brake and a permanent magnet synchronous machine. The prototype is driven to work in the power generation state by using the MD500ET inverter which can control the PM synchronous motor to simulate the wind turbine. In the modeling process, according to the given wind speed and measured generator speed, the export torque of the wind turbine can be

Fig. 9. Photo of the prototype platform

(a) Inner stator phase current

(b) Outer stator phase current

(c) Output voltage on RL Fig. 10. Phase current and output voltage waveform of the RL

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calculated based on the wind turbine characteristics, and used as the control instruction of the PMSM to control the torque output of the PMSM, so as to make it simulate the running characteristics of the wind turbine to carry out the work. Figure 10 and Fig. 8 show the waveforms of dynamic tests and simulation waveforms, which are in good agreement by comparison. And the experimental verifying the accuracy of the logical analysis and emulation results.

5 Conclusion In this study, after targeting the inherent shortcomings of conventional SRM, a new dualstator switched reluctance generator is proposed to compose a small generator system. The motor is divided into the dual structure of inside stator and outside stator, and both of them utilize the U-shaped stator block structure. Changing the polarity assignments of the magnetic fields of the inside and outside stator and improving the position of the excitation phases at the same time can decouple the magnetic fields of the inside and outside stator, which can improve the flexibility of the control of the new generator. The finite element modeling analysis shows that the magnetic field of inside and outside stator has strong decoupling characteristics. Through experiments and simulations, it can be seen that the motor has good performance in power generation. Because of this, the motor can be applied to small-scale wind power supply systems, providing a costeffective solution for areas with underdeveloped power systems or even areas not covered by the power grid. Acknowledgments. This work is supported by Open fund project of State Key Laboratory of New Energy and Energy Storage Operation Control (NYB51202201708).

References 1. Wu, C., Zhang, X., Sterling, M.: Wind power generation variations and aggregations. In: CSEE Journal of Power and Energy Systems 8(1), 17–38 (2022) 2. Yu, L., Dang, L., Xu, L.: Distributed PLL based control of offshore wind turbines connected with diode rectifier based HVDC systems. In: IEEE Transactions on Power Deliery 33(3), 1328–1336 (2018) 3. Das, K., Nitsas, A., Altin, M., Hansen, A.D., Sørensen, P.: Improved load-shedding scheme considering distributed generation. In: IEEE Transactions on Power Delivery 32(1), 515–524 (2017) 4. Beik, O., Schofield, N.: An offshore wind generation scheme with a high-voltage hybrid generator, HVDC interconnections, and transmission. In: IEEE Transactions on Power Delivery 31(2), 867–877 (2016) 5. Wang, Y., Zhu, X., Cheng, M.: Development and testing of a static sealed double stator high temperature superconducting generator for offshore wind power generation. Proceedings of the CSEE 41(23), 8148–8158 (2021). (in Chinese) 6. Zhang, Y., Hu, S., Dong, Z., et al.: Excitation Control of Electric Excitation Wind Turbine. Transactions of China Electrotechnical Society 29(1), 255260 (2014). (in Chinese) 7. Shin, H.U., Lee, K.B.: Optimal design of a 1 kW switched reluctance generator for wind power systems using a genetic algorithm. In: IET Electric Power Applications 10(8), 807–817 (2016)

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8. Sun, Y., Liu, L., Yuan, Y.: Design of a new type of bearingless switched reluctance generator. Small & Special Electrical Machines 44(12), 15–19 (2016). (in Chinese) 9. Bao, Y.J., Cheng, K.W.E., Xue, X.D., Chan, J., Zhang, Z., Lin, J.: Research on a novel switched reluctance generator for wind power generation. In: International Conference on Power Electronics Systems and Applications, pp 1–6. IEEE, Hong Kong (2011) 10. Li, Z., Yu, X., Qian, Z., Wang, X., Xiao, Y., Sun, H.: Generation characteristics analysis of deflection type double stator switched reluctance generator. In: IEEE Access 8, 196175– 196186 (2020) 11. Yan, W., Chen, H., Liao, S., Liu, Y., Cheng, H.: Design of a low ripple double modularstator switched reluctance machine for electric vehicle applications. In: IEEE Transactions on Transportation Electrification 7(3), 1349–1358 (2021)

Research on Short-Circuit Withstand Capability of Transformer Considering the Mechanical Accumulation Characteristics of Insulation Materials Zhihao Liao1,2 , Zhongxiang Li1,2(B)

, Zhiqin Ma1,2 , Dan Zhou1,2 , and Xiang Shu1,2

1 Electric Power Research Institute, Guandong Power Grid Co. Ltd., Guangzhou 510080,

Guangdong, China [email protected] 2 Guangdong Provincial Key Laboratory of Electric Power Equipment Reliability, Guangzhou 510080, Guangdong, China

Abstract. Aiming at the cumulative effect of the insulation pad inside the transformer coil and the paper-wrapped insulation outside the winding wire, a mechanical property accumulation characteristic test was conducted on the insulation paperboard for the coil and the paper-wrapped insulation for the wire, and the accumulation characteristic curve of the deformation of the insulation material under multiple impact tests was obtained. Based on the parameters of a 110 kV power transformer coil, a study on the verification and evaluation method for the short-circuit resistance of power transformer coils taking into account the cumulative mechanical properties of the insulating materials was conducted. Research has shown that under axial compression, the cumulative properties of insulating materials, whether insulating pads or paper-covered insulation for conductors, have a significant impact on the level of short-circuit forces that the transformer coils withstand. After repeated short-circuit shocks, the short-circuit forces experienced by the coils increase significantly, reducing the safety margin of the transformer. Therefore, timely verification of the short-circuit withstand capability of power transformers that have been subjected to short-circuit current shocks can help identify hidden dangers in advance and improve the safe and stable operation of the transformer. Keywords: Transformer · Insulation Pad · Experimental Research · Verification of Short-Circuit Resistance · Cumulative Characteristic

1 Introduction Power transformers may experience multiple short circuit surges during their lifespan, and transformers that experience short circuit surges may not necessarily fail. Typically, after evaluation and testing, transformers can be put back into operation in the power grid [1–3]. However, each short-circuit impact will cause slight deformation of the transformer coil, and when these deformations accumulate to a certain extent, it may © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 684–692, 2024. https://doi.org/10.1007/978-981-97-1072-0_70

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lead to the occurrence of transformer short-circuit faults. Once a short circuit fault occurs, the transformer may cause unforeseeable damage due to the inability to withstand the electrical force of the short circuit impact. The cumulative effect of short circuits refers to the irreversible small changes in certain performance parameters of transformers under the action of short circuit surges, which gradually expand with the increase of short circuit surges [4]. However, currently, neither simulation calculations, experiments, nor post test evaluation methods can effectively reflect the cumulative effects caused by short-circuit impacts. The study of the cumulative effect of short-circuit force includes two aspects: electromagnetic and mechanical properties, especially for the mechanical properties of insulation materials. Reference [4] summarized and analyzed the mechanism of the cumulative effect of short-circuit force, and pointed out that insulation materials such as insulation pads that had already been densified and mechanically stabilized under short-circuit force will reappear compressible plastic deformation, which will weaken the overall compression force of the winding. Reference [5] takes a 220 kV transformer as the research object, establishes a simulation model, and analyzes the relationship between the number of short-circuit impacts and winding deformation of the transformer. It is pointed out that the transformer winding shape variable is closely related to the short-circuit impact action time, short-circuit current level, and cumulative number. Reference [6] designed short-circuit impact tests on actual transformer products, measuring the variation characteristics of transformer leakage magnetic field and electrodynamic force under multiple impact conditions. Reference [7] proposes a method to determine the cumulative effect coefficient of transformer short-circuit through experimental or theoretical research, and analyzes the changes in material characteristics caused by long short-circuit time and thermal effects involved in the cumulative effect. Under the action of thermal stress, long-term operating transformers may experience a decrease in elastic modulus and size shrinkage of insulation materials, leading to changes in coil structure and stress, thereby affecting the short-circuit withstand capacity of the coil [8–10]. Reference [11, 12] considered the impact of thermal aging on the evaluation method of short-circuit withstand capacity of coils in transformer windings, and obtained the mechanical properties of different aged cardboard through experiments. Overall, there is currently limited research on the cumulative effects on the mechanical properties of insulation materials, and there is still a lack of comprehensive experimental data support. This article designs and manufactures test samples and equipment for the insulation material of the inner cushion block of the transformer coil and the paper wrapped insulation of the wire. Experimental research on the cumulative mechanical properties of the coil insulation material under simulated short-circuit impact force was conducted, and the cumulative deformation characteristics of the insulation material under multiple different impact forces were obtained. Based on experimental data, this paper establishes a short-circuit resistance verification model for a three-phase three winding 110 kV power transformer coil, and conducts a study on the short-circuit resistance verification of power transformer coils taking into account the cumulative mechanical properties of insulation materials. The deformation of the winding insulation before and after being subjected to 20 impacts of 80% of the rated short-circuit current was calculated, and

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the stress situation of the winding before and after the short-circuit current impact was checked.

2 Test Methods and Devices 2.1 Test Sample This article selects a single flat copper wire with a thickness of 5 ± 0.1 mm (measured at 1 MPa pressure) using 2 mm insulated cardboard and double-sided wrapping paper for the transformer coil as the experimental object. The insulating cardboard was sampled according to the size of 80 mm in diameter, and the cut three layers of insulating cardboard were stacked into 6 mm thick insulating samples for testing; The insulation paper wrapping method of flat wires should be consistent with the actual wrapping method of wires. The wire width should not be less than 12 mm, the thickness should not exceed 2 mm, and the wire length should be sampled as 100 mm. The test sample is shown in Fig. 1.

Fig. 1. Test sample.

Fig. 2. Sample fixing.

2.2 Test Device and Equipment This article uses a fatigue testing machine to conduct load loading tests on the samples, and the fixing method of the test samples is shown in Fig. 2. The rated dynamic load capacity of the fatigue testing machine is ±1000 kN, with integrated displacement sensor, stroke of 250 mm, displacement measurement accuracy of 0.001 mm, and load accuracy of 0.001 kN. During the experiment, the test sample soaked in oil is clamped by a stainless steel plate, with both sides of the steel plate polished. The thickness of the steel plate is 28 mm, and tightening devices are set at both ends. The sample is placed in the middle of the steel plate.

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2.3 Test Process According to the production process requirements of the transformer manufacturer, a pre pressure is first applied to the test sample in the early stage of the test. This article sets the pre pressure to 3.5 MPa, remains stationary for 2 min, and then continuously loads 15 cycles of pulses, each lasting for 75 ms (20 Hz). After an interval of 1 min, the same impact is continued to be loaded, with a total of 20 repeated impacts. During the test, record the displacement of each group of test samples after impact, and obtain the average deformation of the test samples caused by each impact. The process of applying the test load is shown in Fig. 3.

Fig. 3. Test load application process.

Based on the actual magnitude of short-circuit force that power transformers may be subjected to, this article selects dynamic impact force amplitudes of 20 MPa, 50 MPa, and 80 MPa to load the above dynamic loads respectively. Considering the dispersion of the test, each dynamic impact force shall undergo at least three effective loading tests of the dynamic load, that is, each time the dynamic load shall be loaded according to the complete program, And the deviation of each deformation variable obtained under the same amplitude dynamic impact force test shall not exceed 15%.

3 Analysis of Experimental Data The experimental test data is shown in Figs. 4 and 5. The experimental data shows that whether it is insulation pad or wire wrapped insulation, under multiple impact forces, the cumulative deformation effect of the insulation material is significant. With the increase of impact times, the deformation amount shows an increasing trend. The cumulative deformation percentage of the insulation pad is significantly higher than that of the type of wire paper wrapped insulation, mainly because the compactness of wire paper wrapped insulation is higher than that of the insulation pad material. At the same time, paper wrapped insulation is made by wrapping multiple layers of insulation paper, which also has good resilience after being compressed. In addition, under larger impact forces, such as 50 MPa and 80 MPa, the cumulative deformation of insulation materials is significantly higher than that of 20 MPa impact.

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According to the data analysis in the figure, it can be seen that there are certain differences in the deformation of insulation materials under different pressure impacts, mainly reflected in the difference in the decrease rate of the relationship curve between the deformation amount and the number of tests. Under the same pressure, as the number of impacts increases, the insulation material exhibits different elastic deformation values, and there is still a cumulative effect during the elastic deformation process. Under the impact of short-circuit current, the mechanical accumulation effect of a single long time cannot be ignored.

Fig. 4. Accumulated deformation percentage of insulating cardboard sample.

Fig. 5. Accumulated deformation percentage of wire paper insulation.

4 Method for Short-Circuit Resistance Verification of Cumulative Effects of Insulation Materials 4.1 Basic Parameters of Transformer This section takes the coil data of a three-phase three winding 110 kV power transformer as an example to establish a transformer short-circuit resistance verification model. The basic parameters of the transformer are shown in Table 1.

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Table 1. Basic parameters of power transformers. Types

Content or Value

Structural style

3 phase and 3 winding

Voltage ratio

220±8×1.5%/115/10.5

Capacity

HV/MV/LV:240/240/80MVA

Impedance (%)

U1-2= 14%, U2-3 = 21%, U1-3 = 35%

4.2 Calculation of Short-Circuit Force at 80% Rated Short-Circuit Current Taking the medium low operation and low voltage short circuit conditions of transformers as an example, calculate the force on the coil under the impact of 80% of the rated short circuit current. Based on the electrical and structural parameters of the transformer coil, a calculation model for the short-circuit resistance of the transformer coil can be established. By combining the simulation calculation of coil leakage magnetic field distribution and short-circuit current calculation, the force distribution curves of each pad position in the low-voltage and medium voltage coils can be obtained, as shown in Fig. 6.

Fig. 6. Force distribution curve at each cushion block position of the coil.

4.3 Calculation of Accumulated Deformation of Insulation Components under 20 Times of 80% Rated Current Short Circuit on the Coil By combining the accumulated deformation test data of insulation materials and the calculation results of the short-circuit force borne by the coil, the deformation of the low-voltage winding, the insulation of the medium voltage winding, and the iron yoke after the first impact during low voltage short circuit operation of the transformer can be obtained. By using the interpolation method for 20 iterations, the cumulative deformation of the medium voltage coil and the low voltage coil can be calculated after enduring 20 shocks of 80% of the rated current, as shown in Fig. 7.

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(a) medium voltage coil

(b)low voltage coil

Fig. 7. Relationship between the number of short circuits and insulation deformation.

Based on the actual magnitude of short-circuit force that transformers may be subjected to, this article selects dynamic impact force amplitudes of 20 MPa, 50 MPa, and 80 MPa to load the above dynamic loads respectively. Considering the dispersion of the test, each dynamic impact force shall undergo at least three effective loading. 4.4 Analysis of the Short-Circuit Resistance of the Coil after Withstanding 20 Short Circuits of 80% Rated Current Based on the analysis and calculation of the accumulated deformation of the insulation components of the transformer after 20 short circuits of 80% of the rated current, the short-circuit resistance of the transformer is re evaluated. When calculating, the winding offset is considered as 5 mm plus the accumulated deformation of the insulation. Table 2 shows the comparison of winding forces in the initial state and after 20 short circuit impacts. According to the data in the table, it can be seen that after multiple short circuit impacts on the coil, the overall force on the winding will significantly increase, and the force on the end insulation, pressure plate, pull plate, and clamp parts to withstand continuous impacts will significantly increase. Therefore, during the normal operation of transformers, if they are subjected to significant short-circuit impacts, it is necessary to consider the cumulative effect of coil insulation materials, and verify the transformer’s short-circuit resistance level in a timely manner based on short-circuit current data, in order to identify hidden dangers in a timely manner and ensure the safety and stability of power transformer operation.

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Table 2. The force situation of the winding before and after 20 times of 80% rated current shortcircuit impact. Types

Initial state of low-voltage coil

Status after 20 times of 80% short-circuit current

Initial state of middle-voltage coil

Status after 20 times of 80% short-circuit current

Maximum −593.9 downward force (kN)

−894.2

−318.8

−455.8

Maximum upward force (kN)

716.8

986.0

196.5

246.0

Overall force (kN)

122.9

209.4

−122.2

−209.7

Zero crossing rebound force (kN)

430.1

591.6

191.2

273.4

5 Conclusion (1) Whether it is insulation pad or wire wrapped paper insulation, under axial compression, the cumulative effect is obvious, and the deformation shows an increasing trend with the increase of impact times. (2) Under the same level of mechanical impact force, the cumulative deformation of insulation pads is significantly higher than that of wire wrapped insulation. (3) Considering the relationship between the axial short-circuit resistance of the transformer and the compression force and axial equivalent stiffness coefficient, combined with experimental data, it can be concluded that as the number of short-circuit faults increases, the transformer will inevitably experience corresponding plastic deformation, causing a decrease in axial preload. At the same time, the stiffness coefficient of the elastic system formed by insulation and copper wire will increase, affecting its natural frequency, The cumulative effect of the impact needs to be analyzed in conjunction with the overall winding parameters. (4) Timely conducting short-circuit resistance checks on power transformers that are subject to short-circuit current impacts can help identify potential hazards in advance and improve the safe and stable operation level of transformers. Acknowledgments. This work was funded by the Technology Project of China Southern Power Grid (No. GDKJXM20202005).

References 1. Fu, Y., Zhou, Z., Pan, B., et al.: Status detection system of transformer based on effect of short-circuit impulse. J. Shanghai University of Electric Power 04, 1–6 (2001)

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2. Li, B.: Research on the Mechanism of the Cumulative Effect of Power Transformers’ ShortCircuit Impact. Huazhong University of Science and Technology (2016) 3. Chen, Y., Chen, J., He, D., et al.: Evaluation of short-circuit resistance ability of distribution transformer based on monte carlo simulation and comprehensive evaluation method. Guangdong Electric Power 35(1), 60–69 (2022) 4. Li, L., Li, Z., Sun, S., et al.: Research review on short-circuit cumulative effect of power transformer. Transformer 54(2), 24–31 (2017) 5. Wang, W., Wang, W., Zhang, X., et al.: Evaluation technology for accumulated effects of transformer short circuit impulse. Electrotechnical Appl. 36(18), 44–48 (2017) 6. Wang, H.: Research on Electromagnetic and Accumulation Effects of Transformers Under Multiple Short Circuit Conditions. Shenyang University of Technology (2018) 7. Sun, W., Li, Y., Lin, C., et al.: Evaluation method and test analysis of accumulation effect of transformer short-circuit. Guangdong Electric Power 32(6), 137–144 (2019) 8. Prevost, T.A.: Maintaining Short Circuit Strength in Transformers. Weidmann Second Annual Technical Conference (2003) 9. Emsley, A.M., Heywood, R.J., Ali, M., et al.: On the kinetics of degradation of cellulose. Cellulose 4(1), 1–5 (1997) 10. Zhang, F., Ji, S., Naranpanawe, L., et al.: Investigation of overall and local vibration characteristics of disk-type windings. IET Gener. Transm. Distrib.Distrib. 14(18), 3685–3691 (2020) 11. Zhang, F., Li, X., Zhu, X., et al.: Assessment of the withstand ability to short circuit of inner windings in power transformers considering the degree of thermal aging. Proceedings of the CSEE 42(10), 3836–3845 (2022) 12. Li, Z., Tan, Y., Li, Y., et al.: Radial stability and cumulative test of transformer windings under short-circuit condition. Electric Power Syst. Res. 217, 1–11 (2023)

Calculation and Analysis of Temperature Field Characteristics of Power Transformers in Oil During Short Circuit Processes Linglong Cai1,2 , Bin Tai1,2 , Zhiqin Ma1,2 , Yuhui Jin1,2 , Shuo Jiang1,2 , and Zhongxiang Li1,2(B) 1 Electric Power Research Institute, Guandong Power Grid Co. Ltd., Guangzhou 510080,

Guangdong, China [email protected] 2 Guangdong Provincial Key Laboratory of Electric Power Equipment Reliability, Guangzhou 510080, Guangdong, China

Abstract. The current increases rapidly under the condition of short-circuit, leading to a rise in the winding temperature. Currently, the standard formulas in IEC 60076–5 are commonly used to calculate the temperature rise, but there is limited analysis of the temperature variation process and local hotspots during the short circuit fault. To address this issue, this paper performs a fluid and temperature dependent field simulation of the transformer through simulation software FLUENT. First, a static temperature dependent field simulation is conducted under rated conditions. Then, in the static simulation, the temperature and oil flow distribution characteristics during the 2-s short circuit process are simulated. Finally, the simulation results are compared with the results obtained from national standard calculations to validate the accuracy of the simulation method. And mechanical performance tests on copper conductors at different temperatures is conducted. Keywords: Oil-immersed power transformer · Short-circuit temperature rise · FLUENT · Fluid-temperature coupled field

1 Introduction Power transformers are key equipment in the power grid [1]. Among various transformer faults, short-circuit faults are the most common, and among them, three-phase shortcircuits pose the most severe threat to transformers due to their high short-circuit currents. The thermal effects caused by short-circuits pose a critical challenge to transformers [2]. The current increases rapidly under the condition of short-circuit, leading to a rapid rise in winding temperature.According to IEC 60076–5-2006 [3], the maximum allowable average temperature for copper windings in oil-immersed transformers after a short circuit is 250°C.Reference [4] derived a formula for calculating the average temperature distribution of the windings coil after a short circuit, considering the transient component of the short-circuit current. Reference [5] derived the national standard formula and provided a calculation example of the short-circuit temperature for the SF11–180000/220 © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 693–701, 2024. https://doi.org/10.1007/978-981-97-1072-0_71

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power transformer. However, existing literature does not analyze the local temperature characteristics and fluid properties of the components after a short circuit in oil-immersed power transformers. In this paper, fluid analysis software FLUENT is used to simulate the fluidtemperature coupled field of the transformer in oil, with the SFSZ9–40,000/110 oilimmersed power transformer as the object of study.Firstly, the static temperature field analysis is conducted under rated operating conditions. Then, in the static analysis, the temperature and fluid flow distribution characteristics during a 2-s short-circuit process are simulated and demonstrated. Finally, the finite element simulation results are compared with the calculation results obtained using the national standard method to validate the accuracy of the simulation mode method proposed in this paper.

2 Temperature Characterisation of Transformer during a Short Circuit Fault 2.1 Transformer Heat Source Analysis During the operation of power transformers, due to the presence of core and winding losses, the losses generated by each heating component will be converted into thermal energy and dissipated outward, leading to an increase in transformer temperature. When the transformer reaches a steady state, its heating and heat dissipation process reaches a dynamic balance, and the temperatures of each component will also tend to be stable. At this point, the transformer temperature can be solved. The distribution of transformer heat sources is shown in Fig. 1.

Fig. 1. Transformer heat source distribution

2.2 Transformer Heat Flux Analysis During the analysis of a transformer, heat is mainly diverge to the surrounding air flow through convection of the transformer oil [6]. In engineering compute, the oil wraping the transformer is approximated as an incompressible fluid. According to the axiom of mass conservation, momentum conservation, and energy conservation, the convective heat transfer equation can be simplified to the solid heat transfer equation when the fluid velocity is zero.

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2.3 Calculation of Wire Temperature After Short Circuit According to IEC 60076–5-2006, the average temperature of the winding after shortcircuit is shown in Eq. (1). For specific meanings of the letters, please refer to the relevant standards. θ1 = θ0 +

2 × (θ0 + 235) 106000 J 2 ×t

−1

(1)

Due to the fact that the winding material is copper, which has a relatively low specific heat, and the oil has a relatively high specific heat, the temperature rise of the winding after a short circuit for 2 s is significant.

3 Transformer Physical Modelling When using FLUENT simulation, the transformer model is simplified into a twodimensional model [8, 9]. The high and medium voltage windings are divided into 68 segments, and the main technical parameters are shown in Table 1. Table 1. Basic Parameters of Transformer. Parameters

Numerical value

Transformation ratio parameter

110 ± 8*1.25%/38.5/10.5 kV

Turns of high voltage winding

556

Turns of medium voltage winding

195

Total height

1042 mm

Current density of high-voltage

2.84 A/mm2

Current density of Medium-voltage

3.56 A/mm2

Cooling method

ONAN

Fuel tank size (mm)

5260*1820*2670

4 Temperature Rise Analysis 4.1 Initial Condition Setting Fill the oil tank with oil, and the material parameters of the oil change with temperature rise. Assign corresponding material parameters to each structural component separately. The parameters of oil, such as density, specific heat, thermal conductivity, and dynamic viscosity, vary with temperature [6, 10]. The main source of heat generation in the transformer temperature field simulation is the losses in the windings and iron core. The heat source for FLUENT simulation is

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applied by loading the loss density [11]. During the transient temperature field shortcircuit temperature rise process, the loss density will continuously change over time. The winding part is mainly copper loss, ignoring the influence of eddy current loss. The loss amount is proportional to the square of the current. During the short-circuit process, it is approximately assumed that the loss density of the iron core remains unchanged. The loss calculation results are shown in Table 2. Table 2. Loss Density. Character radical

Dilapidation (W)

Volumetric (m3 )

Loss density (W/m3 )

High voltage section

1.0372ik2 R

0.1608

6.4502ik2 R

Medium voltage section

1.0449ik2 R

0.0945

11.0571ik2 R

Iron core

34686

1.6791

20657.50

4.2 Temperature Distribution under Rated Conditions The calculation and analysis of transient temperature rise is based on the rated operating state. Firstly, the temperature rise in the rated operating state is simulated and solved, and the results are shown in Fig. 2. The hot spot temperature in the transformer is 69.77°C. Temperature rise analysis mainly focuses on two aspects: hot spot temperature rise and average temperature rise. Due to heat conduction, temperature rise gradually increases from bottom to top. By solving and iterating, the temperatures of each component tend to stabilize, and the average temperatures of the high and medium voltage windings are 62.89°C and 65.36°C, respectively.

Fig. 2. Rated Operating Temperature.

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4.3 Temperature Distribution during the 2 s Short Circuit Process Based on the calculation results of transformer rating, conduct transient temperature rise analysis for short circuit 2 s. The end coil shown below is coil number 1, and the top coil is coil number 68. Due to the consistent height and number of segments of the high and medium voltage windings in this prototype, there is only a difference between the thickness of the winding and the width of the oil passage, the same labeling method is used. The transient temperature results at 2 s is shown in Fig. 3.

Fig. 3. Temperature Results after 2 s.

Transformer in the short circuit after 2 s, the maximum value of high voltage winding temperature is 77.73 °C, located in the 47th line cake, the average temperature value is 72.74 °C, the temperature distribution trend has not changed, only on the basis of the original temperature rise increase, the average temperature rise is 9.85 K. Mxediumvoltage winding temperature maximum value is 85.29°C, located in the 58th line cake, the average temperature is 80.87°C. On the basis of rated operation, the temperature rise has increased by 15.51 K. Transformer short circuit 2s after the core, tank temperature distribution as shown in Fig. 4 and Fig. 5, the core temperature was upper high and lower low distribution. The maximum temperature is 62.59°C, and the temperature is an increasing process. The temperature is also distributed in the upper high and lower low, and the maximum temperature is 45.93°C. 4.4 Oil Flow Analysis After Short Circuit for 2 s The oil flow distribution cloud map as illustrated in Fig. 6. Due to the influence of temperature on the material parameters of the oil, after being heated by the heating component, the hot oil flows upwards, while the cold oil flows back, ultimately forming a vortex shape in the upper part of the oil tank [12, 13]. The oil passage tends towards oil flow as shown in Fig. 7, and the oil flow at the main air channel in the upper part of the winding is faster, the fastest being 0.0563 m/s.

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Fig. 4. Iron Core Temperature Cloud Map

Fig. 5. Oil Tank Temperature Cloud Map

Fig. 6. Oil Flow Distribution Vector

Fig. 7. Oil Flow Vector Diagram of Oil Passage Position

5 Bending Test of Copper Conductors at Different Temperatures Take a flat enameled copper flat wire with a length of about 200 mm as a sample, place the wire in a drying oven at a temperature of 120°C for 24 h, take the sample out and cool it at room temperature for at least 6 h, then place the sample at 20°C, 60°C, 105°C, and 120°C for 1 h at constant temperature, and carry on the bending tests on wire samples at different temperatures. At a temperature of 105°C, the sample is shown in Fig. 8 before and after the bending test. Through experiments, it can be seen that as the temperature increases, the overall bending strength and bending resistance of copper wires show a downward trend. The bending modulus of the wire sample increases from 20°C to 60°C, and then decreases with the increase of temperature. The curve of the bending strength, bending modulus, and bending force of copper wire with temperature is shown in Fig. 9.

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Fig. 8. Comparison before and after conductor sample test at 105°C

a. Curve of bending strength changing with temperature

b. Curve of bending modulus changing with temperature

c. Curve of bending resistance changing with temperature Fig. 9. Curve of bending strength, bending modulus and bending force of copper wire with temperature

Within the temperature range of 20°C to 60°C, the mechanical strength of copper wire does not change significantly; Within the temperature range of 60°C to 105°C, the mechanical strength of copper wire decreases rapidly. Under normal operation, the hot spot temperature of the winding of a power transformer generally does not exceed 105°C. According to the test results, its mechanical strength has decreased compared to room temperature.

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6 Comparison of Temperature Calculation Results after Short Circuit The comparison results between the national standard calculation formula and the simulation are shown in Table 3. Table 3. Result Verification. Average temperature

Rated results

HV-winding

62.89°C

MV-winding

65.36°C

Simulation value after short circuit

Calculated value after short circuit

Temperature deviation

72.74°C

71.35°C

1.39 K

80.87°C

79.16°C

1.71 K

In this paper, the simulation values of the high and medium voltage windings after a short circuit had an error of less than 2 K compared to the calculated values based on the national standard. The temperature rise simulation analysis will simplify some structural components, resulting in an error of 1.91% and 2.11% in the final results of the high and medium voltage windings, respectively. Both errors were less than 5%, indicating that the simulation results are accurate and can provide the distribution pattern of local hotspots.

7 Conclusion The following conclusions were obtained through simulation analysis: (1) After comparing the results, it can be seen that the short-circuit process does not affect the distribution trend of temperature. Due to the significant increase in instantaneous loss, it will lead to an increase in temperature, with high and medium voltage temperature appreciation of 9.85 K and 15.51 K, respectively. (2) The simulation results show that after a 2-s short circuit in the transformer, the overall distribution of winding temperatures is higher at the top and lower at the bottom. The maximum temperature rise position of the high and medium voltage winding is not at the top, mainly due to the large oil heat dissipation area near the top, and the temperature is not the maximum. The maximum temperature rise is at a position close to 70% of the winding axis, with the maximum temperatures being 77.73°C and 85.29°C, respectively. (3) By comparing the analytical results with the national standard calculation formula, the temperature rise error of the high-voltage winding is 1.91%, and the temperature rise error of the medium voltage winding is 2.11%. Both errors are less than 5%, which verifies the effectiveness of the method proposed in this paper. Acknowledgments. This work was funded by the Technology Project of China Southern Power Grid (No. GDKJXM20202005).

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References 1. Xiong, H., Zhang, S., Zhao, Z., et al.: Analysis method of radial bending stress of power transformer windings. High Voltage Eng. 46(03), 931–938 (2020) 2. Guan, Q.-G., Meng, J., Lyu, X.-P.: Derivation and analysis of theoretical formula for current calculation in transformer short-circuit test. Transformer 57(12), 1821 (2020) 3. IEC 60076–5–2006. Power transformers Part 5: Ability to withstand short circuit (2008) 4. Yu, B., Liu, W., Xing, Y., et al.: Analysis and calculation of winding thermal stability in power transformer under short-circuit conditions. Transformer 53(06), 8–11 (2016) 5. Tian, H.-L., Li, J.-J., Fu, H.-Y.: GB1094.5, power transformer part 5: ability to withstand short circuit-derivation of the formula for calculating heat stabilization average temperature of transformer after sudden short-circuit test. Transformer 51(05), 7–11 (2014) 6. Xie, Y., Li, L., Song, Y., et al.: Multi-physical field coupled method for temperature rise of winding in oil-immersed power transformer. Proceedings of the CSEE 36(21), 5957–5965, 6040 (2016) 7. Smolka, J., Nowak, A.J.: Experimental validation of the coupled fluid flow, heat transfer and electromagnetic numerical model of the medium-power dry-type electrical transformer. Int. J. Therm. Sci. 47(10), 1393–1410 (2008) 8. Liu, F., Guo, Z., Jing, C., et al.: Research on influence factors and calculation of winding hot spot temperature of oil-immersed transformer. Transformer 51(06), 22–26 (2014) 9. Wang, R., Li, Z., Yang, J., et al.: Converter transformer no-load inrush current based on FEM magnetic field simulation and force analysis. Guangdong Electric Power 33(07), 113120 (2020) 10. Wakil, N.E., Chereches, N.C., Padet, J.: Numerical study of heat transfer and fluid flow in a power transformer. Int. J. Therm. Sci. 45(6), 615–626 (2006) 11. Wang, D., Yang, C., Wang, G., Han, X.: Analysis of two-dimensional temperature field in ultra-high voltage transformer based on fluent. High Voltage Apparatus 51(06), 161–165 (2015) 12. Tao, C.: Calculation and Analysis of Transient Temperature Rise of Transformer Windings. Hebei University of Technology (2020) 13. Liu, S., Han, D., Yang, Y., et al.: Establishment and research of transformer winding vibration model based on fourier neural network. Guangdong Electric Power 31(08), 62–68 (2018)

Refinement of Short-Circuit Withstand Capability Calculation for Power Transformers and Application in Fault Analysis Yuhui Jin1,2 , Xian Yang1,2 , Zhiqin Ma1,2 , Chunyao Lin1,2 , Jiangnan Liu1,2 , and Zhongxiang Li1,2(B) 1 Electric Power Research Institute, Guandong Power Grid Co. Ltd., Guangzhou 510080,

Guangdong, China [email protected] 2 Guangdong Provincial Key Laboratory of Electric Power Equipment Reliability, Guangzhou 510080, Guangdong, China

Abstract. Power transformers inevitably face various short-circuit faults during their normal operational processes, and their ability to withstand these faults is a critical performance indicator. This article is based on actual data from a 110 kV three-phase double-winding power transformer that experienced a fault due to inadequate short-circuit withstand capability. It introduces a refined method for calculating the short-circuit withstand capability of power transformers, establishes a refined model for this capability calculation, and accurately calculates the axial and radial forces on each turn of wire in different operating conditions. The calculated results are compared with the dismantling phenomena of the faulty transformer, demonstrating that the calculated results effectively reflect the stress characteristics and weak points of the transformer’s coil components. This approach can significantly support the design optimization of transformer short-circuit withstand capability and facilitate fault analysis tasks. Keywords: Transformer · Short-circuit withstand capability · Refined calculation · Leakage magnetic field distribution · Fault analysis

1 Introduction Power transformers are one of the essential electrical devices in power systems, and their operational state directly impacts the overall safety and stability of the electrical grid. Once a power transformer experiences a fault, the consequences are extensive, the maintenance period is prolonged, and it leads to severe economic losses and adverse social impacts [1, 2]. During normal operation, power transformers inevitably undergo various short-circuit fault tests, with their short-circuit withstand capability being a critical performance metric. Instances of transformer failures due to inadequate shortcircuit withstand capability are common in power grids, resulting in significant damage such as coil deformation and insulation breakdown, which may even lead to fires [3, 4]. In recent years, insufficient short-circuit withstand capability has become a major factor affecting the safe operation of power transformers. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 702–709, 2024. https://doi.org/10.1007/978-981-97-1072-0_72

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Calculation of short-circuit withstand capability for transformers is a crucial method for assessing their short-circuit stability. According to the national standard GB 1094.5, the calculation involves comparing the actual winding force values to their permissible limits. If the winding forces are lower than the limits, the transformer is deemed to have adequate short-circuit withstand capability [5]. Reference [6] developed software for calculating the short-circuit withstand capability of large transformers, which automatically evaluates their thermal, radial stability, and axial stability capabilities. References [7–9] utilized finite element methods to solve simplified 2D static leakage magnetic fields of transformers and conducted coil short-circuit withstand capability calculations. With advancements in computer performance and numerical computing technology, certain references achieved accuracy up to each individual wire within the leakage magnetic field calculations [9–11], significantly enhancing the precision of transformer short-circuit withstand capability assessments. In this study, a 110 kV three-phase double-winding power transformer that experienced a fault due to insufficient short-circuit withstand capability is taken as an example. A refined model of the transformer’s coils is developed, enabling precise calculations of axial and radial forces on each turn of wire within the coil subjected to short-circuit forces. Based on accurate force analysis of each wire, stress curves for various stress indicators in the coil are computed. A comparison with the dismantling phenomena of the transformer indicates that the results of the calculation effectively reflect stress characteristics and weak points in the transformer’s coil components.

2 Refined Method for Calculating Short-Circuit Withstand Capability of Transformers 2.1 Calculation of Leakage Magnetic Field Distribution The validation process is carried out using finite element simulation technology to accurately compute the leakage magnetic field distribution for each individual coil disc. It’s important to consider the maximum operating conditions stipulated by GB1094.5 in terms of the apparent short-circuit capacity and perform validation calculations for the most severe scenarios that the transformer might encounter within its actual operational environment. This study utilizes the internationally recognized finite element simulation commercial software core to ensure the accuracy of the transformer’s leakage magnetic field calculation results. Based on transformer parameter data, the main components of the transformer body such as the core, coils (each coil disc as shown in Fig. 1), clamps, and the tank are parameterized and automatically modeled. This enables the parameterized and automated modeling of the transformer’s short-circuit withstand simulation and automatic solving of transient magnetic field or harmonic leakage magnetic field distribution. This process provides crucial parameters for calculating short-circuit forces (both magnitude and angle), significantly enhancing work efficiency. 2.2 Coil Stress Analysis After obtaining the leakage magnetic field distribution of the coils, automated secondary scripts are employed to extract the magnitude of leakage magnetic fields for each coil

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Fig. 1. Automatic Modeling of Transformer and Leakage Magnetic Field Calculation.

disc and turn. Subsequently, based on the short-circuit current passing through each turn, the radial and axial force distribution for the coils is calculated sequentially. The calculation of short-circuit forces can be performed with precision down to the axial and radial forces on each coil disc and wire. Based on the accurate force analysis of each wire, various stress parameters are computed, including: – Average circumferential tensile/compressive stress within the coil’s circular arrangement – Axial/radial bending stress of the wire – Maximum axial compression force exerted on the winding – Compression stress on the wire’s insulation and radial pad – Compression stress on the paper layer end turns – Compression stress on the helical winding’s protrusion – Compression stress on common compression rings or plates – Tensile stress on pull plates For each of these parameters, both allowable values and calculated values are determined. The calculated results are then compared against the requirements of GB1094.5 and IEC60076-5 standards to assess whether the design meets the specified criteria. By employing the aforementioned validation and calculation methods, the accuracy of leakage magnetic field distribution can be significantly enhanced.

3 Basic Information of the Faulty Transformer On December 28th, 2019, at 10:22 AM, the main transformer unit of a certain 110 kV substation, labeled as #2, experienced heavy gas action. Prior to the tripping of the main transformer, a three-phase short circuit occurred in a 10 kV equipment within a certain user’s facility, leading to a tripping event. Following this, the line automatically reclosed, but it reclosed onto the fault. As a result, the line switch tripped again, followed by the heavy gas action on the main transformer, causing both sides of the main transformer to trip open. The basic information of the faulty transformer is presented in Table 1. The recorded waveform of the transformer fault indicated that 10.8 s before the main transformer fault occurred, a three-phase ground short circuit took place in the 10 kV feeder line connected to the low side of the main transformer. Approximately 0.34 s after the short circuit, the line switch of the feeder line tripped. About 9 s later, the line automatically reclosed onto the fault, but 0.34 s later, the line switch tripped again.

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Table 1. The basic information of the transformer. Index

Value

Transformer Model

SZ10-40000/110

Rated Capacity

40000 MVA

Rated Voltage

110 ± 8 * 1.25%/11 kV

Short-Circuit Impedance

Approximately 10.7% (at rated tap)

Manufacturing Date

August 2007

Around 0.4 s after this, the main transformer experienced heavy gas action, causing both sides of the main transformer to trip open. Both instances of the low-side short circuit on the main transformer lasted for 0.34 s, and the effective value of the short-circuit line current was measured at 12.9 kA.

4 Faulty Transformer Short-Circuit Capability Calculation 4.1 Short-Circuit Current Calculation Considering the actual conditions of the power grid and the existing impedance, the recommended system capacity values from GB1094.5 were used for the calculations. The high-voltage to low-voltage short-circuit mode was considered, and the calculation results are presented in Table 2. Table 2. Short-Circuit Current Calculation. Short-Circuit Mode

Tap

Operating Mode

Impedance Voltage (%)

Peak Fault Current in High-Voltage Coil (A)

Peak Fault Current in Low-Voltage Coil (A)

Three-Phase

1

H-L

11.40

4135.97

26266.91

Three-Phase

9

H-L

10.70

4803.84

27734.98

Three-Phase

17

H-L

10.47

5398.51

28051.49

4.2 Establishment of Short-Circuit Analysis Model Based on the detailed coil design parameters provided by the supplier, a short-circuit analysis model is established, as shown in Fig. 1. The model is designed on a per-disc basis, accurately incorporating the turns count for each disc and the dimensions of the insulation blocks between discs. This meticulous approach fully reflects the arrangement of turns within the coil, ensuring the accuracy of axial force calculations.

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4.2.1 Mode 1: Rated Tap, Without Considering Offset of Coil Reactance Center In this case study, the offset of the coil reactance center is not considered, and the calculation results are presented in Table 3. In the table, Item 1 represents the average circumferential tensile stress in the outer coil; Item 2 represents the average circumferential compressive stress in the inner coil; Item 3 represents the transverse bending stress in the wire within the span between support blocks or insulation blocks; Item 4 represents the axial bending stress in the wire within the span between insulation blocks in the transverse direction; Item 5 represents the maximum axial compressive force on each physical winding related to the inclination of the wire; Item 6 represents the compressive stress on the insulation blocks in the transverse direction; and Item 7 represents the compressive stress on the paper layer winding. Table 3. Coil Short-Circuit Force Calculation Results. Calculation Items (MPa)

Low-Voltage Coil

High-Voltage Coil

Tap-Changing Coil

Calculated Value

Guaranteed value

Calculated Value

Guaranteed value

Calculated Value

Guaranteed value

Item 1

/

/

37.27

135

1.84

135

Item 2

32.08

52.5

/

/

/

/

Item 3

59.79

135

/

/

/

/

Item 4

5.5

135

3.54

135

19.35

135

Item 5

1592.57

1205.6

1561.04

1916.8

85.65

109.6

Item 6

29.29

80

31.02

80

3.98

80

Item 7

19.52

80

20.68

80

2.65

80

Based on the calculation results from Table 3, it is evident that the weak points in the short-circuit strength of the transformer coil are primarily associated with Item 5: the maximum axial compressive force on each physical winding related to the inclination of the wire does not meet the requirements; and considering the failure of a support block, Item 3 exhibits transverse bending stress in the wire within the span between support blocks or insulation blocks exceeding the allowable value. 4.2.2 Mode 2: Rated Tap, Considering Offset of Coil Reactance Center In this case study calculation, considering a downward shift of 5mm in the high-voltage coil’s reactance center, the offset of the reactance center significantly impacts the axial force on the coil and consequently affects the pressure on the insulation blocks. The variations in other forces are minor. The calculation results are presented in Table 4.

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Table 4. Coil Short-Circuit Force Calculation Results. Calculation Items (MPa)

Low-Voltage Coil

High-Voltage Coil

Tap-Changing Coil

Calculated Value

Guaranteed value

Calculated Value

Guaranteed value

Calculated Value

Guaranteed value

Item 5

1853.71

1205.6

1920.45

1916.8

95.85

109.6

Item 6

34.09

80

4.46

80

80

38.53

5 Comparison with Disassembly Phenomenon 5.1 Insufficient Low-Voltage Transverse Bending Strength From the analysis of the calculation results, it is evident that there is insufficient transverse bending strength in the low-voltage coil. Upon inspection, significant distortion in the coil was observed during the core suspension check, which aligns with the calculated findings, as shown in Fig. 2.

Fig. 2. Distortion Phenomenon in the Low-Voltage Coil.

5.2 Insufficient Low-Voltage Tilt Resistance The low-voltage coil is wound with flat wire, which has weaker resistance against tilting. From the calculation analysis, it is evident that the low-voltage coil has insufficient resistance against tilting and collapse due to its design with flat wire. Additionally, the high-voltage coil also exhibits inadequate tilt-collapse resistance, and the situation worsens when the center of inductance is displaced. During the core suspension check, clear indications of multiple instances of tilting and collapse were observed in the lowvoltage coil, as well as localized tilting and collapse in the high-voltage coil (Figs. 3 and 4). The main possible reasons for the analysis period are as follows: 1) The design tolerance is small, and after prolonged operation, insulation accumulation deformation

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Fig. 3. Low-voltage winding tilting diagram and relationship with calculation results.

Fig. 4. High-voltage winding tilting diagram and relationship with calculation results.

may cause axial tightening failure of the coil, potentially leading to increased axial force in the relaxed coil, thereby causing tilting of the low-voltage coil. 2) For this product, after lowering the coil through the pressure cylinder and placing it on a pad, the retaining pin is released to tighten the coil. This method may not effectively control the axial tightening force, which could result in situations where the coil is not tightly compressed.

6 Conclusion This article provides a detailed introduction to the refined verification process of the short-circuit withstand capability of power transformers. Taking a 110 kV three-phase dual-winding power transformer with insufficient short-circuit withstand capability as an example, a refined model for verifying the short-circuit withstand capability of the transformer is established. The model accurately calculates the axial and radial forces on each coil and each wire under different operating conditions. The verification results are compared with the dismantling phenomena of the faulty transformer, indicating that the verification results can effectively reflect the stress characteristics and weak points of various parts of the transformer coils. The conclusions of this article are as follows: (1) Establishing a transformer coil short-circuit withstand capability verification model refined down to individual winding layers allows for an accurate reflection of the axial force distribution within the coils. This supports the optimization of transformer short-circuit withstand capability design and facilitates fault analysis efforts. (2) Looking at the short-circuit verification data from the faulty transformer, it is observed that without considering coil reactance center displacement, the margin for the low-voltage winding’s resistance to tilting is insufficient. When considering

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a coil reactance center displacement of 5 mm, both the low-voltage and high-voltage winding’s resistance to tilting lack sufficient margin. Acknowledgments. This work was funded by the Technology Project of China Southern Power Grid (No. GDKJXM20202005).

References 1. Zhang, F., Yang, S., Zhan, J., et al.: Comprehensive management technology research on short-circuit withstand capability of power transformers. Transformer 57(09), 12–17 (2020) 2. Li, K.: Research on calculation model and evaluation technology of power transformer shortcircuit withstand capability. Thesis from Nanjing University of Aeronautics and Astronautics (2016). (in Chinese) 3. Ding, G., Chen, Q., Tian, Y., et al.: Case analysis of insufficient short-circuit withstand capability of transformers and technical supervision suggestions. Transformer 53(11), 57–60 (2016) 4. Jiang, Y., Wang, Y.: Importance of short-circuit withstand capability testing for transformers. Transformer 11, 26–29 (2008) 5. Chen, L.: A review of coil short-circuit strength calculation for transformers. Transformer 21(05), 1–19 (1974) 6. Li, W.: Research on short-circuit withstand capability verification method for large power transformers. Thesis from North China Electric Power University (2014). (in Chinese) 7. Gao, W.: Research on short-circuit withstand capability verification method for operating power transformers. Thesis from Fuzhou University (2010). (in Chinese) 8. Zhang, M.: Research on short-circuit withstand capability verification for large transformers. Thesis from Huazhong University of Science and Technology (2012). (in Chinese) 9. Dong, C., Li, D., Zhou, J., et al.: Numerical simulation on winding force of 220 kV transformer short-circuit condition. Guangdong Electric Power 31(07), 124–129 (2018) 10. Li, Z., Tan, Y., Li, Y., et al.: Radial stability and cumulative test of transformer windings under short-circuit condition. Electric Power Syst. Res. 217, 1–11 (2023) 11. Wu, T.: Research on dynamic stability of winding short-circuit in power transformers. Thesis from North China Electric Power University (2018). (in Chinese) 12. Yu, S., Fan, G., Li, Z., et al.: Control strategy of thyristor controlled phase shifting transformer to suppress short-circuit current. Guangdong Electric Power 35(06), 41–49 (2022)

Image-Based Modeling and Numerical Simulation Analysis of Transmission Towers Lizhong Qi1 , Yaping Zhang1(B) , Xiaohu Sun1 , Jingguo Rong1 , Weijing Ma1 , and Hui Xiao2 1 State Grid Economic and Technological Research Institute CO, LTD, Beijing 102209, China

[email protected] 2 State Grid Hunan Electric Power Company, Changsha 410004, China

Abstract. Currently, the main challenge in the fine modeling of transmission towers lies in the representation of weak positions, such as node connections and spatial structures. To address this limitation, image recognition technology can be effectively utilized. This paper proposes a method based on 2D image scanning, which allows for the construction of 3D numerical models of transmission towers. Additionally, it enables the automatic establishment of mapping relationships and the conversion from landscape models to numerical 3D models. By integrating CAE simulation technology, the dynamic response of transmission towers under various environmental factors can be simulated. The simulation results demonstrate that the static calculation of the transmission tower model accurately reflects real-world conditions. Accordingly, the research findings presented in this paper can provide valuable technical guidance and insights for power grid construction and maintenance. Keywords: Image Recognition · Image Modeling · Transmission Tower · Numerical Simulation

1 Introduction Digital image recognition, as a new type of technology, can effectively promote the digital transformation of power grid construction. Image recognition technology is mainly used for monitoring and diagnosing the status of power grid equipment in the digital transformation of the power grid. By analyzing the images of the equipment, the status of the equipment can be monitored in real-time, abnormal situations can be identified, and measures can be taken promptly to prevent equipment failures or accidents. Furthermore, image recognition technology can also establish digital twin models of the equipment, conduct simulation analysis on the equipment, explore the operating status of the equipment under different working conditions, and provide technical support for the design, maintenance, and management of power grid equipment. The application of digital twin technology in the field of civil engineering has been extensively researched by domestic and international scholars [1–3]. Alice [4] proposed a decision support © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 710–722, 2024. https://doi.org/10.1007/978-981-97-1072-0_73

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tool using digital twin technology to assist road operators in road inspection, maintenance, and upgrading. Vladimir [5] studied an information model as a data framework tool applied to railway anti-counterfeiting and safety work. Gang Yu [6] established a digital framework based on digital twin technology for tunnel decision-making and maintenance. Therefore, digital twin technology has been widely accepted and applied in various fields. Furthermore, Jia-Xiang Li et al. [7] conducted a study on the failure mechanisms of transmission towers under dynamic and static loads using numerical simulations and experiments. They analyzed the ultimate load capacities, failure modes, and failure sequences of the components. F.G.A. Albermani et al. [8] utilized a nonlinear analysis technique to simulate and evaluate the final structural response of lattice trans-mission towers. Xing Fu et al. [9] and Li Tian et al. [10] analyzed the ultimate performance of transmission towers using a full-scale tower. Other scholars have conducted research on the mechanical response of transmission tower pylons and node connections in various forms [11–15]. These scholars researched and analyzed the structural behavior of transmission towers through either numerical simulations or experimental methods. However, there is a lack of exploration on the establishment of models. Although most numerical and experimental models have guiding significance for practical engineering structures, the process of model development for actual structures remains challenging. Additionally, the extent of damage and mechanical response are still not clear. This paper introduces an innovative approach that combines numerical simulation with image recognition modeling. It presents a transmission tower structural analysis process based on image recognition and CAE (Computer-Aided Engineering) simulation analysis. The process involves extracting model information within the image through software calculations and generating a three-dimensional model suitable for numerical computations through an automatic mapping process. By conducting a comparative analysis of the structural damage characteristics, it becomes evident that this method is effective in enhancing the operation and safety monitoring of transmission towers.

2 Image Recognition Modeling This paper proposes a novel approach to create a 3D computational model from 2D images. The process involves importing captured videos or images into specialized software for analysis. Segmentation is performed on the 2D images to create a 3D model. The physical coordinates of 3D point clouds are then computed from the feature projection points present in the 2D images, leading to the generation of solid 3D models. Once the models are exported, they are utilized for numerical calculations using CAE software. However, it is important to note that when analyzing 2D images with Get3D software, the accumulated errors tend to increase as the number of images grows. This makes manual intervention necessary to fine-tune the digital model after its initial generation. The image recognition modeling method relies on establishing the mapping relationship between 2D images and 3D models. The method is illustrated by conducting a model reconstruction experiment of a 30 cm transmission tower landscape model. The step-by-step process for image modeling is presented below (See Fig. 1).

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Fig. 1. Image recognition modeling flowchart

2.1 Model Capturing The transmission tower model was placed in a well-lit and spacious indoor environment to ensure accurate modeling and avoid potential interference from exposure, noise, and other environmental factors. To capture a comprehensive set of image data required for the experiment, the model was systematically rotated. These images were then imported into the Get3D software for thorough computation and analysis. To guarantee model precision, a 39-s video was subdivided into 770 frames, with a time interval of 0.05 s. The software performed automatic photogrammetric computations on these images, identifying the connection points and feature points for each frame. This process resulted in the creation of a point cloud representing the 3D real-world model and facilitated the calculation of scene coverage for the primary scenes captured in all images. Figure 2(a) visually displays the model scene coverage, with red indicating areas covered by 768 images and blue representing regions with limited coverage from fewer images. Figure 2(b) provides a distribution analysis of the connection point reprojection error. This error quantifies the disparity between the projection and reprojection of real 3D points onto the image plane and accounts for inaccuracies in the homograph matrix calculation and image point measurements. The XY, ZY, and XZ planes illustrate the top, side, and front views, respectively, of the reprojection error points in the reconstructed model, with colors signifying reprojection errors measured in pixels. Figure 2(b) reveals a minimum reprojection error of 0 pixels and a maximum error of 2.972 pixels. To optimize computational efficiency and conserve model memory, non-essential elements of the scene outside the primary model were omitted, retaining only the tiled region encompassing the transmission tower model. During this stage, slight inclinations in the real-world model’s coordinate axis may occur, which can be manually adjusted later for precise alignment.

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Fig. 2. Calculation result of aerial triangle. (a) Model Scene Coverage. (b) Reprojection Error Point Distribution

2.2 Model Repair and Construction Figure 3 presents the image modeling results of the transmission tower. As can be seen from the figure, the surface texture of the real-world model appears rough, making it infeasible to directly establish a numerical model. Therefore, it is necessary to perform segmentation on the main body of the transmission tower and the surrounding objects in the real-world model. This segmentation process facilitates the creation of a computable 3D digital model that can be exported in a file format suitable for editing and modification. To achieve precision refinement and three-dimensional modeling of the main body, modeling software is employed. The resulting digital model, depicted in Fig. 4, consists of line segments that closely resemble the shape of the real-world model and its physical counterpart. In terms of size, the model measures 29.87 cm, with an error of just 0.43% when compared to the actual size of 30 cm. This meticulous process successfully transforms the 2D image information into a highly accurate 3D digital computational model.

Fig. 3. Image modeling rendering. (a) Solid model. (b) Landscape model. (c) Numerical model

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Fig. 4. Three-dimensional digital model

2.3 Numerical Calculation The individualized digital model is imported into modeling software like GID after manual refinement, and this step is essential for facilitating subsequent monitoring, obtaining numerical calculation results, and promptly adjusting the model’s coordinates if needed. Two meshing approaches, segmented meshing or size-based meshing can be utilized for the geometric model consisting of line segments. The selection between these methods depends on the desired precision and model scale since the number and type of mesh elements directly influence the accuracy of the results. Once the meshing process is completed, the mesh file is imported into the CAE simulation software GDEM for conducting relevant operational condition calculations. 2.4 Image Acquisition In the field of building structures, image acquisition has wide applications. It can be utilized for structural monitoring and safety inspection, capturing potential safety issues in real-time. Image acquisition is the process of converting images into digital images through sampling and quantization, and inputting and storing them in a frame buffer. Furthermore, it plays a significant role in structural health monitoring by promptly identifying and addressing issues related to physical structures. The Thousand-Eye Wolf image acquisition system is equipped on the PC side with image processing and display capabilities, as shown in Fig. 5. This system can rapidly capture and store images from cameras and allow for the transmission of image data to a PC via serial communication. The camera in the system converts light into electrical signals through lenses or sensor elements, which are then further transformed into digital signals for processing, analysis, and storage on the PC. The software included in the system allows for analysis of the position, velocity, and acceleration of targets. By integrating with 3D reconstruction techniques, the system enables functionalities such as 3D measurements, attitude angle analysis, and impact point detection. Consequently, this facilitates convenient comparison and validation with numerical simulation results.

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Fig. 5. Acquisition equipment and processing interface

3 Theoretical Formulas 3.1 Image Modeling Principle In the natural world, any scene observed by humans can be seen as a continuous image, with its shape and appearance determined by the colors at various positions in the image [16, 17]. Pixels in an image and vertices and triangles in a 3D model reside in different coordinate systems, and their mapping relationship can be restored through coordinate transformations. The camera model involves four coordinate systems: the pixel plane coordinate system (u, v), the image physical coordinate system (x, y), the camera coordinate system (Xc ,Yc ,Zc ), and the world coordinate system (Xw ,Yw ,Zw ). Under the camera model, spatial coordinates are mapped to points on the image, where the point represents the intersection of the line connecting the spatial point and the projection center on the image plane. By performing transformations among these coordinate systems, the conversion from a point in the world coordinate system to pixel coordinates can be determined. ⎤ ⎡ ⎤⎡ ⎡ ⎤ ⎡ 1 ⎤ Xw  0 u u f000 0 ⎥ R t ⎢ ⎥ ⎢ dx 1 ⎢ Yw ⎥ v0 ⎦⎣ 0 f 0 0 ⎦ T (1) Zc ⎣ v ⎦=⎣ 0 dy 0 1 ⎣ Zw ⎦ 1 0010 0 0 1 1 where, dx, dy represents the horizontal and vertical dimensions of an individual pixel, respectively; u0 , v0 representing the horizontal and vertical coordinates of the principal point on the image plane coordinate system; f represents the camera focal length; R represents a 3 × 3 rotation matrix composed of camera exterior orientation elements, 0T as (0, 0, 0); t as the translation vector representing the camera optical center in the world coordinate system; Xw , Yw , Zw represents the three coordinate values of that point in the world coordinate system; u, v represents the horizontal and vertical coordinates of that point in the pixel plane coordinate system.

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3.2 CDEM The governing equations of the CDEM method are as follows: The ContinuumDiscontinuum Element Method (CDEM) establishes rigorous governing equations based on the Lagrangian energy system [18–20]. It achieves a unified description of continuum and discontinuum behavior by employing the dynamic relaxation method for explicit iteration. By considering block boundaries and internal fractures, CDEM enables simulations from continuous deformation to fracture and subsequent motion, thus analyzing material progressive failure.

 ∂L d ∂L + = Qi (2) dt ∂v ∂ui where, vi , ui as the generalized coordinates; L as the energy of the Lagrangian system; Qi as the work done by non-conservative forces. The dynamic relaxation method is used, eliminating the need to solve the overall stiffness matrix like in traditional finite element methods, resulting in improved computational efficiency. The rod element model, known as the “pile” model, defines the mechanical characteristics of each rod structural unit based on its geometric properties, material properties, and coupled spring properties. In this model, a rod is represented as a straight segment with a uniform symmetrical cross-section between two nodes. Each rod has its independent local coordinate system shown in Fig. 6, which is used to define the material’s interface moments of inertia and applied distributed loads, as well as the forces and moments acting on each rod. The coordinate system for the rod element “pile” is defined as follows: 1. The central axis coincides with the X-axis; 2. The positive direction of the x-axis points from node 1 to node 2; 3. The y-axis is aligned with the projection of Y on the cross-section of the rod. The shear and normal behaviors between rods are fundamentally viscous and frictional, with the coupled spring properties associated with each rod distributed at the rod nodes.

Fig. 6. Definition diagram of member coordinate system

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4 Numerical Model To validate the rationality of the model, the drum-shaped transmission tower model with a height of 29.87 cm, as previously constructed, is uniformly scaled to a height of 87.3 m. The computed results are then compared with conclusions obtained from previous research. By doing so, the influence of model dimensions on simulation outcomes is eliminated. 4.1 Transmission Tower Model Figure 7 shows the design of the transmission tower, which consists of four main parts: the tower head, tower cage, tower body, and cross arms. The tower is divided into several sections, labeled as sections 1 to 7 in the figure, to monitor stress distribution under different loads. Monitoring points, represented by the red-marked points D1 to D7, are used to measure overall displacement and stress distribution at different parts under various loading conditions. The transmission tower has a height of 87.3 m and is composed of 378-line elements and 140 nodes. A structured meshing approach with fixed element sizes (0.02 m) is employed, resulting in a total of 14,132 elements. The Continuum Discontinuum Element Method (CDEM) simulation process automatically handles the connection between the nodes of the tower structure. Furthermore, the node velocities at the base of the tower are constrained to limit displacements and rotations in all three directions.

Fig. 7. Schematic diagram of the transmission tower model. (a) Distribution of transmission tower monitoring points. (b) Transmission tower structure name

4.2 Numerical Simulation The most common failure mode of a transmission tower, a typical high slender space frame structure, is buckling instability. However, the collapse of the tower is not primarily caused by the loss of material strength. Rather, it occurs due to the buckling failure of components when subjected to heavy pressure. Consequently, this paper conducts

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numerical simulations on a transmission tower model to investigate its behavior under gravity load and gravity load with conductor load. The stress distribution of the rods is analyzed under these two loading conditions. Parameter Settings The transmission tower model shown in Fig. 8 is grouped into two types: blue and gray. The blue parts represent the main material, which is made of Q420 steel, while the gray parts represent the auxiliary material, made of Q345 steel. The material parameters for both types of steel are listed in Table 1.

Fig. 8. Three-dimensional view of the transmission tower

Table 1. Material parameters of members Type

Modulus of elasticity (GPa)

Yield strength (MPa)

Tensile strength (MPa)

Compressive strength (MPa)

Q345

206

476

603

603

Q420

206

395

499

499

Results of Gravity Load Analysis. The static analysis of the transmission tower model was performed from 0 to 150 s to reach a stable state in the calculation process. Figure 10 displays the variation of forces in the transmission tower over time. In the initial stage, the forces are transmitted upward through the vertical rods with the bottom nodes of the tower legs fixed. The tower legs experience compressive forces since the entire weight of the tower frame is concentrated at the support points, indicated by negative values. At approximately 10 s, the forces are transmitted to the tower cage section, while the forces at the top of the tower are not prominent due to the lesser number of components at that level. Consequently, the normal forces on the rods gradually decrease as the height increases, and the horizontal bars of the transmission tower, including the tower body and cage, experience tensile forces to maintain stability in the XY plane and limit the vertical rods’ displacement. By 30 s, the forces on the vertical rods and horizontal bars continue to increase, with the effect of the horizontal arms becoming more pronounced. The upper horizontal arms

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function as bridge diagonals, pulling the lower horizontal arms to prevent them from falling, resulting in tension forces. In contrast, the lower horizontal arms experience compressive forces. At 80 s and 150 s, the tower body, cage, and horizontal bars undergo continuous force increment, with the diagonal braces providing support to prevent significant vertical displacement. Overall, it can be observed that the vertical rods, as the main material, bear the primary support function and experience the largest force, reaching up to 200 kN. The horizontal and diagonal rods play auxiliary roles in enhancing structural stability. Although the magnitudes of tensile forces are smaller than those of compressive forces relative to the entire tower frame, they are crucial in preventing displacement and ensuring the transmission tower’s normal operation and structural stability (Fig. 9).

Fig. 9. Normal force change diagram under gravity field of transmission tower

Figure 10(a) illustrates the displacement time history with D1 to D7 representing the vertical displacement time variations (i.e., Z-axis displacement) at different monitoring points within different sections. It can be observed from the graph that the displacements at various sections gradually increase as the height of the tower frame increases. The point at section ➀ located at the bottom of the tower body exhibits the smallest vertical displacement, stabilizing at 1.7 mm. In contrast, the point at section ➆ located at the tower peak shows the largest vertical displacement, stabilizing at 9.1 mm. The vertical displacements of the tower frame experience a noticeable increase within the first 20 s and then stabilize for the remaining time. While the displacement at monitoring point D1 remains stable after reaching its maximum value, the curves for D2 to D7 exhibit distinct fluctuations. This indicates that the tower’s stability process displays a spring-like jumping behavior. After 135 s, the tower frame enters a stable phase, with displacements at all monitoring points reaching their maximum values and remaining relatively constant for the next 15 s. The tower legs experience the highest forces, making them a critical area susceptible to instability and damage, consistent with the structural damage characteristics described by previous research. In Fig. 10(b), the variations in normal forces exhibit a similar trend to the displacement time history. Therefore, the transmission tower model created from

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the 2D image can be used for calculations and to simulate the force conditions of the transmission tower.

Fig. 10. Transmission tower gravity field calculation curve. (a) Time course curve of vertical displacement of each section point of the tower. (b) Time curve of normal force at each section point of the tower

5 Conclusion The feasibility of the proposed method has been validated through modeling experiments on a small-scale transmission tower landscape model and comparing the numerical simulation results under static conditions. This paper presents an innovative method for automatically constructing a computable 3D digital model based on 2D images. Consequently, the following conclusions can be drawn from the research. 1. The establishment of numerical models through image recognition modeling method is efficiently and accurately achieved, by utilizing Get3D software to process 2D images and construct a 3D real-world model. The generated 3D model is then further processed by modeling software to create a computable 3D numerical model. This approach simplifies the process of numerical model creation. 2. This study assists in optimizing the design of practical engineering by analyzing the force and displacement at different nodes in various sections of the transmission tower. The forces at the tower legs are the highest, reaching up to 200 kN under gravity, as they bear the weight of the entire tower body and external loads. In order to ensure the stability of the transmission tower, reinforcement is required at the tower legs. Additionally, the application of wire loads on the cross arms needs optimization to prevent bending failure of components and to maintain the normal operation of the transmission tower. 3. Image recognition modeling enables rapid identification of geometric dimensions and material properties based on actual structures, offering targeted guidance for engineering projects and facilitating macroscopic-scale simulation and prediction of structural behaviors. This novel modeling approach also streamlines the modeling

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process for large-scale structures. However, precision still requires manual refinement, indicating the potential for extensive optimization and further research in the future. Acknowledgements. This research was funded by State Grid limited technology project, grant number 5700-202256191A-1-1-ZN.

References 1. Opoku, D.-G.J., Perera, S., Osei-Kyei, R., Rashidi, M.: Digital twin application in the construction industry: a literature review. J. Build. Eng. 40, 102726 (2021) 2. Katzorke, N., Vinçon, C., Kolar, P., Lasi, H.: Fields of interest and demands for a digital proving ground twin. Transp. Res. Interdisc. Perspect. 18, 100782 (2023) 3. Jiang, F., Ma, L., Broyd, T., Chen, K.: Digital twin and its implementations in the civil engineering sector. Autom. Constr. 130, 103838 (2021) 4. Alice, C., et al.: Towards a digital twin-based intelligent decision support for road maintenance. Transp. Res. Procedia 69, 791–798 (2023) 5. Aksenov, V., Semochkin, A., Bendik, A., Reviakin, A.: Utilizing digital twin for maintaining safe working environment among railway track tamping Brigade. Transp. Res. Procedia 61, 600–608 (2022) 6. Yu, G., Wang, Y., Mao, Z., Hu, M., Sugumaran, V., Wang, Y.K.: A digital twin-based decision analysis framework for operation and maintenance of tunnels. Tunnelling Underground Space Technol. 116, 104125 (2021) 7. Li, J.-X., Zhang, X.-H., McClure, G.: Numerical and full-scale test case studies on post-elastic performance of transmission towers. Eng. Struct. 259, 114133 (2022) 8. Albermani, F.G.A., Kitipornchai, S.: Numerical simulation of structural behaviour of transmission towers. Thin-Walled Struct. 41(2–3), 167–177 (2003) 9. Fu, X., Wang, J., Li, H.-N., Li, J.-X., Yang, L.-D.: Full-scale test and its numerical simulation of a transmission tower under extreme wind loads. J. Wind Eng. Ind. Aerodyn. 190, 119–133 (2019) 10. Tian, L., Pan, H., Ma, R., Zhang, L., Liu, Z.: Full-scale test and numerical failure analysis of a latticed steel tubular transmission tower. Eng. Struct. 208, 109919 (2020) 11. Luo, R., Liu, Y., Zhu, H., Hu, C.: Numerical and experimental investigation of a floating overhead power transmission system. Ocean Eng. 284, 115085 (2023) 12. Liu, W., Zhu, L., Ling, L.-P., Liu, Y.-D., Zhao, G.-Y., Gao, X.-B.: Experimental and numerical study on the ultimate bearing capacity of a K-type tube-gusset plate joint of a steel transmission tower. Case Stud. Constr. Mater. 17, e01523 (2022) 13. Sharaf, H.K., Ishak, M.R., Sapuan, S.M., Yidris, N., Fattahi, A.: Experimental and numerical investigation of the mechanical behavior of full-scale wooden cross arm in the transmission towers in terms of load-deflection test. J. Market. Res. 9(4), 7937–7946 (2020) 14. Kumar Singh, V., Kumar Gautam, A.: Analysis of transmission line tower subjected to wind loading. Mater. Today Proc. 65, 1739–1747 (2022) 15. Singh, R., Samanta, A.: Numerical finite element simulation and structural behaviour of cold-formed steel members. Mater. Today Proc. 65, 3300–3305 (2022) 16. Borji, A.: Qualitative failures of image generation models and their application in detecting deepfakes. Image Vis. Comput. 137, 104771 (2023) 17. Kim, J., Chi, S., Kim, J.: 3D pose estimation and localization of construction equipment from single camera images by virtual model integration. Adv. Eng. Inform. 57, 102092 (2023)

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18. Wang, H., Bai, C., Feng, C., Xue, K., Zhu, X.: An efficient CDEM-based method to calculate full-scale fragment field of warhead. Int. J. Impact Eng. 133, 103331 (2019) 19. Sun, B., et al.: Modeling of projectile penetrating fiber-reinforced concrete via the continuum discontinuum element method. Eng. Fract. Mech. 276, 108887 (2022) 20. Kang, Y., Hou, C., Xu, C., Liu, B., Xiao, J.: Investigation on mechanical behavior of pretensioned bolt in fractured rock mass using Continuum Discontinuum Element Method (CDEM). Eng. Anal. Boundary Elem. 151, 30–40 (2023)

Analysis of Mechanical Properties of Polypropylene Cable Insulation at Different Aging Temperature Fanwu Chu(B) , Tao Xu, Chao Peng, Kai Deng, Mingzhong Xu, and Zhenpeng Zhang China Electric Power Research Institute, Wuhan 430072, China [email protected]

Abstract. This paper aims to explore the influence of different aging temperature on the mechanical properties of polypropylene cable insulation. Through thermal aging on polypropylene cables, the tensile strength and breaking elongation rate were measured to analyze the mechanical properties of polypropylene cable insulation material under different aging temperature. The results show that with the increase of aging temperature, the mechanical properties of polypropylene cable insulation material vary from a certain degree. Moreover, the higher the aging temperature, the faster the mechanical properties decline. The scanning electron microscopy observation shows that the surface of polypropylene material appears laminar structure after thermal aging, which is the degradation and fracture of polypropylene molecule chains and the material has cracks. This study has certain reference significance for the use of polypropylene cables and the estimation of their service life. Keywords: Polypropylene Cable · Thermal Aging · Mechanical Properties

1 Introduction As the infrastructure of the distribution and transmission system, power cables play an increasingly important role in the national economy. Due to its superior heat resistance, dielectric properties, and mechanical properties, cross-linked polyethylene (XLPE) has become the main insulation for power cables currently. However, the production of XLPE insulated cables has high energy consumption, high carbon emissions, long production cycles, and many cross-linking by-products can affect insulation performance. Meanwhile, XLPE insulated cables are allowed to operate at a lower temperature of 90 °C and cannot be recycled but can only be incinerated or buried, which will cause significant environmental pollution in the future [1]. This means that XLPE material is difficult to meet the development needs of high capacity, green and environmentally friendly cables. Polypropylene, as a non-polar thermoplastic insulation material, has many advantages, such as excellent insulation performance, high temperature tolerance level, no cross-linking by-products, and plastic recycling, making it a potential suitable and environmentally friendly cable insulation material [2, 3]. However, due to its stiff texture and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 723–730, 2024. https://doi.org/10.1007/978-981-97-1072-0_74

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high elastic modulus, polypropylene is not resistant to low temperature environments and easy to age [4, 5]. It is difficult to directly use as cable insulation material. Recently, the research focus of domestic and foreign experts on polypropylene cables mainly is on the modification of polypropylene, production and manufacturing methods, and high voltage DC polypropylene cables [6]. The modification methods mainly include blending, co-polymerization, and grafting [7, 8], which have been used to improve the mechanical properties and low-temperature characteristics of polypropylene insulation cables. However, the engineering application of polypropylene cables is still relatively short. During the operation of polypropylene cables, inevitable factors such as high temperature, ultraviolet rays, mechanical stress, and electrical field radiation will inevitably trigger these weak bonds and defects. In addition, high temperature is the main factor leading to polypropylene aging [9, 10]. Thermal aging tests on polypropylene cable insulation were conducted at different temperatures, and the tensile strength and elongation at break of the material at different aging times were measured in this paper. By analyzing the changes in the mechanical properties of polypropylene cable insulation under thermal aging conditions, the aging resistance of polypropylene insulation can be evaluated, which can provide a basis for promoting the large-scale application of polypropylene cables in the future.

2 Sample Preparation and Testing Method 2.1 Preparation of Test Samples and Aging Sampling Settings The experimental samples were taken from a 35 kV polypropylene insulated cable with a specification of PV62-26/35 1 * 400. Dumbbell specimens were prepared according to the provisions of GB/T 2951.11-2008, with a thickness of 1 mm, a length of 75 mm, and an average width of 4mm in the middle. The dumbbell pieces were placed in a naturally ventilated test chamber for aging. Considering that the melting temperature of PP is around 160 °C, accelerated thermal aging tests of dumbbell sheets were conducted at 125 °C, 140 °C, and 155 °C, and sampling tests were conducted according to the time specified in Table 1. 2.2 Testing Method Before aging, the width and minimum thickness of the dumbbell piece are measured and multiplied to obtain the cross-sectional area of the sample. Before the mechanical tensile test, two marking lines with a spacing of 20 mm should be marked in the middle of a set of heat-aged dumbbell pieces, and the tensile failure point should appear in the middle of the marking lines. At room temperature (23 °C ± 5 °C), mechanical tensile tests were performed on the heat-aging PP dumbbell specimens using a computer controlled electromagnetic universal tensile machine with a setting of the tensile rate at 25 mm/min. The tensile strength (MPa) and the fracture elongation (%) of each specimen were calculated, and the changes in tensile strength and fracture elongation of the material before and after ageing were studied.

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Table 1. Aging sampling time setting at 125 °C, 140 °C, and 155 °C Serial Number

Order number of the experimental group placed in the air oven

Order number of the experimental group taken out of the air oven

0

ABCDEFGHI

A0

1

BCDEFGHI

B1

2

CDEFGHIJ1

—

3

CDEFGHIK2

—

4

CDEFGHIJ1 K2 L3

—

5

DEFGHIJ1 K2 L3

C5

6

EFGHIJ1 K2 L3

D6

7

EFGHIJ1 K2 L3

—

8

EFGHIJ1 K2 L3

—

9

FGHIJ1 K2 L3

E9

10

FGHIJ1 K2 L3

F10

σb =

Pb F0

(1)

Here, Pb is the tensile force of the specimen (N), and F0 is the original cross-sectional area of the specimen (mm2). Please translate the above text into English. The fracture elongation is used to measure the ratio of the marked length of the break sample to the original length of the sample when it is stretched to break. δ=

L1 − L0 × 100% L0

(2)

In the formula, the L 1 is the length of the tensioned specimen after it is pulled to break, which is set to 20 mm. The L 0 is the original length of the tensioned specimen, which is set to 20 mm.

3 Experimental Results and Analysis 3.1 The Changes in Mechanical Properties of Polypropylene Cable Insulation Under Different Aging Temperature Figure 1 shows the mechanical tensile test process curves of the five polypropylene insulated dumbbell samples before aging. It can be obtained that the elongation before aging of PP is 698.58%, and the tensile strength is 24.59 MPa. According to the experimental tests, the mechanical properties of polypropylene cable insulation material under the temperature of 125 °C, 140 °C, and 155 °C were obtained, as shown in Tables 2, 3 and 4.

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Fig. 1. Mechanical tensile test of unaged polypropylene insulation

Based on the data in Tables 2, 3 and 4, it can be seen that after the aging at 125 °C for 119 days, the elongation of insulation at 125 °C decreased by 35.04% compared with the initial condition, and the tensile strength decreased by 13.54%. After the aging at 140 °C for 60 days, the elongation of insulation at 140 °C decreased by 26.80%, and the tensile strength decreased by 4.35%, but after 70 days, the insulation sample of polypropylene aging broke down, and the elongation and tensile strength decreased by 100%, as shown in Fig. 2. After the aging at 155 °C for 30 days, the elongation of insulation at 155 °C decreased by 32.34%, and the tensile strength decreased by 21.48%, but after 35 days, the mechanical properties of polypropylene aging had significant declines. Among them, the elongation of insulation at 155 °C decreased by 66.77%, and the tensile strength decreased by 28.06%. When the aging of 155 °C thermal aging continued to 40 days, the insulation sample of polypropylene broke down and the elongation and tensile strength decreased by 100%.

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In addition, the mechanical properties of polypropylene insulation under different temperature will show a certain rebound phenomenon during the aging process. After the rebound phenomenon occurs, its mechanical properties will continue to decline. This may be because polypropylene is a crystalline polymer, and it may undergo a deepening and perfection of crystallization in a certain time under the aging environment. The increase in crystallinity makes PP’s tensile strength and elongation rate have a great extent of increase. During this period, thermo-oxidation degradation occurs on the surface of PP material, and the degree is very weak, still in the initiation stage. Table 2. Mechanical properties of polypropylene insulation under different aging time at 125 °C Aging days

Tensile strength/MPa

Decrease degree

0

24.59

/

7

21.85

11.14%

35

21.12

14.11%

42

21.92

10.88%

63

22.66

7.85%

70

21.93

10.82%

91

22.53

8.38%

119

21.26

13.54%

Table 3. Mechanical properties of polypropylene insulation under different aging time at 140 °C Aging days

Tensile strength/MPa

Decrease degree

0

24.59

/

14

22.99

6.51%

21

24.38

0.87%

30

25.88

−5.25%

60

23.52

4.35%

70

0

100.00%

3.2 The Thermal Aging Mechanism of Polypropylene Cable Insulation The images of polypropylene insulating material under 140 °C after different aging time, shown in Fig. 3, were analyzed using scanning electron microscopy (SEM). As the aging process continues, the volume of spherical particles on the surface of the polypropylene insulation material increases (Fig. 3(d)). After yellowing (Fig. 3(d)), the surface of the

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Table 4. Mechanical properties of polypropylene insulation under different aging time at 155 °C Aging days

Tensile strength/MPa

Decrease degree

0

24.59

/

7

22.72

7.60%

14

24.19

1.63%

21

22.56

8.26%

30

21.48

12.65%

35

17.69

28.06%

40

0

100.00%

(a)70d

(b)74d

(c)78d

Fig. 2. Polypropylene insulating dumbbells under different aging time at 140 °C

material appears layered structures and the roughness is significantly increased. The phenomenon occurred because the internal of the sample underwent oxidation degradation, which caused the breakdown of the polypropylene molecular chain, resulting in cracks and even fractures in the material. The macroscopic manifestation was that the mechanical properties of the polypropylene insulation were significantly decreased.

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(a)0d

(b)30d

(c)60d

(d)78d

729

Fig. 3. The SEM views of polypropylene insulation under different aging time at 140 °C

4 Conclusions The thermal aging tests on polypropylene insulation under different temperature were conducted and mechanical properties tests and scanning electron microscopy observations after thermal aging were performed. In the same aging time, it can be observed that the frequency of cracking elongation and tensile strength can be different in different aging temperature. The higher the temperature, the faster the aging reaction will occur. The more rapid the reaction, the faster the oxidant will be consumed in the material interior, and the more rapid the chemical reactions will be, resulting in a decrease in the mechanical properties of insulators as the temperature increases. As the aging degree continues to increase, the fracture elongation and tensile strength of the polypropylene insulation present a downward trend, but this is not a continuous trend, and there will be a significant rebound. It should be noted that this phenomenon is due to the deepening of crystallization of the polypropylene insulation at the beginning of thermal aging, which is the result of the continuous deepening of crystallization in the high aging temperature. The mechanical properties of the polypropylene insulation have been enhanced. The thermal aging test of polypropylene insulation materials has reached a certain stage, and the aging temperature has not reached the melting point of the material. The

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fracture and oxidation of molecular chains mainly occur in the amorphous region. When some molecular chains in the amorphous region break, the degradation of the amorphous structure can lead to a significant decrease in the tensile strength and elongation at break of polypropylene insulation. Acknowledgment. This job is supported by Innovation Fund Project of China Electric Power Research Institute (SZ83-22-004).

References 1. He, J., Peng, L., Zhou, Y.: Research progress of environment-friendly HVDC power cable insulation materials. High Voltage Eng. 43, 337–343 (2017). (in Chinese) 2. Jana, R.N., Nando, G.B., Khastgir, D.: Compatibilised blends of LDPE and PDMS rubber as effective cable insulants. Plastics Rubber Compos. 32, 11–20 (2003) 3. Esthappan, S.K., Joseph, R.: Resistance to thermal degradation of polypropylene in presence of Nano Zinc Oxide. Prog. Rubber Plastics Recycling Technol. 30, 211–220 (2014) 4. Yoshino, K., Demura, T., Kawahigashi, M., Miyashita, Y., Kurahashi, K.: The application of novel polypropylene to the insulation of electric power cable. IEEJ Trans. Fundam. Mater. 122, 872–879 (2002) 5. Yoshino, K., Demura, T., Kawahigashi, M., Miyashita, Y., Kurahashi, K., Matsuda, Y.: Application of a novel polypropylene to the insulation of an electric power cable. Electr. Eng. Japan 146, 18–26 (2004) 6. Zhao, Y., Liu, G., Su, Y., Dong, X., Wang, D.: Multilayer structure regulation of polypropylene: progress in nucleation and alloying. Polymer Sci. Bull. 6, 35–47 (2021) 7. Fan, L., Li, Q., Yuan, H., Huang, S., He, J.: Influence and mechanism of grafting on thermal oxidative aging of polypropylene. Proc. CSEE 42, 4227–4237 (2022). (in Chinese) 8. Zhao, P., Ouyang, B., Huang, K., Zhao, J., Tian, Y., Chen, H.: Thermal aging characteristics and selection of different modified polypropylene cable insulating materials. High Voltage Eng. 48, 2642–2649 (2022). (in Chinese) 9. Huang, X., Zhang, J., Jiang, P.: Thermoplastic insulation materials for power cables: history and progress. High Voltage Eng. 44(5), 1377–1398 (2018).(in Chinese) 10. Romano, R.S.G., Oliani, W.L., Parra, D.F., Lugao, A.B.: Accelerated environmental degradation of gamma irradiated polypropylene and thermal analysis. J. Thermal Anal. Calorim. 131, 823–828 (2018)

Influences of Secondary Width on Forces and Losses in Linear Induction Motors with Transversally Asymmetric Secondary Dihui Zeng1 , Ke Wang1,2(B) , and Qiongxuan Ge1,2 1 Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering,

Chinese Academy of Sciences, Beijing, People’s Republic of China [email protected] 2 School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, People’s Republic of China

Abstract. Since the secondary structure and relative position to the primary are the important parameters for the traction characteristics in linear induction motors, this study focuses on the influences of transversally asymmetric displacements of the secondary with multiple widths of the non-ferromagnetic and ferromagnetic layers, on motor performances, e.g., electromagnetic forces and secondary induced eddy current, in the linear motors. First, an analysis model to the threedimensional numerical method, which is based on finite element analysis, is built, and the ranges of variable parameters for the simulation are given. Second, the calculation results for electromagnetic forces with the transversal displacement and the transversal width of the two layers of the secondary are shown and analyzed. At last, the relationship between motor parameters of the linear induction motor and the optimal width of the secondary is concluded based on the analysis results. Keywords: Asymmetric secondary · three-dimensional electromagnetic force · single-sided linear induction motors · secondary width · secondary displacement

1 Introduction Since single-sided linear induction motors (SLIMs) have many advantages when used for traction of rail transit vehicles, e.g. strong climbing ability, small tunnel cross-section, and simple traction mechanical structure, the application range of linear induction motors in rail transit is getting wider [1, 2]. When the vehicle driven by the linear induction motor is traveling on a straight track, the motor primary works with a transversally symmetric secondary, as shown in Fig. 1(a); when the vehicle is traveling on a curve, the primary works with an asymmetric secondary [3, 4], as shown in Fig. 1(b), the performance of the motor in the asymmetry changes greatly from the asymmetry, and is related to the secondary width. Therefore, the impact of the asymmetry on motor performance needs to be further studied. In addition, the electromagnetism analysis should consider the end effects, which increases the difficulty of electromagnetic field analysis in the linear motor [5]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 731–739, 2024. https://doi.org/10.1007/978-981-97-1072-0_75

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z Primary

Fz

Secondary

z

Primary

FFz z

Secondary

c1

c1

y c2

x

Center

Fx

(a)

c2

x

y

Fn

Center

Fx

Fy c2

y

y

(b)

Fig. 1. Train driven by LIMs: (a) Train on straight rails (b) Train on curve rails

In [6, 7], a force decoupling control with the novel equivalent circuit considering the asymmetry and the 3D electromagnetic forces, i.e. thrust (x-axis), vertical (z-axis) and transversal forces (y-axis), was proposed. In [8], an electromagnetic forces prediction model based on machine learning algorithm is proposed, which is able to consider the transversal force generated by the asymmetry. In [9], the influences of different secondary widths on motor performance were analyzed using FEM, but the asymmetry was not considered. However, few literatures have analyzed the motor performance changes with different secondary widths under the asymmetry. In this paper, 3D FEM models are firstly established for the two prototypes in order to analyze and calculate the change of electromagnetic forces and induced eddy current. Second, the variation of the 3D electromagnetic forces with the asymmetric displacement is shown for different secondary widths. Third, the secondary induced eddy current in the case of the asymmetry and the influence of its change on the 3D electromagnetic forces are analyzed in detail. Finally, the optimal widths of the secondary conductive layer and the ferromagnetic layer and the significance of this paper are obtained.

2 Methodology The electromagnetic analysis of the motor uses three-dimensional finite element analysis software. First, a three-dimensional analysis model of the motor is established based on the mechanical parameters of the SLIM. Then, based on the actual working conditions of rail transit, the transversal displacement range of primary core of the SLIM is determined and parameterized calculations are set up. 2.1 Analysis Model In Fig. 2(a), it shows the model for 3D finite element method of the SLIM and Cartesian coordinate system: the x-axis (longitudinal axis) represents the mechanical motion

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direction of the motor, which is also the motion direction of traveling wave of magnetic field; the y-axis (transversal axis) represents the normal direction of the core laminations; the z-axis (vertical axis) represents the normal direction of the secondary plate of the motor, which is also the normal direction of the tooth of the primary core. Owing to the interaction between the induced eddy current on the secondary plate and the air-gap magnetic flux, the electromagnetic force is formed, and the force contains three components, which are along the x-, y- and z-axis respectively, then, the three components of the electromagnetic forces are called thrust F x , transversal force F y and vertical force F z , respectively. In Fig. 2(b), the cross-section view shows the motor primary collaborates with a transversally symmetric secondary, which contains the conductive layer (aluminum plate) and ferromagnetic layer (back-iron). If the secondary horizontally (transversally) moves along the y-axis, it will have an asymmetric displacement y, and the widths of conductive layer and ferromagnetic layer are w1 and w2 , respectively. In this paper, it analyzed and compared electromagnetic forces in two prototype SLIMs, as listed in Table 1, under the different conditions, and y, w1 , w2 are defined as variables in the numerical analysis.

1 2

(a)

(b)

Fig. 2. 3D analysis model to FEM: (a) Oblique view (b) Cross-section view

Table 1. Two prototype single-sided LIMs Item

M1

M2

Unit

Number of poles

8

6

Pole pitch

292

250

mm

Length of primary core

2.5

1.7

m

Thickness of back-iron

25

25.4

mm

Thickness of aluminum plate

7

2.5

mm

Width of primary core lamination

300

101

mm (continued)

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M1

M2

Unit

Gap length

11

15

mm

Rated input current

230

200

A

Rated power frequency

35

40

Hz

2.2 Parametric Setup In the electromagnetic FEM calculation, this paper determines different parameter ranges for the two prototype SLIMs. As listed in Table 2, the numerical calculation uses parameterized settings, and the computer automatically calculates the motor performance at each operating point according to the step size and the ranges. Generally, the maximum width of the secondary is 2 to 3 times the width of the primary core, and the minimum width of that is equal to the width of the primary core. Table 2. Parameterized parameters for M1 and M2 No.

Item

Min (mm)

Max (mm)

Step (mm)

y (mm)

M1-1

Conductive layer w1

300

600

10

0–50

Ferromagnetic layer w2

Equal to w1

M1-2

Conductive layer w1

Fixed to 600

Ferromagnetic layer w2

300

600

10

M2-1

Conductive layer w1

101

301

10

Ferromagnetic layer w2

Equal to w1

Conductive layer w1

Fixed to 301

Ferromagnetic layer w2

101

301

10

M2-2

0–50 0–50 0–50

3 Results According to the parameterized settings of the two prototype SLIMs, as listed in Table 2, the calculation results are obtained. For M1, the curves of the electromagnetic forces, i.e. thrust F x , vertical force F z , transversal force F y , with the transversally asymmetric displacement y under different w1 and w2 of secondary plate are shown in Figs. 3 and 4, when I 1 = 230 A, sf = 5 and 35 Hz. For M2, the curves of those are shown in Figs. 5 and 6, when I 1 = 200 A, sf = 5 and 40 Hz. Besides, for F z , the positive force is an attractive force, and the negative is a repulsive force; for F y , the positive force is a centralizing force, and the negative is a decentralizing force.

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3.1 Electromagnetic Forces In Fig. 3(a), the sf (slip-frequency) is low, when w1 ≥ 480 mm, the F x and F z change are insensitive to y; in Fig. 3(b), sf is high, the trend of F y curve is similar to that at low frequency, but the other two electromagnetic forces become insensitive to y when w1 ≥ 540 mm. In Fig. 3, the average values of the three electromagnetic forces do not increase with w1 . In Fig. 4(a), when w2 ≥ 420 mm, the F x changes stably. On the contrary, when w2 ≤ 360 mm, the F z and F y change stably; in Fig. 4(b), under high sf point, only when w2 = 300 mm, the change rate of the three electromagnetic forces are smallest. In Fig. 5(a), when w1 ≤ 151 mm, the F x and F z change are sensitive to y, but the average value of the F x becomes significantly smaller; in Fig. 4(b), when w1 ≥ 201 mm, the change rate of the F x and F z are become smaller. In Fig. 6(a), when w2 ≥ 201 mm, the change rate of the three electromagnetic forces begin to become smaller; in Fig. 6(b), when w2 > 151 mm, the rate of change of the F x begins to become smaller. When w2 < 151 mm, the change rates of the F z and F y begin to become smaller.

Fig. 3. Secondary asymmetric displacement y of M1 v.s. thrust (F x ), vertical force (F z ), transversal force(F y ) with different Al plate widths w1 under (a) sf = 5 Hz (b) sf = 35 Hz

3.2 Eddy Current In order to reduce the length of this paper, this paper only uses the prototype M1 (the primary stack thickness is 300 mm) to demonstrate the change of the secondary eddy current when the secondary is transversally offset. In Fig. 7, y is 10 mm, and the induced eddy current density increases at the reduced portion of the secondary transversal end,

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Fig. 4. Secondary asymmetric displacement y of M1 v.s. thrust (F x ), vertical force (F z ), transversal force (F y ) with different back-iron plate widths w2 under (a) sf = 5 Hz (b) sf = 35 Hz

Fig. 5. Secondary asymmetric displacement y of M2 v.s. thrust (F x ), vertical force (F z ), transversal force (F y ) with different Al plate widths w1 under (a) sf = 5 Hz (b) sf = 40 Hz

especially when the sf increases. In Fig. 8, y is 50 mm, and the induced eddy current density at the reduced portion of the secondary transversal end increases significantly. In Fig. 7, the asymmetry is small at this time, and the y-component in the secondary induced eddy current in the primary-secondary coupling area is less affected; in Fig. 8, due to the large asymmetry, the proportion of the y-component decreases, the proportion

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Fig. 6. Secondary asymmetric displacement y of M2 v.s. thrust (F x ), vertical force (F z ), transversal force (F y ) with different back-iron plate widths w2 under (a) sf = 5 Hz (b) sf = 40 Hz

of x-component increases. In addition, a larger sf increases the y-component of induced eddy currents. According to tensor theory, the F x is directly related to the y-component in the induced eddy current, and the F y is related to the x-component. Since the asymmetry changes the distribution of the x- and y-component in the induced eddy current, the F x and F y in the motor will vary with this phenomenon.

(a)

(b)

Fig. 7. Vector line of eddy currents on the asymmetric secondary (w1 = w2 = 480 mm, y = 10 mm) of M1 when sf = (a) 5 Hz (b) 35 Hz

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(a)

(b)

Fig. 8. Vector line of eddy currents on the asymmetric secondary (w1 = w2 = 480 mm, y = 50 mm) of M1 when sf = (a) 5 Hz (b) 35 Hz

4 Conclusions From the analysis results, the width of aluminum plate w1 and secondary displacement y has a great influence on the electromagnetic forces in the SLIM. Based on the empirical equation, which aims to minimize the fluctuations of three electromagnetic forces with the asymmetry, the optimal w1 (conductive layer) is [10]. w1 = wp +

2τp π

(1)

where wp is the primary core width, τ p is the pole pitch of primary windings. Regarding the ferromagnetic layer width w2 , from the above simulation results, a larger w2 cannot improve the performance of the motor under the asymmetry, and a larger w2 may cause the excitation inductance to be too large and reduce the power factor. Therefore, the recommended value of w2 is τ p + 20–40 mm. In future works, the influence of the secondary width and the degree of the asymmetric displacement on the equivalent parameters in the motors will also be considered, as well as the changes in the air-gap magnetic density and eddy current density distribution. Acknowledgement. This work was partly supported by Beijing Natural Science Foundation (L211011 and 3222060), CAS Project for Young Scientists in Basic Research (YSBR-045).

References 1. Boldea, I.: Linear Electric Machine, Drives, and MAGLEVs Handbook, pp. 55–128. CRC Press, U.K., London (2013) 2. Lv, G., Yan, S., Zeng, D., Zhou, T.: An equivalent circuit of the single-sided linear induction motor considering the discontinuous secondary. IET Elect. Power App. 13(1), 31–37 (2018) 3. Lv, G., Zeng, D., Zhou, T.: A novel M.M.F distribution model for 3-D analysis of linear induction motor with asymmetric cap-secondary for metro. IEEE Trans. Magn. 53(9), Art. ID 8107907 (2017)

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4. Zeng, D., Lv, G., Zhou, T.: Equivalent circuits for single-sided linear induction motors with asymmetric cap-secondary for linear transit. IEEE Trans. Energy Convers. 33(4), 1729–1738 (2018) 5. Gieras, J.F.: Linear Induction Drives, pp. 1–51. Clarendon Press, U.S., New York (1994) 6. Lv, G., Zeng, D., Zhou, T., Degano, M.: A complete equivalent circuit for linear induction motors with laterally asymmetric secondary for urban railway transit. IEEE Trans. Energy Convers. 36(2), 1014–1022 (2020) 7. Zeng, D., Ge, Q., Zhang, L.: Decoupling control of three-dimensional electromagnetic forces in linear induction motors based on novel equivalent circuit. IEICE Electron. Express, Article ID 20-20230219 (2023) 8. Zeng, D., Ge, Q., Degano, M.: A comparison of prediction models with machine learning algorithms for traction characteristics in linear traction induction motors. IEEJ Trans. Elect. Electr. Eng. 17(3), 470–478 (2022) 9. Zeng, D., Wang, K., Ge, Q.: Influences of secondary width on traction characteristics in linear induction motors with flatted composite secondary. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), pp. 496–500 (2023) 10. Nasar, S.A., Boldea, I.: Linear Motion Electric Machines. Wiley-Interscience Publication, Wiley, New York (1976)

Current Characteristics and Overcurrent Suppression in Segmented Power Switching Process of Long Primary Dual Three-Phase Linear Motors Yanfei Li1,2 , Zixin Li1,2 , Cong Zhao1(B) , Fei Xu1,2 , Liming Shi1,2 , and Yaohua Li1,2 1 Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering,

Chinese Academy of Sciences, Beijing, China {liyf,lzx,zhaocong,xufei,limings,yhli}@mail.iee.ac.cn 2 University of Chinese Academy of Sciences, Beijing, China

Abstract. In high-speed applications, thyristor-based switches are usually used to achieve fast power supply switching for segmented linear motors. However, thyristor-based switches can only be turned off at zero-crossing of currents, which makes stator currents seriously asymmetric during switching process, leading overcurrent. In this paper, the current dynamic characteristics of two segments involved in power supply switching are analyzed, and the analytical expressions of the both stators’ currents are also derived during switching process. Furthermore, the required electrical angle to complete turn-off and the maximum current at the converter side are obtained through numerical calculation method. Based on the aforementioned analysis, a power supply switching method is proposed, featuring both fast switching and overcurrent suppression. Simulation results verify the correctness of the presented analysis and the effectiveness of the proposed switching method. Keywords: Segmented Power Supply · Dual Three-Phase Linear Motor · Thyristor-Based Switch · Turn off Process Characteristics · Switching Method · High-Speed Scenarios

1 Introduction Linear motor (LM) can generate linear motion without the help of gear box and does not rely on adhesion between the wheels and the rail. Thus, it has great application potential in railway transport, military aircraft launchers and aerospace area, etc. [1–3]. Among the different possible configurations, the long primary linear motor is suitable for accelerating heavy load to high speed within a short distance [4, 5]. In general, the long primary is divided into several electrically independent segments to reduce power supply capacity and improve the power factor [4–6]. Therefore, with the movement of the mover, it is necessary to achieve power supply switching between the stator segments. In low-speed occasions, the stator segment can be activated 3– 4 τ (τ is the time constant of the one stator segment) before the mover enters [7]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 740–755, 2024. https://doi.org/10.1007/978-981-97-1072-0_76

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However, in ultra-high-speed applications, especially when higher speeds are obtained over short distances, such as electromagnetic aircraft/space launch, it is impossible to provide such a long time for the power supply switching. For example, when the distance between two segments involved in power supply switching is in the order of meters or even decimeters and the mover speed is sonic or supersonic, the time for power supply switching is at most 3–4 ms. Therefore, the thyristor-based switches is usually used to realize the ultra-high speed power supply switching, but the current zero-crossing turnoff characteristic of the thyristor makes the stator current asymmetrical seriously, which leads to overcurrent in the switching process. To solve the above problems, reference [8] and [9] proposed the phase-cutting segment power supply strategy, and the stator windings must be required being delta connected or neutral points of two segments being connected. However, for dual three-phase linear motors, current zero crossing points occur every 30° electrical angle. The time for switching of each phase is as short as 167 μs if the fundamental frequency is 500 Hz. Therefore, it is very difficult to achieve accurate current zero-crossing points detection. This paper studied the current characteristics of the segmented power supply switching process. And a fast and smooth segmented power supply switch method is proposed according to these characteristics. The rest of this paper is organized as follows. In Sect. 2, the operation principle of dual three-phase linear motors with no load is presented. The current dynamic characteristics of the dual three-phase LM is analyzed in detail when the thyristor-based switch is turned off in Sect. 3. And based on analysis results in Sect. 2 and Sect. 3, an novel switching method is proposed aiming at preventing large overcurrent and switching fast in Sect. 4. Simulation results are presented in Sect. 5, and the conclusion remarks are drawn in Sect. 6.

2 Operation Principle of Dual Three-Phase Linear Motors with No Load To provide a clear depiction of the segmented power supply switching issue, Fig. 1 illustrates a simplified example. In Fig. 1 (a), the linear motor comprises a mover and only three stator segments. The mover can be either an induction plate or a permanent magnet, while the stator utilizes dual three-phase windings, which helps in reducing the converter’s single-phase capacity. As shown in Fig. 1 (b), the two sets of three-phase windings are spaced apart by a 30° electric angle [10]. Both windings are star-connected, and their neutral points are independent. When the mover is in the position shown in the Fig. 1 (a), only stator 1 and stator 2 need to be activated, which are powered by converters 1 and 2, respectively. However, converter 1 needs to switch the power supply from stator 1 to stator 3 when the mover leaves the stator 1, thus the segmented power supply switching process occurs. The power supply switching needs to be completed before the mover enters the stator 3, so that the converter 1 is only related to the stator 1 and stator 3 during the switching process, but has nothing to do with the mover, whose energy is completely provided by the converter 2. Therefore, the analysis of power supply switching process is based on the no-load operation principle of the dual three-phase linear motor.

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To simplify the problem, this paper has the following two assumptions: (1) The time of the power supply switching process is short, and it is assumed that the speed of the mover almost remains unchanged during this period. (2) The parameters of the stator winding are balanced, that is, the static end effect of the linear motor is not obvious, which can be achieved as long as the number of stator poles in single segment is greater than 6. o1 uu uv u

o2 ux uy u

u

v

x

y

u1

v1

x1

y1

n11

x3

n12

n21 n22

y3

u3

v3

n31

n32

(a)

(b)

Fig. 1. Schematic of a segmented power supply for a linear motor

To expedite the reaching of the target currents in stator 3, the earliest possible turn-on time occurs when the mover has completely moved away from stator 1. At this point, both stator 3 turns on and stator 1 turns off simultaneously. However, this results in a parallel connection between stator 1 and 3, posing a risk of overcurrent in the converter. To mitigate this overcurrent, a straightforward approach is to reduce the voltage amplitude of converter 1. During the power supply switching process, it is worth considering using open-loop control with reduced voltage amplitude. Nonetheless, closed-loop control must be employed to regulate the currents when the mover is coupled with the stator to maintain thrust stability. However, converter 1 no longer needs to provide thrust for the mover during the switching process. In addition, due to the zero-crossing turn-off characteristic of the thyristor, it is not possible to turn off all six-phase currents of stator 1, denoted as i1 = [iu1 ix1 iv1 iy1 iw1 iz1 ]T , simultaneously, leading to distortion in i1 .

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Consequently, the six-phase currents of stator 3, denoted as i3 = [iu3 ix3 iv3 iy3 iw3 iz3 ]T , are also affected since the closed-loop system’s control objective is the sum of i1 and i3 . This inevitably hinders the quick and stable attainment of the target value for i3 . This mutual interference between i1 and i3 could be eliminated by employing open-loop control during the switching process. It is necessary to understand the states of voltage and current at the moment before the power supply switching, which are the initial conditions of the switching process. It is assumed that i1 were controlled being symmetrical well, which is the condition of thrust stability. In this condition, i1 has the initial values as (1) at t = 0, when turning off of stator 1 begins, ⎧ ⎪ ⎨ iu1 (0) = Im sin(φu0 ), iv1 (0) = Im sin(φu0 − 2π/3) iw1 (0) = Im sin(φu0 + 2π/3), ix1 (0) = Im sin(φu0 − π/6) (1) ⎪ ⎩ iy1 (0) = Im sin(φu0 − 5π/6), iz1 (0) = Im sin(φu0 + π/2) where, I m is the amplitude of the current, and ϕ u0 (ϕ u0 ∈ (0, 2π]) is the initial phase angle of iu1 (t). At t = 0, the six-phase voltages of converter 1, denoted as u = [uu , ux , uv , uy , uw , uz ]T , are also symmetrical for the relationship between u and i1 is as follows at that time, u = Rs i1 + Lpi1

(2)

where, u = [uu , ux , uv , uy , uw , uz ]T , ui (i = u, x, v, y, w, z) is six-phase port voltages of converter, respectively. It should be pointed out that due to the six-phase parameters of the stator winding are balanced, the potential of the o1 and o2 is equal to that of the neutral points ni1 and ni2 (i = 1,2,3,…)which are shown in Fig. 1 (a), respectively. Therefore, the converter port voltage is the stator winding phase voltage. Rs is phase resistance of stator segment, and L is, ⎡

L=

Ls ⎢ √3 ⎢ 2 Lms ⎢ 1 ⎢ − Lms ⎢ √2 ⎢ ⎢ − 23 Lms ⎢ 1 ⎣ − 2 Lms 0

√ 3 2 Lms

Ls 0 −√21 Lms − 23 Lms − 21 Lms

√ ⎤ − 21 Lms − 23 Lms −√21 Lms 0 ⎥ 1 0 − L − 23 Lms −√21 Lms ⎥ √ 2 ms ⎥ 3 3 1 ⎥ L 2 Lms − 2 Lms − 2 Lms ⎥ √ s ⎥ 3 1 Ls 0 − L 2 Lms √ 2 ms ⎥ ⎥ 3 ⎦ −√21 Lms 0 L 2 Lms √ s 3 3 1 − 2 Lms − 2 Lms 2 Lms Ls

(3)

where, L s = L ms + L ls , L ls and L ms are the leakage and the phase magnetizing inductance of stator segment, respectively.

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Based on (1) and (2), the open-loop voltage during the switching process can be represented as u = [u’u , u’x , u’v , u’y , u’w , u’z ]T , as shown in (4). It can be observed from (4) that the phase of the open-loop voltage remains continuous with that of the closed-loop voltage. However, the amplitude of the open-loop voltage is k (0 < k < 1) times the amplitude of the closed-loop voltage at its final moment. Furthermore, the open-loop six-phase voltage remains symmetrical and varies sinusoidally with time.

⎧ 2π ⎪   ⎪ uu = kIm z1 sin(ωs t + ϕu0 + ϕz1 ), uv = kIm z1 sin ωs t + ϕu0 − + ϕz1 ⎪ ⎪ 3 ⎪ ⎪ ⎪

⎨   2π π + ϕz1 , ux = kIm z1 sin ωs t + ϕu0 − + ϕz1 uw = kIm z1 sin ωs t + ϕu0 + ⎪ 3 6 ⎪ ⎪

⎪   ⎪ 5π π ⎪ ⎪ ⎩ uy = kIm z1 sin ωs t + ϕu0 − + ϕz1 , uz = kIm z1 sin ωs t + ϕu0 + + ϕz1 6 2 (4) where, ωs is angular speed of stator current. ϕz1 and z1 are as follows, ⎧ ⎨ ϕz1 = arctan(ωs (3Lms + Lls )/Rs )  ⎩ z1 = ω2 (3Lms + Lls )2 + R2 s s

(5)

When the open-loop voltage is applied to stator 3 with the same parameters as stator 1, the voltage-current relationship of stator 3 is shown in (6). u = Rs i3 + Lpi3 According to (4), (5) and (6), zero-state response of i3 is shown in (7), ⎧ iu3 = kIm sin(ωs t + ϕu0 ) + kIm sin(π + ϕu0 )e−t/τ ⎪ ⎪ ⎪

⎪ ⎪ ⎪ ⎪ iv3 = kIm sin ωs t + ϕu0 − 2π + kIm sin π + ϕu0 − 2π e−t/τ ⎪ ⎪ ⎪ 3 3 ⎪ ⎪

⎪ ⎪ 2π 2π ⎪ ⎪ ⎪ + kI e−t/τ i = kI sin ω t + ϕ + sin π + ϕ + w3 m s u0 m u0 ⎨ 3 3   π π  −t/τ ⎪ ⎪ + k sin π + ϕu0 − e ix3 = kIm sin ωs t + ϕu0 − ⎪ ⎪ 6 6 ⎪ ⎪

⎪ ⎪ 5π 5π −t/τ ⎪ ⎪ + kIm sin π + ϕu0 − e iy3 = kIm sin ωs t + ϕu0 − ⎪ ⎪ ⎪ 6 6 ⎪ ⎪     ⎪ ⎪ ⎩ i = kI sin ω t + ϕ + π + kI sin π + ϕ + π e−t/τ z3 m s u0 m u0 2 2

(6)

(7)

where, τ = (3Lms + Lls )/Rs

(8)

Based on (7), the dynamic characteristics of i3 are analyzed as follows. As can be seen from (7), the sine term of i3 is only different from the target current in amplitude, and the phase is exactly the same. What needs to be stated here is the target value of i3 .

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In the short process of power supply switching, the ωs and thrust reference are almost unchanged, so the target value of i3 is the time continuation of i1 , which is proportional to the first sine term but the amplitude is I m . And the dc attenuation term has an important feature: its phase and amplitude are exactly the same as the sine term at tπ = π/ωs , which is half of the stator current period, if (9) is considered. And (9) is especially correct and reasonable in high-speed situations. e−tπ /τs ≈ 1

(9)

And i3 can be written as in (10) at tπ . Obviously, if k = 0.5, the instantaneous value of i3 is almost exactly the same as the target value at tπ . If i1 has been turned off at tπ , and the overcurrent at the converter side is not very large from t = 0 to t = tπ , then the switching will be completed quickly and smoothly in the tπ . The most surprising thing is that the faster the mover is, the shorter the switching time is.

⎧ 2π ⎪ ⎪ i sin(ω t + ϕ sin ω t + ϕ − ≈ 2kI i ≈ 2kI (t ) ), (t ) u3 π m s π u0 v3 π m s π u0 ⎪ ⎪ 3 ⎪ ⎪ ⎪

⎨  2π π , ix3 (tπ ) ≈ 2kIm sin ωs tπ + ϕu0 − iw3 (tπ ) ≈ 2kIm sin ωs tπ + ϕu0 + ⎪ 3 6 ⎪ ⎪

⎪   ⎪ 5π π ⎪ ⎪ ⎩ iy3 (tπ ) ≈ 2kIm sin ωs tπ + ϕu0 − , iz3 (tπ ) ≈ 2kIm sin ωs tπ + ϕu0 + 6 2 (10) Therefore, the turn-off time of i1 and the overcurrent of the converter during the power supply switching process will be analyzed in the Sect. 3.

3 Characteristics Analysis of Thyristor-Based Switch Turning Off Figure 2 shows the typical steady-state currents waveform of the dual three-phase linearmotor. According to Fig. 2, there exists 12 current zero crossing points (every 30° electrical angle) in a fundamental period. In practice, thyristor-based switches can be turned off at any moment, and the current that is first turned off can be any phase. However, the current characteristics during turn off process are similar as the six-phase currents are always symmetrical. Hence, it is reasonable assume that ϕu0 ∈ (π/6, π/3], indicating that w-phase current is turned off firstly. Under this assumption, the current characteristics are analyzed as follows with thyristor-based switches turned off. When the power supply switching starts, the excitation becomes the open-loop voltage, and the voltage equation is as follows: u = Rs i1 + Lpi1

(11)

where, k = 0.5 for u . And the initial values of the six-phase currents are shown in (1). Due to the turn-off characteristic of the thyristor, the six-phase current will have a symmetrical operation stage during which none of the six-phase windings are opened.

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Fig. 2. Typical steady-state currents waveform of the dual three-phase linear motor.

3.1 Symmetrical Operation Stage Due to the symmetry of voltages, parameters and initial values, the response is also symmetrical. Therefore, i1 has the following relationship at this stage. ⎧ √ √ ⎪ i (t) − iy1 (t) = 3iu1 (t), iy1 (t) − iz1 (t) = 3iv1 (t) ⎪ ⎨ x1 √ √ (12) iz1 (t) − ix1 (t) = 3iw1 (t), iu1 (t) − iw1 (t) = 3ix1 (t) ⎪ √ √ ⎪ ⎩ iv1 (t) − iu1 (t) = 3iy1 (t), iw1 (t) − iv1 (t) = 3iz1 (t) According to (11) and (12), each phase current is decoupled, as described in (15). u = Rs i1 + (3Lms + Lls )pi1

(13)

Then, it is easy to obtain the current expressions at this stage as follows: ⎧ iu1 (t) = 0.5Im sin(ωs t + ϕu0 ) + 0.5 sin(ϕu0 )e−t/τ ⎪ ⎪ ⎪



⎪ ⎪ 2π 2π −t/τ ⎪ ⎪ + 0.5 sin ϕu0 − e iv1 (t) = 0.5Im sin ωs t + ϕu0 − ⎪ ⎪ ⎪ 3 3 ⎪ ⎪

⎪ ⎪ 2π 2π −t/τ ⎪ ⎪ ⎪ iw1 (t) = 0.5Im sin ωs t + ϕu0 + + 0.5Im sin ϕu0 + e ⎨ 3 3     π π −t/τ ⎪ ⎪ + 0.5Im sin ϕu0 − e ix1 (t) = 0.5Im sin ωs t + ϕu0 − ⎪ ⎪ 6 6 ⎪ ⎪

⎪ ⎪ 5π 5π −t/τ ⎪ ⎪ + 0.5I e i sin ω t + ϕ − sin ϕ − = 0.5I (t) ⎪ y1 m s u0 m u0 ⎪ ⎪ 6 6 ⎪ ⎪     ⎪ ⎪ ⎩ i (t) = 0.5I sin ω t + ϕ + π + 0.5I sin ϕ + π e−t/τ z1 m s u0 m u0 2 2

(14)

From (14), iw1 will cross zero first, and the corresponding time will be denoted as t w , as described in (15),

2π 2π −tw /τ + 0.5Im sin ϕu0 + e = 0 (15) iw1 (tw ) = 0.5Im sin ωs tw + ϕu0 + 3 3

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From the moment of t w , the turning-off process has entered one-phase turned off stage. And the current characteristics at that stage will be further analyzed as follows. 3.2 One-Phase Turned Off Stage According to (4) and (11), the following equations for phase u, v and y can be obtained.   ⎧ √  ⎪ 3 3 ⎪  ⎪ uu = Rs iu1 + Lms p iu1 + ix1 − iy1 + Lls piu1 ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ ⎪   √ ⎪ ⎪ ⎪   3 3 ⎪ ⎨ u = Rs iv1 + Lms p iv1 + iy1 − iz1 + Lls piv1 v 2 2 (16) ⎪ √  ⎪ ⎪ ⎪ 3 3 ⎪  ⎪ ⎪ ⎪ uy = Rs iy1 + Lms p 2 (iv1 − iu1 ) + 2 iy1 + Lls piy1 ⎪ ⎪ ⎪ ⎪ √ ⎪ ⎩  uu − uv = − 3uy Then the following differential equations can be obtained,    √ √ Rs  p (iv1 − iu1 ) − 3iy1 = − (iv1 − iu1 ) − 3iy1 Lls

(17)

According to (17) and the values of iu1 , iv1 and iy1 at tw , the relationship between iu1 , iv1 and iy1 at this stage is as follows: iv1 − iu1 =

√ 3iy1

(18)

In fact, this relationship also existed in the symmetrical stage. Moreover, substituting (18) into the third formula of (16), the voltage equation of y-phase is exactly the same as that of the previous stage. Which means iy1 is not affected by the turning-off of phase w, and its current expression is shown in (19).

5π 5π −t/τ + 0.5Im sin ϕu0 − e iy1 (t) = 0.5Im sin ωs t + ϕu0 − (19) 6 6 According to the KCL, iu1 = −iv1 , when the phase w has been turned-off. And from (18), the expressions of iu1 and iv1 at this stage are as follows: √

√

3 3 5π 5π −t/τ Im sin ωs t + ϕu0 − − Im sin ϕu0 − e iu1 = −iv1 = − (20) 4 6 4 6 At this stage, the constraint relationship satisfied by ix1 and iz1 is the line voltage equation,

3 Lms + Lls p(ix1 − iz1 ) ux − uz = Rs (ix1 − iz1 ) + (21) 2

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Based on the values of ix1 and iz1 at tw , following can be derived: √   3z1 π ix1 (t) − iz1 (t) = Im sin ωs t + ϕu0 − + ϕz1 − ϕz2 + Cxz e−(t−tw )/τ2 2z2 3

(22)

where, ⎧ ϕz2 = arctan(ωs (3/2Lms + Lls )/Rs ) ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ ⎪ = ωs2 (3/2Lms + Lls )2 + R2s z ⎪ 2 ⎪ ⎨

3 τ = + L L 2 ms ls /Rs ⎪ ⎪ 2 ⎪ ⎪ ⎪ √ ⎪   ⎪ ⎪ 3z1 π ⎪ ⎩ Cxz = − Im sin ωs tw + ϕu0 − + ϕz1 − ϕz2 2z2 3

(23)

According to KCL, −ix1 (t) − iz1 (t) = iy1 (t)

(24)

So, expressions of ix1 and iz1 at this stage are as follows, according to (19), (22) and (24), ⎧ ⎛ ⎞   1 π 1 π  −t/τ ⎪ ⎪ Im sin ωs t + ϕu0 + + Im sin ϕu0 + e + ⎪ ⎪ ⎟ 1⎜ 2 6 2 6 ⎪ ⎪ ⎟ √ ix1 (t) = ⎜ ⎪   ⎪ ⎝ ⎠ ⎪ 3z1 π 2 ⎪ −(t−t w )/τ2 ⎪ Im sin ωs t + ϕu0 − + ϕz1 − ϕz2 + Cxz e ⎨ 2z2 3 ⎛ ⎞ (25)  1   1 π π  −t/τ ⎪ ⎪ ⎪ I + I e sin ω t + ϕ + sin ϕ + + m s u0 m u0 ⎪ ⎟ ⎪ 1⎜ 2 6 2 6 ⎪ ⎟ ⎪ √ iz1 (t) = ⎜ ⎪   ⎪ ⎝ ⎠ ⎪ 3z1 π 2 −(t−t )/τ ⎪ w 2 ⎩ − Im sin ωs t + ϕu0 − + ϕz1 − ϕz2 − Cxz e 2z2 3 According to the analytical expressions of i1 at this stage, the phase z will be turnedoff after the opening of phase w, which is consistent with the zero-crossing sequence when the six-phase currents are symmetrical. When the iz1 passes through zero, the corresponding time is t z , as described in (26). Then, the turn-off process enters two-phase turned off stage. ⎛ ⎞   1 π 1 π  −tz /τ Im sin ωs tz + ϕu0 + + Im sin ϕu0 + e + ⎟ 1⎜ 2 6 2 6 ⎟=0 √ iz1 (tz ) = ⎜   ⎝ ⎠ 3z1 π 2 −(tz −tw )/τ2 − Im sin ωs tz + ϕu0 − + ϕz1 − ϕz2 − Cxz e 2z2 3 (26)

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3.3 Two-Phase Turned Off Stage According to KVL and KCL, the voltage-current relationship is as follows at this stage.   √ ⎧ 3 3 ⎪ ⎪ iy1 + 2Lls piu1 ⎪ uu − uv = 2Rs iu1 + Lms p 3iu1 − ⎪ ⎪ 2 ⎪ ⎪ ⎪   ⎪ √ ⎨ 3 3   (27) iu1 − 2Lls piy1 ux − uy = −2Rs iy1 + Lms p −3iy1 + ⎪ 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ix1 = −iy1 ⎪ ⎪ ⎩ iu1 = −iv1 Similarly, combining the values of iu1 and iy1 at t z , following can be obtained: ⎛  ⎧ √ ⎪ 6 − 3 3z1 ⎪ ⎪ Im sin ωs t + ϕu0 + ϕz1 − − ⎜ ⎪ ⎪ ⎜ 4z ⎪ 1 3 ⎪ ⎪  ⎪ iu1 (t) = ⎜ √ ⎪ 2⎜ ⎪ ⎝ ⎪ 6 + 3 3z1 ⎪ ⎪ − Im sin ωs t + ϕu0 + ϕz1 − ⎪ ⎪ 4z4 ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ iv1 (t) = −iu1 (t) ⎛  √ ⎪ ⎪ 6 − 3 3z1 ⎪ ⎪ Im sin ωs t + ϕu0 + ϕz1 − ⎪ ⎜− ⎪ ⎪ ⎜ 4z3 ⎪ ⎪ iy1 (t) = 1 ⎜  ⎪ √ ⎪ ⎪ 2⎜ ⎪ ⎝ 6 + 3 3z1 ⎪ ⎪ ⎪ + Im sin ωs t + ϕu0 + ϕz1 − ⎪ ⎪ 4z ⎪ 4 ⎪ ⎪ ⎩ ix1 (t) = −iy1 (t)

⎞

5π − ϕz3 + Cu+y e−(t−tz )/τ3 ⎟ ⎟ 12 ⎟ ⎟

⎠ 11π −(t−t )/τ z 4 − ϕz4 + Cu−y e 12 ⎞

5π − ϕz3 + Cu+y e−(t−tz )/τ3 ⎟ ⎟ 12 ⎟ ⎟

⎠ 11π −(t−t )/τ z 4 − ϕz4 − Cu−y e 12

(28)

where,   ⎧ 2 2     √ √ ⎪   ⎪ 6 − 3 6+3 3 3 ⎪ ⎪ 2 2, z = 2 ⎪ z L L = ω + L + R ω + L + R2s 3 ms 4 ms ls ls ⎪ s s s ⎪ 4 4 ⎪ ⎪ ⎪ ⎪     ⎪ √ √ ⎪ ⎪ 6−3 3 6+3 3 ⎪ ⎪ ⎪ τ3 = Lms + Lls /Rs , τ4 = Lms + Lls /Rs ⎪ ⎪ 4 4 ⎪ ⎪ ⎪ ⎪       √ √ ⎪ ⎪ ⎪ ωs 6 − 3 3 ωs 6 + 3 3 ⎪ ⎪ ϕz3 = arctan Lms + Lls , ϕz4 = arctan Lms + Lls ⎪ ⎪ ⎪ Rs 4 Rs 4 ⎪ ⎪ ⎪ ⎨  √ 

1 1 3 5π 5π −tz /τ Im sin ωs tz + φu0 − + Im sin φu0 − e Cu+y = 1 − ⎪ ⎪ ⎪ 2 2 6 2 6 ⎪ ⎪ ⎪  ⎪ √

⎪ ⎪ ⎪ 6 − 3 3z1 5π ⎪ ⎪+ − φz3 Im sin ωs tz + φu0 + φz1 − ⎪ ⎪ ⎪ 4z3 12 ⎪ ⎪  ⎪ √ 

⎪ ⎪ ⎪ 1 1 3 5π 5π −tz /τ ⎪ ⎪ I + I e = − 1 + sin ω t + φ − sin φ − C u−y m s z u0 m u0 ⎪ ⎪ 2 2 6 2 6 ⎪ ⎪ ⎪ ⎪ ⎪  √

⎪ ⎪ ⎪ 6 + 3 3z1 11π ⎪ ⎩+ − φz4 Im sin ωs tz + φu0 + φz1 − 4z4 12

(29)

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According to the analytical expression of currents in the two-phase turned off stage, the iu1 and iv1 will cross zero at the same time after the turning-off of phase z. And when the two pass through zero, the corresponding time is t u , as described in (30). Then, the turn-off process enters four-phase turned off stage. iu1 (tu ) ⎛

 √ 6 − 3 3z1 Im sin ωs tu + ϕu0 + ϕz1 − ⎜− 4z3 1⎜ = ⎜  √ 2⎜ ⎝ 6 + 3 3z1 − Im sin ωs tu + ϕu0 + ϕz1 − 4z4

⎞

5π − ϕz3 + Cu+y e−(tu −tz )/τ3 ⎟ ⎟ 12 ⎟=0 ⎟

⎠ 11π −(tu −tz )/τ4 − ϕz4 + Cu−y e 12

(30)

3.4 Four-Phase Turned Off Stage At the four-phase turned-off stage, there is only one line voltage equation as follows, uy − ux = 2Rs iy1 + (3Lms + 2Lls )piy1

(31)

The analytical expression of iy1 can be obtained according to (31) and the value of iy1 at t u : √ iy1 (t) = −

3z1 Im sin(ωs t + ϕu0 + ϕz1 − ϕz2 ) + Cy e−(t−tu )/τ2 4z2

(32)

where, √

3z1 Cy = Im sin(ωs tu + ϕu0 + ϕz1 − ϕz2 ) 4z2  √

6 + 3 3z1 11π − ϕz4 − Cu−y e−(tu −tz )/τ4 Im sin ωs tu + ϕu0 + ϕz1 − + 4z4 12

(33)

when iy1 passes through zero, the corresponding time is ty , as described in (34). At that time, the whole turn-off process is over. √     3z1 iy1 ty = − Im sin ωs ty + ϕu0 + ϕz1 − ϕz2 + Cy e−(ty −tu )/τ2 = 0 (34) 4z2 Given ϕu0 and angular speed ωs , t y can be obtained by numerically solving the nonlinear Eqs. (15), (26), (30) and (34). And the electric angle required for the turn-off of stator 1, denoted as θ y , can be obtained by multiplying the ty by the angular speed ωs . Figure 3 (a) shows the values of θ y at different frequencies and ϕ u0 with the segment parameters shown in Table 1. As shown in Fig. 3 (a), in the case of a certain frequency, with the increase of ϕ u0 , the θ y becomes smaller and smaller. In the case of a certain ϕ u0 , the higher the frequency, the greater the θ y required. But the θ y will not exceed 180° even if the frequency is as high as 1000 Hz, which means i1 has been turned off at tπ .

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Table 1. Parameters of Stator segment Segment parameters

Rs

L ls

L ms

Values

90 m

100 μH

100 μH

Furthermore, based on the analytical expressions of i1 and i3 , the maximum instantaneous current of the converter can be obtained. As shown in Fig. 3 (b), under the same parameters in Table 1, the higher the frequency is, the closer the ϕ u0 is to the π/3, which is the right end of the interval (π/6,π/3], and the greater the maximum instantaneous current of the converter is. But it does not exceed 1.15 although the frequency and ϕ u0 vary in a large range.

(a)

(b)

Fig. 3. Numerical calculation results based on the analytical expressions. (a) θ y at different frequencies and ϕ u0 , (b) Maximum converter-side current for different frequencies and ϕ u0.

4 Proposed Segmented Power supply Switching Strategy According to the analysis aforementioned, a power supply switching strategy is proposed, and the block diagram is presented in Fig. 4. The indirect field-oriented control (IFOC) is utilized during steady-state operations, and it should be changed to open-loop control when power supply switching needs to be completed.

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Fig. 4. The power supply switching control diagram of the converter 1.

For simplicity, taking the power supply switching between the stator 1 and the stator 3 as an example to explain the implementation of the proposed method. As shown in Fig. 4, when the secondary starts to move from the stator 1, the IFOC is enabled, that is the d-q axis currents adopt closed-loop control mode. Simultaneously, the outputs of two PI controllers (Ud and Uq) are recorded in real time by the ‘storage_d’ and the ‘storage_q’ respectively, and are updated once in each control cycle. When the system detects that the mover has just left the stator 1, the IFOC is not enabled, and the proposed power supply switching method should be adopted. It needs to be pointed out that the following two steps should be implemented simultaneously: (1) Turn off the stator 1 and turn on the stator 3; (2) Ud and Uq are taken from the recorded value, and only half of the recorded value are applied to the motor. After half of the stator current period, the control method changes from the openloop control to the IFOC. The recorded values in the ‘storage_d’ and the ‘storage_q’ are assigned to the integrators of the two PI controllers respectively to achieve better dynamic performance.

5 Simulation Result The proposed segmented power switching strategy was verified using simulations. In these simulations, the fundamental frequency of stator current is 500 Hz, and the parameters of the segmented stator are shown in Table 1. Figure 5(a) shows the simulation results of power supply switching between stator 1 and stator 3 using the proposed method. Figure 5(b) is the simulation results with the closed-loop method, different from the proposed method, there is just no open-loop voltage part. It is obvious that the proposed method can suppress the overcurrent from 30.30% to 13.73%, which is within theoretical result 15% obtained in Sect. 3.

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Fig. 5. Simulation results. (a) proposed method, (b) closed-loop method.

In Fig. 5 (a), the shadow part covers the time when the open-loop voltage has been applied, thus the time span is half of the stator current period. It can be seen that the sixphase currents of stator 1 have been turned at the end of open-loop process. In addition, the error of the current could be quickly eliminated, although at that time which was not the ideal zero but 10%, for the dc term had actually attenuated at that time. For comparison, the shadow parts of the same size and position are drawn in Fig. 5(b). It can be seen that the six-phase current of stator 1 has also been turned off within half of the stator current period, but the error of current is about 15% at that time. Moreover, in the following time, the current error increases and then decreases gradually due to the accumulated historical error of the integrators of PI controller (the area of the error in the figure) are too much. Therefore, the current settling times of closed-loop method is longer than those of the proposed method as shown in Table 2. And the latter are almost equal to half of the stator current period, which is consistent with the theoretical results of Sects. 2 and 3.

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Method

Current index in power supply switching process Overcurrent

Settling time of id (±2%)

Settling time of iq (±2%)

Close loop method

30.30%

5.01 ms

2.01 ms

Proposed method

13.73%

1.21 ms

1.11 ms

6 Conclusion In this paper, a segmented power supply switching strategy of dual three-phase linear induction motor using thyristor-based switches is proposed. The switching current consists of turn-on current and turn-off current. For the turn-on current, the instantaneous value of which is close to the reference value in half of the stator current period, when the open-loop voltage whose amplitude is half of that before the switching is applied in the switching process. And when the open-loop voltage is supplied, the turn-off sixphase currents have crossed zero within half a cycle. In addition, the overcurrent of the converter current is less than 15% during this process. Finally, the simulation results verify the effectiveness of the proposed switching method. Acknowledgment. The authors thank the Youth Innovation Promotion Association CAS (2022137) and the Institute of Electrical Engineering, CAS (E155320101) for financial support.

References 1. Palka, R., Woronowicz, K.: Linear induction motors in transportation systems. Energies Rev. 14(9), Article no. 2549 (2021) 2. Ma, W., Lu, J.: Thinking and study of electromagnetic launch technology. IEEE Trans. Plasma Sci. 45(7), 1071–1077 (2017) 3. McNab, I.R.: Electromagnetic space launch considerations. IEEE Trans. Plasma Sci. 46(10), 3628–3633 (2018) 4. Zhang, M., Shi, L.: Modeling and cooperative control of segmented long primary double-sided linear induction motor. IEEE Trans. Industr. Electron. 70(2), 1706–1716 (2023) 5. Zhang, M., Shi, L., Guo, K., et al.: Modeling and analysis of segmented long primary doublesided linear induction motor. Trans. China Electrotech. Soc. 36(11), 2344–2354 (2021). (in Chinese) 6. Leidhold, R., Mutschler, P.: Speed sensorless control of a long-stator linear synchronous motor arranged in multiple segments. IEEE Trans. Industr. Electron. 54(6), 3246–3254 (2007) 7. Li, L.Y., Zhu, H., Ma, M.N., Chan, C.C.: Research on power supply strategies of long stroke primary segmented permanent magnet linear synchronous motor. Appl. Mech. Mater. 416– 417, 209–214 (2013) 8. Sepe Jr, R.B.: Block Switching Transient Minimization for Linear Motors and Inductive Loads, United States Patent Appl. 20080284360 (2008)

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9. Liu, J., Shi, L., Guo, K., Zhou, S., Xu, F., Fan, E.: A low current fluctuation switching strategy for long primary linear motors. In: 2021 13th International Symposium on Linear Drives for Industry Applications (LDIA), pp. 1–4, 1–3 July 2021 10. Yifan, Z., Lipo, T.A.: Space vector PWM control of dual three-phase induction machine using vector space decomposition. IEEE Trans. Ind. Appl. 31(5), 1100–1109 (1995)

Short-Term Wind Power Prediction Based on AVMD-SMA-LSSVM Combined Model Dan Zhang1(B) , Pijiang Zeng1 , Changsheng He2 , Xiongbiao Wan2 , Botao Shi3 , and Yiming Han3 1 Yunnan Power Grid Co., LTD., Kunming 650051, China

[email protected]

2 Yunnan Electric Power Experimental Research Institute (Group) Co., LTD., Kunming 650217,

China 3 Faculty of Electric Power Engineering, Kunming University of Science and Technology,

Kunming 650500, China

Abstract. This research proposes a combined wind power prediction model to increase wind power forecast accuracy and energy consumption efficiency. To begin, the adaptive variational mode decomposition (AVMD) method is used to deconstruct the wind power signal at various scales and create a number of sub sequences. Second, a prediction model for subsequences is built using the slime mold algorithm (SMA) and least squares support vector machine (LSSVM) parameters that are adaptively determined. Finally, the subsequence prediction values are weighted and fused to get the final wind power forecast value. Using the AVMD approach to minimize non-stationary and noise interference in signals and increase subsequence prediction accuracy. Developing a novel intelligent optimization technique that combines SMA and LSSVM to eliminate mistakes caused by human parameter setup. Weighted fusion is used to subsequence prediction results, completely using the prediction information of each subsequence to increase the stability and reliability of the prediction outcomes. The proposed model has greater prediction accuracy and reduced prediction error, as demonstrated by example analysis in this article. Keywords: Wind power prediction · Adaptive variational modal decomposition · Slime mold algorithm · Least squares support vector machine

1 Introduction Wind power is a clean energy source that converts wind energy into electricity [1]. It has the benefit of being low in carbon and emitting no pollution, and it is a key component of future energy. However, wind power production is also hampered by wind speed and force instabilities, which complicates wind farm operation and management. As a result, precise wind power generation forecast is critical for improving wind farm efficiency and safety, reducing conflict between wind power and the power grid, and optimizing wind farm scheduling and maintenance. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 756–765, 2024. https://doi.org/10.1007/978-981-97-1072-0_77

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Scholars have suggested a range of ways to handle the problem of wind power generation prediction, which may be roughly classified into physical methods [2] and statistical methods [3]. Physical approaches, which are based on numerical weather prediction [4] (NWP) data, explain the process of transforming wind energy into electricity through the development of complicated physical models. Statistical approaches are built on a data-driven notion of fitting the link between historical data and wind power generation [5]. Statistical approaches are often faster and more accurate than physical methods, although concerns such as data quality and feature selection must be taken into account [6]. With the advancement of artificial intelligence (AI) technology in recent years, machine learning and deep learning approaches have become widely applied in wind power forecast [7]. Literature [8] reported Support Vector Machine (SVM) prediction approach in short-term wind power prediction based on machine learning algorithms, which employs ensemble empirical modal decomposition methodology to deconstruct and forecast wind power sequences, enhancing prediction accuracy. Literature [9] proposed a novel LSSVM model for wind power prediction that decreases data complexity while improving forecast accuracy. Furthermore, signal decomposition methods are frequently used to deconstruct the original data into a number of sub-modalities in order to decrease the non-stationarity of the original data. As an adaptive and totally non-recursive decomposition approach, Variational Mode Decomposition (VMD) is more noise resistant. Literature [10] solved the empirical modal decomposition (EMD) modal aliasing problem by using VMD to eliminate the wind power sequence noise and mining the main features of the original sequence. However, VMD requires that the number of decomposition layers be pre-set, and this parameter has an effect on the decomposition outcomes. Literature [11] presented a whale optimisation technique to adaptively identify the appropriate VMD decomposition parameters, hence resolving the problem of VMD over- or under-decomposition. A wind power prediction model combining adaptive variational modal decomposition, genetic algorithm, slime mould algorithm, and LSSVM is proposed in this research. The model first decomposes the wind power signal into multiple sub-sequences, then predicts each sub-sequence with different methods, and finally fuses the prediction results in a weighted manner to obtain the final value. Example analysis shows that the model has high accuracy and low error.

2 Wind Power Signal Processing 2.1 Variational Modal Decomposition VMD is a non-recursive approach for breaking down a time series y(t) into K modes {uk (t)}K k=1 . Each mode uk (t) has a centre frequency ωk , and the goal of VMD is to minimize the sum of each mode’s predicted bandwidths. To estimate the bandwidth of all modes, the following variational optimisation model is developed: ⎧  ⎨ min K ∂t (δ(t) + j/(π t)) ∗ uk (t) e−jωk t 2 k=1 2 {uk },{wk } (1) ⎩ s.t. K u (t) = y(t) k k=1

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where * denotes the convolution; {uk } = {uk (t)}K k=1 denotes the set of decomposed modal signals; {wk } = {wk (t)}K signifies the collection of center frequencies; δ(t) is k=1 the Dirac function, the Hilbert transform of (δ(t)+j/(π t)∗uk (t) is uk (t), and δt signifies the bias operator with respect to t, j2 = −1. To solve the aforementioned optimisation issue, first create the augmented Lagrangian function as indicated in Eq. (2). L({uk }, {ωk }, λ) 2 K      =α ∂t (δ(t) + j/(π t)) ∗ uk (t) e−jωk t  k=1 2  2

 K K     +y(t) − uk (t) + λ(t), y(t) − uk (t) k=1

(2)

k=1

2

where the quadratic penalty factor is α and α > 0; ., . is the function inner product operator; λ is the Lagrange factor. ADMM is used to update ukn+1 , ωkn+1 and λn+1 alternately. When {uk }, {wk } and λ are provided, the Fourier transform of ukn+1 (t) is updated first as shown in Eq. (3).  ˆ uˆ i (ω) + λ(ω)/2 yˆ (ω) − uˆ kn+1 (ω) = Update centre frequency: ωkn+1

i=k

n+1 2 ∫+∞ ˆ u ω (ω) dω 0 k = 2 n+1 ∫+∞ ˆ k (ω) d ω 0 u

Update Lagrange multipliers:

K ˆλn+1 (ω) = λˆ n (ω) + τ yˆ (ω) −

uˆ n+1 (ω) k=1 k

n+1

n



(3)

1 + 2α(ω − ωk )2

(4)

 (5)



where u k (ω), u i (ω), y(ω) and λ(ω) are the Fourier transforms of ukn+1 (ω), uin (ω), y(ω) and λ(ω) respectively; τ is the noise tolerance and τ > 0. Finally, the iteration is terminated when the iteration termination condition Eq. (6) is satisfied.    n+1 n 2 u   k − uk  2 < e (e > 0) (6)  n 2   k u  k 2

To accomplish signal-noise separation, the VMD method decomposes the input signal into many modal variables, including signal and noise components. The VMD principle analysis exposes two important factors in the solution process: the decomposition factor K and the penalty factor, both of which have a direct impact on the decomposition effect of the signal. In this study, the evolutionary algorithm is used to enhance and optimize the VMD technique, and the optimal combination of parameters is chosen adaptively dependent on the kind of input signal.

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2.2 Adaptive Variational Modal Decomposition Based on Genetic Algorithm Optimisation The signal processing impact is affected by K and α in the VMD method. K is too large to over-decompose the signal and lose features, K is too little to not decompose enough and make distinguishing the signal from the noise difficult. α is too vast for the signal to be lost in the frequency spectrum; on the contrary, the information is unnecessary. Sample entropy (SampEn) is employed as the fitness function of evolutionary algorithms in this study [12]. It is a more accurate estimate of entropy for measuring time series complexity. The lower the sample entropy, the more concentrated the spectrum and the greater the sequence self-similarity; the more intricate the sequence and the wider the spectrum, the higher the sample entropy. SampEn’s algorithm is as follows: To begin, the signal X is specified as an N-length time series as follows: X = {x1 , x2 , ...xN }

(7)

(1) As an m-dimensional vector, construct the signal X as follows: X (i) = {xi , xi+1 , ...xi+m−1 }

(8)

where, i = 1, 2, 3, ..., N − m + 1, m is the window length. (2) Define the distance parameter d [Xi , Xj ] to denote the maximum distance difference between Xi and Xj as follows: (9) d [Xi , Xj ] = maxk∈(0,m−1) xi+k − xj+k (3) Set the similarity tolerance level r, count the d [Xi , Xj ] < r, and construct a ratio N − m based on the total number of vectors.   Bim (r) = 1/(N − m)num d [Xi , Xj ] < r (10) (4) For all r, the average of all proportion statistics: Bm (r) = 1/(N − m + 1)

N −m+1 i=1

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(11)

(5) Steps (1) through (4) are repeated with m increased (m = m + 1). (6) Determine the sample entropy of this signal sequence using the following formula: SampEn = − ln[Bm+1 (r)/Bm (r)]

(12)

In summary, the sample entropy of each component sequence decomposed by the VMD algorithm for different K and α is obtained. Finally, the decomposition method with the smallest chromosome and the smallest average fitness value is sought. Meanwhile, the optimal K and α are obtained by comparison (Fig. 1).

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[K , ]

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3 AVMD-SMA-LSSVM Combined Prediction Model 3.1 Slime Mould Algorithm Slime mould algorithm [13] is a meta-heuristic optimization method introduced by Li Shimin et al. in 2020 that is based on slime mould foraging behavior. Approaching the meal, surrounding the food, and seizing the food are the three steps of the SMA algorithm. Each person in the population represents a potential solution in the SMA algorithm, and the behavior of slime molds simulates the migration, aggregation, and dispersion processes of people. When looking for food, the slime mold calculates the weight of each location based on the fitness function of the current position, and the individual chooses the new position depending on the weight. 3.2 Least Squares Support Vector Machine Model Least Squares Support Vector Machine is a machine learning approach that may be used for classification and regression and is based on statistical learning theory. It improves on the traditional support vector machine by replacing inequality constraints with equality constraints that can be solved by a system of linear equations. y(x) = ωT ϕ(x) + b

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As demonstrated in Eq. (14), the goal function and limitations of the least squares support vector machine. ⎧ N ⎨ min J (w, b, e) = 1 ωT ω + 1 γ e2 i=1 i w,b,e 2 2 (14) ⎩ s.t.yi = ωT ϕ(xi ) + b + ei , i = 1, 2, 3, · · ·, n where, γ is the penalty factor; ei is the variable for slack. The optimisation problem is then transformed into a Lagrangian function to be solved. The expression is as follows: L(ω, b, e, λ) = J (ω, b, e)   N λi ωT ϕ(xi ) + b + ei − yi −

(15)

i=1

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Fig. 2. AVMD-SMA-LSSVM prediction model structure

3.4 Indicators for Model Evaluation Four regularly used error metrics will be selected for examination in this research in order to examine the prediction accuracy of the algorithms described in this work and the comparison algorithms, and the validity of the models will be validated by comparing the magnitude of the errors. As assessment measures, they are mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and coefficient of determination (R2 ). The formulas for each evaluation index are as follows: 1 n |ˆyi − yi | EMAE = (18) i=1 n 1 n EMSE = (19) (ˆyi − yi )2 i=1 n  1 n (ˆyi − yi )2 (20) ERMSE = i=1 n 2 n yi − yi ) i=1 (ˆ ER2 = 1 − n (21) yi − yi )2 i=1 (ˆ where n is the number of sampling points; yi and yˆ i are the predicted and real values of the i wind power point in the test set, respectively.

4 Example and Result Analysis The generating power data of a wind farm in the north in 2020 is used as an example in this article. And the combined AVMD-SMA-LSSVM model is used to make a prediction and compared with the SMA-LSSVM model.

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In order to accurately assess the model performance, the annual data is divided into quarters, and the first 75% of the data in each quarter is the training set, and the last 25% is the test set. The experimental results show that the combined model proposed in this paper is superior in wind power prediction. When processing the data, the time dimension is selected as 15 min, which takes into account the influence of historical data and avoids the contribution of too far historical data being too small. In addition, the time dimension of 15 min retains more data features, which is conducive to the modal decomposition mapping out the historical relationship between the training data and the test data, and improving the prediction accuracy. In the experiment, abnormal data were eliminated and filled to ensure the accuracy of the experimental results. Therefore, the first 15 days of data in February, May, August and November, the typical months of the four seasons, are selected as the experimental data. 60

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In this paper, each IMF component obtained by decomposing with GA-VMD adaptive model and substituting it into the optimised combinatorial model training, each IMF can be predicted more accurately than the original sequence. In order to test the effect of the algorithm, this paper divides the original dataset into nine subsets and processes them with the GA-VMD adaptive optimisation algorithm to build the SMA-LSSVM and AVMD-SMA-LSSVM prediction models respectively. In the paper, the typical months of spring, summer, autumn and winter are selected for simulation verification, and the simulation results are shown in Fig. 3. Figure 3 shows that the combined AVMD-SMA-LSSVM model outperforms the SMA-LSSVM model and is able to adaptively track the changes during wind decay.

Fig. 4. Error comparison under different prediction models

In this paper, MAE, MSE, RMSE and R2 evaluation metrics are chosen to evaluate the errors of SMA-LSSVM and AVMD-SMA-LSSVM combination prediction models under training and prediction sets. As shown in Fig. 4, the data of typical month February is selected to analyse the error comparison under different prediction models. According to the comparison of prediction indexes, it can be seen that after the AVMDSMA-LSSVM combination prediction model is obviously better than the SMA-LSSVM prediction model, and the overall prediction accuracy is the highest.

5 Conclusion To address the issue of a lack of wind farm data in cluster wind farms, which makes accurate short-term wind power prediction more difficult, this paper proposes a short-term wind power prediction method based on the combined AVMD-SMA-LSSVM model using historical data with short-term wind farms, and verifies the prediction method through case analysis. The following are the primary conclusions: (1) The AVMD approach is utilized to minimize signal non-stationarity and noise interference while improving subsequence prediction accuracy. (2) The errors caused by human-set parameters are avoided by constructing SMA and LSSVM. (3) Weighted fusion of the sub-sequence prediction results, making full use of the prediction information of each sub-sequence to increase the prediction results’ stability and dependability.

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(4) The combined AVMD-SMA-LSSVM prediction model can follow wind power changes adaptively at the time of wind power fluctuation, and the forecast is more accurate. Acknowledgments. This work was funded by the Key Science and Technology Project (No. YNKJXM20220025) of China Southern Power Grid Co.

References 1. Yin, M., Wang, C., Ge, X., et al.: Comparison and analysis of wind power development in China and Germany. Trans. China Electrotech. Soc. 25(09), 157–162+182 (2010). (in Chinese) 2. Feng, S., Wang, W., Liu, C., et al.: Research on physical methods for power prediction of wind farm. Proc. CSEE 30(02), 1–6 (2010). (in Chinese) 3. Wan, C., Qian, W., Zhao, C., Song, Y., Yang, G.: Probabilistic forecasting based sizing and control of hybrid energy storage for wind power smoothing. IEEE Trans. Sustain. Energy 12, 1841–1852 (2021) 4. Miao, C., Wang, X., Li, H., et al.: Wind power day-ahead forecast based on wind speed error correction of numerical weather forecast. Power Grid Technol. 46(09), 3455–3464 (2022). (in Chinese) 5. Gao, Y., Liu, D., Cheng, H., et al.: Short-term wind power output forecasting based on datadriven calibration forecasting model. Proc. CSEE 35(11), 2645–2653 (2015). (in Chinese) 6. Hanifi, S., Liu, X., Lin, Z., Lotfian, S.: A critical review of wind power forecasting methods— past, present and future. Energies 13, 3764 (2020) 7. Liu, Y., Fan, Y., Bai, X., et al.: Wind power short-term prediction based on feature crossover mechanism and error compensation. Trans. China Electrotech. Soc. 38(12), 3277–3288 (2023). (in Chinese) 8. Yue, X., Peng, X., Lin, L.: Short-term wind power prediction by Whale optimized support Vector Machine. J. Electr. Power Syst. Autom. 32(02), 146–150 (2020). (in Chinese) 9. Wang, R., Chen, Z., Lu, J.: Short-term wind power prediction based on VMD and IBALSSVM. J. Hohai Univ. (Nat. Sci.) 49(06), 575–582 (2021). (in Chinese) 10. Shi, J., Zhao, D., Wang, L., et al.: Short-term wind power prediction based on RR-VMDLSTM. Power Syst. Prot. Control 49(21), 63–70 (2021). (in Chinese) 11. Yu, M., Niu, D., Gao, T., et al.: A novel framework for ultra-short-term interval wind power prediction based on RF-WOA-VMD and BiGRU optimized by the attention mechanism. Energy 269, 126738 (2023) 12. Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol.-Heart Circulatory Physiol. 278(6), H2039–H2049 (2000) 13. Li, S., Chen, H., Wang, M., Heidari, A.A., Mirjalili, S.: Slime mould algorithm: a new method for stochastic optimization. Futur. Gener. Comput. Syst. 111, 300–323 (2020)

Design of Grid Model Parameter Test System for New Energy Power Station Shoude Jiang(B) , Deshun Wang, and Haojie Yu State Grid Shanghai Energy Internet Research Institute Co., Ltd., Nanjin 210003, China [email protected]

Abstract. With the increasing proportion of photovoltaic and wind power generation installed capacity, when large-scale access to the power grid system, due to the inherent unstable factors of photovoltaic and wind power generation, if they are not strictly connected to the grid model parameter test, there will be great security risks to the safety of power grid operation. This paper mainly focuses on 10 kV/35 kV new energy power stations. A design method for testing model parameters of photovoltaic and wind power stations with multiple voltage levels (10 kV/35 kV) is proposed, and practical demonstration is carried out through field test to support the grid connection detection of new energy. Keywords: New energy sources · Photovoltaic (pv) · Wind power generation · Grid connection test · Model parameter testing · High and low voltage pass through

1 Introduction In recent years, the grid-connected standards for new energy have been increasingly improved. With the release of GB/T 19963-2016 Technical Provisions for Wind Farm Access to Power System [1] and GB/T 19964-2012 Technical Provisions for Photovoltaic Power Station Access to Power System [2], photovoltaic and wind farms are required to meet the test standards for grid-connected access. Only after passing the grid-connection detection can it run and be connected to the grid. Current research, more is through the test system high voltage [3], low voltage across the test system [4, 6], rarely to satisfy both high voltage through the test, low voltage test, high and low voltage continuous through testing [7], testing frequency disturbance voltage disturbance, etc., as one of the testing equipment for research, this article expounds a kind of model parameter test system, Detection of new energy power station high voltage crossing, low voltage crossing, high and low voltage continuous crossing, frequency disturbance and other capabilities.

2 Design Principle of Model Parameter Testing System The topology diagram of the model parameter test system is shown in Fig. 1. The test system includes step-down variable container, analog power supply container and stepup variable container. One liter container, step-down transformer, high voltage side can © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 766–779, 2024. https://doi.org/10.1007/978-981-97-1072-0_78

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be realized through different tap 35 kV and 10 kV voltage level switch, low voltage side can be implemented through different tap 380 v or 690 v two voltage levels of output, according to the requirements to make corresponding test capacity, simulation testing system can adapt to light and wind farm grid test. Test system in series connection photovoltaic or wind power plant, by simulating the container container internal circuit breaker switch switching control litres, step-down transformers, enter the test condition, through the analog network power supply container through the internal control system for high voltage and low voltage through continuous, high and low voltage across, threephase voltage balance, active/reactive power, voltage/frequency disturbance detection test.

Fig. 1. Topology of model parameter test system

3 Hardware Structure Design of Model Parameter Testing System 3.1 Step-Down Transformer Container Design Step-down transformer container is used to transform the power grid voltage of 35 kV (or 10 kV) to the voltage level applicable to the analog power supply container. The power grid is connected to the grid through the switch cabinet on the grid side, and 380 V (or 690 V) is output through the low-voltage side of the step-down transformer, and provides measurement, protection and other functions. Its primary principle is shown in Fig. 2. The internal electrical insulation design of containers is designed according to the operating environment of 4000 m above sea level [8] and pollution grade iv (25 mm/kV). According to GB 50060=2008 Design Code for High-voltage Power Distribution Devices, insulation distance D of 35 kV is ≥300 mm (d = 350 mm), and is modified according to formula (1) high altitude K factor. High altitude insulation distance is calculated according to Formula D = d ∗ Ka . Ka =

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Fig. 2. Principle diagram of step-down transformer container

3.2 Step-Up Transformer Container Design Step-up transformer container is used to transform the power output of the analog power container into the 35 kV (or 10 kV) power supply required by the tested equipment, and provide measurement, protection and other functions. The wiring principle of the analog power supply is shown in Fig. 3. The output power of the analog power supply container is boosted to 35 kV (or 10 kV) by the transformer and then connected to the tested product by the T-joint side of the machine switch cabinet. The current transformer and voltage transformer with protection and measurement functions are designed at the outgoing side of the bus, and the current and voltage signals are collected as the test basis.

Fig. 3. Primary schematic diagram of booster container

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3.3 Analog Power System Container Design The container of analog power supply system is mainly composed of bidirectional rectifier control unit [9], inverter control unit, feedback control unit, control unit, protection unit, man-machine touch interface, communication unit and sampling unit. Each unit is composed of circuit function modules, and the low voltage side of step-down transformer is connected to AC power supply. Through the bidirectional rectifier control unit, inverter control unit and output transformer, the analog output 0–690 V single-phase, two-phase or three-phase AC power supply is connected to the booster and low-voltage side. The functional diagram is shown in Fig. 4.

Fig. 4. Function diagram of analog power supply

In order to simulate the power supply required by the grid-connection test, the voltage control instruction is issued to the control unit of the analog power supply through manmachine touch interface Ua∗ , Ub∗ , Uc∗ . Under ideal grid conditions, three-phase voltage is sinusoidal and symmetric, and its voltage instruction is: ⎧ ∗ ∗ ⎨ Ua = A+ sin(ω  ∗t) 2π  ∗ (2) U = B+ sin ω t + 3  ⎩ b∗ Uc = C+ sin ω∗ t + 4π 3 In the formula A+ , B+ , C+ —Amplitude of fundamental wave component of threephase voltage; ω∗ —Grid angular frequency, ω∗ = 2 π f ; f —Grid frequency. In formula (2), the voltage amplitude of each phase can produce three-phase voltage symmetric or asymmetric sags or elevated faults in the control unit, and complete the tests of high voltage crossing, low voltage crossing and continuous high and low voltage

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crossing. Similarly, the fluctuation of power grid voltage can be simulated according to the specified vector changes given, A+ , B+ , C+ ; The frequency drift of power grid can be simulated by changing the frequency instruction in real time. In Formula (2), the grid angular frequency is integrated θ ∗ = ∫ ω∗ dt. The voltage phase Angle is obtained θ ∗ , To add a certain size and change direction of the interference signal θ ∗ , Can simulate a variety of phase Angle jump. When the grid voltage contains negative sequence and harmonic components, formula (2) can be transformed into:   ⎧ ∗ ∗ t) + A sin(−ω∗ t) + A sin n(ω∗ t) ⎨ Ua = A+ sin(ω − n        ∗ 2π ∗ . (3) t ± 2π U ∗ = B+ sin ω∗ t + 2π 3  + B− sin −ω t - 3 + Bn sin n ω 3   ⎩ b∗ ∗ t + 2π + C sin n ω∗ t ± 4π + C sin −ω Uc = C+ sin ω∗ t + 4π − n 3 3 3 In the formula A− , B− , C− —Amplitude of fundamental wave negative sequence component of three-phase voltage; An , Bn , Cn —Amplitude of the NTH harmonic component of the three-phase voltage. By setting the amplitudes of fundamental wave negative order component and harmonic component in Formula (3), power grid voltage imbalance and harmonic distortion fault can be simulated, with strong flexibility. Schematic diagram of analog power supply is shown in Fig. 5.

Fig. 5. Schematic diagram of analog power supply

4 Model Parameter Testing System Software and Control Part Design 4.1 System Software Functions The host computer is a professional testing software. The host computer communicates with the analog power supply, power analyzer and step-down/step-up container protection control device to achieve the following four functions; 1) Control the analog power supply and test relevant standards; 2) Temperature and humidity control inside the container;

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3) Communication and joint control of the front and rear end transformer container system; 4) The functions that can be added: control DEWETRON equipment through communication to realize “start saving” and “stop saving” of data. 4.2 System Control The core control part of the test system includes A/D conversion module, D/A conversion module, FPGA [10] and DSPA/D conversion module [11]. The control flow chart is shown in Fig. 6. A/D conversion module, the analog power output voltage signal and current signal data transformation sent to FPGA. FPGA, the voltage signal and current signal for logical processing, will be processed after the signal sent to THE DSP, and has signal acquisition, A/D conversion, output protection signal and DSP data interaction and other functions. FPGA sends the collected voltage, current, logic processing information to DSP through the data bus, so that it can calculate the effective value and real time value of voltage and current, and control the voltage and current analog quantity. DSP controls the output signal of the inverter unit according to the voltage signal and current signal sent by FPGA, and sends the output signal and fault alarm signal to the upper computer of the monitoring system in the power station. D/A conversion module converts digital signals into analog signals, which is the same as the control of A/D conversion module. DSP transmits signals to DSP according to the voltage signal and current signal logic processing sent by upper computer to FPGA, and IGBT, the light isolation driver module, processes and controls them according to the DSP output signal. And output to the bidirectional rectifier module and inverter module, and then through the isolation transformer and filter LCL, output frequency stable variable

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AC source, can accurately and effectively carry out high voltage crossing, low voltage crossing, high and low voltage continuous crossing, frequency disturbance and other tests.

5 System Function 5.1 Signal Acquisition and Processing Functions The model parameter test system is equipped with a data acquisition unit and an automated data processing platform. The system acquisition unit has a data acquisition progress of no less than 0.2 level. The acquisition unit is installed on both sides of the bi-directional rectifier module and the inverter module, which can accurately measure and record all the data in the test process. It includes the measurement data records of all transient and steady-state processes in any time period from before high and low voltage test to after voltage recovery. The data acquisition unit is equipped with high-precision data acquisition equipment, which can simultaneously collect at least 16 analog signals for voltage and current measurement on input and output sides of the fault simulation system. At the same time, the acquisition unit can transmit the collected data to the operation platform, which can be connected with high-precision detection equipment (Devectron, etc.), and can communicate with the operator station in real time, calculate the current, voltage, active power and other data in real time, and display them in curves and other types. 5.2 Detection Function According to GB/T 19963-2016 Technical Provisions for Wind Farm Access Power System and GB/T 19964-2012 Technical Provisions for Photovoltaic Power Station Access Power System, the following tests can be performed by the model parameter test system: Adaptive grid adaptability test function (frequency adaptability, power quality, voltage adaptability), active/reactive power adjustment test function, the power factor adjustment test, overload ability tests, unbalanced three-phase voltage testing capabilities, harmonic testing function, involving network protection function, unscheduled island protection test function, etc. The test system includes automatic test procedures for high voltage crossing and low voltage crossing. According to the provisions of [Dispatch Word [2020] No. 23 Qinghai Electric Power Dispatching Control Center on issuing the Notice on relevant technical requirements of New energy power station of Qinghai Electric Power Network], the function of high and low voltage continuous crossing is designed. Automatic detection to obtain data for high voltage, drop amplitude, action time, rise/drop amplitude network voltage fluctuation, active, reactive power support analysis, internal system is equipped with various test function template, the operator only need input specific parameters, the system according to the data acquisition unit to establish the corresponding database file, The results of processing and analysis are displayed in the form of graphs and tables.

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5.3 Safety Protection Function The model parameter testing system has the top protection of centralized control system, emergency stop control, safety chain locking control, relay protection and so on. With local/remote manual emergency cutting function, you can manually cut the model parameter test system from the power grid at any time. Set of control system of the top protection: inside the software operating on the set of corresponding increased the locking function, when the voltage rise or fall can’t modify the voltage amplitude, test methods, test time, only after completing one voltage rise or fall behind to choose test method, test time, avoid the wrong operation cause equipment failure caused by power grid voltage fluctuation. Stop, safety chain control and protection: when the fault occurs, can manually taken urgent stop, a complete set of test system will immediately from the grid side resection, and will stop, smoke alarm, temperature alarm, threshold position in series to the safety chain, any failure or risk into charged interval, etc. will be removed immediately in and out of the power supply, ensure the safety of the equipment and personnel. Relay protection: each circuit breaker cabinet is configured with high-precision, high-sensitivity relay protection unit, when there is over voltage, over current, short circuit and other faults, relay protection automatically cut off the test equipment, to avoid the test fault voltage and current caused by the power grid side switch trip, to prevent the expansion of the fault range.

6 Spot Test This paper takes the test of a large and medium-sized 35 kV photovoltaic power station in Qinghai Province as an example. According to relevant standards, the main test items of photovoltaic power station are as follows: Power quality test, active/reactive power control ability test, voltage and frequency adaptation ability test, high voltage pass through, low voltage pass through, high and low voltage continuous pass through, this paper mainly analyzes the low voltage pass through test, high voltage pass through test, high and low voltage continuous pass through test of the power station. The installed capacity of the measured photovoltaic power station is 30 MWp, and there are 30 MW sections. Each section has two 500 kW inverters to complete DC/AC conversion. After the PHOTOVOLTAIC inverter outputs AC380 V, it rises to 35 kV through 35/0.38 kV box transformer, and then connects to 35 kV bus through the high voltage switch inside the station. Then the complete set of equipment such as boost transformer is connected to 110 kV bus. The electrical topology is shown in Fig. 7. The photovoltaic power station adopts 4 inverters of different models, each of which has a power of 500 kW. Main technical parameters of the tested inverter: starting voltage 470 V; Rated voltage 380 V/400 V/415 V; Output frequency 50 Hz/60 Hz (adaptive); Maximum output AC power 550 kVA; Maximum DC power 560 kW; Dc operating voltage 300–900 V; MMPT tracking DC voltage 450 V–820 V; Maximum input current 1.2 kA; Maximum total harmonic distortion 0.99. The electrical parameters of the other three inverters are roughly the same as those of this one.

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Fig. 7. Electrical topology of photovoltaic power station

6.1 Low Voltage Traversal Test According to the standard GB/T 19964-2012 technical provisions for photovoltaic power station access to power system, the test curve of low voltage crossing is shown in Fig. 8. When the voltage of connection point is higher than curve 1, photovoltaic power station can be cut off from the grid.

Fig. 8. Requirements of GB/T 19964-2012 for low voltage through-through capability

The low voltage crossing test point is at the grid-connected place of the measured power generation unit. When the three-phase voltage of the power grid falls at 0%Un, 20%Un, and 80%Un, the model parameter testing system simulates the key waveform of the boost and high voltage side as shown in Fig. 9, 10 and 11. In the figure Ua , Ub , Uc are the voltages of line A, line B and line C on the side of boosting and changing high

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voltage respectively, Ia , Ib , Ic is the current of line A, B and C on the side of voltage boost to high voltage.

Fig. 9. Waveform of three-phase symmetric 0%Un voltage sag high voltage side

Fig. 10. Waveform of three-phase symmetric 20%Un voltage sag high voltage side

Fig. 11. Three-phase symmetric 80%Un voltage sag high-voltage side waveform

The parameter test system of this model can accurately simulate the grid voltage no matter the three-phase voltage falls to 80%Un or 20%Un symatically or the extreme zero voltage crossing. In the waveform, the voltage maintenance time of zero voltage crossing in Fig. 9 is 150 ms, and the voltage maintenance time of 20%Un voltage sag in Fig. 10 is 625 ms. When 80%Un voltage sag is shown in Fig. 11, the voltage maintenance time is 1000 ms, each waveform has no obvious distortion, and the voltage step adjustment time should be less than 20 ms. During the test, there is no off-grid operation of photovoltaic power station, and all low-voltage tests meet the grid connection standard of photovoltaic power station. 6.2 High Voltage Traversal Test According to the standard GB/T 19964-2012 technical provisions for photovoltaic power station access to power system, the operating regulations of photovoltaic power station

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within the voltage range of different connection points are stipulated. The operating curve is shown in Fig. 12, which requires that photovoltaic power station cannot be operated off-grid.

Fig. 12. GB/T 19964-2012 operating regulations of PV in the voltage range of different junction points

The high voltage crossing test point is at the grid-connected place of the measured power generation unit. The model parameter test system simulates the three-phase voltage of the power grid 130%Un and 120%Un, and the voltage increases. See Fig. 13 and Fig. 14 for the key waveform of the boosting and high-voltage side. In the figure Ua , Ub , Uc is the voltage of line A,B and C on the side of boosting and changing high voltage Ia , Ib , Ic is the current of line A,B and C on the side of voltage boost to high voltage.

Fig. 13. High voltage side waveform of 130%Un voltage

Fig. 14. Waveform of three-phase symmetrical 110%Un voltage increase

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In Fig. 13, 130%Un voltage increases, the duration of voltage increase is 500 ms; in Fig. 14, 110%Un voltage increases, the duration of voltage increase is 10000 ms. During the test, photovoltaic power station has no off-grid operation, and high voltage crossing meets the test requirements. 6.3 High and Low Voltage Continuous Crossing Test According to the scheduling of qinghai word [2020] no. 23 Qinghai electric power dispatching control center about print and distribute of qinghai power grid technology requirements related to new energy power station notification rules, requires so new energy power station must have high and low voltage crossing ability continuously, and new energy power station site in the following changes, as shown in Fig. 15 curve should not run off net.

Fig. 15. Continuous high-low voltage crossing curve

Figure 16 shows the waveform of the continuous high-low voltage traversal test. It can be seen from the waveform that it takes about 11 ms for the three-phase voltage to drop from 1.0PU to 0.2PU and from 1.3 to 0.2PU. It took 6.5 ms to increase from 0.2 to 1.3 PU. The voltage maintenance time of 0.2PU and 1.3PU is 100 ms. Through the model parameter test system, the high and low voltage of the photovoltaic power station also meets the grid-connection detection standard.

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Fig. 16. Test waveform of continuous high-low voltage crossing

7 Conclusion This paper proposes a new energy power plant model parameter test system developed, separately expounds the structure of hardware design, software design, key design point detection and safety protection, the system can accurately simulate the grid voltage, frequency, power, harmonic and so on change, in this paper, combined with a 35 kV, 30 MWP pv power station site inspection situation, The rationality of the design of the model parameter testing system is verified. The testing system can comprehensively, effectively and accurately detect the grid connection parameters of the new energy power station, and ensure the safety and reliable operation of the power grid.

References 1. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China. Technical regulations for connecting wind farms to power systems: GB/T19963-2016 (2016) 2. General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, Standardization Administration of the People’s Republic of China. Technician requirements for connecting photovoltaic power station to power system: GB/T 19964-2012 (2012) 3. Li, D., Yang, J., Yan, H., Ynag, K.: Application design of high voltage ride through test platform for Qinghai new energy power station. Qinghai Electr. Power 40(03), 39–43 (2021) 4. Ying, L.: Low voltage ride through control technology for photovoltaic grid connected power generation system. Yizhong Technol. 04, 66–68 (2023) 5. Mohseni, M., Masoum, M.A.S., Islam, S.M.: Low and high voltage ride-through of DFIG wind turbines using hybrid current controlled converters. Electr. Power Syst. Res. 81(7), 1456–1465 (2011) 6. Eskander, M.N., Amer, S.I.: Mitigation of voltage dips and swells in grid-connected wind energy conversion systems. In: International Conference on Control, Automation and Systems, 18–21 August, Fukuoka, Japan, pp. 885–890 (2009) 7. Qinghai Province Power Dispatching Center of China, Dispatching Zi [2020] No. 23 Notice of Qinghai Power Dispatching and Control Center on Issuing Technical Requirements for New Energy Power Stations in Qinghai Power Grid (2020)

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8. Yu, L., Su, J., Jiang, Y., Lin, J., Zhang, J.: Electrical insulation design of string photovoltaic inverters. Electromech. Inf. 2023(17), 23–26 (2023) 9. Teixeira, G.J., Stanimir, V., Rui, M., Alcides, G., Frede, B.: Hybrid three-phase rectifiers with active power factor correction: a systematic review. Electronics 10(13), 1520–1520 (2021) 10. Schussheim, D.T., Gibble, K.: A many-channel FPGA control system. Rev. Sci. Instrum. 94(8), 085101 (2023). https://doi.org/10.1063/5.0157330 11. Dong, C.: Design of A/D conversion module based on ADS7821. Electron. Tech. 45(04), 63–64+59 (2016)

Parametric Design of Railgun Armature Based on Functional Zoning Bo Gao, Xuan Li, Liang Chen, and Qunxian Qiu(B) Zhengzhou Institute of Mechanical and Electrical Engineering, Zhengzhou 450002, China [email protected]

Abstract. As the key part of electromagnetic railgun, the geometry structure of armature deeply affect the lunch performance of railgun during the lunch progress. In the launching process of electromagnetic railgun, strong current flows on the contact surface between armature and track, and local high temperature will lead to melting of metal materials, thus affecting the contact performance. Thus reasonable structure of armature should be chosen for the optimization of electromagnetic, heat and stress characteristic to improve anti-ablation. Based on the structure character of C-shaped armature in this paper, parameter model is established, and the ANSYS software is used to investigate the current density distribution law of armature and the mechanical character influence of armature with the changing of geometry parameter of structure area. Moreover the initial interference of the armature and material selection were analyzed. The result of this paper have important reference value for the research and design for armature. Keywords: functional zoning · railgun · parameterization · C-shaped armature · armature design

1 Introduction Armature is an important component of electromagnetic railgun, and the most direct part that converts electric energy into kinetic energy. Its performance parameters are directly related to the launching performance of railgun. The design quality of armature is closely related to the ablation of track. At present, the armatures selected for research can be divided into two categories: solid armature and plasma armature [1]. C-shaped solid armature is the classical and main form of armature used in electromagnetic railguns. For electromagnetic railgun, the most important function of armature is to realize the stability of sliding electrical contact at high speed and high current density on the basis of ensuring the strength and integrity of armature. For C-shaped armature, many researchers have done a lot of theoretical and experimental researches and put forward some effective improvement methods. Richard Marshall proposed a liquid-like armature concept to adapt to the dynamic lateral deformation of the guide rail during launch [6]. Laura Rip et al. proposed an armature form with a saddle-shaped throat structure to homogenize the current density distribution inside the armature and avoid local concentration of stress and heat [4]. Trevor et al. investigated the melting of C-shaped armature throats due to © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 780–791, 2024. https://doi.org/10.1007/978-981-97-1072-0_79

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heat concentration [5]. Xia Shengguo et al. studied the stress concentration phenomenon caused by armature interference design under specific conditions, and analyzed the melting wave ablation caused by local current concentration [2, 3]. Anthony J. Johnson et al. studied the influence of guide rail stiffness on contact pressure of C-shaped armature during launching [7–15] [16, 17]. Based on the functional decomposition of armature, a parametric model of typical C-shaped armature is established in this paper. The current density distribution law of armature and the influence of generated electromagnetic force on mechanical properties of armature are studied by using finite element software when geometric parameters of each functional area change, so as to provide an initial basis for armature design.

2 Parametric Armature Model The armature launching process of electromagnetic railgun is mainly divided into three stages, i.e. current rising stage (the armature is located at the breech), current flat-top stage (most of the launching is completed) and current falling stage (the armature reaches the muzzle). Macroscopically, the armature is mainly divided into three parts: armature arm, armature throat and armature shoulder, as shown in Fig. 1.

Fig. 1. Parametric Armature Model

The main function of the armature arm is to provide contact pressure to ensure that it always contacts the guide rail during the whole launch process. In the initial stage (with small current), the initial contact pressure is mainly provided by a certain amount of interference. The main function of the armature throat and shoulder is to ensure the strength of the armature under the action of large current, high temperature and electromagnetic force.

3 Influence Law of Main Armature Parameters on Characteristics 3.1 Basic Assumptions Since the armature movement process in railgun involves multi-field coupling of electromagnetic, thermal, structural and velocity, and they influence each other, the current simulation means are not enough to truly simulate the actual process. Therefore, before modeling, the following reasonable assumptions are made to simplify the model [2]:

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1) Since the deformation of track and armature is very small, it has little influence on electromagnetic field, so the deformation of armature and track is ignored in electromagnetic analysis; 2) The calculation assumes that the contact between the armature and the track is full contact, that is, the difference between the contact surface in the model and the actual contact surface is not considered; 3) Because the electromagnetic railgun is designed as a sealed structure, the convective heat exchange between the electromagnetic railgun system and the air is ignored. In this model, the type of elements used in armature, track and surrounding free space is three-dimensional magnetic vector potential. The element solid 97, the armature and track finite element model and the applied pulsed power supply current waveform are shown in Figs. 2 and 3.

Fig. 2. Finite Element Model of Armature and Track

Fig. 3. Power Supply Current Waveform

The basic dimensions of armature parameters and their analysis range are shown in Table 1. 3.2 Parametric Analysis of Armature Arm It can be seen from the parametric armature model shown in Fig. 1 that the dimensions related to the armature arm are mainly armature arm spacing L2, total tail width L3 (the interference contained in L3 is not considered during electromagnetic field analysis)

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Table 1. Basic Dimensions and Variations of Armature Parameters Parameter value (mm)

L2

H2

H1



R1

R2

Scope

33–37

36–44

6–14

12–20

8–12

10–14

and armature arm length H2. The power supply current waveform shown in Fig. 3 was applied to the end face of the track, and univariate change analysis was carried out on relevant parameters. The analysis results are shown in the figure (Figs. 4 and 5).

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 4. Effect of L2 Change

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 5. Effect of H2 Change

The simulation results of armature arm parameters show that: 1) The influence of armature arm spacing L2 on the maximum current density and maximum equivalent stress of the armature is not linear. For the range given in Table 1, when L2 is set an intermediate value (L2 = 36), the maximum current density and maximum equivalent stress of the armature are minimum; therefore, for this type of armature design, L2 should be selected around this value; 2) The increase of the armature arm length H2 can effectively reduce the maximum current density of the armature, and its influence on the equivalent stress of the armature remains stable but shows a decreasing trend. Therefore, under the premise that the mass allows, the value of H2 can be appropriately increased.

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3.3 Parametric Analysis of Armature Throat As can be seen from the parametric armature model shown in Fig. 1, the dimensions related to the armature throat are mainly the throat thickness H1 and the throat opening angle ϕ. The power current waveform shown in Fig was applied to the track end face, and the univariate change of the above parameters was analyzed. The analysis results are as follows (Figs. 6 and 7).

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 6. Effect of H1 Change

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 7. Effect of ϕ Change

The simulation results of relevant parameters of the armature throat demonstrate that: 1) The increase of throat thickness H1 can not only reduce the maximum current density of the armature, but also effectively reduce the maximum equivalent stress, thus improving the overall mechanical properties. Therefore, on the premise that the mass allows, the value of H1 can be appropriately increased. 2) With the increase of throat opening angle ϕ, the maximum current density and the maximum equivalent stress of the armature decrease; therefore, when designing this type of armature, the value of ϕ can be appropriately increased on the premise that the mass allows.

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3.4 Parametric Analysis of Armature Shoulder As can be seen from the parametric armature model shown in Fig. 1, the dimensions associated with an armature shoulder are mainly a shoulder inner diameter R1 and a shoulder outer diameter R2. The power current waveform shown in Fig was applied to the track end face, and the univariate change of the above parameters was analyzed. The analysis results are as follows (Figs. 8 and 9).

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 8. Effect of R1 Change

a˅Maximum Armature Current Density

b) Maximum Equivalent Stress of Armature

Fig. 9. Effect of R2 Change

The simulation results of the relevant parameters of armature shoulder indicate that: 1) Increasing the inner diameter R1 of the shoulder reduces the maximum current density of the armature, but it has little effect on the maximum equivalent stress. Therefore, for this type of armature design, the value of R1 can be appropriately increased. 2) An increase in the shoulder outer diameter R2 results in an increase in the maximum current density of the armature as well as the maximum equivalent stress. Therefore, the value of R2 can be appropriately reduced for this type of armature design. 3.5 Analysis on Initial Interference of Armature It can be seen from the parametric armature model shown in Fig. 1 that the armature arm spacing parameter L3 directly affects the initial contact pressure between the armature and the track. The parameter L3 is mainly determined according to the “1g/1A” contact

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pressure principle. When the armature is in the starting position, the contact force is provided by the interference fit of the armature with the track. The contact force between the armature and the track is mainly composed of the mechanical force (i.e., interference contact force between the armature and the track) FJY of the armature arm and the electromagnetic expansion force FDY of the armature arm, where: 1 FDY = α ∗ L I 2 2

(1)

α is the ratio of armature arm electromagnetic force to forward electromagnetic thrust, taken as 0.2 to ensure redundancy; β is the relationship between contact force and current, generally taken as 1 A per gram force. In order to ensure redundancy, it is taken as 0.02 N/A. Therefore, the required interference contact force between armature and track is: 1 FJY = βI − α L I 2 2

(2)

Where, L is the inductance gradient of the launching device. According to previous design experiences, the inductance gradient is taken as 0.42 × 10−6 H/m. The relationship between the interference contact force and current between armature and track is calculated as shown in Fig. 10.

Fig. 10. Relationship between Interference Contact Force and Current between Armature and Track

It can be seen from the figure that 2400 N contact force needs to be provided through interference fit at the initial stage, which can meet the requirements. The contact force corresponding to the armature arm spacing L3 changing from 40.2 mm to 41 mm is calculated, and the results are shown in Table 2. According to the above calculation, if the initial contact force requirement of the armature is met, the interference on one side of the armature should be 0.2 mm. Considering the wear and bore diameter deformation (about 0.2 mm on one side) during launching, the parameter value of armature spacing L3 is taken as 40.8 mm.

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Table 2. Relationship between Armature Arm Spacing L3 and Contact Force L3 length/mm

40.2

Single-side interference/mm Contact force (N)

40.4

0.1

40.6

0.2

1508.50

3058.61

40.8

0.3

41

0.4

4749.01

0.5

7375.70

11075.52

4 Optimization Results According to the previous analysis, in order to ensure the best electromagnetic and structural characteristics of the armature, the main dimensions of the armature are shown in Table 3. Table 3. Dimensions after Optimization of Armature Parameters Armature part

Armature arm

Parameter

L2

H2

L3

Armature throat H1



Armature shoulder R1

R2

Optimum (mm)

36

44

40.8

14

20°

12

10

Through simulation calculation, the armature current density distribution diagram and equivalent stress distribution diagram can be obtained as shown in Figs. 11 and 12.

Fig. 11. Armature Current Density Nephogram

The calculation results indicate that the maximum current density at the contact surface between armature and track is 2.13e9 A/m2 , mainly distributed on the upper and lower edges of throat. The maximum equivalent stress of the armature is 187 MPa, mainly distributed near the shoulder of the armature, and this value is far less than the strength limit of the armature material. Therefore, the electromagnetic and structural characteristics of the armature are obviously optimized by gradually analyzing the main structural parameters of the armature.

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Fig. 12. Armature Equivalent Stress Nephogram

5 Armature Materials Selection In order to meet the electromagnetic launching requirements, the armature shall have the following properties: 1) Conductivity Under the condition of carrying megaampere-level current for several milliseconds, the armature shall have certain conductivity as a moving current element. 2) Strength performance The armature is subjected to a pressure of several hundred MPa in the bore, while it is subjected to electromagnetic expansion force inside the armature, which will also generate a large amount of internal stress. 3) High temperature resistance requirements Due to the large current of pulse power supply, the local current density of armature will be concentrated, and the temperature is proportional to the square of the current density, so the armature material needs to have a high melting point. According to the above performance requirements of armature, its material shall have a high characteristic value of melting point current-carrying capacity and a low mass density. Based on this requirement, the main factors influencing armature quality are deduced from armature quality, and different materials are compared to select appropriate armature material. Taking an ideal rectangular armature as an example, its mass   √  √  gm ∗ l ∗ G m = ρm lA = ρm l G gm = ρm Where: is the armature density; A is the current-carrying area; is the muzzle width; G is the current-carrying capacity; is the material characteristic value of melting point current.

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The formula shows that the parameters in parentheses are related only to the material itself. It characterizes the mass required to carry the launching current, and its value should be as small as possible. In order to match the two, twice the density requires four times the characteristic value of current-carrying capacity, so for material selection of the armature, the density is more important than the characteristic value of current-carrying capacity. Table 4 shows the performance comparison of common materials: Table 4. Performance Comparison of Common Armature Materials Density ρm (kg/m3 )

Characteristic value of melting current gm (A2 s/mm4 )

Melting point Tm (K)

Aluminium alloys 7075-T6

19800

750–908

2800

520

20

Pure aluminium

25238

933

2700

140

17

Pure copper

80492

1356

8940

260

32

Pure tungsten 24270

3695

19240

310

124

Pure Titanium

1935

4595

140

83

3034

Yield Strength σY (MPa)

ρ / √m gm

Materials

The right column presents the ratio of mass density to characteristic value of melting point current-carrying capacity for various materials. By comparison, pure aluminum can better perform the function of carrying high current at low mass, and the yield strength of the material determines the allowable pressure limit in the bore. Therefore, a high-strength aluminum alloy AL 7075 is usually selected as the armature material instead of pure metal.

6 Conclusion In this paper, a parametric model is established based on the arm, throat and shoulder of solid C-shaped armature. The main parameters of each functional area are put forward, and a three-dimensional transient finite element model of electromagnetic railgun is built by using finite element software; Around the influence of each parameter change on the maximum current density and equivalent stress caused by electromagnetic force, univariate analysis is carried out. At the same time, the initial interference amount and material of armature are analyzed, and the following conclusions are drawn: 1) The armature can be designed from the perspective of reducing the maximum current density and equivalent stress of the armature. The length H2, Armature throat thickness H1, throat opening angle ϕ of the armature arm and the armature shoulder

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inner diameter R1 can be appropriately increased, while the outer diameter R2 of the armature shoulder can be reduced; However, the armature arm spacing L2 does not have a linear relationship with the maximum current density and the maximum equivalent stress of the armature, so the specific value should be selected according to different boundary conditions. 2) The contact pressure between the armature and the track consists of two parts: initial interference force and electromagnetic expansion force. At the initial stage of launch, good contact is maintained mainly by mechanical interference force. With the continuous increase of current and the continuous wear of the armature, the electromagnetic expansion force plays a leading role in maintaining the fit between the armature and the track; According to the “1g/1A” empirical formula, taking certain margin into account, the required contact force can be evaluated. Considering the deformation of bore diameter during launching, the required dimension value of armature arm spacing L3 can be obtained. 3) As a parasitic mass of the whole launching assembly, the armature mass shall be as small as possible. Therefore, while increasing or decreasing certain parameters may improve the relevant performance of the armature, they must be limited to a range that does not affect the payload ratio of the overall launching assembly. 4) According to the analysis of material density, current-carrying capacity and strength, high-strength aluminum alloy is a better choice for armature materials.

References 1. Ying, W., Feng, X.: Principles of Electric Gun. National Defense Industry Press, Beijing (1995) 2. Xia, S., Chen, L., Xiao, Z., He, J., Pan, Y., Li, J.: Effects of contact pressure concentration in rail/armature surface at startup of a railgun launch 3. Xia, S., Chen, L., Xiao, Z., Li, J.: Studies on interference fit between armature and rails in railguns. IEEE Trans. Plasma Sci. 39, 186–191 (2011) 4. Rip, L., Satapathy, S., Hsieh, K.-T.: Effect of geometry on the current density distribution in c-shaped armature. IEEE Trans. Magn. 39(1), 72–75 (2003) 5. Watt, T., Stefani, F.: Experimental and computational investigation of root-radius melting in c-shaped solid armatures. IEEE Trans. Magn. 41(1), 442–447 (2005) 6. Marshall, R.A., Ying, W.: Railguns: Their Science and Technology. China Machine Press (2004) 7. Johnson, A.J., Moon, F.C.: Elastic waves in electromagnetic launchers. IEEE Trans. Magn. 43(1), 141–144 (2007) 8. Cao, Z.: Research on the characteristics of c-type solid armature in electromagnetic emission. Huazhong University of Science and Technology, Wuhan (2006) 9. Sikhanda, S., Trevor, W., Chadee, P.: Effect of geometry change on armature behavior. IEEE Trans. Magn. 43(1), 408–412 (2007) 10. Laura, R., Sikhanda, S., Kuo-Ta, H.: Effect of geometry change on the current density distribution in C-shaped armatures. IEEE Trans. Magn. 39(1), 72–75 (2003) 11. Hsieh, K.T., Satapathy, S., Hsieh, M.T.: Effects of pressure-dependent contact resistivity contact interfacial conditions. IEEE Trans. Magn. 45(1), 313–318 (2009) 12. Li, Z., Tiecheng, L., Bo, Z., et al.: Multi-physics coupling analysis of rough surfaces using 3D fractal model. Trans. China Electrotech. Soc. 30(14), 226–232 (2015). (in Chinese)

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13. Zhonghua, C., Bo, T., Guang, S., et al.: Optimal pressure load under multi-objective sliding electric contact in the pantograph-catenary system. Trans. China Electrotech. Soc. 30(17), 154–160 (2015). (in Chinese) 14. Longwen, J., Jun, L.: Similarity of lubrication in armature-rail interface under the condition of electromagnetic railgun’s physical field scaling method. High Volt. Eng. 42(9), 2850–2856 (2016). (in Chinese) 15. Bai, L., Junyong, L., et al.: Effect of interfacial roughness of sliding electrical contact on the melting characteristics of armature. Trans. China Electrotech. Soc. 33(7), 1607–1615 (2018). (in Chinese)

Study on the Optimizing Impact of Hydrogen Equipment in Integrated Energy Systems Yue Cheng(B) Xi’an University of Science and Technology, Xi’an 710600, China [email protected]

Abstract. In recent years, comprehensive energy systems have emerged as a focal point of research. However, the practical application of hydrogen energy as a primary source within these systems necessitates further investigation. This paper systematically reviews common physical models of electrical, thermal, cooling, storage, and hydrogen energy devices. By establishing a mixed-integer linear programming model, with a primary objective of overall economic optimization, considering energy balance constraints and equipment operational constraints, the paper computes the optimal configuration of comprehensive energy systems considering the utilization of hydrogen energy devices. Furthermore, the study analyzes the impact of fluctuations in hydrogen energy prices on the configuration results. It is observed that the interconnection of different types of comprehensive energy devices can enhance energy efficiency, and the integration of hydrogen energy devices can lead to a reduction in the total cost of the system through hydrogen sales. Keywords: Comprehensive Energy · Hydrogen Energy · Mixed-Integer Linear Programming · Optimization Configuration

1 Introduction Comprehensive energy system research can be divided into various stages, starting from initial planning and gradually progressing to the development of models and operational frameworks. Integrated Energy Systems (IES) present two fundamental challenges: short-term operations suitable for immediate implementation, and long-term planning involving considerations of equipment, building systems, and financing. Regarding system temperature control, Reference [1] established a configuration model powered by cooling, heating, and electricity, optimizing simulations while adhering to investment and operational maintenance cost constraints. To demonstrate the economic benefits of multi-area integrated planning over single-area independent planning, the research has matured in two-dimensional energy integration planning, such as electric-thermal and electric-gas systems. However, the study of three-dimensional integrated energy systems involving electric-thermal-gas integration is still at the forefront. Within the Chinese academic community, there has been a systematic classification and development of theories regarding system structures and models [2]. Xian-Dong Xu et al. [3] © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 792–800, 2024. https://doi.org/10.1007/978-981-97-1072-0_80

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provided an overview of the historical emergence and developmental directions of integrated systems, emphasizing the similarities and differences between integrated systems and the energy internet. Jian-Zhong Wu et al. [4] elucidated the development status of integrated systems in different regions, such as Europe, and proposed driving factors and inspirations that China could draw from. Dan Wang et al. [5] systematically summarized the methods of practical implementation of comprehensive energy systems and provided detailed descriptions of modeling theories, optimization, and assessment methods. Yi Wang et al. [6] analyzed two types of integrated energy systems, electric-thermal coupling and electric-gas coupling, as a focal point for addressing the issue of accommodating new energy sources. The above reviews have introduced the characteristics and development forms of comprehensive energy systems, defined the framework and modeling of integrated systems. However, there is still room for further research on the access forms of comprehensive energy systems and emerging technologies. Building on previous studies, this paper will further expand the forms of energy coupling, increase the types of comprehensive energy equipment, and enhance the application of emerging technologies to meet the evolving demands for comprehensive energy systems in this era. Reference [7] designed an optimization model for IENG, incorporating multiple time units, with real-time optimization scheduling at 60-s intervals to ensure rational energy distribution. In addition to real-time monitoring and control of actual loads and predicted loads based on time units, optimization scheduling can also be conducted using uncertainty theory. For instance, stochastic optimization, founded on mathematical statistics theory, generates scenarios based on uncertain data and optimizes scheduling with the expected mean as the direction of optimization. References [8, 9] introduced the Monte Carlo method for stochastic optimization of comprehensive energy configuration. From the above research, it can be seen that the academic community has conducted extensive research on the configuration of integrated energy systems including electricity, heating, and gas. References [10, 11] provide an overview of integrated energy systems. This includes applications of IENG models, stochastic optimization, robust optimization, and the application of ENERGY HUB models. Additionally, operations research methods have been used for multi-objective planning to address economic issues faced in practical applications. However, there has been limited research on the comprehensive consideration of various forms of energy such as electricity, heating, cooling, gas, and hydrogen. Particularly, there is still a lack of further research on how hydrogen energy can be synergistically configured with other forms of energy in integrated energy systems. Studies on the application of hydrogen energy equipment, such as electrolyzers, fuel cells, and hydrogen storage, in comprehensive energy systems are also lacking. Therefore, this paper will focus on addressing this gap in research.

2 Flexible Load Modeling 2.1 Objective Function and Constraints The comprehensive energy system includes investment and construction costs, discrete equipment such as gas turbine (GT) and gas boiler (GB), and continuous equipment like photovoltaic power generation (PV), heat pump (HP), electric refrigeration unit (EC), absorption refrigeration unit (AC), fuel cell (FC), electrolyzer (EL), and various

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energy storage devices (ES). The annual investment costs, operational expenses, and the quantified costs of electricity, gas, and hydrogen transactions in the comprehensive energy system are integrated to form the objective function, aiming to evaluate the overall economic feasibility of the system.  LX     l(1+l)Y LS LS + C LX U LX (1+l) + θd λLS Y −1 n Un,d , en,t,d n   con d n t       buy buy  gas buy  H sell     LS + sell 2h + θd λLX et,d θd e θ (S g ) + θ (P ) Sd ,t ed ,t − Sdsell + d d d ,t ,t d ,t d ,t

min S=



d

LS LS bLS n Pn Un

t



LS l(1+l)Y (1+l)Y −1 n t

d

d

t

t

d

(2-1) In the equation, S represents the cost expenses, P represents electric power, b represents the number of configurations, u represents unit investment cost, C represents the rated power of continuous equipment, l represents annual interest rate, Y represents equipment service life, λ represents operational cost under unit power, e represents equipment operating power, n represents the number of days in a typical day, θ represents the unit price of natural gas heat value, G represents profit, and ρ represents the unit energy price after conversion. 1) Electric power balance constraint:

GT pk,d ,t +

k



buy

sell dis cha pdPV,t + pdFC ,t + pd ,t − pd ,t + pEES,d ,t − pEES,d ,t = PLd ,t +

k



pdEC ,t +



k

EL pdHP ,t + pd ,t

k

(2-2) 2) Thermal power balance constraint: k

GT + qk,d ,t

k

GB + qk,d ,t



EL FC dis cha qdHP =1,t + qd ,t + qd ,t + pTES,d ,t − pTES,d ,t = QLd ,t +

k



qdAC ,t

(2-3)

k

3) Cold power balance constraint: EC HP dis cha rdAC ,t + rd ,t + rt,d =2,3 + pCES,d ,t − pCES,d ,t = CLd ,t

(2-4)

4) Natural Gas Power Balance: gas

fd ,t =

GT Pk,d ,t k

ηkGT

+

GB Pk,d ,t k

ηkGB

(2-5)

5) Hydrogen Power Balance: HP,h HP HP 0 ≤ pdHP ,t λcop < c , d = 1, rd ,t = 0

(2-6)

6) GT equipment operation constraints: GT GT GT GT GT αmin,n bGT n Pn ≤ pn,d ,t ≤ bn Pn

(2-7)

GT GT GT GT qk,d ,t = ωk pk,d ,t βk

(2-8)

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7) GB equipment operation constraints: GB GB GB GB GB nGB αmin,n k Qk ≤ qk,d ,t ≤ nk Qk

(2-9)

8) PV equipment operation constraints:

S cPV Sd ,t , 0 ≤ Sd ,t ≤ S pdPV,t = cPV , Sd ,t > S

(2-10)

9) Constraints on the Operation of Electric Chiller (EC): EC EC 0 ≤ λEC cop pd ,t < c

(2-11)

10) Constraints on the Operation of Absorption Chiller (AC): AC AC 0 ≤ λAC cop qd ,t ≤ c

(2-12)

11) Operational Constraints for Fuel Cell (FC): FC FC 0 ≤ λFC cop hd ,t < c   FC FC FC qdEC = 1 − λ cop hd ,t β ,t

(2-13) (2-14)

12) Electrolyzer Operation Constraints: EL EL 0 ≤ λEL cop pd ,t ≤ c   EL EL qdEL,t = 1 − λEL cop pd ,t β

(2-15) (2-16)

13) Energy Storage Equipment Operational Constraint:

Ek,d ,t =

0 Ek,d = rk0 ckES

(2-17)

0 Ek,d ,t=T = Ek,d

(2-18)

⎧ ⎪ 0 + pcha ηcha − ⎨ (1 − ςk )Ek,d k,d ,t k

dis pk,d ,t

ηkdis

⎪ ⎩ (1 − ςk )Ek,d ,t−1 + pcha ηcha − k,d ,t k

,

dis pk,d ,t

ηkdis

t=1 ,t>1

(2-19)

cha min ES pk,d ,t ≤ vk ck

(2-20)

dis max ES pk,d ,t ≤ vk ck

(2-21)

14) Electrical Power Exchange Constraint: buy

buy,max

0 ≤ pd ,t ≤ udele,t pd ,t

ele sell,max 0 ≤ pdsell ,t ≤ (1 − ud ,t )pd ,t

(2-22) (2-23)

15) Hydrogen Power Exchange Constraint: dis 0 ≤ hSELL d ,t ≤ pHES,d ,t

(2-24)

where q represents thermal power, r represents cooling power, f represents natural gas power, h represents hydrogen power, q_min represents minimum output ratio, w represents the electric-to-thermal ratio, β represents efficiency, Q represents thermal power, C represents configuration capacity, and I represents light intensity.

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3 Model Solution and Calculated Examples This paper utilizes the MATLAB R2016b platform and calls the YALMIP software package for solving.

Fig. 1. Comprehensive Energy System Structure

The integrated energy system depicted in Fig. 1.encompasses power generation equipment, heat-providing facilities, and cooling load devices. Moreover, it allows the park to either procure electricity from the external grid or sell excess electricity back to it.In this study, distributed photovoltaic (PV) technology was chosen for PV power generation. Due to spatial constraints within the park, the installation capacity was capped at 5000 kW. The additional pre-configured equipment includes two gas turbines (GT1 and GT2) equipped with waste heat recovery capability (with a waste heat recovery efficiency of 0.85).In this particular scenario, based on the distinct characteristics of different typical days, winter typical days (100 days), summer typical days (120 days), and transitional typical days (145 days) were defined. The electrical, thermal, and cooling load profiles for these different typical days are illustrated in Fig. 2. The system adopts a three-stage time-of-use pricing strategy, including peak, offpeak, and flat rates, for purchasing electricity from the external grid. In cases where excess energy is generated within the system, it is permitted to be sold back to the grid at 50% of the corresponding purchase price for that time period. The price of natural gas is 2.07 yuan per cubic meter, with a lower heating value of 9.73 (kW·h) per cubic meter, resulting in a unit energy price of 0.2127 yuan per (kW·h). The selling price for hydrogen produced via electrolysis is set at 1.2 yuan per (kW·h). The carbon emission

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Fig. 2. Different Typical Daily Cold/Hot/Electric Load Profiles.

intensity of natural gas is estimated at 0.184 kg per (kW·h). The average carbon emission intensity for electricity supply is 0.55 kg per (kW·h). Additionally, the carbon tax is set at 0.02 yuan per kilogram.The annual interest rate is assumed to be 6%.

4 Scheme Configuration This paper primarily explores four scenarios, outlined as follows: 1. Scenario S1: Gas Turbine, Gas Boiler, Photovoltaic Power Generation, Heat Pump, Electric Chiller, Absorption Chiller. 2. Scenario S2: Scenario S1 Equipment + Electric, Thermal, and Cold Storage. 3. Scenario S3: Scenario S1 Equipment + Electrolyzer, Fuel Cell, Hydrogen Storage. 4. Scenario S4: Scenario S2 Equipment + Electrolyzer, Fuel Cell, Hydrogen Storage. Analysis of Comprehensive Energy System Costs Based on Different Configuration Scenarios Fig. 3.presents a detailed breakdown of the comprehensive energy system costs under four different scenarios. It is evident that in Scenario S1, there is a limited variety of equipment configurations, and the electricity, heat, and cooling powers are generated and utilized instantaneously. Despite having the lowest operational costs, a substantial amount of natural gas needs to be purchased to meet the current load demands.Comparing Scenario S1 with S2, the addition of energy storage equipment results in a slight increase in both initial investment and operational costs. Additionally, the system requires a modest increase in gas procurement to fulfill the energy storage power requirements. However, the application of energy storage equipment enables the system to increase its electricity dispatch, reducing power purchases during periods of high electricity prices. This, in turn, enhances profits from electricity sales, ultimately leading to a reduction in overall energy transaction costs. In Scenario S2, the decrease in energy transaction costs stands out as the primary factor contributing to the lower total costs compared to Scenario S1. Similarly, a comparative analysis between Scenarios S3 and S4 reveals that changes in energy storage yield similar conclusions. Comparing Scenario S1 with S3, or Scenario S2 with S4, the impact of hydrogen equipment on the comprehensive energy system becomes evident. The addition of a series of hydrogen equipment, including water electrolyzers, fuel cells, and hydrogen storage, can lead to a reduction in investment costs. This is because hydrogen equipment facilitates the mutual conversion of electricity, hydrogen, and heat, thereby increasing energy efficiency.The application of hydrogen equipment significantly increases the system’s demand for electricity. Since electrolyzing water requires a substantial amount of electrical energy, the electricity generation within the comprehensive energy system is

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Fig. 3. Detailed Comprehensive Energy System Costs Under Different Scenarios

insufficient to meet the demand for hydrogen production. This leads to a substantial increase in electricity purchases, resulting in a sharp rise in energy transaction costs and an increase in the environmental cost of external electricity procurement. However, at the same time, the profits from selling hydrogen offset the increase in energy transaction costs. Overall, hydrogen equipment still holds cost-saving significance for the comprehensive energy system. There is a notable difference in hydrogen sales profits between Scenario S3 and S4. The addition of energy storage equipment leads to a decrease in hydrogen sales profits in the integrated energy system with hydrogen-containing equipment. This is because the system converts more hydrogen energy into other forms to meet internal energy needs, reducing energy consumption costs, which is more economically viable than direct sales. From Table 1, it can be observed that photovoltaic power generation, as a clean and costeffective electrical power supply equipment, reaches its maximum configured capacity in all scenarios. The addition of hydrogen equipment results in a decrease in the capacities of gas turbines, electric refrigeration units, and absorption refrigeration units, as hydrogen equipment helps alleviate the system’s insufficient supply of thermal power, reducing the need for gas turbines. Additionally, the ample supply of thermal power leads to an increase in the configuration of heat pumps and a significant reduction in the capacity of thermal energy storage. Comparing Scenario S2 with Scenario S4, the configuration of hydrogen equipment imposes a more stringent requirement for electricity. With only water electrolysis as the sole source of hydrogen production, the system is more sensitive to electricity prices. Therefore, Scenario S4 includes a significant amount of electric energy storage to meet the electricity demand during peak periods. Additionally, regardless of whether hydrogen equipment is installed or not, the addition of energy storage equipment leads to an increase in the configured capacity of electric refrigeration units and a decrease in the configured capacity of absorption refrigeration units. This is due to the more pronounced peak-valley differences in electricity pricing costs within this system. The effect of increased energy storage equipment on reducing electricity costs is more significant, leading the system to preferentially allocate capacity to electric refrigeration units over absorption refrigeration units. However, due to their smaller capacity configurations and unit costs, the cost proportion between electric refrigeration units and absorption refrigeration units remains relatively stable.None of the four configurations of this comprehensive energy system include cold energy storage.

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Table 1. Comprehensive Energy System Equipment Capacity Configuration Under Different Scenarios (Unit: Kilowatts) Scheme Gas Electric Absorption Heat PV Turbine Chiller Chiller pump

E E S T E S Electrolyzer H E S

S1

2420

711

1946

789

5000

0

0

0

0

S2

2420

828

1554

639

5000

452

3133

0

0

S3

1210

438

865

987

5000

0

0

658

1644

S4

1210

490

823

1012

5000 2342

179

537

1342

This is attributed to the small and relatively stable nature of the cold load. The advantages of load-shifting with cold energy storage are not prominent, hence its absence in the configuration.

5 Conclusion This paper primarily investigates the optimization, configuration, and operational scheduling of comprehensive energy systems incorporating hydrogen equipment. The main conclusions are outlined below: 1. Configuration and Benefits of Comprehensive Energy Equipment: Expanding the variety of comprehensive energy equipment and their interconnection can enhance energy utilization, thereby reducing the overall configuration costs. Notably, photovoltaic generation, despite its higher unit cost, plays a crucial role in the configuration due to its economic and environmentally-friendly attributes. 2. Dual Impact of Energy Storage Equipment: While augmenting energy storage equipment configuration may increase investment and operational costs, it enables peak-shifting of electricity, consequently lowering electricity transaction costs. 3. Economic Benefits of Hydrogen Equipment: Integrating hydrogen equipment enhances the system’s energy coupling, thus improving energy utilization. With an increase in the selling price of hydrogen, the system becomes more reliant on hydrogen equipment, especially hydrogen production equipment. This, in turn, reduces the total system costs through hydrogen sales profits. 4. Hydrogen Selling Strategy and Electric Power Costs: Due to the characteristics of electrolyzers, the system predominantly engages in hydrogen sales during the early morning and midday periods when electricity costs are lower, achieving a high degree of alignment with low electricity costs.

References 1. Monadi, M.H., Hajinazari, M., Jamasb, S., et al.: An energy management system (EMS) strategy for combined heat and power (CHP) systems based on a hybrid optimization method employing fuzzy programming. Encagx 49, 86101 (2013)

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2. Li, Y., Qi, F., Zhu, Y., et al.: Preliminary exploration of construction mode for multi-energy complementary comprehensive energy power system. J. Electr. Power Sci. Technol. 34(01) (2019). (in Chinese) 3. Yu, X., Xu, X., Chen, S., et al.: A brief introduction to comprehensive energy system and energy internet. J. Electr. Eng. 31(01), 1–13 (2016). (in Chinese) 4. Wu, J.: Drivers and current status of comprehensive energy system development in Europe. Autom. Electr. Power Syst. 40(05), 1–7 (2016) 5. Jia, H., Dan, W., Xu, X., et al.: Research on several issues of regional comprehensive energy system. Autom. Electr. Power Syst. 39(07), 198–207 (2015). (in Chinese) 6. Yang, J., Zhang, N., Wang, Y., et al.: Multi-energy systems for renewable energy integration: review and prospects. Autom. Electr. Power Syst. 42(04), 11–24 (2018). (in Chinese) 7. Zhang, W., Chen, J., Li, J., et al.: Multi-time scale scheduling of integrated electricity and natural gas system considering the dynamic flow of natural gas. In: Proceedings of 2018 IEEE Innovative Smart Grid Technologies Asia (ISGT Asia), 22–25 May 2018, Singapore, pp. 356–361 (2018) 8. Zhang, X., Shahidehpour, M., Alabdulwahab, A., et al.: Hourly electricity demand response in the stochastic day-ahead scheduling of coordinated electricity and.natural gas networks. IEEE Trans. Power Syst. 31(1), 592–601 (2015) 9. Chaudry, M., Wu, J., Jenkins, N.: A sequential Monte Carlo model of the combined GB gas and electricity network. Energy Policy 62(9), 473–483 (2013) 10. Guo, L., Liu, W., Cai, J., et al.: A two-stage optimal planning and design method for combined cooling, heat and power microgrid system. Energy Convers. Manage. 74, 433–445 (2013) 11. Gu, W., Wu, Z., Bo, R., et al.: Modeling, planning and optimal energy management of combined cooling, heating and power microgrid: a review. Int. J. Electr. Power Energy Syst.Electr. Power Energy Syst. 54(1), 26–37 (2014)

Design of Variable Stress Fatigue Strength for Mechanical Parts of Gun Equipment Qunxian Qiu, Haitong Song, Jun Xu, and Pengfei Li(B) The 713th Research Institute of CSSC, Zhengzhou 450015, Henan, China [email protected]

Abstract. For a long time, the design method of static strength design verification and improvement of static strength safety factor used in gun equipment has not been conducive to the improvement of equipment lightweight level, nor can it directly reflect the service life parameters of the equipment. The dynamic response of gun equipment under excitation such as heavy torque, swaying or bumping inertia force, recoil resistance, and inertia force of the follow-up gun reflects the typical characteristics of time-varying stress. It is necessary to use the variable stress fatigue strength of number of coupled stress cycles, which is the service life, for design. Especially for large-mass electromagnetic guns, where three types of cyclic stress exist simultaneously under excitation such as recoil resistance, only by ensuring that the structural fatigue strength safety factor meets the basic requirements can lightweight design be truly carried out. At present, finite element simulation analysis based on fully flexible body modeling has become popular. Combining variable stress test data from shooting experiments, carrying out the design of variable stress fatigue strength for gun equipment is of great significance in promoting the improvement of equipment lightweight level and the friendliness of installation elements. Keywords: Gun equipment · variable stress · fatigue strength design · safety factor

1 Introduction Artillery, naval guns, electromagnetic guns, and other types of gun equipment will face various external stimuli during their service life, such as changes in the center of mass, accompanying movement with the gun, swaying of ships or vehicle body vibrations during movement, and dynamic firing. These stimuli include gravitational stimuli, pitching/rotational power stimuli, swaying or vibrational inertial force stimuli, and recoil resistance stimuli. As a mechanical part of gun equipment, one important characteristic parameter of its vibration response is the structural stress, which reflects the timevarying nature and the coupling between steady-state and non-steady-state conditions. The lightweight design and long service life of gun equipment, particularly for electromagnetic gun equipment, are the current directions of technological development in this field. Due to the unique characteristics of high initial velocity achieved through electrical © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 801–808, 2024. https://doi.org/10.1007/978-981-97-1072-0_81

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energy, electromagnetic barrels exhibit significant increases in weight, size, moment of inertia, and unbalanced torque compared to traditional artillery barrels. According to China Defense Science and Technology Information Network, the 32-megajoule electromagnetic gun barrel announced by the United States weighs about 18 tons. To achieve compatibility with its relative mounting elements, during the overall design of an electromagnetic gun system with the electromagnetic barrel as the driven load, it is necessary to conduct lightweight design of the mechanical parts of the gun body, such as the cradle and gun mount. However, the precondition for lightweight design is to ensure that the mechanical parts do not experience structural strength issues throughout the service life of the electromagnetic gun. A significant achievement that indicates the level of lightweight design for the mechanical parts of electromagnetic guns is when the mass ratio between the mechanical parts and the electromagnetic barrel is smaller than or significantly smaller than the mass ratio between traditional artillery mechanical parts and the artillery barrel. In other words, the traditional design methods for artillery engineering, which have relied on static analysis and static strength checks, are no longer applicable. Designing with a higher static strength safety factor (such as a safety factor of 2 or more as specified in the manual) cannot achieve optimal structural design and material utilization for mechanical parts, nor can it meet the requirements for lightweight design of electromagnetic guns. As a carrier platform that experiences strong shock and vibration during firing, artillery systems have encountered failures or accidents such as barrel rupture, chamber explosion, and mechanical part fractures or plastic deformations. A significant portion of these incidents is attributed to vibration fatigue failure induced by dynamic loads or excitations during firing. Mechanical parts of gun equipment can experience fatigue failure even at stress levels below the elastic limit when subjected to certain alternating loads. Foreign data show that vibration-induced issues account for approximately 30% of the failure events caused by artillery environmental stress [1]. During the research of launching armor-piercing projectile from a high bore pressure gun, it was found that despite having a high static strength safety factor, there were multiple incidents of round failures, indicating that dynamic strength has become the main concern [2]. Many scholars have conducted extensive research on variable stress methods, variable stress reliability assessment, and other related topics, which have contributed to the application of variable stress fatigue strength design methods in mechanical products [3– 8]. Nevertheless, classical variable stress fatigue strength design methods still maintain a high level of design accuracy. Therefore, using classical variable stress fatigue strength design methods to verify the safety factor of mechanical parts in gun equipment still maintains a high level of confidence. By incorporating the dynamic results obtained from finite element software calculations, along with variable stress fatigue testing data from firing trials, conducting variable stress fatigue strength design for mechanical parts under complex excitations in gun equipment is of significant importance to promote lightweight design and compatibility with mounting elements.

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2 Basic Methods of Variable Stress Fatigue Strength Design Under excitation conditions such as external firing, the mechanical parts of gun equipment experience variable stresses that exhibit significant time-varying characteristics. Based on the typical international service life of 20 to 30 years for equipment, the number of variable stress cycles experienced by mechanical parts shall be at least 105 cycles or more. According to the design theory for mechanical parts, fatigue failure will be the primary mode of failure for such mechanical parts. It is necessary to perform fatigue strength verification for them according to the safety-life design criteria [9], and conduct fatigue calculations considering the finite life and high-cycle fatigue calculation corresponding to the σ − N fatigue curve (refer to Fig. 1). When the variable stress cycles of mechanical parts exceed 103 cycles, high-strength alloyed steel is generally used. In this case, there is no infinite fatigue life zone, and the cycle count is typically taken as N0 = 107 .

Fig. 1. Typical fatigue curve of metals (double logarithmic coordinates)

In the figure, N - number of cycles, N0 - base number of cycles, and σrN - fatigue limit under cycle characteristic r. The equation for the fatigue curve within the finite life m N = σ m N = C (C is a test constant). The zone 103 (104 ) < N < N0 is given by σrN  r 0  fatigue limit at N cycles is given by: σrN = m NN0 σr = kN σr , kN = m NN0 , where kN is the life factor. For high-strength alloyed steel of mechanical parts, m = 9 (applicable to structural tensile stress, bending stress and shear stress). Taking into account the influences of stress concentration, dimensions, and surface condition of mechanical parts, a combined influence factor (kσ )D and life factor kN [10] are introduced to perform fatigue strength calculation of mechanical parts using the allowable stress diagram, as shown in Fig. 2. The horizontal axis σm represents the mean stress, and the vertical axis σa represents the stress amplitude. σb represents the tensile strength of the material, σs represents the yield strength of the material, σ0 represents the fatigue limit under pulsating cycles, and σ−1 represents the fatigue limit under symmetric cycles. The working stress (σm , σa ) of point C in mechanical parts must fall within OAES when externally excited. Where, OAE is the fatigue safety zone of the part and OES is the plastic safety zone. When designing mechanical parts for gun equipment, it is necessary to perform fatigue strength design for any working point C on the part.

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The C(σm , σa ) must fall within either the OAE fatigue safety zone or the OES plastic safety zone. The intersection point C(σm , σa ) of the line connected by points O and C and AE is considered as the ultimate allowable fatigue strength (σm  + σa ) during the fatigue strength design of the part.

Fig. 2. Allowable limit stress diagram when the cyclic characteristic r is constant

Generally, the safety factor Sσ = σmax /σs is checked based on static strength, while the formula for calculating the safety factor for fatigue strength is as follows [9]: Sσ a =

kN σ−1 σ = σ (kσ )D σa + ψσ σm

(1)

Where, ψσ = 2σ−1σ0−σ0 is the equivalent coefficient of mean stress reduced stress amplitude. It can be seen from formula (1) that during fatigue strength design, the mean stress and stress amplitude of materials are affected due to coupling life factor. The allowable   fatigue strength σm + σa will generally be less than the yield strength σs of materials. This indicates that when designing for static stress strength where material yield does not occur, the resulting safety factor may be excessively high, leading to a significant reduction in the actual fatigue strength safety factor. Alternatively, if the static strength safety factor is designed to be just sufficient, the fatigue strength safety factor may be less than 1, posing a risk of failure during the service life of the mechanical part. Therefore, it is crucial to perform fatigue strength design for mechanical parts in gun equipment, especially for electromagnetic guns.

3 Analysis of Variable Stress Cycle Characteristics for Mechanical Parts of Gun Equipment As an example, only the variable stresses produced by the recoil resistance excitation during firing on the mechanical parts of the gun equipment are analyzed. When subjected to the gravitational forces exerted by the barrel and other components, main load-bearing parts such as the cradle and gun carriage experience variable stresses due to the change in the center of mass. The stress state of these parts is formed under the influence of gravity after the complete assembly of the gun system. During the firing tests, stressstrain measurements are typically conducted at key locations. However, the strain gauge only corresponds to the dynamic component of the part during the firing vibration cycle.

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Therefore, the typical variable stresses in main load-bearing components such as the cradle and gun mount include two types of stresses: gravity-induced stresses and stresses resulting from the recoil forces. The combined effect of these stresses can be considered as non-symmetric cyclic (non-steady-state) variable stress, as shown in Fig. 3(a). For reinforcing ribs, top structures, crossbeams, and other parts of the cradle, gun mount, and turret that do not support external heavy loads and have relatively small mass, they are only excited by the recoil forces during firing. The combined stress in these parts can be considered as symmetric cyclic (non-steady-state) variable stress, as shown in Fig. 3(b). For parts such as the recoil mechanism and ammunition handling system, which are not subject to gravity-induced stresses, they are only excited by the recoil mass during firing. These parts experience stress variations ranging from 0 to the maximum value, and their combined stress can be considered as pulsating cyclic variable stress, as shown in Fig. 3(c).

(a) Asymmetric cyclic variable stress (b) Symmetric cyclic variable stress (c) Pulsating cyclic variable stress Fig. 3. Classification of variable stress in mechanical parts

In the figure, for stress amplitude σa = (σmax − σmin )/2, the stress amplitude is always positive; mean stress σm = (σmax + σmin )/2 and cyclic characteristics r = σmin /σmax = (σm − σa )/(σm + σa ), −1 ≤ r ≤ 1. For symmetrical cyclic variable stress r = −1, for pulsating cyclic variable stress r = 0. Based on finite element simulation analysis and measured data of launch vibration stress, it is possible to obtain the variable stress curves for the critical locations of the parts under consideration. These curves can be classified and processed to determine the stress amplitude and mean stress. Then, using the selected material properties, the ultimate fatigue strength curve shown in Fig. 2 can be plotted for fatigue strength checks and design.

4 Fatigue Strength Design Based on Launch Vibration Data A part is made of structural steel, and it is estimated to undergo 2 × 105 cycles of asymmetric cyclic tensile-compressive stress during its service life, with a life factor of

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Fig. 4. Variable stress curve of a certain structural point excited by gravity and recoil resistance

Figure 4 represents the simulation result diagram of variable stress curve after a structural point is excited by gravity and recoil resistance, which is a typical asymmetric cyclic variable stress curve. In the figure, the fluctuating curve near the horizontal axis represents the lateral stress at that point, which is not considered in this analysis. The focus is primarily on the variation of another stress curve during the upward and downward vibrations. Based on the aforementioned variable stress curves, σmin = 25 MPa, σmax = 195 MPa and r = 0.128 can be obtained, thus σm = 110 MPa and σa = 85 MPa can be calculated. This will allow us to determine certain parameters and subsequently conduct structural design using three types of low-alloy structural steel: Q345, Q460, and 616. The recommended approximate tensile-compressive fatigue strength and pulsating fatigue strength factors for structural steel, as suggested by the mechanical design handbook, will be used for the conversion, so as to obtain the allowable limit stress diagram under the same structure and three different materials, as shown in Fig. 5.

(a) Q345 material

(b) Q460 material

(c) 616 material

Fig. 5. Variable stress curve of a certain structural point excited by gravity and recoil resistance

Please refer to Table 1 for a summary of the relevant parameters and calculation results. From Fig. 5 and Table 1, it can be observed that for the same structure, when using Q345 material, the safety factor based on static strength is 1.76, while the safety factor based on fatigue strength is only 1.27. From the perspective of service life, the fatigue strength of this structural component appears to be slightly insufficient. When using Q460 material, the safety factor based on static strength increases to 2.35, meeting the minimum safety factor requirement for general artillery structural components. However,

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Table 1. Related calculation parameters for three different materials Parameter

Q345

Q460

616

σ−1 / (MPa)

212

247.5

630

σ0 / (MPa)

380

445

1134

ψσ

0.11

0.11

0.11

(kσ )D

2.87

2.87

3.13

Sσ a

1.27

1.48

3.48

Sσ

1.76

2.35

5.38

considering the service life, the fatigue strength safety factor is just approaching 1.5, which still has a small margin compared to the minimum safety factor for general highcycle fatigue machinery. If considering factors such as recoil-induced motion, rocking inertia forces, or vibration inertia forces during service, the fatigue strength safety factor is not sufficient. By using 616 steel, the fatigue strength safety factor reaches 3.48. From the perspective of shooting-induced vibration and stress variations, it can be considered safe for service within the expected service life. From the measured launch vibration stress at different locations, it is also evident that there are structures subjected to pulsating cyclic variable stress and symmetric cyclic variable stress (as shown in Fig. 6). The fatigue strength design process is the same as above, which will not be repeated here.

Fig. 6. Measured variable stress spectrum of two structural points

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5 Conclusions (1) For large-mass gun equipment subjected to barrel loads, traditional static strength safety factors often result in excessive design margins, which are not conducive to lightweight design of gun equipment. Therefore, it is necessary to conduct fatigue strength design considering variable stress. Coupling the fatigue strength design with the expected service life is essential to ensure the overall quality of the equipment throughout its service life. (2) Under the combined effect of gravity and recoil forces, different points of structures and mechanisms experience different types of variable stress. These include symmetric cyclic variable stress, asymmetric cyclic variable stress, and pulsating cyclic variable stress. (3) For the same structure and material, when the elastic modulus and yield strength are the same, the static strength safety factor of the structure, which is not coupled with the service life, generally tends to be higher than the fatigue strength safety factor when considering the service life. This calculation method is inappropriate. To compensate for the limitations of static strength calculations, it is common to increase the static strength safety factor, which often results in additional structural weight and is not conducive to the improvement of the lightweight level of equipment. Therefore, fatigue strength design is necessary for typical variable stress gun equipment. (4) For the variable stress design of mechanical parts in gun equipment, it is possible to achieve both lightweight design and fatigue strength safety throughout the service life by improving the performance grade of the materials. Acknowledgments. This work was funded by Key Program of National Natural Science Foundation of China (92266203).

References 1. Kang, S.: Finite Element Dynamic Analysis and Fatigue Life Prediction of a Gun Cradle. Nanjing University of Science and Technology, Nanjing, Jiangsu Province (2008) 2. Yang, Y., Zhang, J., Shang, W.: Dynamic diagnosis of armor-piercing projectile launch faults. J. Rocket Guid. 29(3), 186–188 (2009) 3. Wang, Z., Liu, A., Wang, X.: Fatigue study of mechanical parts under long-term alternating stress at high temperatures. Mech. Des. Res. 26(3), 67–69 (2010) 4. Zhao, Z., Song, B., Wang, X., et al.: Application of acceleration coefficient in product variable stress reliability assessment. Mech. Des. 29(6), 7–9 (2012) 5. Huang, C.: Design and fatigue life analysis of a torsion bar bidirectional balancing machine. Mech. Des. 27(9), 72–75 (2010) 6. Zhang, J., Tang, W., Peng, S.: Prediction of low cycle fatigue characteristics of gun steel. Mech. Des. Manuf. 1, 197–200 (2013) 7. Guo, Y., Deng, H., Liu, B., et al.: Fatigue life prediction of carburized 12crni3 alloy steel and reliability study of residual life under variable stress levels. Manuf. Technol. Mach. Tools 29(12), 120–126 (2021) 8. Zhang, P., Mi, Z., Zhu, Z.: Stress test and fatigue analysis of flexible parts in artillery suspension system. J. Nanjing Univ. Sci. Technol. 30(3), 273–275 (2006) 9. Xuanhuai, Q.: Mechanical Design [M], 4th edn. Higher Education Press, Beijing (1997) 10. Hao, X.: Mechanical Design Manual, 2nd edn. China Machine Press, Beijing (1995)

Optimization Configuration of Energy Storage System Considering the Cost of Retired Power Battery Life Yuan Jiang1(B)

, Suliang Ma2 , Qian Zhang3 , Wenzhen Chen1 , and Qing Li1

1 Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education,

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China [email protected], [email protected], [email protected] 2 Energy Storage Technology Engineering Research Center, North China University of Technology, Beijing 100144, China [email protected] 3 International Student Center, University of Science and Technology Beijing, Beijing 100083, China

Abstract. For discovering a solution to the configuration issue of retired power battery applied to the energy storage system, a double hierarchy decision model with technical and economic layer is introduced in this paper. Due to the high uncertainty of wind speed, the output of the thermal power plant will vary with the fluctuation of wind power, aggravating the fatigue and wear of the unit equipment, and affecting the steadiness of the system. The time-power sequence of the energy storage system is acquired by particle swarm optimization, and the power and capacity are configured according to the possibility density role curve of the energy storage output curve. The simulation of the IEEE-30-node model shows that the optimal energy storage configuration strategy put forward herein can control the power fluctuation and strengthen the stability of the wind-fire complementary system, and has good practicability. Keywords: Energy Storage Configuration · Retired Power Battery · Power Fluctuation · Double Layer Decision

1 Introduction According to the prediction of quality warranty period, battery cycle life, vehicle service conditions and other data, the amount of retired batteries in China will reach a peak between 2020 and 2023, with the recycling amount approaching 25 GWh [1] . If there is no proper treatment, the environmental pollution and resource waste will be very huge. If the decommissioned power batteries are recycled, economic benefits can be effectively improved. Energy storage system is currently recognized as the most important scenario for the cascade utilization of power batteries [1–3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 809–817, 2024. https://doi.org/10.1007/978-981-97-1072-0_82

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The energy storage system is generally adopted together with the reusable energy power generation system [4]. In Ref. [5], the correlation between the discharge depth of the energy storage battery and its operating life is considered, so as to hold down the power fluctuation of the photovoltaic power station. The best configuration of energy storage system is a vital problem in designing a new power system. For the one with photovoltaic power production, wind power production and typical loads, a combination method of moving average and standard correction is proposed in Ref. [6] to separate the grid-connected component and fluctuation component of wind power. In Ref. [7], spectral approach is taken to configure the power of the system. However, all the above researches possess one drawback, with only fluctuations in the output of new energy as the optimization objective, without considering the remaining lifespan and cost of the energy storage system. Ref. [8] takes the load power loss rate and the full life cycle cost as multiple objectives, a capacity configuration of the energy storage system in a hybrid energy storage system with wind-solar power generation is put forward. Taking the calming effect and cost of the energy storage system as the goal, the configuration capacity of the energy storage system is solved in Ref. [9] according to the output fluctuation law of the new energy in the micro-grid. Aiming at the lowest cost, optimal power matching and the best smoothness of reusable energy output power, a configuration method for energy storage system is proposed in Ref. [10] and [11], but the power fluctuations of the outbound link line is not considered. Considering the stability and economy of the system, an optimized allocation method for energy storage capacity based upon a two-layer decision model is proposed in Ref. [12]. Aiming at the recycling and utilization of decommissioned power batteries, the cascade energy storage system is introduced into the micro-grid, and the optimal energy storage configuration and economic evaluation method are proposed based on demand side management in Ref. [13]. In conclusion, considering power battery life cost, this article establishes an optimal configuration model for energy storage system. The model consists of both economic layer and technical layer. Taking IEEE-30 nodes as an example, the optimal configuration plan of energy storage is acquired.

2 Optimal Configuration Model of Energy Storage System 2.1 Technical Layer For the wind - fire complementary power system, the balance node is generally selected in the bus of a frequency-modulation thermal power plant. Due to the unstable and discontinuous characteristics of wind power, so as to ensure power balance, the power system needs to supplement the power supply, resulting in the power fluctuation of thermal power generation. The wide range fluctuation of active power in thermal power plant is against the steadiness of the system. Therefore, the objective function of technical layer model is:   2 1 n  pb (i) − pb (1) FTec = min i=1 n

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where, pb (i) is the active power of the thermal power plant at time i, and pb is the average active power. pb (i) can be calculated according to the power flow:  pb = fpowerflow P, Q, U , δ (2) where, P means active power, and Q refers to reactive power, and U stands for voltage, and δ means phase difference matrix. The power restrictions and voltage restrictions of the power system are shown below: ⎧    ⎪ ⎨ Pi = Ui j∈i Uj Gij cosδij + Bij sinδij  (3) Qi = Ui j∈i Uj Gij sinδij − Bij cosδij . ⎪ ⎩U min ≤ Ui ≤ Umax where, Pi and Qi stand for the active and reactive power of node i. U i and U j stand for voltage amplitudes of node i and j. Gij and Bij mean the branch admittance between node i and j. δ ij refers to the angle diversity between nodes i and j. U min and U max are the least and most node voltages 2.2 Economic Layer For the energy storage system consisting of retired power batteries, the objective function of the economic layer is as follows:    2 1 n  ps (i) − ps + k4 C (4) FEco = min k1 Ps + k2 Es + k3 i=1 n where, PS is the configured power of the system, and k 1 means the power-related cost coefficient. E S is the configuration capacity of the system, and k 2 is the cost coefficient related to the capacity. ps (i) means the charging and discharging power of the energy storage system at time i, and ps is the average charging and discharging power, and k 3 is the cost coefficient related to the fluctuation of battery output. C is the switching times of charging and discharging state, and k 4 is the cost coefficient related to life. The constraint condition is as follows: ⎧ Ps ≤ Pmax ⎪ ⎪ ⎪ ⎨ Es ≤ Emax (5) −Pmax ≤ ps (i) ≤ Pmax ⎪ i ⎪ ⎪ ηps (i)Δt ⎩ SOCmin ≤ SOC0 + j=1 Es ≤ SOCmax where, Pmax is the most power of the system, and E max means the most capacity of the system. SOCmin and SOCmax are the minimum and maximum state of charge of the energy storage system respectively. η is the charge and discharge efficiency of the battery.

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3 Solution Method 3.1 Particle Swarm Optimization Particle Swarm Optimization is a stochastic optimization algorithm proposed on basis of the study of bird foraging behavior. The initial state of the optimization process is a group of random particles. The speed and direction of particles are decided according to the individual and global information in the solution space, and the optimal solution is obtained through iteration. In iteration k, the velocity vid (k+1) and position vid (k+1) of the component d for the particle are updated by the equations below:     (k+1) (k) (k) (k) (k) (k) (6) vid = ωvid + c1 r1 pbestid − xid + c2 r2 gbestd − xid (k+1)

xid

(k)

(k+1)

= xid + vid

(7)

In the Eqs. (6) and (7), ω means the inertia weight adjusting the search scope of solution space. c1 and c2 stand for acceleration elements used to modify the most step length of iteration. r 1 and r 2 are random numbers to grow the randomness of search. Pbestid (k) is the component d of particle i in the optimal position vector of iteration k. gbestid (k) is the component d of the global optimal position vector in the iteration k. In this article, each component of the vector x represents the charging or discharging power of the system at each time, and gbest is the power vector of the system which minimizes the objective function of the technical layer. 3.2 Interval Estimation Assuming that the population p obeys the normal distribution N(μ, σ 2 ), and the energy storage power sequence [p1 , p2 ,…, pn ] is the sample of the p, when the confidence level is 1-α, the interval of the mean is estimated as   σ σ (8) p − z α2 √ , p + z α2 √ n n The maximum absolute value of the confidence interval will be selected as the configured power PS of the battery energy storage system. If the energy storage battery has the capacity of E S , and the initial number of the battery is ρE S, and with a maximum quantity limit is βE S and the minimum quantity is γ E S, the configured capacity of the system can be obtained as   t ∫0 pdt ∫t0 pdt , (9) Es = max β −ρ ρ−γ

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4 Discussion This article uses the IEEE-30-node bus power system for simulation, and Fig. 1 shows its structure. The configuration and simulation coefficients of the system are as follows: the thermal power plant is planned at node 1, with a maximum capacity of 360 MW as the balance node of the system. Node 11 is used for wind power generation with a maximum capacity of 200 MW. The energy storage system is added to node 13, and the capacity is to be configured. The allowable voltage range of system nodes is 0.9–1.05 p. u.

Fig. 1. Structure of IEEE-30-node power system

4.1 The Power System Without Energy Storage This article takes the typical daily power of a wind farm in western China is regarded as the power sequence for node 11. The wind speed is high in the early morning and low in the afternoon, and the power production varies with the wind speed. In the actual running of the power system, if the power increases or decreases, the balance node will change its output to keep the power balance of the whole system. Therefore, the output of the thermal power plant will vary with the fluctuation of the wind power. As shown in Fig. 2, when the peak-valley diversity of wind power is 194.9 MW, the peak-valley diversity of the thermal power plant will reach 204.7 MW. 4.2 The Power System with Energy Storage In order to decrease the power changes in thermal power plants, an energy storage power station is configured at node 13 in Fig. 1. The calculation of the power and capacity required by the energy storage system is made. Figure 3 shows charging power curve of energy storage power station.

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Fig. 2. Output fluctuation of thermal power plant caused by wind power fluctuation

Fig. 3. The charging and discharging power of energy storage station

In Fig. 3, the energy storage system has the output basically consistent with wind power. Positive power means battery charging, and negative power means battery discharge. When the wind power surpasses the load demand, the energy is kept by energy storage station. In case of insufficient wind power to satisfy the load need, the energy

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storage station releases electricity. Figure 4 shows the iterative process of solving the energy storage power sequence by PSO, and the number of iterations is 98.

Fig. 4. The optimization process of energy storage power

Figure 5 shows the output of the thermal power plant without and with the energy storage power station in the configuration of node 13. The comparison shows that the power fluctuation of thermal power plant is obviously improved. After adding energy storage, the average value of thermal power is 198.1 MW, with a variance of MW2 . The maximum power is 206.4 MW, and the minimum power is 189.8 MW, with the peak-valley difference 16.6 MW. The peak-valley difference is decreased by 91.9%, and the fluctuation is obviously suppressed.

Fig. 5. Output of thermal power plant before and after adding energy storage

On basis of the obtained energy storage and charging power, calculate the configuration power and capacity of the energy storage system at various confidence degrees using Eqs. (8) and (9). With the confidence level, the increase in configuration power and capacity will also increase, as shown in Fig. 6.

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Fig. 6. Relationship between energy storage configuration and confidence level

When the confidence level is high, the capacity and power value of the energy storage battery are larger, ensuring the stability of the wind fire complementary system is better, and the investment cost is also higher. The configuration scheme is shown in Table 1. The system stability savings are calculated based on the peak-valley diversity before and after adding the energy storage battery to node 13, and the economic benefit is the difference between the system stability savings and the energy storage costs. Table 1. Configuration scheme Result Optimal configuration of power Optimal configuration of capacity

Value 23.78 31.70

Unit MW MWh

cost of energy storage configuration

125.66

Million yuan

System stability saves money

282.15

Million yuan

Economic benefits

156.49

Million yuan

5 Conclusions An optimal energy storage strategy for wind and fire complementary system is proposed in this paper. The research results show that:

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1 From the output, it can be seen that when wind power surpasses the load demand, energy storage stations will store energy. In case of insufficient wind power to provide the load demand, the energy storage will release energy. 2) Due to the increase in energy storage, the power peak valley difference of thermal power plants has been reduced by 91.9%, effectively avoiding the output fluctuations. 3) When the confidence level is high, the capacity and power of the energy storage battery are large, and the effect of ensuring the stability of the wind fire complementary system is better with high input cost. The simulation results show that when the confidence level is 90%, the economic benefit reaches 150 million yuan. Acknowledgments. This work is supported by National Natural Science Foundation of China (52177127), Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515110725), and Aviation Science Fund (2020Z025074001).

References 1. Rocha, A.V., Maia, T.A.C., Filho, B.J.C.: Improving the battery energy storage system performance in peak load shaving applications. Energies 16(1), 382 (2023) 2. Dascalu, A., Sharkh, S., Cruden, A., et al.: Performance of a hybrid battery energy storage system. Energy Rep. 8(11), 1–7 (2022) 3. Pusceddu, E., Zakeri, B., Gissey, G.C.: Synergies between energy arbitrage and fast frequency response for battery energy storage systems. Appl. Energy 283, 116247 (2021) 4. Carraro, G., Danieli, P., Boatto, T., et al.: Conceptual review and optimization of liquid air energy storage system configurations for large scale energy storage. J. Energy Storage 72(B), 108225 (2023) 5. Lin, D., Zhao, B., Li, P.: Real-Time Fluctuation smoothing method for photovoltaic power station using lead carbon battery. Power Syst. Technol. 42(5), 1518–1525 (2018). (in Chinese) 6. Ma, S., Jiang, X., Ma, H., et al.: Capacity configuration of the hybrid energy storage system for wind power smoothing. Power Syst. Prot. Control 42(8), 108–114 (2014). (in Chinese) 7. Zhou, N., Yan, L., Wang, Q.: Research on dynamic characteristic and integration of photovoltaic generation in microgrids. Power Syst. Prot. Control 38(14), 119–127 (2010). (in Chinese) 8. Yang, J., Zhang, J.C., Zhou, Y., et al.: Research on capacity optimization of hybrid energy storage system in stand-alone wind/PV power generation system. Power Syst. Prot. Control 41(4), 38–44 (2013). (in Chinese) 9. Kargarian, A., Hug, G.: Optimal sizing of energy storage systems: a combination of hourly and intrahour time perspectives. IET Gener. Transm. Distrib. 10(3), 594–600 (2016) 10. Tan, X., Wang, H., Zhang, L., et al.: Multiobjective optimization of hybrid energy storage and assessment indices in microgrid. Autom. Electr. Power Syst. 38(8), 7–14 (2014). (in Chinese) 11. Tian, P., Xiao, X., Ding, R., et al.: A capacity configuring method of composite energy storage system in autonomous multi-microgrid. Autom. Electr. Power Syst. 37(1), 168–173 (2013). (in Chinese) 12. Li, J., Guo, B., Niu, M., et al.: Optimal configuration strategy of energy storage capacity in wind/PV/storage hybrid system. Trans. China Electrotech. Soc. 33(6), 1189–1196 . (in Chinese) (2018) 13. Han, X., Wang, F., Chen, M.: Economic evaluation of micro-grid system in commercial parks based on echelon utilization batteries. IEEE Access 7, 65624–65634 (2019)

Calculation of Electric Field for UAV Cross-Inspection in 220 kV Substation Ying Zhang1 , Jianming Liu1 , Duanjiao Li1 , Yongchao Liang1 , Jianhong Su1 , Kaixuan Chen2 , and Wensheng Li2(B) 1 Guangdong Power Grid Co. Ltd., Guangzhou 510080, China 2 Guangdong Engineering Technology Research Center of Special Robots for Special

Industries, China Southern Power Grid Technology Co. Ltd., Guangzhou 510080, China [email protected] Abstract. With the rapid development of smart grids, efficient and fast substation inspections have become increasingly important. Compared to traditional manual inspections and robot inspections, unmanned aerial vehicle (UAV) inspections offer various advantages such as low cost, flexibility, high efficiency, and close observation distance. However, UAVs are susceptible to the complex electromagnetic field environment within the substation. In this article, we focused on the Genie 4 UAV and performed three-dimensional electric field modeling of the 220 kV substation to investigate the safe distance and distribution of the power frequency electric field during the UAV’s traversing inspection of high-voltage equipment in the substation. The maximum surface electric field intensity of the UAV increases as the horizontal distance between the UAV and the high-voltage equipment decreases. Considering only the electric field, it is safe for the UAV to maintain a horizontal distance of 0.5 m from the high-voltage equipment during the traversing inspection. Keywords: UAV inspection · High-voltage equipment · Safety distance

1 Introduction Substations play a crucial role as hubs for power system and the transmission of electrical energy. In the event of damage or failure to important equipment within a substation, if not addressed promptly, it may result in further malfunctions in other high-voltage devices or even damage to an entire line within the substation. Traditional substation inspections heavily rely on manual labor, subjective judgments, and experiential knowledge of operating and maintenance personnel. This approach is costly, inefficient, and prone to errors, no longer meeting the demands for stability in modern substations [1]. Manual inspections are gradually being replaced by robotic inspections in substations [2]. Inspection robots can pre-plan inspection routes and are equipped with various sensors to analyze the operational condition of substation equipment, significantly enhancing inspection efficiency [3]. However, inspection robots also have limitations: firstly, they have low inspection perspectives, making it susceptible to blind spots. Secondly, the dense arrangement of high-voltage equipment within a substation presents significant limitations for the inspection paths that the robot can undertake. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 818–826, 2024. https://doi.org/10.1007/978-981-97-1072-0_83

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UAV inspections offer numerous advantages, including low labor costs, immunity to terrain constraints, high flexibility, easy operation, and low error rates. UAV inspections significantly improve inspection quality and efficiency, effectively addressing the challenges faced by both robotic and manual inspections [4]. However, UAVs carry multiple electronic devices internally, which could be susceptible to interference from the complex electromagnetic environment present within a substation. Additionally, the presence of UAVs themselves may lead to charge accumulation and distortions in the electric field, thereby increasing the probability of discharge [5]. Consequently, the electromagnetic safety concerns associated with UAV inspections in substations are particularly prominent. Indeed, UAV inspection technology for transmission lines has been gradually maturing. Ye et al. proposed the real-time object detection network (RTD-Net) in UAV-vision to address the challenges of detecting a large number of small objects and severe occlusions. The average detection accuracy of this method in the UAV image dataset reached 86.4%mpA [6]. Sadykova et al. utilized the YOLO deep learning neural network model, trained on a dataset of 56,000 samples, to successfully perform real-time detection of outdoor high-voltage insulators using UAVs [7]. Chen et al. established a finite element model for electromagnetic field simulation of 500 kV cat head tower UAV inspection operations to address the issue of unclear safety distance control during transmission line inspection. Combined with the average breakdown field strength of rod plate gaps and the electromagnetic compatibility limit of UAVs, the safety distance for UAV inspection was comprehensively determined [8]. Currently, UAVs have gradually been applied to substation inspections. However, there is currently a lack of quantitative data to support the determination of safety distances for UAV operations in substation inspections [9, 10]. It relies solely on the subjective judgment of the operators based on their experience, which makes it difficult to fully leverage the advantages of UAVs in terms of flexibility, convenience, and high efficiency. In order to promote UAV substation inspections and the construction of intelligent substations to the fullest extent, further in-depth research and corresponding experimental support are still needed. This article establishes an electric field simulation model for UAV and 220 kV substation to study the safety distance of UAV when traversing and inspecting live equipment in substations. Traversing and inspecting two-phase equipment is closer to the real inspection conditions compared to inspecting neighboring single-phase equipment. The research results are more universal and can serve as a reference for the safe distance of UAV operations in substation inspections. This article also provides data support for future research in this field.

2 Electric Field Calculation Model This article utilizes three-dimensional electromagnetic field modeling software to analyze and compute the distribution of power-frequency electromagnetic fields. The simulation calculations are based on the finite element method. The traditional finite element method is based on the principle of variation. It transforms the given mathematical model of a differential equation into the corresponding variational problem, which involves seeking the extremum of a functional. Then, using partition interpolation, the

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discretization of the variational problem becomes an extremum problem of an ordinary multivariate function. Ultimately, it is reduced to a set of multivariate algebraic equations, the solution of which yields the numerical solution to the desired boundary value problem. The selected UAV model for this article is the Genie 4 UAV. The Genie 4 UAV belongs to the small rotary-wing UAV category. It has a compact size, high navigation accuracy, and flexible flight operation, making it more suitable for conducting inspections within confined spaces such as substations. The four motors and integrated gimbal camera of the Genie 4 UAV are made of metal, while the rest of the shell is made of composite plastic material. As a result, the electric field of the UAV mainly concentrates on the gimbal and motors. The metal screws used to secure the motors are located at the bottom of the motors and are completely embedded in the plastic base, which does not affect the electric field distribution on the surface of the UAV. Therefore, they can be neglected in the electric field simulation. To simplify the calculation, the geometric simulation model of the Genie 4 UAV can be approximated as a cylindrical assembly with a diameter of 20 cm, disregarding the small components of the body. The physical and simulation models of the UAV are shown in Fig. 1.

Fig. 1. The physical and simulation models of UAV.

This article primarily examines the electromagnetic field distribution when the UAV traverses and inspects the 220 kV switchyard. To simplify the calculations, the singlephase line of the substation is approximated as a circuit consisting of transmission lines passing through disconnect switch, current transformer, circuit breaker, voltage transformer, and lightning arrester. The maximum phase voltage for the 220 kV transmission line is set at 179 kV. When considering calculations involving two phases, a phase difference of 120° is taken into account, and the voltage of the other phase is set at 89.5 kV. The disconnect switch is in a closed state. The section connected to the conductor is set at a voltage terminal of 179 kV, while the middle section made of metal is set at 89.8 kV. The bottom of the pillar insulator and cement column are grounded. The current transformer is connected to the primary side of the conductor and set at a voltage terminal of 179 kV, while the flange and cement column part are grounded. When the circuit breaker is in normal operation, the movable and stationary contacts in the arc extinguishing chamber are in a connected state. Therefore, the section connected to the conductor in the arc extinguishing chamber is set at a voltage terminal of 179 kV, while the bottom of the pillar insulator, flange, and cement column are grounded. The voltage transformer has the high-voltage end set at a voltage terminal of 179 kV, the middle part has the low-voltage end set at 10kV, and the electromagnetic unit at the bottom is set at

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57 V. The cement column is grounded. The lightning arrester has the top connected to the conductor and equalizing ring set at a voltage terminal of 179 kV. In normal operation, the lightning arrester is in an open state. Therefore, the internal structure of the lightning arrester is ignored. The middle flange is set at a floating potential, while the bottom flange and cement column are grounded. Based on the above-described settings, the simulation model of the 220 kV substation is shown in Fig. 2.

Fig. 2. The simulation models of 220 kV substation.

3 Simulation As the UAV traverses the substation during inspections, it primarily moves between the phases of the substation. It needs to consider the electric fields generated by the two-phase conductors. The corresponding inspection route can be simplified as shown in Fig. 3. Throughout the entire inspection process, the UAV will always maintain the same horizontal plane as the conductors. The initial position of the UAV is in the middle between the two phases. Due to a phase distance of 3 m, the UAV is positioned 1.5 m away from each phase on both the left and right sides. The gimbal camera on the UAV is oriented towards the high-voltage side. The UAV inspection starts from the disconnect switch. Adjust the horizontal distance between UAV and high-voltage equipment (disconnect switch, current transformer, circuit breaker, voltage transformer, lightning arrester) to 1.5 m, 1 m, 0.9 m, 0.8 m, 0.7 m, 0.6 m, and 0.5 m respectively, and conduct electric field simulation calculations. When the horizontal distance between the UAV and various high-voltage equipment is 0.5 m, the surface electric field distribution and nearby distorted electric field distribution of the UAV are shown in Fig. 4, 5, 6, 7, 8, 9 and 10. It can be observed that during the traversing inspection, the surface electric field is mainly concentrated around the four motors and the central part of the four wings. The surface field strength is highest for the front motor closest to the side of the disconnect

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Fig. 3. The UAV traversing inspection route diagram.

Fig. 4. The electric field distribution cloud map when the distance between the UAV and the first insulated pillar of the disconnect switch is 0.5 m.

Fig. 5. The electric field distribution cloud map when the distance between UAV and the second insulated pillar of the disconnect switch is 0.5 m.

Fig. 6. The electric field distribution cloud map when the distance between UAV and the third insulated pillar of the disconnect switch is 0.5 m.

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Fig. 7. The electric field distribution cloud map when the distance between UAV and the current transformer is 0.5 m.

Fig. 8. The electric field distribution cloud map when the distance between UAV and the circuit breaker is 0.5 m.

Fig. 9. The electric field distribution cloud map when the distance between UAV and the voltage transformer is 0.5 m.

Fig. 10. The electric field distribution cloud map when the distance between UAV and the lightning arrest is 0.5 m.

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switch. There is also a small amount of electric field distribution on the surface of the gimbal camera. The rest of the UAV has relatively low electric field strength. Throughout the process of traversing inspection in the substation, the maximum surface electric field strength is shown in Table 1. Figure 11 shows the variation of the maximum surface electric field strength on the UAV’s surface with respect to the UAV’s position. From that, it can be observed that during the traversing inspection, the maximum surface electric field strength on the UAV’s surface increases as the horizontal distance between the UAV and the high-voltage equipment decreases. The maximum value is 1140 kV/m. This maximum surface field strength is lower than the breakdown field strength of the air gap, indicating that corona discharge will not occur. Therefore, the UAV traversing inspection is safe. The surface field strength near the surge arrester during the UAV’s traversing inspection is higher than the surface field strength near other high-voltage equipment. Table 1. The maximum electric field intensity on the surface of UAV (kV/m). Distance from high-voltage equipment (m)

0.5

0.6

0.7

0.8

0.9

1

1.5

The first insulated pillar of the disconnect switch

772

632

587

528

460

412

163

The second insulated pillar of the disconnect switch

817

656

612

543

423

355

229

The third insulated pillar of the disconnect switch

844

676

637

562

473

392

233

Current transformer

774

615

589

518

378

337

211

Circuit breaker

732

643

577

527

368

354

216

862

711

617

543

364

382

236

1140

1062

917

843

783

757

318

Voltage transformer Lightning arrest

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Fig. 11. The maximum electric field intensity on the surface of the UAV with distance.

4 Conclusion This study investigates the safe distance and electric field distribution during the UAV’s traversing inspection of high-voltage equipment by constructing a simulation model of the UAV and 220 kV substation. The simulation results demonstrate that the maximum surface electric field strength of the UAV increases as the horizontal distance decreases. The electric field intensity is highest near the lightning arrester, with a maximum value of 1140 kV/m, which is lower than the breakdown field strength of air. Considering only the electric field, it is safe for the UAV to maintain a horizontal distance of 0.5 m from the high-voltage equipment during the traversing inspection. Acknowledgments. This work was financially supported by the China Southern Power Grid Corp funded science and technology project (GDKJXM20220879).

References 1. Lu, S., Zhang, Y., Su, J.: Mobile robot for power substation inspection: a survey. IEEE/CAA J. Automatica Sinica 4(4), 830–847 (2017) 2. Wang, H., Zhou, B., Zhang, X.: Research on the remote maintenance system architecture for the rapid development of smart substation in China. IEEE Trans. Power Deliv. 33(4), 1845–1852 (2018) 3. Yuan, L., Zhang, W., Zhang, Z., Lin, G.: Research on behaviour planning for power substation inspection robot based on fuzzy cognitive map. J. Phys. Conf. Ser. 2390(1), 012116 (2022) 4. Shao, M., Liu, Z., Fu, J., Tan, J., Chen, Y., Zhou, L.: Research progress in unmanned aerial vehicle inspection technology on overhead transmission lines. High Volt. Eng. 46(1), 14–22 (2020). (in Chinese) 5. Zhang, Y., Yuan, X., Li, W., Chen, S.: Automatic power line inspection using UAV images. Remote Sens. 9(8), 824 (2017) 6. Ye, T., Qin, W., Zhao, Z., Gao, X., Deng, X., Ouyang, Y.: Real-time object detection network in UAV-vision based on CNN and transformer. IEEE Trans. Instrum. Meas. 72, 1–13 (2023)

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7. Sadykova, D., Pernebayeva, D., Bagheri, M., James, A.: IN-YOLO: real-time detection of outdoor high voltage insulators using UAV imaging. IEEE Trans. Power Deliv. 35(3), 1599– 1601 (2020) 8. Chen, D., Guo, X., Huang, P., Li, F.: Safety distance analysis of 500 kV transmission line tower UAV patrol inspection. IEEE Lett. Electromagn. Compat. Pract. Appl. 4(02), 124–128 (2020) 9. Deng, C., Wang, S., Huang, Z., et al.: Unmanned aerial vehicles for power line inspection: a cooperative way in platforms and communications. J. Commun. 9(9), 687–692 (2014) 10. Jiang, F., Song, Q., Li, C.P., et al.: Application of power ubiquitous Internet of Things technology in intelligent inspection of unattended substation. In: Second International Conference on Electronic Information Engineering and Computer Communication, EIECC 2022, pp. 37–42. SPIE, Xi’an (2023)

Magnetic Field Safety Analysis of UAV Inspection in 220 kV Substation Yun Chen1 , Ying Zhang1 , Duanjiao Li1 , Jianming Liu1 , Zihan Yang1 , and Wensheng Li2(B) 1 Guangdong Power Grid Co. Ltd., Guangzhou 510080, China 2 Guangdong Engineering Technology Research Center of Special Robots for Special

Industries, China Southern Power Grid Technology Co. Ltd., Guangzhou 510080, China [email protected]

Abstract. Unmanned aerial vehicles (UAVs) demonstrate high practical value in substation inspections, addressing the limitations in vision and path restrictions encountered by robotic inspections. However, the UAV systems’ internal modules that are sensitive to electromagnetic fields and their related wireless signal links are susceptible to strong electromagnetic interference. This study employs Genie 4 UAV and Mavic 2 UAV to perform magnetic field simulation calculations and investigate the safety distance issue during close inspection and crossing inspection in 220 kV substation. The safety distance of UAVs is dependent on the load current. When the load current is 300 A, the safety distance for close inspection of Genie 4 UAV is 40 cm, and the safety distance for crossing inspection is 50 cm. For Mavic 2 UAV, the safety distance for close inspection is 40cm, and the safety distance for crossing inspection is 60 cm. Keywords: UAV inspection · High-voltage equipment · Safety distance

1 Introduction Substations are crucial components in power system, responsible for transmission and distribution. Ensuring the stable operation and reliability of the power system is of utmost importance. Therefore, conducting timely and accurate inspections of substations is vital. With the advent of the information age, inspections of substations are gradually moving towards intelligent solutions. The development of substation inspections has led to various methods, including traditional manual inspections, robot inspections, and UAV inspections. Traditional manual inspection mainly relies on maintenance personnel’s subjective judgment and experience, resulting in high costs, low efficiency, and a higher likelihood of errors [1]. In order to align with the development of modern substations, both domestic and foreign researchers are actively studying intelligent robot inspection, which is an emerging interdisciplinary approach [2]. Li et al. proposed a standardized detection algorithm based on geometric fitting methods to enhance the autonomy of inspection robots by combining the main categories of image recognition by inspection robots [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 827–834, 2024. https://doi.org/10.1007/978-981-97-1072-0_84

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Wu et al. introduced a new method using image retrieval and multi-view geometry for visual localization, effectively solving the positioning problem of robots in substations [4]. Wang et al. proposed a method for collaborative inspection of multiple inspection robots based on a bio-inspired neural network algorithm [5]. However, robot inspections have a low perspective and find it difficult to directly detect the upper surface of electrical equipment or equipment that is obstructed. On the other hand, due to the numerous and densely packed equipment inside substations, the inspection route of robots can be easily restricted. Using UAV inspection can indeed overcome these problems, as UAVs have a wide field of view and more options for path planning. Currently, UAVs are predominantly used for inspecting transmission lines. Yin et al. studied and optimized the impact of three UAV operating parameters (shooting distance, angle, and height) on the detection of insulators in transmission lines by establishing a 3D model of ceramic insulators [6]. Xu et al. developed a UAV system with advanced embedded processors and binocular vision sensors, which is used to generate real-time guidance information for power lines and enables automatic inspection of transmission lines [7]. Nardinocchi et al. proposed a new algorithm for fully automatic point cloud analysis in transmission line corridors, which allows UAVs to automatically detect obstacles in transmission corridors [8]. Currently, UAV inspection technology for substations is still in the developmental stage. UAV inspection systems mainly consist of power subsystems, flight control systems, navigation subsystems, and communication systems. The internal modules sensitive to electromagnetic interference and the related wireless signal links may be susceptible to strong electromagnetic fields. There is currently no quantitative data supporting the safe distance for UAV inspection operations in substations [9, 10]. To fully promote UAV inspection of substations and the construction of intelligent substations, further research and corresponding experiments are still needed for support. This study presents a magnetic field simulation model for the UAV and a 220 kV substation, and analyzes the variations in the UAV’s surface magnetic field during inspections. The inspection scenarios are categorized into two types: proximity inspection of single-phase equipment and traversal inspection of two-phase equipment. The research findings of this study can provide a reference for the safe distance of UAV inspections in substations.

2 Magnetic Field Calculation Model This article employs a three-dimensional electromagnetic field modeling software to analyze and calculate the distribution of the power-frequency magnetic field. The simulation calculation is based on the finite element method. Based on the calculation of power frequency electromagnetic fields, the entire solution process mainly includes the establishment of geometric models for unmanned aerial vehicles and substations, the setting of corresponding parameters such as material properties and boundary conditions for the field and boundaries, mesh generation of the established model, and post-processing analysis of the calculation results. When establishing a geometric model, appropriate simplification is required, and material properties and boundary conditions should be set according to the actual situation. When meshing, appropriate refinement should be made according to the situation, so that the calculation results are closer to the actual magnetic field distribution during UAV inspection.

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The overall magnetic field simulation model mainly consists of three components: the conductors, the air, and the UAV. In order to simplify the calculations due to the dense interweaving of conductors in the substation, this article simplifies the magnetic field excitation source in the substation to a horizontally distributed three-phase conductor. The spacing between phases is set to 3 m, the cross-sectional area of the conductor is 300 mm2 , and the length is taken as 4 m. The required magnetic field conditions are determined by the current density of the conductor, which can be calculated based on the cross-sectional area of conductor and the current passing through it. For a typical 220 kV substation, the single-phase load current is 300 A, which gives a current density of 1e6 A/m2 . The small UAVs are suitable for use in substation inspections. There are two models of UAVs used in the simulation: Genie 4 UAV and Mavic 2 UAV. These UAVs have small size, high navigational accuracy, and flexible flight operations, making them more suitable for inspections in compact substations. Both UAVs consist of the same components, including the body, four motors, wings, landing gear, and an integrated gimbal camera. However, they differ in their geometric shapes. Additionally, the four wings and arms of the Mavic 2 UAV are foldable, while those of the Genie 4 UAV are fixed. The internal motor of the UAV contains magnetic materials, typically made of silicon steel sheets. For the sake of calculation convenience, the motor’s materials can be considered equivalent to silicon steel sheets. The rest of the UAV is made of composite carbon fiber materials and non-magnetic metal materials. The material properties that need to be set in the magnetic field simulation are shown in Table 1. The geometric models of two UAVs are shown in Fig. 1. After setting the boundary conditions and material parameters, mesh generation is performed as shown in Fig. 2. The entire geometric model consists of 43 domains, 273 faces, 521 edges, and 312 points. The mesh model as a whole contains 97,603 elements, with an average quality of 0.62. The mesh quality is sufficiently good to proceed with the magnetic field simulation calculations. Table 1. Material properties of substation model. Material

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Fig. 1. The simulation models of UAVs.

Fig. 2. The diagram of mesh generation.

3 Simulation When Genie 4 UAV is conducting close inspections of the single-phase conductor, the load current is set to 100 A, 200 A, 300 A, 400 A, 500 A, and 600 A. The horizontal distance between the UAV and the conductor is adjusted from 1 m to 0.2 m. The corresponding variation of maximum magnetic field strength with horizontal distance is illustrated in Fig. 3. From Fig. 3, it can be observed that as the horizontal distance between the UAV and the conductor decreases, the maximum magnetic field strength of the main control section increases significantly. Additionally, as the load current increases, the magnetic field strength also increases. At the same horizontal distance, a higher load current leads to a larger maximum magnetic field strength of the main control section. According to the literature, when the magnetic field strength of the UAV’s main control section exceeds 200 µT, the electromagnetic sensitive module of the main control section may be affected. Therefore, the safe distance for the UAV during close inspection depends on the load current. When the load current is 300 A, the safe distance for the Genie 4 UAV during close inspection is 40cm. When Genie 4 UAV is conducting inspections while crossing two-phase conductors, the load current is also set from 100 A to 600 A. The horizontal distance between the UAV and the conductors is adjusted from 1.5 m to 0.5 m. The corresponding variation of maximum magnetic field strength with horizontal distance is depicted in Fig. 4. From Fig. 4, it can be observed that as the horizontal distance between the UAV and the conductors decreases, the maximum magnetic field strength of the main control section increases significantly. Similarly, as the load current increases, the magnetic field strength also increases. At the same horizontal distance, a higher load current results in a larger maximum magnetic field strength of the main control section.

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Fig. 3. The variation of magnetic field intensity in the main control section with distance when Genie 4 UAV conducting close inspection.

Fig. 4. The variation of magnetic field intensity in the main control section with distance when Genie 4 UAV conducting crossing inspection.

Due to the influence of the two-phase conductors, the relationship between the maximum magnetic field strength and distance is not strictly monotonic. For example, when the distance between the UAV and one phase conductor is 90 cm, the maximum magnetic field strength may be higher compared to distances of 100 cm and 80 cm. Considering a threshold magnetic field strength of 200 µT, when the load current is within 600 A, the safe distance for the Genie 4 UAV during crossing inspections is 50 cm. When Mavic 2 UAV is conducting close inspections, the load current is set from 100 A to 600 A. The horizontal distance between the UAV and the conductor is adjusted from 1m to 0.2 m. The corresponding variation of maximum magnetic field strength with horizontal distance is shown in Fig. 5. From Fig. 5, it can be observed that as the horizontal distance between the UAV and the conductor decreases, the maximum

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magnetic field strength of the main control section increases significantly. Similarly, as the load current increases, the magnetic field strength also increases. At the same horizontal distance, a higher load current results in a larger maximum magnetic field strength of the main control section. Considering a threshold magnetic field strength of 200 µT, when the load current is 300 A, the safe distance for the Mavic 2 UAV during close inspections is 40 cm.

Fig. 5. The variation of magnetic field intensity in the main control section with distance when Mavic 2 UAV conducting close inspection.

When Mavic 2 UAV is conducting crossing inspections, the load current is set from 100 A to 600 A. The horizontal distance between the UAV and the conductor is adjusted from 1.5 m to 0.5 m. The corresponding variation of maximum magnetic field strength of

Fig. 6. The variation of magnetic field intensity in the main control section with distance when Mavic 2 UAV conducting crossing inspection.

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the UAV’s main control section with horizontal distance is shown in Fig. 6. From Fig. 6, it can be observed that as the horizontal distance between the UAV and the conductor decreases, the maximum magnetic field strength of the main control section increases significantly. Similarly, as the load current increases, the magnetic field strength also increases. Considering a threshold magnetic field strength of 200 µT, when the load current is 300 A, the safe distance for the Mavic 2 UAV during crossing inspections is 60 cm.

4 Conclusion This study investigates the safety distance issue during close inspection and crossing inspection processes of UAVs in the 220 kV substation by establishing a magnetic field simulation model. The simulation results indicate that as the horizontal distance between the UAVs and the conductor decreases, the maximum magnetic field intensity of the control section increases significantly. The magnetic field intensity also increases with the increase of the load current. Under the same horizontal distance, the larger the load current, the greater the maximum magnetic field intensity of the control section. The safety distance for close inspection and crossing inspection of UAVs is related to the load current. When the load current is 300 A, the safety distance for close-range inspection of Genie 4 UAV is 40 cm, and the safety distance for crossing inspection is 50 cm. The safety distance for close-range inspection of Mavic 2 UAV is 40 cm, and the safety distance for crossing inspection is 60 cm. Acknowledgments. This work was financially supported by the China Southern Power Grid Corp funded science and technology project (GDKJXM20220879).

References 1. Lu, S., Zhang, Y., Su, J.: Mobile robot for power substation inspection: a survey. IEEE/CAA J. Automatica Sinica 4(4), 830–847 (2017) 2. Wang, H., Zhou, B., Zhang, X.: Research on the remote maintenance system architecture for the rapid development of smart substation in China. IEEE Trans. Power Deliv. 33(4), 1845–1852 (2018) 3. Li, B., Yang, J., Zeng, X., Yue, H., Xiang, W.: Automatic gauge detection via geometric fitting for safety inspection. IEEE Access 7, 87042–87048 (2019) 4. Wu, H., Wu, Y., Liu, C., Yang, G.: Visual data driven approach for metric localization in substation. Chin. J. Electron. 24(04), 795–801 (2015) 5. Wang, Z., et al.: Combined inspection strategy of bionic substation inspection robot based on improved biological inspired neural network. Energy Rep. 1(7), 549–558 (2021) 6. Yin, L., et al.: Parameters optimization of UAV for insulator inspection on power transmission line. IEEE Access 10, 97022–97029 (2022) 7. Xu, C., Li, Q., Zhou, Q., Zhang, S., Yu, D., Ma, Y.: Power line-guided automatic electric transmission line inspection system. IEEE Trans. Instrum. Meas. 71, 1–18 (2022) 8. Nardinocchi, C., Balsi, M., Esposito, S.: Fully automatic point cloud analysis for powerline corridor mapping. IEEE Trans. Geosci. Remote Sens. 58(12), 8637–8648 (2020)

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9. Deng, C., Wang, S., Huang, Z., et al.: Unmanned aerial vehicles for power line inspection: a cooperative way in platforms and communications. J. Commun. 9(9), 687–692 (2014) 10. Jiang, F., Song, Q., Li, C.P., et al.: Application of power ubiquitous Internet of Things technology in intelligent inspection of unattended substation. In: Second International Conference on Electronic Information Engineering and Computer Communication, EIECC 2022, pp. 37–42. SPIE, Xi’an (2023)

Insulated Bucket Arm Vehicle Bucket Arm Spatial Motion Path Planning and Algorithm Analysis Design Cong Hu1 , Wanying Zhang2,3(B) , Xin Yang1 , Li Cai2,3 , Jianguo Wang2,3 , and Yadong Fan2,3 1 Foshan Power Supply Bureau, Guangdong Power Grid Co., Foshan, China 2 Engineering Research Center of Ministry of Education for Lightning Protection and

Grounding Technology, Wuhan University, Wuhan, China [email protected] 3 School of Electrical Engineering and Automation, Wuhan University, Wuhan, China

Abstract. Insulated bucket arm vehicle operations are the primary method for live-line work in the power grid. Operating the bucket arm involves high operational complexity and the risk of errors and accidental contact. Currently, research on the automatic control of bucket arm vehicles is limited. This article is based on research methods for the automation of robotic mechanical arms, focusing on the automatic control of bucket arm vehicle mechanical arms. A modified Rapidlyexploring Random Tree (RRT) algorithm tailored to the specific characteristics of insulated bucket arm vehicle mechanical arms is proposed. By introducing distance criteria and improving the algorithm’s branching and expansion methods, computation speed is accelerated. Additionally, a collision detection function is implemented to enhance obstacle avoidance capabilities, thereby increasing its functionality. Finally, the application of the RRT algorithm in path planning for the bucket arm vehicle’s body and the selection of feasible stopping areas is investigated, demonstrating its feasibility. Keywords: Insulated bucket arm vehicle · RRT Algorithm · Path Planning

1 Introduction The Insulated Bucket Arm Vehicle is a specialized vehicle for live-line operations on distribution lines. It is a special vehicle used in situations with convenient transportation and complex wiring for equipotential work. Its work bucket, work arm, control hydraulic system, as well as the bucket-arm junction, all have certain insulation performance specifications and come with a grounding wire. The work arm provides primary insulation protection for the operator while working with live equipment [1]. Using insulated bucket arm vehicles for live-line operations offers advantages such as easy elevation, strong maneuverability, a large working range, high mechanical strength, and good insulation performance. They have been widely used in live-line operations in power distribution. In China, insulated bucket arm vehicles have a history of over 40 years of application. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 835–844, 2024. https://doi.org/10.1007/978-981-97-1072-0_85

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They have evolved from initially having low working heights, small radii, and inconvenient operation to stages where the working radius and height have increased, and the operation has become simple and reliable [2]. Due to the constraints of phase spacing and phase-to-ground distance in 10 kV distribution lines, the accident rate of personnel being electrocuted during maintenance is relatively high compared to other types of work. In response to the manual operation of live-line work, the current approach being proposed is the development of a live-line work robot system for 10 kV distribution lines [3, 4]. Zhang Liming et al. developed a dual-arm live work robot system designed to operate in complex and unstructured environments, addressing the challenges and issues faced in the design and application of current live work robots [5]. Ting Lei et al. utilized a combination of series-parallel robotic arms and a six-axis force-torque sensor to construct the hardware for a remotecontrolled robot system. This system was developed for high-voltage live work and is designed to meet the requirements of live electrical operations to the maximum extent [6]. Current research is primarily focused on studying mobile robots mounted on bucketarm vehicles, but there is relatively little research on the bucket-arm vehicle itself and its mechanical arm. The bucket arm of an insulated bucket-arm vehicle can be considered as a mechanical arm. Kinematics of the mechanical arm involves establishing a kinematic model of the mechanical arm to analyze how the positions, velocities, accelerations of the arm’s joints, and the end-effector of the arm change in space over time. Path planning algorithms can be categorized into two types: traditional methods based on graph search and intelligent bio-inspired methods based on derivatives [7, 8]. Rapidly Exploring Random Trees (RRT) is a common and straightforward algorithm in the traditional methods. Using an unmanned aerial vehicle (UAV) three-dimensional modeling and imaging system, this article proposes an improved algorithm based on the Rapidly Exploring Random Tree (RRT) algorithm for automatic control of the bucket-arm vehicle’s mechanical arm movement in three-dimensional space. This algorithm is designed to plan the path of the mechanical arm from the starting point to the target point. Furthermore, the algorithm has been optimized and improved to suit the characteristics of three-dimensional modeling in electrified work environments and the movement of the insulated bucket arm vehicle’s bucket arm. These optimizations reduce computational complexity, accelerate processing speed, and add automatic obstacle avoidance capabilities to meet the requirements of electrified work environments.

2 Principles and Improved Design of the RRT Algorithm The Rapidly-exploring Random Trees (RRT) algorithm, proposed by Lavalle in [7], has a relatively simple algorithm principle. The main idea is to start with an initial point as the root node and then randomly sample points in space. The nodes in the tree calculate distances and select the nearest node to the sampled point. Then, they grow from this node towards the sampled point by a fixed length until the final goal is reached. The advantage of this algorithm is its ability to avoid local optima and explore complex

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spaces. However, its drawback is the high randomness in the search, leading to nonsmooth paths. Currently, most robotic arm path planning algorithms use RRT due to its simplicity and relatively high search efficiency. Here is an example of the principle of the RRT algorithm in a two-dimensional plane. As shown in Fig. 1(a), the yellow node represents the initial node, the green node represents the goal node, and the purpose of path planning is to find a feasible path between the initial and goal nodes.

(a)

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(c) Fig. 1. Expansion principle of RRT algorithm.

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The algorithm initially selects a point in space arbitrarily, as shown by the blue node in the diagram, and treats it as the goal node. It calculates the distance from existing nodes to this node, selects the nearest node, and uses the line connecting that node to the goal node as the growth direction. With a predefined growth step length, it generates an extension node, as shown by the black node in the diagram. By repeatedly executing these steps, the tree’s branches and leaves are continually expanded, as shown by the black nodes in Fig. 1(b). When a newly expanded node is within a certain distance from the goal node, as indicated by the purple circle in Fig. 1(b), it means that the tree has expanded to the goal position. The final goal node is included in the path, and the expansion algorithm concludes. Finally, by searching for the parent node of each node and traversing from the goal node backward to the initial node, the resulting path is obtained, as shown by the bold red line in Fig. 1(c). Because the control of the robotic arm needs to be performed in three-dimensional space, we need to extend this method to three-dimensional space. Below, we will introduce the practical application of the RRT algorithm in a three-dimensional plane: In a 2000 × 2000 × 2000 three-dimensional space, the goal is to find a path from the lower-left red starting point to the upper-right green target node. • First, we need to set the map boundaries XL, YL, and ZL, the expansion length D, the distance TR for determining when a node enters the target node’s range, and a function g(x) to calculate the straight-line distance between nodes. • The second step is to obtain a random coordinate P (x, y, z) as the expansion direction, which can be achieved using the rand function in Matlab. • The third step is to use the function g(x) to find the nearest node to the newly generated random coordinate P (x, y, z) and set that point as T old (x , y , z ). • The fourth step involves calculating the direction between the new and old nodes and extending in that direction from T old (x , y , z ) by D to generate a new node T new (x, y, z). This new node is included in the tree T, and T old (x , y , z ) is defined as its parent node. The expansion ends. • The fifth step checks whether the newly generated node has entered the target node’s range. If it has, the algorithm ends; otherwise, it returns to the second step. • In the sixth step, after the expansion algorithm ends, the target node is included in the tree T, and a reverse search is performed to find the parent node for each node, ultimately finding a path from the target node to the starting point. As shown in Fig. 2, it is one of the results of running the code. The lower-left red node is the initial node, and the upper-right green node is the target node. The thin red lines represent the branches extended by the RRT algorithm, and the thick red line represents the found target path. From the figure, you can see that the branches generated by the RRT algorithm cover the entire space, indicating that it has good completeness. The basic RRT algorithm can find the target path, but it still has some shortcomings in terms of speed and functionality, and further optimization can make it more suitable for practical situations. The branches generated by RRT do not always grow directly towards the goal. While this approach helps explore the entire space more comprehensively, it significantly increases the pathfinding time. Therefore, in environments where

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space permits, we can selectively discard some random nodes to eliminate unnecessary computations and speed up the expansion process. This can also greatly reduce the redundancy of the tree and reduce the program’s storage requirements.

Fig. 2. The application of RRT in three-dimensional space.

Fig. 3. Optimized RRT Search Path.

The specific method is as follows: Firstly, perform an initial screening to identify newly generated nodes T new that are closer to the target node than the old node T old . Considering a certain level of environmental complexity, perform a second screening among the nodes that do not meet the criteria. In this second screening, select nodes T new that are closer to the target node than T old , considering only one of the xy, yz, or xz planes at a time. As shown in Fig. 3, this process involves evaluating the distance between the

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newly generated node T new and the target node relative to the distance between the old node T old and the target node, and filtering out ineffective nodes. From Fig. 3, it can be observed that the newly generated tree has fewer branches compared to Fig. 2, indicating that its completeness is lower than before the optimization. However, it can still find a suitable path, demonstrating its feasibility. At the same time, there is a significant improvement in speed compared to before the optimization, and the storage space required for the tree has decreased. In actual environments, the motion path of the bucket arm vehicle may encounter obstacles. Therefore, when the algorithm is running, it must consider collisions between the mechanical arm and obstacles. As shown in Fig. 4, the dark green rectangles represent obstacles, and the path needs to avoid these obstacles to reach the target node. Therefore, the tree branches cannot expand arbitrarily. Instead, the algorithm checks whether the line segment between the new and old nodes collides with obstacles. If a collision occurs, as indicated by the thin yellow line in the figure, the newly generated node should be discarded, and the algorithm should search for the next node. A collision detection function is implemented in Matlab, which is inserted into the step of generating a new T new node after checking for collisions, thereby filtering out unreasonable paths. Matlab’s image processing functions are used to convert the image into a numerical matrix. This tool generates a matrix with coordinates based on the size of the image and assigns grayscale values to each corresponding coordinate. Using this coordinate matrix, obstacle avoidance detection for the RRT algorithm can be implemented.

Fig. 4. The obstacle avoidance mechanism of the RRT algorithm.

Its basic principle is illustrated in Fig. 5. The RRT algorithm extends its branches as shown by the thin red lines in the figure. These branches are evenly divided into several points, such as point A represented by the blue dot in the figure. The algorithm calculates four integer coordinates around point A, denoted as A1 to A4, and checks the corresponding grayscale values in the matrix. If the grayscale values for all four coordinates are less than a specified threshold, it means that the planned path does not collide with obstacles. If any of the grayscale values for the coordinates exceeds the threshold, it indicates a collision with obstacles, and a new path needs to be chosen.

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Fig. 5. The collision detection principle based on the image recognition matrix.

Figure 6 shows the results after adding distance filtering and collision detection. The dark green cuboid in the figure represents the assumed obstacle, and the algorithm needs to find a collision-free path from the lower-left red starting point to the upper-right green target node. The thick red line in the figure represents the final path found, and the purple lines are paths selected through collision detection and distance filtering from tree nodes. This demonstrates the feasibility of the algorithm. It can be seen that both the branches and the main paths of the tree avoid the obstacles, and the final target path is found, verifying the correctness of the algorithm.

Fig. 6. RRT Algorithm with Collision Detection

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3 Path Planning Within the Working Range of the Insulated Bucket Arm Vehicle’s Bucket Arm The RRT algorithm can be applied not only to the trajectory planning of the bucket arm vehicle’s mechanical arm end but also to the planning of the vehicle’s body movement trajectory. Here, we will use a two-dimensional plane as an example to explore the application of the RRT algorithm in the path planning and stopping of the bucket arm vehicle’s body. This article is based on the principle of three-dimensional environmental modeling using unmanned aerial vehicle (UAV). When operating the bucket arm vehicle, an auxiliary UAV is used to capture images of the surrounding environment. These images are then used to generate a three-dimensional model of the environment with the target electrical potential for live-line work. In the example provided, the black areas in Fig. 7 represent the designated obstacles in the environment.

Fig. 7. Obstacle image.

Based on the collision detection principle mentioned earlier, we can implement collision detection for both the bucket arm vehicle’s body and the bucket arm’s motion path. We can add this to the application of the RRT algorithm in a two-dimensional plane to obtain the path planning as shown in the diagram. Figure 8(a) represents the RRT algorithm without distance criteria, it can be observed that its branches in the plane are numerous, almost covering the entire space, indicating a strong completeness. In contrast, in Fig. 8(b), we have applied the RRT algorithm with distance criteria. The branches in the plane are all growing toward the target node, and it is also capable of finding feasible paths quickly under simple obstacles, demonstrating its ability to rapidly obtain feasible paths in such scenarios. Once the bucket-arm vehicle has moved along the planned path to its destination, it still needs to detect the surrounding environment to determine a feasible parking location for the vehicle. By utilizing image recognition functions and an RRT algorithm with collision detection capabilities, it is possible to anchor the parent node at the starting point to select a feasible parking area. As shown in Fig. 9, the bottom-right corner represents the current position of the bucket-arm vehicle, and the goal is to find a feasible parking area among the obstacles. The pink area in the figure represents the feasible parking area obtained by the algorithm.

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Fig. 8. RRT Algorithm 2D Plane Obstacle Avoidance Planning.

Fig. 9. The parking location for the vehicle.

4 Conclusion This article has provided an introduction to the fundamental principles of the Rapidlyexploring Random Trees (RRT) algorithm. Building upon this foundation, the basic applications of the RRT algorithm in both two-dimensional planes and three-dimensional spaces were demonstrated using Matlab software. Furthermore, to address the specific requirements of bucket-arm vehicle arm motion, improvements were made to the RRT algorithm. These improvements included the addition of distance criteria and enhancements to the way branches were extended in the RRT algorithm. These changes reduced computational complexity, increased algorithm execution speed, and minimized memory usage. Additionally, collision detection functions were developed to enhance the algorithm’s obstacle avoidance capabilities, thereby increasing its overall functionality. Finally, the article explored the practical applications of the RRT algorithm with collision detection in the context of bucket-arm vehicle path planning and feasible parking area selection. Acknowledgments. This study was supported by the technology project of Southern Power Grid Corporation (Project No. 030600KK52220016).

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References 1. Cai, J., Li, T., Tang, C.: Application of insulating boom type aerial for non-service interruption working in distribution network. Distrib. Util. 32(05), 27–30 (2015) 2. Deng, H., Cai, W., Yu, X.: Methods and safety protection of live working on 66 kV transmission lines by aerial device with insulating boom. High Volt. Eng. 41(09), 3091–3096 (2015) 3. Liu, T., Tang, P., Zhou, B.: Experiment research of minimum approach distance for live working used of 500 kV insulated aerial vehicles. High Volt. Eng. 42(07), 2315–2321 (2016) 4. Li, G., Yang, S., Zhan, P.: Design of robot system for live-line working on distribution network. Mach. Tool Hydraul. 50(09), 66–70 (2022) 5. Li, M., Yu, L., Shan, J.: Mechanical design and finite element analysis of live working robot for 10 kV distribution power systems. Procedia Comput. Sci. 183, 331–336 (2021) 6. Lei, T., Xie, Z., Wang, K.: Design of high voltage live operation robot system. In: 2021 International Conference on Wireless Communications and Smart Grid (ICWCSG), pp. 473–476. IEEE (2021) 7. Lavalle, S.M.: Rapidly-Exploring Random Trees: A New Tool for Path Planning. Computer Science Department (1998) 8. Wang, W., Song, H., Yan, Z.: M universal index and an improved PSO algorithm for optimal pose selection in kinematic calibration of m novel surgical robot. Robot. Comput. Integr. Manuf. 50, 90–101 (2018)

Simulation Modeling and Forward/Inverse Kinematic Analysis of Insulated Bucket Arm Vehicles Cong Hu1 , Wanying Zhang2,3(B) , Qiao Shi1 , Xin Yang1 , Li Cai2,3 , Jianguo Wang2,3 , and Yadong Fan2,3 1 Foshan Power Supply Bureau, Guangdong Power Grid Co, Foshan, China 2 Engineering Research Center of Ministry of Education for Lightning Protection and

Grounding Technology, Wuhan University, Wuhan, China [email protected] 3 School of Electrical Engineering and Automation, Wuhan University, Wuhan, China Abstract. As the reliability requirements for power distribution networks continue to increase, uninterrupted operation of low-voltage distribution networks has become a critical task for power supply companies. Insulated bucket arm vehicle operations have become the primary method for live-line work in distribution networks. An analysis of the common structural components of insulated bucket arm vehicles’ arms was conducted, and a three-dimensional model of the mechanical arm was created using SolidWorks software. The DH parameter modification method was then employed to establish a parametric model. Subsequently, based on the 3D model of the bucket arm vehicle’s mechanical arm and the DH parameters, the mathematical model underwent forward and inverse kinematic analysis. Through forward kinematic analysis, research was conducted on the transformation matrices between coordinate systems. Through inverse kinematic analysis, a solution procedure for a special case of the insulated bucket arm vehicle’s inverse kinematics was obtained. Keywords: Insulated bucket arm vehicle · DH parameter improvement method · Kinematic analysis

1 Introduction In recent years, with rapid economic development and the continuous improvement of people’s living standards, the demand for power supply reliability has been increasing. To reduce power outage occurrences and enhance power supply reliability, conducting live-line maintenance on electrical grids in urban and rural areas has become an essential daily task for power supply companies. Insulated bucket arm vehicles serve as specialized vehicles for live-line maintenance of distribution networks. Typically, these vehicles are designed for high-voltage operations, starting from 10 kV and above. Their working bucket, articulated arm, control hydraulic system, and interconnection components possess specific insulation performance criteria. The articulated arm provides primary insulation protection for personnel during live-line operations between relative electrical potential levels [1]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 845–854, 2024. https://doi.org/10.1007/978-981-97-1072-0_86

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Substations play a crucial role as hubs for power system and the transmission of electrical energy. In the event of damage or failure to important equipment within a substation, if not addressed promptly, it may result in further malfunctions in other high-voltage devices or even damage to an entire line within the substation. Traditional substation inspections heavily rely on manual labor, subjective judgments, and experiential knowledge of operating and maintenance personnel. This approach is costly, inefficient, and prone to errors, no longer meeting the demands for stability in modern substations [2]. Manual inspections are gradually being replaced by robotic inspections in substations [3]. Inspection robots can pre-plan inspection routes and are equipped with various sensors to analyze the operational condition of substation equipment, significantly enhancing inspection efficiency [4]. However, inspection robots also have limitations: firstly, they have low inspection perspectives, making it susceptible to blind spots. Secondly, the dense arrangement of high-voltage equipment within a substation presents significant limitations for the inspection paths that the robot can undertake. To address this situation, Zhong Liqiang et al. proposed the research and development of a maintenance robot for 500 kV high-voltage overhead transmission lines, elucidating the environmental challenges that such a maintenance robot would need to confront [5]. Xia Lei et al. proposed a live robot based on the actual power maintenance needs of the electrical grid. They conducted MATLAB simulations of two position tracking control methods, demonstrating their feasibility [6]. Tan Li and Yinbo Du et al. [7, 8] studied the safety of high-voltage charged robots. Current research efforts are primarily focused on studying robots mounted on bucket arm vehicles, but there is comparatively less research dedicated to the study of the bucket and the mechanical arm of these carrier platforms. Given the mentioned issues and the current demand for live-line operations using bucket arm vehicles, there is a need for reliable on-site survey results, precise bucket arm vehicle operation, and a strict set of operational procedures. This approach can promote the intelligence of power grid maintenance while ensuring the safety of live-line workers. Currently, research on the automatic control of bucket arm vehicles is relatively limited. Therefore, this article will explore automated control methods based on robot mechanical arms, specifically focusing on the control of bucket arm vehicle mechanical arms.

2 Modeling of the Insulated Bucket Arm The bucket arm of an insulated bucket arm vehicle can be considered as a mechanical arm, typically composed of multiple linked segments, which can be viewed as rigid bars connected end to end. To study the motion of this mechanical arm, it is necessary to first establish a parametric model and then utilize mathematical methods to describe its posture and movements. The DH parameter method is a simplified theory for modeling robot kinematics, initially introduced by Denavit and Hartenberg in 1955 [9]. It effectively describes the parameter relationships between the links of a robotic arm. The main idea behind this method is to establish coordinate systems on each link of an open-chain mechanism. By determining the relative displacement relationships between adjacent coordinate systems, forward kinematic equations are developed to represent the relationships

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between different segments of a robot’s mechanical arm. Subsequently they also proposed improvements to the DH parameter method. In comparison to the traditional DH parameter method, which establishes coordinate systems on the transmission axes of the links, it can lead to ambiguities in describing parallel or tree-structured robotic arms. The DH parameter improvement method, as illustrated in Fig. 1, addresses the ambiguity issue by placing coordinate systems on the drive axes of the links. This approach provides a clearer description of the motion of the robotic arm and resolves the ambiguities associated with the original DH parameter method. Therefore, this article adopts the DH parameter improvement method.

Fig. 1. The DH parameter link coordinate relationships.

In this article, through the structural analysis of the traditional insulated bucket arm vehicle’s mechanical arm, as shown in Fig. 2, the mechanical arm of the bucket arm vehicle is divided into six parts: the rotating base, the lower arm, the upper arm, the telescopic arm, the balancing device, and the working bucket. Based on this division, a simplified model of the actual object was created, focusing on its critical components. In this article, SolidWorks software was used to create a 3D model of the insulated bucket arm vehicle, as depicted in Fig. 3. To perform a parametric analysis of the insulated bucket arm vehicle’s mechanical arm, it’s essential to establish the relevant coordinate systems for the mechanical arm. Following the requirements of the DH parameter improvement method, parameter coordinate systems are set up for each part of the bucket arm. Then, based on the 3D model of the insulated bucket arm vehicle and the DH parameter relationships for each mechanical arm coordinate system, DH parameters are determined, as shown in Table 1. Furthermore, to prevent the working bucket from tilting, the balancing device should always remain parallel to the ground, and under normal circumstances, the following condition should be met: θ4 = −θ2 − θ3 .

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Fig. 2. Illustration of the physical appearance of the insulated bucket arm vehicle.

Fig. 3. 3D modeling schematic diagram of the insulated bucket arm vehicle.

Table 1. DH parameters of insulated bucket arm vehicle. Name

ai−1

αi−1

di

θi

Value range

Rotating base

0

θ1

0

0

(−π , π )

Lower arm

0.8

−π 2

0

−π + θ 2 2

(0, π2 )

Upper arm

8

0

0.5

(−π , 0)

Telescopic arm

3 + d1

0

0

π + θ3 0

(0, 5)

Balancing device

6.15

0

0

θ4

Bucket

0.2

π 2

π ( −π 2 , 2)

0

θ5

π ( −π 3 , 3)

According to the DH parameter settings, configure the coordinate parameters for the 3D model in SolidWorks. Convert the configured file into a urdf file and import it into MATLAB. To verify if the motion of the bucket arm vehicle’s mechanical arm conforms to the specified coordinate transformations, we can assess its correctness by modifying its DH parameters, set the initial positions for [θ1, θ2, θ3, d1, θ4, θ5] as [0, 0, 0, 0, 0, 0]. Then, separately set [θ1, θ2, θ3, d1, θ4, θ5] to [1, 1, −2, 2, 1, 0.5]. We can observe the mechanical arm’s posture before and after the modifications as shown in Fig. 4. It

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demonstrates that each mechanical arm of the bucket arm vehicle rotates and extends in the intended directions as specified, confirming the correctness of the model validation.

Fig. 4. The mechanical arm is in its initial state and after modifying the parameters.

3 Kinematic Solution A mechanical arm, as a general rigid body, possesses six degrees of freedom in space. Therefore, when the position and orientation of a rigid body in a coordinate system are known, its pose in three-dimensional space can be described using a pose matrix, as shown in Eq. (1): ⎡

mx ⎢ my Rt = ⎢ ⎣ mz 0

nx ny nz 0

qx qy qz 0

⎤ px py ⎥ ⎥ pz ⎦

(1)

1

In space, homogeneous transformation matrices can be used to represent translation and rotation transformations between rigid bodies or coordinate systems. When applying transformations to a fixed coordinate system, we only need to left-multiply by the corresponding transformation matrix. However, when applying transformations to a rotating coordinate system, we need to right-multiply by the corresponding translation transformation matrix Trans. When a rigid body or coordinate system moves along the X, Y, and Z axes by distances x, y, and z, respectively, it can be represented using Eq. (2): ⎡

⎤ 100x ⎢0 1 0 y⎥ ⎥ Transx, y, z = ⎢ ⎣0 0 1 z ⎦ 0001

(2)

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When a rigid body or coordinate system rotates about the X, Y, or Z axis by an angle θ in space, it can be represented using Rot (X, θ ), Rot (Y, θ ), and Rot (Z, θ ) as shown in Eq. (3): ⎡ ⎤ 1 0 0 0 ⎢ 0 cosθ sinθ 0 ⎥ ⎥ Rot(X , θ ) = ⎢ ⎣ 0 sinθ cosθ 0 ⎦ 0 0 0 1 ⎤ cosθ 0 sinθ 0 ⎢ 0 1 0 0⎥ ⎥ Rot(Y , θ ) = ⎢ ⎣ sinθ 0 cosθ 0 ⎦ 0 0 0 1 ⎤ ⎡ cinθ − sinθ 0 0 ⎢ sinθ cosθ 0 0 ⎥ ⎥ Rot(Z, θ ) = ⎢ ⎣ 0 0 10 ⎦ 0 01 0 ⎡

(3)

The transformation matrix T (i−1, i) is used to represent the transformation from coordinate system (i−1) to coordinate system (i). It can be expressed as shown in Eq. (4): T (i − 1, i) = Rot(xi , αi−1 ) × Trans(xi , αi−1 ) × Rot(zi−1 , θi ) × Trans(zi−1 , di ) (4) Based on the coordinate transformation relationship from the rotating base to the working bucket, we can multiply the individual transformation matrices in sequence to obtain T (0,6), representing the final position of the end-effector in the overall coordinate system. It can be expressed as shown in Eq. (5): T (0, 6) = T (0, 1) × T (1, 2) × T (2, 3) × T (3, 4) × T (4, 5) × T (5, 6)

(5)

In typical scenarios, manipulating a mechanical arm requires knowing the angles or extensions of its joints at various moments. Based on the transformation matrices obtained from forward kinematics, and given the premise of knowing the end-effector’s angles and position, the parameters of the mechanical arm are reverse-engineered. This solution is known as the inverse kinematic solution. Mechanical arms exhibit high coupling, non-linearity, and other characteristics. Solving the inverse kinematics problem for a mechanical arm requires analyzing its specific structure to determine an appropriate inverse solution method. The upper arm, telescopic arm, and balancing device of the bucket arm vehicle are all located in the same plane, and the plane where the lower arm is located is parallel to this plane. Therefore, we can first determine the position of this plane, represented by θ1. This reduces the original three-dimensional problem to a two-dimensional one. Assuming the end-effector coordinates are P = [x, y, z], in some cases, it may be necessary to rotate the working bucket for operations. Therefore, the discussion includes finding special solutions when the working bucket is rotated by a certain angle. Assuming that the coordinate system of the working bucket is rotated by θ5 and the length of the working bucket is 1.1 m, the positional relationships in various planes will be as shown in Fig. 5:

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Fig. 5. Initial working plane and end-effector position projection of the mechanical arm.

When the working bucket is rotated by θ5, the plane where the forearm is located is parallel to the plane where the upper arm is located, the projection of the end-effector position P onto the plane of the upper arm is considered. The perpendicular line’s length is denoted as L, and the mathematical relationship is expressed as shown in Eq. (6): L = 0.5 + 1.1 sin θ5

(6)

According to Fig. 5, the rotation parameter θ1 of the rotary table can be obtained, as shown in Eq. (7): θ1 = α1 − α2 = arctan √

L z 2 +y2

− arcsin

z y

(7)

It can be observed that the value of θ1 is determined by both the end-effector position P and θ5. Modifying the value of θ5 appropriately can change the magnitude of θ1. After obtaining the rotation angle of the rotating base, set the projections of the lower arm and the end-effector position on the XY plane as Y and P2 , respectively, as shown in Fig. 6. In this case, the working range of the lower arm is a semicircle, and the coordinates of the end-effector position projection P2 are represented as (y , x ). The mathematical relationship is given by Eq. (8), and the projection of the target working plane of the upper arm is shown in Fig. 7. ⎧ z  2 2 ⎪ ⎨ y = |z| z + y × cos α2  (8) x = x − 0.8 ⎪ ⎩ tanθ × x −8 cos θ2 = −1 2 y −8 sin θ2 In Fig. 7, the red line represents the length of the projection of the working bucket on this plane. Its length changes with the variation of θ5. However, since the balancing device is always in the same plane as the upper arm, its projection length remains

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Fig. 6. The projection of the lower arm and the end-effector position.

Fig. 7. The projection of the working bucket and the upper arm.

constant. Let the projection length of both be D, and the mathematical relationship is given by Eq. (9): D = 1.1 cos θ5 + 0.2

(9)

By substituting the L value, we can calculate θ3, d1, and θ4 as shown in Eq. (10):

⎧ ⎪ l = (x − 8 cos θ2 )2 + (y − 8 sin θ2 )2 ⎪ ⎪ ⎪ ⎪ ⎪ L2 = l 2 + D2 − 2L ⎨  θ2  2× D2 × 2sin l +L −D (10) θ = − arccos 3 2×L×l ⎪ ⎪ ⎪ ⎪ d1 = L − 8.15 ⎪ ⎪ ⎩ θ4 = −θ2 − θ3

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Based on the 3D model obtained before, we can validate the inverse kinematic analysis results using Matlab. Assuming the end-effector position of the mechanical arm is (14, −4, 4) and that the working bucket is not rotated (θ5 = 0), we obtain the inverse solution as [−0.8739, 0.20497, −1.684, 2.2882, 1.4792, 0]. By applying these values to the parameters of the 3D model, we get the results shown in Fig. 8. The red dot represents the specified end-effector position. It can be observed that the mechanical arm correctly reaches the target point, indicating that the special solution process is correct.

Fig. 8. Schematic representation of the bucket arm posture.

4 Conclusion This study utilizes Solidworks for 3D modeling of the insulated bucket arm vehicle’s mechanical arm. By analyzing its structure and employing the DH parameter improvement method, a parameterized model for the mechanical arm of the bucket arm vehicle is presented. The article also derives motion constraints from the DH parameters of the mechanical arm and validates the accuracy of the arm’s modeling using Matlab. It introduces the fundamentals of robot arm kinematics, analyzes the forward kinematics of the bucket arm vehicle’s mechanical arm, and calculates the transformation matrices between different coordinate systems using the improved DH parameters. Through practical analysis, it provides a procedure for solving the inverse kinematics of the mechanical arm under certain constraints and validates this solution using Matlab and its 3D model. Acknowledgments. This study was supported by the technology project of Southern Power Grid Corporation (Project No. 030600KK52220016).

References 1. Cai, J., Li, T., Tang, C.: Application of insulating boom type aerial for non-service interruption working in distribution network. Distrib. Utilization 32(05), 27–30 (2015) 2. Zhang, X.: Comparison of live working between insulated rod and insulated bucket truck. Rural Electrician 20(10), 26–27 (2012)

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3. Li, G., Yang, S., Zhan, P.: Design of robot system for live-line working on distribution network. Mach. Tool Hydraulics 50(09), 66–70 (2022) 4. Feng, Y., Wu, S., Zhan, F.: Research on intelligent management and control system for live working safety of bucket arm vehicle. Telecom World 11, 194–195 (2018) 5. Zhong, L., Xie, Z., Wang, K.: Research on robot for repairing broken strands in 500kV high voltage live operation. J. Phys: Conf. Ser. 2030(1), 012088 (2021) 6. Xia, L., Wang, S., Xiang, H.: Research on control system of live working vehicle. In: 2016 4th International Conference on Mechanical Materials and Manufacturing Engineering, pp. 382– 384 (2016) 7. Du, Y., Tan, L., Xia, L.: Research on safety system of high altitude live working vehicle. In: 2016 4th International Conference on Mechanical Materials and Manufacturing Engineering, pp. 625–628 (2016) 8. Li, T., Cheng-jimng, W.: Research on insulation protection system for HV live working robot. In: International Conference on Integrated Circuits and Microsystems (ICICM), pp. 367–370. IEEE (2016) 9. Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. J. Appl. Mech. (1955)

Optimization of Insulated Bucket Arm Vehicle Bucket Arm Motion Trajectory and Analysis of Collision Detection Algorithms Cong Hu1 , Wanying Zhang2,3(B) , Xin Yang1 , Qiao Shi1 , Li Cai2,3 , Jianguo Wang2,3 , and Yadong Fan2,3 1 Foshan Power Supply Bureau, Guangdong Power Grid Co., Foshan, China 2 Engineering Research Center of Ministry of Education for Lightning Protection and

Grounding Technology, Wuhan University, Wuhan, China [email protected] 3 School of Electrical Engineering and Automation, Wuhan University, Wuhan, China

Abstract. Insulated bucket arm vehicle operation is currently the primary method for live-line work in the distribution network. Implementing automated path planning for the bucket arm to reach the target node will significantly improve the efficiency and safety of live-line operations. This research focuses on reducing the discretization of arm trajectories through the D-H parameterized modeling of the bucket arm and an enhanced RRT path planning algorithm. The study also involves using cubic and quintic interpolation functions to interpolate the arm’s trajectory and investigating their impact on arm motion speed and acceleration. Additionally, the research explores collision detection methods for the bucket arm, including comparing suitable bounding boxes for various parts of the arm. Keywords: Insulated bucket arm vehicle · Mechanical arm simulation research · Collision detection

1 Introduction Reducing power outages and improving power supply reliability have become important tasks for power supply companies. Non-outage operations in low-voltage distribution networks are essential for this purpose. Insulated bucket arm vehicles are a primary method for live-line work in distribution networks due to their high mobility, extensive operational range, and good insulation performance [1]. However, this method also carries certain risks due to the limitations of low-voltage distribution networks, and accidents resulting from improper operation of bucket arm vehicles are relatively common. Due to the limitations in phase spacing and ground clearance in 10 kV distribution lines, the incidence of electric shock accidents during maintenance is relatively higher compared to other types of work. In response to this issue, a proposed solution is the development of a live-line robot system for 10 kV distribution lines, aiming to reduce the need for manual operations in energized environments [2, 3]. Current research primarily © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 855–863, 2024. https://doi.org/10.1007/978-981-97-1072-0_87

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focuses on the direction of adding maintenance robots to the working bucket, with limited studies related to the autonomous control of the bucket arm vehicle itself. The bucket arm of an insulated bucket arm vehicle can be considered as a robotic arm. The study of robotic arm kinematics involves establishing a kinematic model of the robotic arm to analyze the changing positions, velocities, and accelerations of the arm’s joints and the end effector in space over time. The bucket arm can be modeled using the D-H parameter method, and the Rapidly-exploring Random Tree (RRT) algorithm based on a three-dimensional modeling and imaging system for unmanned drones [4, 5]. Viewing the bucket arm as a general robotic arm allows for the implementation of automatic control of the insulated bucket arm vehicle’s bucket arm in three-dimensional space, enabling it to reach the target position. The combination of robotic arm research with software like Matlab is currently a research direction. Sun Jun studied the DH modeling, kinematic analysis, trajectory planning algorithms, and simulation of the DOBOT robotic arm in the Matlab environment. Through simulation analysis, they obtained the displacement, velocity, acceleration, and end-effector trajectory of each joint of the robotic arm under the influence of trajectory planning algorithms [6]. Zheng Ying conducted research on modeling and trajectory planning for a six-degree-of-freedom robotic arm. They established the DH parameter model for the robotic arm and performed joint space trajectory planning using third and fifth-degree polynomials. Additionally, they conducted linear trajectory planning in Cartesian coordinates [7]. Wang Yumin utilized an improved DH method to perform kinematic modeling of a robotic arm. They conducted research on enhancing the thirddegree polynomial interpolation algorithm to address situations in which the angular velocity and angular acceleration change curves undergo abrupt variations during the motion of the robotic arm [8]. This article presents an improved and optimized robotic arm trajectory planning and collision detection method tailored for the structure of the insulated bucket arm on an insulated bucket arm vehicle. It introduces spatial trajectory planning methods for the robotic arm, as well as collision detection methods using bounding boxes. Third-degree and fifth-degree interpolation functions are employed to interpolate the robotic arm’s trajectory, and their impact on the robotic arm’s velocity and acceleration is studied. Additionally, the article explores collision detection methods for the bucket arm of the bucket arm vehicle, outlines the bounding box detection method, and investigates the appropriate bounding boxes for the various components of the bucket arm.

2 Bucket Arm Trajectory Planning The motion planning for the bucket arm of the bucket arm vehicle includes both path planning and trajectory planning. The RRT algorithm can be used to determine the path of the bucket arm vehicle’s end effector, and through inverse kinematics, the DH parameters corresponding to the arm’s movement at various points can be obtained. However, the results obtained using this method are relatively discrete and do not meet the requirements for precise control of the insulated bucket arm vehicle’s arm. Therefore, trajectory planning is necessary. Trajectory planning for the mechanical arm refers to the process of planning the angles, velocities, and angular velocities of the various joints of the arm within a given

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workspace along a specific working path. In practical situations, the motion of the mechanical arm is typically executed by electric motors or hydraulic systems, and the results of trajectory planning directly impact the performance of these devices in terms of the arm’s angles, velocities, and angular velocities. Trajectory planning for a mechanical arm can be categorized into two main types based on its motion: joint space trajectory planning and Cartesian space trajectory planning. Joint space trajectory planning involves controlling the mechanical arm by regulating joint angles or extensions, offering a direct means of controlling the arm without the complexities of dealing with multiple inverse solutions and singularities that can be present in inverse kinematic analysis. On the other hand, Cartesian space trajectory planning directly focuses on the end-effector of the mechanical arm, providing a clear representation of the arm’s motion and allowing an intuitive understanding of its pose. However, this method, which solely considers the end-effector’s position, still necessitates addressing the challenges arising from multiple solutions and singularities in the context of multi-degree-of-freedom mechanical arms, making it more complex. Since this paper derives the end-effector path of the mechanical arm based on the RRT algorithm and then obtains the DH parameters for various points along the path through special solutions, Cartesian space trajectory planning is not necessary. This paper focuses solely on small-scale joint space trajectory planning for the mechanical arm. After specifying the initial joint angles and target joint angles, we may need to use polynomial interpolation to make the motion curve of the mechanical arm more continuous. For any joint trajectory planning where the given parameters only include the initial and target joint angles, we do not need to consider joint motion speed and acceleration. Simply connecting them end to end can be accomplished with linear interpolation. However, in most cases, before reaching the target angles, the joints need to go through several intermediate angles to arrive. In this situation, if we want to ensure continuous changes in joint angles, we need to increase the interpolation dimension, which means using polynomials for interpolation. If we don’t consider the issue of acceleration in joint angle changes, we can use cubic interpolation. However, if we need to ensure that the acceleration curve of the mechanical arm’s motion, obtained from joint trajectory planning, is smooth, we need to use polynomials of degree five or higher for interpolation. This article will introduce cubic and quintic polynomial interpolation. Taking the example of the rotation table of the bucket-arm vehicle, let’s assume its initial angle θ 0 , target angle θ m , and the motion time from t 0 to t 1 . We’ll use θ (t), θ ’(t), and θ ”(t) to represent its angle, velocity, and acceleration as functions of time, respectively. The parameters should satisfy Eq. (1): Where m0 , m1 , m2 , and m3 are the coefficients of the interpolation polynomial to be determined. Assuming the initial and final values of the arm’s rotation speed are both 0, the boundary conditions for the interpolation function are as shown in Eq. (2): ⎧ ⎨ θ (t) = m0 + m1 t + m2 t 2 + m3 t 3 (1) θ  (t) = m1 + 2m2 t + 3m3 t 2 ⎩  θ (t) = 2m2 + 6m3 t

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⎧ θ (t0 ) = θ0 ⎪ ⎪ ⎨ θ (t1 ) = θm ⎪ θ  (t ) = 0 ⎪ ⎩  0 θ (t1 ) = 0

(2)

After substituting the boundary conditions, the coefficients of the interpolation polynomial can be determined as shown in Eq. (3): ⎧ ⎪ m0 = θ0 ⎪ ⎪ ⎪ ⎨ m1 = 0 (3) m2 = t32 (θm − θ0 ) ⎪ ⎪ 1 ⎪ ⎪ m = − 2 (θ − θ ) ⎩ 3

t13

m

0

Based on the above information, we can derive the cubic interpolation polynomial trajectory planning for the turntable from the initial angle to the target angle as shown in Eq. (4): θ (t) = θ0 +

3 (θ t12 m

− θ0 )t −

2 (θ t13 m

− θ0 )t 3

(4)

Set θ 0 = 0, θ m = 1, t 0 = 0, t 1 = 1. Using Matlab for simulation experiments, we can plot the rotation angle of the turntable, the rotation speed, and the rotation acceleration as a function of time, as shown in Fig. 1. The horizontal axis represents time (t), the red curve represents the curve of the turntable speed with respect to time, the brown curve represents the speed as a function of time, and the yellow line represents the curve of acceleration with respect to time.

Fig. 1. Simulation results for cubic interpolations.

From Fig. 1, we can observe that both the initial and final velocities are zero. However, the initial and final accelerations are not zero. Therefore, this interpolation method cannot ensure a smooth acceleration curve and should only be used when there are no specific requirements for acceleration.

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Three-degree polynomial interpolation cannot guarantee a smooth acceleration curve. Unsmooth acceleration can lead to uneven forces on the robot arm’s joints and may result in the arm not coming to a stop at the intended position after reaching the endpoint. Therefore, additional constraints should be introduced to ensure that the acceleration curve meets the requirements. Hence, we attempt five-degree polynomial interpolation, and its parameters should satisfy Eq. (5): ⎧ ⎨ θ (t) = m0 + m1 t + m2 t 2 + m3 t 3 + m4 t 4 + m5 t 5 (5) θ  (t) = m1 + 2m2 t + 3m3 t 2 + 4m4 t 3 + 5m5 t 4 ⎩ θ  (t) = 2m2 + 6m3 t + 12m4 t 2 + 20m5 t 3 where m0 , m1 , m2 , m3 , m4 , m5 are the coefficients of the interpolation polynomial. In addition to assuming that the initial and final angular velocities of the robot arm are both 0, this time, it should be assumed that both the initial and final accelerations are 0. Therefore, the initial conditions for the interpolation function are given by Eq. (6): ⎧ ⎪ θ (t0 ) = θ0 ⎪ ⎪ ⎪ ⎪ θ ⎪ ⎪ (t 1 ) = θm ⎨ θ (t0 ) = 0 (6) ⎪ θ  (t1 ) = 0 ⎪ ⎪ ⎪ ⎪ θ  (t0 ) = 0 ⎪ ⎪ ⎩  θ (t1 ) = 0 According to Eq. (6), the coefficients of the quintic interpolation polynomial can be calculated as shown in Eq. (7): ⎧ ⎨ m0 = θ0 (7) m =0 ⎩ 1 m2 = 0 The values of m3 , m4 , and m5 can be obtained by solving the matrix equation given in Eq. (8): ⎤ ⎡ 3 4 ⎤−1 ⎡ ⎤ θ1 m3 t1 t1 t15 ⎣ m4 ⎦ = ⎣ 3t 2 4t 3 5t 4 ⎦ · ⎣ 0 ⎦ 1 1 1 m5 6t1 12t12 20t13 0 ⎡

(8)

Therefore, we can obtain the trajectory planning using the fifth-degree polynomial interpolation. Similarly, assuming θ 0 = 0, θ m = 1, t 0 = 0, t 1 = 1, we can conduct simulation experiments using Matlab to plot the rotation angle, rotation speed, and rotation acceleration over time. The results are shown in Fig. 2, where the horizontal axis represents time (t), the red curve represents the rotation speed over time, the brown curve represents the speed with respect to time, and the yellow line represents the acceleration over time. From Fig. 2, we can observe that the rotation table’s angular acceleration follows the desired pattern, indicating that the five-degree polynomial interpolation is superior to the three-degree interpolation in controlling acceleration.

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Fig. 2. Simulation results for quintic polynomial interpolations.

3 Collision Detection Methods and Applications The working environment for an insulated bucket arm vehicle generally involves static obstacles. Therefore, this paper primarily focuses on research related to static obstacles. When performing collision detection, analyzing the original shape of objects can be challenging. Hence, simplified geometric shapes, known as bounding volumes, are often used. Common collision detection methods include cylinder bounding, sphere bounding, and cube bounding. Each type of bounding volume has its advantages and disadvantages. When the bounding volume poorly fits the object’s shape, it might not accurately reflect the object’s state, leading to false positives. On the other hand, if the bounding volume closely matches the object’s shape, it may increase computational complexity. Therefore, the choice of bounding volume should depend on the specific modeling requirements of different objects. Here, we will describe the mechanisms and suitable applications for various bounding volumes. The cylinder bounding method involves using a cylinder to approximate the shape of an object. It determines whether a collision occurs by checking if the object enters a specific range around the line segment provided by the model. As shown in Fig. 3, the left image illustrates the modeling of the arm of an insulated bucket arm vehicle, while the right image shows the model enclosed within a cylinder bounding volume. Similarly, obstacles typically encountered in the operation of bucket-arm vehicles, such as utility poles and tree trunks, can all be represented using bounding cylinders. In this case, the problem can be simplified to determine whether the cylinder representing the robot arm (R1 ) intersects with the cylinder representing the obstacle (R2 ). The equation of the line representing the center axis of cylinder R1 , with its endpoints at coordinates (x 1 , y1 , z1 ) and (x 2 , y2 , z2 ), and with scale factor k, radius r, can be expressed as shown in Eq. (9): x−x1 x2 −x1

=

y−y1 y2 −y1

=

z−z1 z2 −z1

=k

It can be simplified to Eq. (10): ⎧ ⎨ X (k) = kx2 + (1 − k)x1 Y (k) = ky2 + (1 − k)y1 ⎩ Z(k) = kz2 + (1 − k)z1

(9)

(10)

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Fig. 3. Simulation results for quintic polynomial interpolations.

Similarly, setting the coordinates of the two endpoints of the obstacle cylinder as (a1 , b1 , c1 ) and (a2 , b2 , c2 ), with a proportionality constant m and a radius of R, its simplified line equation is as shown in Eq. (11): ⎧ ⎨ A(m) = mx2 + (1 − m)a1 (11) B(m) = mb2 + (1 − m)b1 ⎩ C(m) = mc2 + (1 − m)c1 By solving for the straight-line distance between the obstacle and the robot’s cylinder, we can determine whether the two cylinders have collided. Let the straight-line distance be denoted as D. The relationship between these quantities is as shown in Eq. (12):

(12) D = [X (K) − A(M )]2 + [Y (K) − B(M )]2 + [Z(K) − C(M )]2 When D > R + r, it indicates that the robot’s arm and the obstacle have not collided, and the path is feasible. When D ≤ R + r, it indicates that the robot’s arm and the obstacle have collided, and the path is not feasible. We need to choose a different path. This collision detection method based on cylinder approximations simplifies the analysis and decision-making process for path planning in the presence of obstacles. It’s a practical approach for ensuring the robot’s arm doesn’t collide with obstacles during its operation. Ball envelope method involves modeling the object using a sphere. It determines whether a collision has occurred by checking if the object enters a specific range around the model’s given line segment. This is a common method for envelope representation. The advantage of this method is its simple structure, where it merely follows the translation of the object and doesn’t change with the object’s rotation. Consequently, it is suitable for collision detection in the work bucket of an insulated bucket arm vehicle. As shown in Fig. 4. Assuming the sphere’s center position is (x 0 , y0 , z0 ) and the envelope sphere’s radius is r, the expression for this envelope sphere in three-dimensional space is as shown in Eq. (13):  (13) S = {(x, y, z)| (x − x0 )2 + (y − y0 )2 + (z − z0 )2

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Fig. 4. Simulation results for quintic polynomial interpolations.

For obstacles described by points, assuming their coordinates are represented as Z (x, y, z), we can calculate the distance D between them and the center of the sphere using Eq. (14). D = (x − x0 )2 + (y − y0 )2 + (z − z0 )2

(14)

When obstacles are enclosed in cylindrical bounding boxes with a radius of R, we can modify the spherical bounding box’s radius to r1 = R + r. We can then treat the obstacle as a line segment and determine if a collision has occurred by calculating the distance between the line segment and the center of the sphere. Assuming the two endpoints of the line segment are represented as (a1 , b1 , c1 ) and (a2 , b2 , c2 ), and the scaling constant is m with a radius of R, we can calculate the orthogonal projection of the sphere’s center onto the line segment with the coordinates (Am , Bm , C m ) as shown in Eq. (15): ⎧ ⎨ Am = ma2 + (1 − m)a1 (15) Bm = mb2 + (1 − m)b1 ⎩ Cm = mc2 + (1 − m)c1 Similarly, we can calculate the distance D between the orthogonal projection and the center of the sphere using Eq. 4.13 to determine whether a collision has occurred.

4 Conclusion This study initially investigated trajectory planning for the robotic arm, using both cubic interpolation and quintic interpolation functions to interpolate the arm’s trajectory. The study examined their effects on the arm’s motion velocity and acceleration. Cubic interpolation results in a smooth velocity curve for the robotic arm but does not control the acceleration curve, while quintic interpolation can achieve both smooth velocity and acceleration curves, providing better control over the arm’s motion. Furthermore, the paper explored collision detection methods for the bucket arm of the insulated bucket arm vehicle, introducing the concept of bounding box detection. The study also researched

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which types of bounding boxes are suitable for different components of the bucket arm. In this context, cylindrical bounding boxes are more suitable for the upper arm, lower arm, and telescopic arm of the robotic arm, while spherical bounding boxes are better suited for the working bucket of the insulated bucket arm vehicle. Acknowledgments. This study was supported by the technology project of Southern Power Grid Corporation (Project No. 030600KK52220016).

References 1. Cai, J., Li, T., Tang, C.: Application of insulating boom type aerial for non-service interruption working in distribution network. Distrib. Utilization 32(05), 27–30 (2015) 2. Liu, T., Tang, P., Zhou, B.: Experiment research of minimum approach distance for live working used of 500 kV insulated aerial vehicles. High Volt. Eng. 42(07), 2315–2321 (2016) 3. Li, G., Yang, S., Zhan, P.: Design of robot system for live-line working on distribution network. Mach. Tool Hydraulics 50(09), 66–70 (2022) 4. Lavalle, S.M.: Rapidly-exploring random trees: a new tool for path planning. Computer Intelligence Department (1998) 5. Wang, W., Song, H., Yan, Z.: M universal index and an improved PSO algorithm for optimal pose selection in kinematic calibration of m novel surgical robot. Robot. Comput.-Integr. Manuf. 50, 90–101 (2018) 6. Sun, J., Zhang, J., Ma, L.: Research on modeling and simulation, and trajectory planning algorithms for robot manipulators. Mach. Electron. 34(6), 72–75 (2016) 7. Zheng, Y., Wang, M., Xu, Q.: Research on modeling and trajectory planning of 6-DOF manipulator. J. Huanghe S&T Coll. 23(11), 10–14 (2021) 8. Wang, Y., Qin, F.: Research on kinematics modeling and trajectory planning of 5-DOF manipulator. Electr. Eng. (08), 62–66+69 (2022)

Research on Winding Electrodynamic Force and Hot Spot Temperature Rise of Environmental Stereo Wound Core Transformer Junchao Wu, Haipeng Tian(B) , Wei Cheng, Zhitao Song, Qing Wu, and Chi Yuan State Grid Hubei Power Supply Limited Company, Ezhou Power Supply Company, Ezhou 436000, China [email protected]

Abstract. In order to study the short-circuit electrodynamic force of the environmental stereo wound core transformer and the influence of the structure of the transformer core, high and low voltage winding and transformer shell on the temperature profile, the finite element field-circuit coupling model and the stereo fluid-temperature field simulation model are established by ANSYS simulation software. The short-circuit electrodynamic force of the transformer is calculated, and the influence of the structure of the transformer core, high and low voltage winding and transformer shell on the temperature profile of the transformer is analyzed. The results show that the amplitude force of the high-tension inner and outer windings shows an outward pull, while the axial force shows an inward pressure as a whole. The amplitude force of the low-voltage inner and outer windings shows an inward pressure, and the axial force is the same as that of the high-tension winding. The hot spot temperature of the transformer winding is 379.5K, which appears at the top of the outer low-voltage winding. The maximum temperature of the transformer core is 331.3K, which appears near the top of the core and the low-voltage winding. Keywords: Tridimensional wound-core transformer · Electromechanical short-circuit force · Multi-physics · Temperature profile

1 Introduction With the vigorous promotion of energy conservation and emission reduction in China, energy-saving transformers have been widely used and promoted in recent years. As one of the energy-saving transformers, tridimensional wound-core transformers have been increasingly used because of their small size, light weight, high energy efficiency, and superior mechanical and electrical performance compared to traditional three-phase planar stacked-core transformers. The heat dissipation problem of transformer has always been the focus of transformer research [1–4]. Many scholars have done a lot of research on the heat dissipation problem © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 864–871, 2024. https://doi.org/10.1007/978-981-97-1072-0_88

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of environmental stereo wound core transformer [5–8]. J Ruan and other scholars [9] proposed an inversion method to estimate the transient hot spot temperature of 10 kV oilimmersed transformer; Reference [2] provides a method that can calculate the maximum temperature of the transformer and the life of the power transformer under limited information. R Kebriti and other scholars [10] conducted a multi-step temperature rise test on a copper distribution transformer according to the IEC standard. In reference [11], computational fluid dynamics (CFD) parameter scanning and correlation based on multi-layer least squares were performed. The relationship between H and Re and Pr of the fixed winding geometry with uniform loss distribution is obtained. In order to analyze the short-circuit electromotive force of the stereo coil-core transformer and the influence of the structure of the transformer core, high-tension and lowvoltage windings and transformer shell on the temperature profile, In this paper, the finite element field-circuit coupling model is established to calculate the short-circuit electromotive force of the transformer, and then the influencing factors and laws of the temperature profile of the transformer are analyzed.Transformer parameters and models.

2 Transformer Parameters and Model The overall structure of the stereo triangular coil core transformer studied in this paper is shown in Fig. 1(a). The stereo coil core transformer mainly includes iron core, hightension coil, low-tension coil, oil tank, transformer oil and body. The corresponding material properties are shown in Table 1. Table 1. Material characteristics of each part of transformer Material

Resistivity (10−8 ·m)

High voltage coil (flat copper wire)

1.79

1

212

Low voltage coil (flat copper wire)

1.79

1

118

Iron core

–

5000

664

Oil

–

1

375

Oil tank

–

1

365

Relative permeability

Weight

The transformer is a triple-phase oil-type transformer, and the high-tension winding coil is triangularly connected. There are 13 small layers, which form two large layers separated by the oil channel. The low tension winding coil adopts star connection mode, in which there are two layers, and the two layers are separated by the oil channel. The turns of high tension coil and low tension coil are 845 and 20 respectively, and both of them are flat copper wire structure.The finite element model of environmental stereo wound core transformer is shown in Fig. 1.

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Fig. 1. Finite element model of environmental stereo wound core transformer

3 Calculation of Short-Circuit Electrodynamic Force of Transformer For the short-circuit electrodynamic analysis of the low-voltage side winding, the normal operation of the transformer under the rated voltage is simulated, and then the sudden short-circuit of the secondary side is simulated. At this time, because the short-circuit current is much larger than the load current, the load current can be ignored, that is, the transformer is considered to be empty before the short circuit, and the time when the short circuit occurs is 0 s. Since the three phases are electrically symmetrical, here we consider the case of the most serious phase A. The computational boundary conditions are shown in Table 2. Table 2. Calculation boundary conditions for short-circuit electrodynamic force Location

Loading condition

Primary side circuit

Voltage 10000/1.732 (V)

Primary side circuit

The initial phase Angle of the A phase voltage is 0

Secondary side circuit

Short circuit

Outer boundary

AX = 0, AY = 0, AZ = 0

The field-circuit coupling calculation is carried out according to the boundary conditions in Table 2, and the transient current changes of the high and low voltage windings of each phase can be obtained. The transient changes of phase A high and low voltage side line currents are shown in Fig. 2. From the results of Fig. 2, the peak currents of the high and low voltage sides show a tendency to decay after short-circuit, and will eventually tend to the steady-state shortcircuit current. The maximum short-circuit current of the high-tension winding occurs at 0.01 s after the short-circuit, and the amplitude is 1128 A. Due to the maximum value of short-circuit transient electrodynamic force occurring at 0.01 s, this time was selected for key analysis, and the vector diagram of the electrodynamic force distribution of the A-phase winding at this time is shown in Fig. 3. From the results of Fig. 3, for low-tension windings, the force trend of the inner and outer windings is consistent, with inward pressure in the amplitude direction and inward

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Fig. 2. High and low tension side short circuit instantaneous current

pressure in the axial direction. For high-tension windings, the force trend of the inner and outer windings is also consistent. The maximum short-circuit electrodynamic force of the whole high tension winding and low tension winding occurs in the middle of the outer low tension winding and the middle of the inner high tension winding respectively. The reason for this phenomenon is that the leakage inductance near the oil gap between the high-low voltage winding is the highest.

Fig. 3. Peak time A phase winding electrodynamic vector diagram

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4 Fluid-Temperature Field Analysis of Environmental Stereo Wound Core Transformer 4.1 Stereo Fluid-Temperature Field Simulation Model In the stereo fluid-temperature field analysis, the influence of transformer core, high and low tension winding and transformer shell on temperature profile is mainly considered. The transformer winding adopts a layered structure, in which the longitudinal oil channel width in the low-tension winding, the longitudinal oil channel width in the high-tension winding, and the longitudinal oil channel width between the high and low voltage windings are 3 mm, 4 mm, and 7 mm, respectively. In the simulation of fluid-temperature field of environmentally friendly transformer, the indirect coupling method is adopted. Firstly, the stereo magnetic field simulation of the transformer is carried out in ANSYS. The calculated core losses and winding losses are used as loading conditions to simulate the fluid-temperature field in CFX. 4.2 Transformer Fluid-Temperature Field Simulation Results The nonlinearity and anisotropy of amorphous alloy material of transformer core are considered. The magnetic flux density and vector diagram distribution inside the transformer core calculated by the time-harmonic field are shown in Fig. 4.

Fig. 4. Electromagnetic field calculation results of stereo coil core transformer

From the results of Fig. 4, the maximum magnetic flux density of the core appears at the corner of the single frame of the core. And the magnetic circuit inside the core is distributed along the shortest path of a single frame. Ignoring the error caused by model grid discretization and numerical solution at the corner of the single frame of the core, it is considered that the maximum magnetic density in the transformer core column is close to 1.3 T. The fluid-temperature multi-physical field analysis of the transformer is carried out in CFX, and the original temperature of the surrounding environment is set to 298.15 K. The temperature profile of the transformer core and winding is calculated as shown in

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Fig. 10. The highest temperature of the winding is 377 K, which appears in the outer low-tension winding, and the winding temperature is higher than the core temperature. The transformer core is selected as the observation object, and the temperature profile of the core surface is shown in Fig. 5(b). It can be found that the maximum temperature of the core is 331.3K, which appears near the upper end of the core and the low-tension winding. The temperature at the bottom of the core is low, and the minimum temperature is 323.7K.

Fig. 5. Core and winding temperature profile of environmental stereo wound core transformer

The low-tension winding is selected as the observation object, and the temperature profile of the low-tension winding is shown in Fig. 6. The maximum temperature of 379.5K appears at the top of the outer low-tension winding, and the maximum temperature of the inner winding is 378.6K.

Fig. 6. Temperature profile of low-tension winding of environmental stereo wound core transformer

Through the simulation results, the temperature profile diagram of the high voltage winding is shown in Fig. 7. The highest temperature of the high voltage winding occurs in the upper and lower parts of the inner winding, and the temperature reaches 351.0 K. Due to the good heat dissipation condition of the outer layer, the temperature of the outer

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high voltage winding is significantly lower than that of the inner high voltage winding, and the highest temperature is 338.4K.

Fig. 7. Temperature profile of high tension winding of environmental stereo wound core transformer

The observation surface is selected in the middle of the transformer core, and the temperature profile of each part of the observation surface is shown in Fig. 8 (a). The internal low tension winding has poor heat dissipation conditions and high temperature. The distribution of transformer oil flow velocity on the selected observation surface is shown in Fig. 8 (b). The flow rate of transformer oil inside the winding is very small, which corresponds to the winding temperature in Fig. 8 (a), and the flow rate is large in the center and outside of the three-phase winding.

Fig. 8. Results of observation surface in the middle of transformer

5 Conclusion In this paper, ANSYS simulation software is used to establish a finite element field-circuit coupling model and a stereo fluid-temperature field simulation model, calculate the shortcircuit electric dynamics of the stereo coil core transformer, analyze the influence of transformer core, high and low voltage winding and transformer shell on the temperature profile of transformer, and obtain the following conclusions:

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(1) The amplitude force of the inner and outer windings of high voltage shows an outward pulling force, while the axial force is downward at the upper end of the winding and upward at the lower end, and the overall pressure is inward; The amplitude force of the low-voltage inner and outer windings is different from the situation of the high-tension winding, and they all show the pressure inward, while the axial force is the same as the high-tension winding. (2) The maximum temperature of the transformer winding is 379.5K, which appears at the top of the outer low-voltage winding. The highest temperature of the inner low-voltage winding is 378.6 K; the highest temperature of the high-voltage winding is 351.0 K, which appears at the top of the inner high-voltage winding. (3) The maximum temperature of the transformer core is 331.3 K, which appears near the top of the core and the low-tension winding. Acknowledgments. This manuscript was supported in part by the State Grid Hubei Electric Power Co., Ltd, under Grant B315F0222836.

References 1. Caijiang, L., Linfeng, L., Zixuan, L., et al.: Location and corrosion detection of tower grounding conductors based on electromagnetic measurement. Measurement 199 (2022). (in Chinese) 2. Rommel, D.P., Di Maio, D., Tinga, T.: Transformer hot spot temperature prediction based on basic operator information. Int. J. Electr. Power Energy Syst. 124, 106340 (2021) 3. Gonzólez-Cagigal, M.Á., Rosendo-Macías, J.A., Gómez-Expósito, A.: Parameter estimation for hot-spot thermal model of power transformers using unscented Kalman filters. J. Mod. Power Syst. Clean Energy 11(2), 634–642 (2022) 4. Rezaeealam, B., Askary, S.: Real-time monitoring of transformer hot-spot temperature based on nameplate data. IET Gener. Transm. Distrib. (2023) 5. Lei, C., Bu, S., Wang, Q., Zhou, N., Yang, L., Xiong, X.: Load transfer optimization considering hot-spot and top-oil temperature limits of transformers. IEEE Trans. Power Delivery 37(3), 2194–2208 (2021) 6. Akbari, M., Mostafaei, M., Rezaei-Zare, A.: Estimation of hot-spot heating in OIP transformer bushings due to geomagnetically induced current. IEEE Trans. Power Delivery 38(2), 1277– 1285 (2022) 7. Luo, C., et al.: Influence of insulation paper on the hot spot temperature of oil-immersed transformer winding. Mod. Phys. Lett. B 35(28), 2140021 (2022) 8. Park, T.W., Han, S.H.: Numerical analysis of local hot-spot temperatures in transformer windings by using alternative dielectric fluids. Electr. Eng. 97, 261–268 (2015) 9. Ruan, J., Deng, Y., Quan, Y., Gong, R.: Inversion detection of transformer transient hot spot temperature. IEEE Access 9, 7751–7761 (2021) 10. Kebriti, R., Hossieni, S.H.: 3D modeling of winding hot spot temperature in oil-immersed transformers. Electr. Eng. 104(5), 3325–3338 (2022) 11. Zhang, X., Wang, Z., Liu, Q.: Interpretation of hot spot factor for transformers in OD cooling modes. IEEE Trans. Power Delivery 33(3), 1071–1080 (2017)

Maintenance Strategy of Microgrid Energy Storage Equipment Considering Charging and Discharging Losses Xi Cheng1 , Yafeng Liang1 , Lihong Ma1 , Jianhong Qiu1 , Rong Fu2 , Zaishun Feng2 , Yangcheng Zeng2 , and Yu Zheng3(B) 1 Hainan Power Grid Co., Ltd., Haikou 570100, China 2 Hainan Power Grid Co., Ltd., Sansha Power Supply Bureau, Sansha 573199, China 3 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

Abstract. As the key equipment for smooth load and reliability improvement of independent microgrids due to its high controllability, it is of great significance to adopt reasonable operation and maintenance strategies to improve the safety and reliability of energy storage equipment. The existing O&M strategy has not considered the impact of charge and discharge loss of energy storage batteries, and insufficient utilization of its operating data will lead to high overall O&M costs of equipment. This paper proposes an operation and maintenance strategy considering the number of charging and discharging and loss of energy storage batteries, and verifies the effectiveness of the operation and maintenance strategy proposed in this paper based on the historical history of on-site operation and maintenance of a microgrid energy storage power station. Keywords: Microgrid · Energy storage equipment · Charge and discharge loss · Operational policies

1 Introduction Energy storage configuration is of great significance for the safe and stable operation of microgrids [1, 2]. In recent years, with the continuous growth of energy storage equipment, the reports of energy storage station accidents have also increased, which has brought serious threats to the safe operation of microgrids [3, 4]. The operation and maintenance experience of the existing main equipment of the power grid shows that if scientific and reasonable operation and maintenance is adopted before the failure, the equipment failure rate can be effectively reduced. Therefore, it is necessary to study the operation and maintenance technology of microgrid energy storage equipment. At present, there are some relevant standards for the maintenance and operation and maintenance of electrochemical energy storage power stations, such as GB/T365492018 “Operation Indicators and Evaluation of Electrochemical Energy Storage Power Stations” and the upcoming GB/T43215-2023 “Maintenance Regulations for Electrochemical Energy Storage Power Stations” in China. These standards provide a reference © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 872–879, 2024. https://doi.org/10.1007/978-981-97-1072-0_89

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for the operation and maintenance of microgrid energy storage power stations. However, due to the difference in the operating environment of energy storage power stations, such as in the strong corrosion environment of tropical islands, the battery state may be accelerated due to the corrosion microenvironment, thereby affecting its performance. Therefore, it is necessary to conduct targeted analysis according to the actual operation data of energy storage power stations, and there are few studies on the status assessment and operation and maintenance of microgrid energy storage power stations, and relevant research needs to be carried out urgently. There is energy loss in the process of charging and discharging of energy storage power stations, and its efficiency affects the economy of energy storage power stations and restricts the promotion and application of energy storage power stations [5, 6]. It is of great significance to formulate corresponding operation and maintenance strategies around the changing characteristics of charge and discharge losses of energy storage power stations. The energy loss of energy storage power station is affected by many factors such as power station scale, operating conditions, environmental conditions, etc., and is also related to the dynamic performance attenuation of energy storage batteries, converters and other parts of equipment [7–10]. In this paper, by studying the characteristics of charge and discharge loss changes during the operation of actual microgrid energy storage power stations, an online evaluation method for microgrid energy storage power station losses based on the online monitoring data of charge and discharge capacity of grid-connected converters is established, and the optimization of operation and maintenance strategies of energy storage power stations considering charging and discharging losses is proposed. The research results have important reference significance for the formulation of reliability operation and maintenance strategies for microgrid energy storage power stations.

2 Energy Loss Model of Microgrid Energy Storage Station Mechanism According to the different functions of each part of the electrochemical energy storage station, it can be divided into energy storage unit, power conversion system, monitoring and dispatching management system and auxiliary power consumption system. The energy storage unit consists of an energy storage battery pack and a corresponding battery management system (BMS); Power conversion system (PCS) consists of an energy storage converter and a corresponding control system; The monitoring and dispatch management system includes a central control system and an energy management system (EMS); The auxiliary power system mainly includes lighting system, temperature control system, etc., to provide guarantee for the normal operation of the energy storage station. The historical data such as PCS charge and discharge used in this analysis were collected from March to November 2022, which was put into operation in March 2021 and has been in operation for three years. This paper mainly analyzes the loss variation characteristics of 1# PCS energy storage unit composed of battery, line and PCS system, and the total energy loss of the energy storage unit is the sum of the energy loss of battery, line and PCS system, which can also be calculated by the difference between PCS charge and discharge.

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Since the battery pack in the energy storage unit is put into use, the performance decay phenomenon of the battery with the increase of charge and discharge time and cycle times, and its energy storage efficiency changes accordingly, so that there is a certain law in the historical cumulative loss change of the energy storage power station. At the same time, because the energy consumption of equipment is greatly affected by environmental factors such as operating conditions and temperature of energy storage power stations, the loss change characteristics of the main body of energy storage equipment also have seasonal change characteristics. Therefore, the loss variation characteristics of energy storage power stations are divided into two parts: cumulative loss variation characteristics and monthly loss variation characteristics, and are studied separately.

3 Variation Characteristics of Energy Loss in Energy Storage Power Station 3.1 Analysis of Battery Loss and Life Attenuation Causes The energy storage power station studied in this paper uses lithium iron phosphate battery pack as the main energy carrier. The number of discharge cycles of lithium iron phosphate batteries is affected by the working environment, temperature, Depth of discharge (DOD), state of charge (SOC) and other factors. The charge and discharge behavior of the battery determines the number of charge and discharge cycles, in which the cumulative energy of the battery system charging and discharging reaches the capacity of the battery system as 1 charge and discharge cycle, and the calculation formula of the charge and discharge cycle number is as follows:     Pout dt Pin dt = (1) N= Q0 Q0 where Q0 is the battery system capacity, Pin is the charging power, Pout is the discharge power, and [] is the rounded symbol. Figure 1 shows the life characteristic curve of lithium iron phosphate batteries provided by battery manufacturers. This data comes from battery charge-discharge cycle experiments, which start from the same state of charge and repeatedly cycle charging and discharging at the same depth of charge. As can be seen from the figure, the depth of discharge and temperature have a great influence on the battery life (number of cycles). The number of cycles of battery energy storage shows a decreasing trend with the increase of discharge depth, that is, the deeper the discharge depth, the fewer cycles. At the same depth of discharge, the number of cycles shows a nonlinear downward trend with the increase of the operating temperature, that is, the higher the temperature, the fewer the number of cycles. Classical battery loss theory holds that the rated number of cycles of a battery has an exponential relationship with its rated discharge depth. However, under the actual operating state, the discharge depth of the battery will change every day and month with the operation and charging and discharging strategy. The effect of battery operation on the number of cycles at different discharge depths is not the same.

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Fig. 1. Life characteristic curve of lithium iron phosphate battery

3.2 Energy Cumulative Loss Rate Analysis In order to reflect the aging degree of the battery, the cumulative loss rate index is proposed. The cumulative loss rate is calculated as follows: η=

QC − Qn × 100% Qc

(2)

where QC represents the cumulative charge and Qn represents the cumulative discharge amount. The cumulative charge and cumulative discharge of the battery are important characteristic quantities that reflect its charge and discharge cycle. The cumulative charge and cumulative discharge represent the total charge and total discharge from the battery to the present. The cumulative loss is defined as the difference between the cumulative charge amount and the cumulative discharge amount, which can reflect the cumulative loss characteristics of the energy storage battery since it was put into operation. Taking the first day of data acquisition as the zero point of the cumulative charge and discharge amount, the cumulative loss rates from battery cluster 1, 2 and 3 were calculated respectively, and the results are shown in Fig. 2(b). The loss rate curves of the three clusters of batteries showed good consistency, which increased with the increase of operating time, and the growth rate slowed down after July, reflecting the saturation trend.

Fig. 2. (a) Battery cluster cumulative loss rate curve without considering historical data (b) Cumulative loss rate curve of energy storage unit

Figure 2(b) shows the change curve of the cumulative loss rate of charge and discharge at a PCS of the energy storage power station calculated by taking the first day of data acquisition as the zero point of charge and discharge. It can be seen from the figure that since the first data collection date, with the increase of operation time, the cumulative loss rate of PCS gradually increases, and when the cumulative loss rate reaches about

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23%, there is a saturation trend, which is consistent with the change trend of the cumulative loss rate curve of the three cluster batteries, indicating that the cumulative loss rate change characteristics of the corresponding battery can be reflected by analyzing the cumulative loss rate of the energy storage unit. 3.3 Variation Characteristics of Monthly Loss of Energy Storage Unit In order to further analyze the influencing factors of the overall energy storage unit and the monthly energy loss change of the battery, the monthly cumulative charging capacity and loss power curves of battery cluster 1, 2 and 3 are plotted respectively, as shown in Fig. 3(a)(b)(c). The monthly cumulative charging curve of the three-cluster battery generally showed an inverted triangle change law, that is, from March to June, the monthly cumulative charging capacity decreased approximately linearly with the increase of the month, and gradually increased with the increase of the month from June to October. It shows that the summer energy storage of the battery is significantly greater than that of the battery energy storage in spring and autumn, which may be caused by the increase in the power loss of auxiliary power equipment such as air conditioning systems in summer. The monthly cumulative power loss trend of the three-cluster battery is opposite to the monthly cumulative charging trend, that is, from March to June, the monthly cumulative power loss generally increases with the increase of the month, and from June to October, it slowly decreases with the increase of the month. This may be caused by a change in the state of charge of the battery. The monthly cumulative charge of the three-cluster battery first decreases slowly with the increase of the month, and then slowly increases with the increase of the month, reaching the lowest value in June. The monthly cumulative power loss first gradually increases with the increase of the month, and then slowly decreases with the increase of the month, reaching the highest value in June, so that the monthly cumulative loss rate, which characterizes the ratio of the monthly cumulative power loss to the cumulative charge, shows a trend of increasing first and then decreasing with the increase of the month. The charging and discharging behavior of energy storage batteries will cause their energy loss. In order to analyze the influencing factors of the monthly power loss of the energy storage unit, the 1# battery cluster was selected to analyze its state-of-charge behavior. The depth of discharge has a nonlinear relationship with the number of cycles, and the average depth of discharge in the month can reflect the equivalent number of cycles of the battery in that month. The monthly average discharge depth change curve of the 1# battery cluster is shown in Fig. 3, and its change characteristics are similar to the cumulative charging amount, showing an inverted triangle change trend as a whole, that is, the monthly average discharge depth first decreases approximately linearly with the increase of the month, and then slowly increases with the increase of the month, and its monthly average discharge depth reaches the lowest point in June.

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Fig. 3. Monthly cumulative charge and loss power curve of battery (a) 1#battery (b) 2#battery (c) 3#battery

4 Operational Strategy 4.1 Self-test Operation and Maintenance Mode Based on Real-Time Charge and Discharge Loss In the existing state maintenance strategy of energy storage power station, the characteristic quantities to evaluate the operation health state of energy storage power station are mostly external state quantities such as BMS and PCS cabinet appearance, odor, abnormal noise and temperature, and less involve the characteristic amount of charge and discharge loss related to the real-time operation status of the energy storage unit. The cumulative loss and monthly loss of energy storage unit and corresponding battery change law is obvious, which has a strong correlation with the dynamic performance attenuation of battery components, and it is easy to realize online monitoring and early warning of equipment, so the cumulative loss rate and monthly loss rate related characteristic quantities of energy storage unit are introduced when evaluating the health status of energy storage stations, and the self-diagnosis and operation and maintenance decisions of energy storage unit operation status are carried out in real time according to online monitoring data, and the manual operation and maintenance mode is shifted to self-test operation and maintenance mode.

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4.2 Reasonably Formulate Charging and Discharging Strategies Unreasonable charging and discharging behaviors such as battery overcharge and overdischarge are the main reasons for the increase of energy loss of energy storage units. In order to reduce the charge and discharge loss of the energy storage unit and increase the storage efficiency, it is necessary to reasonably set the battery charging and discharging strategy to ensure that the SOC is relatively stable. In order to prevent the frequent occurrence of abnormal charging and discharging behaviors such as battery overcharge and overdischarge, it is recommended to set the maximum and minimum SOC thresholds in the charging and discharging process to 80% and 20%, respectively, and try to control the charging and discharging depth to about 60%, so as to ensure the stability of the SOC state and make full use of the battery energy storage capacity.

5 Conclusions Through the charge and discharge loss analysis of PCS and battery in energy storage power station, the following conclusions are obtained: (1) The cumulative energy loss rate of the energy storage unit and the corresponding battery cluster slowly increases with the increase of operation time, and the performance decay state of the energy storage battery can be reflected through the energy accumulation loss rate. (2) The monthly energy loss rate of the energy storage unit and the corresponding battery cluster gradually increases with the increase of the month, and then slowly decreases, and the monthly cumulative loss rate reaches the maximum in June. This is caused by the smallest monthly cumulative charging capacity of energy storage units in June, while the cumulative power loss is the largest. (3) In order to reduce the loss, it is necessary to reasonably formulate a charge and discharge strategy to ensure the stability of the battery SOC state. Acknowledgments. This work was funded by Key R&D Program of China Southern Power Grid Co., Ltd, China (074800KK52200009).

References 1. Li, J., Li, Y., et al.: Research on power distribution strategy considering the safety of energy storage power station. Trans. China Electrotech. Soc. 37(23), 5976–5986 (2022) 2. Li, F., Gu, Y., Wei, F., et al.: Fine-grained dispatch of isolated island microgrid under flexible access of wave energy hydraulic power generation system. Trans. China Electrotech. Soc. 38(13), 3499–3511 (2023) 3. Yan, L., Li, X., Zhang, B., et al.: Energy storage capacity allocation method with cascade utilization based on battery health in microgrids. Power Syst. Technol. 44(5), 1630–1638 (2020) 4. Sarasketa, E., Gandiaga, I., Rodriguez, L.M., et al.: Calendar ageing analysis of a LiFePO4/graphite cell with dynamic model validations: towards realistic lifetime predictions. J. Power Sources 275, 573–587 (2014)

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5. Sun, S., Zhou, Z., Xu, Z., et al.: Improved High-rate charge/discharge performances of LiFePO4/C via V-doping. J. Power Sources 193, 841–845 (2009) 6. Shin, H., Park, B., Jang, H., et al.: Rate performance and structural of Cr-doped LiFePO4/C during cycling. Electrochim. Acta 53(27), 7946–7951 (2008) 7. Zhou, A., Liu, X., Zhang, S., Cui, F., Liu, P.: Wind tunnel test of the influence of an interphase spacer on the galloping control of iced eight-bundled conductors. Cold Regions Sci. Technol. 155, 354–366 (2018) 8. Huang, Y., Feng, Z., Feng, Q., et al.: Battery loss evaluation and energy storage capacity strategy considering real-time SOC and dynamic cycle efficiency. J. Solar Energy 43(11), 413–423 (2022) 9. Wang, Z., Zhang, Z., Yin, S., et al.: Energy reduction technology of container energy storage system. Energy Storage Sci. Technol. 9(6), 1872–1877 (2020) 10. Schimpe, M., Naumann, M., Truong, N., et al.: Energy efficiency evaluation of a stationary lithium-ion battery container storage system via electro-thermal modeling and detailed component analysis. Appl. Energy 210, 211–229 (2018)

Research on Application of Carbon Fiber-Steel Materials in Lightweight Gun Equipment Jun Xu, Qunxian Qiu(B) , and Chao Zhang The 713 Research Institute of CSSC, Zhengzhou 450015, China [email protected]

Abstract. Purpose: A typical rectangular cradle on the gun equipment main bearing members is introduced. The effect of carbon fiber-steel composites on maintaining the bending stiffness and torsional stiffness of rectangular cradles is analyzed. Method: Based on the finite element simulation, the maximum deflection of the typical rectangular cradle under bending load and torsional load is calculated. Bending test and torsion test are performed by making specimens, and the deflection in the two groups of specimens in guiding lightweight is compared. Results: Under 5 kN bending load, the deformation of steel specimen is larger than that of carbon fiber-steel composite specimen, but the deformation is similar at 10 kN bending load. Under 500 Nm torsion load, the deformation of carbon fiber-steel composite specimens R4 and R5 is less than that of steel specimen of the same weight. Conclusion: Replacing some of the steel with carbon fiber for rectangular cross-section structures can effectively improve the torsional stiffness and can increase the bending stiffness under a low bending load. Keywords: Gun Equipment · Carbon Fiber · Lightweight · Stiffness

1 Introduction The cradle and gun carriage are the main stressed structural members of gun equipment, and their stiffness, mode shape, and force transmission design have a great impact on performance. Qiu Qunxian, Yao Haoze, et al. have carried out a large number of analytical studies on the carriage structure based on finite element technology [1–3]. The main bearing parts of typical gun carriages and cradles are mostly rectangular section cavity structures with good comprehensive performance in all directions. Such structures can be approximated as rectangular cradles [4, 5]. The application of new materials has engineering practice significance for the continuous pursuit of lightweight design of the carriage. Carbon fiber reinforced polymer (CFRP) is characterized by lightweight, high strength, and corrosion resistance. The carbon fiber-steel composites have certain advantages in the practical application of carriage weight reduction [6, 7]. Therefore, this paper studies the lightweight of carbon fiber-steel composites with equivalent stiffness.

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 880–887, 2024. https://doi.org/10.1007/978-981-97-1072-0_90

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2 Materials and Parameters The upper base material of the rectangular cradle test piece is carbon fiber laminated plate, the lower base material is steel plate, and the upper and lower base test pieces are bonded with epoxy resin adhesive. The model parameters are shown in Table 1. Table 1. Test Material Performance Parameters Material characteristics

Carbon fiber

Steel Q235B

E51 resin

Elastic modulus (Gpa)

240

206

2.5

Poisson’s ratio

0.3

0.3

0.38

Tensile strength (Mpa)

2300

375–460

53

Density (g/cm3 )

1.6

7.8

1.18

The physical parameters of the test specimen are shown in Table 2. Specimens R1, R2, and R3 are of the same wall thickness, different materials, and different weights. Specimens R3, R4, and R5 are of the same weight, different wall thickness, and different materials. The carbon fiber cloth laying process is adopted for specimen R4 and the carbon fiber prepreg process for specimen R5. Table 2. Physical Parameters of Specimen Material characteristics

Specimen R1 Specimen R2 Specimen R3 Specimen R4 Specimen R5

Section size/mm

100 * 200

100 * 200

100 * 200

100 * 200

100 * 200

Length/mm

500

500

500

500

500

Steel wall thickness/mm

6

–

6

4

4

Are there No lightening holes?

No

Yes

No

No

Carbon fiber thickness/mm

–

6

–

2

2

Total weight/kg

14

0.4

9.4

9.4

9.4

3 Simulation and Test 3.1 Simulation Modeling Figure 1 is a schematic diagram of the stress on the frame. The gyration acceleration motion in the direction of gun equipment generates torsional load, and gravity and recoil resistance generate bending load. The main beam of the frame is stressed in multiple

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directions under the launching condition, which can be simplified into typical rectangular beam torsion and bending conditions.

Fig. 1. Schematic Diagram of the Stress on the Frame

Figure 2 is a schematic diagram of the simulation calculation model. C3D8 element is used to calculate bending deformation with fixed supports at both ends, and a force of 10 kN is applied to the middle part of the square tube. One end is fixed to calculate torsional deformation, with a torsional load of 500 Nm.

Fig. 2. Simulation Calculation Model

3.2 Simulation Calculation By comparing a variety of different carbon fiber ply modes, 0°/45°/90°/135° carbon fiber ply mode has good stiffness under bending and torsion conditions, so this ply direction is preferred. Specimens R3, R4 and R5 are the comparison of different materials with the same weight and thickness. Specimen R3 is a steel structure and needs to add a lightening hole with a diameter of 20 mm which meets the comparison conditions without affecting its rigidity (Figs. 3, 4 and Table 3).

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Fig. 3. (a) Bending Deformation Nephogram of Specimen R1. (b) Bending Deformation Nephogram of Specimen R2. (c) Bending Deformation Nephogram of Specimen R3. (d) Bending Deformation Nephogram of Specimens R4 and R5

Fig. 4. (a) Torsional Deformation Nephogram of Specimen R1. (b) Torsional Deformation Nephogram of Specimen R2. (c) Torsional Deformation Nephogram of Specimen R3. (d) Torsional Deformation Nephogram of Specimens R4 and R5

3.3 Tests The three-point bending test is carried out by an MTS machine, with a span of 400 mm, loading and supporting shaft diameter of 40 mm, and length of 126 mm. The loaded load is 10 kN and the loading rate is 50 N/s. The bending test procedure is shown in Fig. 5.

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Simulation item

Specimen R1 Specimen R2 Specimen R3 Specimen R4 Specimen R5

Max. bending 0.499 deformation/mm

3.288

2.916

2.906

2.906

Max. torsional 0.0514 deformation/mm

0.0445

0.152

0.070

0.070

Fig. 5. Bending Test

The torsion test is carried out by an MTS machine with the top fixed, a loaded load of 500 Nm at the bottom, and a loading rate of 0.005°/s. The torsion test procedure is shown in Fig. 6.

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Fig. 6. Torsion Test

4 Test Data Analysis The force-displacement curve during the loading process of the bending test is shown in Fig. 7. With the increase of load, the displacement also gradually increases and their change trend is basically the same. The deformation of steel specimen R3 with lightening holes, and carbon fiber-steel composite specimens R4 and R5, which three are of the same thickness and mass, is greatly varied under a load below 5 kN. The deformation of R3 is greater than that of R4 and R5, and the deformation is similar when the load is about 10 kN. The deformation trend of full carbon fiber specimens R2 is the same as that of carbon fiber-steel composite specimens R4 and R5, with similar deformation. The torque-angle curve during torsion test loading is shown in Fig. 8. With the increase of the torsional moment, the torsion angle also gradually increases and their change trend is basically the same. The torsion angle of steel specimen R3 with lightening holes, and carbon fiber-steel composite specimens R4 and R5, which three are of the same thickNess and mass, is greatly varied under the same working conditions. The deformation of carbon fiber-steel composite specimens R4 and R5 is smaller than that of the steel specimen under the same working conditions. The deformation trend of full

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Fig. 7. Force-Displacement Curve of Bending Test

carbon fiber specimen R2 is the same as that of carbon fiber-steel composite specimens R4 and R5 and R2 has the minimum deformation.

Fig. 8. Torque-Angle Curve of Torsion Test

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5 Conclusion Replacing some or all of the steel with carbon fibers under low bending loads for rectangular cross-section structures can effectively improve flexural stiffness, and thus lightweight can be achieved by using carbon fibers for equivalent stiffness requirements. Under a large bending load, the stiffness of carbon fiber-steel composites cannot be improved for the time being by using ordinary processes. Replacing some or all of the steel with carbon fiber under the torsional load for rectangular cross-section structures can effectively improve the torsional stiffness. Carbon fiber-steel composites have obvious advantages in lightweighting under torsional conditions. Through the application research of carbon fiber-steel structure on lightweight gun equipment, the resulting data and conclusions provide test data support for the lightweight design of gun equipment.

References 1. Tan, L., Zhang, X., Guan, H., et al.: Introduction to Artillery. Beijing Institute Technology Press, Beijing (2005) 2. Qiu, Q., Liu, K., Gao, B.: Analysis of navy gun carriage’s responses and reaction force supporting by board foundation under recoil resistance. Ship Sci. Technol. 42(5), 127–132 (2020) 3. Yao, H.: Optimization design of artillery carriage and shock absorber for accuracy. Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian (2014) 4. Yao, S., Jin, F., Rhee, K.Y., et al.: Recent advances in carbonfiber-reinforced thermoplastic composites: a review. Compos. B Eng. 142, 241–250 (2018) 5. Hegde, S., Satish Shenoy, B., Chethan, K.N.: Review on carbon fiber reinforced polymer (CFRP) and their mechanical performance. Mater. Today Proc. 19, 658–662 (2019) 6. Zhu, J., Pan, Y., Sun, M.: Topology optimization design of certain type gun cradle structure. Ordnance Ind. Autom. 36(6), 17–20 (2017) 7. Sun, Q., Yang, G., Ge, J.: Improved design for top carriage of a gun. Acta Armamentarii 33(11), 1281–1285 (2012)

Author Index

B Bai, Huan 657 Bao, Meijun 590 Baoan, Chen 89 C Cai, Li 835, 845, 855 Cai, Linglong 693 Cao, Jinxin 545 Cao, Tian 555 Cao, Wangbin 66 Cao, Xinyu 555 Cao, Yu 207 Cao, Zihao 423 Chen, Dan 628 Chen, Guangwu 190 Chen, Guofu 638 Chen, Hao 674 Chen, Huapeng 555 Chen, Jingyun 598 Chen, Kaixuan 818 Chen, Liang 780 Chen, Lisi 240 Chen, Qianyi 448 Chen, Qingfa 448 Chen, Ruifeng 433 Chen, Siyi 16 Chen, Wenfeng 466 Chen, Wenzhen 809 Chen, Xi 256 Chen, Yufei 545 Chen, Yun 827 Cheng, Wei 864 Cheng, Xi 872 Cheng, Yue 792 Chu, Fanwu 723 Congrui, Zhang 89 Cui, Yanjie 16 D Dai, Jing 232 Dai, Zhuocheng

287

Deng, Kai 723 Deng, Yingcai 123 Ding, Jiaxin 308 Ding, Sheng 628 Ding, Yi 131 Ding, Yujian 42 Dong, Hang 232 Dong, Kai 415 Dong, Pengxin 457 Duan, Wei 482 F Fan, Dongmei 523 Fan, Hui 28, 148 Fan, Liguo 620 Fan, Yadong 835, 845, 855 Fan, Yuanshang 433 Feng, Zaishun 872 Fu, Rong 872 G Gao, Bo 780 Gao, Chao 198 Gao, Jin 114 Ge, Qiongxuan 731 Gu, Peng 423 Gu, Yingbin 407 Guanghui, Mao 89 Guo, Duange 665 Guo, Huan 665 Guo, Jian 370 Guo, Lijuan 503 Guo, Penghong 510 Guo, Zhenwei 123 H Han, Ruoyu 256 Han, Xiao-ming 562 Han, Xiaotao 457 Han, Yiming 756 Hao, Geng 50 Hao, Jianying 264

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1169, pp. 889–893, 2024. https://doi.org/10.1007/978-981-97-1072-0

890

Hao, Xiaoguang 28, 148 He, Changsheng 756 He, Darui 300 He, Zhifei 415 Hongsheng, Su 81 Hou, Shuai 379 Hou, Yanyan 510 Hou, Zhongwei 207 Hu, An 323 Hu, Changbin 148 Hu, Cong 835, 845, 855 Hu, Jiangpeng 674 Hu, Qinran 57 Hu, Sidong 1 Hu, Zhengwei 66 Hua, Hua 323 Huang, Jianyang 657 Huang, Jiemei 123 Huang, Jingjing 523 Huang, Peifeng 407 Huang, Qian 123 Huang, Tailin 638 Huang, Weibiao 572 Huang, Xueqi 379 Huang, Zebo 123 J Ji, Baoxian 606 Ji, Wangwei 181, 440 Jia, Yuqi 370 Jia, Zihao 308 Jianfeng, Gao 89 Jiang, Jun 482 Jiang, Qihang 649 Jiang, Shoude 766 Jiang, Shuo 693 Jiang, Yuan 809 Jin, Fubao 114 Jin, Guangxiang 545 Jin, Liang 342 Jin, Xu 57 Jin, Yuhui 693, 702 L Lan, Zhiming 482 Lei, Xiaoyan 398 Li, Bing 173 Li, Dechao 448 Li, Duanjiao 818, 827

Author Index

Li, Fan 323, 482 Li, Guangmao 181, 440 Li, Guocheng 440 Li, Hailong 674 Li, Hengjie 334 Li, Jialing 598 Li, Jianfeng 28, 148 Li, Jinyu 398 Li, Li 240 Li, Liang 598 Li, Pengfei 256, 801 Li, Qiang 562 Li, Qing 809 Li, Rui 351 Li, Shiqiang 503 Li, Wei 466 Li, Wengen 665 Li, Wenlong 370 Li, Wensheng 818, 827 Li, Xia 466 Li, Xiangjun 510 Li, Xiaohang 359 Li, Xinqi 224 Li, Xinyao 415 Li, Xuan 780 Li, Yanfei 740 Li, Yanwei 598 Li, Yaohua 740 Li, Yuan 598 Li, Zhengxi 114 Li, Zhiwei 42 Li, Zhongxiang 684, 693, 702 Li, Zixin 740 Liang, Xiaolin 66 Liang, Yafeng 872 Liang, Yongchao 818 Liao, Zhihao 684 Lin, Chunyao 702 Ling, Zhongbiao 433 Linhan, Chen 139 Liu, Guoqiang 503, 620 Liu, Hengyi 379 Liu, Hui 217 Liu, Jiang 207 Liu, Jiangnan 702 Liu, Jianming 818, 827 Liu, Ping 264 Liu, Quan 207 Liu, Runze 457 Liu, Tianyi 334

Author Index

891

Liu, Tingxiang 114 Liu, Weiwei 523 Liu, Wenming 606 Liu, Wenxuan 628 Liu, Xinyue 351 Liu, Zhengzheng 423 Liu, Zhijian 232 Lizhou, Wu 50 Long, Li 398 Lu, Jiahao 433 Lu, Lijuan 606 Lu, Ming 198 Lu, Yuzhe 510 Luo, Bing 649 Luo, Feng 440 Luo, Shanna 148 Lv, Jiaju 649 Lv, Zhiguang 503 M Ma, Lihong 872 Ma, Rui 28, 148 Ma, Shangang 114 Ma, Shaoqi 433 Ma, Suliang 809 Ma, Weijing 710 Ma, Xin-ke 562 Ma, Zhiqin 684, 693, 702 Matharage, Shanika Yasantha Matharage, Shanika 103 Mei, Yucong 323 Meijin, Gao 89 Mu, Xiaobin 638 N Nie, Shiqi

598

P Pan, Wenwu 198 Pang, Guohui 16 Pang, Qiang 181 Peng, Chao 723 Peng, Cheng 351 Q Qi, Donglian 173 Qi, Lizhong 710 Qi, Wei 139 Qiao, Shengya 181, 440

Qiao, Xinhan 466 Qiao, Yujiao 103 Qimei, Chen 474 Qiu, Jianhong 872 Qiu, Peng 57 Qiu, Qunxian 780, 801, 880 R Ren, Chunguang 224 Ren, Yijin 66 Ren, Ziqian 224 Rong, Fei 638 Rong, Jingguo 710

131

S Shams, Haseeb 273 Shang, Jiang 224 Shen, Hao 217 Shen, Shuhang 248 Shen, Xiaojun 287 Shi, Botao 756 Shi, Hailin 16 Shi, Jianqiang 190 Shi, Liming 740 Shi, Qiao 845, 855 Shi, Shuo 342 Shi, Xingyu 665 Shu, Xiang 684 Siyi, Xia 165 Song, Haitong 801 Song, Juheng 342 Song, Xianjin 620 Song, Zhitao 864 Su, Jianhong 818 Su, Ning 572 Su, Yu 42 Sun, Wenwen 674 Sun, Xiaohu 710 Sun, Yong 16 T Tai, Bin 693 Tan, Liu 89 Tang, Lize 407 Tangrong, Wang 474 Tian, Haipeng 864 Tian, Zihao 264 Tong, Chao 323

892

Author Index

W Wan, Xiongbiao 756 Wan, Yuan 370 Wang, Chen 448 Wang, Chengsheng 482 Wang, Deshun 766 Wang, Haojing 351 Wang, Hengyi 493 Wang, Jianguo 545, 835, 845, 855 Wang, Jiayi 657 Wang, Juan 407 Wang, Kaijun 582 Wang, Ke 731 Wang, Lei 42 Wang, Li 582 Wang, Manyu 256 Wang, Menglei 256 Wang, Rui 287 Wang, Ruofei 379 Wang, Shunjiang 57 Wang, Tinghua 300 Wang, Weiwang 649, 657 Wang, Xianchun 545 Wang, Xiang 638 Wang, Xiaofeng 407 Wang, Xiaoyi 217 Wang, Xin 131 Wang, Xinbing 510 Wang, Zhongdong 103, 131, 248 Wangbin, Cao 165 Wei, Ge 139 Wei, Nanzhe 224 Wei, Qi 545 Wei, Yong 545 Weijun, Hong 139 Wenbin, Wang 165 Weng, Jia 407 Wu, Chenyu 240 Wu, Jingyun 300 Wu, Juan 256 Wu, Junchao 864 Wu, Lipeng 620 Wu, Qing 864 Wu, Ruohan 423 Wu, Tianbao 657 Wu, Zelin 457 X Xia, Hui 620 Xiao, Chengqian

308, 359

Xiao, Hui 710 Xie, Dong 590 Xie, Fa 379 Xie, Zhiyuan 66 Xie, Zhongxin 173 Xiong, Jun 181, 440 Xu, Fei 740 Xu, Feiran 582 Xu, Jun 801, 880 Xu, Ke 466 Xu, Lianggang 606 Xu, Man 379 Xu, Mingjie 173 Xu, Mingzhong 723 Xu, Ruoyu 131, 248 Xu, Tao 723 Xu, Yongsheng 649 Xu, Zhaoran 287 Xue, Qiaozhi 224 Xueke, Gou 50 Y Yan, Bo 300 Yan, Jijing 323 Yan, Wenju 674 Yan, Yunfeng 173 Yang, Bingxue 42 Yang, Haonan 248 Yang, Hongwei 674 Yang, Lei 287 Yang, Libin 114 Yang, Lingrui 232 Yang, Qiongtao 482 Yang, Sen 440 Yang, Wei 433 Yang, Xian 702 Yang, Xin 835, 845, 855 Yang, Yong 423 Yang, Zihan 827 Yao, Xiuyuan 42 Yi, Chenying 448 Yi, Ding 89 Yi, Jiliang 466 You, Yuwei 198 Yu, Han 89 Yu, Haojie 766 Yu, Jie 273 Yu, Kun 240 Yu, Shuo 555 Yu, Songsong 207

Author Index

Yu, Yue 657 Yuan, Chi 864 Yuan, Dian 57 Yuan, Wei 256 Yuan, Yalei 638 Yuqi, Li 81 Yurong, Gou 474

Z Zeng, Dihui 731 Zeng, Pijiang 756 Zeng, Xiangjun 240 Zeng, Yangcheng 872 Zhai, Liming 359 Zhan, Jiangyang 590 Zhan, Yunpeng 379 Zhang, Chao 562, 880 Zhang, Chen 628 Zhang, Chenyuan 342 Zhang, Dan 756 Zhang, Dandan 198 Zhang, Jian 42 Zhang, Qian 809 Zhang, Shu 308 Zhang, Wanying 835, 845, 855 Zhang, Wenhao 545 Zhang, Wenwei 503, 620 Zhang, Xiaoquan 466 Zhang, Xiaoyang 510 Zhang, Xing 323 Zhang, Xu 370

893

Zhang, Yanbing 308, 359 Zhang, Yaping 710 Zhang, Ying 818, 827 Zhang, Youpeng 190 Zhang, Yu 351 Zhang, Yuanshi 57 Zhang, Zhenpeng 723 Zhang, Zhijin 16 Zhao, Cong 740 Zhen, Pang 89 Zhen, Xiaoya 308 Zheng, Hong 590 Zheng, Xueqin 572 Zheng, Yu 872 Zhengwei, Hu 165 Zhiyuan, Xie 165 Zhong, Jianwen 433 Zhou, Chao 217 Zhou, Dan 684 Zhou, Dengtao 114 Zhou, Guowei 590 Zhou, Hengxing 433 Zhou, Hongling 181, 440 Zhou, Lu 665 Zhou, Mingyu 131, 248 Zhou, Wanpeng 114 Zhou, Yuzhen 131 Zhu, Lihua 264 Zhu, Lingyu 398 Zhu, Weiping 423 Zhu, Zhifang 523 Zhu, Ziwei 323