The Proceedings of the 18th Annual Conference of China Electrotechnical Society: Volume V 9789819710645, 9819710642

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Lecture Notes in Electrical Engineering 1167

Qingxin Yang Zewen Li An Luo   Editors

The Proceedings of the 18th Annual Conference of China Electrotechnical Society Volume V

Lecture Notes in Electrical Engineering

1167

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

The book series Lecture Notes in Electrical Engineering (LNEE) publishes the latest developments in Electrical Engineering—quickly, informally and in high quality. While original research reported in proceedings and monographs has traditionally formed the core of LNEE, we also encourage authors to submit books devoted to supporting student education and professional training in the various fields and applications areas of electrical engineering. The series cover classical and emerging topics concerning: • • • • • • • • • • • •

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Qingxin Yang · Zewen Li · An Luo Editors

The Proceedings of the 18th Annual Conference of China Electrotechnical Society Volume V

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 978-981-97-1063-8 ISBN 978-981-97-1064-5 (eBook) https://doi.org/10.1007/978-981-97-1064-5 © 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

Transformer Temperature Prediction Method Based on Digital Twin Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ziyi Ren, Xiongying Duan, and Jia Tao Study of Anomalous Breakage of Closing Resistors of Circuit Breakers for 750 kV AC Filter Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hao Wang, Hongliang Zhang, Hai Jin, Hong Wang, Yifan Li, and Zhiyin Ma High-Frequency Signal Injection-Based Various Cable Connection Fault Diagnostics of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yitong Li, Wei Xu, Jiyao Wang, Zhen Jin, and Shuhua Fang Transient Stability Analysis of Grid Following Converter Intergreted with Synchronous Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Huanhuan Yang, Jian Qiu, Jianxin Zhang, Guanghu Xu, Deping Ke, Jian Xu, Cai Yan, and Junquan Chen Insulation Performance of Polyimide Materials Under Cable Arc . . . . . . . . . . . . . Xiahaoyue Yun, Zeli Ju, Yibo Zhang, Fancong Kong, Chang Ma, and Xiongying Duan Research on Transverse Compression Electromechanical Characteristics of CORC Cable Under Curved Load Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yangyang Shi, Yifan Wang, Tao Ma, and Shaotao Dai

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Oil Fire Detection Technology Based on Fractal Geometry . . . . . . . . . . . . . . . . . . Fuze Chen, Yonggang Zuo, Yuting Hu, Yuliang Zhang, Meichun Wu, Jiansheng Huang, Zekun Li, and Guangchuan Song

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A IPMSM Current Control Method Based on Reinforcement Learning . . . . . . . . Qinghui Meng, Nannan Sun, Hanrui Wang, and Shankun Jia

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Development and Performance Test of DC High-Voltage Generation System for Boron Neutron Source Device Based on Accelerator . . . . . . . . . . . . . . Longyang Wang, Rixin Wang, Lizhen Liang, Congguo Gong, Jun Tao, and Jieping Lu

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Research on the Control of Optical-Storage Grid-Connected Technology Based on Virtual Synchronous Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jingxiu Li, Hongsheng Su, and Xin Mao

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Influence of Rock Inclination on the Relaxation and Deformation of the Surrounding Rock in Underground Chambers . . . . . . . . . . . . . . . . . . . . . . . . 107 Xi Chen, Lan Jiang, Rongtian Zhang, and Bo Tang Impact Analysis of Multiple Electro-mechanical Actuators on More Electric Aircraft Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Chang Cai and Xinran Zhang Study on Modeling of Electromagnetic-Thermal Multi-field Coupling of Rail Electromagnetic Launcher and Its Electromagnetic Field and Temperature Field Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Pengfei Lu, Luyao Liu, Hongshun Liu, Yizhen Sui, Ruxue Zhao, and Hongbin Zhang Study on the Temporal and Spatial Characteristics of Transient Temperature in Electromagnetic Emission System . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Luyao Liu, Pengfei Lu, Hongshun Liu, Yizhen Sui, Ruxue Zhao, and Hongbin Zhang Effect of Crystal Orientation on Vacuum Breakdown Characteristics of Copper Nanoelectrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Xinyu Gao, Zihe Li, Zhenyu Zhao, Jun Zhao, and Wen Yan Vibration Simulation of High Voltage Cables Laid on the Stress Absorption Mechanical Device Composed of Three Arcs in the Bridge Offset . . . . . . . . . . . . 151 Yun Cong, Gencheng Wang, Jianliang Xu, Zhenpeng Zhang, and Songsheng Hou Consider the Collaborative Optimization Strategy of Electric Vehicles Under Dynamic Electricity Price Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Wangsheng Chen, Shudong Wang, Huiquan Wang, and Weiqiang Tang Effect of UV Irradiation on the Surface Morphology and Chemical Structure of Epoxy Resin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Shaoming Pan, Lei Zhang, Jian Zhao, Yi Su, Xiajin Rao, Liangyuan Chen, and Dajian Li Study on the Influence of Key Component on the Fast Vacuum Switch . . . . . . . . 176 Zhaowei Peng, Shiyang Huang, Dangguo Xu, Peng Song, Linru Ning, and Yamei Li

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Study on Thermal Aging Characteristics of Typical Electromagnetic Coil Glass Fiber/Epoxy Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Dejiang Yu, Yanbo Ma, Yadong Zhang, and Huilong Wan Wide Area Protection Scheme for Power Distribution Systems with Renewable Energy Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Yadong Liu, Zhe Shi, Feitong Yu, Kuizhong Wu, Jingshan Wang, and Yuanchao Hu Research on Verification Technology for Data Analysis Function of 110 kV(66 kV)–500 kV Cable Lines Partial Discharge Online Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Rong Xia, Jianjun Yuan, Ge Wang, Songhua Liu, and Lihong Li Optimal Distributed Power Allocation for Isolated DC Microgrids Based on Projected Subgradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Meng Yue, Xiaolan Wang, Tengfei Wei, Rui Hao, Lixin Wang, Jiarui Wang, and Zhaohui Li Active Recovery Control Strategy Under Nonlinear Unbalanced Load with Multiple Micro-source Islanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Lixin Wang, Xiaolan Wang, Tengfei Wei, Jiarui Wang, Rui Hao, Meng Yue, and Zhaohui Li Design of DC Surge Suppression for Airborne Computer . . . . . . . . . . . . . . . . . . . . 233 Xuejian Wang, Kai Dong, Ruoxuan Wang, Fei Feng, Zihe Li, and Wen Yan Speed Control of Ultrasonic Motor Based on Sliding Mode Control . . . . . . . . . . . 241 Boyang Ye, Long Jin, Zhike Xu, Junyu Fan, and Qizhi Sui The Fault Analysis and Performance Improvement of Pulse Reactors . . . . . . . . . 250 Wu Lizhou, Liu Daqing, Geng Hao, Zhao Yingjie, Gao Bo, and Qiu Qunxian Interval Prediction of Dynamic Line Rating of OHL Based on Improved Affine Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Hanru Li, Zhijian Liu, Tao xu, Liyong Lai, Lingyu Huang, Bin Xu, Ren Liu, and Tang Bo Accurate Calculation Method for Radiation Field Generated by Lightning Waves Entering Substation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Ninghui He, Xutao Wu, Yifan Lang, and Yangchun Cheng

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Position and Speed Measurement Method for Segmented Long Primary Double-Sided Linear Motor Based on Polynomial Fitting . . . . . . . . . . . . . . . . . . . 276 Shijiong Zhou, Yaohua Li, Liming Shi, Manyi Fan, and Jinhai Liu Sampling Analysis and Optimization Suggestions on Long Term Operation Metering Performance of Low Voltage Current Transformer . . . . . . . . . . . . . . . . . 285 Yicheng Bai, Shuai Gao, Lin Zhao, Zhengyu Jiang, Yuan Chi, Xuepeng Wei, and Yin Zhang Design and Experiments of Voltage Sensor Based on Electric Field Coupling Principle and Differential Input Structure . . . . . . . . . . . . . . . . . . . . . . . . . 293 Jianghan Li, Qing Xiong, Chen Zhang, Xiaoxiao Zhao, Tonghao Zhou, and Shengchang Ji In-Situ Detection of Thermal Runaway Gases of Lithium-Ion Batteries Based on Fiber-Enhanced Raman Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Bing Luo, Dibo Wang, Qiang Liu, Tongqin Ran, and Fu Wan Research on Power Accurate Control Method of Ramp-Type Gravity Energy Storage System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 Ming Li, YaXiaEr TuErHong, Zilin Hao, Jianwang Gao, Tian Gao, Linlin Dong, and Shuyang Fang Development of Contact Resistance Measurement Device for GIS Main Circuit Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Shuai Sun, Xingwang Li, Congwei Yao, Bin Tai, Linglong Cai, Jianjun Li, and Xiaofeng Pang Multi-criteria Integrated Early Warning of Thermal Runaway Risk . . . . . . . . . . . 330 Yaoming Chen, Liguo Weng, Bingcheng Zhao, and Deqiang Lian Simulation Study on Temperature Rise Characteristics of 550 kV/8000 A Combined Electrical Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 Liuhuo Wang, Shuai Sun, Rongchang Xie, and Qiang Sun A Data-Driven Method for Improving Voltage Quality of Large-Scale Distributed PV in Distribution Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Zhikun Xing, Haoran Lian, Fan Wang, Yabo Hu, Hao Wang, and Zhiyuan Chang Research on Classification Forecasting Method Based on Global Load Division of Typical day and Holiday Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Junwen He, Fang Zhijian, Quanhui Li, and Ji Lv

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Temperature Distribution Study of Armature and Guideway Under High-Speed Sliding Electrical Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 Hang Geng, Li Zhang, Xu Jiang, and Yuanxin Teng Improved Pre-synchronization and Grid Connection Strategy Based on Virtual Synchronous Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 Haihong Huang, Xiaoyi Qu, and Haixin Wang Analysis of Electromagnetic Characteristics of Dual-Rotor Induction Machines Based on Modularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Hao Luo, Kunshuo Zhu, Yifan Xiao, Xijun Ni, and Gang Wu Research on Identification Method of Subsynchronous Oscillation Parameters Based on FSST and STD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 XiaoBiao Fu, Peng Zhang, XiaoZhe Song, Changjiang Wang, and Hao Ding Induction Motor Fault Diagnosis Based on SSA-SVM . . . . . . . . . . . . . . . . . . . . . . 401 Manqiang Liu and Jie Wu Study on Design and Feasibility of Acrylic-Based Repair Liquid for Buffer Layer Ablation Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410 Mengdi Qian, Shiyi Zhou, Jing Cai, Yongli Wang, Wei Guo, and Zhou Ge Infrared Image State Evaluation of Power Cables Based on Mask R-CNN and BP Joint Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 Yang Zhao, Yingqiang Shang, Jun Xiong, and Xuehan Li Research on Stability of a 4-Channel Amplifier in Engineering Applications . . . 428 Kai Dong, Xuejian Wang, Zhifei He, Guofei Teng, and Qing Lin Multi-Objective Optimization Design of Rotor Parameters of External Rotor Synchronous Reluctance Machine Parameters Based on Mixed Surrogate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 Shaoyu Ke, Yaojing Feng, Chenxi Xia, Tan Wang, and Shoudao Huang Analysis and Improvement Measures for a 66 kV Shunt Capacitor Fault . . . . . . . 446 Jianying He, Qingyang Tian, and Zhiyu Liu A New Safety System Architecture and Design for High-Speed Trains . . . . . . . . 457 Xin Zhou, Guangwu Chen, Yongbo Si, and Pengpnge Li

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Harmonic Voltage Effect on Partial Discharge Characteristics of Oil-Paper Insulation Under Non-uniform Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 Weiju Dai, Zhihu Hong, Shan Wang, Guochao Qian, Jie Wu, and Ruochun Xia Effect Mechanism of Ambient Temperature and Humidity on Polyimide Partial Discharge Under High Frequency Electrical Stress . . . . . . . . . . . . . . . . . . . 477 Yiwei Wang, Li Zhang, and Huangkuan Xu Research on Intrinsic Shaft Voltage in Permanent Magnet Synchronous Wind Generators with Sectionalized and Overlapped Stator Laminations . . . . . . 486 Yali Hao, Ruifang Liu, Liangliang Zhang, Weili Li, and Lei Jia A Robust H∞ CKF-Based Dynamic State Estimation Method for Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 Su Zicong, Liu Min, Wang Kai, and Man Yanlu Detection of Bearing Fault in Induction Motor Based on Improved Adaptive Chirp Mode Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 Wei Li, Chidong Qiu, Ruihan Liu, and Zhengyu Xue Detection of Bearing Fault in Induction Motor Based on Improved Adaptive Local Iterative Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512 Guomin Wang, Chidong Qiu, Shuai Hong, and Zhengyu Xue Detection of Bearing Fault in Induction Motor Using Multi-parameter Optimized Resonance Sparse Signal Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 520 Meitao Li, Chidong Qiu, Shuai Hong, and Zhengyu Xue Chopping Compensation Control and Low Frequency Pulse Suppression Strategy of DC Side Current in Lithium Battery Energy Storage System . . . . . . . 528 Yiyang Liu, Weichao Li, Liang Zhou, and Jinyang Han Research on Preliminary Integrated Design of Electric Ducted Fan . . . . . . . . . . . 539 Ye Li, Qi Li, Tao Fan, and Xuhui Wen Analysis of Restraining Circulating Current with Parallel H-bridge Power Supply Current Sharing Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 Haihong Huang, Guang Yang, and Haixin Wang Simulation Analysis of the Electrical and Thermal Characteristics of Water Ingress Defects Within High-Voltage Direct Current Cable Terminals . . . . . . . . . 555 Yang Zhao, Tian Guo, Boxiang Ma, Yingqiang Shang, and Yaogang Wang

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Research on Electric Load Forecasting Considering Node Marginal Electricity Price Based on WNN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Xiaolu Li, Jun Li, Shijun Chen, Mingli Li, Bangyong Pan, Jie Luo, and Min Liu Distribution Characteristics of Electric Field Under Defect State of Large Shielding Ball in Valve Hall of Converter Station . . . . . . . . . . . . . . . . . . . . . . . . . . . 572 Yitao Zhang, Lingjiang, Yongsheng Zhang, Yu Su, Chenglei Zhang, and Shengcheng Dong Research on Fault Diagnosis of Neural Network Power Transformer Based on Dung Beetle Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Song Xiaofei, Dang Cunlu, Wang Weiwei, and Yao Dengyin A New Secondary Frequency Control Method for Distributed VSGs in Island Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 Yuting Teng, Wei Deng, Guoju Zhang, Shiyi Zhang, and Wei Pei Research on the Early Warning Method of Thermal Runaway of Lithium Battery Based on Strain Detection of Explosion-Proof Valve . . . . . . . . . . . . . . . . . 602 Hangyu Luo, Tao Cai, Aote Yuan, and Song He Research on High-Speed Uniaxial Stretching Method Based on Magnetic Pulse Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Hao Shi, Weihao Li, Shiyu Hao, Qiancheng Hu, Chengcheng Li, Ran An, Li Chen, and Xingwen Li Research on Variable Droop Control Method for Improving Stability of Low-Voltage DC Distribution System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626 Yantao Liu, Wei Deng, Xuekui Mao, Shiyi Zhang, and Wei Pei Electromagnetic Performance Analysis of PM Linear Synchronous Motor with Star-Delta Windings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 Ma Mingna, Wang Lei, and Zhang Xin Design of Portable Rechargeable Plasma Generator . . . . . . . . . . . . . . . . . . . . . . . . 644 Zicheng Wang, Zhongbo Hou, Jiayang Zhang, Qiaojue Liu, and Zhanhe Guo Research on Improved Disturbance Observation Method for Photovoltaic MPPT Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656 Haoran Li, Yupeng Xiang, Junhong Chen, Shitao Hao, Xiaopin Yang, Cui Wang, Bing Zeng, and Fanxing Rao

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Study on the Effect of Sand on the DC Discharge Character Curve of Air Gap in an Altitude of 3500 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Xudong Ma, Shengfu Wang, Guangxiuyuan Zhu, Chenglei Zhang, Yuan Li, and Taohui Yang Development and Application of Edge Intelligent Monitoring Device for Hidden Danger of Transmission Channel Based on AI Chip . . . . . . . . . . . . . . 671 Zhen Wang, Yanjie Hu, Ziquan Liu, Hai Xue, and Xueqiong Zhu Multi-objective Optimization Design of Multiphase Permanent Magnet External Rotor Pulsed Alternator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684 Sun Chengxu, Li Qi, Wang Youlong, and Li Ye Study on the Deterioration Characteristics of ECR Glass Fiber in Composite Insulators Under Acid-Heat Conditions . . . . . . . . . . . . . . . . . . . . . . . 694 Ziheng Huang, Dandan Zhang, Ming Lu, Chao Gao, Zhenbiao Li, Zhiyu Wan, Yuwei You, and Zehong Wang A PVDF-Based Ultrasonic and UHF Sensing Technology for PD Detection of GIS Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Xiaotian Liu, Xingyu Yu, Guozhi Zhang, and Xiaoxing Zhang Research on Allocation of Energy Storage System in Microgrid Based on Improved Particle Swarm Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . 715 Liansheng Gao, Yonghong Xia, Yongkang Xiong, Guanhong Song, and Jianbo Xin Study on the Influence of Current Unbalance for Three-Phase Open-Winding Permanent Magnet Synchronous Motor Based on Linear Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Yifei Ma, Meng Zhang, Yucong Xiong, Xiaoli Zhu, and Jiaoyan Liang Reliability Prediction of UHF Partial Discharge Sensor Based on Inverse Gaussian Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740 Yipeng Chen, Jinpeng Sun, Shike Wei, Chenyu Jiang, and Yishuai Cui Harmonic Analysis and Suppression of Position Sensorless Control by PMSM High Frequency Signal Injection Method Considering Inductive Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749 Yuguang Feng, Jian Gao, Kun Liu, Chengxu Li, and Qitao Yu Research on Circuit Breaker Aging in HVDC Converter Station and Prediction of Remaining Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 Xianshan Guo, Xiaolin Shen, Ao Wang, Yang Chao, Weiwei Cai, Xiao Yang, and Bo Qi

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Path Planning of Substation Inspection Robot Based on SA-GA Algorithm . . . . 768 Xiangyi Xu, Zeyang Zhao, Shihao Yang, Bengang Wei, and Yakun Liu Failure Mechanism Study of Silicon Rubber Under High-Low Temperature Cycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Ziyong Li, Qingdan Huang, Haoyong Song, Huihong Huang, and Jing Liu Thermal Aging State Evaluation Method for Submarine Cable Insulation Based on High-Voltage Frequency Domain Dielectric Characteristic Quantity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783 Zhen Gao, Weilong Peng, Haolun Che, Xiaobo Lin, Tianyu Ruan, and Jian Hao A Six-Phase Permanent Magnet Synchronous Motor Cogging Torque Weakening Method Based on Multi-parameter Composite Optimization . . . . . . . 792 Jianwei Liang, Zhangsheng Liu, Xinhua Wang, Peiyao Guo, and xiubin Zhu Computation and Experimental Test of Magnetostrictive Deformation in a Single-Phase Transformer Core Model Taking the External Stress into Account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802 Fuzeng Zhang, Xiaoguo Chen, Long Di, Dezhu You, Yonghao Liu, Kai Liu, and Wei Lu Battery Safety Algorithm Function Research Report . . . . . . . . . . . . . . . . . . . . . . . . 810 Sichao Chen, Hua Fan, Hongda Shen, and Haohan Ying Research on Metamodel-Driven Deployment Model for Converter Station Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824 Kanghang He, Juzhen Wu, Ning Luo, Zhichao Liu, and Shusheng Zheng Design Optimization of a New Energy Vehicle Drive Motor Based on Genetic Algorithm and Taguchi Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835 Wei Li and Quanwei Shen Comparative Study on the Performance of Arc Fault Detection Devices Under Household Load Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844 Jing Xu, Congxin Han, Guoliang Cai, Fengyi Guo, and Yanli Liu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853

Transformer Temperature Prediction Method Based on Digital Twin Technology Ziyi Ren, Xiongying Duan(B) , and Jia Tao School of Electrical Engineering, Dalian University of Technology, Dalian, Liaoning, China [email protected]

Abstract. The transformer is a key link in the power system, and its internal temperature has a decisive effect on the health status of the transformer and various decisions on it. Therefore, it is of great significance to study how to accurately predict the oil temperature of transformers. In this paper, a method for predicting transformer hot spot temperature based on digital twin technology is proposed. First, a transformer twin model is built in the virtual space, and multi-physics field coupling simulations are performed on it under various working conditions, and the transformer oil temperature data is saved as the twin body temperature database. Then combined with algorithms such as the extreme learning machine (ELM) in the neural network, the database data can be learned and the oil temperature can be actively predicted. Finally, the predicted temperature is compared with the actual temperature data to verify the accuracy of this method. The results show that the extreme learning machine algorithm has better prediction accuracy than other algorithms. This hot spot temperature prediction method based on digital twin technology can provide a certain reference value for the stable operation of the power system. Keywords: Digital twin · Transformer · Extreme learning machine

1 Introduction As an important power equipment in the power grid, oil-immersed power transformers face the problem of hot spot temperature caused by excessive load fluctuations and longterm operation. Therefore, it is of great significance to study a transformer winding hot spot prediction method and obtain the transformer winding hot spot temperature timely and accurately to ensure the efficient, safe and reliable operation of the transformer. At present, the methods for obtaining hot spot temperature of transformers can be mainly divided into the following categories: direct measurement method, guide calculation method, model calculation method and intelligent learning method. The direct measurement method [1–3] has large errors and many problems. At present, the guideline calculation method [4, 5] mainly adopts the hot spot temperature calculation formula recommended by IEEE C57.91–1995 and the national standard GB/T1094.7–2008. This method is similar to the empirical formula, and the obtained results are far from the measured data. Model calculation method establishes a 3D model of the transformer © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 1–8, 2024. https://doi.org/10.1007/978-981-97-1064-5_1

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based on the finite element theory, and then calculates the overall temperature field of the transformer to obtain the hot spot temperature. This method is more accurate, but the finer the model, the slower the overall simulation process, which is not conducive to the use of temperature judging the working status of the transformer. The intelligent learning method uses the historical data of transformer operation or factory test data to construct a relationship model between each variable and the hot spot temperature, and then accomplish the prediction of the hot spot temperature. [6] Currently commonly used intelligent learning methods mainly include neural network, Kalman filter, improved parameter identification and so on. In view of this, this paper proposes an oil temperature prediction method based on digital twin technology.

2 Prediction of Transformer Hot Spot Temperature 2.1 Establishment of Transformer Digital Twin This paper constructs a digital twin model corresponding to the transformer entity, which is driven by model and data respectively. The model-driven approach is the mapping of transformer physical entities to multiphysic mechanisms during transformer operation. First construct the 3D geometric model of the transformer, and then parameterize and integrate the characteristics of the transformer into the 3D model during operation. Data-driven [7] is to build a data-driven digital twin model through BP neural network algorithm, extreme learning machine algorithm, support vector machine and other algorithms, with the help of a large amount of data generated by the model. The combination of the two is the complete digital twin. 2.2 Simulation Analysis of 3D Model of Transformer Calculation of Simulation Governing Equations. As the most important heat dissipation substance inside the transformer, insulating oil follows three basic laws of heat transfer: the law of mass conservation, the law of momentum conservation and the law of energy conservation. Based on the finite volume method and heat transfer theory, the governing equations of the three laws in the oil flow process inside the transformer are shown below. The mass conservation equation of the oil flow process is as follows [8]: ∇ ·U =0 where, U is the oil flow velocity vector. ⎧ ⎪ ∂p ∂(ρu) ⎪ ⎪ ⎪ ∂t + ∇ · (ρuU ) = ∇ · (μ∇u) − ∂x ⎪ ⎨ ∂p ∂(ρv) ∂t + ∇ · (ρvU ) = ∇ · (μ∇v) − ∂y ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ∂(ρw) + ∇ · (ρwU ) = ∇ · (μ∇w) − ∂p ∂t ∂z

(1)

(2)

where, t is time, ρ is density, u, v, w are the velocity components of U in x, y, and z directions in the Cartesian coordinate system, p is pressure, and μ is viscosity coefficient.

Transformer Temperature Prediction Method

The energy conservation equation of the oil flow process is as follows:   ∂(ρT ) k + ∇ · (ρUT ) = ∇ · ∇T + S ∂t C

3

(3)

where, T is the temperature, k is the thermal conductivity, C is the specific heat capacity, and S is the total heat source, that is, the transformer loss. Building of the Simulation Model. The transformer studied in this paper is a power transformer of S11-1000 kVA/6 kV type. Due to the large number of internal components of the transformer, the structure is relatively complicated. In order to reduce the difficulty of simulation analysis and simulation time, the following reasonable simplified assumptions are made for the transformer model in this paper. (1) The materials of the components inside the transformer are regarded as uniform and isotropic; (2) The field quantity in the field changes sinusoidally with time; (3) The influence of other metal parts such as tie rods and clamps is not considered. The established model is shown in Fig. 1. Among them, the iron core adopts a coretype laminated structure, and the windings are divided into low-voltage windings and high-voltage windings. They all use full-copper layer windings and are arranged in a nested manner. The outer side is a high-voltage winding, and the inner side is a lowvoltage winding. The areas outside of them are all filled with transformer oil to wrap them.

Fig. 1. Simulation Model of Oil-immersed Transformer.

Afterwards, the model material is further set, and the main parameters of each part of the material are shown in Table 1. The transformer insulating oil and air in the table are all materials under 300 K. Set the ambient temperature to 25 °C, and the temperature distribution cloud images after the transformer runs for1, 3, 6, and 8 h are shown in the Fig. 2. When the transformer starts to run, its temperature starts to rise rapidly, and as the running time increases, the heat dissipation system gradually takes effect, and the rising speed of the transformer temperature also gradually slows down. After a long time of running, at about 8 h, The highest hot spot of the transformer has reached equilibrium and no longer rises, and the highest temperature in the transformer has reached 84 °C at this time. Saving the temperature data can provide data support for the subsequent digital twin prediction model.

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Z. Ren et al. Table 1. Material parameters of main parts of transformer

Component

Material

Density(kg/m3 )

Specific heat capacity(J/kg.K)

Thermal conductivity(W/m.K)

Winding

copper

8900

385

397

Iron core

Silicon steel

7550

450

52

Insulating oil

mineral oil

878

1881

0.13

Outside air

air

1.18

1006.3

0.026

Fig. 2. The temperature distribution diagram of the transformer running for different time

2.3 Prediction Model of Transformer Hot Spot Temperature The Extreme Learning Machines. The extreme learning machine [9, 10] was proposed by Huang of Nanyang Technological University in 2004. It is a typical single hidden layer feedforward neural network structure, as shown in Fig. 3. The neural network shown in Fig. 3 includes an input layer, a hidden layer, and an output layer, which are composed of n, l, and m neurons respectively. αij is the connection weight between the ith neuron in the input layer and the jth neuron in the hidden layer, βjk is the connection weight between the jth neuron in the hidden layer and the kth neuron in the output layer.

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Fig. 3. The structure of extreme learning machine neural network.

PSO-ELM Predictive Model. The input and output of the ELM model are determined by the actual problem. The measurable and valuable characteristic quantities for calculating transformer hot spot temperature θ h are load rate K, ambient temperature θ a and top oil temperature θ top . Therefore, the input layer of the ELM model is  (4) x = K θa θtop In the prediction process of the ELM model, there are still some defects. Its random weight and threshold greatly improve the fitting speed but still sacrifice part of the accuracy. Based on this, a particle swarm optimization algorithm [11] (PSO) is proposed to optimize the random parameters in the optimization of the ELM model to find the parameters with the highest precision while retaining the advantage of fast fitting speed of the ELM model. The flow chart of PSO-ELM calculation model is shown in Fig. 4.

3 Results and Analysis Randomly combine the three input parameters of different load rates, ambient temperature, and top oil temperature, and the output parameter hotspot temperature, and use them as twin data to generate 600 samples. According to the ratio of 8:2 between the training set and the test set, the twin transformer model is trained and tested. Figure 5 is a comparison chart of the actual value and the predicted value using the PSO-ELM algorithm and the BP algorithm respectively. Figure 6 is the prediction error curves of the two algorithms respectively. The real value temperature data is a random combination of the three input data of ambient temperature, top oil temperature, and load rate. It is obtained from the previous transformer temperature simulation, and the temperature distribution is in the range of [30–100] °C.

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Fig. 4. PSO-ELM neural network flow chart

Fig. 5. The predictive value and the real value of the two algorithms

After comparison, it can be seen that the overall error of the PSO-ELM algorithm is smaller than that of the BP algorithm. Most of the error points are distributed between ± 1°C, and the highest error does not exceed ± 2°C. However, the overall error of the BP algorithm is relatively large, and the error of some individual points has reached ± 6°C. Table 2 shows the error parameters of the prediction results when using the PSO-ELM algorithm and the BP algorithm.

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Fig. 6. The error value of the two algorithms Table 2. The error parameters of the two algorithms Algorithm

PSO-ELM

BP

Calculating time

1.23 s

1.31 s

Root mean square error (RMSE)

0.5654

1.6018

Coefficient of determination(R2)

0.9981

0.9866

Mean absolute error (MAE)

0.4562

0.8377

4 Conclusion This paper proposes a method for predicting transformer hot spot temperature based on digital twin technology. Firstly, the three-dimensional temperature field simulation of the transformer is established, and the hot spot temperature data is saved as a twin database. Then use the extreme learning machine (ELM) algorithm in the neural network to learn from the database and actively predict the oil temperature. Finally, compare its performance with BP algorithm. The results show that the accuracy of the optimized ELM algorithm is greatly improved, which can prove the superiority of this algorithm. This hot spot temperature prediction method based on digital twin technology can provide a certain reference value for the stable operation of the power system.

References 1. Mcnutt, W.J., Mciver, J.C., Lerbinger, G.E., et al.: Direct measurement of transformer winding hot spot temperature. IEEE Trans. Power Appar. Syst. 103(6), 1155–1162 (1984) 2. Alves, R.V., Wickersheim, K.A.: Fluoroptic thermometry: Temperature sensing using optical fibers. In: Photon 83 International Conference on Optical Fibers, Paris, pp. 146–152. SPIE (1984) 3. Liu, J., Chen, W.G., Zhao, J.B.: Measuring technology of transformer internal temperature based on FBG sensors. High Voltage Eng. 35(3), 539–543 (2009). (in Chinese)

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4. China National Standardization Management Committee.: power transformers-Part 7: Loading guide for oil-immersed power transformers, GB/T 1094. 7. Standards Press of China, Beijing (2008). (in Chinese) 5. IEEE.: IEEE guide for loading mineral-oil-immersed transformers. Piscataway, IEEE Std C57. 91–1995. The Institute of Electrical and Electronics Engineers, Piscataway (1995) 6. Liao, C.B., Ruan, J.J., Wei, C., et al.: Review of study methods on hot-spot temperature of transformer. High Voltage Apparatus 54(7), 79–86 (2018). (in Chinese) 7. Wang, X.T., Zou, Y., Yu, C.Y.: Research on prediction of transformer winding hot spot temperature based on GA-BP neural network. Northeast Electric Power Technol. 42(02), 1–4+8 (2021). (in Chinese) 8. Zhou, L.J., Tang, H.L., Wang, L.J., et al.: Simulation of three-dimensional temperature field and oil flow field of oil-immersed transformer based on polyhedral mesh division. High Voltage Eng. 44(11), 3524–3531 (2018). (in Chinese) 9. Wang, J., Lu, S., Wang, S.H., et al.: A review on extreme learning machine. Multimed Tools Appl. 81, 41611–41660 (2022) 10. Yang, R.X., Xiong, R., Shen, W.X., Lin, X.F.: Extreme learning machine-based thermal model for lithium-ion batteries of electric vehicles under external short circuit. Engineering 7(3), 395–405 (2021) 11. Gad, A.G.: Particle swarm optimization algorithm and its applications: a systematic review. Arch. Computat. Methods Eng. 29, 2531–2561 (2022)

Study of Anomalous Breakage of Closing Resistors of Circuit Breakers for 750 kV AC Filter Fields Hao Wang, Hongliang Zhang(B) , Hai Jin, Hong Wang, Yifan Li, and Zhiyin Ma College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected]

Abstract. Closing resistors are mainly used in line circuit breakers of 800 kV and above and AC filter circuit breakers of 550 kV and above to suppress the closing inrush current and transient overvoltage during the closing process of circuit breakers. Due to the special characteristics of its operating conditions, it needs to be cast and cut frequently, resulting in frequent failures of the closing resistor piece. In this paper, the electric field and modal simulation model of the closing resistor stack is established. Simulation results show that when the closing resistor is broken, the electric field around it produces distortion, which is 39% higher than the normal working condition, harming the normal operation. Modal simulation results show that the resonance frequency of the resistor stack in the first 6 orders is 18.7–43.37 Hz, which is close to the intrinsic frequency of general trucks and vans, and the vibration should be reduced as much as possible to avoid resonance of the resistor stack in the transportation process to ensure the reliability of the product. Keywords: Closing resistors · overvoltage · electric field simulation · Modal simulation

1 Introduction 1.1 A Subsection Sample In recent years, with the rapid development of China’s power industry, a large number of ultra-high voltage, ultra-high voltage transmission lines into operation, in the “14th Five-Year Plan” period, the State Grid planning and construction of UHV project “24 cross 14 straight”, involving more than 30,000 km of lines, the ultra-high voltage market size has reached hundreds of billions of levels [1, 2]. UHV transmission lines are often affected by various factors during operation, and when the line is tripped by lightning, the line load can not be instantly transferred, which will cause the system to generate overvoltage; System voltage fluctuations can also be caused when there is a sudden change in load, and transmission line short circuits can lead to overvoltage on the lines [3, 4]. As can be seen from the above scenarios, the presence of overvoltage seriously © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 9–16, 2024. https://doi.org/10.1007/978-981-97-1064-5_2

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affects the balance and stability of the power system, including voltage fluctuations, harmonics and electromagnetic interference, etc. Therefore, in order to minimize the adverse effects of harmonics on the transmission system, it is required to install AC filters on the AC busbar. Due to the large capacity (capacitive) and frequent casting and switching of the filter bank, which leads to its frequent faults, it is necessary to carry out a study on the ACF circuit breaker closing resistance damage. Regarding the research on the characteristics of circuit breaker closing resistance, scholars at home and abroad have carried out relevant researches for different problems, but there are fewer researches on the circuit breaker failure caused by broken closing resistance. Ni Hui et al. took the frequent occurrence of 750kV AC side filter circuit breaker accidents in 800 ± 800 kV converter station as the background, and simulated the closing inrush current, closing overvoltage, and the maximum heat that can be absorbed by the closing resistor generated during the closing process of different filter combinations with the use of PSCAD/EMTDC, and investigated the influences of the closing resistor resistance and the closing phase angle on the law of closing transient state [8]. Helmut Heiermeier and other scholars in the study of closing resistance input can be consumed in the process of closing energy and reduce the closing process of the possible energy impact, found for the closing resistance absorbed power test technology is not clear, so pointed out a test of the power of the closing resistance and give the details of the procedure [9]. Lazimov Tahir et al. investigated the transition process of circuit breakers with closing resistors for opening high-voltage capacitor banks, noting that proper resistance values and opening and closing times can both reduce switching currents and stabilize the resistors [10]. In view of this, this paper establishes a circuit breaker simulation model for the AC filter field and a modal simulation model for the closing resistor stack, and carries out electric field simulation and modal simulation for the closing resistor stack. The simulation results show that when the closing resistor structure is intact, the field strength near the resistor stack is smooth, and when there is a break in the closing resistor, it will lead to distortion of the field strength around the closing resistor sheet, which increases by 39% compared with the normal working condition. The resonance frequency of the first 6 orders of the closing resistor stack is 18.7–43.37 Hz, while the vibration generated by the transportation truck in the transportation process is mainly distributed in 0 –20 Hz, so the reliability of the product should be reduced as much as possible to avoid the resonance caused by the transportation vibration of the closing resistor part.

2 Modeling of Circuit Breaker for AC Filter Field 2.1 Physical Modeling This paper takes the can-type circuit breaker produced by a domestic company as the research object. The circuit breaker as a whole consists of equalizing cap, static side shielding plate, closing resistance stack, insulating rod core, shell and connecting components, and the overall structure is shown in Fig. 1. The closing resistor stack of 6 columns is connected in series, and the number of resistor tabs per column is 24, 19, 17, 17, 19, and 14, respectively, and the closing resistor is connected in series to the

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insulating bar core, which is held in place by spring compression above. The springs and connecting members are ignored in the simulation model, and the housing is hidden. 17

Fig. 1. Circuit breaker model

Considering that the main objective of the simulation is the electric field distribution inside the circuit breaker, the simulation components are consistent with the actual shape and size in order to simulate the working conditions inside the circuit breaker in the real situation as much as possible. The material parameters used in the simulation are shown in Table 1. Table 1. Material Parameter Material Name

Relative Permittivity

Conduction(S/m)

Remarks

Epoxy-glass

4.5

0

Insulation bar, layer

SF6

1.0024

0

Air Domain

Alloy Steel

∞

2 × 106

Housing

Aluminum alloy

∞

3.6 × 107

Uniform pressure cap

Carbon-Ceramic

13

0.021097

Pre-insertion resistors

2.2 Electric Field Calculation Model The core of the electric field simulation calculation is a set of Maxwell’s equations, which can be considered to be in an electrically quasi-static field when the circuit breaker for the AC filter field is investigated, and the calculation model is as follows [11, 12]: ∇ ×E =0 ∇ ×H =J + ∇ ×D =ρ

∂D ∂t

(1)

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where E, H , D, J , ρ are the electric field strength, magnetic field strength, potential shift vector, conduction current density and body charge density, respectively. By the material’s ontological relationship:  D = εE (2) J = γE where ε and γ are the relative dielectric constant and conductivity of the material. The governing equations under electrically quasi-static fields in conjunction with the relationship between electric field and potential:      ∂ε 1 ∂ ∂ϕ ∂2 γ +ε (3) r + 2 =0 ∂t γ ∂ϕ ∂r ∂z The above equation characterizes the contribution of both conductance and displacement currents to the electric field and is applicable to the electric field distribution under various excitations. 2.3 Modal Simulation Theory In the modal analysis of the circuit breaker closing resistor stack, the whole system can be regarded as a linear free vibration system [13]. The equation of motion is: [M ]{¨x} + [C]{˙x} + [K]{x} = {0}

(4)

where [M ] is the mass; [C] is the damping matrix; [K] is the stiffness coefficient matrix; ·· • [x] is the acceleration; [x] is the velocity; and [x] is the displacement matrix. In the study of the intrinsic frequency of the structure, the damping coefficients are so small that they have almost no effect on the analysis of the modes, so the differential equation can be rewritten as: [M ]{¨x} + [K]{x} = {0}

(5)

Simple harmonic vibration of an object consists of free vibration and its displacement is a sinusoidal function: x = x sin t

(6)

([K] − ω2 [M ]){x} = {0}

(7)

Substituting into Eq. (5) gives:

From the above equation, the intrinsic frequency of the circuit breaker resistor stack is obtained, and the modal vibration pattern is the displacement vector corresponding to the eigenvalue of the equation.

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Fig. 2. Resistive stack cross-section field strength

3 Analysis of Electric Field Calculation Results 3.1 Resistance Stack Strength Under Normal Operating Conditions Figure 2 for the resistance piece of normal operation and no defects along the horizontal direction from the bottom of the shielding plate 300 mm at the cross-section of the electric field distribution, you can see that the electric field from the 6-column resistor sheet group to the outside to reduce the resistance piece of the field strength measured within the field strength distribution is small, the overall distribution of the field strength is smooth. 3.2 Field Strength at Outer Breakage of Resistor Tabs In this paper, we take the resistor string composed of 24 pieces of resistor pieces as an example, and set the notch on the edge of the lowest resistor piece to view the field strength distribution at the broken position and compare the field strength when there is no breakage, and the results are shown in Fig. 3. The results of the field strength comparison show that the maximum field strength around the bottom resistor sheet increases by 39% when there is a break in the resistor sheet located at the bottom. The axial field strength fluctuates, and the overall trend of the rest of the parts is basically the same as that of the field strength distribution when there is no rupture, except that the rupture leads to the distortion of the field strength around the bottom resistor sheet, and the field strength of the rest of the parts does not fluctuate greatly.

4 Modal Analysis of Closing Resistor Stack and Closing Resistor Chip In order to determine the effect of transportation vibration on the closing resistor during the transportation of the circuit breaker, a modal analysis of the closing resistor stack and the monolithic closing resistor is required to determine the intrinsic frequency and deformation trend of each order. There is no need to apply loads and constraints in the modal analysis of resistive stacks[14]. The first 6 orders of self-oscillating frequencies

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Fig. 3. Comparison of electric field distribution with and without breakage

and formations obtained after modal analysis of the resistive stack structure are shown in Fig. 4. The intrinsic frequency variation waveforms of the monolithic closing resistor obtained from experimental tests are shown in Fig. 5. The results of modal analysis show that the overall structural stiffness of the closing resistor stack is high, and the main deformation point of the first 6 steps is at the insulating rod. The resonance frequency of the first 6 orders is 18.7–43.37 Hz. According to the relevant literature, the vibration of transportation vehicles is caused by the excitation of the engine, and the inherent frequency of general delivery trucks and vans is 8– 20 Hz [15]. So the first three orders of the modal analysis are exceptionally important. Therefore, during transportation, the vibration should be reduced as much as possible to ensure that it does not cause the resonance of the closing resistor stack to ensure product reliability. The intrinsic frequency of the monolithic closing resistor is close to 50Hz, which is similar to the operating frequency of industrial frequency alternating current (AC), in which case the operating condition of the closing resistor needs to be studied more thoroughly.

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(a) 1st order eigenfrequency

(b) 2nd order eigenfrequency

(c)3rd order eigenfrequency

(d) 4th order eigenfrequency

(e)5th order eigenfrequency

(f)6th order eigenfrequency

Fig. 4. Resistive stack modal analysis results

Fig. 5. Single resistor chip intrinsic frequency

5 Conclusion The key contributions of the paper can be summarized as follows: (1) When the closing resistor is broken, it will cause the distortion of the surrounding field strength, compared with the normal working condition, the field strength increases by 39%, the actual operation should be ensured that it is operated under normal conditions.

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(2) Generally, the vibration generated during the transportation of trucks and vans may resonate with the closing resistor, so the vibration should be reduced as much as possible during transportation to ensure that it does not cause the resonance of the closing resistor stack and to ensure the reliability of the product. Acknowledgements. This work was supported by a special project (22CX8GA111) of the Science and Technology Commissioner of Gansu Province and the State Grid Corporation of China.

References 1. Shu, Y., Chen, W.: Research and application of UHV power transmission in China. High voltage 3(1), 1–13 (2018) 2. Zhang, Y., Wang, A., Zhang, H.: Overview of smart grid development in China. Power Syst. Protect. Control 49(5), 180–187 (2021). (in Chinese) 3. Yuan, T., Wang, X., Sima, W., et al.: Research on fusion algorithm of lightning strike trip warning for mountain transmission lines. In: 2022 4th Asia Energy and Electrical Engineering Symposium (AEEES), pp. 662–666. IEEE (2022) 4. Fang, S., Zhang, L., Zou, L., et al.: Study on lightning overvoltage and commutation failure in UHV AC/DC hybrid system. Journal Eng. 2019(16), 2677–2682 (2019) 5. Liu, Z., Zhang, J., Wu, W.: Study on suppressing VFTO of 1000 kV GIS disconnector by closing resistor. High Voltage Apparatus 57(05), 1–6 (2021). (in Chinese) 6. Meng, W., Yin, F., Chang, Y., Tang, W., Wei, J.: Research of closing resistor in 800 kV sf6 tank circuit breaker. High Voltage Apparatus 56(08), 109–113 (2020). (in Chinese) 7. Saafan, E., Lazimov, T.: Numerical research of operation circuit breakers with pre-insertion resistors at switching power capacitor banks. International Organization (2022) 8. Hui, N., Xiaohui, C., Chunying, H.E.: Switching transient characteristics and its suppression measures of 750 kV AC filter circuit breaker. High Voltage Eng. 48(5), 1846–1854 (2022). (in Chinese) 9. Heiermeier, H., Raysaha, R.B.: Power testing of pre-insertion resistors: limitations and solution. IEEE Trans. Power Delivery 32(4), 1688–1695 (2016) 10. Lazimov, T., Saafan, E.A., et al.: Transitional processes at switching-off capacitor banks by circuit-breakers with pre-insertion resistors. In: 2015 Modern Electric Power Systems (MEPS), pp. 1–4. IEEE (2015) 11. Feng, C., Ma, X.: Introduction to engineering electromagnetic fields. Monographs of the High Education Press (2000). (in Chinese) 12. Lü, A., Li, J., Zhang, Z., Song, H., Lin, X.: Finite element analysis for the influence of clamp on the thermal characteristics of high voltage insulated power cable. Trans. China Electrotech. Soc. 37(1), 283–290 (2022). (in Chinese) 13. Dai, Y., Cui, S., Song, L.: Finite element method modal analysis of driving motor for electric vehicle. Proc. CSEE 31(9), 100–104 (2011). (in Chinese) 14. Wang, X., Xiong, J.: Analysis of vibration characteristics of ground rod auxiliary drilling rig. J. Vibration Shock 42(8), 152–159 (2023). (in Chinese) 15. Jafarian, K., Darjani, M., Honarkar, Z.: Vibration analysis for fault detection of automobile engine using PCA technique. In: 2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA), pp. 372–376. IEEE (2016)

High-Frequency Signal Injection-Based Various Cable Connection Fault Diagnostics of PMSM Yitong Li , Wei Xu(B) , Jiyao Wang, Zhen Jin, and Shuhua Fang School of Electrical Engineering, Southeast University, Nanjing, Jiangsu Province, China [email protected]

Abstract. This paper presents a comprehensive diagnostic method for cable connection faults in permanent magnet synchronous motor (PMSM). The method utilizes high-frequency voltage injection at zero speed and considers single and multiple faults, including the misconnection of two-phase powerlines, disconnection of one-phase powerlines, and cable swap of position sensors. Mathematical derivations of the response current are provided and an offline diagnosis is performed using a support vector machine (SVM). The SVM is trained with a range of response signals, and feature extraction algorithms are employed to enhance the classification accuracy. Experimental results demonstrate the effectiveness of the proposed method in detecting, identifying, and locating faults, thereby achieving a comprehensive and highly accurate diagnosis for various PMSM cable faults with different causes. This contributes to the overall reliability of the system. Keywords: Cable Faults · Fault Diagnosis · High-Frequency Injection · Permanent Magnet Synchronous Motor · Support Vector Machine

1 Introduction Fault diagnosis and localization are important research directions in the field of motors. Currently, motor fault diagnosis techniques generally fall into three categories: modelbased [1–6], signal-based [7–13], and intelligent algorithm-based methods [14–20]. Model-based fault diagnosis utilizes the motor model to estimate the faulty signal, calculating the error between the actual and estimated signals for fault detection. This method is effective for detecting single faults [1, 2]. [3] establishes a PMSM model that considers inter-turn short-circuit (ITSC) faults in the stator winding. [4] proposes a diagnosis method for ITSC faults based on the difference between actual and estimated stator currents. [5] applies the symmetrical component method to obtain the diagnostic variable expression, while [6] calculates the number of short-circuit turns to assess fault severity. Accurate models are necessary for the above methods, however, actual motor parameters often deviate from mathematical models in practice. Therefore, signal-based fault diagnosis methods have been explored to enhance diagnostic accuracy [5–7], which analyzes the time-frequency domain characteristics of the faulty output to identify and locate the fault. For example, applying Fourier transform of the zero-sequence voltage component, monitoring harmonic amplitude [8], extracting the second harmonic from © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 17–39, 2024. https://doi.org/10.1007/978-981-97-1064-5_3

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the voltage vector [9], and using the wavelet transform to collect and normalize fault variables from the cost function [10, 11]. In recent times, there has been significant progress in the development of fault diagnosis techniques utilizing high-frequency injection. Specifically, for open-circuit (OC) faults, a rotating high-frequency voltage is injected into stator windings, while response current [12] and zero-sequence voltage [13] are extracted for diagnosis, while [14] computes the average absolute value of the high-frequency response signal. To evaluate the asymmetry and locate the fault, [15] uses the amplitude ratio between the positive and negative sequence components of the current as the diagnostic indicator. Model-based and signal-based diagnosis methods rely on the combination of mathematical calculation and experimental verification. While achieving high accuracy, these methods are usually affected by specific motor parameters and have low generalizability [16]. By leveraging intelligent algorithms, it becomes feasible to gather, process, and analyze operational data without necessitating the construction of a precise mathematical model. Support Vector Machine (SVM) is an intelligent classification algorithm in machine learning. It effectively addresses the challenge of encountering local minimums during neural network training and showcases promising performance in fault diagnosis [17–19]. [20] conducts spectrum analysis on the phase current signal and its envelope, utilizing SVM for the diagnosis of ITSC fault. [21] uses the Empirical Mode Decomposition to extract the features of the phase current under OC fault, thereby enhancing the accuracy and anti-interference capability of SVM. Increasing intelligent algorithms with faster learning speed and smaller computing memory are also applied to optimize the SVM in fault diagnosis [22–25]. The cable connection fault of PMSM is often attributed to improper operation, which will lead to rotor jamming, current excessing, and even burning out. Currently, few studies are focusing on cable connection faults in the field of fault diagnosis. [26] highlights the significant resemblance between the mathematical models of external cable connection fault, ITSC fault, and OC fault, indicating the potential for shared diagnostic strategies. However, [27] further investigates the different fault phenomena shown in the external cable connection faults due to the complicated operating environment. As a result, the diagnostic performance will be limited practically. Based on the aforementioned research, this paper introduces an SVM classification method for the cable connection fault diagnosis of the PMSM. Taking the high-frequency response current at zero speed as the analysis object, we propose an offline comprehensive strategy that can significantly improve the accuracy of cable connection fault diagnosis. The rest of this paper is organized as follows: In Sect. 2, the expressions of high-frequency response current under cable connection fault are deduced and analyzed. Section 3 briefly introduces the fault classification method and the principle of SVM. Simulation verifications are conducted in Sect. 4. The proposed strategy is tested on an IPMSM control system and gained considerable performance in Sect. 5.

High-Frequency Signal Injection-Based Various Cable Connection

19

2 Cable Fault Analysis Based on High-Frequency Injection 2.1 Mathematical Model of PMSM Based on the nonlinear transformation method and back-EMF model [28–30], a PMSM model is established and then simplified according to the high-frequency injection theory. The detailed derivation refers to Appendix 1. The simplified PMSM voltage equation is: ⎧ ⎪ ⎨ ud = Rid + Ld did dt (1) ⎪ di ⎩ u = Ri + L q q q q dt where Ld and Lq are the inductance components of the d and q axes, respectively. And R is the equivalent resistance of the stator winding. id is only induced by ud , and iq is only induced by uq . Define the average inductance as L = (Ld + Lq )/2, the half difference inductance as L = (Ld − Lq )/2, and denote the time differential operator as p, , we have (2) and (3). The detailed derivation refers to Appendix 2.        id L + L cos 2θe −L sin 2θe id ud = pLeq =p (2) uq iq −L sin 2θe L − L cos 2θe iq ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ L−L cos 2θe L sin 2θe i u u ⎢ d⎥ L2 −L2 ⎥⎢ d ⎥ −1 −1 ⎢ d ⎥ −1 ⎢ L2 −L2 (3) ⎣ ⎦ = p Leq ⎣ ⎦ = p ⎣ ⎦⎣ ⎦ L sin 2θe L+L cos 2θe iq uq uq L2 −L2 L2 −L2 In this study, the adoption of the rotating high-frequency voltage signal for injection is motivated by its robust control stability and the promising performance it offers in steady-state conditions, which aligns with the requirement of driving the PMSM during its stable operation stage [31, 32]. Moreover, under the rotating voltage injection, the coupling can be eliminated through coordinate transformation. Under this precondition, two high-frequency voltage signals with a phase difference of 90° are injected into the d and q axes respectively, where the amplitude and angular frequency are denoted as vc and ωc in (4).     Udc cos(ωc t) = vc (4) Uqc sin(ωc t) Generally speaking, the three-phase cable refers to the powerline that connects the inverter and the three-phase winding of the PMSM. The output and input terminals of the inverter are marked as ABC and UVW, respectively. The correct connection method is ABC-UVW, while the rest methods are mistaken. Among them, single faults of the powerline are divided into two-phase misconnection and one-phase disconnection. Two-phase misconnection includes reverse connections (ACB-UVW, CBA-UVW, BAC-UVW) and co-direction connections (CAB-UVW, BCA-UVW). Co-connection methods will not be discussed in this paper because the response current differs from normal only by 120° electrical. One-phase disconnection,

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Y. Li et al. Table 1. Several Cable Connection Fault Types. Single Fault

Type

Multiple Fault

Health

Two-phase Misconnection

One-phase Disconnection

U

A

A

C

B

0

A

A

A

0

C

B

A

C

B

V

B

C

B

A

B

0

B

B

C

0

A

C

B

A

W

C

B

A

C

C

C

0

C

State

a' '

b Number of States

'' ''

'' ''

'' ''

'' ''

'' ''

'' ''

'' ''

Powerlines only

Sensor

'' ''

Sensor and Powerlines

B

A

0

B

A

C

'' ''

'' ''

'' ''

'' ''

'' ''

'' ''

ab

ab

ab

ab

ab

ab

ab

ba

ab

ab

ab

ba

ba

ba

1

2

3

4

5

6

7

11

8

9

10

12

13

14

also called phase loss, means that one of the three input terminals is floated (marked as 0) while the phase sequence remains unchanged (0BC-UVW; A0C-UVW; AB0-UVW). Multiple faults of the powerline include three situations (0CB-UVW, C0A-UVW, BA0UVW), in which two-phase misconnection and one-phase disconnection occur simultaneously. The remaining six types (B0C-UVW, CB0-UVW, AC0-UVW, 0AC-UVW, 0BA-UVW, A0B-UVW) will not be discussed for the same reason as above. Compared with the before-mentioned three cases, the form and amplitude of the response current have not changed. The position sensor used in this drive system is an incremental encoder, which converts relative displacement into a periodic electrical signal. Three pulse signals are output from cables named a, b, and Z respectively. The Z line is used for positioning and is generally connected first. And if the two output cables ‘a’ and ‘b’ are swapped (a’-b”, b’-a”), the recorded rotation direction and the value of the position angle at this time is reversed. The impact of the position sensor cable fault on the motor is similar to the two-phase misconnection of the powerline. If the two-phase powerline and the two sensor cables are misconnected simultaneously (ACBa’b’-UVWb”a”, CBAa’b’UVWb”a”, BACa’b’- UVWb”a”), the fault type should be determined by analyzing the response current. All the fault types mentioned above are listed in Table 1. This system adopts the PMSM vector control mode with id = 0, the given speed is 0, thus ud = uq = 0 can be obtained. Therefore, the excitation corresponding to the response current only comes from the high-frequency signal injected. The subsequent mathematical derivation processes are based on this precondition. 2.2 Response Current Under Cable Connection Faults This section calculates and analyses the response current under the healthy and fault states. Vectors of injected voltage and response current are also plotted for analysis. Detailed calculation processes of all states are shown in Appendix 3.

High-Frequency Signal Injection-Based Various Cable Connection

21

Healthy Working Condition State 1: When the three-phase powerlines are all connected correctly: ⎡

⎤   uu T  Udc ⎢ ⎥ = vc cos(ωc t + θe ) − cos(ωc t + π3 + θe ) − cos(ωc t − π3 − θe ) ⎣ uv ⎦ = T2r/3s Uqc uw



⎡

⎡

⎤

⎢ iar ⎢ ⎢ ⎢ ib ⎢ r ⎣ icr

⎤

ud uq





= T3s/2r uu uv uw ⎡

T



= vc

cos(ωc t) sin(ωc t)



(6) ⎤

vc ⎢ idr ⎥ ⎢ L sin ωc t − L sin(ωc t + 2θe ) ⎥ ⎣ ⎣ ⎦=  2 ⎦ 2 ωc L − L iq r −L cos ωc t − L cos(ωc t + 2θe ) ⎡

⎤

⎡

L sin(ωc t + θe ) − L sin(ωc t + θe )

⎥ ⎢ ⎥ ⎢ ⎢ idr ⎥ vc ⎥ ⎢ ⎥=   ⎥ = T2r/3s ⎢ ⎣ ⎦ ω L2 − L2 ⎢ ⎥ ⎢ −L sin(ωc t + θe + c ⎦ ⎣ iqr −L sin(ωc t + θe −

(5)

(7) ⎤ ⎥ ⎥ ⎥

π ) + L sin(ω t + θ − π ) ⎥ c e 3 3 ⎥ π ) + L sin(ω t + θ + π ) c e 3 3

(8)

⎦

By examining Eqs. (7) and (8), it is evident that whether the response current is expressed in a two-phase or three-phase manner, it can be decomposed into two sinusoidal components distinguished by varying amplitudes and angles. The first component, characterized by an amplitude of L, exhibits a rotation direction that aligns with the injected signal. Conversely, the second component possesses a rotation direction opposite to that of the injected signal. The term L denotes the positive sequence component, while the term L represents the negative sequence component. If the angle and velocity are set to zero, θe is also zero. Uuvw can be expressed as: ⎡ ⎤ ⎡ ⎤ uu ua   ⎣ uv ⎦ = ⎣ ub ⎦ = vc cos(ωc t) cos(ωc t − 2π ) cos(ωc t + 2π ) T (9) 3 3 uw ⎡ ⎤ uc 



ud uq

⎡ ⎤      1   sin(ωc t) uu vc ⎣ idr cos(ωc t) ud ⎢ ⎥ Ld 0 Ld −1 ⎦ , = T3s/2r ⎣ uv ⎦ = vc =p = c t) ωc − cos(ω 0 L1 iqr uq sin(ωc t) Lq q uw

(10)

Thus, idr and iqr can be written as functions of vc , ωc , Ld , Lq . Define two amplitudes Idm = vc /(ωc Ld ), Iqm = vc /(ωc Lq ). Both signals show a sinusoidal pattern, with iqr trailing idr by 90° in the electrical angle which is shown in Fig. 1(a). Single Faults of Powerlines State 2–4: In State 2, the amplitude and angle of idr remain unchanged, while iqr has a 90° electrical angle ahead of idr . The response current of State 2 are given in (11) (12). Vectors of all three types of faults are shown in Fig. 1(b), (c) and (d). ⎡ ⎤ ⎡ ⎤ uu ua   ⎣ uv ⎦ = ⎣ uc ⎦ = vc cos(ωc t) − cos(ωc t − π ) − cos(ωc t + π ) T (11) 3 3 uw ub

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a.

b.

c.

d.

Fig. 1. Vectors of injected voltage and response current under State (a) No. 1; (b) No. 2; (c) No. 3; (d) No. 4.



ud uq



 = vc

   vc  sin(ωc t) cos(ωc t) i , dr = Ld iq r − sin(ωc t) ωc

 cos(ωc t) T Lq

(12)

Misconnections of two-phase powerlines can cause a change in the electrical angle difference between iqr and idr , but the angle between Udqr and Idqr remains the same. By studying their phase angle, these three types of faults can be classified.

a.

b.

c.

d.

e.

f.

Fig. 2. Vectors of injected voltage and response current under State (a)No. 5; (b)No. 6; (c)No. 7; (d)No. 8; (e)No. 9; (f)No. 10.

State 5–7: In State 5, the amplitude of idr reduces to Idm /3, while the phase angle remains unchanged. The iqr trails idr by 90° in electrical angle, which is same as the healthy State 1. The response current of State 5 are given in (13) (14). Vectors of all three types of faults are shown in Fig. 2(a), (b) and (c). ⎡ ⎤ ⎡ ⎤ 0 uu   ⎣ uv ⎦ = ⎣ ub ⎦ = vc 0 − cos(ωc t + π ) − cos(ωc t − π ) T (13) 3 3 uw uc  sin(ωc t)    1    vc cos(ωc t) ud id r 3Ld 3 = vc = , (14) sin(ωc t− π2 ) uq iq r sin(ωc t) ωc L q

When the one-phase powerline disconnected, it may result in a change in the amplitude of the response current. Furthermore, if the disconnected phase happens to be B

High-Frequency Signal Injection-Based Various Cable Connection

23

or C, there will be a difference in the angle from idr to iqr . These three faults can be distinguished by observing the changes in angles and amplitudes. Multiple Faults of Powerlines State 8–10: In State 8, the amplitude of idr reduces to Idm /3. Same as State 2, iqr has a 90° electrical angle ahead of idr . The response current of State 8 are given in (15) (16). And vectors of all three types of faults are shown in Fig. 2(d), (e) and (f). ⎡ ⎤ ⎡ ⎤ uu 0   ⎣ uv ⎦ = ⎣ uc ⎦ = vc 0 − cos(ωc t − π ) − cos(ωc t + π ) T (15) 3 3 uw ub  sin(ωc t)    1    v ud cos(ω t) i c 3Ld c d r = vc 3 = , (16) sin(ωc t+ π2 ) uq iq r − sin(ωc t) ωc L q

When the two-phase powerlines are misconnected while the remaining one-phase powerline is floated, the fault expression of the response current exhibits a superposition of two single faults. The rotation direction of Idqr exhibits an opposite to that of the one-phase disconnection. Thus, only by observing the waveform could the sequence of these two kinds of signals be determined, and the multiple faults can be distinguished from the single faults of powerlines. Cables Swap of the Position Sensor State 11: If the two cables of the position sensor are swapped, the output angle it records will always be opposite to the actual position angle, and the rotation direction obtained by the position sensor is also inversed. Thus we define the feedback angle as θe = −θe . The following formula is applied to discuss the change in response current.   cosθe sinθe  (17) Tp = −sinθe cosθe     vc id r L sin ωc t − L sin(ωc t − 2θe )  =  2 (18) iq r ωc L − L2 −L cos ωc t − L cos(ωc t − 2θe ) The expression of Idqr changed because the wrong feedback angle is used by the coordinate transformation block Tp for the calculation of the inductance matrix. Idqr at (18) is also composed of two components. Compared with (7), the positive sequence component remains unchanged, while the angle of the negative sequence component trails by 4θe . The response current is influenced by the swapped position sensor cable. Due to the given zero speed, the rotor position remains at zero, thus θe is still considered to be 0. In this context, we have the new expression of Idqr :   T vc  id r = (19) sin(ωc t)/Ld − cos(ωc t)/Lq iq r ωc The waveform of the response current did not change. Therefore, in the case that the other cables in the system are correctly connected, it is difficult to determine whether the position sensor cable is swapped only by monitoring the waveform of Idqr .

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Multiple Faults of the Position Sensor State 12–14: The expression in (19) has been found to be identical to (10). Consequently, there will be no difference even further substitutions are made in the expression for powerline misconnection. It is difficult to determine whether a fault involves misconnection of sensor cables only by observing the response current waveform.

3 Classification of Cable Fault Based on SVM 3.1 Fault Classification Based on High-Frequency Response Current When the four types of faults involving the misconnection of sensor cables (State 11, 12, 13, and 14) occur, the signal measured by the sensor is no longer actual. To address this issue, this paper considers using the negative sequence component, extracted from the response current by using the Synchronous Reference Frame Filter (SRFF) module [33], to estimate the real-time rotor position. This approach will not be affected by rotor speed and sensor faults, which serve as a basis for reliable fault diagnosis. Based on the previous analysis, a comparative investigation is conducted between thirteen fault states and the normal state using three characteristics of the response current. The fault classification method based on the response current is summarized in Table 2, where the values 0 and 1 represent whether the response current Idqr has remained unchanged or changed, respectively. The determination of the calculated response current in the preceding section is influenced by factors such as the injected voltage, rotor position angle, and stator winding inductance. Theoretical analysis reveals that the response current exhibits distinctive characteristics across different fault states, thereby facilitating the identification and classification of fault types. However, in the presence of a sensor cable misconnection fault, the current expression may become convoluted with other fault states, posing challenges in distinguishing them solely by waveform observation. Table 2. Fault Classification Based on Response Current. State

Amplitude Angle Difference Phase Sequence

1,11

0

0

0

2, 3, 4, 12, 13, 14 0

0

1

5

1

0

0

6,7

1

1

0

8

1

0

1

9,10

1

1

1

High-Frequency Signal Injection-Based Various Cable Connection

25

3.2 Introduction of SVM Fault Classification SVM is an intelligent learning algorithm that constructs an optimal separation plane in a high-dimensional feature space. It is effective for handling non-deterministic data relationships. Its core concept revolves around establishing a classification hyperplane, the decision plane, to maximize the separation margin between positive and negative samples. To describe the relationship between PMSM fault data and fault categories, this paper establishes an SVM prediction model for diagnosing and classifying external cable faults in PMSM. To achieve this, a nonlinear support vector machine capable of handling incomplete classification is employed, utilizing the kernel function K(x, z) which represents the inner product between two instances after a nonlinear transformation. The following convex quadratic programming problem (20) is constructed according to the Karush-Kuhn-Tucher (KKT) conditions, where C > 0 is a penalty parameter specified for the non-linear classification setup. Denote xi as the i-th feature vector of a given training data set T in the feature space, yi as the corresponding class label. The training objectives are formulated as follows: ⎧ N N N    ⎪ 1   ⎪ ⎪ αi αj yi yj K xi , xj − αi ⎨ min α = 2 i=1 j=1 i=1 (20) N ⎪  ⎪ ⎪ s.t. αi yi = 0 0 ≤ αi ≤ C, i = 1, 2, ..., N ⎩ i=1

Solving (20), the optimal solution is obtained: T  α ∗ = α1∗ , α2∗ , ..., αN∗

(21)

Select a component that satisfies 0 < αj∗ < C to further construct the separation hyperplane and the decision function: b∗ = yj − f (x) = sign

 N  i=1

N 

  αi∗ yi K xi , xj

(22)

i=1

αi∗ yi

   ||x − z||2 ∗ +b exp − 2σ 2

(23)

The RBF kernel based on the radial Gaussian kernel function is selected, which can better solve nonlinear problems with fewer hyperparameters:   ||x − z||2 (24) K(x, z) = exp − 2σ 2 where σ is the width of the kernel function. In the subsequent experiments, a collection of real-time state data from the motor is gathered. 90% of the data is utilized as the training set, enabling the adjustment of relevant parameters to achieve maximum classification accuracy. The remaining portion is designated for testing, where the trained SVM model is employed for classification and offline comprehensive diagnosis. The flow chart of the classification algorithm based on SVM is illustrated in Fig. 3.

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PMSM

response HF current

Feature Extraction

SVM Training

Classification

Fig. 3. Classification algorithm flow diagram based on SVM.

4 Simulation Model Establishment and Analysis 4.1 Establishment of the Simulation Model PMSM and its control system models are built with MATLAB-Simulink. The structure diagram of the PMSM closed-loop control system based on high-frequency injection and the detailed current control module are shown in Fig. 4(a), (b), respectively. To verify the effectiveness of the proposed diagnostic method, the three-phase powerline of the motor and the position sensor cables are modified to simulate various PMSM external cable connection faults. In Fig. 4(a), the sensor voltage output by the PMSM is converted into response current by the voltage-current module, the pulse count output is converted into real-time position and speed signals by the incremental encoder module. These three signals are then fed into the current control module for feedback control based on high-frequency injection. To simulate the motor state upon power-on before reaching its rated speed, the speed command is set to 0. Additionally, the rotor position is initialized to 0 using a zero vector in the current control module. The detailed parameters of the motor are listed in Table 3. To minimize the signal-to-noise ratio, the rotating voltage signal should be injected with a frequency not exceeding 50% of the PWM carrier frequency and an amplitude not exceeding 1/10 of the DC bus voltage. The parameters of the injected voltage signal are listed in Table 4. Table 3. Parameters of the Physical Model Motor. Parameter

Ld

Lq

pole pairs

Flux linkage

Inertia

Stator resistance

Initial Angle

DC Bus Voltage

Unit

H

H

/

Wb

kg × m2



rad

V

Value

2.6e-3

3.4e-3

4

1.3e-2

8.35e-5

0.1465

0

600

4.2 Data Processing and Result Analysis On the simulation platform, data was collected for the 14 working states of the PMSM control system, resulting in a total of 13 data sets. The collected data includes the response current in various coordinate systems (ABC natural, d-q synchronous rotating,

High-Frequency Signal Injection-Based Various Cable Connection

27

Table 4. Parameters of the Injected Voltage Signal. Parameter

Amplitude

Frequency

Initial Angle of d-axis Signal

Initial Angle of q-axis Signal

Value

10

500

π/2

0

Unit

V

Hz

rad

rad

Voltage Calculation Velocity Command

e

PI

Feedforward decoupling

q-axis current

Velocity

Inverter Current Pulse Control

Position Incremental Encoder

PMSM

e

Cosine Wave

abc

0 dq

Phase Current Voltage to Current

High Frequency Injection

iabc

Transducer Voltage

PI

iq PI

e

+

+

dq +

SVPWM

Pulse

+

Encoder Count

Sine Wave

a.

b.

Fig. 4. (a) Structure of the PMSM control system; (b) Structure of the current control module.

α-β static), the high-frequency component extracted from the response current, as well as the positive and negative sequences. Real-time rotor position angle data was also collected. The sampling duration was limited to 2 s–2.05 s with a sampling step of 0.1 ms to ensure efficient and rapid diagnosis. This specific data segment corresponds to the smooth response phase of the motor, avoiding any inherent micro vibrations that occur after power-on. It accurately reflects the characteristics of the response current under different fault states and will be utilized for SVM training. Based on the previous mathematical derivation, differences in current waveforms among various fault states are attributed to factors such as phase angle, amplitude, rotation direction, and phase sequence. Figure 5(a), (b) show the initial waveforms of the response current in the d-q and ABC synchronous coordinate systems for State 1, 2, 5, 8, and 12. Notably, there is minimal distinction between the waveforms of State 2 and 12, while the waveforms of State 5 and 8 differ only in q-phase sequence. These observations align well with theoretical calculations. Consequently, it becomes challenging to achieve prompt and accurate fault classification and localization based solely on waveform analysis. To enhance diagnostic accuracy, time-frequency domain feature values are employed for classification instead of using the original data. Figure 6(a), (b) illustrate two representative time-domain features, skewness and root mean square (RMS), out of the total 26 features extracted from the response current. It is observed that data after feature extraction exhibits noticeable differences in both the time and frequency domains, which facilitates accurate classification by SVM. In addition, such pre-processing in the time-frequency domain has been proven to generate effective diagnostic variables such as the RMS value of the response current used in [34]. The simulation results are summarized in Table 5.

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a.

b.

Fig. 5. Response currents of simulation in (a) d-q; (b) ABC coordinate system in five different states. Skewness

RMS

1.1

State 1

State 1

1 0 -1

1 0.9

State 2

0

0.8 0.6 1.9

1

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State 8

-1

0 -1

1.8 1.7 1

State 12

3

State 12

1 0.9 1

1

State 5

State 5

State 2

1.1 0.5 0 -0.5 -1

2.5 2 2

2.01

0.8 0.6

2.02

2

2.01

Time (s)

2.02

Time (s)

a.

b.

Fig. 6. Time-domain features (a) Skewness; (b) RMS of the response current in five different states. Table 5. Simulation Results Type

Powerline Faults Misconnection

Disconnection

Single

Multiple

Sensor cables Faults

Misconnection Faults

All

Amount

3

3

6

3

4

7

14

Accuracy

100%

98.67%

98.33%

100%

100%

99.43%

97.57%

High-Frequency Signal Injection-Based Various Cable Connection Simulation Model with 14 Types

Experimental Model with 14 Types 1 49 1

4

2

55

3

2 38

4

2

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6

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3

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1

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50 50 50

9 10 11 12 13 14

Prediction Class

a.

50

13

50 1

50

6

12

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13

2 31

5

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40 3 9

4

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3 1

The Actual Class

The Actual Class

1 50

10

29

50

14 1

2

3

4

5

6

7

8

9 10 11 12 13 14

Prediction Class

b.

Fig. 7. Confusion matrix for all-state classification results in (a) the simulation system; (b) the experiment system.

From the previous analysis, it can be known that compared with the healthy state, only the position sensor cable misconnection fault does not change in characteristics of the response current such as amplitude, angle, and phase sequence. However, the introduction of SRFF and negative-sequence current makes the collected data more accurately reflect the rotor position, thereby improving the diagnostic performance of this method for position sensor-related faults. The classification accuracy of the four sensor cable faults reaches 100%. In the situation of a two-phase misconnection fault of the powerline, only the phase angle of the response current changes. Even if there is a significant difference from the original state after feature extraction, the discrimination between the three types of faults is still lower than those of the other states. After optimizing the SVM, the classification accuracy of these three faults reaches 98.67%, while the comprehensive accuracy reaches 97.57%–98.33%. For seven kinds of misconnection faults with highly similar mathematical expressions, the classification accuracy reaches 99.43%, which can effectively identify whether the fault includes the swapping of the sensor cable. The full-state comprehensive diagnosis results obtained in the simulation system are also drawn as a confusion matrix shown in Fig. 7(a).

5 Experimental Verification 5.1 Physical Model Establishment The Speedgoat hardware system includes a real-time target machine, an IO board installed in the target machine, cables, and terminal blocks for the IO board. In this paper’s experimental part, Speedgoat’s real-time driver board is combined with the servo motor to establish a rotor-in-loop model. The driver board and the controlled motor used are shown in Fig. 8(a), (b) respectively.

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a.

b.

Fig. 8. (a) Embedded brushless motor driver board; (b) AC servo motor system.

a.

b.

Fig. 9. Response currents of experiment in (a) d-q; (b) ABC coordinate system in five different states.

Waveforms of the feedback current are recorded in the cable fault states. After the time-frequency domain features are extracted, the comprehensive fault diagnosis is carried out with the trained SVM. 5.2 Analysis of Experimental Results The original waveforms of the response currents obtained from the experimental part in the d-q and the ABC coordinate systems are plotted in Fig. 9(a), (b), respectively. Meanwhile, the skewness and RMS of the response current derived after time-domain feature extraction are plotted in Fig. 10 (a), (b), respectively. Similar to the results obtained in the simulation section, the response current waveform does contain information such as fault phase and fault type, but it is difficult to determine the status of the position sensor cable. Nevertheless, it can be seen that after feature extraction, the time-frequency domain feature data used to train the SVM exhibits differentiations which can be identified by machine learning.

High-Frequency Signal Injection-Based Various Cable Connection Skewness

RMS

0 -0.5

State 1

0.2 -0.2

2.9

2.4

State 5

State 5

0

1.8 1.6 2

State 8

0

1.8

State 12

-2 2

State 8

2.8

2.2

-1 2

2.4

-2

State 12

3

State 2

State 2

State 1

0.6

31

0 -0.5 -1 2

2.01

2.02

1.6

2.2 2

2.01

2.02

Time (s)

Time (s)

a.

b.

Fig. 10. Time-domain features (a) Skewness; (b) RMS of the response current in five different states. Table 6. Experimental Results. Type

Powerline Faults Disconnection

Single

Multiple

Sensor cables Faults

Misconnection Faults

All

Misconnection Amount

3

3

6

3

4

7

14

Accuracy

100%

96.67%

97%

100%

100%

98.57%

95.71%

The classification accuracy obtained from the experiments is similar to the simulation one. Due to errors caused by motor friction and noise, the accuracy for two-phase misconnection of powerlines is 96.67%, while the accuracies of other groups including misconnection faults also drop to 95.71%–98.57%. However, a higher precision fault diagnosis and classification is achieved, and the validity of the diagnosis method proposed in this paper has been tested. Theoretical derivation and practical analysis demonstrate that when both the fault of the position sensor cable misconnection and the two-phase powerlines misconnection occur simultaneously, the mathematical model and fault manifestation show great resemblance to those of a position sensor cable without any faults. However, the proposed method effectively distinguishes these two fault types and accurately identifies whether the multiple faults involve the misconnection of the position sensor cable. Detailed experimental results are summarized in Table 6, and the confusion matrix of the full-state comprehensive diagnosis results is shown in Fig. 7(b).

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6 Conclusion This paper proposes a comprehensive fault diagnosis scheme for detecting external cable connection faults in Permanent Magnet Synchronous Motor (PMSM) control system based on a Support Vector Machine (SVM) by introducing a rotating high-frequency voltage at zero speed, analyzing the response current, and employing a multi-classification algorithm to identify the fault type and location. Thirteen representative faults are focused on, with mathematical derivations conducted on the response current in order to enable the classification of cable connection faults. Furthermore, time-frequency domain feature extraction is performed on the collected data and the SVM is trained accordingly. To validate the proposed diagnosis strategy, actual control system faults are simulated. The results show that the classification accuracy of this strategy is close to or reaches 100% for different types of cable faults. Moreover, the intervention at zero speed and zero initial position fulfills the requirements of detecting cable connection faults before high-speed rotation, ensuring operational reliability. The response current expressions and vector diagrams obtained in this study under different fault states can serve as a reference for future research on cable faults. The proposed diagnosis strategy enables effective fault localization without the need for external sensors, offering non-professional operators a quick diagnostic reference. Furthermore, it is independent of the saliency effect and applicable for diagnosing cable connection faults in both IPMSM and SPMSM control systems. Acknowledgments. This research was funded by the National Natural Science Foundation of China under Grant 52275009.

Appendix 1. Modification and Simplification of PMSM Define the basic coordinate transformation matrices Tc and Tp :     2 1 −1/2 −1/2 cos θe sin θe √ √ Tc = , Tp = − sin θe sin θe 3 0 3/2 − 3/2 where θe refers to the real-time electrical angle of the rotor position.   2π cos θe cos(θe − 2π T 3 ) cos(θe + 3 ) , T T3s/2r = Tc Tp = 2r/3s = T3s/2r 2π ) − sin(θ + ) − sin θe − sin(θe − 2π e 3 3

(25)

(26)

In the d-q synchronous coordinate system, the voltage equation can be written as:  ud = Rid + Ld didtd − ωe Lq iq (27) di uq = Riq + Lq dtq − ωe (Ld id + f ) In (27), f represents the flux linkage of the permanent magnet, ωe is the electrical angular velocity; Ld and Lq are the d and q axis inductance, respectively. In the natural coordinate system, the sum of the self-inductance and mutual inductance of the stator windings is expressed as an inductance matrix L3s .

High-Frequency Signal Injection-Based Various Cable Connection

33

Transform (27) into ABC coordinate system: ⎤ ⎤ ⎡ ⎤ ⎡   EMFa ia ua d u ⎣ ub ⎦ = T2r/3s d = (Rs + L3s )⎣ ib ⎦ + ⎣ EMFb ⎦ uq dt uc ic EMFc ⎧ EMFa = −k f ωe sin θe ⎨ EMFb = −k f ωe sin(θe − 2π 3 ) ⎩ 2π EMFc = −k f ωe sin(θe + 3 ) ⎡

(28)

(29)

where the proportionality factor k is a constant. When the rotor position remains zero, the back electromotive force (back-EMF) of phase A is zero, while the back-EMF of phase BC still exists. But when the motor speed is zero, the back-EMF of all three phases return to zero. In this paper, to eliminate the influence of back-EMF on high-frequency response, and to detect faults before starting, the experiments are carried out at zero speed and zero initial position. In this procession, the inductive cross-coupling terms ωe Lq iq and ωe Ld id will also be ignored. Therefore, the voltage model in (27) can be simplified as:  ud = Rid + Ld didtd (30) di uq = Riq + Lq dtq

Appendix 2. Derivation of Inductance Matrix

 cosθe sinθe −sinθe cosθe        ud Rd + pLd −ωe Lq id 0 = + uq ωe Lq Rq + pLq iq λpm 

Tp =

(31) (32)

Since high-frequency voltage injection is performed under zero-speed (ωe = 0), the voltage drop from the back-EMF ωe λpm and the cross-coupling terms ωe Ld and −ωe Lq in (32) are all treated as zero. Define p as the time differential operator. For high-frequency injection, the inductance item is far greater than the resistance item in amplitude. Therefore, the influence of resistance is ignored in subsequent calculations.      pLd 0 id ud = (33) uq 0 pLq iq       ud pLd 0 i = Tp (θerr ) Tp−1 (θerr ) d (34) uq iq 0 pLq If the d-q axis that the high-frequency signal injecting into does not coincide with the actual d-q axis of the rotor, the position error θerr will appear. In (34), θerr represents the difference between the virtual position angle extracted from the high-frequency

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injecting signal and the real-time rotor position angle participating in the closed-loop control system.      L cos2 θerr + Lq sin2 θerr (Lq − Ld ) cos θerr sin θerr id ud =p d (35) uq (Lq − Ld ) cos θerr sin θerr Ld sin2 θerr + Lq cos2 θerr iq Define the average inductance L = (Ld +Lq )/2, and the half-difference inductance L = (Ld − Lq )/2, we have: 

ud uq





L + L cos(2θerr ) −L sin(2θerr ) =p −L sin(2θerr ) L − L cos(2θerr )



id iq

 (36)

If the initial position and the given speed are both 0, θerr is considered to coincides with the real real-time position θe . Thus, the inductance matrix of (38) is obtained. θerr = θe  Leq =

(37)

L + L cos(2θe ) −L sin(2θe ) −L sin(2θe ) L − L cos(2θe )

 (38)

The voltage equation in the d-q synchronous coordinate system is as (39).      ud L + L cos(2θe ) −L sin(2θe ) id =p uq −L sin(2θe ) L − L cos(2θe ) iq

(39)

Appendix 3. Detailed Calculation of Response Current in All States The derivations of the high-frequency response current expressions are provided for one healthy working condition and thirteen fault conditions. Further analysis and classification of the fault response currents are presented in the main text with more detailed information. Normal Working Condition State 1: ⎡ ⎤ ⎡ ⎤ ua uu  ⎣ uv ⎦ = ⎣ ub ⎦ = vc cos(ωc t) cos(ωc t − uw ⎡ ⎤ uc 



ud uq

2π 3 )

cos(ωc t +

 2π T 3 )

⎡ ⎤      1   sin(ωc t) uu vc ⎣ idr cos(ωc t) ud ⎢ ⎥ Ld 0 Ld −1 ⎦ , = T3s/2r ⎣ uv ⎦ = vc =p = c t) ωc − cos(ω 0 L1 iqr uq sin(ωc t) L q q uw

Define Idm = vc /(ωc Ld ), Iqm = vc /(ωc Lq ).

(40)

(41)

High-Frequency Signal Injection-Based Various Cable Connection

35

Single Faults of Powerlines State 2: ⎡ ⎤ ⎡ ⎤ uu ua   ⎣ uv ⎦ = ⎣ uc ⎦ = vc cos(ωc t) − cos(ωc t − π ) − cos(ωc t + π ) T 3 3 uw ub       vc  sin(ωc t) cos(ωc t) T ud cos(ωc t) i = vc , dr = Ld Lq uq iq r − sin(ωc t) ωc

(42)

State 3: ⎡ ⎤ ⎡ ⎤ uu uc   ⎣ uv ⎦ = ⎣ ub ⎦ = vc − cos(ωc t − π ) − cos(ωc t + π ) cos(ωc t) T 3 3 uw ua ⎡ ⎤       sin(ωc t+ 2π 3 ) vc ⎣ ud − cos(ωc t − π3 ) id r Ld ⎦ = vc = , 5π uq iq r sin(ωc t − π3 ) ωc sin(ωc t− 6 )

(43)

(44)

(45)

Lq

State 4: ⎡ ⎤ ⎡ ⎤ uu ub   ⎣ uv ⎦ = ⎣ ua ⎦ = vc − cos(ωc t + π ) cos(ωc t) − cos(ωc t − π ) T 3 3 uw uc ⎡ ⎤       sin(ωc t− 2π 3 ) π v − cos(ωc t + 3 ) ud i c⎣ Ld = vc , dr = π ⎦ uq iq r sin(ωc t + π3 ) ωc sin(ωc t− 6 )

(46)

(47)

Lq

State 5: ⎡

⎤ ⎡ ⎤ uu 0   ⎣ uv ⎦ = ⎣ ub ⎦ = vc 0 − cos(ωc t + π ) − cos(ωc t − π ) T 3 3 uw uc  sin(ωc t)  1      v cos(ω t) ud i c 3Ld c d r = vc 3 = , sin(ωc t− π2 ) uq iq r sin(ωc t) ωc L

(48)

(49)

q

State 6: ⎡

⎤ ⎡ ⎤ uu ua   ⎣ uv ⎦ = ⎣ 0 ⎦ = vc cos(ωc t) 0 − cos(ωc t − π ) T 3 uw uc ⎡√ ⎤     √   7 sin(ωc t− 13 ) 3 5 vc ⎣ √ 3Ld ud cos(ω t) + 6 sin(ωc t) i ⎦ = vc 6 √3 c , dr = 3 sin(ωc t− π3 ) π uq i ω qr c 3 cos(ωc t − 3 ) 3L q

(50)

(51)

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State 7: ⎤ ⎡ ⎤ ua uu   ⎣ uv ⎦ = ⎣ ub ⎦ = vc cos(ωc t) − cos(ωc t + π ) 0 T 3 uw 0 ⎡ √ ⎤     √   7 sin(ωc t+ 13 ) 3 5 v ud cos(ω t) − sin(ω t) i c c 6 ⎣ √ 3Ld 2π ⎦ √ c , dr = = vc 6 3 sin(ωc t− 3 ) uq iq r ωc − 3 cos(ωc t + π ) ⎡

3

3

(52)

(53)

3Lq

Multiple Faults of Powerlines State 8: ⎡ ⎤ ⎡ ⎤ 0 uu   ⎣ uv ⎦ = ⎣ uc ⎦ = vc 0 − cos(ωc t − π ) − cos(ωc t + π ) T 3 3 uw ub  sin(ωc t)    1    vc cos(ωc t) ud idr 3Ld 3 = vc = , sin(ωc t+ π2 ) uq iq r − sin(ωc t) ωc L

(54)

(55)

q

State 9: ⎤ ⎡ ⎤ uc uu   ⎣ uv ⎦ = ⎣ 0 ⎦ = vc − cos(ωc t − π ) 0 cos(ωc t) T 3 uw ua ⎡ √ ⎤     √   − 7 sin(ωc t− 57 ) vc ⎣ − 23 cos(ω√c t) − 33 sin(ωc t) ud id r ⎦ √ 3Ld = vc = , − 3 sin(ωc t) uq iq r ωc − 3 cos(ωc t) ⎡

3

(56)

(57)

3Lq

State 10: ⎤ ⎡ ⎤ ub uu   ⎣ uv ⎦ = ⎣ ua ⎦ = vc − cos(ωc t + π ) cos(ωc t) 0 T 3 uw 0 ⎡ √ ⎤     √   − 7 sin(ωc t+ 57 ) 3 2 vc ⎣ − 3 cos(ω t) − 3 sin(ωc t) i ud ⎦ √c √ 3Ld , dr = = vc 3 3 sin(ωc t) uq i ω qr c cos(ω t) c 3 3L ⎡

(58)

(59)

q

Cables Swap of the Position Sensor. State 11:     vc L sin ωc t − L sin(ωc t − 2θe ) id r  =  2 iq r ωc L − L2 −L cos ωc t − L cos(ωc t − 2θe ) Due to the given zero speed, θe is still considered to be 0, there are:   T vc  id r = sin(ωc t)/Ld − cos(ωc t)/Lq iq r ωc

(60)

(61)

High-Frequency Signal Injection-Based Various Cable Connection

Multiples of Sensor Cables and Powerlines. State 12: Combine (61) and (43).   T vc  idr = sin(ωc t)/Ld cos(ωc t)/Lq iq r ωc State 13: Combine (61) and (45).   vc  id r = sin(ωc t + iq r ωc State 14: Combine (61) and (47).   vc  id r = sin(ωc t − iq r ωc

(62)

T 5π 6 )/Lq

2π 3 )/Ld

sin(ωc t −

2π 3 )/Ld

sin(ωc t − π6 )/Lq

37

T

(63)

(64)

(62) and (43), (63) and (45), (64) and (47) are exactly the same.

References 1. Da, Y., Shi, X., Krishnamurthy, M., Health monitoring, fault diagnosis and failure prognosis techniques for Brushless Permanent Magnet Machines. In: 2011 IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, pp. 1–7 (2011) 2. Li, H., Chen, T., Yao, H.: Mechanism, diagnosis and development of demagnetization Fault for PMSM in electric vehicle. Trans. China Electrotech. Soc. 28(8), 276–284 (2013). (in Chinese) 3. Fonseca, D.S.B., Santos, C.M.C., Cardoso, A.J.M.: Stator faults modeling and diagnostics of line-start permanent magnet synchronous motors. IEEE Trans. Industry Appli. 56(3), 2590– 2599 (2020) 4. Mazzoletti, M.A., Bossio, G.R., De Angelo, C.H., Espinoza-Trejo, D.R.: A Model-based strategy for interturn short-circuit fault diagnosis in PMSM. IEEE Trans. Industr. Electron. 64(9), 7218–7228 (2017) 5. Ge, Y., Song, B., Pei, Y., Mollet, Y.A.B., Gyselinck, J.J.C.: Analytical expressions of isolation indicators for permanent-magnet synchronous machines under stator short-circuit faults. IEEE Trans. Energy Convers. 34(2), 984–992 (2019) 6. Qi, Y., Bostanci, E., Zafarani, M., Akin, B.: Severity estimation of interturn short circuit fault for PMSM. IEEE Trans. Industr. Electron. 66(9), 7260–7269 (2019) 7. Hang, J., Yan, D., Xia, M., Ding, S., Wang, Q.: Quantitative fault severity estimation for high-resistance connection in PMSM drive system. IEEE Access 7, 26855–26866 (2019) 8. Urresty, J.-C., Riba, J.-R., Romeral, L.: Application of the zero-sequence voltage component to detect stator winding inter-turn faults in PMSMs. Electric Power Syst. Res. 89, 38–44 (2012) 9. Boileau, T., Leboeuf, N., Nahid-Mobarakeh, B., Meibody-Tabar, F.: Synchronous demodulation of control voltages for stator interturn fault detection in PMSM. IEEE Trans. Power Electron. 28(12), 5647–5654 (2013) 10. Hang, J., Zhang, J., Xia, M., Ding, S., Hua, W.: Interturn fault diagnosis for model-predictivecontrolled-PMSM based on cost function and wavelet transform. IEEE Trans. Power Electron. 35(6), 6405–6418 (2020)

38

Y. Li et al.

11. Chen, Y., Liang, H., Wang, C., Liang, S., Zhong, R.: Detection of stator inter-turn short-circuit fault in pmsm based on improved wavelet packet transform and signal fusion. Trans. China Electrotech. Soc. 35(zk1), 228–234 (2020). (in Chinese) 12. Sun, C., et al.: High-frequency voltage injection-based fault detection of a rotating rectifier for a wound-rotor synchronous starter/generator in the stationary state. IEEE Trans. Power Electron. 36(12), 13423–13433 (2021) 13. Hang, J., Zhang, J., Cheng, M., Ding, S.: Detection and discrimination of open-phase fault in permanent magnet synchronous motor drive system. IEEE Trans. Power Electron. 31(7), 4697–4709 (2016) 14. Jiang, X., Xu, D., Gu, L., Li, Q., Xu, B., Li, Y.: Short-circuit fault-tolerant operation of dualwinding permanent-magnet motor under the four-quadrant condition. IEEE Trans. Industr. Electron. 66(9), 6789–6798 (2019) 15. Huang, W., Du, J., Hua, W., Fan, Q.: An open-circuit fault diagnosis method for PMSM drives using symmetrical and DC components. Chin. J. Electr. Eng. 7(3), 124–135 (2021) 16. Alex Gong, C.-S., Simon Su, C.-H., Tseng, K.-H.: Implementation of machine learning for fault classification on vehicle power transmission system. IEEE Sensors J. 20(24), 15163– 15176 (2020) 17. Chen, L., Huang, J.: Motor broken rotor bar fault diagnosis with support vector machine. Trans. China Electrotech. Soc. 21(8), 48–52 (2006). (in Chinese) 18. Qiu, W., et al.: Cyber-attack identification of synchrophasor data Via VMD and multifusion SVM. IEEE Trans. Industry Appli. 58(2), 1456–1465 (2022) 19. Song, X., Zhao, J., Song, J., Dong, F., Xu, L., Zhao, J.: Local demagnetization fault recognition of permanent magnet synchronous linear motor based on S-transform and PSO–LSSVM. IEEE Trans. Power Electron. 35(8), 7816–7825 (2020) 20. Orlowska-Kowalska, T., et al.: Fault diagnosis and fault-tolerant control of pmsm drives-state of the art and future challenges. IEEE Access 10, 59979–60024 (2022) 21. Wu, Y., Zhang, Z., Li, Y., Sun, Q.: Open-circuit fault diagnosis of six-phase permanent magnet synchronous motor drive system based on empirical mode decomposition energy entropy. IEEE Access 9, 91137–91147 (2021) 22. Aydin, I., Kaner, S., Akin, E., Gurusamy, V.: A Bayes optimized SVM and frequency estimation for diagnosis of eccentricity faults. In: 2021 IEEE 13th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), Dallas, TX, USA, pp. 5–10 (2021) 23. Wu, Y., Sun, X., Zhang, Y., Zhong, X., Cheng, L.: A power transformer fault diagnosis method-based hybrid improved seagull optimization algorithm and support vector machine. IEEE Access 10, 17268–17286 (2022) 24. Gou, B., Xu, Y., Xia, Y., Wilson, G., Liu, S.: An intelligent time-adaptive data-driven method for sensor fault diagnosis in induction motor drive system. IEEE Trans. Industr. Electron. 66(12), 9817–9827 (2019) 25. Shi, L., Wang, P., Hu, Y., Han, L.: Broken rotor bar fault diagnosis of induction motors based on bare-bone particle swarm optimization and support vector machine. Trans. China Electrotech. Soc. 29(1), 147–155 (2014). (in Chinese) 26. Lee, S.B., Tallam, R.M., Habetler, T.G.: A robust, on-line turn-fault detection technique for induction machines based on monitoring the sequence component impedance matrix. IEEE Trans. Power Electr. 18(3), 865–872 (2003) 27. Cheng, S., Zhang, P., Habetler, T.G.: An impedance identification approach to sensitive detection and location of stator turn-to-turn faults in a closed-loop multiple-motor drive. IEEE Trans. Industr. Electron. 58(5), 1545–1554 (2011) 28. Ghafari-Kashani, A.R., Faiz, J., Yazdanpanah, M.J.: Integration of non-linear H∞∞and sliding mode control techniques for motion control of a permanent magnet synchronous motor. IET Electr. Power Appl. 4(4), 267–280 (2010)

High-Frequency Signal Injection-Based Various Cable Connection

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29. Chen, Z., Tomita, M., Doki, S., Okuma, S.: An extended electromotive force model for sensorless control of interior permanent-magnet synchronous motors. IEEE Trans. Indus. Electr. 50(2), 288–295 (2003) 30. Yang, S.-C., Lorenz, R.D.: Surface permanent magnet synchronous machine position estimation at low speed using eddy-current-reflected asymmetric resistance. IEEE Trans. Power Electron. 27(5), 2595–2604 (2012) 31. Chaudhary, M.P., Patel, V., Jamnani, J.G.: Sensorless vector control of PMSM drive using heterodyne technique. In: 2008 11th International Conference on Optimization of Electrical and Electronic Equipment, Brasov, Romania, pp. 93–99 (2008) 32. Tang, Q., Shen, A., Luo, X., Xu, J.: IPMSM sensorless control by injecting bidirectional rotating HF carrier signals. IEEE Trans. Power Electron. 33(12), 10698–10707 (2018) 33. Lorenz, R.D.: Practical issues and research opportunities when implementing zero speed sensorless control. In: ICEMS 2001. Proceedings of the Fifth International Conference on Electrical Machines and Systems (IEEE Cat. No. 01EX501), Shenyang, China, vol. 1, pp. 1–10 (2001) 34. Gajanayake, C.J., Bhangu, B., Nadarajan, S., Jayasinghe, G.: Fault tolerant control method to improve the torque and speed response in PMSM drive with winding faults. In: 2011 IEEE Ninth International Conference on Power Electronics and Drive Systems, Singapore, pp. 956–961 (2011)

Transient Stability Analysis of Grid Following Converter Intergreted with Synchronous Generator Huanhuan Yang1 , Jian Qiu1 , Jianxin Zhang1 , Guanghu Xu1 , Deping Ke2 , Jian Xu2 , Cai Yan2(B) , and Junquan Chen3 1 Power Dispatching Control Center of China Southern Power Grid, Guangzhou 510663, China 2 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430074, China

[email protected] 3 Electric Power Dispatching and Control Center of Guizhou Electric Power Grid Co., Ltd.,

Guiyang 550002, China

Abstract. As a large number of grid-following converters (GFLs) have joined the power system, transient characteristic of the power system is profoundly being changed. Aimed at the case of coupling system integrated by GFL and synchronous generator (SG), it is necessary to analyze synchronization stability of coupling system in the large-disturbance case. To address that, this paper investigates the coupling system between GFL and SG firstly. Then, the equivalent model of coupling system is derived. Next, transient stability analysis of GFL based on the equivalent model is conducted to detect the transient instability mechanism. Two instability modes of GFL are defined. Finally, time-domain simulation results verify the correctness of theoretical analysis. Keywords: Grid-following converter · synchronous generator · phase-locked loop · large-disturbance

1 Introduction With the determination of the double carbon goal, the development of renewable energy is rapid [1]. A large number of power sources dominated by GFLs are integrated into the power grid [2]. However, these power sources must be synchronized with the power grid via phase locked loop (PLL) [3]. The synchronization stability mechanism of GFLs after large disturbances is not yet clear. It is necessary to further study the corresponding large disturbance stability mechanism. The integration of renewable energy and SGs at the same point of common coupling (PCC) is widely used as a coupling system [4–6], which can be equivalent to a coupling system of GFLs and SGs in parallel. It is necessary to analyze the large disturbance mechanism in the coupling system integrated with GFLs and SGs [7]. The relevant literature attempts to analyze the transient synchronization instability problem caused by the interaction between multiple GFLs [8–10]. In Refs. [2, 3], a GFL is regarded as a form of the second-order rotor dynamic equation of a SG. Based on that, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 40–47, 2024. https://doi.org/10.1007/978-981-97-1064-5_4

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the corresponding low-voltage control is added to the control block diagram in the form of second-order damping torque to analyze the transient instability characteristics during the process of fault ride through. However, little focus has been paid to the problem of large disturbance synchronization stability in the coupling system composed by GFLs and SGs. To solve the above problems, this paper firstly establishes a coupling system between a GFL and a SG. Then, the equivalent model of the coupling system is derived. Next, based on the proposed model, this paper conducts a comparative analysis to explore transient instability mechanism and defines two instability modes for GFL. Finally, time-domain transient simulation results verify the correctness of the theoretical analysis.

2 Coupling System Figure 1 shows the scenario of a GFL coupling with a SG into an infinite power grid.

Fig. 1. A Structure of a GFL integrated with SG.

In Fig. 1, I dq is the current reference value of GFL. U PCC and U 2 are the terminal voltages of GFL and SG, respectively. U g is the infinite grid voltage. X 1 and X 2 are the equivalent impedances between GFL, SG and the infinite grid, respectively. X g is the equivalent impedance between the common connection point and the infinite grid. I 1 and I 2 are the output currents of GFL and SG, respectively. δ w is the included angle between U PCC and U g . The topology shown in Fig. 1 can be simplified to the circuit structure in Fig. 2.

Fig. 2. Simplified circuit of a GFL coupled with SG.

where ·

·

·

·

Ug X2 Xg X2 Ug +Xg U2 U2 Xs = X2 //Xg = , Us = ( + )Xs = X2 + Xg Xg X2 X2 + Xg

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3 Analytical Model of Coupling System 3.1 Equivalent Model Based on Fig. 2, q-axis component of PCC voltage can be obtained UPCCq =Id1

X2 Xg Xg X2 − Ug sin δw + Id1 X1 − U2 sin(δw − δg ) X2 + Xg X2 + Xg X2 + Xg

According to PLL dynamics, it can be obtained   δw = [(KP + KI )UPCCq ]

(1)

(2)

Substituting (1) into (2), and we can get Mw δ¨w + Dw δ˙w + Pew = Pmw + DDw

(3)

where δ g is the phase angle of SG. K P and K I are the proportional and integral coefficients corresponding to PI controller of PLL in the GFL, respectively. I d1 is the d-axis component of the output current of GFL and L L

Mw = Dw =

g 1 − KP ω0 (L22 +L Id1 − KP ωL10 Id1 g)

KI

Lg L2 Lg KP L2 L1 [ Ug cos δw + U2 cos(δw − δg )] − Id1 Id1 − KI L2 + Lg L2 + Lg ω0 (L2 + Lg ) ω0 Pew =

Lg L2 Ug sin δw + U2 sin(δw − δg ) L2 + Lg L2 + Lg Pmw = DDw =

L2 Lg Id1 + L1 Id1 L2 + Lg

KP Lg U2 cos(δw − δg )δ˙g KI L2 + Lg

3.2 Active Power Calculation Furthermore, consider the dynamics of SG, the output power of SG is calculated as follows:  Seg = Peg + jQeg = U2 ejδg [(U2 ejδg − U0 ejδ0 ) (jX2 )]∗ (4) It can be rearranged as Peg =

U2 Ug U2 Xg sin δg − Id1 cos(δg − δw ) X2 + Xg X2 + Xg

(5)

where Peg is output electromagnetic power of SG. It can be seen from (5) that after considering the dynamics of SG, the interaction between GFL and SG affects their respective equivalent electromagnetic power.

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4 Transient Stability Comparative Analysis Based on Equivalent Model Considering the different time scales of GFL and SG, the transient stability of the coupling system will be determined by the one with the smaller stability margin. 4.1 Determinant Factor of Instability Mode According to the above equation, it can be concluded that: Pew =

Lg L2 Ug sin δw + U2 sin(δw − δg ) L2 + Lg L2 + Lg

(6)

Let Acosα = L g U 2 cosδ g + L 2 U g , Asinα = L g U 2 sinδ g . Equation (6) is derived as Pew =

1 A sin(δw − α) L2 + Lg

(7)

The condition for the coupling system to remain stable is Pew = Pmw , that is L2 Lg 1 A sin(δw − α) = ( + L1 )Id 1 L2 + Lg L2 + Lg

(8)

Under the given operating conditions, the stable equivalent point δ wSEP and unstable equivalent points δ wUEP of GFL can be obtained, that is L2 Lg 1 A≥( + L1 )Id 1 L2 + Lg L2 + Lg

(9)

It can be seen from Eq. (9) that |L U −L Ug | 1) When Id 1 ≤ L2 Lgg+L2 1 (L22 +L , δg ≤ π and δgmax = π . g) L U −L U L U +L Ug | g| 2) When L2 Lgg+L2 1 (L22 +L < Id 1 ≤ L2 Lgg+L2 1 (L22 +L , it can be obtained that δgmax = g) g) [L2 Lg +L1 (L2 +Lg )]2 −(Lg U2 )2 −(L2 Ug )2 . 2L2 Lg U2 Ug Lg U2 +L2 Ug When Id 1 > L2 Lg +L1 (L2 +Lg ) , GFL cannot keep synchronization with the power system

arccos 3)

and will become unstable. Similarly, let Peg = Pmg , under the given operating conditions, the stable equivalent point δ gSEP and unstable equivalent points δ gUEP of SG can be obtained. Obviously, the existing instability mode can be determined by comparing δ gmax and δ gUEP . 4.2 Instability Mode of GFL Definition of Instability Mode. From the above analysis, it can be seen that when δ gmax < δ gUEP , there is no equilibrium point in the GFL and it will lose stability firstly. Meanwhile, it can be further divided into two scenarios: when there is a significant difference

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between δ gmax and δ gUEP , δ wUEP < π. When GFL loses stability, the maximum swing angle of SG does not reach δ gUEP . δ g of SG will swing back normally and keep stable after several cycles. However, due to the instability of GFL, PCC voltage drops and the angle decreases, resulting in δ g of SG is reduced below the normal value. In this paper, that case is defined as the instability mode 1 of GFL. When the difference between δ gmax and δ gUEP is relatively small, δ wUEP > π. δ g of SG reaches δ gmax and GFL loses stability. Afterwards, the maximum swing angle of SG reaches δ gUEP . Meanwhile, SG will also lose power angle instability and rotor speed increases. δ g increases continuously. However, due to the damping coefficient, after a period of out of step, SG will resynchronize with the system, and GFL is still in unstable mode. This case is defined as the instability mode 2 of GFL in this paper. Parameter Impact of PLL. The characteristics of PLL are mainly determined by two parameters, that is, the damping ratio (ξ ) and setting time (t s ). The relationship between the two parameters and the controller parameters of PLL is as follows: ⎧  ⎨ ξ = KP Ug 2 KI (10) ⎩ ts = 9.2 Ug KP The parameters impact of PLL on the instability mode of GFL is further observed.

5 Simulation Results 5.1 Instability Mode 1 of GFL The parameter configuration is shown below. Under normal operating conditions, U 2 = 1.05, L 2 = 0.5, Pmg = 0.7, M g = 20, Dg = 30. I d1 = 0.7, L 1 = 0. U g = 1, L g = 0.15. At 15 s, the terminal voltage drops from 1 to 0.6 and returns to 1 after 1 s. The system response with different damping ratio ξ is shown in Fig. 3 (t s = 0.1 s). As shown in Fig. 3, as ξ increases, the transient stability of the coupling system is improved. Furthermore, the impact of PLL parameters on system response is observed. Under normal operating conditions, U 2 = 1.05, L 2 = 0.5, Pmg = 0.7, M g = 20, Dg = 50. I d1 = 0.7, L 1 = 0. U g = 1, L g = 0.15. At 15 s, the terminal voltage drops from 1 to 0.6. The system response at different setting times t s is shown in Fig. 4 (ξ = 0.1). It can be seen from Fig. 4 that when other parameters remain unchanged, there exists a significant impact of the setting time on the transient stability of the coupling system. As K P decreases, the setting time corresponding to PLL increases. The transient stability margin of the system increases. However, according to Eq. (3), K P is proportional to the equivalent damping coefficient of GFL. As K P decreases, the equivalent damping of GFL decreases and the oscillation amplitude increases.

Transient Stability Analysis of Grid Following Converter Intergreted 100

500

1

50

w

-500

-1

=0.1 =0.3

-1000 -2

0

0

(c)

0

(b)

(a)

w

2

w

1000

2

16

18

-100 14.9

20

Time(s)

w

(e)

g

(f)

g

g

(d)

1 0.8

1

1.2

0.4 14

1.4

1 0.998

0.6 0.8

15.2

1.002

1.002

0.998

15.1

1.004

1.2

1

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1.4

1.004

0.6

0 -50

-2 14

4

45

16

18

0.996 14

20

16

Time(s)

g

18

20

Time(s)

Fig. 3. System response with different ξ: (a) phase portrait of GFL (b) δ w of GFL, (c) ωw of GFL, (d) phase portrait of SG, (e) δ g of SG, (f) ωg of SG. 1000

4

1000

2

500 w

w

0 -500

(c)

(b)

(a)

w

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t s=0.1 t s=0.3

-1000 -2

0

2

-2 14

4

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-500 16

18

20

14

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w

16

18

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18

20

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1.4

1.004

1.004

1.2

1

1.002 g

1

(f)

(e)

(d)

g

g

1.002

0.8

1

0.6 0.998 0.6

0.8

1

1.2

1.4

0.4 14

g

16

18

Time(s)

20

0.998 14

16

Time(s)

Fig. 4. System response with different t s : (a) phase portrait of GFL (b) δ w of GFL, (c) ωw of GFL, (d) phase portrait of SG, (e) δ g of SG, (f) ωg of SG.

5.2 Instability Mode 2 of GFL The parameter configuration is shown below. Under normal operating conditions, U 2 = 1.05, L 2 = 0.5, Pmg = 0.5, M g = 6, Dg = 20. I d1 = 1, K I = 1400. U g = 1, L g = 0.5. At 10s, the terminal voltage dropped from 1 to 0.5 and returned to 1 after 0.136 s. The system response at different K P is shown in Fig. 5. It can be seen from Fig. 5 that as K P decreases, the transient stability of the coupling system is improved.

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20

KP =30

30 20

2 w

10

w

KP =60

0 -10

1.5

(c)

(b)

(a)

w

2.5 30

1

10 0 -10

-20 0

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0.5

3

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(e) 5 g

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1.02 1

2 0

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1.04

6

(f)

g

g

1.02

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(d)

14

Time(s)

w

0.98

0 10

12

14

16

Time(s)

18

20

10

15

20

Time(s)

Fig. 5. System response with different K P : (a) phase portrait of GFL (b) δ w of GFL, (c) ωw of GFL, (d) phase portrait of SG, (e) δ g of SG, (f) ωg of SG.

6 Conclusion This paper investigates the large disturbance stability characteristic in a parallel system of GFL and SG. It can be found that the transient stability of coupling system is mainly determined by the one with the smaller stability margin between the two. PLL parameters will also affect the transient stability of coupling system integrated with GFL and SG. Acknowledgments. This work was funded by China Southern Power Grid Company Limited, the Science & Technology project: Coupling mechanism and control of new power system with large disturbance stability (0000002022030101XT00031).

References 1. Ke, D., Feng, S., Liu, F., et al.: Rapid optimization for emergent frequency control strategy with the power regulation of renewable energy during the loss of DC connection. Trans. China Electrotech. Soc. 37(5), 1204–1218 (2022) (in Chinese) 2. Wu, H., Wang, X.: Design-oriented transient stability analysis of PLL-synchronized voltagesource converters. IEEE Trans. Power Electron. 35(4), 3573–3589 (2020) 3. Hu, Q., Fu, L., Ma, F., et al.: Large signal synchronizing instability of PLL-based VSC connected to weak AC grid. IEEE Trans. Power Syst. 34(4), 3220–3229 (2019) 4. Yan, C., Yao, W., Wen, J.: Impact of active frequency support control of photovoltaic on PLL-based photovoltaic of wind-photovoltaic thermal coupling system. IEEE Trans. Power Syst. Early Access (2022) 5. Sun, H., Zhai, H., Wu, X.: Research and application of multi-energy coordinated control of generation, network, load and storage. Trans. China Electrotech. Soc. 36(15), 3264–3271 (2021) (in Chinese) 6. Yan, C., Yao, W., Cui, Y., et al.: Small disturbance stability analysis of wind-thermal coupling system considering virtual inertia and droop control. Electric Power Autom. Equip. 42(8), 19–28 (2022) (in Chinese)

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7. Jiang, S., Zhu, Y., Konstantinou, G.: Settling-angle-based stability analysis for multiple current-controlled converters. IEEE Trans. Power Electron. 37(11), 12992–12997 (2022) 8. Wang, Z., Ding, L., Gao, X., et al.: Improved active current control scheme of wind energy conversion systems with PLL synchronization during grid faults. IEEE Trans. Sustain. Energy 14(1), 717–729 (2023) 9. Hu, Q., Ji, F., Ma, F., et al.: Matching analysis of LVRT grid code and injection current dependent voltage response of WTC connected to high impedance AC grid. IEEE Trans. Energy Convers. 37(3), 2236–2239 (2022) 10. Yang, Z., Ma, R., Cheng, S., et al.: Problems and challenges of power-electronic-based power system stability: a case study of transient stability comparison. Acta Physica Sinica 69(08), 103–116 (2020) (in Chinese)

Insulation Performance of Polyimide Materials Under Cable Arc Xiahaoyue Yun1 , Zeli Ju1 , Yibo Zhang2 , Fancong Kong3 , Chang Ma3 , and Xiongying Duan3(B) 1 State Grid Shaanxi Electric Power Research Institute, Xi’an, Shaanxi, China

{yunxiahaoyue,juzeli}@dky.sn.sgcc.com.cn

2 State Grid Shaanxi Electric Power Company Limited, Shaanxi Xi’an, China

[email protected]

3 School of Electrical Engineering, Dalian University of Technology, Dalian, Liaoning, China

{kongfancong19970425,machang,xyduan}@dlut.edu.cn

Abstract. As cities grow, cables play an increasingly important role as part of the power transmission system. But as the number of cables increases, so do the safety hazards that come with them: the generation of cable arcs and even the start of fires. Cable fire blankets are necessary to protect against the initial stages of cable fires. In this paper, three different pairings are compared and analyzed by a combination of experiments and simulations. These include Kevlar-Teflon, Polyimide-Teflon, and Kevlar-Polyimide material pairings. The study illustrates the possibilities of polyimide materials for the application of cable fire blankets. The bearer of the simulation part is COMSOL software. By combining experiments and simulations with each other, the excellent fire protection properties as well as the arc resistance of polyimide are illustrated for the use of polyimide in cable protection blankets and also provide theoretical support for the application of polyimide in the field of cable protection. Keywords: Arc protection · Polyimide · COMSOL · Cable fire

1 Introduction With the development of society, electricity is more widely needed. The production development of society and people’s life are inseparable from electricity. As the main bearer of the power transmission system, the cable has an irreplaceable role. With the increasing application of cables, accidents are also occurring more commonly. According to reports, cable accidents caused by fire accounted for more than 1/3 of the total incidence of fire accidents in 2020 [1, 2]. Local insulation defects in cables are often caused by prolonged overload, insulation aging, external damage, etc. Insulation breakdown occurs gradually internally when the defect occurs, but it is not easy to observe [3]. Once a complete breakdown of the cable occurs, it can cause a fire. Cable fires are rapid, accompanied by a large amount of smoke generated, while the electrical shock will pose a threat to the surrounding equipment and rescue personnel. So it is necessary to pay attention to the protection of cable fires. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 48–55, 2024. https://doi.org/10.1007/978-981-97-1064-5_5

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Cable fire blanket as one of the means of cable fire prevention as well as initial protection, its protective effect is remarkable [4]. Currently for the main fire blanket structure analysis on the market, the main role of the Teflon material, Kevlar fabric. At the same time the current development of new polymer materials, a number of fireretardant polymer materials appear in the field of vision, including polyimide materials, as a representative of fire-retardant materials, because of its intrinsic flame retardancy and good chemical resistance, aging resistance and other characteristics [5, 6]. Widely used in aerospace, construction and other fields [7, 8]. Meanwhile, at present, polyimide materials are also applied in electronic and electrical research, such as the research of arcproof clothing for non-stop operation [9], but for polyimide in cable fire protection has not been studied yet. All three materials have good electrical insulation, stable chemical properties, and flame-retardant properties. This paper intends to use a combination of simulation and experiment to analyze the degree of difference between Teflon, Kevlar and flame-retardant polyimide materials for cable fire protection, to provide a theoretical basis for the subsequent breakthrough and innovation of cable protection materials, and to provide a reference for the research development in the field of electric power protection.

2 Simulation of Fabric Under the Arc 2.1 Simulation Geometry The direct cause of cable fires is the aging of the insulation layer, resulting in discontinuous discharge of the electric arc inside the cable, which constantly continues to erode the insulation layer, and once the insulation layer is completely destroyed, the cable arc will continue to discharge, resulting in high temperatures. To address this phenomenon, this paper uses COMSOL Multiphysics finite element simulation software to construct a two-dimensional axisymmetric model containing the part of the cable that generates the arc and the part of the fabric material wrapped around the outside, as shown in Fig. 1. Using the central axis of the cable as the axis of symmetry, the section is selected for modeling, where the simulated air region is a rectangle of 50 mm in length and 40 mm in width. The single-core cable section is stripped of the outer metal shield and its outer surface layer, leaving the insulation layer. The upper end of the cable is connected to a 50 Hz high voltage power supply on the upper side and the lower end of the cable is grounded. A double layer of fabric is wrapped around the copper core of the cable. Since the polyimide fabric and the Kevlar fabric contain holes, the model in the figure shows not a continuous fabric structure. Also, since it is impossible for the fabric to fit completely on the surface of the copper core when wrapped, the simulation is represented by a 1 mm air gap. The simulation duration is 40 ms, and the initial temperature is 293.15 K. The simulation parameters of polyimide, Kevlar and Teflon materials are shown in Table 1. According to the research, it is found that most of the commercially available cable fire blankets are made of Kevlar with Teflon, assisted by an outer layer of vitrifiable silicone rubber, and other protective effect layers. Therefore, three cases of KevlarTeflon, Kevlar-Polyimide and Polyimide-Teflon were selected for comparative study to analyze the thermal insulation of the three matching methods.

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Fig. 1. Schematic diagram of the creation of the simulation model

Table 1. Simulation material related parameters Materials

Thickness /(mm)

Density /(kg/m2 )

Relative dielectric constant

Relative permeability

Electrical conductivity /(S/m)

Polyimide

0.35

1440

3.5

1

1*10–15

Kevlar

0.27

1391

3.5

1

1*10–13

Teflon

0.22

2140

2.1

1

1*10–17

2.2 Analysis of Results Set the cable load current to 250 A, and the frequency is 50 Hz. Change the different materials with the simulation analysis, and select the temperature measurement points as shown in Fig. 2. The four measurement points are (15 mm, 25 mm), (20 mm, 25 mm), (25 mm, 25 mm), (30 mm, 25 mm), respectively, to measure the temperature change of the cable arc through the fabric. The simulation time constant is 40 ms. As shown in Fig. 3, the temperature distribution at 40 ms for three different pairing cases is shown in Fig. 3(a) for Kevlar-Teflon, Fig. 3(b) for Kevlar-Polyimide, and Fig. 3(c) for Polyimide-Teflon. The picture shows that the arc-burning phenomenon occurs in the middle of the cable at both ends, and the temperature is transferred from the three combined materials from inside to outside, and the temperature keeps spreading into the surrounding air.

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Fig. 2. Distribution map of temperature measurement points

Fig. 3. The arc temperature field diagram of different combinations at 40 ms

As shown in Fig. 4, the temperature variation curves for three different pairing cases are plotted, Fig. 4(a) for Kevlar-Teflon, Fig. 4(b) for Kevlar-Polyimide, and Fig. 4(c) for Polyimide-Teflon. As Fig. 5 shows the comparison of the temperature profiles of the three pairings at the temperature measurement point (15 mm, 25 mm). It can be observed that the polyimide- Teflon combination has the best insulation effect and can better hinder the diffusion of high temperature gases from the cable arc. The temperature

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diffusion from the high temperature gas to the low temperature gas leads to a relative decrease at the near point and a gradual increase at the far point. For the Kevlar-Polyimide combination shown in the figure, it can be observed that its thermal insulation effect is poor, and the rapid penetration of the high temperature gas causes the temperature to exceed 1000 K at the beginning of 3 ms, while the commercially available Kevlar-Teflon combination shown in the figure has a slightly worse thermal insulation effect than the Polyimide-Teflon combination. According to the related work we have done before [10, 11], it is shown that polyimide has good arc resistance, and the figure illustrates the excellent thermal insulation properties of polyimide. Therefore, for the components of cable fire blanket, it is feasible to replace Kevlar with polyimide material.

Fig. 4. The temperature distribution curve of the three pairings

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Fig. 5. Comparison chart of temperature curves of the three pairings

3 Material Heat Transfer Experiment In this paper, an electric arc furnace was used as a constant radiation heat source and preheated for 20 min. The fabric materials were cut to the same size and placed at a certain distance from the heat source according to three combinations of Kevlar-Teflon, Kevlar-polyimide and polyimide-Teflon to study the heat insulation effect of different combinations. Windproof panels were erected around the experimental equipment to prevent the influence of outside air flow on the experimental results. Each group of paired experiments lasted for 36 s, and the temperature of the back side of the fabric was measured using a temperature sensor to obtain the temperature distribution images shown in Fig. 6. As shown in the figure, it can be found that the heat transfer change curve of polyimide-Teflon is basically the same as that of Kevlar-Teflon, which finally stays at about 480 K, while the heat transfer change curve of Kevlar-polyimide shows that its temperature changes faster and rises more rapidly, while the final temperature stays above 500 K, indicating that its heat insulation effect is worse than that of the other two groups. This can show that the heat insulation effect of polyimide-Teflon and KevlarTeflon is similar, which is the same as the conclusion of the experiment, and can show that the polyimide material can replace the Kevlar material in the application of cable fire blanket.

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Fig. 6. Heat transfer comparison curves for the three pairings

4 Conclusions This paper simulates and compares and analyzes the heat insulation effect of three different material combinations on cable arc, the combination of polyimide material and Teflon material has the best heat insulation effect, followed by the combination of Kevlar material and Teflon material, the worst heat insulation performance is the combination of Kevlar material and polyimide material, which makes the external temperature after placing more than 30% higher than the other components, while the difference between the other two groups is less than 10%. The simulation analysis shows that the polyimide material can replace the Kevlar fiber as a component of the cable fire blanket from the heat insulation point of view. The correctness of the simulation is also confirmed by experimental means. it is shown through experiments that the breakdown resistance characteristics of the combination of polyimide material and Teflon are similar to those of the combination of Kevlar material and Teflon material, and it is shown from the perspective of arc breakdown resistance characteristics that polyimide material can replace Kevlar fiber as a component of cable fire blanket. Acknowledgments. This work was supported by the State Grid Shaanxi Electric Power Company Limited and the State Grid Shaanxi Electric Power Research Institute (Project No. 5226KY230010).

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References 1. Ge, F., Qiu, T., Zhang, M., et al.: Experimental research on the thermal characteristic of low-voltage alternating current (AC) arc faults. Fire Saf. J.Saf. J. 136, 103732–103739 (2023) 2. Li, C., Chen, J., Zhang, W., et al.: Influence of arc size on the ignition and flame propagation of cable fire. Energies 14(18), 5675–5687 (2021) 3. Li, L., Li, Y., Zhou, X., et al.: Modeling of internal multiform intermittent arc fault for 10kV XLPE Cable. Trans. China Electrotech. Soc. 37(23), 6104–6115 (2022). (in Chinese) 4. Huang, H., Wu, Z., He, W., et al.: Research on segmental barrier technology of non-flameretardant cables based on fire blanket. Electr. Eng.. Eng. 24, 155–158 (2021). (in Chinese) 5. Zhang, M., Niu, H., Wu, D.: Polyimide fibers with high strength and high modulus: preparation, structures, properties, and applications. Macromol. Rapid Commun.. Rapid Commun. 39(20), 1800141–1800154 (2018) 6. Zhang, Q.H., Dong, J., Wu, D.Z.: Advanced polyimide fibers. Advanced Polyimide Materials, pp. 67–92. Elsevier (2018) 7. Morgan, A.B., Putthanarat, S.: Use of inorganic materials to enhance thermal stability and flammability behavior of a polyimide. Polym. Degrad. Stab.. Degrad. Stab. 96(1), 23–32 (2011) 8. Cai, G., Xu, Z., Li, W., et al.: Experimental investigation on the thermal protective performance of nonwoven fabrics made of high-performance fibers. J. Therm. Anal. Calorim.Calorim. 121, 627–632 (2015) 9. Hou, Z., Ma, C., Ju, Z., et al.: Analysis of arc-proof performance of polyimide fabrics. Cotton Textile Technol. 50(03), 44–47 (2022). (in Chinese) 10. Ma, C., Duan, X., Yue, P., et al.: Comparative analysis of polyimide and aramid fabrics as arc protective materials. Textile Res. J. (to be published). https://doi.org/10.1177/004051752 31158819 11. Tang, M., Yue, P., Duan, X., et al.: Research on the influence of fault Arc on polyimide insulation materials. J. Phys. Conf. Ser. 2419(1), 012081–012087 (2023)

Research on Transverse Compression Electromechanical Characteristics of CORC Cable Under Curved Load Block Yangyang Shi(B) , Yifan Wang, Tao Ma, and Shaotao Dai School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China [email protected]

Abstract. CORC cables have the advantages of high current density, low inductance, and ease of manufacturing, making them one of the best candidate cables for fusion projects. In fusion projects, there is a huge background magnetic field, and the current carrying capacity of the CORC cable can reach the level of ten thousand amperes. Therefore, CORC cables are often affected by significant transverse compressive electromagnetic forces. Excessive transverse compression load can cause irreversible degradation of the current carrying capacity of the CORC cable, thereby affecting its normal operation in fusion projects. Therefore, it is crucial to improve the ultimate transverse compressive load that CORC cables can withstand. This article investigates the influence of different winding methods of superconducting tapes under arc-shaped load blocks, as well as the copper plating thickness of superconducting tapes, on the transverse compression load performance of CORC cables. The experimental results show that reducing the number of layers, increasing the number of superconducting tapes per layer, and reducing the copper plating thickness of superconducting tapes can effectively increase the ultimate transverse compression value of CORC cables when the number of superconducting tapes is constant; When the number of superconducting tapes per layer is fixed, increasing the number of superconducting tape layers can also increase the ultimate transverse compressive load value of CORC cables. When the number of layers is fixed, increasing the number of winding layers of the superconducting tape material in each layer can also increase the ultimate transverse compressive load value of the CORC cable. The research results of this article provide a theoretical basis for the parameter design of CORC cables in the future. Keywords: electromechanical performance · transverse compression load · winding method

1 Introduction In recent years, the development of controllable nuclear fusion has attracted much attention [1]. With the continuous development of the second generation high temperature superconducting tape technology, it has received extensive attention in its © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 56–63, 2024. https://doi.org/10.1007/978-981-97-1064-5_6

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application. The current-carrying capacity of the second generation of high temperature superconducting tapes under high background magnetic field is much stronger than that of the first generation of low temperature superconducting conductors. Therefore, the second generation high temperature superconducting tape is very suitable for making high current-carrying composite conductors used in fusion projects. At present, many high-current-carrying composite superconducting cables composed of secondgeneration high-temperature superconducting tapes have been born, such as Roebel cable [2], TSTC cable [3], quasi-isotropic cable [4] and so on. Among them, CORC cable has the advantages of low inductance, high current density and easy to manufacture, so it is regarded as one of the best spare cables for the next stage of fusion project. At present, some scholars have studied the performance of CORC cable. Through the study of the AC loss of CORC cable, it is found that the loss of CORC cable can be reduced by notching the skeleton [5, 6]. The study of the effect of the metal skeleton size of CORC cable on the critical current of superconducting tape provides a basis for the selection of the central skeleton size of CORC cable [7]. Another important problem faced by the application of CORC cable in fusion project is the problem of electromechanical characteristics: due to the huge background magnetic field and the large current carrying capacity of CORC cable, the cable will be affected by huge transverse compression electromagnetic force. If the transverse compression electromagnetic force of CORC cable exceeds its limit lateral compression load, its current carrying capacity will decline irreversibly. Therefore, the research on how to improve the ultimate lateral compression load of CORC cable becomes very important. Professor Vandeer Laan et al. obtained the influence law of some parameters on the mechanical and electrical characteristics of CORC cable lateral compression through experimental research [8]. JiangtaoYan of Lanzhou University and others studied the influence of different parameters on the mechanical-electromagnetic properties of CORC cable lateral compression [9]. However, there are many parameters that affect the lateral compression performance of CORC cable, which need to be studied further. In this paper, four CORC cables with different parameters are fabricated. The winding mode of CORC cable under the main pin concave pressing block and the influence of copper plating thickness of superconducting tape on its transverse compression properties are studied. The results show that under the same number of superconducting tapes, reducing the number of layers, increasing the number of winding elements of each layer and reducing the thickness of copper plating of superconducting tapes can effectively improve the transverse compression performance of CORC cables; when the number of superconducting tapes per layer is constant, increasing the number of superconducting tapes can also improve the lateral compression load performance of CORC cables. The research results of this paper provide a theoretical basis for the design of CORC cable in the future.

2 Sample Preparation In this paper, four CORC cable samples with different parameters are made, and the specific parameters of the cable are shown in Table 1. The central skeletons of all CORC cables are solid copper rods with an outer diameter of 5.26 mm, and the superconducting

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layers of the superconducting tapes are wound on one side of the central skeleton. In order to better control the variables and make the comparison more convincing, the four sample cables are all wound with superconducting tape produced by Suzhou New Materials Research Institute. Among them, sample 1 and sample 2 can compare the effect of copper coating thickness on the lateral compression performance of CORC cable; sample 2 and sample 3 can compare the effect of superconducting tape layers on the transverse compression performance of CORC cable; sample 3 and sample 4 can compare the effect of different superconducting tape winding methods on the transverse compression performance of CORC cable under the same number of superconducting tapes. Table 1. Parameters of CORC cable samples Sample number Outer diameter of Number of layers Number of strips Thickness of skeleton(mm) per floor unilateral copper plating layer(µm) 1#

5.26

2

2

5

2#

5.26

2

2

15

3#

5.26

3

2

15

4#

5.26

2

3

15

3 Experiment The transverse compression tests of four CORC cable samples were carried out to simulate the situation when they were subjected to the transverse compression electromagnetic force in the fusion project, and the critical current was measured at the same time. The specific exterior view of the CORC cable is shown in Fig. 1. Both sides of the CORC cable are welded into a round copper tube as the current lead of the cable. It is worth noting that the superconducting tape should be in full contact with the solder in the copper tube to ensure that the current can be injected into the superconducting tape from the copper tube. The voltage leads of the CORC cable are shown in red and black lines in Fig. 1. The voltage leads are directly connected to the superconducting tape instead of the ends on both sides, thus avoiding the error caused by the introduction of connector resistance.

Fig. 1. CORC cable sample appearance

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The structure of the groove pressing block and the specific experimental principle of the experiment are shown in Fig. 2. In order to ensure the mechanical strength of the pressing block, the pressing block material is selected as stainless steel. The part of the red dotted frame in the picture is the groove structure of the pressing block, the groove is an arc structure, its radius is slightly larger than the outer diameter of the CORC cable, and the groove structure can embed part of the CORC cable into the pressing block. The principle of applying the lateral compression load is as follows: the lower arc compression block remains fixed, and the upper arc compression block is driven downward by the servo motor to apply the lateral compression load to the CORC cable, so as to simulate the transverse compression electromagnetic force in the fusion project. The upper pressing block is connected with a pressure sensor, and the pressure equipment control system can adjust the displacement of the upper pressing block according to the lateral compression load we need to apply.

Fig. 2. Schematic diagram of CORC cable transverse compression experiment

The critical current experiment of CORC cable adopts the classical four-lead method, as shown in Fig. 3. Use the DC power supply KEYSIGHT 6680A to direct the CORC cable. The shunt in series plays a role in accurately measuring the current of the measuring circuit. The control system includes two functions: signal acquisition and DC power supply control. The voltage signals of CORC cable are collected by Keithley 2182 m, and the voltage signals at both ends of the shunt are collected by Keithley 2000 m. The collected signals are input to the control system for processing, so the computer can detect the voltage and current signals in real time. When the CORC cable is in a superconducting state, the computer controls the current source steadily to raise the current, and when the CORC cable is quenched, the computer controls the DC power supply to drop the current rapidly.In this paper, 1 µ V/cm is used as the quenching criterion of superconducting cable [10]. The specific experimental steps are as follows: first, the critical current of CORC cable without transverse compression load is measured, and the critical current value is used as the basis for later calculation of normalized critical current. Then apply a small lateral compression load to the CORC cable, wait for the lateral compression load to reach stability, measure the critical current value of the cable, after the critical current value test, increase the lateral compression load on the CORC cable according to a certain gradient, wait for the load to stabilize, and test the critical current of the CORC cable

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Fig. 3. CORC cable critical current measurement system

again. By repeating the above experimental process, the variation trend of normalized critical current of CORC cable with transverse compression load can be obtained. Until the critical current of the CORC cable decreases obviously compared with the initial critical current, the actual test is completed.

4 Analysis of Experimental Results After the transverse compression experiment of the sample, the variation curve of the normalized critical current with the increase of load is compared, and the excellent lateral compression performance of CORC cables with different structures can be compared. All the samples in this paper take the transverse compression load at 95% critical current retention value as the ultimate lateral compression load limit of CORC cable. The first is the comparison of the transverse compression properties of sample 1 and sample 2 under the groove indenter, as shown in Fig. 4.

Fig. 4. Comparison of thickness of copper-plated layers of HTS tapes

As shown in Fig. 4, the black curve is the regression curve of sample 1 normalized critical current with the increase of transverse compression load, and the red curve is the regression curve of sample 2 normalized critical current with the increase of transverse compression load. The ordinate corresponding to the bright green dotted line is the normalized critical current value of 0.95. The Abscissa of the intersection point between the bright green dotted line and the CORC cable regression curve is the ultimate lateral compression load value of the cable. The ultimate lateral compression

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load values of sample 1 and sample 2 under groove indentation are 485 kN/m and 137.5 kN/m, respectively. The ultimate lateral compression load of sample 1 is 3.5 times that of sample 2. It can be found that the transverse compression performance of CORC cable wound with 5 µm copper-coated superconducting tape is much better than that of CORC cable wound with 15 µm copper-coated superconducting tape. This shows that in order to improve the transverse compression performance of CORC cable under the groove pressing block, the superconducting tape with thinner copper layer should be chosen to wind CORC cable.

Fig. 5. Comparison of different number of HTS tape layers

Figure 5 shows the comparison of lateral compression load performance of CORC cables with different layers of superconducting tapes under grooved pressing blocks. The black curve is the regression curve of sample 2 normalized critical current with the increase of transverse compression load, and the red curve is the regression curve of sample 3 normalized critical current with the increase of transverse compression load. The ultimate lateral compression loads of sample 2 and sample 3 under grooved indentation are 137.5 kN/m and 170 kN/m, respectively. The ultimate lateral compression load of sample 3 is 23.6% higher than that of sample 2. Therefore, we come to the conclusion that increasing the number of layers of superconducting tape can increase the ultimate transverse compression load of CORC cable.

Fig. 6. Comparison of the number of HTS tape in each layer

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Figure 6 shows the comparison of the lateral compression load performance of CORC cables with different number of superconducting tapes in each layer under the grooved pressing block. The black curve is the regression curve of sample 2 normalized critical current with the increase of transverse compression load, and the red curve is the regression curve of sample 4 normalized critical current with the increase of transverse compression load. The ultimate lateral compression loading values of sample 2 and sample 4 are 137.5 kN/m and 195 kN/m, respectively. The ultimate lateral compression load of sample 4 is 41.8% higher than that of sample 2. Therefore, in the case of the same number of layers, increasing the number of superconducting tapes in each layer can effectively increase the ultimate lateral compression load of CORC cable.

Fig. 7. Comparison of different winding methods

Figure 7 shows the comparison of the lateral compression performance of CORC cables with different winding methods under the same number of superconducting tapes under the grooved pressing block. The red curve is the regression curve of sample 3 normalized critical current with the increase of transverse compression load, and the black curve is the regression curve of sample 4 normalized critical current with the increase of transverse compression load. The ultimate lateral compression load of Sample 3 and sample 4 is 170 kN/m and 195 kN/m, respectively. The ultimate lateral compression load of sample 4 is 14.7% higher than that of sample 3. Therefore, we conclude that under the same number of superconducting tapes, reducing the number of superconducting tapes and increasing the number of superconducting tapes wound in each layer of superconducting tapes can effectively increase the ultimate transverse compression load of CORC cables under grooved pressing blocks. In the regression curve of the normalized critical current of four CORC cables with different structures, it is also found that the normalized critical current degradation rate of CORC cables increases with the increase of transverse compression load. It shows that at the initial stage of the transverse compression load on the CORC cable, the damage of the superconducting layer in the superconducting tape is small, so the decline rate is relatively slow, but when the transverse compression load increases to a certain extent, the superconducting layer in the superconducting tape on the cable will break due to excessive compression load, and once the fracture occurs, the degradation rate will increase rapidly.

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5 Conclusion In this paper, four kinds of CORC cables with different structures are made, and the transverse compression load experiments of CORC cables are carried out to study the effects of different winding methods of superconducting tapes on their transverse compression properties. The results show that when other cable parameters are the same, reducing the copper plating thickness of superconducting tape (from 15 µm to 5 µm) can increase the ultimate lateral compression load of CORC cable by 3.5 times, increasing the number of superconducting tape layers can increase the ultimate lateral compression load of CORC cable by 23.6%, and increasing the number of winding elements in each layer can increase the ultimate lateral compression load of CORC cable by 41.8%. Under the same number of superconducting tapes, the ultimate lateral compression load of CORC cable can be increased by 14.7% by reducing the number of superconducting tapes and increasing the number of superconducting tapes per layer. There are many kinds of lateral compression load blocks, and the lateral compression load performance of CORC cables under other types of compression blocks will be studied in the future work.

References 1. Zhang, Z., Zheng, J., Song, Y., Liu, X., Lu, K.: Stability Analysis of high performance Nb3Sn CICC conductor of longitudinal field superconducting magnet of china fusion engineering experimental reactor. Trans. China Electrotech. Soc. 35(24), 5031–5040 (2020). (in Chinese) 2. Hao, L., Shen, B., Ma, J., et al.: Conceptual design and optimisation of HTS Roebel tapes. IEEE Trans. Appl. Supercond. 32(4), 1–5 (2022) 3. Li, X., Song, D., Wu, Y., et al.: Current-carrying capability and magnetic behavior of the HTS twisted stacked-tape conductor cable for the compact fusion reactor. IEEE Trans. Appl. Supercond. 32(4), 1–5 (2021) 4. Wang, R., Pi, W.: Study on transmission loss of quasi-isotropic superconducting strands in different temperature regions. Cryogenics Superconductivity 51(04), 8–12, 32 (2023). (in Chinese) 5. Hao, J.: Study on AC loss of CORC type superconducting cable. Beijing Jiaotong University, Beijing (2021). (in Chinese) 6. Liu, L.: Analysis of AC loss characteristics of CORC superconducting cables for fusion. Beijing Jiaotong University, Beijing (2022). (in Chinese) 7. Xiao, G., Liu, F., Jin, H., et al.: The effect of metal core size on the critical energy of REBCO strip of CORC cable. Cryogenics Superconductivity 48(03), 35–36, 46 (2020). (in Chinese) 8. Van Der Laan, D.C., McRae, D.M., Weiss, J.D.: Effect of transverse compressive monotonic and cyclic loading on the performance of superconducting CORC cables and wires. Superconductor Sci. Technol. 32(1), 015002 (2018) 9. Yan, J., et al.: Investigating the effect of transverse compressive loads on the electromagnetic performance of superconducting CORC cables. Superconductor Sci. Technol. 35(11), 11500 (2022) 10. Zhang, Y., Cai, C., Zhao, Y., et al.: Study on the standardization of transmission critical current of the second generation high temperature superconducting long tape. Standard Sci. (S1), 96102 (2022). (in Chinese)

Oil Fire Detection Technology Based on Fractal Geometry Fuze Chen(B) , Yonggang Zuo, Yuting Hu, Yuliang Zhang, Meichun Wu, Jiansheng Huang, Zekun Li, and Guangchuan Song Army Logistics Academy, Chongqing 401311, China [email protected]

Abstract. Image fire detection technology is a new fire detection technology, which often needs to segment fire images according to their brightness, color, texture and other characteristics. The more features that are used, the more detailed the segmentation is often performed. This paper studies the application of fractal features in image segmentation, proposes an improved image box dimension measurement method without the fitting algorithm for many times, and finally simulates the oil fire, which provides some reference for the detection of oil fire. Keywords: Image type · fractal · oil fire · detection

1 Development Status of Fire Detection Technology Fire detection technology is a comprehensive technology based on physical signals such as light, heat, sound, radiation, vibration and other physical signals generated during the occurrence of fire, and through the use of various sensors to complete signal processing and transmission [1], and finally realize the early detection of fire. Distinguished by the stage of development, it can be divided into traditional fire detection technology and modern fire detection technology. Traditional fire detection technology is mainly supported by various types of physical information traps, including light detectors, temperature detectors, smoke detectors, gas detectors and comprehensive detectors and other detection sirens [2]. However, the data and information that these traditional detection sirens can collect are always not comprehensive enough, and due to the interference of many factors such as space size, dust concentration, airflow velocity, corrosive environment, etc., and misstatements, late reports, and under-negatives often occur, and the sirens themselves are also prone to failure [3]. For example, temperature detectors and smoke detectors, only when the scale of the fire reaches a certain level can capture enough alarm physical information, will cause the alarm response time is too long, resulting in the spread of fire, and ultimately delay the best time to extinguish the fire. Especially for oil storage areas in large spaces such as oil depots, the contradiction between the low efficiency of physical signal capture and the rapid spread of oil fires due to the fast dissipation speed of dust and smoke is extremely sharp. Therefore, traditional fire alarms are usually used in shopping malls, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 64–72, 2024. https://doi.org/10.1007/978-981-97-1064-5_7

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stations, schools and other public places with a large flow of people, easy to find fires, and easy for rescue personnel to reach, playing a certain auxiliary alarm role. Modern fire detection technology generally refers to image-based fire detection technology [4]. With the deepening of research, it has been found that the image of the signal source containing shape, intensity, location and other information has certain advantages for fire monitoring and detection, and the automatic fire alarm system based on image processing has also emerged. This system is a kind of automatic fire alarm system with computer as the core, integrated optoelectronic technology and digital image processing technology [5]. Through the camera to monitor the scene, the captured video is transmitted in the form of pictures, and finally entered into the computer for analysis, so as to achieve the purpose of early detection of fire. Compared with traditional fire detection technology, image-based fire detection technology mainly relies on high-speed computer processing image signals, and the processing speed is very fast, which can basically realize the detection and positioning of large and complex space fires. Walter et al. [6]. of the University of Central Florida proposed a flame recognition algorithm based on flame color features; Hou Jie [7] proposed a fire detection method for high-rise buildings based on video images; Benxi Wang [8] proposed image fire detection technology based on single- &- dual-band theory. However, these new detection methods do not work well in practice. The main reason is that the image segmentation is not sufficient. Image segmentation is simply the whole process of tracking and annotating all pixels appearing in the picture, so that the same pixels are marked to produce common visual features, which is also a basic computer vision technology. It can be said that the result of image segmentation directly affects the understanding of the image, because image segmentation is the key to the processing to analysis of the image, and without the correct segmentation, it is impossible to have the correct recognition.

2 Principles of Digital Image Processing Technology Digital image processing technology is a kind of computer as the core, through computer technology to segment, restore, remove noise, enhance, extract features and other operations of the image, so as to obtain a certain expected effect. Its essence is to analyze and process the pixel data in the collected image based on a certain recognition requirement, and finally modify or reassign the processed pixels one by one. Because the function of digital computers is to process data, the continuous signal to be processed is converted into corresponding discrete data before processing, which is called the digitization process. The digitization of images includes two processes: sampling and quantification. Sampling refers to the operation of converting a continuous image in two-dimensional space into a discrete set of sampling points, that is, the discretization of spatial coordinates, and the essence of sampling is how many points are used to describe an image. Quantization is the conversion process of the gray value (or color component) of each pixel obtained by sampling from continuous quantity to discrete quantity, that is, the discretization of grayscale, and the more levels of quantification, the richer the level of the obtained image. This paper mainly processes grayscale images, grayscale level quantization is 0–255, a total of 256 grayscale sets, 0 means all black, 255 means all white, and the grayscale of each pixel is represented by one byte [9].

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The methods of digital image processing are mainly divided into two types [10]: spatial domain processing and frequency domain processing: the former is processed in the spatial domain of the image, that is, the grayscale of the pixel is directly optimized in the image space, so as to achieve the purpose of improving image quality; The latter is to convert the image from the spatial domain to the frequency domain, perform various processing in the frequency domain, and then change back to the spatial domain of the image to form the processed image. In general, the calculation results of spatial domain technology are relatively simple and efficient, and the operation steps are few, based on the above two points, this paper chooses to perform image processing in the spatial domain [11].

3 Improved Box-Dimensional Algorithms Suppose z = A (x, y) is a grayscale digital image with a resolution of M × M. x and y are the number of rows and columns of any pixel, and z is the pixel grayscale value. Suppose a box of size L × L × L, L is the length of the box on the x and y axes, L is the length of the box on the Z axis, and there is L = GL/M, where G is the total number of gray levels of the digital image, and the equation L /G = L/M holds. Let r = L/M be the box scale. Then suppose that many boxes of the scale r cannot overlap to contain A, and let N r represent the minimum number of boxes required to eventually contain A. Assuming that A is an ideal fractal surface, then the box dimension D we define as: D = lim

log(Nr )

r→0 log(1/r)

For digital images that are discrete grayscale surfaces, different r values are often set, and 1 < L ≤ M/2 is satisfied, and its N r value is calculated, and many data pairs are obtained. These data pairs are then processed using the least squares method, and finally a straight line is fitted, and the slope of this fitted line is the box dimension of the digital image of the discrete grayscale surface. Let the black point in Fig. 1 be a list of points on the discrete grayscale surface A (x, y), where the x-coordinate of any black point is the row number of the pixel, where x = 1,2, …, M; The ordinate of this black point z = int (zM/G), z is the gray value corresponding to this black point, where z = 1,2,…, G. So there exists z = 1,2,…, M. Each grid in Fig. 1 has a side length of 1, which is the smallest size box we need. Next, you need to compare the height of the adjacent black points z = (x, y) with  z = (x + 1, y). Once z = (x, y) = z = (x + 1, y), that is, assuming z = (x, y) < z = (x + 1, y), then insert int(z (x + 1, y)--´z (x + 1, y)-z (x, y)/2) above the black dot z = (x, y) and below z = (x + 1, y) and below z, as shown in Fig. 1. Points around z = (x, y) are treated in this way. By processing, the distribution of discrete points is closer to a continuous situation. Then the total number of all black and white points at this time is the number of boxes of the smallest size we have found. Mark it as Nrmin , and rmin = 1/M . So, get the box dimension of this image: D=

log(Nrmin ) log(M)

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Figure 2 shows a schematic diagram of the original grayscale surface and its upper and lower envelopes after we artificially insert supplementary points. The blue curve in Fig. 2(a) represents what we call the upper envelope, the red curve represents what we call the lower envelope, and the black curve represents what we call the original grayscale surface.

Fig. 1. Schematic diagram of grayscale surface Fig. 2. The envelope of the grayscale surface insertion supplemental points. after inserting the supplementary point.

4 Experiments and Analysis 4.1 Fractal Brownian Motion Surface Test Fractal Brown Motion (FBM) is very suitable as a test object for box-dimensional algorithms because of its statistical self-similarity on its surface. Suppose A (x, y) is a two-dimensional stochastic process with the following properties: 1) Any random increment A = A(x 1 ,y1 ) − A(x 2 ,y2 ) are Gaussian random variables with a meanof 0; 2H  (x1 − x2 )2 + (y1 − y2 )2 . 2) var(A) ∝ A random surface A (x, y) that satisfies the above conditions can be considered to be an FBM surface with a fractal dimension of D = 3-H. FBM surfaces can be approximated using the random midpoint offset method. For example, an FBM image of 129 × 129 is generated, and the side length of the image is written as M, as shown in Fig. 3.

(33,1)

(1,129)

(1, 65)

(1,1)

(33, 65) (33,33)

(33,97) (65, 65)

(65,1)

M

2M /2

(129,1) M /2

(129,129)

Fig. 3. Schematic diagram of the random midpoint offset method

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1) The first step is to determine the values of the four vertices of the image, as shown by the black dots in Fig. 3. You can take A (1,1), A (1,129), A (129,1) as random numbers with a mean of 0 and a variance of σ02 = 1. Random numbers can be generated by the corresponding functions in MATLAB; 2) First iteration: generate point A (65,65): A(1, 1) + A(1, 129) + A(129, 1) + A(129, 129) + R1 4 √ Since the distance from A (65,65) to the four vertices is 2M /2, from the above equation and σ02 = 1, we can get R1 as a random number with a mean of 0 and a  √ 2H  H = 21 . variance of σ12 = σ02 22 3) Iterate again: generate the 4 black square points in Fig. 3, using A (1,65) as an example: A(65, 65) =

A(1, 1) + A(1, 129) + A(65, 65) + R2 3 Since A (1,65) is at a distance of M/2 from its 3 nearest known points, R2 is σ02 = 1  2H  1 H a random number with a mean of 0 and a variance of σ12 = σ02 21 = 4 . 4) Run this way until all points are assigned. In Fig. 3, it can be seen that the white square is the third iteration generation point, while the triangle is the fourth iteration generation point. It should be noted that A (33,1) needs to be generated by three adjacent points A (1,1), A (33,33), and A (65,1), while A (33,65) needs to be generated by four neighboring points A (1,65), A (33,33), A (65,65), A (33,97). Take D = (2,2.1,2.2,…,3) 11 values, and each value generates 20 FBM images (Fig. 4). A(1, 65) =

Fig. 4. Example of an FBM surface generated using the random midpoint offset method.

Generate 20 random FBM images for each value of D, corresponding to an estimate of 20 D’s. Figure 5 shows the maximum, mean, minimum, and variance of the estimates obtained using different methods. It can be seen that the trends of the estimates obtained by various methods are similar, but by comparing the distribution centers of the estimates, it can be found that the distribution centers of the estimates are closer to the median value of 2.5, which is the method proposed in this paper, and the smallest variance is also the same.

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Fig. 5. Comparison of fractal dimension estimates of FBM images obtained by different methods.

4.2 Image Test with Drastic Changes in Brightness Figure 6 shows a set of images with a drastic change in brightness.

Fig. 6. A set of images characterized by drastic changes in brightness.

It can be inferred that the later the image is relatively smoother, the closer its box dimension should be to 2; The further forward the image becomes coarser, its box dimension should be close to 3 (Fig. 7).

Fig. 7. Estimates of this set of image box dimensions for different methods are shown.

After comparing the final data, it can be seen that the data processed by the proposed method have better linearity and discrimination ability.

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4.3 Spike Image Test In Fig. 8, we use images of spike pulses of different densities for comparison:

Fig. 8. Image of spikes of different densities

Fig. 9. Estimates of this set of image box dimensions by different methods

It can be seen that except for the methods in this paper, the estimates obtained are reasonable, and other methods will obtain unreasonable estimates to varying degrees (Fig. 9). 4.4 Natural Texture Image Testing Finally, a set of 256 × 256 natural texture images selected from the Brodatz database was tested, as shown in Fig. 10.

Fig. 10. Brodatz texture image

You can see that for natural texture images, the relative distribution trends of the estimates for the five methods are similar (Fig. 11).

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Fig. 11. Fractal dimension estimation of a Brodatz texture image

4.5 Processing of Oil Flame Images Figure 12 shows the simulated oil flame image and its image processed by this method, and you can see that the sky, wall, and flame are brighter in the figure. Figure A is divided into several 32 × 32 subblocks, and the fractal dimension value of each subblock is obtained by the algorithm in this paper, and the result is shown in Figure B, in which the calculated fractal dimension value has been mapped to the range 0–255 for easy display. You can see that the fractal dimension of the sky and the wall in the figure is very low, and its color is darker; The fractal dimension of the flame and tree areas is larger and brighter in color. This distinguishes flames from the sky and walls. Figure C shows the artificial segmentation effect obtained by setting the area between 16–200 to white and the rest to black.

Fig. 12. Image of oil flame and image of its treatment

5 Conclusions This paper designs a new estimation algorithm for box dimension based on fractal geometry, which changes the traditional thinking and estimates the box dimension more intuitively with the number of boxes at the minimum scale of the digital image, and

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the estimation process has no fitting step. This algorithm is simple, intuitive, and easy to implement. The proposed method has been verified by many experiments and has better estimation accuracy and stability. In addition, this new method does not need to calculate the number of boxes at different scales, so the calculation amount is greatly reduced. Finally, the fractal dimension distribution of the algorithm used to obtain the oil flame image is programmed and implemented, and the obtained fractal dimension distribution is manually segmented, which can effectively supplement the brightnessbased segmentation, verify the feasibility of this new method, and provide a certain reference for the detection technology of oil fire.

References 1. Li, Y., Duan, X., Wang, H.: Research on lightweight BIM terrain model based on fractal geometry. Railw. Eng. 62(12), 95–100 (2022) 2. Li, C., Zhang, S., Wang, H., et al.: Numerical simulation of conductivity vs. permeability of porous media based on fractal geometry. Comput. Techniq. Geophys. Geochem. Explor. 44(05), 605–614 (2022) 3. Wang, H.: Research on The Extraction of Oil Fire Characteristic Pollution Information Based on Multi-source Remote Sensing Fusion. Guilin University of Technology (2021) 4. Jiang, X., Wang, B., Yan, X., et al.: Design and analysis for small unit apartment. J. Logist. Eng. Univ. 28(03), 24–29+65 (2012) 5. Lin, H., Wan, X.: Fire detection location system of industrial electric furnace substation based on smoke detector. Ind. Heat. 52(06), 58–62 (2023) 6. Zhang, Y.: Research on Early Fire Characteristic Gas Detection System Based on Cavity Enhanced Absorption Spectroscopy. Jilin University (2023) 7. Geng, P., Zhang, Y.: Design of remote fire real-time detection and alarm system based on artificial intelligence. Comput. Knowl. Technol. 19(18), 18–20+25 (2023) 8. Wang, C., Liu, H., Chen, Y., et al.: Study on image-type fire detection technology of pipe gallery based on multi-feature dimensionless vector. J. Safety Sci. Technol. 19(04), 14–20 (2023) 9. Xue, S., Jiang, X., Duan, J., et al.: An improved image box dimension calculation method. J. Univ. Sci. Technol. China 48(06), 504–511 (2018) 10. Yang, Y.F., Yang, J.B., Han, J.K., et al.: Study on the limited values of foundation deformation for a typical UHV transmission tower. IEEE Trans. Power Delivery 25(4), 2752–2758 (2010) 11. Yang, S.C., Hong, H.P.: Nonlinear inelastic responses of transmission tower-line system under downburst wind. Eng. Struct. 123, 490–500 (2016)

A IPMSM Current Control Method Based on Reinforcement Learning Qinghui Meng1,2(B) , Nannan Sun1,2 , Hanrui Wang1,2 , and Shankun Jia1,2 1 Weichai Power Co. Ltd., Weifang 261000, China

[email protected] 2 State Key Laboratory of Engine and Powertrain System, Weifang 261000, China

Abstract. The control problem of Interior Permanent Magnet Synchronous Motor (IPMSM) under external disturbance has always been a difficult problem in the industry, although H∞ control can effectively improve the robustness, it is difficult to solve the Game Algebra Riccati Equation (GARE) analytically due to the time-varying uncertainty of motor parameters. To solve this problem, this paper proposes an off-policy reinforcement learning method, which uses the data-driven way to learn the solution of GARE online, completely without the mathematical model of the motor, successfully realizes the H∞ optimal control of the time-varying system, and applies it to the current control of IPMSM. Firstly, using the saddle point theory of game theory and the linear discrete mathematical model of the motor, the H∞ optimal control problem was transformed into a twoplayer zero-sum game problem, and the GARE equation was constructed. Then, the reinforcement learning algorithm based on Actor-Critic framework is used to update the Q function and the strategy by using the input and output data of the system, and the optimal H∞ controller satisfying Nash equilibrium is learned. The test results of Processor In Loop (PIL) prove the feasibility of the proposed scheme, and its performance is far superior to PI control. Keywords: current control · data drive · Game Algebra Riccati Equation · H∞ control · interior permanent magnet synchronous motor · reinforcement learning

1 Introduction Interior Permanent Magnet Synchronous Motor (IPMSM) has the advantages of high power density, large speed range and so on. It is widely used in the field of motion control. The control strategy is mainly based on the vector control of PI (Proportive Integral) regulator. However, it cannot meet the application scenarios with high robustness requirements. Although sliding mode control has strong robustness, its disadvantage is that chattering problem caused by switching of sliding mode surfaces cannot be completely eliminated [1, 2]. Active Disturbance Rejection Control (ADRC) can observe and compensate the system Disturbance in real time, and the anti-disturbance ability is improved, but the disadvantage is that there are many parameters and the tuning is difficult [3]. Finite control set model predictive control has excellent dynamic performance © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 73–85, 2024. https://doi.org/10.1007/978-981-97-1064-5_8

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and disturbance rejection performance, but it has disadvantages such as uncertain switching frequency, high ripple current and large noise [4]. Although the continuous control set model predictive control does not have these disadvantages mentioned above, the calculation is very complicated and it is difficult to meet the real-time control requirements of motors [5]. H∞ control is a robust control strategy, the advantage is that it has a strong ability to suppress the external disturbance of the system, and it also has excellent tracking performance. It does not have the above disadvantages, but requires the system model to be precisely known. For the time-varying motor parameters of IPMSM, the Game Algebra Riccati Equation (GARE) cannot be solved by analysis. How to achieve optimal H∞ control under time-varying uncertainty of parameters is an important research direction in the industry [6, 7]. In order to solve this problem, Literature [8] designed robust H∞ output feedback control based on Takagi-Sugeno (TS) fuzzy model for vehicle parameter uncertainty and actuator instability to improve autonomous driving performance. This above method can increase the perturbation range of allowable parameters, but the fault-tolerant ability is still limited. In recent years, the model-free data-driven reinforcement learning method is often used to solve the adaptive optimal control problem, but the data-driven reinforcement learning method does not make use of the mechanism model information at all, with no robustness, low learning efficiency and high training cost [9]. In order to overcome the above disadvantages, some scholars combine reinforcement learning and H∞ control, and use data-driven method to learn the optimal H∞ controller. Literature [10] adopts the design of H∞ tracking controller for nonlinear continuous time systems with completely unknown model, and introduces the general bounded L2 gain tracking problem with discounted performance function. Literature [11] adopts the Actor-CRITIC framework based on neural network and deduces the least square neural network weight updating algorithm based on the weighted residual method. Reinforcement learning introduced in the above literatures is relatively complex, and it is quite difficult for motor control that requires high real-time performance [12–14]. To solve the above problems, this paper proposes an off-policy reinforcement learning method, which combines reinforcement learning and H∞ control to learn the solution of GARE online in a data-driven way, completely without the mathematical model of the motor, successfully realizes the H∞ optimal control of the time-varying system, and is applied to the current control of IPMSM. Firstly, using the saddle point theory of game theory and the linear discrete mathematical model of the motor, the H∞ optimal control problem was transformed into a two-player zero-sum game problem, and the GARE equation was constructed. Then, the framework based on 2 Actors and 1 Critic is adopted, and the Q function is iteratively updated with the input and output data of the system, and the optimal H∞ controller satisfying Nash equilibrium is finally learned.

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2 IPMSM Mathematical Model The mathematical model of PMSM in the synchronously rotating dq coordinate system can be expressed as [15]: ⎧ d ⎪ ⎨ ud = Rs id + ψd − ωe ψq dt (1a) ⎪ ⎩u = R i + d ψ + ω ψ q s q q e d dt  ψd = Ld id + ψf (1b) ψq = Lq iq J

d ωe = 1.5p(ψf iq + (Ld − Lq )id iq ) − TL dt

(1c)

where ud and uq represent the stator voltages of d-axis and q-axis, respectively; id and iq are dq-axes currents, respectively; ωe denotes rotor electrical angular velocity (rad/s); ψf is permanent magnet flux linkage; Ld , Lq , and R represent the stator inductance of d-axis and q-axis and winding resistance, respectively; J is the rotational inertia of PMSM; TL is the load torque. Employing the forward Euler method discretization formula, the time-varying linear discretization state-space model (1a, 1b, 1c) can be obtained as follows (2) xk+1 = Ak xk + Bk uk T T   where xk = id , iq , ωe , uk = ud ,uq represent the state shift matrix and control input vector matrix, respectively; k represents the sampling time instant; The matrix Ak , Bk are ⎤ ⎡ Tω L T  1 − TLs Rd s s Lde q 0 s ⎥ ⎢ −Ts ωe Ld 0 0 T R L s s d 1 − Lq 1 ⎥ Ak = ⎢ ⎦, Bk = 0 Ts 0 ⎣ Lq Lq 1.5p2 ψf Ts 0 1 J where Ts represent the sample period. Due to the fact that dq axis inductance Ld and Lq are greatly affected by the current, the matrices Ak , Bk , and Gk in the equation are all time-varying uncertain, hence the designed current controller should have a strong robustness.

3 H∞ Robust Control H∞ control strategy characterized with robustness, not only has a strong ability to suppress the external disturbance of the system, but also has excellent tracking performance. For convenience, the H∞ norm of the closed-loop transfer function Tzw from the interference input vector w to the evaluation output vector Z is less than or equal to a given positive number γ , namely Tzw (s)∞ =

Z ≤γ w

(3)

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where Z is the evaluation output signal, w is the interference input, γ is the upper bound of disturbance attenuation, where γ ≤ 1. Let xref as the reference value of state variance x, the tracking error x = x − xref can represent the tracking error. For convenience, the Gaussian noise wk is introduced to represent the influence of xref , measurable noise ωe , and other uncertainties in the controlled system on the plant. The state-space equation of (2) can be rewritten: xk+1 = Ak xk + Bk uk + Ek wk

(4)

T   = id , iq , ωe , Ek is noise coefficient matrix. where xk+1 The matrix Ak is simplified as: ⎤ ⎡ Tω L 1 − TLs Rd s s Lde q 0 ⎥ ⎢ −Ts ωe Ld 1 − TLs Rq s 0 ⎥ Ak = ⎢ ⎦. ⎣ Lq 0

1.5p2 ψf Ts J

1

Based on the saddle point theory of game theory, a two-player zero-sum game method is proposed to solve the traditional standard H∞ control problem. The optimal control quantity Uk∗ and the worst disturbance quantity wk∗ correspond to the Nash equilibrium point, and the objective function is minimized and maximized, respectively. The optimal objective function can be designed as  ∞  xiT Rxi + uiT ui − γ 2 wiT wi (5) J (xk ) = min max uk

wk

i=k

where R is the coefficient matrix of x. Assuming that there is a solution to the optimal objective function in the infinite time domain, (5) can be simplified as: J (xk ) = xkT Pk xk

(6)

where Pk is a parameterized positive definite matrix. By solving GARE, Pk can be obtained as [14]: Pk = ATk Pk+1 Ak +R − [ ATk Pk+1 Bk ATk Pk+1 Ek ] −1  BkT Pk+1 Ek I + BkT Pk+1 Bk × EkT Pk+1 Bk EkT Pk+1 Ek − γ 2 I × [ ATk Pk+1 Bk ATk Pk+1 Ek ]T Hence, the corresponding solution of (4) can be obtained [16]  uk = Kk xk wk = Lk xk where, Kk and Lk are state feedback coefficients, which can be rewritten as: Kk = (EkT Pk Ek − γ 2 I − EkT Pk Bk (I + BkT Pk Bk )−1 BkT Pk Ek )−1

(7)

(8)

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× (EkT Pk Bk (I + BkT Pk Bk )−1 BkT Pk Ak − EkT Pk Ak )

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(9)

Lk = (I + BkT Pk Bk − BkT Pk Ek (EkT Pk Ek − γ 2 I )−1 EkT Pk Bk )−1 × (BkT Pk Ek (EkT Pk Ek − γ 2 I )−1 EkT Pk Ak − BkT Pk Ak )

(10)

In order to ensure the uniqueness of the saddle point of the linear control strategy, the following inequality must be satisfied I − γ −2 EkT Pk Ek > 0

(11)

I + BkT Pk Bk > 0

(12)

Due to the fact that the absence of influence of the measurable disturbances vk and xref on the plant in (4), the control quantity of the original control problem is uˆ k = Kk (xk − xref ) − Bk−1 [(Ak − I )xk + Gk vk ]

(13)

4 Reinforcement Learning Algorithm Due to the presence of time-varying parameters, it is difficult to get the analytical solution of the GARE in (7). As is well known, reinforcement learning is good at learning the solution to these equations. Therefore, reinforcement learning algorithm based on actorcritic framework is adopted to get the exact numerical solution of the time-varying GARE equation. Control variable uk and disturbance variable wk are treated as the actors introduced in (8). The Q function is the critic, which reflects the optimal objective function in (5) or (6). By employing least squares iteration, the Q function is updated. Finally, the optimal H∞ controller, which satisfied Nash equilibrium, is obtained. 4.1 A Subsection Sample Define Reinforcement Learning Value Function The optimal objective function J of H∞ controller is assigned to the optimal state value function V ∗ , and it can be obtained from (5) and (6) [14].  ∞  xiT Rxi + uiT ui − γ 2 wiT wi V ∗ (xk ) = min max uk

=

wk

xkT Pk xk

i=k

(14)

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Using the quadratic expression form of the optimal state value function V ∗ , the optimal action value function Q∗ can be expressed as Q∗ (xk , uk , wk ) = rk + V ∗ (xk+1 ) T Pk+1 xk+1 = xkT Rxk + ukT uk − γ 2 wkT wk + xk+1 ⎤⎡ ⎡ ⎤T ⎡ ⎤ xk xk R0 0 = ⎣ uk ⎦ ⎣ 0 I 0 ⎦⎣ uk ⎦ wk wk 0 0 −γ 2 I ⎡ ⎤T ⎡ T ⎤ ⎡ T ⎤T ⎡ ⎤ xk Ak Ak xk +⎣ uk ⎦ ⎣ BkT ⎦Pk+1 ⎣ BkT ⎦ ⎣ uk ⎦ wk EkT EkT wk

(15)

=zkT Hk zk where rk (xk , uk , wk ) = xkT Rxk + ukT uk − γ 2 wkT wk is the reward at moment k of T  Markov’s decision-making process; and zk = xkT ukT wkT zk ∈ Rq q = n + m1 + m2 , where n, m1 , and n1 are the dimensions of state xk , control uk and noise wk , respectively; Hk is the undetermined parameter of Q∗ , which can be expressed as ⎡ T ⎤ ATk Pk+1 Ek Ak Pk+1 Ak + R ATk Pk+1 Bk ⎦ Hk = ⎣ BkT Pk+1 Ak BkT Pk+1 Bk + I BkT Pk+1 Ek T T T 2 Ek Pk+1 Ak Ek Pk+1 Bk Ek Pk+1 Ek − γ I Based on Bellman equation, the optimal action value function Q∗ can be expressed as T Hk+1 zk+1 + rk Q∗ (xk , uk , wk ) = zkT Hk zk = min αzk+1 uk+1

(16)

where α is the discount factor,α ∈ [0, 1], and its size determines the weight ratio of the system to current rewards and future rewards. 4.2 Reinforcement Learning Training Method In order to improve the training efficiency of reinforcement learning, the least-squares iteration strategy is adopted to fit the Q function. Meanwhile, the empirical playback method is adopted to reduce the overfitting problems caused by training. In each iteration, N sample data are taken as the BatchSize. In this process, the state feedback coefficients K and L remain unchanged while M iterations are carried out. Q function of the i-th iteration of in (16) can be written: Q∗ (xk , uk , wk ) = zkT Hi zk T = min αzk+1 Hi−1 zk+1 + rk

(17)

uk+1

It is obviously that Hi is not an explicit solution. So, the least square method can be adopted to get the non-explicit solution of Hi in (17). Since Hi is q × q-dimensional

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symmetric matrix, one can change the quadratic form zkT Hi zk to a linear function of the upper triangular matrix on Hi . hi is denoted as a q × (q + 1)/2-dimensional column matrix corresponding to the number of elements of the upper triangular matrix formed by matrix Hi , which can be expressed in the form Hij + Hji , and the column vector is defined at the same time z = (z12 , z1 z2 , ..., z1 zq , z22 , z2 z3 , ..., z2 zq , ..., zq−1 z1 , zq2 )T

(18)

It has the least squares form zkT Hi zk = z Tk hi

(19)

Therefore, Eq. (17) can be written as z Tk hi = min z Tk+1 hi−1 + rk = dk uk+1

(20)

where dk is the estimated value of the action value function Q∗ (xk , uk , wk ) at the current moment k. N samples are selected, and their matrix form can be expressed as Zhi = Y

(21)

T  Z = z 1 z 2 z 3 ... z N T  Y = d1 d2 d3 ... dN

(22)

Among them,

The least square method is used to realize the estimation of the matrix hi hi = (Z T Z)−1 Z T Y

(23)

In order to enhance the exploration of the unknown region and ensure the invertibility of the matrix Z T Z, Gaussian noise is added to the control input and disturbance terms, respectively, namely ⎤ ⎡ ⎤ xk xk zk = ⎣ uk ⎦ = ⎣ uk + n1k ⎦ wk wk + n2k ⎡

(24)

where, n1k and n2k are normal distributions with mean 0 and variance σ1 and σ2 , respectively; namely n1k ∼ N (0, σ1 ), n1k ∼ N (0, σ1 ). In summary, the matrix hi can be obtained. On this basis, the matrix Hi can be obtained. The matrix Hi is expressed as the following form ⎡

⎤ i Hi Hi Hxx xu xw i Hi Hi ⎦ Hi = ⎣ Hux uu uw i i Hi Hwx Hwu ww

(25)

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The state feedback coefficients Ki and Li can be expressed as i i i −1 i −1 Ki = (Hww − Hwu (Huu ) Huw ) i i −1 i i × (Hwu (Huu ) Hux − Hxx ) i i i −1 i −1 − Huw (Hww ) Hwu ) Li = (Huu i i −1 i i × (Huw (Hww ) Hwx − Hux )

(26)

As the number of iterations increases, Ki gradually approaches K, and the optimal control strategy uk∗ can be obtained by substituting K into Eq. (13). In order to verify the training effect of fitting Q function based on the least square iteration strategy, the time difference error can be measured, as shown below T TDerr = Q(xk , uk , wk ) − (min α zk+1 Hi−1 zk+1 + rk ) uk+1

(27)

5 Test and Analysis 5.1 A Brief Introduction to the Test System Compared with the real motor bench, PIL test has better convenience and flexibility, and is more suitable for algorithm research. In order to verify the effectiveness of the proposed scheme, the TI DSP processor TMS320C28344 (main frequency 300 MHz) was selected as the target chip, the algorithm simulation model was built in MATLAB/Simulink, the simulator was used to connect the target DSP board, and the automatically generated code was downloaded and PIL test was carried out. KDS 2000N • M motor is adopted as the control object, and the motor parameters are shown in Table 1. For current control, PI controller parameters and H∞ control parameters are shown in Table 2 and Table 3, respectively. Table 1. KDS-2000 Motor Parameters. Parameter name

Parameter value

Permanent magnet flux linkage coefficient

0.293 2 Wb

Stator phase resistance

0.0249 

Rated D axis inductance L d

1.185 9*10–3 H

Rated Q axis inductance L q

2.915 7*10–3 H

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Table 2. PI Controller Parameter Configuration Parameter name

Parameter value

d/q axis proportional coefficient

2.981/7.328

d/q axis integral coefficient

813.5

Table 3. Parameter Configuration of H∞ Control Based on Reinforcement Learning Parameter name

Parameter value

Discount factor α

1

Allowable error ε

0.001

The upper bound of the noise is γ

1

Weighting matrix R

[9 0;0 9;]

Number of iterations M

5000

BatchSize N

200

5.2 Test Results and Analysis Dynamic Performance Test In order to verify the excellent dynamic performance of the algorithm proposed in this paper, given the rotational speed of 1000 r/min and keeping id = −200 A unchanged, iq is given as the step input. At 0.4 s, iq jumps from 0 A to 300 A, and at 0.8 s, iq drops from 300 A to 0 A. The step response curves of current are shown in Fig. 1 and Fig. 2. The maximum overshoot of Q-axis current controlled by PI is 20 A, and the step response time is 33 ms; the fluctuation amplitude of D-axis current is 142 A and the fluctuation time is 18 ms. Under the same working condition, the maximum overshoot of the Q-axis current controlled by H∞ is almost 0 A, the step response time is 3 ms, and the Daxis current basically does not fluctuate. Therefore, H∞ control has a more satisfactory dynamic control effect, and there is no coupling disturbance, and the performance is far better than PI control. Dynamic Performance Test Under Constraint Conditions Because H∞ control is linear state feedback control, and there is no integral desaturation problem, it has better dynamic performance than PI control under constraint conditions. In order to verify the dynamic performance of the algorithm proposed in this paper under constrained conditions, given the rotating speed of 2000 r/min, the current id = −200 A remains unchanged, the iq rises from 0 A to 300 A with a certain slope at 0.4 s, and the iq drops from 300 A to 0 A at 0.8 s. As can be seen from Fig. 3, compared with PI control entering depth integral saturation with 230 ms delay, H∞ control can quickly track the given value and exit saturation quickly with almost no delay time. Therefore, the dynamic performance of H∞ control is far better than that of PI control under constraint conditions.

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Fig. 1. Step response curve of Q-axis current.

Fig. 2. Step response curve of D-axis current.

Parameter Mismatch Test In order to further demonstrate the robustness of the algorithm proposed in this paper under the condition of parameter mismatch, the inductance and resistance parameters are changed within the range of ±20%. Specific parameter configuration is shown in Fig. 4 and Fig. 5, where Ld, Lq and RS are the inductance and phase resistance of DQaxis under the rated torque condition respectively. According to Fig. 4 and Fig. 5, the maximum overshoot controlled by PI is 12 A and the response time is about 36 ms; the maximum overshoot controlled by H∞ is almost 0 A and the response time is about 3 ms. Therefore, under the condition of parameter mismatch, H∞ control has stronger robustness, and overshoot and response time are much smaller than PI control.

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Fig. 3. Q-axis current curve under saturation condition.

Fig. 4. PI controlled Q-axis current step response curve with the variation of motor parameters

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Fig. 5. H∞ controlled Q-axis current step response curve when motor parameters change.

6 Conclusions In order to solve the H∞ optimal control problem of time-varying systems, this paper combines H∞ control with reinforcement learning. Firstly, the H∞ optimal control problem is transformed into a two-player zero-sum game problem, and the GARE equation is constructed. Then, off-policy reinforcement learning method was adopted to learn the GARE solution online in a data-driven way, without the need for motor mathematical model, and it was successfully applied to the current control of IPMSM. The test results of Processor In Loop (PIL) prove the feasibility of the proposed scheme, and its performance is far superior to PI control.

References 1. Li, X., Wang, Y., Cheng, Y., Li, D., Qu, R.: An overview of high-efficiency synchronous reluctance machines. CES Trans. Electric. Mach. Syst. 7(1), 81–91 (2023). https://doi.org/ 10.30941/CESTEMS.2023.00030 2. Qiao, Y., Zhao, T., Gui, X.: Overview of position servo control technology and development of voice coil motor. CES Trans. Electric. Mach. Syst. 6(3), 269–278 (2022). https://doi.org/ 10.30941/CESTEMS.2022.00037 3. Zhu, L., et al.: Nonlinear active disturbance rejection control strategy for permanent magnet synchronous motor drives. IEEE Trans. Energy Convers. 37(3), 2119–2129 (2022). https:// doi.org/10.1109/TEC.2022.3150796 4. Yan, S., Cui, Y., Li, C., Gao, X., Cai, Y.: An improved FCS-MPC based on novel sector optimization and capacitor charge balance algorithm for T-Type 3P–3L converters. IEEE Trans. Power Electron. 38(4), 4559–4571 (2023). https://doi.org/10.1109/TPEL.2023.323 3996 5. Ren, B., Zhu, Y., Sun, X., Pan, Z., Zhao, W.: Dynamic performance improvement of continuous control set model predictive control for high-frequency link matrix converter. IEEE Trans. Indust. Electron. 70(9), 9057–9066 (2023). https://doi.org/10.1109/TIE.2022.3215447

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6. Peng, G., Peng, K.: An H∞ output tracking control approach to sampled-data control for nonlinear networked control systems. IEEE Access 8, 143644–143653 (2020). https://doi. org/10.1109/ACCESS.2020.3014210 7. Lee, D.H., Joo, Y.H., Tak, M.H.: Periodically time-varying H∞ memory filter design for discrete-time LTI systems with polytopic uncertainty. IEEE Trans. Autom. Control 59(5), 1380–1385 (2014). https://doi.org/10.1109/TAC.2013.2289705 8. Guo, J., Wang, J., Luo, Y., Li, K.: Takagi–Sugeno fuzzy-based robust H∞ integrated lanekeeping and direct yaw moment controller of unmanned electric vehicles. IEEE/ASME Trans. Mechatron. 26(4), 2151–2162 (2021). https://doi.org/10.1109/TMECH.2020.3032998 9. Schenke, M., Kirchgässner, W., Wallscheid, O.: Controller design for electrical drives by deep reinforcement learning: a proof of concept. IEEE Trans. Industr. Inf. 16(7), 4650–4658 (2020). https://doi.org/10.1109/TII.2019.2948387 10. Valadbeigi, A.P., Sedigh, A.K., Lewis, F.L.: H∞ Static output-feedback control design for discrete-time systems using reinforcement learning. IEEE Trans. Neural Netw. Learn. Syst. 31(2), 396–406 (2020). https://doi.org/10.1109/TNNLS.2019.2901889 11. Luo, B., Wu, H., Huang, T.: Off-policy reinforcement learning for H∞ control design. IEEE Trans. Cybernet. 45(1), 65–76 (2015). https://doi.org/10.1109/TCYB.2014.2319577 12. Wu, H., Liu, Z.: Data-driven guaranteed cost control design via reinforcement learning for linear systems with parameter uncertainties. IEEE Trans. Syst. Man Cybernet. Syst. 50(11), 4151–4159 (2020). https://doi.org/10.1109/TSMC.2019.2931332 13. Yang, X., He, H.: Event-driven H∞ constrained control using adaptive critic learning. IEEE Trans. Cybernet. 51(10), 4860–4872 (2021). https://doi.org/10.1109/TCYB.2020.2972748 14. Zhang, H., Xiao, G., Liu, Y., Liu, L.: Value iteration-based H∞ controller design for continuous-time nonlinear systems subject to input constraints. IEEE Trans. Systems Man Cybernet. Syst. 50(11), 3986–3995 (2020). https://doi.org/10.1109/TSMC.2018.2853091 15. Sun, Z., Deng, Y., Wang, J., Yang, T., Wei, Z., Cao, H.: Finite control set model-free predictive current control of PMSM with two voltage vectors based on ultralocal model. IEEE Trans. Power Electron. 38(1), 776–788 (2023). https://doi.org/10.1109/TPEL.2022.3198990

Development and Performance Test of DC High-Voltage Generation System for Boron Neutron Source Device Based on Accelerator Longyang Wang1,3

, Rixin Wang1 , Lizhen Liang2,3 , Congguo Gong3 , Jun Tao1(B) , and Jieping Lu4

1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China

[email protected], {rixin.wang,Jun.Tao}@ahu.edu.cn 2 Institute of Plasma Physics, Hefei Institute of Physical Sciences, Chinese Academy of Sciences, Hefei 230031, China [email protected] 3 Institute of Energy, Hefei Comprehensive National Science Center (Anhui Energy Laboratory), Hefei 230001, China 4 CGN Dasheng Accelerator Technology Co., Ltd., Suzhou 215214, China [email protected]

Abstract. Boron Neutron capture Therapy (BNCT) is an advanced targeted radiotherapy method with great application prospect and rapid development. BNCT has become a new hotspot in the research and development of energetic particle therapy and one of the important options for future tumor treatment. The DC high-voltage accelerator is an important component of the accelerator based BNCT device, which utilizes a DC high-voltage electric field to accelerate charged particles. The DC high-voltage generation system is one of the indispensable components of the DC high-voltage accelerator, providing megavolt level DC high-voltage for the DC high-voltage accelerator tube. According to the design requirements of the prototype project of the 2.5 MV accelerator Neutron source device for the DC high-voltage power supply, this paper first proposes the structural design scheme of the 2.5 MV DC high-voltage generation system, and then briefly introduces the components of the 2.5 MV DC high-voltage generation system, mainly including controllable silicon DC stabilized power supply, high-frequency high-voltage oscillator, high-frequency high-voltage transformer and voltage doubling rectifier system, And briefly analyzed the principle of the core component of the DC high voltage generation system, the voltage doubling rectifier circuit, derived the output voltage of the voltage doubling rectifier circuit, and simulated the 2.5 MV voltage doubling rectifier circuit in this study. Finally, the output performance of the 2.5 MV DC high voltage generation system was experimentally tested. The experimental results show that the 2.5 MV DC high-voltage generation system meets the design requirements of the 2.5 MV accelerator Neutron source device prototype project, and lays a certain foundation for the physical experiments of the 2.5 MV accelerator Neutron source device prototype. Keywords: Boron Neutron Capture therapy · DC High Voltage Generation System · Voltage Doubling Rectifier Circuit · Components

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 86–97, 2024. https://doi.org/10.1007/978-981-97-1064-5_9

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1 Introduction Boron Neutron Capture Therapy (BNCT) [1] is a method that uses the nuclear reaction between boron (10 B) and neutrons to treat tumors. It is based on the 10 B(n,α)7 Li reaction [2]. It has the advantages of high accuracy and high efficiency, can reduce damage to normal cells [3], and has special therapeutic advantages for a wide range of diffuse malignant tumors and intermediate and advanced cancers [4]. Boron neutron capture therapy equipment is a new medical system for cancer treatment, which is developed based on the principle of binary targeted radiotherapy of boron neutron capture therapy. Compared with reactor-based BNCT, accelerator-based BNCT devices have the advantages of low manufacturing and maintenance costs, can be used to treat deep tumors, and are easy to deploy in densely populated locations [5]. Currently, the accelerator types available for BNCT devices mainly include cyclotron, RFQ electromagnetic accelerator and DC highvoltage accelerator [6, 7]. Among them, both the cyclotron and RFQ electromagnetic accelerator operate in pulse mode, which cannot meet long-term steady-state operation. There are some problems in cyclotron, such as inconvenient installation of heavy magnets and high magnetic field power consumption. The RFQ electromagnetic accelerator needs longer beam shaping space and higher acceleration power consumption. While the DC high-voltage accelerator has the advantages of easy operation and maintenance, high beam current, stable operation, and relatively low power consumption, so it is the best choice for accelerator-based BNCT devices [8]. As the core component of the DC high-voltage accelerator, the DC high-voltage generation system can generally adopt transformer cascade voltage doubling DC high-voltage power supply, DC high voltage power supply based on series core magnetic ring transformer, and DC high voltage power supply based on cascade voltage doubling rectifier circuit [9]. Among them, the transformer cascade voltage doubling DC high voltage power supply has problems, such as large internal inductance, large power consumption and large voltage drop. Due to the insulation problem between the primary and secondary windings, the DC high voltage power supply based on series core magnetic ring transformer limits the increase of DC voltage. While the DC high voltage power supply based on cascade voltage doubling rectifier circuit has simple circuit structure and low ripple voltage, so it can be cascaded according to the demand voltage. Therefore, the 2.5 MV accelerator neutron source device prototype project adopts DC high-voltage accelerator, and adopts capacitor parallel-coupled cascade voltage doubling rectifier circuit as its DC high-voltage generation system.

2 Overall Design of DC High-Voltage Generation System According to the design requirements of the DC high-voltage accelerator in an independent project of the Institute of Energy, Hefei Comprehensive National Science Center (Development and Industrial Application of Compact Boron Neutron Capture Therapy Technology for Cancer Treatment), Table 1 gives the specific design indicators of the DC high-voltage generator. Based on these design indicators, the basic structural block diagram of the DC high-voltage generation system is proposed, as shown in Fig. 1. In this design, the DC high-voltage generating system is mainly composed of SCR DC stabilized power supply, high-frequency and high-voltage oscillator, high-frequency and

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high-voltage transformer, and rectifier voltage doubling system. The three-phase power frequency AC power supply provides power input for the SCR DC stabilized power supply and outputs a DC negative high voltage to the high-frequency and high-voltage oscillator. The LC oscillation circuit in the high-frequency and high-voltage oscillator (composed of the oscillation tube in the high-frequency and high-voltage oscillator and the high-frequency and high-voltage transformer coil L and high-frequency electrode C in the main steel cylinder of the accelerator) produces a high-frequency power signal of about 120 kHz. This high-frequency power signal can generate a high-frequency voltage of about 200 kV on the high-frequency electrode after being boosted by a high-frequency and high-voltage transformer. After coupling through the corona ring, this voltage is rectified into a megavolt DC negative high voltage on the high voltage electrode through the parallel voltage doubling rectifier circuit [10] (main components are high-frequency electrode, corona ring and high-frequency and high-voltage rectifier silicon stack). This DC high voltage will be applied to the accelerating tube to accelerate the electrons generated by the electron gun to obtain a high-energy electron beam. Table 1. Specific Design Indicators of DC High Voltage Generation System Serial number

Parameter name

Design specifications

1

Input voltage

Three-phase AC 380 V, 50 Hz

2

Maximum output voltage

DC 2500 kV

3

Maximum output current

40 mA

Fig. 1. Block diagram of DC high-voltage generation system

3 Detailed Design of DC High-Voltage Generation System 3.1 SCR DC Stabilized Power Supply First of all, the SCR DC voltage stabilized power supply [11] is used to deal with the municipal power in the power grid, which needs to provide a DC negative high voltage for the oscillating tube. After the power frequency three-phase power supply is input into the power supply, the power frequency three-phase step-up transformer is boosted, and then rectified and filtered by the three-phase bridge rectifier filter unit, thus the DC negative high voltage of 0 to 18 kV and 0 to 25 A is output. In order to achieve the purpose that the accelerator terminal voltage and beam power need to be adjusted, the

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SCR regulating unit is placed in the primary circuit of the transformer, and the DC working parameters of the oscillating tube are adjusted by changing the primary input voltage. In order to stabilize the energy of the accelerator, the SCR regulating unit can also obtain the signal from the accelerator high voltage measuring unit and then regulate it by computer. 3.2 High-Frequency and High-Voltage Oscillator As the main power supply of DC high-voltage generation system, high-frequency and high-voltage oscillator [12] needs to convert the DC negative high voltage output of the SCR DC voltage stabilized power supply into high frequency electric energy of about 120 kHz, then output to the high-frequency and high-voltage transformer to boost voltage, and then doubles with the voltage doubling rectifier circuit to become the DC high voltage needed by the accelerator. The performance of high-frequency and highvoltage oscillator can determine the maximum beam power and beam power conversion efficiency of the accelerator. The basic component of the high-frequency and high-voltage oscillator is the oscillator tube, as shown in Fig. 2. In order to simplify the cooling circuit of the oscillator tube, the cathode of the oscillator tube is connected to DC negative high voltage and the anode is grounded. The resonant loop is composed of an inductor L and a capacitor C. The inductor L is designed as a ring autotransformer in the steel cylinder, and the capacitor C is composed of the distributed capacitor between the high frequency electrode of the half cylinder and the inner wall of the steel cylinder and the voltage doubling rectifier core column. The anode of the oscillating tube is connected to the primary coil of the toroidal transformer by a high-frequency cable. The coupling capacitance between the cylinder and the high-frequency electrode generates a positive feedback voltage input to the grid. 3.3 High-Frequency and High-Voltage Transformer As shown in Fig. 3, the toroidal transformer is a key component of the DC high voltage generation system. According to the characteristics of the DC high voltage generation system and the design requirements of the accelerator, it is required to work under the conditions of high frequency, high voltage and high-power load, and it needs to achieve small magnetic flux leakage and high Q value. In this design, the loss of the toroidal transformer is higher [13], which is second only to the oscillating tube in the system, which will greatly affect the beam power conversion efficiency of the accelerator. A considerable part of the energy loss of the transformer will be converted into heat energy, so it is very important to cool the inside of the steel cylinder and other components. In order to dissipate these heat energies, the heat exchanger and the air-cooling system are designed and installed at the top of the steel cylinder. 3.4 Voltage Doubling Rectifier Circuit In this design, the high voltage multiplier design principle of DC high-voltage generation system [14] is shown in Fig. 4. The left part of Fig. 4 is the high frequency

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Fig. 2. High-frequency and high-voltage oscillating tube

Fig. 3. High-frequency and high-voltage transformer

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oscillating power supply, the annular high frequency autotransformer L2 is represented by the inductor with a center tap in the Fig. 4, and C is the parasitic capacitance between the semi-cylindrical high frequency electrode and the high voltage steel cylinder. The inductance L and parasitic capacitance C of ring autotransformer together with high power triode G produce high frequency oscillation to form high frequency oscillation power supply. The two symmetrical semi-corona rings installed on the connection point of silicon stack correspond exactly with the two symmetrical semi-cylinder high-frequency electrodes fixed on the inner wall of the steel cylinder, and the design of the semi-corona rings and high-frequency electrodes is accurate. The distributed capacitor Cse is formed between each semi-corona ring and the high frequency electrode. The parasitic capacitor Cse formed by the semi-cylinder through the high-frequency electrode and the corona ring (usually its value is about 10 pF) is coupled with the silicon stack, and the energy in the power grid is coupled to the rectified silicon stack to turn alternating current into high-voltage direct current. The distributed capacitance in parallel on the rectifier silicon stack (the main component is the diode) is CAC , and the load of the circuit is particle beam acceleration system. The geometrical structure between corona ring and high-frequency electrode is very similar to that of electrostatic accelerator, so the design must not only meet the requirements of high frequency coupling parameters, but also take into account the design of high voltage electrostatic field. The corona ring consists of a steel pipe bent into a “bow” shape. The smooth and flat surface of the corona ring can make the surface electric field as uniform as possible, avoid spark discharge and corona phenomenon, and form a coupling capacitor Cse with the high-frequency electrode, which is connected by rectifier silicon stack. The rectifier element is one of the key components of high-frequency and high-voltage accelerator. Choosing the high-frequency and high-voltage silicon stack as the rectifier element can save the equipment such as filament transformer, greatly reduce the volume and simplify the process. The silicon stack is composed of a rectifier core and a metal shielding box with a protective ball gap. The rectifier core is composed of hundreds of silicon high frequency diodes with unidirectional conductivity connected in series, and its circuit structure uses the design of voltage sharing and current limiting. The high frequency inductance L1 shows high inductance to high frequency current, but the resistance to the DC current is relatively low, so the high frequency AC voltage is basically consumed on the high frequency inductor, which greatly reduces the output ripple coefficient of the DC voltage. The output voltage of the DC high-voltage output electrode is higher, and the uniformity of the electric field is taken into account in the design, and the appropriate curvature and high finish are required to avoid corona discharge as far as possible. As a DC work load, the accelerator tube behaves as a DC resistance when accelerating electrons. In this design, the distributed capacitance formed between the DC high-voltage output electrode and the ground electrode is used as the filter capacitor Cf , which is actually mainly formed between the high-voltage electrode and the ground high-voltage steel cylinder shell. The filter capacitor Cf can greatly reduce the AC component in the output DC high voltage.

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o 2 1

1

2

Fig. 4. High voltage multiplier design principle of DC high-voltage generation system

All components are sealed with a grounded steel cylinder and filled with high pressure SF 6 dry insulating gas to form a safe enough insulation strength and good coupling effect. After receiving electricity from the power grid, the high-frequency oscillator generates high-frequency voltage and feeds it into the LC resonant loop. After the voltage is boosted by the high-frequency transformer, the voltage is directly transmitted to the two smooth semi-circular arc high-frequency electrodes. Due to the high frequency of the voltage, the potential of the two high-frequency electrodes changes alternately. Through the coupling capacitor and the rectifier silicon stack, the corona rings are charged on both sides, and the coupling capacitors located on one side are charged at the same time. The rectifier silicon stack has unidirectional conductivity, so the direction of charging can only be carried out in one direction, so that DC high voltage V0 can be obtained on each distributed capacitor CAC in the rectifier silicon stack itself, and the potential is gradually increased until the high voltage ball cap at the end of the rectifier silicon stack chain after each stage, then the DC high voltage NV 0 (N is the order of the rectifier silicon stack in the circuit) can be obtained. The DC high voltage eventually generated by the rectifier silicon stack chain determines how much energy the electron beam acceleration system can accelerate the electron beam [15]. As an important booster component, the voltage doubling rectifier system is responsible for most of the boosting tasks. Its structural design is shown in Fig. 5. Two PVC insulating plates are vertically fixed on the steel cylinder bottom plate as structural support parts of the voltage doubling rectifier system, and a row of silicon stacks are uniformly arranged on each of the two insulating plates from bottom to top. The two rows of silicon stacks are connected to each other in turn to form a spirally rising silicon stack rectifier chain. A semi-corona ring is installed horizontally at the connection point of each silicon stack for corona suppression, and two rows of semi-corona rings arranged up and down completely symmetrically are used to shield the silicon stack and form the cylindrical appearance of the voltage doubling rectifier system.

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High-voltage ball cap High frequency choke Silicon stack Semi-corona ring

Steel cylinder

PVC insulating plate

Steel cylinder bottom plate

oubling rectifier core

Voltage divider

Semi-corona ring

High frequency electrode Silicon stack

High frequency choke

Front view of voltage doubling rectifier core

Fig. 5. Voltage doubling rectifier core column

4 Principle Analysis and Simulation Calculation of Voltage Doubling Rectifier Circuit From the above analysis, it can be seen that the voltage doubling rectifier circuit is a system that directly supplies power to the acceleration tube load, and because it bears an important task of boosting voltage in the booster system, the structural design and optimization of the voltage doubling rectifier circuit and the exploration of electrical performance are particularly important in the whole DC high-voltage generation system. The DC high voltage generated by the voltage doubling rectifier circuit of the DC high voltage generation system is directly applied to the accelerator tube, which largely determines the final energy obtained by the particle beam. In this study, the cascade voltage

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doubling rectifier circuit of DC high voltage generation system is composed by means of parallel coupling of capacitors developed from the multiplier circuit. The basic principle of DC high voltage multiplier is exactly the same as that of ordinary voltage multiplier circuit, but because the accelerator’s own structure in this design can form capacitor C, there is no need for additional capacitor. In the Fig. 6, K is a high-frequency and high-voltage rectifier silicon stack, the power supply is a high-frequency transformer, and RL is a DC high-voltage output terminal. The average output voltage of the voltage doubling rectifier circuit is: V = NVa − (N − 1)

i 1 i − fCs 2 fCs

(1)

Fig. 6. Simulation model of voltage doubling rectifier circuit

In the Eq. (1), f is the frequency, N is the series of the voltage doubling rectifier circuit, Va is the voltage amplitude, i is the current added to the stable load at the high voltage end, and the capacitance values of Cs are all equal. In this design, Va is set at 200 kV and f is set at 120 kHz. Based on Eq. (1) and considering a certain margin, the series of voltage doubling rectifier circuit is set at 54.The simulation circuit is established as shown in Fig. 6, and the simulation results are shown in Fig. 7. It can be seen from Fig. 7 that this circuit can output an average voltage of −2.565 MV, and the effective value of the output voltage ripple is 14.752 kV. It can be seen that this circuit can meet the design requirements of voltage doubling rectifier circuit for DC high-voltage generation system.

5 Experimental Performance Testing According to the above design, the 2.5 MV DC high voltage generation system developed and installed is shown in Fig. 8, and the experimental results are shown in Fig. 9. The experimental results show that the developed 2.5 MV DC high voltage generation system can achieve stable operation with load of 2.5 MV, 6 mA and 40 min, which can meet the design requirements of the 2.5 MV accelerator neutron source prototype project.

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Fig. 7. Simulation results of voltage doubling rectifier circuit

Fig. 8. Developed 2.5 MV DC high-voltage generation system

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Fig. 9. Test results of 2.5 MV DC high-voltage generation system (positive voltage: Oscillating tube anode voltage; positive current: Oscillating tube anode current)

6 Conclusion The high voltage DC power supply provides high voltage environment and energy supply for accelerator. As one of the core equipment of the DC high-voltage accelerator, it plays a crucial role in the design of the accelerator. According to the design requirements of the project, the structural design scheme of the DC high-voltage generation system is proposed in this study. The structure design of 2.5 MV DC high-voltage generation system in this study is introduced briefly, which mainly includes SCR DC stabilized power supply, high-frequency and high-voltage oscillator, high-frequency and highvoltage transformer and voltage doubling rectifier circuit. As the core component of DC high-voltage generation system, the voltage doubling rectifier circuit is briefly analyzed and simulated, and the output performance of 2.5 MV DC high-voltage generation system is tested experimentally. After simulation verification and experimental test, the DC highvoltage generation system can meet the power source design requirements of 2.5 MV accelerator neutron source prototype project. Acknowledgments. This research is funded by the University Synergy Innovation Program of Anhui Province under the contract No. GXXT-2021-014 and the Institute of Energy, Hefei Comprehensive National Science Center under Grant Nos. 21KZS202 and 21KZS208.

References 1. Moss, R.L.: Critical review, with an optimistic outlook, on Boron Neutron Capture Therapy (BNCT). Appl. Radiat. Isotopes. 88, 2–11 (2014)

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2. Li, C.: Research on Boron Neutron Capture Therapy Based on Accelerator7li (p, n) Reaction. Chengdu University of Technology (2015). (in Chinese) 3. Aihara, T., Morita, N.: Neutron Capture Therapy: Principles and Applications, pp. 417–424. Springer, Heidelberg (2012) 4. Matsumoto, Y., Fukumitsu, N., Ishikawa, H., Nakai, K., Sakurai, H.: A critical review of radiation therapy: from particle beam therapy (proton, carbon, and BNCT) to beyond. J. Personal. Med. 11(8), 825 (2021) 5. Sakurai, Y., Tanaka, H., Takata, T., et al.: Advances in boron neutron capture therapy (BNCT) at Kyoto University - from reactor-based BNCT to accelerator-based BNCT. J. Korean Phys. Soc. 67, 76–81 (2015) 6. Suzuki, M.: Boron neutron capture therapy (BNCT): a unique role in radiotherapy with a view to entering the accelerator-based BNCT era. Int. J. Clin. Oncol. 25(1), 43–50 (2019). https://doi.org/10.1007/s10147-019-01480-4 7. Chen, J.: Fundamentals of Accelerator Physics, pp. 50–101. Peking University Press (2012). (in Chinese) 8. Tanaka, H.: [Current Status of Accelerator-Based Boron Neutron Capture Therapy (BNCT)]. Igaku Butsuri: Nihon Igaku Butsuri Gakkai Kikanshi = Jpn. J. Med. Phys. J. Jpn. Soc. Med. Phys. 41(3), 117–121 (2021) 9. Qi, D., Wang, N.: Practical Power Supply Technical Manual: Special Power Supply Volume. Liaoning Science and Technology Press (2005). (in Chinese) 10. Luo, J., Chen, X.: Design of a high power voltage doubler rectifier circuit. Electron. Testing 36(21), 20–22 (2022). (in Chinese) 11. Liu, Z., Liou, J.J., Vinson, J.: Novel silicon-controlled rectifier (SCR) for high-voltage electrostatic discharge (ESD) applications. IEEE Electron. Device Lett. 29(7), 753–755 (2008) 12. Zeng, S.: Design of high frequency oscillator and comparative experimental study on its stability. Electron. Qual. 2012(10), 64–67+74 (2012). (in Chinese) 13. Chen, B., Li, L., Liu, H., Lu, Z., Wang, Z.: Calculation and analysis of high frequency transformer leakage inductance and winding loss based on finite element method. New Technol. Electric. Eng. Energy 37(01), 8–14 (2018). (in Chinese) 14. Department of Physics, Tianjin Normal University High Voltage Silicon Stack Technology, pp. 242–250. National Defense Industry Press (1977). (in Chinese) 15. Zhang, R., Chen, C., Wang, C.: High Voltage Test Technology, pp. 59–66. Tsinghua University Press (2009). (in Chinese)

Research on the Control of Optical-Storage Grid-Connected Technology Based on Virtual Synchronous Generator Jingxiu Li(B) , Hongsheng Su, and Xin Mao School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China [email protected]

Abstract. In order to improve penetration rate of new energy on-grid power generation, reduce carbon emissions, promote energy security and environmental protection, and solve the power quality problems caused by frequency and voltage fluctuations in photovoltaic on-grid power generation, the paper uses Voltagecontrolled Virtual Synchronous Generator (VVSG) technology to control gridconnected inverters, which can enable photovoltaic grid-connected power generation to actively take part in the frequency and voltage regulation of power grid, meanwhile it can making the operation of the power system more secure and stable. In the paper, combined with the characteristics for photovoltaic power generation system, a hybrid energy storage link is added, it is used to stabilize DC bus voltage and perform peak shaving and valley filling, set a VVSG mathematical model, and this control strategies of each part, active power-frequency control and reactive power-voltage control are analyzed. Finally, this effectiveness of control strategy is verified by establishing a simulation model in Matlab/Simulink. Keywords: Photovoltaic power generation · Virtual synchronous generator · Grid-connected inverter · Energy storage module

1 Introduction Gradual emphasis on environmental protection worldwide and increasing depletion of fossil energy have promoted the rapid development of renewable energy power generation technology. With the increasing proportion of photovoltaic and other renewable energy power generation in power supply structure, its impact power system planning and operation is becoming more and more obvious [1]. However, the large-scale access of photovoltaic power generation will have impact on the power quality of this system due to its uncertainty. To this end, domestic and foreign scholars have proposed a virtual synchronous generator (VSG) technology. VSG technology is mainly divided into two categories: current control type and voltage control type, but the current control type can operate stably in the large power grid, and the requirements for the power grid are high. Reference [2] proposed a voltage-type VSG control algorithm, which introduces © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 98–106, 2024. https://doi.org/10.1007/978-981-97-1064-5_10

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this mechanical equation and the electromagnetic equation into the synchronous generator (SG) control strategy, and can completely simulate the external characteristics of the SG. Reference [3], that energy storage is introduced to the photovoltaic power generation system, and this dynamic response of the energy storage is used to realize the primary frequency modulation, so that VSG has frequency modulation ability similar to the SG. Reference [4] proposed a control algorithm for the coordination of photovoltaic VSG with battery energy storage and hydropower. Based on the above research, this paper chooses, PV and Energy Storage Module are connected into common DC link through DC/DC converters [5]. Then the same inverter is used for grid connection, and the boost part of the photovoltaic module is controlled by maximum power point tracking (MPPT) [6]. So hybrid energy storage module of lithium ion battery and super capacitor is selected to provide inertial support for VVSG. In paper, the second-order mathematical model VVSG is established, control structure of VVSG is analyzed, and the control strategies of each part are introduced. Finally, the system model is built on the Matlab/Simulink platform and this simulation analysis is carried out to prove this effectiveness of VVSG control strategy.

2 Topology of Photovoltaic and Hybrid Energy Storage On-Grid Power Generation This topology of photovoltaics and hybrid energy storage on-grid power generation system used in this paper (see Fig. 1). System is mainly composed of photovoltaic array, battery, super capacitor, boost circuit, DC/DC bidirectional converter, inverter and so on. The main implementation ideas are as follows: The power generated by the photovoltaic array is incorporated to DC bus through the boost circuit. Since the output characteristics of the photovoltaic array are affected by factors such as light intensity and temperature, MPPT control is required to improve the efficiency of photovoltaic power generation [7]. Similarly, the battery and super capacitor as an energy storage module are connected to this DC bus through the DC/DC bidirectional converter to complete mutual exchange and storage of energy. It plays a role in stabilizing the DC bus voltage and also provides inertial support for VVSG. After that, the electric energy collected in the DC bus is connected into the grid by the DC/AC inverter or used by the load near the step-down direct power supply station. The DC/AC inverter adopts VVSG control, which enables the photovoltaic and hybrid energy storage system to operate according to the external characteristics of the SG, that is, it has inertia and damping characteristics to improve the stability of the system.

3 Control Structure and Mathematical Model of VVSG For VVSG, it’s necessary to simulate rotor motion equation and stator electrical equation of the traditional synchronous generator SG through this control strategy, and the technology we choose is to control the DC/AC inverter by implanting the VVSG strategy of SG characteristics, and to provide reserve capacity and inertia support through the energy storage module, so that inverter can simulate this rotational inertia and damping characteristics of SG, thus ensuring the frequency and voltage of the power grid to remain stable.

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Fig. 1. Topology of photovoltaic and hybrid energy storage on-grid power generation

The control structure of VVSG (see Fig. 2). The implementation process of control algorithm is as follows. Firstly, the power is calculated by measuring the voltage and current incorporated into the front end of the grid. Secondly, the frequency and voltage reference value are obtained according to active-frequency, reactive-voltage control algorithms. Finally, PWM modulation wave is obtained by the VVSG control algorithm and the voltage and current loop control, this PWM pulse waveform is modulated by one signal to act on the inverter [8], this inverter has on-grid characteristics of SG. For the convenience of research, we make the following assumptions for the mathematical model of synchronous generator. (1) Three-phase synchronous generator with non-salient pole machine is used to avoid asymmetry. (2) The number of selected poles is 1, that is, there is only one pair of rotor poles. (3) The iron core is an ideal iron core, the change of magnetic field will not be subject to any restrictions or energy loss. (4) Ignore the damping effect of the rotor in the stop or static state.

34 U

Eref ref

Fig. 2. Control structure of VVSG

Qref Pref

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Based on the above assumptions, a damping term is added to the rotor motion equation for the synchronous generator to simulate this damping effect of rotor during rotation. The obtained VVSG rotor motion equation is as follows. ⎧ dω ⎪ = Tm − Te − D(ω − ω0 ) ⎨J dt ⎪ ⎩ dδ = ω − ω 0 dt

(1)

In the above formula, Tm is mechanical torque, N · m; Te is electromagnetic torque, N · m; D is generator damping coefficient, N · m · s/rad ; J is moment of inertia, kg/m2 , ω 为 actual angular velocity, rad /s; ω0 is grid synchronous angular velocity, rad /s; δ is power angle, rad . Based on stator equation of synchronous generator, the electrical equation of VVSG stator is established as follows. E˙ = U˙ + I˙ (R + jX )

(2)

In the above formula, E˙ is VSG virtual stator potential, U˙ is terminal voltage of the inverter, I˙ is virtual armature current, R is virtual resistance, X is virtual impedance of the stator. Its substance is to imitate one motion equation of SG in basis of this traditional droop control and add virtual inertia time constant J and damping coefficient D [9], this inverter has the inertia and damping of SG, which improves the frequency and voltage regulation ability of the power grid to some extent. For make the photovoltaic power generation system have characteristics of simulated inertia, it’s necessary to adjust the energy storage module to provide the system with the active power necessary for frequency modulation.

4 Control Strategy Analysis of Optical Storage Grid-Connected VSG 4.1 Photovoltaic Power Generation Part Photovoltaic power generation is to convert light energy into electric energy, and the boost circuit selects the Boost circuit. In order to realize the MPPT control of the photovoltaic power supply, the perturbation observation method is selected to get the maximum power point. The basic principle of MPPT control algorithm is to monitor the voltage and current of this input energy system in real time. Through the control algorithm, the working voltage changes in the direction of this maximum power that photovoltaic array may output. The duty cycle is changed to change the equivalent input impedance, so that it can output the maximum power as much as possible and improve the energy conversion efficiency [10]. The disturbance observation method used in the paper is as follows: if the power at time k is equal to the power at time k-1, then return, do not execute any command, if not equal, judge whether the power at time k is greater than the power at time k-1, if greater, judge whether this voltage at time k is greater than voltage at time

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k-1; if it is greater than, the voltage is increased, if it is less than, the voltage is reduced; if it is less than, it is also judged whether voltage at time k is greater than voltage at time k-1. If it is greater than, the voltage is reduced. If it is less than, the voltage is increased, and then the maximum power point tracking is realized. The system operating point is adjusted in real time to make it close to this point, and conversion efficiency of solar energy is maximized. Finally, the PWM modulation technology is used to change the duty cycle to change the equivalent input impedance to match the photovoltaic equivalent output impedance to achieve maximum power output. 4.2 Energy Storage Part When output power of photovoltaic power generation or other load changes abruptly, the inertia required by the VSG grid-connected system in the frequency modulation process is provided by special energy storage unit. Energy storage part needs to be connected to DC bus through one DC/DC bidirectional converter to achieve bidirectional flow of energy. When this converter works in Boost mode, electric energy flows from the energy storage unit to the grid. When the converter works in Buck mode, electric energy flows from the grid to the energy storage unit. Choosing a hybrid energy storage system can overcome this limitations of a single energy storage system and achieve more efficient, reliable and sustainable energy storage under different needs and conditions, helping to balance the load and demand of the power system and provide a stable energy supply. At the same time, the energy storage and release rate can be adjusted in light of needs of power grid, so as to meet the peak demand and frequency regulation of this power system. By pairing and coordinating multiple energy storage technologies, more efficient, stable and sustainable energy management can be achieved. At the same time, the energy storage unit also acts in stabilizing DC bus voltage, so that DC side of front stage of this grid-connected inverter can output the DC voltage that meets the requirements. In addition, this energy storage unit also acts in a stabilizing and buffering between the photovoltaic power and the grid-connected power of the inverter. 4.3 Reactive Power Voltage Control Traditional synchronous generator changes the reactive power output of this generator by adjusting the excitation current or excitation voltage. Similarly, the reactive powervoltage control link of VVSG can simulate the excitation link of the SG, and adjust output voltage and reactive power by adjusting this virtual excitation electromotive force E in the VVSG, thus reflecting the reactive power droop characteristics, which can achieve dynamic load balancing. The reactive power-voltage droop characteristic expression of the VVSG is as follows.   (3) E = Eref + DQ QN − Qsj In the above formula, E is virtual potential, Eref is reference value of the potential, DQ is reactive power-voltage droop coefficient, QN is set value of the reactive power, and Qsj is actual measured value of the reactive power.

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4.4 Active Power Frequency Control Similar to reactive power-voltage control, for meet governor characteristics of traditional synchronous generators, active-frequency control link of VVSG can simulate the droop characteristics of synchronous generator governors [11], which can maintain frequency stability in the power system. The active-frequency droop characteristics of VVSG are expressed as follows.   (4) P = Pref + DP ωN − ωsj In the above formula, P is active power of VVSG, Pref is reference value of active power, DP is active-frequency droop coefficient, ωN is set value of angular velocity, ωsj is actual measured value of angular velocity. 4.5 Reference Signal Synthesis and Current Closed-Loop Control After the VSG generates the power angle offset δ in the active frequency control loop and obtains that virtual excitation electromotive force E in reactive voltage control loop, it is necessary to synthesize that two reference signals to obtain the three-phase reference current signal iref , it is input into the current loop to obtain the reference voltage signal. Finally, the PWM modulation signal generator is used to obtain the trigger pulse of the three-phase inverter [12]. The traditional PI controller can be used in the inverter control system based on the rotating coordinate system design, which can realize the step response without static error tracking. However, for the inverter designed in the stationary coordinate system, it cannot meet the requirements of no static error tracking of the AC signal. Since the PI controller is a first-order controller, the open-loop gain at the fundamental frequency of the grid is limited, which will lead to steady-state error of the system. The steady-state error will cause one phase error between output voltage and current of this inverter and grid voltage and current, which will affect the output power factor and efficiency of this inverter. In stationary coordinate system, the PR controller can adjust AC signal without static error. However, in practical applications, when the grid voltage is disturbed and the non-resonant frequency is generated, the harmonic suppression effect in the grid is not good due to the low gain value of the oscillation term [13]. Therefore, in the current loop of the system, we choose the quasi proportional resonant (PR) controller, whose transfer function is as follows. GZHPR (S) = kp +

2ki ωjz s s2

+ 2ωjz s + ω02

(5)

In the above formula, kp is proportional coefficient of the PR controller, ki is integral coefficient, ωjz is cut-off frequency of first-order low-pass filter, ω0 is fundamental angular frequency of the grid current. The influence of the above parameters on the system is analyzed as follows. With the increase of the proportional coefficient kp in the PR controller, this anti-interference ability of the system is stronger, but it cannot be too large, and it is easy to cause the system to oscillate. With the increase of the integral coefficient kj , he greater the gain

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of the system, the smaller the steady-state error, but the excessive gain will make the harmonic component appear in the system, thus affecting the power quality. With the increase of ωjz , the gain and bandwidth at the non-fundamental frequency will increase, but too large will lead to signal distortion or response delay. Through the analysis of the above parameters, it can be seen that the design of the parameters is not the bigger the better. The optimal solution should be designed according to the specific system, so that the system works in the best state.

5 Experimental Verification and Analysis For verify this correctness of adding hybrid energy storage and adopting VVSG control in photovoltaic power generation system, this paper uses Matlab/Simulink simulation platform to set up the energy storage system model of the control strategy (see Fig. 2). The energy storage system is a combination of lithium ion battery and super capacitor. The capacity of lithium ion battery is 5000 Ah, initial state of charge is 80%, and the super capacitor is two 100 F in parallel. The other main parameters of this system are shown in Table 1. Table 1. Parameters of energy storage system parameter

description

Value

R/ 

resistance

3

Lf /H

inductance

0.05

Cf /F

super capacitor

100

Udc /V

DC bus voltage

2000

The simulation waveform of the optical storage grid-connected power generation system when the given conditions change (see Fig. 3). In the optical storage grid-connected power generation system, we set the illumination from 1000 to 900 at 2 s. After one second, the illumination is changed back to 1000 at 3 s. The active power setting value of VVSG is changed from 150 kW to 140 kW at 4 s, and the active power setting value is changed from 150 kW to 140 kW at 5 s. The simulation time is 6 s. Assuming that the ambient temperature is constant during this period, the lithium-ion battery is controlled at constant power. By analyzing this above diagram, it can be seen that when active power setting value changes, the active power required for the system output can be provided by the super capacitor when the photovoltaic panel cannot generate multiple power; when the light changes, the photovoltaic panel cannot provide the active power required by the system, the super capacitor can also have multiple active power to suppress the influence caused by the light change. The use of hybrid energy storage can make up for the shortcomings of single energy storage components. Lithium-ion batteries are used as energy-type energy storage, and supercapacitors are used as power-type energy storage. Because the model established in the paper doesn’t consider the power distribution between lithium-ion batteries and supercapacitors, the simulation results are not perfect.

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Fig. 3. Waveform diagram of output active power

6 Conclusions and Prospects This paper introduces the topology of VVSG from the theoretical level, establishes the second-order mathematical model of VVSG, and introduces the control strategies about photovoltaic power generation module, energy storage part, reactive power-voltage, active power-frequency and reference voltage synthesis. Finally, one simulation model is built in Matlab/Simulink to verify effectiveness of this control strategy. However, the simulation model established in this paper does not consider the power distribution of lithium-ion battery and supercapacitor module in the face of system fluctuation, so this part can be further studied in the follow-up work.

References 1. Lu, S., Zhou, B., Rao, H., Zhao, W., Yao, W.: Discussion on the structure of China’s long-term power supply under the condition of high proportion of grid-connected photovoltaic power generation. Chin. J. Electric. Eng. S1, 39–44 (2018). (in Chinese) 2. Zhong, Q., Weiss, G.: Synchronverters: inverters that mimic synchronous generators. IEEE Trans. Indust. Electron. 58(4), 1259–1267 (2011) 3. Loix, T.: Participation of Inverter-Connected Distributed Energy Resources in Grid Voltage Control. Katholieke Universiteit, Leuven (2011) 4. Shi, R., Zhang, X., Xu, H., Liu, F., Hu, C., Yu, Y.: Operation control strategy of multienergy complementary isolated microgrid based on virtual synchronous generator. Power Syst. Automat. 18, 32–40 (2016). (in Chinese) 5. Sang, W., Guo, W., Dai, Sh., Tian, Ch., Yu, S., Teng, Yu.: Virtual synchronous generator, a comprehensive overview. Energies (17), 15 (2022) 6. Zhang, Y., Han, M.: Microgrid Inverter control strategy based on virtual synchronous generator. J. Phys. Conf. Ser. (1), 2290 (2022) 7. Ren, Z., Lu, B., Zhao, Y., Liu, X., Zhang, R., Sun, L.: Research on modeling and simulation of photovoltaic virtual synchronous generator. Power Syst. Protect. Control 13, 92–99 (2019). (in Chinese)

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8. Deng, W., Zhong, J., Huang, M., Zhang, J., Zhang, Zh.: Adaptive control strategy with threshold of virtual inertia and virtual damping for virtual synchronous generator. J. Phys.: Conf. Ser. (1), 2203 (2022) 9. Ling, Y., Ruan, Y.: Adaptive control of grid connected inverter based on virtual synchronous machine. J. Phys.: Conf. Ser. (5), 1549 (2020) 10. Chen, W.: Research on Grid-Connected Power Generation Control Technology of Optical Storage Based on Virtual Synchronous Generator. Zhengzhou University (2019). (in Chinese) 11. Zhu, H., Yuan, Sh., Li, Ch.: Control strategy and analysis of virtual synchronous generator in photovoltaic power station with energy storage. Electric. Measur. Instrum. (05), 45–50 (2023). (in Chinese) 12. Xu, J.: Research on Control of Distributed Photovoltaic Power Generation System Based on VSG. Nanchang University (2021). (in Chinese) 13. Liu, Q., Gong, L., Zhang, X.: Research on three-phase photovoltaic grid-connected inverter based on quasi-PR control. J. Hubei Univ. Technol. (01), 12–14+22 (2015). (in Chinese)

Influence of Rock Inclination on the Relaxation and Deformation of the Surrounding Rock in Underground Chambers Xi Chen1 , Lan Jiang2 , Rongtian Zhang2 , and Bo Tang2(B) 1 Economic and Technical Research Institute of State Grid Hubei Electric Power Co,

Wuhan 430000, China 2 College of Electrical and New Energy, China Three Gorges University, Yichang 443002, China

[email protected]

Abstract. In this paper, a generalized model of underground refuge is established with the size of a typical pumped storage power plant, and the values of rock parameters, contact surface parameters, stresses and boundary conditions are determined in the surrounding layers of the model. In order to analyze the influence of rock dip angles on the relaxation and deformation of underground caverns, we conducted numerical simulations on ten different rock dip angles. Comparison analysis of the deformation displacement and relaxation deformation characteristics of the surrounding rock under ten different inclination angles of rock formations is carried out, and the influence of the inclination angle of rock formations on the relaxation deformation of underground chambers is concluded. Keywords: rock inclination · relaxation deformation · surrounding rock · underground chamber

1 Introduction Energy is the foundation and driving force of a country’s economic development, as well as a fundamental material necessary for people’s daily lives [1]. With the continuous development of society and economy, people’s demand for energy is also increasing. In this context, the application value of pumped storage technology has been widely recognized and valued. Pumped storage energy is currently the most technologically mature, economically optimal, and capable of large-scale development in the power system [2, 3]. It is a green, low-carbon, clean, and flexible regulating power source, and has good coordination effects with wind power, solar power generation, nuclear power, thermal power, etc. Accelerating the development of pumped storage energy is an urgent requirement for building a new type of power system with new energy as the main body, and an important guarantee for the large-scale development of renewable energy [4]. The large-span, high-sided wall underground chamber is the main or key control project of pumped storage power plant construction, which occupies an increasingly important position in China’s infrastructure construction and resource development, and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 107–113, 2024. https://doi.org/10.1007/978-981-97-1064-5_11

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the safety of its construction is related to the overall safety of major national projects [5]. Compared with conventional water conservancy and hydropower projects, the safe construction of large-span, highwall underground chambers in pumped storage power plants has always been an issue of concern in the industry [6]. During the excavation of large-span, highwall underground chambers, the damage and deformation of the surrounding rock and the main control factors have a great impact on the stability and safety of the chamber. Many engineering cases have shown that the relaxation and deformation characteristics of the surrounding rock after the excavation of the chamber are significantly affected by the inclination and orientation of the rock layer. Therefore, we need to conduct in-depth research on the influence of rock inclination angle on the relaxation deformation of surrounding rock in underground caverns [7, 8].

2 Probabilistic Model and Calculation Parameters for Underground Chambers 2.1 Probabilistic Model of an Underground Chamber Figure 1 based on the size of the underground powerhouse of a typical pumped storage power plant, a simulation model of the underground cavern was established. The overall parameters of the model are 200 m (length) × 200 m (width) × 2 m (thickness), and the dimensions of the underground plant are 58 m (height) × 26 m (width).

Fig. 1. Simulation model

2.2 Numerical Calculation Parameters The numerical calculations are analyzed using the Moore-Cullen elastic-plastic model for the intra-layer rock mass, and the Cullen contact model for the inter-layer structural surfaces Tables 1 and 2 show the values of the numerical calculation parameters. 2.3 Initial Ground Stress and Boundary Conditions The self weight stress field is the initial geostress field of the model, and the horizontal and vertical lateral pressure coefficients take the average value of 0.5; the buried depth

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Table 1. Values of rock parameters taken in the layer Density of rock (Kg/m3 )

Modulus of elasticity (GPa)

Poisson’s ratio

Angle of internal friction (°)

cohesive force (MPa)

Tensile strength (MPa)

2500.0

28.0

0.20

50.0

1.0

1.5

Table 2. Parameter values of interlayer contact surfaces Normal contact stiffness (GPa)

Tangential contact stiffness (GPa)

friction angle (°)

cohesive force (MPa)

tensile strength (MPa)

8.0

6.0

30.0

0.2

0.2

of the underground plant is 300 m, and in the numerical calculations, uniform stress is applied at the top to simulate the overlying rock body, and the other boundaries are fixed constraints [9].

3 Influence of Different Inclination Angles on the Relaxation and Deformation of the Surrounding Rock in Underground Chambers 3.1 Design of Rock Dip In order to analyze the effect of rock inclination on the relaxation and deformation of the surrounding rock in the underground chamber, the numerical simulation was divided into time, and the numerical calculation models were established for different rock inclination angles, which are shown in Fig. 2, where the different rock inclination angles were set to be 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, and 90°, and the spacing of the rock layers was 4 m. The numerical calculations were carried out in order to analyze the effect of rock inclination on the relaxation and deformation of the surrounding rock. 3.2 Comparative Analysis of Deformation and Displacement of Surrounding Rocks Figure 3 shows the deformation and displacement of the perimeter rock after the excavation of the refuge at different inclination angles [10, 11]. From this figure, it can be seen by comparing the deformation maps of the perimeter rock after the excavation of the chamber under different rock inclination angles that the left and right sides of the chamber showed a symmetric distribution after the excavation under the rock inclination angles of 0° and 90°; whereas, the deformation maps of the left and right side walls of the chamber under other inclination angles showed an asymmetric distribution, and the

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Rock dip 0°

Rock dip 50°

Rock dip 10°

Rock dip 20°

Rock dip 30°

Rock dip 40°

Rock dip 60°

Rock dip 70°

Rock dip 80°

Rock dip 90°

Fig. 2. Model of laminated rock mass at different rock dip angles

maximum deformation was located at the top part of the chamber after excavation under the rock inclination angle of 40° and less than 40°. When the inclination angle of the rock layer is less than or equal to 40°, the largest part of the enclosing rock deformation is located at the top of the chamber, and when the inclination angle of the rock layer is greater than 40°, the largest part of the enclosing rock deformation is located at the side wall after excavation.

Rock dip 0°

Rock dip 10°

Rock dip 20°

Rock dip 30°

Rock dip 40°

Rock dip 50°

Rock dip 60°

Rock dip 70°

Rock dip 80°

Rock dip 90°

Fig. 3. Deformation and displacement of surrounding rock

Figure 4 shows the relationship between the maximum deformation of the surrounding rock and the inclination angle of the rock layer after the excavation of the chamber. From the following figure, it can be seen that when the inclination angle is within 30°, the change of the inclination angle of the rock layer does not have much influence on the maximum deformation of the perimeter rock after excavation, but when the inclination angle of the rock layer is more than 30°, with the change of the inclination angle of the

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rock layer, the maximum deformation of the perimeter rock after excavation shows a tendency of increasing and then decreasing, and the maximum deformation of the perimeter rock after excavation reaches the maximum when the inclination angle reaches 60°.

Fig. 4. Variation curve of maximum deformation versus rock dip

3.3 Comparative Analysis of Contact States at Rock Level Figure 5 shows the change of rock face contact state after excavation at different rock inclinations. From this figure, it can be seen by comparing the changes in the contact state of the rock face at different inclination angles, that at different inclination angles, the rock face around the chamber underwent a certain amount of slippage and tensile damage, and the surrounding rock showed relaxation and deformation characteristics, and the relaxation and deformation characteristics of the surrounding rock at different inclination angles showed obvious differences. Specifically, at 0° and 90°, the relaxation deformation of the perimeter rock in the chamber was symmetrically distributed, while at other inclinations, the relaxation deformation of the perimeter rock around the chamber was asymmetrically distributed due to the inclination of the formation, and the distribution of the relaxation zones shifted as the inclination of the formation changed. In addition, by comparing the relaxation range of the surrounding rock at different inclination angles, it can be seen that the depth of relaxation of the surrounding rock on the left and right side walls reaches the maximum when the inclination angle of the rock formation is 60°. 3.4 Comparative Analysis of Relaxation and Deformation of Surrounding Rock In order to further study the influence of rock dip angle on the relaxation deformation characteristics of surrounding rock, the relaxation and deformation characteristics of the surrounding rock under different rock inclination angles are given in Table 3. From the table, it can be seen that with the change of rock inclination angle, the relaxation depth range of the rock body after excavation shows the trend of increasing and then decreasing, and the relaxation depth range reaches the maximum when the rock inclination angle is 60°, which is about 9–10 times the thickness of the rock layer.

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Rock dip 0°

Rock dip 10°

Rock dip 20°

Rock dip 30°

Rock dip 40°

Rock dip 50°

Rock dip 60°

Rock dip 70°

Rock dip 80°

Rock dip 90°

Fig. 5. Changes in horizontal contact state of rock layers with different rock dip angles

Table 3. Depth of damage to the structural surface of the surrounding rock at different rock dip angles Dip of rock layer

Major rock relaxation sites

Relaxation depth range

0°

Top arch, base plate

1–2 times the thickness of the rock formation

10°

Right side top arch, left side wall, base plate

1–2 times the thickness of the rock formation

20°

Right side top arch, left side wall, base plate

2–3 times the thickness of the rock formation

30°

Right side top arch, left side wall, base plate

3–4 times the thickness of the rock formation

40°

Right top arch, left side wall, right 5–6 times the thickness of the rock side wall formation

50°

Right top arch, left side wall, right 7–8 times the thickness of the rock side wall formation

60°

Right top arch, left side wall, right 9–10 times the thickness of the rock side wall formation

70°

Left side wall, right side wall

8–9 times the thickness of the rock formation

80°

Left side wall, right side wall

5–6 times the thickness of the rock formation

90°

Left side wall, right side wall

1–2 times the thickness of the rock formation

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4 Conclusion By comparing the numerical simulation results of different rock inclination angles, it is found that, in general, with the change of rock inclination angle, the relaxation depth range of the rock body after excavation shows a tendency of increasing and then decreasing; under the same conditions, when the inclination angle of the rock layer is 60°, the relaxation depth range reaches the maximum, and it is about 9–10 times of the thickness of the rock layer; when the inclination angle of the rock layer is 0°–20°, the maximum deformation and the distribution of damage to rock structural surface after excavation mainly appear in the top of the arch and the arch waist; when the inclination angle of the rock layer is 90°, the side wall part of the deformation is the largest, and should pay attention to the instability damage of the side wall rock layer. Acknowledgments. This work was funded by the State Grid Corporation Headquarters Management Science and Technology Project (Name: Research on Key Technologies for Intelligent Construction of Underground Plants of Pumped Storage Power Plants, No. 5200-202322135A-11-ZN).

References 1. Fengling, G., Hailong, S., Junfei, G., et al.: Effects of bedrock strata dip on soil infiltration capacity under different land use types in a karst trough valley of Southwest China. Catena 230, 107253 (2023) 2. Qiang, Z., Yanni, Z.: Geotechnical investigations and support design for an underground powerhouse of pumped-storage power station: a case study in Chongqing, China. Sustainability 14(14), 8481 (2022) 3. Wu, J., Zhang, X.Y., Yu, L.Y., et al.: Rockburst mechanism of rock mass with structural planes in underground chamber excavation. Eng. Failure Analys. 139, 106501 (2022) 4. Wang, D., Luo, J., Wen, S., et al.: Analysis of the influence of rock inclination on the stability of surrounding rock in laminar deviated tunnels. J. Beijing Jiaotong Univ. 46(03), 95–102 (2022). (in Chinese) 5. Wang, S.: Stability analysis of surrounding rocks in water diversion tunnels with stratified rock bodies and refinement of structural surface yield scores in grading. Lanzhou Jiaotong Univ. (2022). https://doi.org/10.27205/d.cnki.gltec.2022.000359.(inChinese) 6. Huang, M., Niu, Q., Fu, T., et al.: Influence of rock inclination on deformation characteristics of schist tunnels. Shanxi Construct. 48(01), 134–136 (2022). https://doi.org/10.13719/j.cnki. 1009-6825.2022.01.042. (in Chinese) 7. Mirenkov, E.V.: Deformation of rock mass in the vicinity of underground opening at great depth. J. Mining Sci. 57(3), 380–385 (2021) 8. Wang, Z., Li, Z., Xu, H., et al.: Investigation on the influence of inclination angle on the stability of surrounding rock in soil-sand interbedded strata. J. Railway Eng. 36(09), 54–59+84 (2019). (in Chinese) 9. Zhao, Z., Chen, J., Hu, G., et al.: Influence of the relationship between rock inclination and tunnel strike on the stability of surrounding rock in large section tunnels. Highway Vehicle Transp. 05, 190–194 (2014). (in Chinese) 10. Nan, Y.: Analysis on surrounding rock mass plastic zone of deep underground chamber based on Hoek-Brown criterion. Adv. Mater. Res. 838–841, 741–746 (2013) 11. Zhao, L.: Optimal design of safety monitoring system for underground plant of pumped storage power station. Inner Mongolia Power Technol. 37(06), 67–70 (2019). (in Chinese)

Impact Analysis of Multiple Electro-mechanical Actuators on More Electric Aircraft Power System Chang Cai and Xinran Zhang(B) School of Automation Science and Electrical Engineering, Beihang University, Beijing, China {caichang,zhangxr07}@buaa.edu.cn

Abstract. More Electric Aircraft (MEA) will drive sustainable development in the aviation industry, reducing environmental pollution and noise. ElectroMechanical Actuators (EMAs) can carry out tasks such as rudder deflection and have great influence on the MEA power system, especially when multiple EMAs act together. However, most previous research focused on the enhancement of EMA performance or the input characteristics of a single EMA, in which the impact of multiple actuators working together on the power system has not been touched. In this article, an MEA power system model with multiple EMAs is built and the impact of multiple EMAs on power system stability is analyzed. Firstly, the functions of different EMAs are reviewed and the working scenes of multiple cooperative EMAs are designed. Afterward, the control schemes of speedcontrolled and position-controlled EMAs are studied, after which the power system model, including generators, uncontrolled rectifiers, and EMAs, is built. Finally, the impact of EMAs on MEA power system stability is simulated in Simulink. The results show that speed-controlled EMA impacts the power system just when the command target changes and lasts for a relatively short period of time. In addition, position-controlled EMA continuously impacts the power system. To conclude, EMAs may cause significant voltage fluctuations in the power system and should be addressed by implementing control methods involving supercapacitors and batteries. Keywords: more electric aircraft · electro-mechanical actuator · power system stability

1 Introduction A significant increase in the aircraft market in the coming decades has already been shown in the market forecast, which will cause a challenge in controlling greenhouse gas (GHG) emissions. Narrow-body aircraft, such as the Boeing 737, is responsible for 43% of aviation GHG while wide-body aircraft, such as Boeing 787, is responsible for 33%. The total aviation GHG was responsible for about 2.4% of all GHG emissions in the United States in 2018 [1]. More electric aircraft (MEA), which aims at replacing most of the major systems with new electrical power systems, is a promising way to © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 114–126, 2024. https://doi.org/10.1007/978-981-97-1064-5_12

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solve the problem. MEA uses less carbon-based fuels, thus resulting in less GHG and NOx emissions [2]. In addition, MEA has a lower weight, better efficiency, and lower noise than traditional aircraft [3]. The advancement of aircraft technology, particularly in range, speed, and control, has resulted in more complex onboard systems. Consequently, maintaining hydraulic and pneumatic systems has become more expensive due to the need to check long, complex, heavy pipes and ducts running throughout the plane. Electro-mechanical actuator (EMA) is an important part of MEA. Due to the replacement of traditional hydraulic and pneumatic by electrical systems, MEA requires more actuators to achieve the required motion. EMA is typically composed of electric motors, power electronics-based control components, mechanical transmission modules, and fail-safe devices. A schematic diagram of the EMA mechanical mechanism is as Fig. 1. Compared with hydraulic and pneumatic systems, EMAs are easier to maintain and cost less. Meanwhile, it can reduce the weight and volume of the system while increasing the safety and reliability of the system [4].

Fig. 1. Structure of an EMA

Previously, EMAs have been utilized in aerospace to carry out non-critical functions that do not require much power. However, with the increasing application of MEA and the continuous and significant improvement in the readiness level of electric and electronic devices, it is now possible to apply EMAs for high-power and critical functions concerning safety [4], like flight control, landing gear, thrust vector control, nose-wheel steering, and brakes. EMA control methods can be divided into speed control and position control. Speed-controlled EMAs are used for landing gears extension or retraction and secondary flight surfaces. Position-controlled EMAs are typically used for primary flight surfaces, nose-wheel steering. The speed control system is a kind of constant power load, which has negative impedance characteristics and has a negative impact on the stable operation of the aviation power supply system [5]. In an MEA powered by a highvoltage DC power supply, the constant power load increases dramatically, which may cause resonance of the system current or voltage and result in severe harm. For the position-controlled EMAs, to control the flight surface influenced by the aerodynamic torque in the specified position, the motor of the EMA often switches back and forward, which brings a significant impact on the power system. In the actual operation of the aircraft, completing a flight control adjustment task may require multiple EMAs to move simultaneously, which further worsen the situation.

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In previous research, researchers have studied the impedance characteristics of multielectric aircraft powered by high-voltage DC power supplies and established a model of a single EMA. Wang analyzed the impedance characteristics of a brushless DC motor control system using the negative impedance compensation method and studied the effects of compensation parameters on power input impedance, voltage transients, and current transients [5]. Wei proposed a fast terminal sliding mode control strategy based on a multi-layer neural network, designed a controller with good parameter adaptation and disturbance rejection capability, and had higher tracking accuracy and faster response speed [6]. Zhang proposed a control strategy for electro-mechanical actuators based on deep reinforcement learning-PI control to improve their control performance [7]. Yan mentioned the input characteristics of EMA in the first and fourth quadrants of the UI coordinate system. This is a non-linear characteristic because EMA absorbs energy from the power source when it is operating and converts the mechanical energy stored in motion into electrical energy, and returns it to the power source when it is braking [8]. However, most previous research has focused on enhancing the performance of EMA, such as adjusting the time or the input characteristics of a single EMA, but lacked research on the impact of multiple EMAs working together on the power system. This article establishes models of multiple EMAs in an MEA, including speed-controlled and position-controlled EMAs. Three typical scenarios are set up: takeoff, steering, and landing in order to study the impact of the coordinated action of multiple EMAs on the power system in these situations. The rest of this paper is organized as follows. Section 2 explains the model of different EMA systems used in this paper and the actions of EMAs in the three scenes. Section 3 introduces the structure of an EMA as well as the control methods. Section 4 presents and analyzes the simulation results in Simulink, including the actions of EMAs and the power, voltage, and current results. Section 5 concludes the impact of EMA on the power system and offers directions for future research.

2 MEA Power System and EMAs In this article, EMAs are mainly used to drive the control surface to the designated position and also in landing gear deployment, retraction, and electric brakes. To study the impact of multiple EMAs on the power system, the EMAs are modeled in Simulink. Simulink provides various functions, such as integrated modules and writing particular device characteristic equations. The entire system consists of a brushless DC generator, an uncontrolled rectifier, and various EMAs. Among the EMAs, both position-controlled and speed-controlled ones are included. For instance, primary flight control like rudders, ailerons, and elevators are position-controlled EMAs, while speed-controlled EMAs include flaps, spoilers, air brakes, and landing gears. The structure of the MEA power system is given in Fig. 2. As a typical and famous MEA, the airbus A380 has four generators with an output power of 150 kVA each, providing a total power of 600 kW. The main electrical equipment includes the avionics system, lighting, cabin pressurization, air conditioning, de-icing, flight control actuators, landing gears, air brakes, cabin doors, electric fuel pumps, and electric hydraulic pumps. These electrical types of equipment consume a

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large amount of power. According to the calculations based on the wing area and the deicing power demand per square meter for commercial airplanes, the total electric power demand for a 150-seat airplane can reach 180 kW, which is a considerable amount for all airplanes. As estimated, the power consumption of the actuators is around 100 kW. The flight control actuators used are marked in Fig. 3.

Aileron Elevator 270V DC Flight control BLDC Generater

Rudder Flap

AC/DC Air brake

BLDC Generater

Positioncontrolled EMAs

Spoiler

AC/DC

Speedcontrolled EMAs

Landing gears

Fig. 2. Structure of the MEA power system

To study the impact of multiple cooperative EMAs, three scenarios are designed: takeoff, steering, and landing. During the takeoff phase, the flaps of the aircraft are raised, which usually occurs with large aircraft or when fully loaded, as this can increase the lift of the aircraft. The landing gear retracts, and the elevator moves downward. During the steering phase, the rudder of the aircraft turns left, the left flap drops, and the right flap rises. During the landing phase, the spoiler rises, which can press the aircraft to the ground, stabilize the aircraft, and increase frictional force. The elevator moves upward, and the air brake is turned on. A summary of three typical scenes are given in Table 1.

Fig. 3. Flight control actuators of a typical MEA

3 Dynamics and Control of EMAs The dynamics of EMAs being multidisciplinary, coupled, and non-linear. As a result, it is significant to build accurate and effective models of EMAs for the research. An EMA usually comprises of an electric motor, power and control electronics, sensors, a mechanical transmission system, and fail-safe devices. The motor for aviation should be highly

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Type of EMA

Action Takeoff

Steering

Landing

Flaps (L/R)

+

0

0

Ailerons (L/R)

0

(±)

0

Elevator (L/R)

(+/+)

0

(−/−)

Spoiler (L/R)

0

0

(+/+)

Rudder

0

−

0

Landing gears (L/R)

−

0

+

Airbrake

0

0

+

efficient and thermally robust. Thus, it should have less weight and volume, otherwise more energy would be consumed. Benefited with higher efficiency, higher power density, and lower rotor heat production, Permanent Magnet Synchronous Machine (PMSM) is more suitable for aviation for this reason [9]. Although the production cost of PMSM is greater, it is still currently the most feasible solution for EMA on aircraft. The control scheme of a speed-controlled EMA is shown in Fig. 4. The control method here is the id = 0 control. The Simulink model of a speed-controlled EMA is shown in Fig. 5.

Fig. 4. The control scheme of a speed-controlled EMA

The speed-controlled EMAs will touch the limit after the motor drives the ball screw to the target position. Currently, the clutch between the motor and the screw will stop the screw from moving forward. Therefore, in the simulation, the control signal for the speed-controlled EMA is not a simple step signal. Instead, the motor speed is calculated and adjusted to 0 after the ball screw reaches the target position. For the ball screw XL = θr ∗ P

(1)

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F=

TL ∗ 2π p

119

(2)

where X L is the distance the ball screw extends, P is the lead of the ball screw, θ r is the motor rotation angle, T L is the load torque, and F is the ball screw output force.

Fig. 5. The model of a speed-controlled EMA in Simulink

The control scheme of a position-controlled EMA is shown in Fig. 6. The Simulink model of a position-controlled EMA is shown in Fig. 7. For position-controlled EMA, the control target is no longer the rotor rotation speed. Thus, this article selected the control target as the rudder deflection angle, as shown in Fig. 8. X L is the distance the ball screw extends, and r is the length of the rudder, following θ r = arctan(X L /r).

Fig. 6. The control scheme of a position-controlled EMA

4 Case Study 4.1 Simulation Environment and Timeline Firstly, the simulation environment is introduced. As shown in previous sections, the simulation model of the MEA power system is built in Simulink. The model of the whole MEA power system in Simulink is shown in Fig. 9, including two BLDC generators,

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Fig. 7. The model of a position-controlled EMA in Simulink

Fig. 8. Rudder deflection angle

Fig. 9. The model of the whole EMA power system in Simulink

power electronics converters and 12 different EMAs. The laptop to run the simulation tasks has a CPU of Intel i5-12500H and 16G RAM. The time step is 1e-6 s. Figure 10 shows the timeline in the simulation, including three phases, i.e. takeoff, steering, and landing. The takeoff phase starts at 0 s and ends at around 1 s in the simulation. At 0 s, the flaps, landing gears, and elevators get the control command and turn to the expected objectives, then the flaps and landing gears will reach their limits at about 0.6 s. The steering phase starts at around 1 s and ends at 2 s in the simulation. At 1 s, the ailerons and rudder turn on, and the control target of landing gears, elevators, and flaps are set to 0. The landing phase starts at 2 s and ends at 3 s in the simulation.

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Flaps Landing gears touch the limit

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Landing Elevators Spoilers Spoilers Landing gears Landing gears Airbrake Airbrake touch the limit turn on Ailerons Rudder turn to 0 2

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Fig. 10. Simulation timeline and three phases

At 2 s, the elevators, spoilers, landing gears, and air brakes get the command, and the ailerons and rudder control target are set to 0. The spoilers, landing gears, and air brake reach their limits 0.6 s later. 4.2 Mechanical Dynamics of the EMAs In this subsection, the mechanical dynamics of the EMAs, including rotation speed, rudder deflection angle and mechanical power, are given in the figures. The load torque of speed-controlled EMA is 8 N·m, the speed control target is ±2000 rpm. The load torque of position-controlled EMA is 15 N·m. Figure 11, Fig. 12, and Fig. 13 show the dynamic actions of different EMAs, including rotation speed signals and rudder deflection angle signals. The red line refers to the EMA’s actual speed or position, and the gray line refers to the reference values. From the figures, it can be observed that all the EMAs in the simulation successfully achieved the expected objectives.

Fig. 11. The rotation speed figures of landing gears and spoilers

Figure 14, Fig. 15, and Fig. 16 show the power signals of all the EMAs. From the figures, it can be observed that the impact of speed-controlled EMAs on the power

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Fig. 12. The rotation speed figures of flaps and air brake, and rudder deflection angle figure of rudder

Fig. 13. The rudder deflection angle figures of ailerons and elevators

of the system is manifested when receiving control commands and reaching the target position. In contrast, the impact of position-controlled EMAs on the system is continuous throughout. 4.3 Electrical Responses of the EMAs In this subsection, the electrical responses of the EMAs, including bus voltage, bus current, and bus power are shown in Fig. 17, Fig. 18, and Fig. 19. Several phenomena can be concluded from the results. Firstly, the peaks of the signals are discussed. From the results, it can be observed that the peaks of the power, voltage and current signals all occur at 0 s, 1.0 s, and 2.0 s. This is because of the command of the actuator changes at these time points. The peaks at 0.5 s and 2.5 s are because the speedcontrol EMAs reached their limits, which means the ball screw reaches the target and so

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Fig. 14. The mechanical power figures of landing gears and spoilers

Fig. 15. The mechanical power figures of ailerons and elevators

the control speed turned to 0. Secondly, the ability of whether the system to maintain its bus voltage, current and power stable is analyzed. The bus voltage is oscillating around 270 V because of the impact of the actuators. The maximal value of bus voltage is 281.4 V, while the minimal value is 247.8 V. As for the bus current signals, they keep fluctuating during the whole simulation process, which is caused by the position-controlled EMAs essentially. The maximal value of bus current is 400 A, while the minimal value is −182.5 A. As a result of the significant variations of bus voltage and current, the total active power of the whole system is also oscillating during the process. The maximal value is about 100 kW, and the minimal value is about −50 kW.

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Fig. 16. The mechanical power figures of rudder, air brake, and flaps

Fig. 17. The voltage figure of the bus

Fig. 18. The current figure of the bus

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Fig. 19. The power figure of the bus

4.4 Discussion From the simulation results, the impact of multiple EMAs on the power system is well demonstrated. The influence of speed-controlled EMA on the power system is evident when a control command is given and when it reaches its target position. On the other hand, the impact of position-controlled EMA on the power system is more frequent, almost constant throughout the flight process. The impact of position-controlled EMA on the power system is further reflected in the continuous fluctuation of its current, with the voltage oscillating around 270 V. This means that the fluctuations occur within the four quadrants of the U-I axis, with (270 V, 0 A) as the origin point. Another important point to note is the voltage fluctuation. In this simulation, the target voltage control is set at 270 V. However, the EMAs cause the voltage to reach a maximum of 281.4 V and a minimum of 247.8 V, resulting in a fluctuation of −22.3 V to 11.4 V. These fluctuations exceed the standard limit for aviation voltage fluctuation by a significant margin. In future studies, it is important to consider the utilization of batteries or supercapacitors for energy storage and help to maintain the bus voltage at 270 V, even during the operations of multiple EMAs [10]. This approach helps to mitigate the voltage fluctuations and maintain a reliable power supply in the system which is important in the future aircraft electrification process.

5 Conclusion In this article, the impact of multiple EMAs on MEA power system is analyzed. The model of the power system is firstly built, including generators, power electronics converters, and EMAs. Then, the impact of cooperative EMAs on the onboard power system is analyzed through simulation. The result of the simulation shows that the speedcontrolled EMAs give a pulse to the system when the command target change. In the contrary, the position-controlled EMAs continuously exert impact on the power system because the speeds of the motors are changing all the time. Consequently, it will cause the voltage and current of the EMA to run across the four quadrants in the U-I axis.

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Another phenomenon worth attention is the excessive fluctuations in bus voltage, which needs to be addressed in future research by implementing control methods involving energy storage systems. Acknowledgments. This paper was supported in part by the National Natural Science Foundation of China under Grant 52107066.

References 1. Graver, B., Zhang, K., Rutherford, D.: CO2 emissions from commercial aviation, 2018. In: The International Council on Clean Transportation, pp. 1–13 (2019) 2. Lukic, M., Giangrande, P., Hebala, A., Nuzzo, S., Galea, M.: Review, challenges, and future developments of electric taxiing systems. IEEE Trans. Transp. Electrific. 5(4), 1441–1457 (2019) 3. Schefer, H., Fauth, L., Kopp, T.H., Mallwitz, R., Friebe, J., Kurrat, M.: Discussion on electric power supply systems for all electric aircraft. IEEE Access 8, 84188–84216 (2020) 4. Qiao, G., et al.: A review of electromechanical actuators for more/all electric aircraft systems. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 232(22), 4128–4151 (2017) 5. Wang, N., Zhou, Y.: Impedance characteristics analysis of speed control system based on negative impedance compensation method. Chin. J. Electric. Eng. 33(33), 50–56+7 (2013). (in Chinese) 6. Wei, K., et al.: Neural network fast terminal sliding mode control of aerospace electromechanical actuators. J. Aviation 42(06), 116–125 (2021). (in Chinese) 7. Zhang, M., et al.: Based on deep reinforcement learning-PI control strategy for electromechanical actuator control. Appl. Sci. Technol. 49(04), 18–22 (2022). (in Chinese) 8. Yan, Y., et al.: Multi-electric airplanes and power electronics. J. Nanjing Univ. Aeronaut. Astronaut. 46(01), 11–18 (2014). (in Chinese) 9. Henke, M., et al.: Challenges and opportunities of very light high-performance electric drives for aviation. Energies 11(2), 344 (2018) 10. Wang, Z., Zhang, X.: Pulse power stabilizing technology based on combined control of hybrid energy storage systems and generator. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, pp. 1214–1219 (2023)

Study on Modeling of Electromagnetic-Thermal Multi-field Coupling of Rail Electromagnetic Launcher and Its Electromagnetic Field and Temperature Field Distribution Pengfei Lu, Luyao Liu, Hongshun Liu(B) , Yizhen Sui, Ruxue Zhao, and Hongbin Zhang Shandong Provincial Key Laboratory of UHV Transmission Technology and Equipment, Shandong University, Jinan 250061, China {202234720,202214621}@mail.sdu.edu.cn, [email protected]

Abstract. Electromagnetic launch technology is a kind of launch technology that uses electromagnetic force to propel an object to high speed or ultra-high speed, which has incomparable advantages over traditional launch methods in terms of launch speed, launch efficiency, controllability, concealment and cost. In order to solve the problem of low service life and low reuse rate caused by ablation damage of copper alloy slide rail in the practical process of rail electromagnetic launcher, an equivalent scaling model under electromagnetic thermal multi-field coupling is established in this paper, and the overall distribution of electromagnetic field and temperature field are simulated. It is concluded that the current density and magnetic induction intensity are concentrated in the armature groove and tail and around the contact point between the armature and the slide rail, and the heat is concentrated in the armature groove and the slide rail. These areas are where the electromagnetic launcher is prone to ablation damage. It provides the guidance for the manufacture and test of electromagnetic launcher. Keywords: Rail Electromagnetic Launch · Electromagnetic Thermal Multi-Field Coupling · Electromagnetic Field Distribution · Temperature Field Distribution

1 Introduction As a technology with broad application prospects, rail electromagnetic launch has the advantages of small size, sufficient power, low energy loss and so on [1]. With the proposal of the strategy of becoming a powerful country in science and technology, the application of this technology in the fields of scientific experiment, military, industry and transportation has become a research hotspot, but there exists the problem of arc ablation of copper alloy slide rail in the practical process. As a result, its service life and reuse rate are low [2].

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Therefore, the model of the rail electromagnetic launcher is established to observe the distribution characteristics of the electromagnetic-thermal field, which can determine the sites prone to ablation, and simulate the development law of armature and slide rail ablation during the launch process [3]. By analyzing the development of armature ablation in different launch stages, the influence of melting wave in slide rail armature on ablation damage can be obtained [4]. Based on the theoretical transition model of velocity skin effect and current wave phenomenon, the material failure caused by slide rail transition ablation can be studied [5]. According to the multi-physical field coupling model of rail gun established by interference fit module, thermal stress and temperature will reduce the mechanical properties of armature [6]. The track temperature distribution under transient conditions can be simulated by ANSYS Workbench. The results show that with the high-speed movement of the armature, the heat caused by friction increases and the heat of the contact part decreases [7]. The influence of Joule heat and friction heat on pivot rail’s temperature field and temperature’s influence on pivot rail’s damage state can be analyzed by ANSYS Workbench and Maxwell [8]. According to the above literature, the research on the modeling and ablation mechanism of electromagnetic launcher has been very detailed and mature, but it does not involve the coupling distribution of electromagnetic field and temperature field in the process of launch. The relationship between the characteristics of multi-field coupling distribution and ablation location still needs further research. In this paper, the electromagnetic-thermal coupling model of the rail electromagnetic launcher is established by using the 3D transient field module of Maxwell and the transient temperature field module of ANSYS Workbench, and then the electromagnetic field distribution and temperature field distribution during the launch process are simulated respectively. From this, it is analyzed that the areas where the current density, magnetic induction intensity and temperature of the launcher are concentrated are the places where ablation and other damage are easy to occur. It provides the guidance of simulation for the manufacture and test of electromagnetic launcher.

2 Establishment of Electromagnetic-Thermal Field Coupling Model of Rail Electromagnetic Launcher 2.1 Geometric Modeling The rail electromagnetic launcher is mainly composed of two slide rails, an armature and a pulse power supply. In order to reduce the complexity of establishing the model and ensure the authenticity of the simulation results, the equivalent scaling model of slide rail and armature is established in Maxwell, as shown in Fig. 1. On the other hand, the pulse power supply is applied to the head of the slide rail using the external circuit module in Maxwell. In Fig. 1 (a), the slide rail is long 500 mm, wide 1.06 mm, and high 2.44 mm. The armature is long 4.237 mm, wide 2.81 mm, high 2.44 mm, thick 0.3 mm at the tail, and the radius of the circular groove at the rear of the armature is 0.53 mm.

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(a) Geometric model of rail electromagnetic launcher.

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(b) Input pulse current waveform.

Fig. 1. Modeling of electromagnetic launching device in Maxwell

2.2 Electromagnetic Field Parameter Setting In Maxwell, a cuboid air domain with length, width and height of 200 mm is set for the electromagnetic launcher to simulate the infinite air environment, and the materials of armature and slide rail are defined as 6061 aluminum alloy and copper alloy respectively. After that, the armature, slide rail and air domain are meshed, and their mesh sizes are 0.5 mm and 1 mm respectively. Then the input pulse current excitation is applied on the slide rail. The pulse current waveform is shown in Fig. 1 (b). The peak value of the pulse current is 20 kV, the rise time is 0.6 ms, and the half-width is 2 ms. Finally, the 3D transient solver is set, the solution step time is set to 3.0 ms, the step size is set to 0.2 ms, and the save time step is set to save the field output results once per 0.2 ms. 2.3 Temperature Field Parameter Setting The geometric model established in Maxwell in Sect. 2.2 is imported into the transient temperature field module Transient Thermal through Ansys Workbench. The materials of 6061 aluminum alloy and copper alloy are also assigned to the armature and slide rail in Transient Thermal, and their grids are divided into 0.25 mm and 0.5 mm respectively. Then a friction contact is set between the armature and the slide rail, with a coefficient of 0.1. Through Ansys Workbench, the electromagnetic field solution results simulated in the Maxwell module are imported into the solution settings of Transient Thermal. In this way, the thermal load calculated by the electromagnetic field can be introduced into the temperature field, that is, thermal generation, and the time step of thermal generation can also be set to 0.2 ms, which is consistent with the step of solving the electromagnetic field, thus the coupling model of temperature field and electromagnetic field can be established. Finally, the transient thermal solver is set, the solution time step is set to 0.2 ms, a total of 15 steps, and the initial temperature of the rail electromagnetic launcher is set to 22 °C.

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3 Analysis of Electromagnetic Field Distribution 3.1 Distribution of Current Density The current density distribution of the model is simulated by using Maxwell’s 3D transient solver. When the input pulse current reaches the 20 kV peak at 0.6 ms, the current density of the rail electromagnetic transmitter is the highest, and its distribution is shown in Fig. 2.

Fig. 2. Current density distribution of electromagnetic launcher during 0.6 ms

As can be seen from Fig. 2, the flow path of the pulse current input to the electromagnetic launcher is as follows: input from one side slide rail to the armature, and then flow out from the other side slide rail to form a loop, so the current density on the slide rail is mainly distributed in the part before contact with the armature, and due to the continuous attenuation of the electric potential in the circulation process, the current density of the current flowing into the side slide rail is higher than that of the current outflow side slide rail. The former is 7.76 × 109 A/m2 and the latter is 7.35 × 109 A/m2 . Among them, the current density around the contact point between the slide rail and the armature tail is the most concentrated, as shown in the red box in Fig. 4, which is 8.72 × 109 A/m2 . In order to observe the variation characteristics of current flow direction and current density distribution with time during armature launch as pulse current inputs, the current density distribution of armature at different times during launch process is made, as shown in Fig. 3.

Fig. 3. Current density distribution in armature at different times

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As can be seen from Fig. 3, no matter when the pulse current is, the current density of the armature during the launch process is always concentrated in the rear groove. This is because the armature tail forms a proximity effect, when it flows through the current in the opposite direction, a strong eddy current and magnetic field will be formed in the middle of the parallel conductor, which will make the total current in the conductor deviate to one side of the adjacent conductor. Therefore, the current will be concentrated on the surface of the adjacent conductor. At this time, the two tail fins of the armature can be regarded as conductors flowing through different directions, so the armature has the condition of proximity effect so that the current density is concentrated on the groove and the inner surface of the tail. Among them, when the input pulse current reaches the peak value, that is, 0.6 ms, the maximum current density in the middle of the armature groove reaches 7.91 × 109 A/m2 . 3.2 Distribution of Magnetic Induction Intensity The 3D transient field solver of Maxwell is used to simulate the magnetic induction intensity distribution of the model on the basis of the current density distribution simulation results. The magnetic induction intensity distribution of 0 ms, 0.2 ms, 0.4 ms, 0.6 ms, 1.2 ms and 2.0 ms in the launching process are simulated, as shown in Fig. 4. 2

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As can be seen from Fig. 4, because the distribution of the magnetic induction intensity of the electromagnetic launcher is closely related to the distribution of its current density, the distribution of the magnetic induction intensity is roughly the same as that of the current density in Fig. 2. The parts with high magnetic induction intensity are also concentrated in the groove at the rear of the armature (m1 point) and the inner surface of the tail wing, as well as on the inner surface of the two slide rails due to the proximity effect. And the magnetic induction intensity around the contact point between the slide rail and the armature tail (m2 point) is also highly concentrated. Among them, when the input pulse current reaches the peak, that is, at the time of 0.6 ms, the maximum magnetic induction intensity of the electromagnetic launcher appears in the middle of the armature groove, up to 6.15 T. Therefore, in the process of launch, the current density and magnetic induction intensity of the electromagnetic launcher are mainly distributed in the groove of the

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armature and the contact points between the slide rail and armature, and these two places are very prone to melting, ablation and other damage.

4 Analysis of Temperature Field Distribution Under Electromagnetic Coupling The calculation and simulation results of the electromagnetic field model in the third section are imported into the Transient Thermal solution module in Ansys Workbench to simulate and analyze the temperature field of the electromagnetic launcher under electromagnetic coupling. The temperature field distribution of 0.4 ms, 0.8 ms, 1.2 ms, 1.6 ms, 2.0 ms, 2.4 ms, 2.8 ms and 3.0 ms in the launch process are obtained by simulation, as shown in Fig. 5.

Fig. 5. Temperature field distribution of electromagnetic launcher at different times

As can be seen from Fig. 5, the area where the heat of the armature is most concentrated is in the rear groove, and this is also the position with the highest temperature of the whole electromagnetic launcher, which indicates that most of the Joule heat generated by the current is concentrated in the groove of the armature. This is basically consistent with the distribution characteristics of current density and magnetic induction intensity in the armature. Due to the high and low electric potential of the two slide rails, the temperature distribution of the slide rail shows that the temperature of the current flowing into the side slide rail is higher than that of the current outflow side slide rail. For example, in 3.0 ms, the temperatures of the two rails are 444.5 °C and 398.4 °C respectively. In the process of launching, the slide rail is superimposed by the Joule heat produced by the input current [9], the friction heat caused by friction with the armature and the heat generated by the contact resistance [10], which makes the slide rail become a component with concentrated temperature distribution second only to the armature groove.

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Figure 6 shows the variation of the maximum temperature at the armature groove with time.

Fig. 6. The variation of temperature with time during launch

As can be seen from Fig. 6, although the pulse current reaches its peak as early as 0.6 ms, the temperature in the armature groove continues to rise until it reaches a maximum of 521.23 °C at about 2 ms. This process of temperature rise is due to the fact that the heat of the resistance of the armature itself is greater than the heat diffused by it, which makes the surface temperature of the armature rise gradually. After 2 ms, with the continuous decrease of the amplitude of the input pulse current, the temperature at the armature groove also shows a downward trend, at this time, the thermal conductivity of the armature material 6061 aluminum alloy gradually decreases, the heat generated by the current is less than the heat diffused by the armature, and the thermal power of the whole device begins to decrease [11]. Therefore, the heat generation of the pulse current and the heat dissipation of the components determine the temperature rise of the electromagnetic launcher.

5 Conclusion The electromagnetic thermal multi-field coupling model of the rail electromagnetic launcher is established by using Maxwell and Transient Thermal in Ansys Workbench, and the distribution of electromagnetic field and temperature field is simulated and analyzed. The distribution rules of current density and magnetic induction intensity during launch are obtained, which are mainly concentrated in the rear groove and tail of the armature and around the contact points between the armature and the slide rail. The temperature is mainly concentrated in the armature groove, and the temperature of the slide rail on the input current side is higher than that on the output side. The temperature rise of the electromagnetic launcher is determined by the heat generation of the pulse current and the heat dissipation of the components. Through the distribution characteristics of the electromagnetic field of the launcher, it is easy to determine the location of ablation on the armature and slide rail, which provides guidance for the safety and tolerance of electromagnetic launch experimental device manufacturing in the next step. Acknowledgment. This research is supported by the National Natural Science Foundation of China (92266112).

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References 1. Teng, T., Tan, D., Wang, Q., et al.: Review of ship-borne electromagnetic launch technology. Ship Sci. Technol. 42(13), 7–12 (2020). (in Chinese) 2. Ma, X., Liao, X., Chen, B.: Research review of hypervelocity projectile by electromagnetic launch at home and abroad. Air Space Def. 4(02), 87–92 (2021). (in Chinese) 3. Mao, B., Zhang, T., Bai, X., et al.: Design of anti-ablation armature structure for electromagnetic rail gun. J. Ordnan. Equip. Eng. 41(03), 67–71 (2020). (in Chinese) 4. Stefani, F., Merrill, R.: Experiments to measure melt-wave erosion in railgun armatures. IEEE Trans. Magn. 39(1), 188–192 (2003) 5. James, T.E.: Why solid armatures fail and how they can be improved. IEEE Trans. Magn. 39(1), 56–61 (2003) 6. Liu, Y., Guo, W., Zhang, T., et al.: Structural design of armature with interference at both ends and analysis of its launching performance. IEEE Trans. Plasma Sci. 48(08), 2922–2931 (2020) 7. Fan, W., Su, Z., Zhang, T., et al.: Spatial-temporal distribution of transient temperature rise in augmented electromagnetic railgun. High Voltage Eng. 47(09), 3346–3354 (2021). (in Chinese) 8. Lu, G., Liu, F., Gao, X., et al.: Wear characteristics between aramture and rails under the action of lorentz force and temperature field. Tribology 41(04), 474–483 (2021). (in Chinese) 9. Lin, Q., Li, B., Kwok, D.Y.: Transient heating effects in electromagnetic launchers with complex geometries: A 3D hybrid FE/BE analysis. Eur. Phys. J. 171(1), 135–143 (2009) 10. Wang, Z., Wan, M., Li, X.: Characteristics of temporal and spatial distribution of railgun contact heat. Chin. J. High Pressure Phys. 30(06), 511–516 (2016). (in Chinese) 11. Li, S.: Study on the Influence of Railgun Caliber on Electromagnetic Characteristics and Temperature Field. Master, Yanshan University, Qinhuangdao (2020). (in Chinese)

Study on the Temporal and Spatial Characteristics of Transient Temperature in Electromagnetic Emission System Luyao Liu, Pengfei Lu, Hongshun Liu(B) , Yizhen Sui, Ruxue Zhao, and Hongbin Zhang Shandong Provincial Key Laboratory of UHV Transmission Technology and Equipment, Shandong University, Jinan 250061, China {202214621,202234720}@mail.sdu.edu.cn, [email protected]

Abstract. Since the proposal of the strategy in strengthening the country with science and technology, electromagnetic emission technology has gained wider and wider application in military, aviation, industry and other fields. Clarifying the thermal damage mechanism of the armature-rail under extreme impact conditions and improving the reuse rate and service life of the device have become a hotspot for researchers at home and abroad. Based on previous achievements, this paper adopts finite element simulation methods to establish a more comprehensive three-dimensional model of the electromagnetic launch system. The temporal and spatial distribution characteristics of the transient temperature at the armature-rail interface are investigated under the coupling analysis of electromagnetic thermal multi-physical field. Furthermore, the influence of externally applied current waveform on temperature peak is analyzed, and the temperature rise mechanism is also analyzed based on the theories such as heat source and skin effect. The series of studies conducted are of great significance for clarifying the working performance of electromagnetic emission systems and guiding the manufacturing, operation and maintenance of the equipment. Keywords: Electromagnetic emission · Temperature characteristics · Multi-field coupling simulation

1 Introduction As an emerging technology with broad application prospects [1], the electromagnetic emission system is fast, long-range, high-precision, and has excellent antielectromagnetic interference performance [2]. Working under the extreme impact conditions of multi-physical field coupling, the Joule heat and friction heat generated by high pulse current and high-speed sliding will seriously consume the performance and service life of the launcher [3]. It is of great significance to carry out research on the temperature distribution of the electromagnetic launch system. Due to limitations in the experimental site and safety considerations, research on electromagnetic emission technology often requires the use of simulation methods [4]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 135–142, 2024. https://doi.org/10.1007/978-981-97-1064-5_14

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Scholars have analyzed the impact of different initial temperatures on the electrical contact performance and emission speed of the armature-rail [5]. Numerical modelling of sliding electrical contact current and heat is explored by accounting for initial contact pressure or velocity skinning effects [6, 7]. After analyzing the sources of heat such as Joule and friction heat in the emission system, scholars proposed a calculation method for interface heat distribution and developed temperature equations [8]. Some scholars have proposed high-temperature suppression schemes such as coating, liquid cooling, and structural optimization based on numerical calculations of heat [9–11]. However, current research focuses on numerical resolution of the heat transfer at the sliding electrical contact interface, and most of them only establish half of the two-dimensional symmetric model in order to simplify operations. The electromagnetic launch system is structurally complex, and it is urgent to refine current models to explore the spatiotemporal distribution characteristics of its global temperature. In this paper, a three-dimensional complete model of the electromagnetic emission system is established using finite element software. Taking into account the computational needs and software convergence, appropriate mesh partition is carried out. The materials of each component are determined based on the research of equipment manufacturers. The coupling of electric-magnetic-thermal field is introduced to study the transient temperature spatiotemporal distribution characteristics of the armature-rail structure, which provides theoretical references for the optimal design of the launch device.

2 Modelling

Fig. 1. Geometric modeling of electromagnetic launch system and the mesh partitioning.

Establish the three-dimensional transient model of the electromagnetic emission system, as shown in Fig. 1, which mainly consists of a guide rail and an armature. The common C-type armature is used, with a total length of 60 mm, a width and height of 30 mm, a thickness of 4 mm at the tail, and a curvature radius of 5 mm at the inner corner. The total length of the rail is 600 mm, with a width of 46 mm and a height of 16mm. The central axis of the armature on the xy cross-section is aligned with that of the rail, moving along the x-axis when simulated. In addition, according to the quadruple caliber law [12], for a square-bore launcher, feeding the armature at a distance of four caliber from the rear of the track can achieve 99% of the thrust. Considering the computational

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convergence and avoiding local singularities caused by sharp edges or close contact surfaces, the initial position of the armature is set at a distance of 20 mm from the start of the rail. It can be seen from Fig. 1 that an additional air domain needs to be constructed to define the magnetic field boundary conditions. Draw a cylinder with a length of 660 mm and a radius of 100 mm, which can be regarded infinite during calculation. Combined with the research opinions of the electromagnetic transmitter manufacturer, the material of the rail is selected as pure copper, and the material of the armature is selected as 7075 aluminum alloy, which is light and high-strength. To highlight the research object and simplify the calculation, the air domain and armature-rail structure are divided into “refined” and “ultra-refined” meshes, as shown in Fig. 1. The current, magnetic field and solid heat transfer interfaces are selected for transient studies.

3 Temperature Characteristics and Influencing Factors of Armature-Rail During the operation of the electromagnetic launch system, its instantaneous current can reach mega-ampere level, causing a large amount of heat generated between the armature and the rail in a short period of time. The accumulation of heat will bring about thermal stress damage, leading to deterioration of armature-rail materials and shortening its service life. Considering the severe oscillation and energy loss caused by directly applying strong pulse current to the orbit, a more gentle trapezoidal current excitation is selected, and the waveform is shown in Fig. 3.

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As shown in Fig. 2, the rising edge phase of the current has a duration of 0–0.5 ms, linearly increasing to an amplitude of 400 kA for 2 ms, then decreasing to 0, and the falling edge stage lasts for 1 ms. Apply the current source to the starting position of one guide rail, ground the other one, and introduce an external current density into the magnetic field interface to explore the transient temperature characteristics of the armature-rail structure.

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3.1 Temperature Distribution Characteristics of the Armature-Rail Interface Current is the main factor affecting Joule heat, and the distribution of current density also determines the distribution of Joule heat, which is the main source of interfacial heat. Firstly, study the simulation results of the distribution of current density in different motion stages, as shown in Fig. 3.

2

Fig. 3. Results of current density at different times.

Figure 3 intercepts the current density distribution on the xy section of the armaturerail device when the armature tail moves to 415 m and 510 m away from the rail tail, respectively. During simulation, it can be observed that the electromagnetic emission model is an axisymmetric structure, and the current at the armature-rail interface is also roughly distributed symmetrically along the centerline of the double rails, which constitutes a rail-armature-rail circuit along with the trajectory of the armature. Under the influence of transient magnetic field diffusion and skin effect, the current mainly concentrates on the inner edge of the guide rail and its prongs in contact with the armature, and has a decreasing trend from the inner side to the outer side and from the tail to the head in a layered manner. Further explore the simulation results of the solid heat transfer module, as shown in Fig. 4. It can be seen from Fig. 4 that the high-temperature area on the contact surface between the armature and the track is mainly concentrated in the thin layer of the tail, which is consistent with the current density distribution characteristics under the skin effect. Further taking the yz cross-section of the track in contact with the armature tail, it can be found that the highest temperature is also concentrated on the inner edge, and the consistency with the current distribution also verifies the validity of the model. The difference is that the diffusion depth of temperature is smaller than that of the current density at the same moment, because the temperature of the launcher increases with the diffusion of current and is affected by magnetic diffusion and velocity skin effect, showing a certain degree of hysteresis. 3.2 Temperature Time-Varying Characteristics of Armature Electromagnetic launcher works under the condition of strong current and high magnetic field, and the speed can be up to a few kilometers per second in a few milliseconds. The

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30

15

0 0

52

26

16

8

0 0

23

46

Fig. 4. Temperature distribution of armature-rail section.

transient temperature distribution of the armature at different times is determined by simulation, as shown in Fig. 5.

Fig. 5. Temperature distribution of the armature at different moments.

From Fig. 5, it can be seen that the armature needs to overcome friction to do work at the beginning of the motion, and the trapezoidal current excitation is still in the rising stage. The transient skin effect and proximity effect make it closely adhere to the inner side of the track and the edge of the armature to form a circuit. The temperature reflects the concentrated distribution of friction heat and contact resistance Joule heat during this stage. 0.5 ms later, the current reaches its peak and the armature has entered a high-speed motion stage, resulting in a shorter contact time with the track. At this point, the flow passage time of the rear end tail of the armature is the longest, and the curvature at the inner corner, especially at the inflection point, is large, which inhibits the diffusion of the current, and the accumulation of heat makes the high-temperature region gradually gather towards these two parts. The armature continues to accelerate, and the speed skin

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effect gradually becomes apparent or even dominates. The current no longer completely adheres to the inner wall of the armature rail, but spreads around, and the temperature of the prongs gradually reduces. High temperature hotspots are significantly concentrated at the sharp edges of the tailplane and the inflection point of the C-type armature, which is also the most prone location for erosion during the service period of the armature. 2.5 ms later, the current is in the decline, and the high-temperature area also diffuses and weakens accordingly. 3.3 Effect of Current Waveform Electromagnetic emission system operating conditions involve complex electromagnetic-thermal and other multi-physical field coupling effects, and there are various factors affecting its temperature characteristics. Considering that the main source of heat between armature and rail is Joule heat, which will accumulate or diffuse over time, this paper studies the effect of applied current waveform. Firstly, clarify the impact of externally applied current amplitude. Keeping the time of each stage of the waveform in Fig. 2 constant, explore the variation of the highest temperature value in the armature-rail at the level of 200−600 kA, as shown in Fig. 6. 440

600 kA 500 kA 400 kA 300 kA 200 kA

420 400

T/K

380 360 340 320 300 280

0

0.5

1

1.5

t / ms

2

2.5

3

3.5

Fig. 6. Results of temperature variation under different current peaks.

As shown in Fig. 6, the overall trend of temperature is roughly from the initial value of 293.15K, gradually increasing to a maximum value and then decreasing. The higher the current amplitude, the greater the temperature peak. This is because the current density in the circuit decreases, and the temperature rise of the armature-rail dominated by Joule heat also follows. Further, the influence of the rise-fall time of current is explored. Maintain the current amplitude at 400 kA and the flat edge pulse width at 2 ms. Set the rise phase time to 0.1 ms, 0.3 ms, 0.5 ms, 0.7 ms, and 0.9 ms respectively, and the corresponding fall phase time to 1.4 ms, 1.2 ms, 1.0 ms, 0.8 ms, and 0.6 ms respectively, that is, the entire feeding

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440 420 400

T/K

380 360 340 0.1ms - 1.4ms 0.3ms - 1.2ms 0.5ms - 1.0ms 0.7ms - 0.8ms 0.9ms - 0.6ms

320 300 280

0

0.5

1

1.5

t / ms

2

2.5

3

3.5

Fig. 7. Results of temperature variation under different current waveforms.

duration is 3.5 ms. The variation of peak temperature between armature-rail is shown in Fig. 7. As shown in Fig. 7, the shorter the rise time of the trapezoidal current, the faster the initial temperature rise, and the armature and orbit can reach very high temperatures in a short period of time. But as the current soon reaches its highest value and enters the falling edge phase, the growth rate of temperature also slows down or even reduces. Analyze the entire simulation process and heat source, the waveform of the excitation source will affect the movement speed of the armature. The slower the current rises, the longer the acceleration time required for the armature, the slower the motion speed in the initial stage, and the slower the generation of Joule heat and frictional heat, thus the initial temperature rise is not obvious. But the accumulation time of heat in the later stage is longer, and the current is falling along a shorter period of time, where the heat has not yet diffused, showing a higher temperature peak.

4 Conclusion In order to clarify the temporal and spatial distribution characteristics of transient temperature in electromagnetic launch systems, this paper establishes a three-dimensional model and conducts multi field coupling calculations of electromagnetic heat. The main conclusions obtained are as follows. 1) The high-temperature area of the armature-rail contact interface is mainly concentrated at the inner edge of the rail, as well as at the tail and corner of the C-type armature, attributed to the skin effect and proximity effect of the current. 2) As the launch proceeds, the temperature of the armature cross-section gradually converges from the inner wall to the tail and inner inflection points, and diffuses towards the outer layer as the current decreases. 3) The higher the amplitude of the externally applied current, the higher the temperature reached by the armature-rail structure. The longer the rise time of the current, the slower the temperature rises, but the higher the total heat accumulated.

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Acknowledgments. This work is supported by the National Natural Science Foundation of China (92266112).

References 1. Wan, X., Yang, S., Li, Y., Li, B.: Inductance gradient in electromagnetic launcher under channel cooling condition. IEEE Trans. Plasma Sci. 51(5), 1312–1319 (2023) 2. Ma, W. M., Lu, J.Y.: Research status and challenges of electromagnetic emission technology. Trans, China Electrotech. Soc. 1–17 (2023). (in Chinese) 3. Wei, F., et al.: Thermal measurement experiments and transient temperature distribution of rapid-fire augmented electromagnetic railgun. IEEE Trans. Plasma Sci. 50(5), 1351–1359 (2022) 4. Ma, S., Lu, S.L., Ma, H.T., et al.: Analysis of the main factors affecting the current density and temperature of electromagnetic rail. IEEE Trans. Plasma Sci. 50(12), 5001–5012 (2022) 5. Xu, W.D., Liu, F., Yuan, W.Q., et al.: The influence of orbital temperature on electromagnetic emission performance. High Volt. Techn. 45(9), 3013–3019 (2019). (in Chinese) 6. Zhou, P., Li, B.: Numerical calculation of magnetic-thermal coupling and optimization analysis for velocity skin effect. IEEE Trans. Plasma Sci. 49(12), 3994–4001 (2021) 7. Zhang, J.W., Lu, J.Y., Tan, S., et al.: Magnetic Diffusion model model of sliding electrical contact interface considering initial contact pressure. Trans. China Electrotech. Soc. 37(2), 488–495 (2022). (in Chinese) 8. Yao, J., et al.: Computational method for heat partition at the rail-armature interface based on least squares regression. IEEE Trans. Plasma Sci. 49(6), 2008–2014 (2021) 9. Gu, G., Wu, L.Z., Geng, H., et al.: Simulation analysis of orbital cooling based on electromagnetic flow field coupling. Trans. China Electrotech. Soc. 35(17), 3601–3608 (2020). (in Chinese) 10. Lv, Q.A., Chen, J.W., Zhang, H.X., et al.: Numerical simulation of temperature field of tin alloy coating armature/rail in electromagnetic rail gun. J. Ordnan. Equip. Eng. 40(4), 10–14 (2019). (in Chinese) 11. Zhang, H.H., Zhang, T., Fan, W., et al.: Analysis of the distribution characteristics of rail temperature field for rail gun thermal management design. J. Artill. Launch Control 42(4), 81–86 (2021). (in Chinese) 12. Ma, S., Yang, F., Nong, A.B., et al.: Effect of active cooling on the temporal and spatial distribution characteristics of current density and temperature of electromagnetic railgun. Thermal Sci. Technol. 21(5), 415–426 (2022). (in Chinese)

Effect of Crystal Orientation on Vacuum Breakdown Characteristics of Copper Nanoelectrode Xinyu Gao(B) , Zihe Li, Zhenyu Zhao, Jun Zhao, and Wen Yan Xi’an Aeronautics Computing Technique Research Institute, AVIC, Xi’an 710065, China [email protected]

Abstract. Aiming at the influence of surface work function and internal atomic structure of nanoelectrodes with different crystal orientations on the theoretical mechanism of vacuum breakdown, the current electrodynamically-coupled molecular dynamics and particle simulation method (ED-MD-PIC) was used in this paper. The effect of crystal orientation on the vacuum breakdown characteristics of copper nanoelectrodes was studied by comparing the evolution of characteristic parameters of different crystal orientations ({100}, {110}, {111}). The emission current and the shielding effect of space charge on the local electric field at the tip of the nanoelectrode at the initial time of different crystal orientations increase with the decrease of the work function of the crystal surface of the material. The necking, sharpening and evaporation of atomic clusters of nanoelectrode tips with different crystal orientations lead to differences in field enhancement factor and internal heat transfer rate. The higher electric-thermal field is the main reason for the lower critical electric field and vacuum breakdown delay of Cu {111} electrode. The maximum difference of the critical electric field of vacuum breakdown of nano-electrode with different crystal orientations is less than 7%. Keywords: Crystal Orientation · Vacuum Breakdown · Nanoelectrode

1 Introduction In recent years, many studies have shown that when the scale of discharge breakdown reaches the nanometer range, the microstructure of the electrode will affect the breakdown process of the vacuum gap. The atomic structure of the tip surface of nanoelectrodes with different crystal orientations mainly affects the work function of the material surface. The work function on the surface of the material is larger for metals with closely packed atoms and smaller for metals with open lattices. The work functions corresponding to different crystal orientations on the bottom surface of copper nanoelectrodes (the internal atoms have different crystal orientations along the Z axis) are {100} = 4.59 eV, {110} = 4.48 eV, {111} = 4.98 Ev [1], and the work functions of different crystal orientations are quite different. The formation process of the breakdown depends on the surface quality of the electrode. When the cathode surface is flat and smooth, the probability of electron emission © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 143–150, 2024. https://doi.org/10.1007/978-981-97-1064-5_15

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and release of secondary electrons on the surface of the metal electrode mainly depends on the work function on the surface of the cathode material [2]. Therefore, the work function of electrode materials plays an important role in the vacuum discharge process of metal electrodes [3, 4]. Existing studies have shown that the selectivity of vacuum breakdown is also closely related to the work function of the close-packed surface of the electrode material [3]. In addition, the internal atomic density and crystal plane spacing of the electrodes with different crystal orientations also affect the deformation of the nanoelectrodes under strong electric field. Therefore, this paper mainly studies the vacuum breakdown characteristics of copper nanoelectrodes with different crystal orientations ({100}, {110}, {111}) under strong electric field. By studying the evolution of characteristic parameters during the initial process of the breakdown, the intrinsic law of the effect of electrode crystal orientation on the nanoscale vacuum pre-breakdown process is obtained from the atomic scale.

2 Simulation Method The finite element mesh model and molecular dynamics model of copper nanoelectrode used in this paper are based on the simulation system established by references [5, 6]. The ED-MD-PIC method, which combines the 3D particle-in-cell (PIC) Particle numerical simulation method [7, 8] with ED-MD simulation, is used to simulate the vacuum breakdown process of the nanoelectrode. The processes, including the solution of Poisson equation, electron emission and thermal diffusion of vacuum three-dimensional electric field distribution of nanoelectrode, are calculated based on finite element mesh. All the computational information is finally integrated into the FEMOCS model. For the specific modeling and solving process of copper nanoelectrodes, see reference [9, 10]. In the process of molecular dynamics modeling of nanoelectrode atomic structure, stacking atoms are generally constructed from the bottom surface of the nanoelectrode located in the XY axis plane, while the stacking mode of atoms along the Z axis mainly depends on the crystal structure of the material and the crystal orientation of the bottom surface. The different crystal orientations along the bottom surface of the XY axis plane affect the atomic density and the interplanar spacing of the internal atoms in different stacking structures. The parameters of the face-centered cubic lattice (FCC) with different crystal faces and different crystal directions are shown in Table 1 and Table 2. For FCC, the crystal plane with the highest atomic density is {111} plane, and the crystal direction with the highest atomic linear density is . Because the spacing of the most densely packed crystal faces is the largest, the lattice resistance is the smallest, and it is easy to slip, so the most densely packed crystal faces in the crystal are the slip planes. In addition, because the lattice spacing along the most densely packed direction is the smallest, the Burgers vector causing the slip dislocation is also the smallest, so the most densely packed crystal direction of the atoms is its slip direction. Therefore, the slip plane of the face-centered cubic crystal is {111}, and the slip direction is .

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Table 1. Different face parameters of face-centered cubic lattice.

Indices of Crystal Face

Atomic Arrangement Diagram of Crystal Face

Atomic Density of Crystal Face (Number of Atoms/Area)

Interplanar Spacing

2 a2

a 2

{100}

{110}

2 a2

{111}

4 3 3a2

2 a 0.3536a 4

1.4 a2

2.3 a2

3 a 0.577a 3

Table 2. Different crystal orientation parameters of face-centered cubic lattice. Indices of Crystal Directio

Atomic Linear Density (Number of Atoms/Area)

Lattice Spacing

1 a √

a



2 1.4 a ≈ a √ 3 0.577 3a ≈ a

√

2 2 a ≈ 0.707a

√

3 a ≈ 1.732a

The atomic structure of the tip surface of nanoelectrodes with different crystal orientations will affect the work function of the material surface. According to the classical field emission Fowler-Nordheim (FN) equation under a strong electric field: √ √ 8π 2m ϕ 3/2 e3 E e3 E 2 exp{− θ( )} JFN = 8π hϕ 3 eE ϕ (1) √ 2 6.85 × 106 ϕ 3/2 3.72 × 10−4 E −6 E = 1.55 × 10 exp{− θ( )}, ϕ E ϕ It can be seen that the reduction of the material work function will increase the emission current density of the emitter, thereby reducing its operating voltage and improving

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its compressive strength [4, 11]. At the macro scale, the breakdown voltage and breakdown delay of metal electrode will increase with the increase of the work function of electrode material [2, 12, 13]. At the same time, the work function, field enhancement factor and local electric field of electrode materials can also be estimated by analyzing the electrode breakdown voltage and vacuum breakdown delay [12, 14]. However, at the nanoscale, the charge density and emission current density on the surface of the needlelike cathode field emitter material are significantly affected by the space-charge limited emission (SCLE). The higher the charge density on the electrode surface, The stronger the shielding effect on the local electric field and electron emission of the electrode tip [15]. Therefore, in this paper, single-crystal copper nanoelectrodes with initial tip radius of 1 nm, electrode length of 100 nm, electrode taper of 3° and different crystal orientations ({100}, {110}, {111}) on the bottom surface were selected for ED-MD-PIC simulation. By analyzing the influence of different crystal orientations on the electron emission characteristics, electron emission thermal effect, vacuum breakdown critical electric field and vacuum breakdown delay, the effect of crystal orientation on the vacuum breakdown characteristics of nanoelectrode under strong electric field was investigated.

3 Effect of Crystal Orientation on Electrothermal Effect of Copper Nanoelectrode Due to the work functions of copper nanoelectrodes with different crystal orientations, {100} = 4.59 eV, {110} = 4.48 eV, {111} = 4.98 eV, the effect of material work function on vacuum breakdown characteristics and electrothermal damage of nanoelectrode is different from that of macroscopic scale under the influence of nanoscale space charge limiting electron emission and shielding effect on local electric field of electrode tip. This section mainly studies the effects of different crystal orientations on the emission current and electric field distribution of nanocedde under the same vacuum breakdown applied electric field (330 MV/m). Figure 1 shows the time evolution curve of the pre-breakdown emission current of copper nanoelectrodes with different crystal orientation under an applied electric field of 330 MV/m. It can be seen from the figure that the emission current at the initial moment of the nano-electrode with different crystal orientations increases with the decrease of the work function of the crystal surface. Because the work function of the Cu {110} electrode is small, the emission current at the initial moment is the highest. With the evolution of time, because the work function difference between Cu {110} electrode and Cu {100} is only 0.11 eV, the emission current alternates up and down during the prebreakdown process, while the Cu {111} electrode always maintains the lowest emission current in the initial stage of pre-breakdown due to its work function being significantly higher than the two. However, with the gradual increase of pre-breakdown current, Cu {111} electrode (vacuum breakdown delay 44.06 ps) and Cu {100} (51.92 ps) will preferentially produce current surge and breakdown than Cu {110} (61.28 ps). This is different from the rule that the higher the work function of the electrode material, the higher the vacuum breakdown delay at the macro scale. Therefore, it is necessary to analyze the local electric field of electrode tip with different crystal orientation.

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Fig. 1. Time evolution curve of pre-breakdown emission current of copper nanoelectrodes with different crystal orientations under 330 MV/m.

As shown in Fig. 2, because the shielding effect of space charge on the local electric field of the tip of the nanoelectrode increases with the decrease of the work function of the electrode material, the surface work function of the Cu {111} electrode is large and the initial emission current is small, the accumulation of space charge on the tip of the Cu {111} electrode is the least under the same applied electric field, so the shielding effect of space charge on the local electric field of the tip is also small. In the pre-breakdown stage, the maximum local electric field at the tip will first reach 20 GV/m and breakdown will occur. Because the surface work function of Cu {110} electrode is the smallest and the initial emission current is large, the local electric field at the electrode tip is always the lowest, so the pre-breakdown current rises most slowly. With the slow increase of the local electric field of the tip of the Cu {100} electrode, the emission current will gradually increase, so that it exceeds the Cu {110} electrode after 20 ps. In general, when the physical properties of materials such as melting boiling point and resistivity are exactly the same, due to the shielding effect of space charge on the local electric field of the electrode tip and the limiting effect on electron emission, the lower the crystal face work function of the nanoelectrode, the stronger the shielding effect of space charge. The vacuum breakdown delay of the nano-electrode with different crystal orientations will increase with the decrease of the crystal face work function. Although the pre-breakdown emission current of Cu {111} electrode is the smallest, the Nottingham heat and Joule heat generated by electron emission and current joule effect are also the smallest, but the local maximum temperature and average temperature of the tip are the highest. Therefore, the thermal damage and heat conduction of the nanoelectrode under the strong electric-thermal field are the main factors affecting the temperature evolution during the pre-breakdown process. It can be seen that the distortion of the local electric field at the tip of the Cu {111} electrode and the change rate of the field enhancement factor are the highest. The higher local electric field at the tip of the Cu {111} electrode and the larger crystal face spacing along the Z axis will lead to the sharpening of the tip of the Cu {111} electrode, which will lead to the reduction of the electrode cross section and the decrease of the current density and heat conduction. The

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Fig. 2. The evolution curve of the maximum local electric field at the tip of copper nanoelectrode with different crystal orientation under 330 MV/m.

highest electric-thermal field is the main reason for the lowest mean vacuum breakdown delay of Cu {111} electrode.

4 Effect of Crystal Orientation on Vacuum Breakdown Characteristics of Copper Nanoelectrode Figure 3 shows the relationship between the vacuum breakdown delay of copper nanoelectrodes with different crystal orientation (R0 = 1 nm, H 0 = 100 nm) and the applied macroscopic electric field. It can be seen that under different macroscopic electric fields, the overall trend of vacuum breakdown delay of copper nanoelectrodes with different crystal orientation is basically similar. Formula 9 in literature [4] was used to fit the vacuum breakdown delay, and the calculated critical electric field of vacuum breakdown E c and related parameters were shown in Table 3.

Fig. 3. Relationship between vacuum breakdown time delay and macroscopic electric field of copper nanoelectrode with different crystal orientation.

As can be seen from the table, considering the influence of space charge on the vacuum pre-breakdown process, the critical electric fields of vacuum breakdown of copper nanoelectrodes (Cu {111}, Cu {100}, Cu {110}) with different crystal orientation

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obtained by ED-MD-PIC simulation are 296 MV/m, 311 MV/m and 316 MV/m respectively. The closely packed surface {111} has the largest work function, but the lowest critical electric field applied by vacuum breakdown. The average vacuum breakdown delay of the nanoelectrode also decreases with the decrease of the applied critical electric field. On the whole, the fitting parameters (τ, th) of different crystal-oriented electrodes differ little, and the maximum difference of applied critical electric field of vacuum breakdown is less than 7%. Table 3. Vacuum breakdown delay fitting parameters of copper nanoelectrodes with different crystal orientation Crystal Orientation

/eV

E c /MV·m−1

E max - E c /MV·m−1

τ /ps

t h /ps

Cu {111}

4.98

296

323

7.05

21.14

Cu {100}

4.59

311

301

5.61

23.75

Cu {110}

4.48

316

273

5.89

26.60

5 Conclusions In this paper, the effect of different crystal orientations on the vacuum breakdown characteristics of copper nanoelectrode under strong electric field is studied. For copper nanoelectrodes with different crystal orientations, the close-packed surface has the highest work function. The emission current and the shielding effect of space charge on the local electric field at the tip of the nanoelectrode at the initial time of different crystal orientations increase with the decrease of the work function of the crystal surface of the material. The necking, sharpening and evaporation of atomic clusters of nanoelectrode tips with different crystal orientations lead to differences in field enhancement factor and internal heat transfer rate. The higher electric-thermal field environment is the main reason for the lower critical electric field and vacuum breakdown delay of Cu {111} electrode. The maximum difference of the critical electric field of vacuum breakdown of nano-electrode with different crystal orientations is less than 7%.

References 1. Michaelson, H.B.: The work function of the elements and its periodicity. J. Appl. Phys. 48(11), 4729–4733 (1977) 2. Pejovi´c, M.M., Bošan, D.A., Krmpoti´c, D.M.: Influence of electrode material on time delay of electrical breakdown in gases. Beiträge aus der Plasmaphysik 21(3), 211–215 (1981) 3. Cao, W.C., Liang, S.H., Zhang, X., et al.: Effect of Mo addition on microstructure and vacuum arc characteristics of CuCr50 alloy. Vacuum 85(10), 943–948 (2011) 4. Chen, W.G., Xing, L.Q., Li, J.S.: Unusual arc distribution on surface and electrical breakdown mechanism of nanocrystalline tungsten copper alloy. Rare Metal Mater. Eng. 36(3), 463–466 (2007)

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5. Veske, M., Kyritsakis, A., Djurabekova, F., et al.: Dynamic coupling between particle-in-cell and atomistic simulations. Phys. Rev. E 101(5), 053307 (2020) 6. Kyritsakis, A., Veske, M., Eimre, K., et al.: Thermal runaway of metal nano-tips during intense electron emission. J. Phys. D-Appl. Phys. 51(22), 225203 (2018) 7. Buneman, O.: Dissipation of currents in ionized media[J]. Phys. Rev. 115(3), 503–517 (1959) 8. Dawson, J.: One-dimensional plasma model. Phys. Fluids 5(4), 445–459 (1962) 9. Gao, X., Nan, L., Kyritsakis, A., et al.: Structural evolution and thermal runaway of refractory W and Mo nanotips in the vacuum under high electric field from PIC-ED-MD simulations. J. Phys. D Appl. Phys. 55, 335201 (2022) 10. Gao, X., Kyritsakis, A., Veske, M., et al.: Molecular dynamics simulations of thermal evaporation and critical electric field of copper nanotips. J. Phys. D-Appl. Phys. 53(36), 365202 (2020) 11. Sakata, T., Masutani, M., Sakai, A.: The work function reduction of the Pt field emitter[J]. Surf. Sci. 542(3), 205–210 (2003) 12. Emelyanov, A.: Breakdown delay in vacuum. In: ISDEIV: Xxth International Symposium on Discharges and Electrical Insulation in Vacuum, Proceedings, vol. 20, pp. 654–659 (2002) 13. Schwirzke, F.R.: Vacuum breakdown on metal-surfaces. IEEE Trans. Plasma Sci. 19(5), 690– 696 (1991) 14. Emel’yanov, A.A.: Electron work function estimated from the delay time of breakdown in vacuum. Tech. Phys. Lett. 29(1), 39–40 (2003) 15. Kyritsakis, A., Veske, M., Djurabekova, F.: General scaling laws of space charge effects in field emission. New J. Phys. 23(6), 063003 (2021)

Vibration Simulation of High Voltage Cables Laid on the Stress Absorption Mechanical Device Composed of Three Arcs in the Bridge Offset Yun Cong1 , Gencheng Wang1 , Jianliang Xu1 , Zhenpeng Zhang2(B) , and Songsheng Hou1 1 Zhoushan Power Supply Company of State Grid Zhejiang Electric Power Co., Ltd.,

Zhoushan 316000, China 2 China Electric Power Research Institute, Wuhan 430074, China

[email protected] Abstract. Considering the mismatch of the intrinsic vibration frequency between the cable and the mechanical device laid in the bridge offset, the vibration mode of the high-voltage (HV) cable and the mechanical device laid in the bridge offset is vital for the condition monitoring of the power transmission systems on the bridge. However, the vibration characteristic of the cable laid in the bridge offset has not been studied by simulation. In this paper, a model considering the electromagnetic force has been established. The results show that the displacement and stress reach their maximum values at the junction between the cable and the mechanical device. The maximum displacement is observed at the right of the junction, measuring 30 µm, while the maximum stress is observed at the left end of the junction, measuring 90 kPa. Besides, the vibration of the mechanical device is trend to move to low frequency. Keywords: HV cable · vibration · mechanical device · bridge offset

1 Introduction With the development of the transportation, more and more bridges across rivers and bays have been constructed. HV cables laid on bridges are increasing rapidly due to the raising demand of power supply of both shores and the low cost comparing with underwater cables [1–4]. Compared to cables laid on the seabed or riverbed, cables laid on bridges have advantages of lower cost, rapid deployment, ease of maintenance and repair. However, the elongating and shortening of the cable and the bridge under the seasonal temperature varying is not matched because of the elastic modulus and passion ratio of the cable and bridge is not equal [5, 6] ore, multiple mechanical devices on which cables are laid are design to absorb the overstretch or the over compression. During the long service life of the cable and mechanical devices, which is typical beyond 30 years, it is hard to avoid the mechanical fault of the cable and the mechanical devices [7]. Thus, it is necessary to model and analyze the vibration of the cable and the mechanical device to lay the foundation of condition monitoring. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 151–158, 2024. https://doi.org/10.1007/978-981-97-1064-5_16

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In the last decade, there have been researchers investigating the deployment and vibration of cables within bridge structures. In literature [8], the dynamic analysis of a cable-stayed concrete-filled steel tube arch bridge under vehicle loading is investigated. In literature [9], a new shape of concrete-filled steel tube (CFST) arch bridge known as the butterfly-shaped bridge is introduced. In literature [10], the cable-arch bridge as a new type of hybrid bridge is presented and its significant engineering importance is highlighted. Although there have been several studies on cables embedded in bridges, research on the vibration simulation of cable installed in the offset of bridges is lacked. To obtain the vibration characteristic of the HV cable on the mechanical devices in the offset under electromagnetic force load, the vibration simulation is investigated. The first section provides an overview of the research status regarding cables embedded in bridges. The second section describes the establishment of the model and the parameter settings. The third section presents the simulation results, while the fourth section outlines the conclusions drawn from the study.

2 Stress Simulation of High Voltage Cables Laid on the Stress Absorption Mechanical Device In this section, the physics model of cable vibration is established firstly. Then, the finite element method to solve the model is introduced. Finally, the geometry and the material parameter settings are presented. Based on solid mechanic theory, the governing equation of cable vibration in frequency domain is given by the following control equation. ρω2 u = ∇ · S + Feiφ

(1)

In which, ρ represents the density of the material, ω represents the angular frequency of the vibration, u represents the displacement vector of the material, ∇·S represents the divergence of the stress tensor, which describes the distribution of stresses in the material, Feiφ represents the external force vector applied to the material, where F is the magnitude and φ is the phase angle. The force can be associated with the excitation or external loading acting on the system. For the AC cable install on the mechanical device, the force F is determined by the load current loop Idl, and magnetic field B generated by the other phases, the equation can be expressed as,  F = B × Id l (2) To better observe the surface stress of the cable and mechanical device, it is necessary to apply the Fourier transform formula to convert the time-domain signal into a frequency-domain signal.  −∞ F(t)e−jωt dt (3) F(ω) = −∞

F(ω) represents the complex-valued function in the frequency domain, indicating the amplitude and phase information of the signal at different frequencies ω. F(t) denotes

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the function or sequence in the time domain, representing the original signal, j is the imaginary unit, ω is the angular frequency of the continuous signal, t represents the sampling time. The photo of the stress absorption mechanical device composed of three arcs is presented in the Fig. 1.

Fig. 1. The photo of the stress absorption mechanical device composed of three arcs

Fig. 2. Geometry model of the stress absorption mechanical device in simulation

As show in Fig. 2, the entire apparatus composes of three cables. The overall length of the mechanical device is 24 m, with a height of 8 m and the bending radius of 5.2 m. The geometric parameters of the 110 kV XLPE cable is introduced in the simulation. The radius of copper conductor is 30.9 mm. The thickness of the inner semiconducting layer, insulation layer and outer semiconducting layer is 2.0 mm, 24.7 mm, 2.0 mm respectively. Besides, the thickness of the buffer layer, the aluminum sheath and the jacket is 10.0 mm, 3.3 mm, 5.0 mm respectively. The mechanical parameters of the cable and the offset are presented in Table 1. Table 1. Mechanical parameters of the cable and mechanical device Item

Elastic modulus (GPa)

copper

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inner semiconducting layer

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1200

insulation layer

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0.47

960

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The boundary condition of the mechanical device in the model is fixed at both ends. The mechanical device in the entire model is discretized using a tetrahedral mesh. The three cables are partitioned using a swept mesh approach, with a cable mesh size of 0.05 × 0.05 m, and the mechanical device mesh size is 0.125 m × 0.125 m. Convergence verification of the cable mesh sizes 0.04 m, 0.05 m, and 0.06 m was conducted, and it was found that the mesh size had minimal influence on the numerical simulation results. Furthermore, to ensure grid quality and computational accuracy, the total number of mesh elements in the entire model is set to 120,000. To determine the stress and displacement of the mechanical device under the influence of vibration on the cables, finite element simulations were performed in the frequency domain at a frequency of 100 Hz, the load current of the cable is set as 500 A, with a phase difference of 120° between phases.

3 The Simulation Results In this section, the simulation results of the overall cable and the mechanical device is presented firstly. Then, the influence of the vibration on the stress and displacement of the cable and the mechanical device in time domain is presented. Finally, the vibration of the mechanical device in frequency domain is analyzed. The simulation results of the stress and displacement distributions of the complete model under vibration are presented in Fig. 3 and Fig. 4. The stress concentration point is on the both ends and the bottom of the arc. The maximum displacement point is found at the bottom of the arc.

Fig. 3. The overall distribution of stresses.

Fig. 4. The overall distribution of the displacement.

In order to obtain of surface stress and displacement of the mechanical device under vibration conditions, a comprehensive simulation of the entire model was conducted in the time domain. The simulation was performed with a time step of 0.04 s, and for each

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stress and displacement simulation, 8 frames were captured. As shown in Fig. 5, the stress distribution of the upper surface of the mechanical device is not changed with the vibration, since that the stress distribution is determined by the elastic modulus and the boundary condition that the cable is fixed at the both end. The electromagnetic force generated by the current has litter influence on the cable stress distribution. As shown in Fig. 6, the displacement distribution of the upper surface of the mechanical device is changed with the vibration cycle, and the cycle is match with 100 Hz electromagnetic force generated by load because of the inertia of the cable and the mechanical device.

Fig. 5. The stress distribution of the upper surface of the mechanical device.

Fig. 6. The displacement distribution of the upper surface of the mechanical device.

To obtain a clear understanding of the stress and displacement at different locations, a straight line is drawn at the connection point between the cables and the mechanical device, enabling the observation of stress and displacement magnitudes at various positions along the line. The stress and displacement between the three-phase cables and the mechanical device are illustrated in Fig. 7 and Fig. 8.

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It can be found that the displacement is highest between the cable and mechanical device in the right end, the value is 30 µm. Moreover, the maximum stress between the cable and mechanical device is found at the left end, and there is a noticeable increase in pressure at the contact point between the cable, the value is 90 kPa. The result of the vibration frequency of the mechanical device is presented in Fig. 9. Comparing with the applied electromagnetic force at 100 Hz, it can be found that the vibration of the mechanical device is trend to move to low frequency. It can be explained by the constrain effect of the inertia of the mechanical device.

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4 Conclusions By the numerical simulation of vibration of the cable and the mechanical device, the vibration characteristic of the cable is obtained. The following findings are concluded: 1) The displacement reaches the maximum values 30 µm at the right junction point between the cable and the mechanical device. 2) The stress appoarches the maximum values 90 kPa at the left junction between the cable and the mechanical device. 3) The frequency of the mechanical device vibration is trend to move to low frequency due to the constrain effect of the inertia.

References 1. Zhang, Z., Zhao, J., Li, W., et al.: Random vibration analysis of a sea-crossing bridge and power cable composited structure under traffic loads. Chin. J. Theor. Appl. Mech. 54(4), 912–920 (2022) 2. Wang, G., Cong, Y., Qi, L., et al.: Simulation of the stress distribution of cable laid in the bridge offset. In: IEEE 6th International Electrical and Energy Conference, Hefei, China, pp. 1278–1281 (2023) 3. Weisun, J., Miao,S., Xu, M.: Effect of large mechanical stress on electrical tree characteristics of silicone rubber. In: IEEE International Conference on the Properties and Applications of Dielectric Materials, Xian, China, pp. 143–146 (2021) 4. Gong, J., Liu, Y., Yan, X., et al.: Research and engineering application of modular bridge-along cable offset. Zhejiang Electric Power 41(2), 67–72 (2022) 5. Zhang, Z., Meng, S., Zhao, J., et al.: Measurement of vibration characteristics of power cable line under typical laying conditions. High Volt. Eng. 41(4), 1188–1193 (2015) 6. Zhang, D., Shang, Q.: Finite element analysis of thermos-mechanical effect of 220 kV singlecore AC cable in serpentine laying. Electr. Meas. Instrument. 57(4), 61–65 (2020)

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7. Wei, W., Yan, W., Deng, L., et al.: Dynamic analysis of a cable-stayed concrete-filled steel tube arch bridge under vehicle loading. J. Bridge Eng. 20(5), 401–408 (2015) 8. Gang, W., Xin, R., Fei, Z., et al.: Static and dynamic evaluation of a butterfly-shaped concretefilled steel tube arch bridge through numerical analysis and field tests. Adv. Mech. Eng. 13(9), 168–176 (2021) 9. Kang, H.J., Zhao, Y., Zhu, H., et al.: Static behavior of a new type of cable-arch bridge. J. Constr. Steel Res. 81, 1–10 (2013)

Consider the Collaborative Optimization Strategy of Electric Vehicles Under Dynamic Electricity Price Mechanism Wangsheng Chen(B) , Shudong Wang, Huiquan Wang, and Weiqiang Tang College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected]

Abstract. Driven by the sustainable development strategy of ‘’dual carbon”, the consumption situation of renewable energy in China is worrying, and it is urgent to need more flexible control resources to adjust Power system networks. To some extent, electric vehicles can interact with the power system network in both directions. When the electric vehicle is not in the driving state, it can transmit excess electrical energy back to the grid, thus playing the role of an energy storage device; And when an electric car needs to be charged, it can take power from the grid to charge it. A large number of electric vehicles continue to be put into market use, and if their charging behavior is not properly guided, it will cause a huge impact on the power system network. Therefore, the focus of this paper is to use the electricity price elasticity matrix to guide the charging behavior of users, It reduces the impact on the power system network, standardizes the charging behavior of electric vehicle users, and ensures high utilization of renewable energy To achieve the maximization of bilateral benefits for both the grid and users in the optimization process, it shows that under the consideration of multiple interests The most effective scheduling method is to adopt the collaborative optimization strategy. Keywords: Renewable energy consumption · Electric vehicle · Dynamic electricity price mechanism · Collaborative optimization strategy

1 Introduction With the continuous advancement of industrialization under the trend of globalization, the consumption of traditional energy in the process of construction is also intensifying, resulting in the continuous depletion of fossil energy, One of the biggest problems is the damage to the environment and serious pollution so the use of effective ways to alleviate the impact of the above phenomenon has become the focus of current scholars. As a mobile energy storage device with the advantages of low carbon emissions and low energy consumption, and As the technology for interacting with electric vehicles and power system networks continues to improve, the use of electric vehicles to alleviate energy pressure and reduce environmental pollution is an efficient means. However, in recent years, the concept of environmental protection has been popularized among © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 159–168, 2024. https://doi.org/10.1007/978-981-97-1064-5_17

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people, and the state has vigorously advocated the use of new energy to protect the environment and reduce traditional energy consumption, so the number of electric vehicles has increased unprecedentedly, power system networks “peak-to-peak”, the difficulty of operation control increases, and the power quality declines [1–5]. The core concept of electric vehicles in optimizing the grid is to consider them as distributed energy storage devices. Through intelligent management and control systems, user charge and discharge behavior can be flexibly controlled according to grid load conditions. During periods of peak grid load, EVs can release stored electricity to provide additional power support to the grid and reduce the pressure. On the contrast, EVs can be charged to store excess power. This approach helps to balance power supply and demand, optimize grid operation, reduce users’ charging costs, and improve energy use efficiency, while also promoting the large-scale application and integration of renewable energy. According to the current existing research, literature [6] establishes the optimization objective of maximizing the reduction of grid operation consumption, and uses the NSGA-II algorithm based on Levy’s flight improvement to optimize the scheduling of the grid only. Literature [7] proposed a strategy for optimal scheduling using cloud adaptive particle swarm algorithm based on time-sharing tariff mechanism by taking the minimum Load mean square deviation and the minimum the difference between the peak and valley values of the grid load curve as the optimization objectives, and considering the minimum cost of carrying out the minimum cost of battery depletion as the optimization objectives on the user’s side. Literature [8] Introduce guiding countermeasures for electric vehicle users to regulate their charging behavior under the co-optimization of price and incentives, which on the one hand coordinates to interact with the power system through the aggregator, and on the other hand also meets the user demand and system needs, and finally verifies that this strategy not only improves the revenue of the aggregator but also reduces the cost of the user to charge and discharge the EV, and at the same time, has certain advantages for the stable operation of the power grid. Certain advantages. Literature [9] proposes a two-layer optimization model for optimizing EV charging and discharging strategies under the carbon trading mechanism, in which The goal of upper-layer optimization is to minimize the cost of operators and improve their economic efficiency. The down-level optimization goal is the minimum volatility of the power system network to improve the stability and reliability of the grid. Through the synergy of these two models, the effective interaction between electric vehicles and the power grid can be realized, and the operational efficiency and economic benefits of the power system can be optimized. From the above analysis under the optimization strategy for electric vehicles, a collaborative optimization under the consideration of dynamic tariff mechanism based on the literature [10], which adopts the linearization technique combined with the secondorder relaxation technique to deal with the optimization scheduling method. The normal operation of the power grid, behaviors of electric vehicles are made more flexible to meet the needs of vehicle owners, while establishing three optimization scenarios, overall optimization effect. By comparing the different scenarios of EV user charging cost, unit operation cost, pollution cost during unit operation, it is verified that the proposed optimization strategy is the most effective scheduling method considering the interests of multiple parties, and achieves the global optimal optimization effect.

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2 Dynamic Tariff Mechanism 2.1 Basic Principles of Dynamic Mechanisms When the power grid consumes a lot of electricity, a higher feedback tariff is set than the charging tariff when EVs are charging in order to enhance the motivation of users to participate in the feed-in behavior. When the grid is in a low period of electricity consumption, a lower feedback tariff is set in order to create a situation of interaction between EVs and the grid. This mechanism is to ensure the normal fully consider the economic interests of users, reducing user charging costs. 2.2 Link Between Charging Demand and Electricity Prices The expression between charging demand and electricity price is shown as follows: X (u) = l − kJ (u)

(1)

From this equation, it can be concluded that the price of electricity is negatively correlated with the demand for electricity, where: J(v): the price of electricity, X(v) is the demand for charging, k: one-time function coefficient, l: fixed intercept on the axis. Electricity price elasticity matrix is given as follows: S(u, u) =

∂J (u) −KJ (u) J (u) × = X (u) ∂X (u) −KJ (u) + l

(2)

2.3 L Power Demand Sensitivity Matrix By dividing the electricity price into three types: valley time price J(v), peak time price J(p), and usual price J(u), the electricity demand corresponding to the three types of price is X(v), X(p), and X(u), respectively, and from this, we can calculate the total cost of charging cost required for EV users to carry out charging behaviors, whose expression is shown as follows: T = J (v)X (v) + J (p)X (p) + J (u)X (u)

(3)

Equation (4) can be further derived from Eqs. (1) and (3): X 2 (v) + lX (p) − k 2 (J 2 (v) + J 2 (u)) + lkJ (u) − k 2 X (u) − kT = 0

(4)

As obtained from Eq. (4), to obtain the electricity demand in the valley hours, the usual tariff can be used to derive: ∂J (u) kl − 2k 2 J (u) = ∂X (v) l 2 + 4[lkJ (u) + lkJ (v) + k 2 J 2 (u) + k 2 J 2 (v)] − kT

(5)

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Divided by 1h as a time scale, a day is 24 h in total, then the free sensitivity and interactive sensitivity of charging demand to electricity price form an electricity demand sensitivity matrix containing 576 element values, and the matrix expression is shown as follows: ⎡ ⎤ ⎡ ⎤ X (1) S(1, 1) · · · S(1, 24) ⎢ . ⎥ ⎢ ⎥ .. .. .. ⎢ . ⎥=⎣ (6) ⎦ . . . ⎣ . ⎦ X (24)

S(24, 1) · · · S(24, 24)

The main diagonal element in this expression represents the free price sensitivity and the other diagonal elements represent the interaction price sensitivity. Considering the strong randomness of the grid load change, if the time-sharing tariff mechanism is used to take incentive users lack of certain timeliness, so the introduction of power demand sensitivity matrix, through the analysis of the grid load can be derived from the power demand sensitivity matrix of each power consumption division time period so as to obtain the power price under the time period, relative to the time-sharing tariffs, the demand side of the resource mobilization is more flexible and efficient, and it also greatly to a certain extent to alleviate the pressure of grid operation. It is more flexible and efficient in mobilizing demand-side resources than time-of-use tariffs, and it also relieves the pressure of grid operation to a great extent.

3 Case Study Through the relevant simulation software, the optimization objectives and their related parameters are set according to the literature [10] and [11]. 3.1 Case 1 Validating the Effectiveness of Electric Vehicles Under This Dynamic Mechanism Considering the total is 100,000, electric vehicles involved in charging accounts for 85% of the total scale, and the number of electric vehicles involved in discharging accounts for 20% of the total scale, and it is stipulated that the charging tariffs and the discharging tariffs are equal during the electricity consumption troughs, and the discharging tariffs are higher than the discharging tariffs in the electricity consumption peak periods. Divided by one hour as a time scale, the charging price and discharge price of electric vehicles for each time period of the day are shown in Fig. 1. Based dynamic tariff as a response mechanism, the status of each unit after the time scale of one hour and the results of operation optimization in Fig. 2. From the operating status and output of the thermal units, it can be seen that all the units are started during the entire optimized dispatch period, and compared to the optimized dispatch period in literature 18, where units 3, 7, 9, and 10 are stopped, the handling and operating status of the thermal units under this dynamic tariff response mechanism have been improved to a large extent. Meanwhile, based on the output ranges of 5–25 MW, 15–35 MW, and 20–45 MW for units 7, 9, and 10, under this mechanism is a higher degree of fine optimization. In terms of operating cost, compared to literature

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2.5

2.0

1.5

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Fig. 1. The charging price and discharge price of the electric vehicle for each time of the day.

Output po

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(b) Unit optimization results

Fig. 2. Unit status and output results at different times

18, unit 1 does not go to run at maximum output power during 8:00, 9:00, and 21:00 time points, indicating that the scheduling strategy under this mechanism the unit’s operating costs were reduced to achieve the desired optimization goals. Under the established objective function, the number of electric vehicles in different states in different periods of time is shown in Fig. 3. 1 105

8 104

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Fig. 3. The Quantity of electric vehicles under optimized charge and discharge scheduling.

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Involved in heavy discharging in wind power scenarios, the time period when users charge EVs is mainly concentrated in 23:00–7:00, which is in the light-loading period when the power consumption of the grid equipment is small, whereas the time periods when EVs are discharged are 8:00–15:00 and 20:00–22:00, which are in the heavyloading period when the power consumption of the grid equipment is large. This is the heavy load period when the power consumption of grid equipment is larger. Through the analysis of the time periods, optimization scheme under the adopted dynamic mechanism plays a staggered role and Achieve the goal of minimum fluctuation of the grid, which not only takes into account demand of the user side, but also ensures that the power grid can operate safely. The optimization results of each cost are shown in Table 1. Table 1. Optimization results for different expenses Full consumption

Unit operation

Environmental destruction

Wind consumption

unit consumption

Charging behavior consumption

163560

670816

28756

0

10759

−546732

Through the statistics of each cost, comparing the literature18 there are two obvious characteristics under this calculation example. 1. The zero wind abandonment cost shows that the optimal scheduling strategy for EVs under the dynamic tariff mechanism makes full use of wind energy and does not result in wind abandonment. 2. The negative cost of charging after participating in the optimal scheduling shows that under the dynamic tariff mechanism, An electric vehicle can be regarded as a mobile distributed power supply unit, which can be guaranteed to work normally when connected to the power system and at the same time, the economic subsidies given to the users enhance their motivation to interact with the power system is more stable and efficient. 3.2 Case 2 Validating the Effectiveness of the Most Efficient Optimization Scheduling Means After Comprehensively Considering Various Optimization Goals Under This Dynamic Mechanism In Example 1, although the operating costs on the grid side, the pollution costs generated by the operation of the units, and the charging costs when the users participate in the optimal scheduling are taken into account, the focus of these considerations is different. The optimization objective for the grid side is to minimize the cost of operating the units, the optimization objective for the user side The cost that the car user charging is consumed to the minimum to minimize, and the optimization objective from the point of view of protecting the environment is to minimize the carbon emission. Determine whether the method proposed by the following conditions can be made to achieve the most efficient scheduling under the purpose of multi-objective cooperative optimization, therefore, based on Example 1, a comparative analysis optimization

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objective of minimizing the operating cost of the unit on the grid side and minimizing the settings of each parameter are consistent with the parameters set up earlier. The operating state diagram of each unit under two different scenarios considering Under the minimum optimization target, the operation of each generator set and the consumption of electric vehicle users is shown in Fig. 4.

1 2 3 4 5 6 7 8 9 10

1 3 4 5 6 7 8 9 10

(a) Minimal running costs

(b) Lowest cost for users

Fig. 4. Operating status of each unit under different optimization objectives.

By comparing the operating state diagrams of each unit under different conditions, it can be concluded that lowest cost of the unit is considered, only Unit 1, Unit 2, and Unit 5 start to run more obviously, and the output power generated by the operation of the other units is almost negligible. And all 10 units are in operation (Fig. 5). 1000

800

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Output power/MW

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1000 800 600 400

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Fig. 5. Optimization results of each unit under different optimization objectives.

Under the minimum optimization target, the operation of each generator set and the consumption of electric vehicle users unit does not exceed 1000 MW. The number of EVs participating in the optimal scheduling of charging and discharging under the two situations are shown in Fig. 6. From the distribution diagram of the number of EVs involved in charging and discharging scheduling, it can be seen that under the dynamic tariff mechanism, EV users

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Lowest running costs Lowest charging costs

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Fig. 6. Quantity allocation diagram of the minimum optimization target, the operation of each generator set and the consumption of electric vehicle users dispatching under different optimization targets.

make full use of the idle power supply capacity of the grid to choose to charge in the early morning hours when the demand for industrial and commercial electricity is low and the users’ household electricity consumption is also relatively low, and the discharging time period is at the peak of the grid load. The comparison of each cost consumption under different optimization objectives is shown in Table 2. Table 2. Cost depletion under different optimization objectives Optimization Objectives

Lowest unit operating costs

Lowest charging costs

Total Cost

608117

1343828

163599

Running Costs

623366

1028715

671016

Pollution Costs

28485

36380

28056

0

844520

0

Unit startup and shut-down costs

6966

35346

10759

Charging Costs

−51200

−572827

−546732

Wind Abandonment Costs

Costs after synergistic optimization

The focus of the research is to reduce the cost of the total unit at runtime, the resulting operating cost of 623,000 RMB is lower than that of 671,000 RMB under the synergistic optimization and that of 1,028,000 RMB under the minimization of charging cost. When maximizing the user’s benefit is considered and the cost of charging is minimized, the user’s benefit at this time is 572,000 yuan higher than 51,000 yuan and 546,000 yuan under the co-optimization. Through the analysis of the results under different optimization objectives optimization results under Just consider one kind of research goal is the best, but from the table can also be seen that Just consider one kind

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of research goal also has certain drawbacks, in terms of the optimization objective for the charging of the lowest cost of cost, the optimization process does not make full use of the wind power resources, and the pollution of the environment is also deeper than that under the other two objectives optimization. Although the unit operation cost and charging cost under synergistic optimization are not the lowest compared to the results under each of the two as single-objective optimization, the difference is not very big, and the wind power resources are fully absorbed, and the degree of pollution to the environment is also the smallest. It can be seen that in order to achieve the best overall optimization results, it is necessary to use the co-optimization scheduling strategy, because in the single-objective optimization process will result in the absence of the interests of many parties, and can not coordinate the interests of all parties.

4 Conclusion Dynamic tariff mechanism is a method conducive to the regulation of energy consumption, which can adjust the price of electricity according to the actual supply and demand situation, regulate the disorderly charging behavior of users, so that there can be a compatible situation of both supply and demand, reduce the pressure of the power consumption of the power system is very large, the phenomenon of maximum resource utilization can be formed while at the same time, it brings certain benefits to the users, and reduces the user’s charging Costs. Meanwhile, a comparison is made between single-objective optimization and cooperative optimization, from which the perspective of the global perspective, it is not very effective to consider that it is impossible to take care of it under one research goal.optimum, so in the process of optimal scheduling, by combining the concept model of collaborative optimization, it has achieved a high-efficiency renewable energy utilization situation to reduce waste of resources. Acknowledgments. This work was supported by the National Natural Science Foundation of China, grant number 61463019.

References 1. Xiu, L., Du, Z., Li, M., et al.: Analysis of dynamic characteristics of DC ptog control electric vehicle system considering the influence of phase locking loop. Electric Power Autom. Equip. 42(05), 61–67 (2022). (in Chinese) 2. Sun, J., Zhao, G., Liu, S., et al.: Research on the dynamic characteristics of cluster electric vehicles participating in power grid frequency modulation based on the improved time delay link. Power Grid Technol. 43(02), 470–480 (2019). (in Chinese) 3. Hamidreza, J., et al.: Plug-in electric vehicle behavior modeling in energy market: a novel deep learning-based approach with clustering technique. IEEE Trans Smart Grid 11(6), 4738–4748 (2020) 4. Gan, L., Chen, X., Kun, Y., Zheng, J., Du, W.: A probabilistic evaluation method of household EVs dispatching potential considering users’ multiple travel needs. IEEE Trans. Ind. Appl. 56(5), 5858–5867 (2020)

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5. Kuljeet, K., Neeraj, K., Mukesh, S.: Coordinated power control of electric vehicles for grid frequency support: MILP-based hierarchical control design. IEEE Trans Smart Grid 10(3), 3364–3373 (2019) 6. Zhou, C., Sheng, G., Li, S.: Multi-objective optimal scheduling of microgrids considering electric vehicle access. J. Electr. Eng. 18(01), 211–218 (2023). (in Chinese) 7. Zhao, Y., Xu, T., Li, Y., et al.: Research on electric vehicle dispatching strategy based on TOU electricity price. Power Syst. Protect. Control 48(11), 92–101 (2020). (in Chinese) 8. Hou, H., Tang, J., Wang, Y., et al.: Long time-scale charging and discharge scheduling of electric vehicles under the combined demand response of price and incentive. Autom. Electric Power Syst. 46(15), 46–55 (2022). (in Chinese) 9. Li, J., He, W., Wang, J.: Charging and discharging optimization of shared electric vehicles under the carbon trading regulation. J. Appl. Sci. 1–15 (2023). (in Chinese) 10. Yin, W., Qin, X.: Cooperative optimization strategy for large-scale electric vehicle charging and discharging. Energy 258, 124969 (2022) 11. Yin, W., Ming, Z., Wen, T.: Scheduling strategy of electric vehicle charging considering different requirements of grid and users. Energy 232, 121118 (2021)

Effect of UV Irradiation on the Surface Morphology and Chemical Structure of Epoxy Resin Shaoming Pan1 , Lei Zhang1 , Jian Zhao1(B) , Yi Su1 , Xiajin Rao1 , Liangyuan Chen1 , and Dajian Li2 1 Guangxi Key Laboratory of Intelligent Control and Maintenance of Power Equipment, Electric

Power Research Institute of Guangxi Power Grid CO., Ltd., Nanning 530023, Guangxi, China [email protected] 2 Guangxi Power Grid CO., LTD., Nanning 530023, Guangxi, China

Abstract. Ultraviolet (UV) irradiation is an environmentally friendly method for material modification. In order to explore the effect of UV irradiation on surface properties of epoxy resin and further explore the feasibility of this method on improving surface flashover of epoxy resin, in this paper we experimentally study the surface morphology and chemical structure of epoxy resin after UV irradiation. It was shown that after irradiation, the surface morphologies and roughness of the samples shown little change. The FTIR results showed that after UV irradiation, the O-H and C=O groups on the surface were increased, while the content of CH2 and CH3 groups was decreased greatly. We further studied the surface chemical components by XPS and it was revealed that the C-C/C-H and C-O-C bonds on the surface decreased significantly by UV irradiation, and the C-O-H and C=O bonds increased significantly. Through molecular simulation calculations, it was found that the bond energies of C-O-C, C-H, and C-C bonds in epoxy molecules are low, and thus they were prone to fracture by UV irradiation. This study elucidated the mechanism of UV irradiation on changing the surface chemical structure of epoxy resin, and provided a basis for improving the surface flashover performance of epoxy resin by UV irradiation. Keywords: Epoxy resin · UV irradiation · surface morphology · surface chemical structure

1 Introduction High Voltage Direct Current (HVDC) strategy is a great energy strategy which not only suits the energy consumption demand, but also low-carbon development trend in the 21st century [1–3]. Scholars have proved that the cornerstone of HVDC system was the strong power network with excellent resistance for insulation failure [4]. In the insulation system, the flashover voltage is much lower than the breakdown voltage of gas and solid dielectrics with the same insulation gap [5]. Therefore, the surface flashover is the weakness in the insulation system of HVDC system and it is necessary to increase the surface flashover voltage of the power equipment. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 169–175, 2024. https://doi.org/10.1007/978-981-97-1064-5_18

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Scholars found that material modification was an effective method to improve the surface flashover of dielectrics [5]. Nano hybrid was used to increase the surface flashover of dielectrics. Li [6] added nano TiO2 and MWCNTs into epoxy resin and significantly increased the surface flashover in vacuum. However, the excellent electrical properties of nano composites are hard to harness. The fillers in the composites are tend to agglomerate and the uneven distribution of fills will weaken the electrical and mechanical performance of composites. Scholars found that material modification was an effective method to improve the surface flashover of dielectrics [5]. Nano hybrid was used to increase the surface flashover of dielectrics. Li [6] added nano TiO2 and MWCNTs into epoxy resin and significantly increased the surface flashover in vacuum. However, the excellent electrical properties of nano composites are hard to harness. The fillers in the composites tend to agglomerate and the uneven distribution of fills will weaken the electrical and mechanical performance of composites. To increase the surface flashover voltage without influencing other properties, some surface modification technologies, such as surface fluorination [7], ozone treatment [1], electron beam irradiation [8], plasma treatment [9]. However, the above-mentioned technologies have some drawbacks such as complex operating procedures, strict requirements for equipment, and the use of harmful gases, which contradict the green development concept. Therefore, there is an urgent need to develop surface modification method which can not only improve flashover performance, but also environmentally friendly. Compared to existing surface modification methods, ultraviolet (UV) irradiation has the advantages of high efficiency and environmentally friendly. Research has shown that UV irradiation can effectively increase the breakdown strength and energy storage performance of organic dielectrics [10, 11]. Meanwhile, Li et al. also reported the effectiveness of UV irradiation on improving the surface flashover voltage of silicone rubber [12]. However, the influence of UV irradiation on the surface performances of epoxy resin is still unclear. Therefore, it is necessary to explore the feasibility about UV irradiation on improving surface flashover voltage of epoxy resin. In this study, the surface morphology and chemical structure of epoxy resin after UV irradiation was studied by atomic force microscopy (AFM), Fourier transform infrared spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS). It was found experimentally that the UV irradiation changed the surface chemical structures greatly. The increasing irradiation time contributes to the lower CH groups and greater C=O and CO-H groups on the surface. This study proved that the UV irradiation could change the surface chemical structures and was a potential method to increase the surface flashover voltage of epoxy resin.

2 Material and Experiment 2.1 Material The experimental materials include bisphenol A epoxy resin (E51, from Nantong Xingchen); hardener methyltetrahydrophthalic anhydride (JH-910, from Jiaxing Lianxing); accelerator N-N dimethylbenzylamine (BDMA, from Xiongrun resin).

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2.2 Sample Preparation The release agent Jiadan 909A was evenly sprayed on the molds and then they were moved into the oven and heated at 120 °C for 2 h. After that, 100 g epoxy resin (WSR618) was added into the three necked flask and stirred at 60 °C for 10 min with degassing. Then 79.5 g hardener (Me-THPA) and 0.6 g accelerator (N-N dimethyl benzylamine) were poured into the flask. The mixture in the flask was stirred at 60 °C for 1 h with degassing. When finished, poured the mixture in flask into molds and cured in an oven. The curring program was 80 °C for 2 h and 140 °C for 12 h. After curring, samples with the thickness of 1 mm and the diameter of 100 mm (for conductivity) and 50 mm (other tests) were token out. Before irradiation, samples were placed in the oven at 50 °C. 2.3 UV Irradiation The wave length of ultraviolet light as 254 nm. The irradiation time in this study was set as 2, 4 and 6 h. After irradiation, the samples were stored in sample bags at 25 °C. The epoxy sample without irradiation was referred to as EP and the irradiated samples were referred to as the irradiation time, that is UV-2 h, UV-4 h and UV-6 h. 2.4 Experiment The 2D and 3D surface morphology was observed by AFM (Bruker Dimension Icon, Germany). The scanning area was 20 um × 20 um and the experimental results were analyzed by Nanoscope Analysis software. The surface chemical structure was characterized by FTIR (Nicolet iS10) in reflection mode. The measurement wavelength was from 3600 to 600 cm−1 with a scanning speed of 40 spectra/second. In addition, the surface chemical structure was also measured by XPS (Thermo Scientific ESCALAB 250Xi, USA).

3 Result and Disscussion 3.1 Surface Morphology Figure 1 shows the microstructure of the epoxy sample before and after UV irradiation. From Fig. 1, it can be observed that although the surface morphologies of the samples were changed by UV irradiation, the difference is not significant in 2D view from Figs. 1(a) to (d). In the 3D morphologies from Figs. 2 (e) to (f), there are obvious differences among different samples. We further summarized the surface roughness of samples by Nanoscope Analysis and represented by the arithmetic mean deviation Ra of the contour and the root mean square deviation Rq . The surface roughness of samples is shown in Fig. 2. As seen, after irradiation by UV for 2 h, the roughness is increased. When the irradiation time is increased to 4 and 6 h, compared to the sample irradiation for 2 h, the surface roughness is reduced slightly. Although the surface roughness is reduced, it is still greater than the sample before UV irradiation. Thus, the roughness of EP is increased by UV irradiation. In addition, it is worth mentioning that all the roughnesses of samples are nano-level and the difference among them is slight. Scholars proved that

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the minimum for the surface roughness influencing surface flashover voltage is 1 µm [12]. Therefore, the change in surface roughness of epoxy resin by UV irradiation can never influence surface flashover in this study. And the difference in surface roughness can be neglected when studying the surface flashover of irradiated EP.

Fig. 1. The Micromorphology of epoxy samples before and after UV irradiation. 2D morphology for (a) 0 h, (b) 2 h, (c) 4 h and (d) 6 h. 3D morphology for (e) 0 h, (f) 2 h, (g) 4 h, (h) 6 h.

q

Fig. 2. Surface roughness of the samples before and after UV irradiation

3.2 Surface Chemical Structure The FTIR spectra of samples was corrected by OMNIC software and shown in Fig. 3. It can be observed that after UV irradiation, although no new chemical groups were formed on the surface of epoxy resin, the intensity of each chemical group was changed. By comparison, it was found that the peaks located at 3500, 1732 and 1507 cm−1 in the figure were significantly increased after UV irradiation (within the red box). Through literature review, it is found that the three aforementioned peaks correspond to the stretching vibration of hydroxyl groups in C-OH, the stretching vibration of C=O, and the bending vibration of C-OH [13], indicating that UV irradiation introduces

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2961

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more oxygen-containing groups such as hydroxyl and carbonyl groups on the surface of epoxy resin, and then increases the content of these groups. The result in Fig. 3 is similar to the one in reference 11 that the UV irradiation can introduce carbonyl groups into the molecules of carbon-based polymers. In addition, in Fig. 3, it is also found that the peak at 2961 and 2927 cm−1 (in the blue box in the figure), which represents the reverse stretching vibration of CH3 and CH2 groups, was significantly decreased after UV irradiation [23], indicating that UV irradiation reduced the CH2 and CH3 groups on the surface of the epoxy resin. Meanwhile, there were also some changes in the peaks related to C-O-C stretching vibration at 1227, 1040 and 829 cm−1 . However, the difference of C-O-C peak by FTIR is hard to distinguish. To further quantitatively study the chemical structure, the C1s and O1s spectra of XPS experiment was analyzed and shown in Fig. 4.

Fig. 3. FTIR spectra of samples before and after UV irradiation

Fig. 4. The XPS spectra of epoxy samples before and after UV irradiation. C1s spectra for (a) 0 h, (b) 2 h, (c) 4 h and (d) 6 h. O1s spectra for (e) 0 h, (f) 2 h, (g) 4 h, (h) 6 h.

Figure 4 (a) to (d) show the C1s spectra of epoxy resin before and after UV irradiation. Based on the molecular structure of the epoxy resin and the FTIR spectra in Fig. 3, five

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chemical groups, including C-C/C-H, C-O, C = C, C = C, and O-C=O, are used to fit the C1s spectra of pristine sample [1]. As seen in Fig. 3, the UV irradiation FTIR only changes the content of each chemical group. Therefore, for the C1s spectra of samples after UV irradiation, we also used the abovementioned five groups to fit the experimental results. As seen, the UV irradiation significantly reduced the C-C/C-H groups and increased the C-O groups. In order to further investigate the changes in oxygen-containing chemical bonds, we analyzed the O1s spectra in Fig. 5(e) to (h). According to previous studies [14, 15], the C-O and C=O bonds in O-C=O groups were fitted to the curve as two independent chemical bonds, and the results are shown in Fig. 5 (e)–(h). It can be observed in Figs. 5 (f)–(h) that after UV irradiation, the C-O-C groups in the O1s spectra of the epoxy resin is significantly decreased, while the C=O and C-O-H bonds is increases by UV irradiation.

4 Disscussion Based on the FTIR results in Fig. 3 and XPS results in Fig. 4, it can be concluded that the UV irradiation reduces the C-C and CHn groups on the epoxy surface, and generates new C=O and C-O-H groups. In addition, it is also found that the O-C=O and C = C groups on epoxy surface are not sensitive to the UV irradiation, which are hardly unchanged after irradiation. Studies proved that the polar groups in organic dielectrics were potential trap centers [16–18]. Meanwhile, Bao also reported that the UV irradiation generated C=O groups could enhance the trap level in polymers. Thus, the UV introduced C=O and C-O-H on epoxy surface may form the deep trap center, which can repress the charge transport and increase the flashover voltage. Therefore, the UV irradiation is proved to be a potential method to increase the surface flashover voltage of epoxy resin.

5 Conclusion In this work, we experimentally studied the surface morphologies and chemical structures of EP and UV irradiated EP by AFM, FTIR and XPS. The main conclusions are followed: 1) The surface morphology and roughness of EP showed little change before and after UV irradiation; 2) UV irradiation reduced the CH2 , CH3 groups on the surface of EP greatly and increased the C=O and C-O-H groups; 3) The C = C, O-C=O on the surface of EP has good resistance to ultraviolet radiation and is basically unaffected by ultraviolet radiation; 4) After UV irradiation, the cross-linking structure of the surface molecules of the epoxy resin is disrupted, resulting in molecular chain segments with O-H and C=O. Acknowledgement. This work was supported by the Science and Technology Project of Guangxi Powr Grid Co., Ltd. (GXKJXM20220024).

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References 1. Li, M., Niu, H., Shang, K., et al.: Mechanism of ozone-improved surface flashover performance of epoxy composites. Mater. Phys. Chem. 289, 126426 (2022) 2. Watson, N., Watson, J.: An overview of HVDC technology. Energies 13(17), 4342 (2020) 3. Li, C., Hu, J., Lin, C., et al.: Surface charge migration and dc surface flashover of surfacemodified epoxy-based insulators. J. Phys. D-Appl. Phys. 50(6), 065301 (2017) 4. Benasla, M., Hess, D., Allaoui, T., et al.: The transition towards a sustainable energy system in Europe: what role can North Africa’s solar resources play? Energ. Strat. Rev. 24, 1–13 (2019) 5. Niu, H., Qu, G., Li, M., et al.: Improved surface flashover voltage of epoxy following polythiourea-assisted coating with high gas adsorption ability. Appl. Surf. Sci. 618, 156546 (2023) 6. Li, Z., Ma, K., Li, B., et al.: Understanding effects of deep traps on DC surface flashover characteristics of Epoxy/MWCNTs-TiO2 nanocomposites in a vacuum. IEEE Trans. Dielectr. Electr. Insul. 29(5), 1838–1846 (2022) 7. An, Z., Yang, W., Xing, Z., et al.: Comparative study on direct fluorination and surface properties of alumina-filled and unfilled epoxy insulators. IEEE Trans. Dielectr. Electr. Insul. 27(1), 85–93 (2020) 8. Huang, Y., Min, D., Li, S., et al.: Surface flashover performance of epoxy resin microcomposites improved by electron beam irradiation. Appl. Surf. Sci. 406, 39–45 (2017) 9. Shao, T., Kong, F., Lin, H., et al.: Correlation between surface charge and DC surface flashover of plasma treated epoxy resin. IEEE Trans. Dielectr. Electr. Insul. 25(4), 1267–1274 (2018) 10. Liu, H., Li, B., Chen, J.: Concurrent enhancement of breakdown strength and dielectric constant in Poly(vinylidene Fluoride) film with high energy storage density by ultraviolet irradiation. ACS Omega 7(30), 25999–26004 (2022) 11. Bao, Z., Ding, S., Dai, Z., et al.: Significantly enhanced high-temperature capacitive energy storage in cyclic olefin copolymer dielectric films via ultraviolet irradiation. Mater. Horiz. 10(6), 2120–2127 (2023) 12. Li, Z., Gao, H., Zhang, L., et al.: Influence mechanism of UVIV on DC surface flashover performances of silicone rubber: from molecule modification to macroscopic characteristics improvement. Appl. Surf. Sci. 635, 157786 (2023) 13. Li, M., Zhao, J., Shang, K., et al.: Effect of fluorine hybridization on dielectric response of epoxy polymer. Polymer 281, 126124 (2023) 14. Briggs, D., Beamson, G.: Primary and secondary oxygen-induced C1s binding energy shifts in X-ray photoelectron spectroscopy of polymers. Anal. Chem. 64(15), 1729–1736 (1992) 15. Briggs, D., Beamson, G.: XPS studies of the oxygen 1s and 2s levels in a wide range of functional polymers. Anal. Chem. 65(11), 1517–1523 (1993) 16. Yuan, H., Zhou, Y., Zhu, Y., et al.: Origins and effects of deep traps in functional group grafted polymeric dielectric materials. J. Phys. D- Appl. Phys. 53(47), 475301 (2020) 17. Yuan, C., Zhou, Y., Zhu, Y., et al.: Improved high-temperature electrical properties of polymeric material by grafting modification. ACS Sustain. Chem. Eng. 10(17), 8685–8693 (2022) 18. Zhu, Y., Qiao, N., Dong, S., et al.: Side-chain engineering of polystyrene dielectrics toward high-performance photon memories and artificial synapses. Chem. Mater. 34(14), 6505–6517 (2022)

Study on the Influence of Key Component on the Fast Vacuum Switch Zhaowei Peng(B) , Shiyang Huang, Dangguo Xu, Peng Song, Linru Ning, and Yamei Li Electric Power Research Institute of State Grid Jibei Electric Power Company Limited, Beijing, China [email protected], {huang.shiyang,xu.dangguo,song.p, ning.linru,li.yamei.a}@jibei.sgcc.com.cn

Abstract. The fast vacuum switch can reach a high open velocity. It is a key part of the mechanical high voltage direct current circuit breaker. The fast vacuum switch is mainly driven by the current flowing repulsive coil. Now many researchers focused on the optical designed of the repulsive mechanism. Some common faults on the key component, including the repulsive coil, the repulsive disk and the bistable spring, were seldom discussed. In order to get a better understanding of the common fault, this paper carried out simulations about the aging of repulsive coil and bistable spring, the deformation of repulsive disk. The simulation results indicated that the aging of repulsive coil and bistable spring showed small effects on the motion of the fast vacuum switch. The deformation of repulsive disk showed obvious effect on the opening process. Keywords: Fast Vacuum Switch · Repulsive Disk · Bistable Spring

1 Introduction The wind power and solar energy are developing fast in recent years. These new energies distribute unevenly and the power generation is intermittent and random. The traditional power system is difficult to adapt to the transmission and consumption of these new energies. The flexible high voltage direct current (HVDC) transmission system is an important way to deal the transmission and consumption of the new energy [1]. Therefore, the flexible HVDC system has caused a lot of concerns. The 500 kV Zhangbei flexible HVDC transmission project was constructed and come into service in 2020. The flexible HVDC transmission system only allowed a very short time to clear the fault in the system. This means that the HVDC circuit breaker only has limited time to interrupt to short line current. The mechanical HVDC circuit breaker is low on-state loss and economical. However, the mechanical HVDC circuit breaker needs interrupt the short-line current in a very short time. The fast vacuum switch is the key part of the mechanical HVDC circuit breaker and it needs to achieve the rated contact gap in a very short time. The traditional spring operating mechanism is not suitable for the above fast current interruption. The electromagnetic repulsion mechanism can offer an adjustable © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 176–183, 2024. https://doi.org/10.1007/978-981-97-1064-5_19

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high open velocity. It has been applied to the fast vacuum switch in the mechanical HVDC circuit breaker [2–6]. The electromagnetic repulsion mechanism contains the repulsive coil, the repulsive disk and the bistable spring and so on. Now researchers mainly focused on the optimal design of the fast vacuum switch. Tian Yu et al. developed a simulation model of the fast vacuum switch and studied the effect of repulsive disk, repulsive disk and capacitors on the motion of the fast vacuum switch [7]. Fang Chunen et al. adopted the multi-strategy particle swarm optimization algorithm to carry out optical design for the fast vacuum switch. [8]. Zhang Ning et al. developed a simulation model for the fast vacuum switch with a coil type repulsive disk. Then optical design for the fast vacuum switch was conducted to improve the energy conversion efficiency [9] Zeng Nanxun et al. studied the effect of electromagnetic buffer on the fast vacuum switch [10]. Now there were still few studies about the influence of key components fault. In order to get a better understanding about the influence of the key components, simulations about aging of the repulsive coil and bistable spring were simulated. Then the influences of the deformation of repulsive disk were also studied. The simulation results indicated that the winding of the coil and the bistable spring constant showed relatively small influences on the motions of the fast vacuum switch. However, the deformation of repulsive disk had obvious effect on the on the motions of the fast vacuum switch.

2 The Simulation Model The electromagnetic force was calculated by the software Maxwell. The motion of the fast vacuum switch was simulated by the software Adams. Figure 1 presents the flow chart of the electromagnetic-mechanical joint simulation. From Fig. 1 we can see that the electromagnetic force taken from Maxwell were loaded to the fast vacuum switch model in Adams. Then the contact strokes were simulated and obtained in Adams. The simulation model was simplified from a 10 kV fast vacuum switch. Figure 2 presents the simulation model of electromagnetic force. The drive parts include two repulsive coils and a repulsive disk as shown in Fig. 2. The size and way of winding of coils or disk were taken from the 10 kV fast vacuum switch. Figure 3 presents the kinetic model of the fast vacuum switch in Admas. This model includes the contacts, overtravel spring, bistable spring and so on. The weight of the moving contact, insulation pull rod were obtained from the 10 kV fast vacuum switch. The bistable spring constant equaled to the value of the 10 kV fast vacuum switch. In order to verify the accuracy of the model, the displacement curves of the contact and drive part were measured by experiments. Figure 4 presents a comparison between the experimental results and simulation results. Figure 4 indicated that the displacement curve of the contact and drive part obtained from simulation were close to that obtained from experiments. This indicated that the simulation model was reliable. Then we carried out further simulation with this elctromagnetic-mechanical joint simulation model.

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g

Fig. 1. The flow chart of the electromagnetic-mechanical joint simulations

d

Fig. 2. The electromagnetic force simulation model in Maxwell.

3 Result and Discussion 3.1 The Influence of Repulsive Coil The repulsive coil was mainly wound by multiple strands of wire. The current flows the repulsive coil in a very short time. The winding of coil is prone to deformation after aging or current impact. Figure 5 presents the schematic diagram of the simulation model. The gap between windings in Fig. 5 (red arrows) were enlarged 1 mm and 2 mm. Figure 6 presents the comparison of electromagnetic repulsive forces with different gap between windings. From Fig. 6 we can see that the electromagnetic repulsive forces

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Fig. 3. The kinetic model of the fast vacuum switch in Admas

Fig. 4. The displacement curve of the contact and drive part obtained from experiments and simulation

with enlarged gap 0 mm, 1 mm and 2 mm were similar. Figure 7 presents the displacement curves with different gap between windings. Figure 7 indicated that the displacement curves with enlarged gap 0 mm, 1 mm and 2 mm were also similar. Therefore, the simulation results indicated that the gap between winding showed small influence on the motion of fast vacuum switch.

Fig. 5. The schematic diagram of the simulation model.

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Fig. 6. The comparison of electromagnetic repulsive forces with different gap between windings.

Fig. 7. The displacement curves with different gap between windings

3.2 The Influence of Bistable Spring The bistable springs are important components to maintain the open state and close state. The bistable spring constant might decrease when the bistable springs work for a long time or many times. There are two bistable springs in a fast vacuum switch. The constant of each bistable spring might also be different. In order to get a better unstanding about the influence of bistable spring, the bistable spring constant decreased to 90%, 80% were simulated. What is more, two bistable springs with different constants were also simulated. Figure 8 presents the displacement curves with different spring constants. From Fig. 8 we can see that there was still small influence on the displacement curve when the

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Fig. 8. The displacement curves with different spring constant.

constant decrease to 80%. Besides, when a bistable spring constant decreases to 90% and another bistable spring constant remains unchanged, the displacement curve (green line) is still close to that of normal constant. 3.3 The Influence of the Repulsive Disk The drive force of fast vacuum switch is closely related to the eddy current in the repulsive disk. The repulsive disk needs to withstand the high-speed impact. Therefore, deformation might occur in the repulsive disk. In this section, the upwarp repulsive disks were simulated with different deformation. The warps of the repulsive disk edge were 1 mm and 2 mm. Figure 9 is the sketch map of deformation of the repulsive disk.

Fig. 9. The sketch map of deformation of the repulsive disk.

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Figure 10 presents the electromagnetic repulsive forces with different deformations. From Fig. 10 we can see that the electromagnetic repulsive forces at about 0.4 ms increases when the upwarp deformation of the repulsive disk increases. Moreover, the buffering electromagnetic repulsive force at about 2 ms decreases when the upwarp deformation of the repulsive disk increases. Figure 11 is the displacement curves with different deformations. Figure 11 shows that the open velocity increases when the upwarp deformation of the repulsive disk increases. The difference of displacement curves with different deformations are large in the later stage of open process.

Fig. 10. The electromagnetic repulsive force with different deformations.

Fig. 11. The displacement curves with different deformations.

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4 Conclusion An electromagnetic-mechanical joint simulation of the fast vacuum switch has been developed in this paper. Then simulations about influences of the repulsive coil, the bistable spring and repulsive disk was studied. The following conclusions can be draw. The aging of repulsive coil shows small influence on the motion of the fast vacuum switch with an enlarged winding gap 2 mm. Moreover, the bistable spring also shows limited influence when the bistable spring constants decrease or become unbalance. The deformation of repulsive disk has obvious effect on the motion of the fast vacuum switch even only a relatively small deformation occurs. It indicated that the repulsive disk deserved more attention. Acknowledgments. This work is supported by the science and technology projects of State Grid Corporation of China (Deepening research on on-site current breaking test technology of HVDC circuit breaker, KJZ2022028).

References 1. Tang, G., Luo, X., Wei, X.: Multi-terminal HVDC and DC-grid technology. Proc. CSEE 33(10), 8–17 (2013). (in Chinese) 2. Peng, C., Husain, I., Huang, A., Lequesne, B., Briggs, R.: A fast mechanical switch for medium-voltage hybrid DC and AC circuit breakers. IEEE Trans. Ind. Appl. 52(4), 2911–2918 (2016) 3. Tan, Y., et al.: Repulsion mechanism applied in resistive-type superconducting fault current limiter. IEEE Trans. Appl. Supercond. 26(6), 1–9 (2016) 4. Zhu, Z., Yuan, Z., Chen, L., He, J., Zhu, Z.: Vibration characteristics of thomson coil actuator based on simulation and experiments. IEEE Trans. Energy Convers. 35(3), 1228–1237 (2020) 5. Wen, W., et al.: No-load dielectric recovery of the ultra-fast vacuum switch in hybrid DC circuit breaker. IEEE Trans. Power Delivery 34(3), 840–847 (2018) 6. Liu, S., Hu, P., Jiang, D., Liang, Y., Zhuang, J.: A fast LVDC vacuum hybrid circuit breaker: dielectric recovery and design consideration. IET Gener. Transm. Distrib. 15(4), 15–21 (2021) 7. Tian, Y., Wang, L., Tian, Y., Li, Z., Dong, E.: Multi-field co-simulation optimization method for high-speed switch in DC circuit breaker. High Voltage Eng. 45(1), 55–62 (2019). (in Chinese) 8. Fang, C., Tang, X., Li, W., Zhang, N., Wei, X., Chen, J.: Optimization design of fast mechanical switch for 500 kV DC circuit breaker based on multi-strategy particle swarm algorithm. High Volt. Apparat. 58(1), 79–88 (2022). (in Chinese) 9. Zhang, N., Wei, X., Gao, C., Chen, L., Gao, Y.: Research on optimization design of coil type electromagnetic repulsion mechanism for fast mechanical switch. Power Syst. Technol. 42(8), 2512–2518 (2018). (in Chinese) 10. Zeng, N., et al.: Research on electromagnetic damping for fast mechanical switch of HVDC circuit breaker. High Volt. Apparat. 56(3), 9–16 (2020). (in Chinese)

Study on Thermal Aging Characteristics of Typical Electromagnetic Coil Glass Fiber/Epoxy Composite Materials Dejiang Yu1 , Yanbo Ma1 , Yadong Zhang2 , and Huilong Wan2(B) 1 Zhongyuan Research Institute of Electronics Technology, Zhengzhou 450047, China

[email protected]

2 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

Abstract. In order to study the insulation characteristics of glass fiber/epoxy composites under extreme physical fields of typical electromagnetic coil launchers, 3240 and G11 glass fiber/epoxy composites were used as research objects. The temperature distribution characteristics of electromagnetic coil launchers were analyzed by finite element method, and an equivalent test platform was constructed for thermal aging test. Combined with macroscopic and microscopic tests, the aging mechanism of glass fiber/epoxy composites for coil launchers was revealed. At 110 °C, 130 °C, 150 °C aging temperature and 24 h(1 d), 72 h(3 d), 144 h (6 d), 216 h (9 d) aging time. The changes of aging characteristic quantities such as mass loss rate and impact strength of glass fiber/epoxy composites were studied respectively. The thermal aging mechanism of glass fiber/epoxy composites was analyzed by scanning electron microscopy and Fourier infrared spectroscopy. The results show that G11 glass fiber/epoxy composites have smaller mass loss rate, greater impact strength and greater elastic modulus than 3240 glass fiber/epoxy composites, which proves that G11 glass fiber/epoxy composites have better thermal aging characteristics. Keywords: Electromagnetic coil · Finite element method · fiberglass/epoxy composite material · thermal aging

1 Introduction The electromagnetic induction coil launcher has the advantages of large volume, large mass range, adjustable launch speed, safety and simplicity, and flexible structure. It is a key component of the new concept electromagnetic weapon and is widely used in scientific research, aerospace, defense and military industry and other related fields [1–3]. Glass fiber/epoxy composite material is an important insulation and structural reinforcement component of electromagnetic coil launcher, which has long been subjected to the extreme conditions of electro-magnetic-thermal-mechanical multi-factor cycle. Its aging failure is an important cause of damage to the electromagnetic coil launcher. Glass fiber reinforced resin matrix composites have the advantages of light weight, high © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 184–192, 2024. https://doi.org/10.1007/978-981-97-1064-5_20

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impact strength, large elastic modulus, good corrosion resistance, good heat resistance and excellent electrical performance [4]. Therefore, it can be used as the insulation material of the inner wall guide tube, interturn insulation, outer layer packaging and other insulation reinforcement parts of the coil for electromagnetic emission. The research in Reference [5] shows that the magnetoresistance and skin effect will cause uneven temperature distribution inside the coil. The research in References [6, 7] shows that with the increase of coil speed, the temperature rise of coils at all levels gradually increases. The research in Reference [8] shows that the ohmic loss will occur during the continuous launch of the coil, resulting in an increase in temperature rise and resistance, which may make the wire and insulation materials reach the temperature limit, and the temperature rise of the coil needs to be controlled. In reference [9], a three-dimensional transient coupled heat transfer model of electromagnetic pulse inductor in liquid cooling mode was established, and the temperature distribution and heat dissipation characteristics of the inductor under continuous discharge conditions were analyzed. Reference [10] introduced the method of measuring the internal temperature of the electromagnetic transmitter coil using thermocouples, and compared it with the calculated average temperature value. In the literature [11], the thermal management of the electromagnetic coil launcher was studied. The methods of energy recovery and improved coil structure design were used to reduce the coil heating and discharge the retained heat energy, and the emission rate of 6–12 rounds/min was realized. Reference [12] proposed a high-strength manufacturing method using a parallel winding scheme to solve the excessively high temperature rise of the coil launcher. The experimental results in [13] show that the electrothermal aging rate of epoxy resin under power frequency pulse voltage is lower than that under power frequency sinusoidal voltage. The experimental results in Reference [3] show that in the process of electrothermal combined aging, the aging effects of electricity and heat are mutually enhanced, which aggravates aging, so that the degree of deterioration of the sample is always greater than the algebraic superposition of the aging effects of the two alone. Therefore, it is of great significance to study the aging effect of glass fiber/epoxy composites under thermal action for analyzing its thermal aging law and state evaluation. In this paper, based on the results of finite element simulation and the establishment of an equivalent test platform, two kinds of glass fiber/epoxy samples, 3240 and G11, were used for thermal aging test. The appearance analysis, mass loss rate, impact strength measurement and elastic modulus measurement of the aged samples were carried out. The variation law of the characteristic parameters of the thermal aging samples was compared, and the thermal aging mechanism was analyzed by scanning electron microscopy and Fourier transform infrared spectroscopy.

2 Thermal Ageing Test 2.1 Finite Element Simulation The finite element simulation software is used to simulate the thermal multi-physical field coupling of a typical electromagnetic launch coil. The coil is a two-dimensional axisymmetric structure and the coil temperature distribution is shown in Fig. 1. Among them, the green area is the insulation layer, the blue area is the coil, the orange area is

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the air domain, and the gray is the armature. There are 8 layers of coils, each layer of coils has 6 turns, a total of 48 turns.

(a) 2D Axisymmetric Model of the Coil

(b) Coil Temperature Distribution

Fig. 1. 2D Axisymmetric Model of the Coil and Coil Temperature Distribution

2.2 Determination of Thermal Aging Temperature The coil temperature is up to 402K (128.85 °C) after multiple launch, as shown in Fig. 1(b). According to GB/T 20112–2015 “Evaluation and Identification of Electrical Insulation Systems, “the thermal aging temperature should be selected at least three temperatures, the selected temperature interval is 20 K, and the highest test temperature should be below the relevant transition temperature. According to JB/T 2197–1996” Electrical Insulation Material Product Classification, Nomenclature and Model Preparation Method,” the temperature index grade of glass fiber/epoxy is 155 °C. Therefore, the thermal aging temperature of this test is 110 °C, 130 °C and 150 °C. 2.3 Determination of Thermal Aging Time In the case of multiple continuous emission, the coil will rise rapidly to the peak temperature. It is assumed that the coil is always at the peak temperature under extreme conditions. Combined with the electromagnetic coil launcher each launch time. The thermal aging test time is 24 h (1 d), 72 h (3 d), 144 h (6 d), 216 h (9 d). 2.4 Determination of the Number of Samples According to the requirements of GB/T 11026.1-2016 ‘Heat resistance of electrical insulation materials Part 1: Evaluation of aging procedures and test results’ and GB/T 1408.1–2016 ‘Electrical strength test method of insulation materials Part 1: Test under power frequency’, 6 samples were used in each group of the test. Therefore, the number of 3240 glass fiber/epoxy and G11 glass fiber/epoxy samples is 96.

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3 Results of the Test 3.1 Micro Analysis (1) Scanning electron microscope Scanning electron microscope (SEM) is an electron microscope that generates images of a specimen by scanning the surface with a focused electron beam. Since the non-conductive sample will collect charge when it is scanned by the electron beam, especially in the secondary electron imaging mode, this will lead to scanning failure and instability of the scanned image. Therefore, for conventional imaging in SEM, the sample must be electrically conductive. The glass fiber/epoxy sample used in this paper is an insulating material, so the surface of the sample needs to be cleaned and sprayed before observation. 110 ºC

130 ºC

150ºC

110ºC

130ºC

150 ºC

0h

24h

72h

144h

216h (a) 3240 glass fiber/epoxy sample

(b) G11 glass fiber/epoxy sample

Fig. 2. Surface morphology of 3240 and G11 glass fiber/epoxy sample

From Fig. 2, it can be seen that the surface of 3240 and G11 glass fiber/epoxy samples before aging is smooth and flat, without surface defects such as cracks, and the structure is relatively complete. With the increase of aging time and temperature, the surface of the sample appears uneven cracks and collapses, and the surface structure of the sample has been damaged. G11 glass fiber/epoxy is similar to 3240 glass fiber/epoxy sample. With the increase of aging time and aging temperature, the surface of G11 glass fiber/epoxy sample appears cracks and becomes uneven, but the structure of the whole sample surface is still relatively

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complete. By comparing Fig. 2, under the same conditions, the surface of G11 glass fiber/epoxy sample is less damaged by thermal oxygen aging than that of 3240 glass fiber/epoxy sample. (2) Infrared spectrum analysis Fourier transform infrared spectroscopy identifies the composition of a substance by measuring the interaction between infrared light and the substance. When infrared light passes through a substance, some of the light is absorbed, while other parts pass through the substance and are detected. This absorption is caused by the vibration and rotation of molecules in the substance.

(a) aging temperature of 110 °C (E)aging temperature of 130 °C (F) aging temperature of 150 °C

Fig. 3. Thermal Aging Infrared Spectrogram of Sample 3240

(a) aging temperature of 110 °C ( )aging temperature of 130 °C ( ) aging temperature of 150 °C

Fig. 4. Thermal Aging Infrared Spectrogram of G11 Sample

The ether bond plays a key role in connecting the carbon skeleton in the epoxy resin. Under the action of thermal oxygen aging, the ether bond in the epoxy resin is broken, so that the original complete molecular chain is broken into many small molecules. Under the action of high temperature, the fracture of the ether bond in the epoxy resin and the fracture of the carbon-carbon bond linking the benzene ring make the phenol, one of the aging products of the epoxy resin, volatilize, resulting in a decrease in the absorption peak value of the benzene ring in the sample. At higher aging temperatures, the carbon-hydrogen bonds in the epoxy resin are oxidized, resulting in a decrease in

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the carbon-hydrogen bonds in the sample. It can be seen from Fig. 3 and Fig. 4 that the higher the aging temperature, the lower the peak value of the absorption peak at the corresponding wave number, indicating that the lower the content of the corresponding functional group, the more serious the damage of the epoxy resin molecule. With the increase of temperature and time, the decrease of the corresponding functional groups of G11 glass fiber/epoxy is comparable to that of 3240 glass fiber/epoxy. 3.2 Macro Analysis (1) Comparison of specimen appearance

110ºC

130ºC

150ºC

3240

G11

Fig. 5. Comparison of Appearance between 3240 and G11 Glass Fiber/Epoxy Specimens

Under different test conditions, the surface color changes of 3240 glass fiber/epoxy sample and G11 glass fiber/epoxy sample are shown in Fig. 5. At the same aging time, the higher the aging temperature, the deeper the color change on the surface of the sample; at the same aging temperature, the longer the aging time, the deeper the color change on the surface of the sample. Compared with 3240 glass fiber/epoxy and G11 glass fiber/epoxy, the color change of 3240 glass fiber/epoxy sample is deeper, indicating that the heat resistance of G11 glass fiber/epoxy is better. (2) Mass loss rate The calculation formula of mass loss rate is m0 − mij × 100% ηi = m0

(1)

In the formula, ηi denotes the mass loss rate of the specimen numbered i. m0 is the initial mass of the sample, and mij is the mass of the sample numbered i after aging at the j aging time. The mass loss curves of the sample under three aging temperature tests are shown in Fig. 6. Under the three aging temperatures of 110 °C, 130 °C and 150 °C, the mass loss rate of the samples showed an upward trend with the increase of aging time. And at the same aging time, the higher the aging temperature, the greater the mass loss rate of the sample. It can be seen from Fig. 6 that the mass loss of G11 glass fiber/epoxy sample is smaller than that of 3420 glass fiber/epoxy sample during aging. It shows that the thermal stability of G11 glass fiber/epoxy is better than that of 3240 glass fiber/epoxy.

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(a) 3240 glass fiber/epoxy sample

(E) G11 glass fiber/epoxy sample

Fig. 6. Mass loss rate of 3240 and G11 glass fiber/epoxy sample

(3) Impact strength The impact test of simply supported beam / cantilever beam can be used to determine the impact strength of non-metallic materials such as plastic electrical appliances, hard plastics, ceramics, nylon, glass fiber reinforced plastics, cast stone, fiber reinforced composites and insulation materials. Impact strength can directly reflect, evaluate or judge the ability of a material to resist impact. In the use of electromagnetic coil launchers, coil insulation materials are often subjected to stress shocks many times. The calculation formula of impact strength is a=

A × 103 b×d

(2)

In the formula, a is the impact strength of the glass fiber/epoxy sample, and the unit is kJ /m2 ; A is the impact energy absorbed by the sample, and the unit is J ; b is the width of the sample, the unit is mm; d is the thickness of the sample, the unit is mm. The impact strength curves of two kinds of glass fiber/epoxy samples under three aging temperature tests are shown in Fig. 7.

(a) 3240 glass fiber/epoxy sample

(E) G11 glass fiber/epoxy sample

Fig. 7. Impact strength of 3240(left) and G11(right) glass fiber/epoxy specimens

It can be seen from Fig. 7 that with the increase of aging time, the impact strength of the samples showed a downward trend. At the same aging temperature, the decrease of impact strength of G11 glass fiber/epoxy is less than that of 3240 glass fiber epoxy,

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indicating that the aging degree of impact strength of G11 glass fiber/epoxy is less than that of 3240 glass fiber/epoxy. (4) Elastic modulus and Poisson’s ratio Elastic modulus is an important performance parameter of engineering materials. From a macro point of view, elastic modulus can characterize the ability of an object to resist elastic deformation, while from a micro point of view, elastic modulus can reflect the chemical bond strength between atoms, ions or molecules that make up the material. The calculation formulas of elastic modulus is: E=

F/A × 106 L/L0

(3)

In the formula, E is the elastic modulus of the sample, the unit is MPa, F is the load loaded on the sample, the unit is N , A is the cross-sectional area of the sample, and the unit is mm2 ; L/L0 is the elongation corresponding to the unit length of the sample, dimensionless unit, which is measured by a static strain gauge.

(a) 3240 glass fiber/epoxy sample

(E) G11 glass fiber/epoxy sample

Fig. 8. Elastic modulus of 3240 and G11 glass fiber/epoxy sample

The displacement rate of the fixture at both ends of the sample was set to 0.1 mm/min. With the increase of aging time, the elastic modulus of 3240 glass fiber/epoxy sample and G11 glass fiber/epoxy sample showed a downward trend. From Fig. 8, The elastic modulus of the G11 sample is larger than that of the 3240 sample. It can be seen that under the same aging time, the higher the test temperature, the faster the elastic modulus of the sample decreases. Under the same conditions, the elastic modulus of G11 glass fiber/epoxy decreases less than that of 3240 glass fiber/epoxy.

4 Results of the Test Through the thermal aging test of 3240 and G11 glass fiber/epoxy materials, the aging characteristics of two kinds of glass fiber/epoxy materials were studied and compared. Firstly, the selection of thermal aging test samples of glass fiber/epoxy samples, the determination of test conditions and the process of thermal aging test were introduced. The micro-analysis and macro-analysis of the samples after thermal aging test were carried out. The following conclusions are drawn:

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(1) Scanning electron microscopy test, with the increase of aging time and temperature, the surface of the sample appeared uneven cracks, collapse and other phenomena. (2) Fourier transform infrared spectroscopy analysis showed that the ether bond was broken and the carbon-carbon bond on the benzene ring was reduced, which revealed the aging mechanism of the two glass fiber/epoxy materials at the micro level. (3) With the increase of aging temperature and time, the mass loss rate of the two glass fiber/epoxy samples showed an upward trend. (4) With the increase of aging temperature and time, the impact strength and elastic modulus of the two samples showed a downward trend. In summary, the thermal aging characteristics of G11 glass fiber/epoxy composites are generally better than those of 3240 glass fiber/epoxy composites.

References 1. Shen, Y.: Research on Aging and Evaluation Technology of Dry-Type Air-Core Reactors. Shanghai Electric Power University, Shanghai (2018) 2. Wang, Y., Wang, S., Huang, Y., Yi, L., Cai, Y.: Research on thermal aging characteristics of epoxy resin for dry-type transformer. High Volt. Technol. 44(01), 187–194 (2018) 3. Wang, Y., Liu, Y., Wang, S., Xu, H.: Effect of electrothermal aging on the properties of epoxy resin in dry-type transformers. Electrotech. J. 33(16), 3906–3916 (2018) 4. Zhang, Y., Gong, Y., Xiong, M., Bao, Q., Niu, X., Li, X.: Research on driving circuit improvement of Coilgun. IEEE Trans. Plasma Sci. 47(05), 2222–2227 (2019) 5. Li, S., Guan, X., Lei, B., Li, Z.: Simulation Analysis of the Temperature Field in an Induction Launcher[J]. IEEE Trans. Plasma Sci. 41(05), 1055–1059 (2013) 6. Zhang, Y., Xiong, M., Dong, M., Lin, X.: Research on fire extinguishing system of electromagnetic catapult. Intense Laser Particle Beam 32(02), 025023-1-6 (2020) 7. Tao, Z., et al.: Research on the temperature field of multistage synchronous induction coilgun. IEEE Trans. Plasma Sci. 45(07), 1295–1301 (2017) 8. Gong, Y.: Research on Electromagnetic Temperature Field of Electromagnetic Induction Coil Transmitter. Wuhan University, Wuhan (2019) 9. Ma, F., Li, B.: Thermal analysis of the pulse inductor for electromagnetic launch under continuous discharge condition. IEEE Access 9, 88027–88036 (2021) 10. Han, W., Lei, B., Li, Z., Guan, X.: Experimental study on internal temperature measurement of electromagnetic actuator drive coil. Micromotor 42(12), 74–76 (2009) 11. Skurdal, B.D., Gaigler, R.L.: Multimission electromagnetic launcher. IEEE Trans. Magn. 45(01), 458–461 (2009) 12. Guan, S., Wang, D., Guan, X., Guo, D., Wang, S., Liu, B.: Current sharing analysis of coil for electromagnetic launching. IEEE Trans. Plasma Sci. 47(05), 2393–2398 (2019) 13. Deng, S.: Saturated Reactor Epoxy Resin Temperature Field Simulation and Electrothermal Combined Aging Test Research. Chongqing University, Chongqing (2018)

Wide Area Protection Scheme for Power Distribution Systems with Renewable Energy Sources Yadong Liu1 , Zhe Shi1 , Feitong Yu1 , Kuizhong Wu2 , Jingshan Wang3(B) , and Yuanchao Hu3 1 Jilin Electric Power Research Institute Co., Ltd., Changchun 130021, China 2 State Grid Jilin Electric Power Co., Ltd., Changchun 130021, China 3 School of Electrical and Electronic Engineering, Shandong University of Technology,

Zibo 255000, China [email protected]

Abstract. The fault characteristics of new power distribution systems are changing significantly due to the development of renewable energy generation. Conventional protection and control methods are difficult to adapt to the problems caused by high penetration of renewables. A wide area protection scheme based on coordination of control and protection is proposed in this paper. The influence of renewable energy sources on distribution system protection is firstly studied. Then partitioning method for active distribution system is introduced to ensure that load can survive and be securely supported by distributed generators in local feeders after system splitting. Next, advanced feeder terminal units and intelligent electronic devices based wide area protection scheme is designed for achieving fast, selective, and reliable operation protection and fault isolation taking account into intentional islanding operation. The activity analysis of the control-protection coordination is conducted as well. Finally, the feasibility and effectiveness of the proposed scheme are analyzed through case studies. Keywords: Renewable energy sources · Distribution system · fault characteristics · coordination of control and protection · activity analysis

1 Introduction Todays, large-scale renewable energy sources are integrated into electric power distribution systems [1]. With the increase of penetration rate of renewable energy, distribution systems are developing into the novel and complex forms. From protection and control perspectives, distribution systems have encountered a number of challenges, e.g. bi-directional power flow might occur, the fault characteristics are complicated and randomized. Conventional protection schemes are difficult to adapt to the novel and complex forms of modern distribution systems, novel protection and control methods need to be developed [2]. Many researches have been done on protection schemes of distribution system with distributed energy resources (DERs), e.g. distributed generators (DG) [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 193–204, 2024. https://doi.org/10.1007/978-981-97-1064-5_21

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Although protection schemes of distribution systems with DG are widely discussed in the literature. However, most of the existing protection and control schemes have either slow responses or poor performance in connecting to the control and operation issues of DG [4, 5], for instance, DG is regarded as fixed power sources with some limitations and must be disconnected from the feeder after it is islanded from the grid [6]. From the future intelligent distribution systems perspective, the protection of active distribution systems should be strongly connected to the control and operation issues of distributed generators [7, 8]. In order to make full use of generating capacity of DERs and improve power supply reliability, conscious islanding is not prohibited and intentional islanding is encouraged according to IEEE1547-2008 and a new standard, i.e., IEEE1547-2011 has been issued to solve the intentional islanding problem. With more and more DERs integrated in the distribution system, DERs are expected to keep supplying power to the islanded feeder continuously when fault occur, e.g. potentially islanded modes of operation [9]. Therefore, intelligence protection and control scheme incorporating DERs islanding approach is strongly required in modern distribution systems. Wide area measurement and control system shows great potential to efficiently protect and control distribution systems integrating DERs [10]. The control modes of wide area system can be divided into two categories: centralized control mode and decentralized control mode. The decentralized mode shows more flexible and efficient and has better performance in protection, fault location, isolation, and restoration for distribution system with distributed-generation integration [11]. Therefore, it is necessary to develop decentralized wide area protection and control methods to adapt to the novel and complex forms of modern distribution systems. In this paper, a wide area protection scheme based on coordination of control and protection was proposed for power distribution systems with increasing renewable DERs penetration. The control-protection coordination scheme integrates protection and DER islanding approach in a coordinated way through advanced feeder terminal units (AFTUs) and intelligent electronic devices (IEDs). A feeder partitioning method for active distribution systems is introduced to deploying DERs in islands after system splitting to ensure that local loads can survive and are securely supported by DERs. On this basis, AFTUs and IEDs based wide area protection scheme is designed for achieving fast, selective, and reliable operation protection and fault isolation taking account into intentional islanding operation. The activity and cooperation analysis of the tripping link and sequential link are conducted. The control-protection coordination scheme adapts to protect power distribution systems with renewable energy sources under different fault types and also taking exploitation and utilization of the capacity of renewable energy sources to supply electric power. The rationality and effectiveness of the proposed scheme are analyzed through case studies.

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2 Influence of DERs on Protection 2.1 Influence on Protection Action When renewable DER is connected in a distribution system, the protection may refuse to act or act falsely, and the sensitivity would probably decrease. Figure 1 gives some schematic fault types. Bi-directional power flow could cause false protection action. When a fault occurs at F1 at the upstream side of DER, QF1 will act to isolate the fault. If the fault current provided by DER flowing through QF2 is beyond the current threshold, QF2 could act falsely.

Fig. 1. Schematic fault types.

When DER is connected, the assistant current generated by DER could cause false protection action. When a fault occurs at F2 at the downstream side of DER, QF4 will act to isolate the fault. If the protective range of protection 3 expands to the next range due to assistant current, QF3 could act falsely and lose cooperation with the downstream protection 4. Figure 2 gives a schematic additional fault state circuit.

Fig. 2. Schematic additional fault state circuit (fault at F2).

The fault current flowing through QF3 without DER is calculated as below.  ICD = UF2 (ZSB + ZBC + ZCD + ZF2 ) The fault current flowing through QF3 with DER is calculated as below.   (ZSB + ZBC )ZG  ICD = UF2 + ZCD + ZF2 ZSB + ZBC + ZG

(1)

(2)

where Z SB is the system equivalent impedance, Z BC and Z CD is the equivalent impedance of section BC and section CD respectively, Z F2 is equivalent impedance of section from D to F2, U F2 is the voltage of F2 before fault occurrence, Z G is the equivalent impedance

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of the DER. Assume that Z SB , Z BC , Z CD , Z F2 and U F2 are fixed values, the fault current would increase when DER is involved. Shunting effect caused by DER could cause refusing action and decrease sensitivity of protection scheme. When a fault occurs at F3 at the downstream side of DER, the fault current of protection 2 will decrease and backup protection will not activated. Figure 3 gives a schematic additional fault state circuit.

Fig. 3. Schematic additional fault state circuit (fault at F3).

The fault current flowing through QF2 without DER is calculated as below  IBC = UF3 (ZSB + ZBC + ZF3 ) The fault current flowing through QF2 with DER is calculated as below   (ZSB + ZBC )ZF3  ZSB + ZBC + ZF3 + = UF3 IBC ZG

(3)

(4)

Where Z F3 is the equivalent impedance of section from C to F3, U F3 is the voltage of F3 before fault occurrence. Assume that Z SB , Z BC , Z F3 and U F3 are fixed value, the fault current flowing through QF2 would decrease when DER is involved. 2.2 Influence on Automatic Reclosing and Island Line Protection When DER is connected in distribution network, reclosing failure may occur if the arc is not timely eliminated. When the breaker between system and DER recloses, asynchronous reclosing may happen if the DER is not disconnected. When an island is disconnected from distribution feeder, the topology structure and power flow are changed, and the protection setting value of the related line may change significantly under the islanded situation.

3 Wide Area Protection Scheme 3.1 Whole Design of the Scheme Figure 4 gives a schematic distribution system. As a distributed processing based wide area protection, the distribution system is partitioned into reasonable protected zones. AFTU and circuit breaker (CB) are installed at the boundary between the adjacent zones. Simultaneously, splitting equipment (SE) is deployed at the boundary CB between zone with DER and zone without DER. AFTU can detect the local information constantly and exchanges information with its adjacent AFTUs. And then AFTUs identify faulted

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zone by comparing the directional fault information on boundary of each zone, and execute corresponding protective and control actions. SE monitor voltage waveform and frequency and detect the directional fault information. After meeting splitting conditions, it sends open commands to the breaker at splitting point. Once receiving trip signal, the corresponding breaker opens to isolate the faulted zone and form planned island. IEDs are situated at controllable switches, e.g. load switch, sectionalizing switch, in partitioned zones.IED can monitor the current information of its corresponding controllable switch continuously, which includes magnitude of current and direction of power flow. When a fault occurs, AFTUs identify the faulted zone and IEDs locate the fault quickly according to local and adjacent information. Then subsequent measures will be taken to isolate the fault section, implement intentional islanding, and reconnect the islands to the distribution system after fault clearance.

Fig. 4. Schematic distribution system.

3.2 Partitioning of Distribution System The proposed protection scheme needs in advance to determine how to partition distribution system into reasonable protected zones. The active distribution system partition scheme takes into account the operational feasibility of partitions for post-segmentation distribution systems [12]. Generation-load balance in certain part of distribution system with DERs after system separation is a priority. In addition, hardware devices should be convenient to be installed at separation points and to execute separation from practical controlled separation perspective. The system partitioning procedure starting from the terminal of active radial feeder, and a local part with island operation capability, which consists of DERs and the system, can be managed as a whole. And the local part is bounded by circuit breakers (CBs), separation points are formed. This approach is simple to implement and enables generation/demand balance in the potential islanding zone. In the zone containing DERs, the maximum output of DERs should meet the normal operation of loads in the corresponding zone, which is expressed as follows. n  i=1

PGi −

k 

PLi ≥ 0

(5)

j=1

where PGi is the output of the ith generator, PLi is the load of the ith node. Distribution system is divided into two types of local system zones according to the partitioning method above: The zone is without DERs, where the loads are supplied by the

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main grid or adjacent power sources in normal operation. Another is the zone containing DERs, where the total generation output of DERs can satisfy the load consumption. According to the preplanned system partition, the controlled separation scheme assumes that splitting equipment (SE) can be installed at predetermined separation points. Distribution system splitting will be implemented by SE when fault occurs. The voltage variation, frequency deviation and over-current information are detected and taken as judging criteria. Meanwhile, the power flow direction is mainly taken as the operation criterion by SE. When SE receives the external trip signal from adjacent AFTU, it implements the splitting procedure. SE splits distribution system immediately into standalone zones by opening the corresponding circuit breaker. Then the distribution system is split into small zones, and the zone containing DERs can be able to operate in islanded mode. Figure 5 shows the logical diagram of splitting point judgment.

Fig. 5. Logical diagram of splitting point.

3.3 Protection Principle After the reasonable distribution system partition, wide area protective devices, i.e. AFTU, IED and SE, are equipped with fast communication capabilities. The faulted zone can be identified and isolated fast and well-succeeded islanding can be obtained under different fault scenarios. In order to reduce the power failure area, the specific fault section can be located accurately and isolated quickly in the faulted zone. As is shown in Fig. 4, the power flow direction from power source toward the downstream loads is defined as the positive direction. The circuit breakers close to system power source are defined as the upstream breakers and the circuit breakers away from system power source are defined as the downstream breakers. The description of protective and control processes are as follows. Faulted Zone Identification. When a fault occurs at F1, the fault current provided by system source flowing through CB1 is positive while the fault current provided by DER flowing through CB2 is negative. When a fault occurs at F2, the fault current provided by upstream grid flowing through CB1 and CB2 is positive. CB1 and CB2 are boundary circuit breakers, which are taken as demarcation points. When a fault occurs at the downstream side of a boundary breaker, the short-circuit directions of flowing through the boundary breaker and its upstream boundary breakers

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are all positive. When a fault occurs at its upstream side, the short-circuit directions of the boundary breaker and its upstream boundary breaker are different. In other words, when distribution system operates normally, the current flowing through all boundary circuit breakers is normal. When a fault occurs inside a zone, the magnitude of the current flowing through its boundary breakers will change hugely and the direction of the short-circuit power flow is different among the upstream boundary breaker andthe downstream boundary breaker. Therefore, by monitoring whether the local current is beyond the limit and comparing the local power flow direction with that of the adjacent circuit breakers through peer to peer communication, the faulted zone can be quickly identified. As is shown in Fig. 4, AFTUs detect the real-time electrical quantity information of their corresponding breakers and exchange information with adjacent AFTUs, and then the faulted zone could be located. Note that AFTU at the power source side only exchanges information with its downstream AFTU. The terminal AFTU only needs to satisfy the over-current condition for faulted zone location and do not need to exchange with upstream. In order to improve the sensitivity of protection and considering the relationship between upstream and downstream protection, the over-current threshold is set according to the maximum load current, which is shown below. Iϕ > IL. max

(6)

where I ϕ is the valid value of phase current, and I L.max is the maximum load current. After the faulted zone is located, the boundary AFTU of the faulted zone sends information to its downstream SEs, and then SEs will receive the external tripping signal sent by the corresponding AFTU. When the splitting condition of SEs is satisfied, the splitting points are disconnected and the islands formed. Fault Section Location. Figure 6 shows the flowchart of identifying the fault section. When a fault occurs at F2, the fault current provided by upstream grid flowing through CB1 and CB2 is positive. IEDs in each zone constitute its corresponding distributed decision structure, which possesses the advantages of less data transmitting and processing time. Moreover, it is not affected by the fault tolerance problem. IEDs detect the current information of corresponding switch continuously. AFTUs send starting signals to IEDs in the faulted zone after isolation of faulted zone, and then the IEDs exchange information with adjacent ones. If the current is detected by an IED while its downstream adjacent IED did not detect fault current signal, it confirms that the fault is between them. The corresponding switch will open to isolate the fault. Intentional Islanding Scheme. In reality, often the output of DER is less than the local load demand. Therefore, the power exchanged between the zone and the rest of grid will result in power imbalance in the zone when it transits to island operation. Load shedding is needed according to the real time load and output of DERs to enable generation/demand balance after island formed. The load voltage and angular frequency can be detected by AFTUs during normal operation. Before island formed, the load curtailment is calculated as below. P/P0 = −(ρKG + KL )f /f0

(7)

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Fig. 6. Flowchart of identifying faulty section.

where ρ is the reserve capacity factor which is the ratio between the system’s reserve capacity and total power-output, P is the sum of generator output variation (positive when increase) and load variation (negative when increase), P0 is the total output of system units, P/P0 is the relative variation of system active power, f /f 0 is the relative variation of the system frequency, K L is the static frequency characteristic constant of load i, and K G is the static frequency characteristic constant of generators. When power deficit occurs in islands, the amount of load curtailment is obtained according to Eq. (7). Load characteristics and load priority are decided according to the actual situation of system. After the island formed, AFTU will send load shedding signal to corresponding IED at load switch to curtail the corresponding load. Then generation and demand get balance inside the islanded zone, and a stable intentional islanding is achieved. The total system power after load shedding can be calculated below.     PJH = Pqe − KPX fhf 1 − Kfhf (8) where PJH is the total system power after load shedding, f hf = ( f e –f hf )/f e is the relative variation of recovery frequency, K is effect coefficient of load regulation, Pqe is the maximum system power deficit, and PX is the total system power before load shedding. To maintain a stable operation, the power deficit of an island must satisfy d = PG − PL < ε

(9)

where d is the power deficit within the island, and ε is the maximum allowable tolerance of active imbalance within the islands.

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Reclosing, Fault Isolation and Reconnection of Intentional Island. More than 80% of distribution system faults are transient faults and reclosing can be used to improve supply reliability. If a reclosing scheme is activated, the upstream IED sends reclosing command after a delay. If the fault is a permanent fault, the breaker will be accelerated to trip, and the fault zone is isolated quickly. The downstream potential islanding zones transitions to islanded mode according to preplanned intentional islanding scheme. After fault is eliminated, the system side switch will be closed. The closure of the boundary switch is directly depends on voltage level in its downstream area. If the downstream area is an island or supplied by other power sources, the boundary switch will be closed at an appropriate moment i.e. re-synchronous moment and reconnection of intentional islanding to the main grid is achieved. If the voltage level in the downstream is too low, the boundary switch will close directly. If the fault is a transient fault, the upstream switch will be reclosed successfully. The closure of the downstream switches according to the control strategies described above.

4 Case Studies A 10 kV distribution system, which is shown in Fig. 7, is used as the test example for validating the proposed scheme. It consists of main source, branches, DER1, DER2 and loads. After island formed, the generation operation mode of DER1 and DER2 transition from constant active power to voltage frequency regulation mode. According to the system partition principle presented in Sect. 3.2, this system can be divided into four zones. Zone 2 and zone 4 are potential intentional islanding zones. AFTU1–AFTU4 are installed at CB1–CB4. SE1, SE2 and SE3 are deployed at CB2, CB3 and CB4. CB2, CB3 and CB4 are regional boundary circuit breakers between zone 1 and zone 2, zone 2 and zone 3, zone 3 and zone 4, respectively. IED2 ~ IED17 are installed at S2–S17. S2–S17 are sectionalizing switches.

Fig. 7. Configuration of distribution system with DER and fault positions.

Current direction from upstream power source to loads is specified as positive. When fault occurs at different places, the protective and control processes for different fault conditions are described as follows.

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4.1 Case 1: Fault in the Zone 1 If at F1 a fault occurs, AFTU1 ~ AFTU4 detect big variations in the current compared to their normal current and start up. As is shown in Fig. 7, each AFTU communicates with its direct neighbors. For two adjacent AFTUs, only AFTU1 and AFTU2 have opposite fault current flow directions. So the faulted zone is identified between AFTU1 and AFTU2, CB1 and CB2 is tripped by AFTU1 and AFTU2 respectively. Meanwhile, SE2 and SE3 satisfy splitting conditions, CB3 and CB4 are opened immediately. Zone2 and zone 4 transition to islands. To improve the reliability of power supply, after a delay AFTU1 sends a signal to CB1 to reclose. As illustrated in Fig. 8, if the fault is transient, CB1 recloses successfully. After that AFTU2 detects the voltage recovery in zone 1 and sends switching signal to CB2 to close after synchronism checking. AFTU3 detects the voltage recovery in zone 2 and closes CB3 without synchronism checking. Then AFTU4 detects the voltage recovery in zone 3 and sends switching signal to CB4 to close after synchronism checking. Then the distribution system restores to normal operation state. If the fault is permanent, CB1 accelerated trip. According to the situation of system partition and pre-set control strategy, zone2 and zone 4 continue operation in islanded mode, while zone 3 is in blackout state. Meanwhile, AFTU1 starts the fault location and isolation process by sending signals to IEDs in zone 1. The adjacent IEDs exchange fault measurement information through peer to peer communication, fast and accurate fault location and isolation are achieved. IED2 detects the fault current of S2, sends query information to IED3, and learn no fault current detected at S3 according to the messages responsed by IED3. It confirms that the fault is between IED2 and IED3. IED2 sends trip command to S2, then S2 is opened to isolate the fault.

Fig. 8. The movement process diagram of protection action and fault isolation.

After fault clearance, supply restoration procedure is initiated. CB1 closes firstly, and the power supply of zone 1 is recovered. Because zone 2 is in islanded operation mode, SE1 starts synchronism checking strategy after it detects the voltage recovery of zone 1. When meeting the requirements of synchronization, AFTU2 sends closing command to CB2 to close. Then the islanding operation mode of zone 2 ends and it is reconnected to the distribution system. After confirming the closure of CB2 by receiving the close-state signal sent by AFTU2, AFTU3 closes CB3 directly because zone 3 is in blackout state.

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The power supply of zone 3 is recovered. Since zone 4 is in islanding operation mode, SE3 also starts the synchronism checking strategy after it detects the voltage recovery of zone 3, and CB4 is closed by AFTU4 when the synchronization is met. Then zone 4 is reconnected to the main grid and the whole system restores to normal operation state. 4.2 Case 2: Fault in the Zone 2 If at F2 a fault occurs, AFTU1–AFTU4 detect the current variation and all of them start up. According to the flowchart of identifying fault section shown in Fig. 6, only AFTU2 and AFTU3 satisfy the faulted zone identification requirements, CB2 and CB3 are opened immediately. Meanwhile, SE3 satisfies splitting conditions. Upon receiving the trip signal from AFTU3, SEs opens CB4 immediately. The distribution system is partitioned into four independence zones. At the same time, AFTU2 sends fault information to IED18 deployed at DER1. And once receiving the information sent by AFTU2, IED18 immediately disconnects DER1 from zone 2 for reducing damage to DER1. According to the pre-set control strategy, AFTU2 sends a signal to CB2 to reclose after a delay. If the fault is transient, CB2 recloses successfully. Then the restoration process is completed step by step. If the fault is a permanent fault, CB2 accelerated trip to isolate the faulted zone. Meanwhile, AFTU2 sends signals to IEDs in zone 2 to start the fault location and isolation. IEDs exchange information with their neighbors, and by comparing the variations of current and flowing directions, the fault is located between IED5 and IED6. So S5 is opened to isolate the fault. 4.3 Case 3: Fault in the Zone 4 If at F3 a fault occurs, all AFTUs detect the current variation and start up. AFTU exchanges fault information with its directly adjacent AFTUs. According to local and adjacent information, the faulted zone i.e. zone4 is identified by AFTU4. Because AFTU4 is the terminal AFTU, it only sends trip command to CB4, and the faulted zone is isolated by opening CB4. Other circuit breakers, e.g. CB1, CB2 and CB3 are kept in closed state. Simultaneously, IED19 disconnect DER2 from zone4 by receiving the trip signal from AFTU4. Then after a delay AFTU4 sends a signal to CB4 to reclose. When the fault is transient, CB4 recloses successfully. Then the reconnection of DER2 is completed by closing S19. When the fault is permanent, CB4 accelerated trip to isolate zone4. AFTU4 starts the fault location and isolation process by sending signals to IEDs in zone 4. IED16 exchanges fault information with IED17, the fault is located between IED16 and IED17 and the isolation of the fault is implemented by opening S16. After fault clearance, CB4 closes firstly. Next, IED19 implements the closing operation of S19 to reconnect DER2 to zone4. Then the distribution system restores to normal operation state. The above results of case studies demonstrate that the wide area protect scheme has good effectiveness in protecting the security of active distribution systems containing high penetration of renewable energy sources under different fault types taking exploitation and utilization of the capacity of renewable energy sources to supply electric power.

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5 Conclusion In this paper, a wide area protect scheme based on the coordination of control and protection was proposed for power distribution systems with high penetration of renewable energy sources. The fault response of new power distribution systems was analyzed, a partitioning method of active distribution system was developed by taking into account the maximum available capacity of renewable DERs. On this basis, AFTU based fault zone identification, IED based fault section location, and whole design of the wide area protection scheme were presented. The activity and cooperation analysis of the tripping link and sequential link were implemented as well. Finally, the rationality and effectiveness of the proposed scheme were verified through case analysis. Acknowledgments. This work was supported by the Science and Technology Program of Jilin Electric Power Research Institute Co., Ltd. Under Grant KY-GS-23-01-03.

References 1. Ma, Z., Zhou, X., Shang, Y., et al.: Form and development trend of future distribution system. Proc. CSEE 35(6), 1289–1298 (2015). (in Chinese) 2. Chen, G., Wang, D., Qiu, Y., et al.: Challenges and development prospects of relay protection technology. Autom. Electric Power Syst. 41(16), 1–11 (2017). (in Chinese) 3. Rajalwal, N.K., Ghosh, D.: Recent trends in integrity protection of power system: a literature review. Int. Trans. Electr. Energy Syst. 30(10), e12523 (2020) 4. Bo, Z.Q., Lin, X.N., Wang, Q.P., et al.: Developments of power system protection and control. Prot. Control Mod. Power Syst. 1(7), 1–8 (2016) 5. Singh, M.: Protection coordination in distribution systems with and without distributedenergy resources–a review. Prot. Control Mod. Power Syst. V2(3), 294–310 (2017) 6. Gao, H., Li, J., Xu, B.: Principle and implementation of current differential protection in distribution systems with high penetration of DGs. IEEE Trans. Power Delivery 32(1), 565– 574 (2017) 7. Fan, X., Xia, Y., Zhang, K., et al.: Research on a principle of systemed protection in distribution system with renewable energy sources. Trans. China Electrotech. Soc. 34(zk2), 709–719 (2019). (in Chinese) 8. Qiao, Y., Wu, H., Wu, T., et al.: A partitioned current protection scheme of distribution system with inverter interfaced distributed generator. Trans. China Electrotech. Soc. 37(zk1), 134–144 (2022). (in Chinese) 9. Heidari, A., Agelidis, V.G., Zayandehroodi, H., et al.: On exploring potential reliability gains under islanding operation of distributed generation. IEEE Trans. Smart Grid 7(5), 2166–2174 (2016) 10. He, R., Yang, S., Deng, J., et al.: Reliability analyses of wide-area protection system considering cyber-physical system constraints. IEEE Trans. Smart Grid 12(4), 3458–3467 (2021) 11. Liu, Z., Su, C., Høidalen, H.K., et al.: A multiagent system-based protection and control scheme for distribution system with distributed-generation integration. IEEE Trans. Power Delivery 32(1), 536–545 (2017) 12. Wang, C., Pang, K., Shahidehpour, M., et al.: Flexible joint planning of sectionalizing switches and tie lines among distribution feeders. IEEE Trans. Power Syst. 37(2), 1577–1590 (2022)

Research on Verification Technology for Data Analysis Function of 110 kV(66 kV)–500 kV Cable Lines Partial Discharge Online Monitoring Systems Rong Xia1,2 , Jianjun Yuan1,2(B) , Ge Wang1,2 , Songhua Liu1,2 , and Lihong Li1 1 China Electric Power Research Institute Co., Ltd., Wuhan 430074, China

[email protected], {wangge,liusonghua,lilihong}@epri.sgcc.com.cn 2 State Key Laboratory of Power Grid Environmental Protection, Wuhan 430074, China

Abstract. Partial discharge (PD) online monitoring of high-voltage (HV) cable systems has been widely applied as an effective means of online monitoring in power systems. The present PD online monitoring systems’ data analysis function, however, differ significantly, and their application has not yet achieved the anticipated impact. Additionally, both locally and globally, there is currently no comprehensive way for verifying and evaluating the data analysis function of HV cable PD online monitoring systems. Therefore, this paper proposes a verification technology for the data analysis function of HV cable PD online monitoring systems. The effective verification schemes and comprehensive evaluation rules have been established. And 3 different types of PD monitoring systems have been verified field by the method. The technical support is provided for the selection of HV cable lines PD online monitoring systems, by verifying the data analysis function of the PD online monitoring systems in this paper. It can also better ensure the intrinsic safety of HV cables and channels. Keywords: High-voltage cable lines · Partial discharge · Online monitoring system · Data analysis function · Verification

1 Introduction In recent years, with the rapid development of the economy, the scale of HV cable lines in urban power grids has steadily increased [1]. The lengths of HV cable lines of State Grid Corporation have exceeded 40000 km [2]. At the same time, with the widespread application of intelligent operation or maintenance technologies and equipment, the numbers of operational HV cable monitoring systems in power grids continue to increase [3]. However, the application effectiveness of these monitoring systems has not fully met expectations, and technical verification is lacking. Among them, the problems of PD online monitoring systems are particularly prominent.

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 205–216, 2024. https://doi.org/10.1007/978-981-97-1064-5_22

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At present, PD is one of the main causes of insulation degradation and failure in cable lines [4]. Detecting cable insulation defects early can effectively prevent failures, and ensure reliable equipment operation [5, 6]. Therefore, PD online monitoring systems have become an important component of comprehensive online monitoring systems for HV cables. In DL/T 2271, the specified requirements of the monitoring, data recording, data analysis, anti-interference, alarm, communication, and human-machine interaction functions are given for PD online monitoring systems [7]. But there is no effective evaluation method or assessment standard for the specific functions, especially in the function of data analysis. In this paper, focusing on the function of data analysis of PD online monitoring systems, the effectiveness verification schemes and comprehensive evaluation rules are established according to DL/T 2271. In addition, an automatic model to discriminate PD maps based on deep learning is developed, verifying the accuracy of the PD maps output from the online monitoring system. The rest of the paper is organized as follows. Section 2 presents the introduction to PD online monitoring technology and methods. Section 3 presents the verification technology for the data analysis function of the PD online monitoring system. Section 4 presents the field application and verification results analysis. Section 5 makes a conclusion.

2 Introduction to PD Online Monitoring Technology 2.1 The Widely Used Technology of PD Online Monitoring PD online monitoring technology is one of the significant means to support the reliable operation of HV cables. Currently, common methods include high frequency current method, ultrahigh frequency method, ultrasonic method, etc. High frequency current method is a PD monitoring method based on the principle of pulsed current. When PD occurs in the insulating medium of power cables, flowing charges will be generated, and pulse current will be generated in the discharge circuit [8]. The pulse current is measured on the cable ground wire through a high frequency current sensor to detect the discharge signal [9]. The high-frequency current method is widely used because of the advantages of strong anti-interference ability and high detection sensitivity. Ultrahigh Frequency (UHF) method. When PD occurs in the insulating medium of power cables, it is accompanied by a process of neutralizing charges and stimulating short pulses [10]. During the process, the excitation point will emit a UHF electromagnetic wave with a peak value of GHz outward. The UHF method detects the PD signal by detecting this UHF electromagnetic wave through an antenna sensor [11]. The advantages of the UHF method are obvious, but further technical research is still needed at present.

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Ultrasonic Method. When PD occurs in power cables, it is accompanied by a relatively wide frequency band of acoustic waves propagating from the excitation point to the surrounding area. Acoustic sensors can detect this acoustic signal to detect PD phenomena in the cables and their accessories. The advantage of the ultrasonic method is that it does not require the establishment of a direct electrical connection to the cable, and it has a strong anti-external interference function [12]. However, considering the propagation and attenuation of acoustic signals in cables, ultrasonic method is widely used in the detection of PD of high-voltage cables. 2.2 High-Frequency PD Online Monitoring Technology Currently, high-frequency current method is widely adopted for online monitoring of PD in HV cables both domestically and internationally, and the monitoring nodes of PD online monitoring systems are often installed at the positions of cable joints, for the cable joints in HV cable systems are prone to faults.

3 Verification Technology for Data Analysis Function of PD Online Monitoring System 3.1 Effectiveness Verification Schemes The real discharge characteristic signal needs to be reproduced and output during the implementation of the verification technology of the PD online monitoring system. Therefore, PDMaster-CT, the portable HV cable PD online monitoring system detecting device, has been designed and developed for the verification of data analysis function, to support the on-site evaluation of the effectiveness of monitoring systems [13, 14]. The field application of PDMaster-CT is shown in Fig. 1. The PDMaster-CT can reproduce the typical PD signals of insulation defect features within the HV cable and its accessories precisely, which are shown in Table 1.

Fig. 1. The field application of PDMaster-CT

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Typical PD atlas

Reproduction output of PDMaster-CT

Internal air-gap discharge of insulation

Insulated air-gap discharge in contact with highvoltage Conductors

Discharge of metal impurities inside the insulation

Jumping discharge of metal particles on the surface of high-voltage conductors

The effectiveness verification schemes involve the precise replication of PD signals at the HV cable joints using PDMaster-CT. The PD signals are coupled to the interior of the cable joints through coupling electrodes, simulating the PD occurrence by adjusting the signal characterization parameters of PDMaster-CT. In order to ensure the real-time of signals output by the PDMaster-CT, high-frequency PD detection device, as an auxiliary

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comparative judgment equipment, high-frequency PD detection device is needed in this occasion, and the device has already undergone effectiveness verification in advance. During the effectiveness verification process, the first step is to connect the wiring of the PDMaster-CT and fixed the coupling electrodes properly. Simultaneously, the high-frequency current transformer (HFCT) of the high-frequency PD detection device is installed on the metal sheath lead-out wire of the cable joint. The reference phase of PDMaster-CT and the high-frequency PD detection device are synchronized. Finally, the characteristic discharge signal maps, output into cable joints through PDMaster-CT, are acquired synchronously by PD monitoring systems and high-frequency PD detection device. Then it is important to compare the data obtained from the monitoring systems at the joint with the data output by PDMaster-CT. A comprehensive analysis is conducted to complete the effectiveness verification of PD monitoring systems, which should consider the results of the comparison and the discharge type identification of PD monitoring systems. An example of its implementation is shown in Fig. 2.

Fig. 2. On-site implementation example of the effectiveness verification

3.2 Comprehensive Evaluation Rules According to the effectiveness verification schemes in Sect. 3.1, the results of the data comparison between the monitoring systems and PDMaster-CT are needed to study and evaluate. Therefore, it is necessary to establish comprehensive evaluation rules based on DL/T 2271. In DL/T 2271, the requirements for data analysis function are that the PD online monitoring system should be able to provide two-dimensional spectra (Q-t, N-t, etc.) and three-dimensional spectra (Q--N, Q-P-t, etc.) that characterize parameters such as amplitude(Q), phase(), discharge frequency(N), as well as partial discharge phase distribution spectra(PRPD), pulse sequence phase distribution spectra (PRPS), or amplitude(Q), phase (), discharge frequency (N), etc., and equivalent time-frequency spectra,

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which are used to describe the discharge characteristics. In addition, the online monitoring system should have discharge type identification functionality, capable of determining the typical types of partial discharge in high-voltage cable lines, or providing possibilities for various types of partial discharge occurrences [7]. According to DL/T 2271, the comprehensive evaluation rules of effectiveness verification results are formed in Table 2. In Table 2, first of all, the points are assigned 0/1 based on whether the PD online monitoring system can provide PD signals maps. On this basis, by analyzing the spectrum detected by PD online monitoring system and reproduced by PDMaster-CT, the scores are divided 0–3 again based on the matching degree between them. The higher the matching degree, the higher the score, with a maximum score of 3 points. Finally, the other points are given in light of whether the PD online monitoring systems has the functionality to identify the types of PD signals. Table 2. Comprehensive evaluation rules for data analysis function of PD online monitoring system Number

Function description

Criteria

Score

1

The ability of PD signals reproduction

Can it provide spectrum data to describe the characteristics of monitoring parameter signals

0/1

Correctly match with the known reproduced typical PD signals spectra

0–3

Does it have the discharge types identification functionality

0/1

2

The functionality of PD types identification

3.3 Automatic Discriminative Model of PD Signals Maps Currently, it was found that the online monitoring system did not have the ability to identify the types of PD signals, which posed difficulties in evaluating the data analysis function of the monitoring system on-site. In order to help online monitoring systems identify PD signals maps, and assess the matching degree between the maps of the online monitoring systems detection and the typical PD signals images. An automatic model to discriminate PD maps based on deep learning will be developed. It can avoid the subjectivity of manual judgment in matching degrees. The processes of the model establishment are shown in Fig. 3. All PD signals maps prepared to train the model are all form typical PD signals images. This model can automatically identify and classify the features of the detected spectra of the online monitoring system, and provide the confidence level. It can support the on-site effectiveness evaluation of the data analysis function of the online monitoring system. Figure 4 shows the discrimination results of the model established in this paper for the typical signal maps detected on-site by the high-frequency PD detection device:

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Fig. 3. The processes of the automatic discriminative model establishment.

internal air-gap discharge of insulation with a confidence level of 77.43% compared to characteristic PD signals images. Therefore, as an auxiliary comparative judgment equipment, the high-frequency PD detection device can establish a connection between the PD online monitoring system and typical PD signals images by using the automatic discriminative model. The matching degrees between the typical PD signals images and the PD signals maps detected by the PD online monitoring system on-site can be calculated. The calculation formula is as follows: M = C1 /C2 · 100%

(1)

M represents the matching degree between the maps from the online monitoring system and the typical PD signals. C 1 represents the confidence level of the signals maps detected on-site by the online monitoring system given by the model. C 2 represents the confidence level of the detected on-site by the high-frequency PD detection device given by the model.

Fig. 4. An example of discrimination based on the automatic discriminative model

4 Field Application and Verification Results Analysis 4.1 Field Application According to the verification method for PD online monitoring system mentioned above, 3 different types of online monitoring systems have been conducted on verifying, the results are shown in Table 3.

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Table 3. The on-site signal detection results of 3 different types of PD online monitoring systems Internal air-gap discharge of insulation

Reproduction output of the PDMaster-CT

Detection onsite of the highfrequency PD detection device

Detection onsite of System A

Detection onsite of System B

Detection onsite of System C

Discharge of metal impurities inside the insulation

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The results of the confidence levels of the maps detected by High-frequency PD detection device and PD online monitoring systems are shown in Table 4. It is found that systems A, B, and C achieved the confidence levels of below 60% for the insulation internal air-gap discharge. And the confidence levels of systems A and B for the discharge of metal impurities inside the insulation was more than 60%, but the confidence level of system C is less than 50%. The results of the matching degrees between the detected maps of the monitoring systems and the typical PD signals images are calculated in Table 6. Analyzing the results of matching degrees, it is found matching degrees for internal air-gap discharge of insulation of 3 monitoring systems are generally lower than these for the discharge of metal impurities inside the insulation. In addition, the matching degrees of system A is slightly higher than other systems by calculating the average (Table 5). Table 4. The confidence levels of the maps detected by High-frequency PD detection device and PD online monitoring systems Internal air-gap discharge of insulation

High-frequency PD detection device

System A

System B

System C

Discharge of metal impurities inside the insulation

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Table 5. The matching degrees between the detection map of the monitoring systems and the typical PD signals images Internal air-gap discharge of insulation

Discharge of metal impurities inside the insulation

Average matching degree

System A matching degree

46.9%

86.4%

66.7%

System B matching degree

45.1%

81.9%

63.5%

System C matching degree

61.7%

64.5%

63.1%

4.2 The Study for the Verification of Data Analysis Function Data analysis is an important specialized function of the PD online monitoring systems. By applying the verification technology on-site, the comprehensive evaluation results of 3 types of systems are shown in Table 6 and Fig. 5. The evaluation revealed that none of the systems has the ability to accurately identify discharge types, making it impossible to achieve precise determination of discharge types based on monitoring data. And system A has the highest scores, performing the prominent function on-site. Table 6. The evaluation results of 3 types of PD online monitoring systems Number

Function description

System A

System B

System C

1

The ability of PD signals reproduction

1

1

1

3

2

1

0

0

0

2

The functionality of PD types identification

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Fig. 5. Summary of comprehensive evaluation results

5 Conclusion This study focuses on the verification technology for the data analysis function of HV cables PD online monitoring systems. 3 distinct kinds of online monitoring systems have been conducted on field verification, and the results indicate that the systems’ performance and utility vary. The verification results reflect the inadequate performance of the data analysis functionality in the PD online monitoring systems. This deficiency is mainly manifested in low matching degrees for typical PD signal maps, which are because of inaccurate signal sampling, incomplete data cleaning, imperfect algorithm models, or insufficient performance of the monitoring host. Therefore, in order to jointly promote the improvement and enhancement of the data analysis function of the PD online monitoring systems, it is imperative to coordinate the efforts of manufacturing businesses, cable operation and maintenance units, research institutions, and other industry stakeholders. Another shortcoming in these systems is their inability to effectively classify discharge types, which makes it challenging to reliably identify anomalous signals that point to internal discharge features in cables and their accessories. To address this issue, the automatic discriminative model based on deep learning is developed. By eliminating subjective human judgments, this model automatically identifies the types of discharge in the detected feature wave patterns from online monitoring systems and provides confidence levels for the classification results. Analyzing the evaluation results, it is evident that the PD online monitoring systems need to further enhance their data analysis functionality, and improve the detection and identification capabilities of abnormal signals indicating internal discharge characteristics in cables and their accessories. Acknowledgments. This work is supported by Research and application of a comprehensive monitoring system for power cables and pipe racks based on integrated sensing and transmission technology (Science and Technology Project of State Grid Co., Ltd, Grant No. 5500-202155420A0-0-00).

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References 1. State Grid Corporation of China: Regulations on the Operation and Maintenance Management of 110 (66) kV Cables and Channels of State Grid Corporation of China. State Grid (Transportation Inspection/3), 980 (2019). (in Chinese) 2. Equipment Department of State Grid Corporation of China: Guiding Opinions on the Construction of Centralized Monitoring in the Transmission Discipline. Equipment transmission, 61 (2021). (in Chinese) 3. Equipment Department of State Grid Corporation of China: Three-year (2022–2024) action plan for the professional high-quality development of high-voltage cables. Equipment transmission, 35 (2022). (in Chinese) 4. IEEE Std 4003—2006: IEEE guide for partial discharge testing of shielded power cable systems in a field environment. IEEE, New York, USA (2007) 5. Wester, F.: Condition Assessment of Power Cables Using PD Diagnosis at Damped AC Voltages. Optima Grafische Communicatie, pp.11–35 (2014) 6. Fuhr, J.: Procedure for identification and localization of dangerous PD sources in power transformers. IEEE Trans. Dielectr. Electr. Insul. 12, 1005–1014 (2005) 7. DL/T 2271-2021. Technical specification for partial discharge on-line monitoring system for high voltage cable. DL: China Electricity Council, China (2021). (in Chinese) 8. Tumanski, S.: Induction coil sensors: a review. Meas. Sci. Technol. 18, 31–46 (2007) 9. Jing, Y., Zhou, Y.: Application of distributed partial discharge on-line monitoring technology in Shanghai 500kV cross-linked polyethylene power cable line. High Volt. Technol. 41(04), 1249–1256 (2015). (in Chinese) 10. Roslizan, N.D., Rohani, M.N.K.H., Wooi, C.L., Isa, M.: A review: partial discharge detection using UHF sensor on high voltage equipment. J. Phys. Conf. Ser. 1432, 012003 (2020) 11. Álvarez, F., Garnacho, F., Ortego, J., Sánchez-Urán, M.Á.: Application of HFCT and UHF sensors in on-line partial discharge measurements for insulation diagnosis of high voltage equipment. Sensors (Basel, Switz.) 15(4), 7360–7387 (2015) 12. Li, J., Han, X., Liu, Z.: Review of partial discharge detection technology of electrical equipment. High Volt. Eng. 41(08), 2583–2601 (2015). (in Chinese) 13. Xia, R., Ouyang, B., Wang, Y.: Method and system for reproduction of partial discharge characteristic signal of insulation defect in high voltage cross-linked cable system. Beijing: CN11294644A, 08, 31 (2021). (in Chinese) 14. Xia, R., Wang, Y., Zhao, J.: Calibration method for high-frequency local discharge and live detection of high-voltage cable accessories. Beijing: CN104502876A (2017). (in Chinese)

Optimal Distributed Power Allocation for Isolated DC Microgrids Based on Projected Subgradients Meng Yue(B) , Xiaolan Wang, Tengfei Wei, Rui Hao, Lixin Wang, Jiarui Wang, and Zhaohui Li School of Electrical Engineering and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected]

Abstract. In this paper, an island DC microgrid composed of wind energy conversion system (WECS), photovoltaic system (PVS), storage battery and electric loads is investigated, and an optimization strategy based on Distributed Projected Subgradient algorithms (DPS) is proposed to solve the problem of power distribution among distributed power sources. First, wind power is used as the main source of power generation and photovoltaic is used as the secondary source, and batteries are used to adjust the power when needed to meet the load demand and maximize the utilization of wind power generation as much as possible, and to improve the charging and discharging process of batteries. To achieve this goal, the DPS algorithm is used to optimize the three subsystems locally, and the power reference values of each subsystem are obtained through information exchange and iterative updating. Then, the local controller adjusts the operating state of each subsystem according to the power reference value to achieve the overall optimized operation of the system. Finally, through simulation analysis, it is proved that using DPS algorithm to deal with the power optimization problem of isolated DC microgrid can well achieve the goals of balancing load supply and demand, making full use of wind power and photovoltaic power generation, extending battery life, and reducing system operation cost. Keywords: Islanded DC Microgrids · Projected Subgradient · Optimal Power Allocation · New Energy Conservation · Battery Life

1 Introduction Since China proposed the “30–60 goal,” distributed power generation technologies such as wind power and photovoltaic have become key planning directions at the distribution level of power systems [1]. While wind and solar resources are heavily influenced by meteorology, they offer complementary benefits in time and space, making hybrid generation systems viable. Additionally, energy storage devices are necessary to ensure continual power supply to the generation system [2]. In practical applications, it is essential to allocate power generation capacities of each device, while considering their © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 217–224, 2024. https://doi.org/10.1007/978-981-97-1064-5_23

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unique characteristics, and to adjust the operational status of the islanded DC microgrid to improve power quality and energy storage system service life all while meeting load demands. Therefore, studying the real-time power allocation of distributed power sources in microgrids is of significant importance. Currently, the primary research methodologies for addressing the microgrid power optimization allocation issue are centralized and distributed approaches. In the centralized methodological framework, literature [3] based on the fruit fly optimization algorithm examines optimal power allocation to minimize annual power generation costs and greenhouse gas emissions while fulfilling the load demand as well. Uncertainty modeling and optimal power allocation for renewable energy generation systems with battery storage are proposed in literature [4] using an improved particle swarm algorithm to train neural network weights. Although the centralized optimization algorithm may acquire optimal results, it overlooks the autonomy of each subsystem and relies heavily on reliable communication guarantees. In the distributed approach, literature [5] suggests a hierarchical step-by-step distributed predictive control strategy employing a two-layer control structure to address the energy optimization control requirements of hybrid generation systems. Literature [6] employs iterative distributed MPC to study the optimal allocation of power in off-grid hybrid generation systems. The problem is decentralized to subsystems to achieve distributed optimization, utilizing the local information of subsystems for coordinated control, thereby safeguarding the privacy of subsystems while maintaining a small amount of computation and high reliability that satisfies the distributed power supply’s “plug-and-play” characteristics. The distributed sub-gradient algorithm is one of the methods being used by researchers to study the distributed optimization of multi-intelligent body systems [7]. Literature [8, 9] proposes sub-gradient algorithms to achieve power supply reliability as the optimization objective, accomplishing the optimal power allocation problem of the system in a distributed realm. This paper presents a power allocation optimization control strategy for the subsystems in an isolated DC microgrid, utilizing Distributed Projected Subgradient algorithms (DPS). The optimization objective function of the system is first formulated, following which the DPS algorithm is applied to optimize the power reference values of the three subsystems - wind energy conversion system (WECS), photovoltaic system (PVS), and battery, taking into account meteorological forecast and predicted load demand. Information is exchanged through the contact line to obtain the power reference value that guarantees global optimization of the system, thus enabling the realization of distributed power optimization of hybrid power generation system based on DPS. A local control strategy is then designed to regulate the operational state of each subsystem, and the feasibility and effectiveness of the optimization control strategy is verified.

2 Structure and Modeling of Islanded DC Microgrids 2.1 Architecture of Wind-Solar-Storage Islanded DC Microgrid The architecture of an islanded DC microgrid consisting of a WECS, PVS, a battery and electric loads is shown in Fig. 1:

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Fig. 1. Islanded DC microgrid structure

2.2 WECS Modeling The model of the WECS can be described as [10]: ⎡ πv i ⎤ ⎡ ⎤ ⎤ ⎡˙ ⎤ ⎡ ⎡ − √ b q ϕm Rs iq ⎢ 3 3L iq2 +id2 − L iq − ωe id + ωe L fw1 gw1 ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ πv i x˙ w = ⎣ ˙id ⎦ = ⎣ fw2 ⎦ + ⎣ gw2 ⎦uw = ⎣ − RLs id − ωe iq ⎦+⎢ ⎢ − √ b 2d 2 ⎣ 3 3L iq +id P (T − 3 Pϕ i ) f g m q ω˙ e w3 w3 4 2J m 0

⎤ ⎥ ⎥ ⎥uw ⎥ ⎦

(1)

where Rs and L are the single-phase stator resistance and inductance, J is the rotational inertia of the impeller, ϕm is the excitation chain of the rotor permanent magnet poles, vb is the voltage on the DC bus, and uw is the control signal of the fan, Tm is the mechanical torque supplied to the PMSG by the wind turbine. The power injected into the DC bus by the wind power system is: π vb  Pw = 0.95iw vb = 0.95 √ id2 + iq2 uw (2) 2 3

2.3 PVS Modeling The model of the PVS can be described as: x˙ s =



v˙ pv = ˙is



fs1 fs2



+

gs1 gs2



⎡ i ⎤ ⎡ i ⎤ pv s − ⎢ C ⎥ ⎢ C ⎥ us = ⎣ v ⎦ + ⎣ v ⎦us pv b − − Lc Lc

(3)

where ipv , vpv are the current and voltage output from the PV array, is is the current injected into the DC bus by the PV array, C and Lc are the electrical parameters of the DC/DC converter, and us is the control signal. The power injected into the DC bus by the PVS: Ps = 0.95is vb

(4)

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2.4 Battery Bank Modeling Batteries connected to a series capacitor Cb and resistor Rb , The model is [11]:  ⎧ π 2 2 ⎪ √ ⎪ ⎨ ib = iw + is − iL =2 3 iq + id uw + is − iL  π vb = Eb + Vc + Rb √ iq2 + id2 uw + is − iL ⎪ 2 3 ⎪ ⎩ v˙ c = Cibb = C1b (iw + is − iL )

(5)

where vc is the voltage across the capacitor Cb . The power injected into the DC bus from the battery is as follows: Pb = ib vb

(6)

The state of charge (SOC) measures the remaining usable capacity of a battery by the percentage of the ratio of the remaining charge Qc to the rated charge QcN .

3 Optimal Power Allocation for Islanded DC Microgrids 3.1 Distributed Optimization Structure for Islanded DC Microgrids In order to realize the problem of optimal power allocation in islanded DC microgrids, this paper proposes a distributed hierarchical optimization control strategy, the structure of which is shown in Fig. 2:

Pwref *

Psref * Pbref *

Psref *

Pwref (k)

vw

Pbref (k)

us

ub

xs

Pw (k)

s

Pbref *

Psref (k)

uw xw

Pwref * Pbref *

,T

xb

Ps (k)

Pwref * Psref *

Pb (k)

SOC

Fig. 2. Distributed hierarchical optimization for an islanded DC microgrid

3.2 Optimization Models This paper focuses on an isolated DC microgrid that is well-suited for providing reliable electric power to residential homes in remote areas with abundant wind and solar

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resources. Our objectives in optimization are to meet load demand, maximize the consumption of wind and solar energy, and extend battery life. To achieve these goals, we define a global optimization performance metric function as:   2 ref (k) − Psref (k) − Pbref (k) arg min f (k) = arg min α PL (k) − Pw ref ,P ref ,P ref ∈X Pw s b

 2 2  ref max + β Pw (k) − Pw (k) + γ SOC(k) − SOC ∗

(7)

Where f denotes the global objective function of the system for the kth iteration; α, β, γ denote the weighting factors of each part of the objective function, which are taken as 1, 0.02, 0.4 according to the trial-and-error method. PL is the load demand, ref , P ref , P ref is the power reference value of the WECS, PVS and battery subsystems, Pw s b max is the maximum power value of the wind power subsystem, and SOC ∗ respectively, Pw is the optimal charging state of the battery. In performing the optimal power allocation of the system, the outputs of the subsystems should be within their constraints X, as specified in Eqs. (8)–(11): WECS output upper and lower bound constraints: ref max (k) ≤ Pw 0 ≤ Pw

(8)

PVS output upper and lower bound constraints: 0 ≤ Psref (k) ≤ Psmax

(9)

Battery output upper and lower bound constraints: Pbmin ≤ Pbref (k) ≤ Pbmax

(10)

Battery SOC upper and lower constraints: 0.2 ≤ SOC ∗ ≤ 0.8

(11)

The above optimization problem is dispersed into three subsystems to distribute the solution, and each subsystem seeks the optimal solution using the global optimization performance metric Eq. (7) as the optimization metric. The optimization solution  for the ref* = arg min f (k) optimization layer of the WECS, DPS1, is denoted as Pw [Psref ,P ref ] , b constrained to Eq. (8); The optimization solution  for DPS2, the optimization layer  of the PVS, is denoted as Psref* = arg min f (k)[P ref ,P ref ] , constrained to Eq. (9); The w

b

optimization solution for the battery optimization layer DPS3 is denoted as Pbref* =  arg min f (k)[Pwref ,Psref ] Constrained to Eq. (10)–(11). 3.3 DPS-Based Optimization Strategy In this section, the DPS algorithm is used to solve the above optimization model in a distributed manner, and the optimization variables are the power reference values of the

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three subsystems of wind, light, and storage, each of which has to estimate its optimal solution, and for convenience, assuming that each subsystem serves as a node, and denoting the ith node’s estimation of the optimal solution by hi = [hi1 hi2 hi3 ]T = ref P ref P ref ]T , i = 1, 2, 3. The algorithm is considered to converge when the h of the [Piw i is ib subsystems are equal to each other. The DPS iteration rule is expressed as: ⎧  ⎨ vi (k) = aij (k)hj (k) j∈Ni (k+1) (12) ⎩ h (k + 1) = P [v (k) − α ∇f (v (k))] i Xi i k i i where αk > 0 is the iteration step, the vector vi (k) is a weighted average computed at node i, Ni (k+1) denotes the node adjacent to i in the k + 1st iteration, aij (k) is the non-negative weight assigned to j by node i, the value according to the literature [9]. Applying the projection operator PX i to the power constraint fixes its value at the limiting boundary if the power exceeds the constraint. The sub-gradient of the local objective function of node i at point hi = vi (k) i.e.: ⎡

⎤ max (k) 2(α + β)h1 (k) + 2αh2 (k) + 2αh3 (k) − 2αPL (k) − 2βPw ⎢ ⎥ ∇fi = ⎣ 2αh1 (k) + 2αh2 (k) + 2αh3 (k) − 2αPL (k) ⎦   2αh1 (k) + 2αh2 (k) + 2 α + γ (ηb Tb )2 h3 (k) − 2αPL (k) − 2γ (SOC0 − SOC ∗ )ηb Tb

(13)

3.4 Local Controller Design With the shift in the relationship between power supply and demand, the wind and photovoltaic power generation subsystems may employ the DPS algorithm for supply and demand power balance optimization or the MPPT algorithm for maximum power point optimization. This paper utilizes a PI controller to control the work state of the wind and photovoltaic power generation subsystems. By comparing the actual output power with the reference value, a PWM signal is generated to regulate the duty cycle of the DC/DC converter, thereby regulating the output voltage and enabling the subsystem to operate in the appropriate work state [12]. The maximum generation capacity of the WECS and the PVS can be found in literature [6].

4 Simulation and Analysis 4.1 Experimental Data In this paper, a typical isolated DC microgrid system is taken as the research object, and the meteorological conditions on a certain day in a place in Gansu are selected as the input data, and the simulation time is 24 h. Figure 3(a) shows the outside wind speed vw , Fig. 3(b), 3(c) for the day of the temperature T and sunshine intensity λs changes, Fig. 3(d) simulates the change of the load demand current iL . MATLAB programming is used to solve the system power optimization allocation problem to verify the effectiveness of the DPS-based power optimization allocation strategy proposed in this paper.

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T( )

iL (A)

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Fig. 3. External environmental conditions and load current

4.2 Simulation Results and Analysis Figure 4 gives the waveforms of the respective power, total power, battery power, and load power of the WECS/PVS power subsystems during 24 h, respectively. It can be seen that the proposed power optimization allocation control strategy can still satisfactorily switch between maximum power tracking and given power tracking despite the changing meteorological environment. Pwmax

Pwref

Pw

Psmax

Psref

Ps

PL

Pw

Ps

Pb

Fig. 4. Islanded DC microgrid power

ib (A)

Figure 5 shows the charging and discharging current of the battery during system operation, and the SOC case kept at 20%–80%, which shows that the battery is basically in a shallow charging and discharging state at each time period.

Fig. 5. Battery current and SOC

5 Conclusion Addressing power optimization in isolated DC microgrids, this paper converts the global optimization objective function into individual subsystem optimization objectives. The implementation of DPS ensures the real-time satisfaction of load demands, stable system operation, and maximizes wind and solar energy utilization to extend storage battery service life. The results provide valuable insights for optimal management of independent power supply systems.

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Acknowledgments. This work was supported by the National Natural Science Foundation of China, grant number 61963024.

References 1. Zhang, Z., Kang, C.: Challenges and perspectives of constructing a new type of power system under the goal of carbon neutrality. Chin. J. Electr. Eng. 42(8), 2806–2819 (2022). (in Chinese) 2. Hao, F., Yuan, Z., Yuan, Z., et al.: Research and practice of steady-state power control strategy for off-grid microgrid. Power Syst. Prot. Control 48(22), 173–179 (2020). (in Chinese) 3. Zhao, J., Yuan, X.: Multi-objective optimization of stand-alone hybrid PV-wind-diesel-battery system using improved fruit fly optimization algorithm. Soft. Comput. 20, 2841–2853 (2016) 4. Masoumi, A., Ghassem-zadeh, S., Hosseini, S.H., et al.: Application of neural network and weighted improved PSO for uncertainty modeling and optimal allocating of renewable energies along with battery energy storage. Appl. Soft Comput. 88, 105979 (2020) 5. Kong, X., Liu, X., Han, M.: Hierarchical stepwise distributed predictive control for wind-solar hybrid power generation system. Sci. China Inf. Sci. 48(10), 1316–1332 (2018). (in Chinese) 6. Wang, X., Wang, Z., Zhang, X., et al.: Distributed predictive control for off-grid hybrid power generation systems. J. Solar Energy 38(9), 2403–2411 (2017). (in Chinese) 7. Zhong, Y.: Distributed subgradient stochastic projection algorithm with communication delay in switching networks. South China University of Technology (2020). (in Chinese) 8. Deng, S., Zheng, T., Chen, L., et al.: Distributed energy optimization management strategy for AC/DC microgrids to improve the reliability of critical load supply. High Volt. Technol. 47(01), 55–62 (2021). (in Chinese) 9. Yang, Y., Lu, Q., Wu, S., et al.: Coordinated primary frequency control for virtual power plant based on distributed subgradient-projection method. In: 2019 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), pp. 1638–1643. IEEE (2019) 10. Valenciaga, F., Puleston, P.F., Battaiotto, P.E.: Power control of a solar/wind generation system without wind measurement: a passivity/sliding mode approach. IEEE Trans. Energy Convers. 18(4), 501–507 (2003) 11. Lamzouri, F.E., Boufounas, E.M., El Amrani, A.: Efficient energy management and robust power control of a stand-alone wind-photovoltaic hybrid system with battery storage. J. Energy Storage 42, 103044 (2021) 12. Chen, S.Y., Chang, C.H.: Optimal power flows control for home energy management with renewable energy and energy storage systems. IEEE Trans. Energy Convers. 38(1), 218–229 (2022)

Active Recovery Control Strategy Under Nonlinear Unbalanced Load with Multiple Micro-source Islanding Lixin Wang(B) , Xiaolan Wang, Tengfei Wei, Jiarui Wang, Rui Hao, Meng Yue, and Zhaohui Li Lanzhou University of Technology University, Lanzhou 730000, China [email protected]

Abstract. Multi-micro-source islanding active restoration is an important measure to protect critical loads and regional power supply under extreme conditions. Load self-organization will cause bus voltage unbalance and frequency fluctuation, in which the nonlinear and unbalanced loads will further aggravate the situation, affecting the safe and stable operation of islanded microgrid active recovery. To address this problem, an unbalanced voltage and frequency fluctuation suppression strategy based on model-free predictive control algorithm is proposed. The strategy outputs the optimal reference power to the sag control in real time according to the load demand. By adjusting the optimal power output, the traditional negative sequence compensation algorithm solves the problem of voltage imbalance and voltage and frequency fluctuation when nonlinear unbalanced loads exist simultaneously at multiple PCC points of islanding active recovery. Finally, the parallel restoration strategy based on the black-start principle is formulated, and the effectiveness of the proposed method is verified by building simulation models under different control modes using simulation software. Keywords: Active recovery · Self-organizing network · Unbalanced load · Parallel recovery · Fluctuation suppression · Predictive control

1 Introduction Distributed power as an important part of the microgrid, can use its own control technology in the grid-connected mode to provide surplus power to the main grid or to obtain the shortage of power from the main grid to supplement its own deficiencies [1]. In recent years, domestic and foreign scholars have conducted several studies on the participation of microgrids in power system restoration. Literature [2] studied the optimization problem of power system reconfiguration when microgrid is used as a black start power source, but the paper did not consider the transient process during load grouping on the black start impact. Literature [3] optimally solved the output power of each DG by model predictive control, but the frequent turning on and off of the disconnecting device is detrimental to the system operation. Literature [4] investigated multi-time load restoration, but the paper did not consider the effect of bus power fluctuations on the load. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 225–232, 2024. https://doi.org/10.1007/978-981-97-1064-5_24

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Literature [5] realized the suppression of voltage and frequency fluctuations through the study of improved sag control, but the system studied does not include load grouping. Literature [6] designed feedforward disturbance compensation to suppress voltage fluctuation, but the unbalanced loads are not considered. The presence of a large number of individual loads affects the voltage balance. There are many research results on the participation of microgrid inverters in unbalance compensation. Literature [7] injected regulated negative sequence currents into the power loop to achieve negative sequence reactive power compensation, but the injected amount was a disturbance component. Literature [8, 9] used hierarchical control to achieve PCC point unbalance suppression, but it did not consider the inverter port unbalance. Literature [10] realized PCC point and output port voltage compensation by generating a negative sequence voltage command, but no in-depth study was made for multiple PCC points. Literature [11] calculated the negative sequence virtual conductance to control the negative sequence current output, and achieved the reduction of negative sequence voltage at PCC points. To address the above issues, this paper proposes a Model-Free Adaptive Predictive Control (MFAPC) strategy for black-start power supply in an islanded microgrid with a high proportion of unbalanced nonlinear loads. The strategy first designs the dynamic linearization function with the microgrid bus power and voltage input and output data; then, based on the existing data, the Pseudo Partial Derivative (PPD) and Pseudo Jacobian Matrix (PJM) are computed and predicted to realize the rolling optimization of the PJM for the future moment, thus forming the black-start power in an islanded microgrid with a high proportion of unbalanced nonlinear loads. The black-start voltage and frequency fluctuation suppression strategy of the isolated microgrid is developed. Based on the black-start principle, an islanding network model is designed and the effectiveness of the proposed strategy is verified by simulation.

2 Controller Design 2.1 Dynamic Linearization Model for Isolated Microgrids The microgrid system has certain nonlinear and coupling characteristics due to the different loads and micro sources carried by the microgrid system [12], so the following nonlinear input-output system model can be established for the microgrid system. Considering that the microgrid system is a multi-intelligence system with multiple isomorphic controllers, the nonlinear dynamic system model of the j controller can be expressed uniformly as follows [13]. yj (k + 1) = f (yj (k), · · · , yj (k − ny ), · · · , uj (k), · · · , uj (k − nu ))

(1)

where, k ∈ [0, 1,…, T ] denotes the moment; j = 1, 2,…, N denotes the j intelligent, yj (k) and uj (k) denote the output and input signals of the j intelligent at the k sampling moment, respectively. For the purpose of analysis, the system satisfies the following two assumptions: Assumption 1: The partial derivatives with respect to each component of the control input uj (k) are continuous. Assumption 2: System meets Lipschitz requirements. Lemma 1 Consider a multi-intelligent system (1) that satisfies assumptions 1 and

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2. If |u(k)| = 0 is satisfied, the system (1) can be transformed into a tight-format incremental data model. yj (k + 1) = Φ j (k)uj (k)

(2)

yj (k + 1) = yj (k + 1) − yj (k); uj (k) = uj (k) − uj (k − 1) where Φ j (k) is a bounded time-varying parameter pseudo Jacobian matrix (PJM) consisting of pseudo partial derivatives (PPD). 2.2 Control Algorithm Design According to the incremental data model, a one-step forward output prediction equation of the following form can be given. y(k + 1) = y(k) + Φ j (k)u(k)

(3)

Based on the above equation, we can further give the N-step forward prediction (N ) equation for the system as follows. Where Y j (k + 1) is the N-step forward prediction (N )

vector matrix; U j (k) is the control input increment vector; and if uj (k +j −1) = 0, j > Nu , then Eq. (3) can be written as the prediction equation. (N )

Yj

(N )

Yj

(k)

(4)

(k + 1) = [yj (k + 1), · · · , yj (k + N )]T ,

(N )

ΔU j

(Nu )

(k + 1) = E(k)y(k) + B(k)U j

(k) = [Δuj (k), · · · , Δuj (k + N − 1)]T ,

where Nu is the control time domain constant; E(k) is the N × N matrix whose elements are all ones; and B(k) consists of the first A(k) columns of the matrix Nu . ⎛ ⎞ Φj (k) 0 0 0 ⎜ Φ (k) Φ (k + 1) 0 ⎟ 0 ⎜ j ⎟ j ⎜ . ⎟ .. .. .. ⎜ . ⎟ . . . ⎜ . ⎟ B(k) = ⎜ ⎟ ⎜ Φj (k) Φj (k + 1) · · · Φj (k + Nu − 1) ⎟ ⎜ . ⎟ .. .. ⎜ . ⎟ ⎝ . ⎠ . ··· . Φj (k) Φj (k + 1) · · · Φj (k + Nu − 1) N ×N u

(N ) ΔU j u (k)

= [Δvuj (k), · · · , Δuj (k + Nu − 1)] , T

In order to minimize the tracking error caused by the prediction error criterion function to the control algorithm, the following criterion function is designed. T (Nu )

) ∗(N ) (N ) T J = [Y j (k + 1) − Y (N (k + 1) − Y j (k + 1)] + λU j j (k + 1)] [Y j

(Nu )

(k)U j

(k)

(5)

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where λ > 0 is the weighting factor; Y j (k + 1) = [y∗ (k + 1), · · · , y∗ (k + N )] in y∗ (k + i) is the desired output signal matrix of the system, combined with Eqs. (4) and (N ) (5) to make the criterion function equal to zero, and the partial derivative of U j u (k), the control law is solved as follows. (Nu )

U j

∗(Nu )

(k) = [BT (k)B(k) + λI]−1 AT1 (k)[Y j

(k + 1) − E(k)yj (k)]

(6)

Therefore, the control inputs at the moment are: u U j (k) = U j (k − 1) + gT U N j (k)

(7)

g = [1, 0, · · · , 0]T . The control block diagram is shown in Fig. 1.

Fig. 1. MFAPC Control Block Diagram

2.3 Characteristic Parameter Identification Considering the PJM with its slow time-varying characteristics, an improved projection algorithm is designed in this section to estimate the PJM. The estimation algorithm is as follows. ηuTj (k − 1) Φ j (k) = Φ j (k − 1) + 2 [y(k) − Φ j (k − 1)uj (k − 1)] μ + uj (k − 1) 





(8) 

Where, η ∈ (0, 2] is the step factor that can make the algorithm more robust, Φ j (k) is the estimated value of Φ j (k). The B(k) in Φj (k + 1), · · · , Φj (k + Nu − 1) cannot be calculated directly from the system data at time k. Therefore, an autoregressive

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model is established to predict the unknown parameters by using the existing estimated sequence value Φ j (1), · · · , Φ j (k), which is satisfied by the estimated sequence, and the autoregressive equation is as follows. 











j (k + 1) = θ1 (k)j (k) + θ2 (k)j (k − 1) + · · · + θnp (k)j (k − np + 1)

(9)

where θi is the coefficient and np is the autoregressive order. From the improved projection algorithm, the estimation of θ (k) is given by 

θ (k) = θ (k − 1) +

ϕc (k − 1) T 2 [φ c (k) − ϕ c (k − 1)θ (k − 1)] δ + ϕc (k − 1) 





(10)

MFAPC, as a multistep prediction improvement algorithm of MFAC, can be developed on the basis of the stability theory of MFAC, and the assumptions and literature citations on the stability of MFAC are first given. First, the assumptions and citations of the existing literature on the stability of MFAC are given [14, 15].

3 Simulation Analysis 3.1 Simulation Model and Steps In order to verify the effectiveness of the proposed black start scheme and black start active power recovery strategy for islanded microgrids, the simulation test platform shown in Fig. 2 is constructed based on the previous discussion.

Fig. 2. Active Recovery Architecture for Isolated Microgrids

The microgrid is equipped with energy storage device (DG1), diesel generator (DG2), photovoltaic generator set (DG3) and wind generator set (DG4), and the specific simulation parameters are shown in Table 1, among which, load 1 is the first-level load; DG4 adopts the maximum power point tracking control; the rated output voltage of DG is 380 V/50 Hz; loads 2–7 and 10 are the second-level loads; loads 8–9 and 11–12 are the third-level loads; and loads 8–12 are the third-level loads. 12 for the three-level load; Load 11 for the non-linear load, using three-phase uncontrolled rectifier circuit to simulate the start with 20 load.

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parameters

PID

MF-APC

KUP = 300, KUI = 100

μ = 0.51, δ = 0.24, λ = 0.85, η = 0.67

KIP = 300, KII = 0.1

ε = 10−4 , np = 3, Nu = 5, M = 4

3.2 Analysis of Simulation Results Figure 3 Simulink results can be seen, With the CFDL-MFAPC strategy, the bus voltage fluctuation can be controlled to within 5 V. Compared with the traditional multi-loop compensation strategy, the bus voltage fluctuation can be better suppressed without the need of positive and negative sequence separation, which ensures the power quality of the grid and the safe and stable operation of the islanded microgrid.

Fig. 3. Maximum Black Start Bus Voltage for Microgrids

Figure 4(a) shows that the traditional multi-loop compensation strategy in the process of microgrid device self-organization frequency offset can reach a maximum of 0.45 Hz, in 0.18 s–0.2 s in the unbalanced loads and nonlinear loads, this situation is more obvious, the system frequency will continue to fluctuate subsequently; the use of input-output data control microgrid frequency offset in 0.1 Hz, effectively weakening the DG and load grouping network. The transient frequency fluctuation generated by DG and load grouping is effectively reduced. Figure 4(b) results can be seen, When the CFDL-MFAPC strategy is adopted, the bus voltage unbalance is basically maintained at about 1%, although the input of nonlinear loads will cause a large step in the bus voltage unbalance, but according to the national standard of the voltage unbalance not exceeding 4% for a short period of time, the proposed strategy can still guarantee the stable operation of the system.

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Fig. 4. (a) Bus Frequency Comparison (b) Comparison of Bus Voltage Unbalance Degrees

4 Conclusion In this paper, a model-free predictive control based on system I/O data is proposed for the black start of an islanded microgrid system, which enables the microgrid to cope with the transient fluctuations of the grid and the startup of different loads in the case of total blackout of the system. First, the CFDL data model is used to describe the power system, which can simplify the description of the microgrid system by not losing the system information and compressing all the features of the system into the characteristic parameters, compared with the linear function or state equation. Second, the stability of the algorithm is proved by BIBO. Finally, simulation experiments show that the strategy in this paper can adapt to the microgrid with multiple unbalanced loads and nonlinear loads when the system is black-started and stabilized, and realize the microgrid power system voltage and frequency regulation without any difference. In future studies, the extension of the obtained results to the black-start of regional interconnected power systems will be considered. Acknowledgments. This work was supported by the National Natural Science Foundation of China, grant number 61963024.

References 1. Qian, F., Pi, J., Liu, J., et al.: A review of microgrid modeling and control theory. J. Wuhan Univ. (Eng. Edn.) 53(12), 1044–1054 (2020). (in Chinese) 2. Zhao, Y., Sun, L., Lin, Z., et al.: Optimization strategy of power system grid reconfiguration with microgrid as black-start power source. Power Syst. Autom. 42(17), 9–17 (2018). (in Chinese) 3. Li, J., Yu, H., Li, C., et al.: A black-start power coordination strategy for wind-solar storage based on model predictive control. Grid Technol. 44(10), 3700–3708 (2020). (in Chinese) 4. Liu, F., Lin, C., Chen, C., et al.: A post-disaster time-sequence load recovery method for distribution networks considering the dynamic uncertainty of distributed new energy. Electr. Power Autom. Equip./Dianli Zidonghua Shebei 42(7), 65–78 (2022). (in Chinese)

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5. Zhang, Y., Wu, Z., Jiang, Q., et al.: Black-start technology and coordinated restoration strategy of recipient grid based on wind-storage combined system. Eng. Sci. Technol. 55(2), 72–83 (2022). (in Chinese) 6. Chen, C., Gao, J., Cao, J., et al.: A smoothing method for voltage and frequency fluctuations during active islanding recovery in multi-source distribution networks. J. Shanghai Jiao Tong Univ. 56(5), 543 (2022). (in Chinese) 7. Wang, T., Nian, H., Zhu, Z.Q., et al.: Flexible compensation strategy for voltage source converter under unbalanced and harmonic condition based on a hybrid virtual impedance method. IEEE Trans. Power Electron. 33(9), 7656–7673 (2017) 8. Andishgar, M.H., Gholipour, E., Hooshmand, R.A.: Voltage quality enhancement in islanded microgrids with multi-voltage quality requirements at different buses. IET Gener. Transm. Distrib. 12(9), 2173–2180 (2018). (in Chinese) 9. Chen, M., Xiao, X.: Distributed voltage unbalance compensation control strategy for islanded microgrids. Power Syst. Autom. 41(8), 45–51 (2017) 10. Lai, J., Xie, T., Su, J., et al.: Coordinated control of voltage unbalance compensation for islanded microgrid based on particle swarm optimization algorithm. Power Syst. Autom. 44(16), 121–129 (2020). (in Chinese) 11. Wu, X., Liu, H., Tang, F., et al.: Negative sequence virtual conductor-based microgrid unbalance control strategy under islanding. J. Electrotechnol. 34(15), 3222–3230 (2019). (in Chinese) 12. Huang, X., Jin, X., Ma, L.: Optimized control scheme for off-grid black start of microgrid. J. Electrotechnol. 28(4), 182–190 (2013). (in Chinese) 13. Hou, Z., Liu, S., Yin, C.: Local learning-based model-free adaptive predictive control for adjustment of oxygen concentration in syngas manufacturing industry. IET Control Theor. Appl. 10(12), 1384–1394 (2016) 14. Hou, Z., Jin, S.: Model Free Adaptive Control: Theory and Applications. CRC Press (2013) 15. Guo, Y., Hou, Z., Liu, S., et al.: Data-driven model-free adaptive predictive control for a class of MIMO nonlinear discrete-time systems with stability analysis. IEEE Access 7, 102852– 102866 (2019)

Design of DC Surge Suppression for Airborne Computer Xuejian Wang(B) , Kai Dong, Ruoxuan Wang, Fei Feng, Zihe Li, and Wen Yan AVIC Xi’an Aeronautics Computing Technique Research Institute, Xi’an 710076, China [email protected]

Abstract. Aiming at the problem of surge voltage and current under 28 V DC power supply environment of airborne computer, this paper designs two kinds of surge current suppression circuit according to the different power and a surge voltage suppression circuit. Firstly, for circuits with 50 W–100 W power, precise control of surge current peaks is not required, a MOSFET based surge current suppression circuit for airborne system is designed by using the Miller plateau effect of MOSFET. Secondly, For circuits with power less than 30 W whose surge current peaks requires precise control, a low-power current surge suppression circuit is proposed by using NPN transistor and bandgap reference. Simulations and experiments are performed on LTspice and application circuit. The simulation and experimental results show that the proposed method can achieve the surge current suppression and surge voltage suppression and have a good application value. Keywords: Surge current suppression · Surge voltage · MOSFET

1 Introduction The surges in the power supply of airborne computers can be divided into voltage surges and current surges [1–3]. In the aircraft power supply system, current surges are usually caused by the charging of capacitors at the moment of power on or sudden changes of load current in the power supply system [4]. Voltage surges are usually caused by fluctuations of input. In order to protect these electrical equipment and prevent damage caused by surge voltage and current, it is necessary to carry out anti-surge treatment on the power circuit of electronic equipment [5–7]. For surge voltage, this paper designs a voltage surge suppression circuit based on MOSFET and boost circuit for 28 V DC input. This circuit has fewer peripheral devices and has the function of suppressing surge voltage for surge current, this article designs two types of current surge suppression circuits according to the power level. Among them, the high-power current surge suppression circuit utilizes the MOSFET Miller plateau effect, which is simple but not precise in control; [8] The low-power current surge suppression circuit can accurately control the maximum surge current through the current amplification characteristics of TL431. However, due to the power consumption © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 233–240, 2024. https://doi.org/10.1007/978-981-97-1064-5_25

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issue of the transistor, the application scenario of this circuit requires low power and some power losses [9, 10]. The national military standard GJB 181B-2012 requires that the surge current of airborne equipment should not exceed 5 times its rated value within 0–100 ms of equipment startup. After 100 ms, the surge current should return to the rated current. This standard only requires the peak and duration of a single surge current.

2 Design of Surge Current Suppression Circuit This section will introduce two types of surge current suppression circuits. 2.1 Surge Current Suppression Circuit Using MOSFET Miller Plateau Effect MOSFET is a voltage type control device that can be used as a switch. The complete conduction resistance RDS (ON) is generally only a few tens of milliohms, with low conduction loss. Moreover, due to its structure and leads, parasitic capacitance will be generated between the gate-source, gate-drain, and drain-source, affecting its switching speed. The equivalent circuit is shown in Fig. 1. CGD CDS CGS

Fig. 1. MOSFET equivalent Circuit

Based on the equivalent circuit of MOSFET, the opening process of MOSFET from micro conduction to complete conduction is analyzed as the voltage between the gate and source gradually increases (Fig. 2). From t0 to t1, the gate-source voltage VGS gradually increases from 0V to the turn-on threshold voltage VGS(th) . At this stage, the VDS of the MOSFET remains unchanged and the IDS = 0. From t1 to t2, the gate-source voltage VGS increases from the threshold voltage VGS(th) to the platform voltage (Miller plateau). The gate-source voltage charges the gate-source parasitic capacitor CGS . At this stage, the MOSFET begins to conduct, enters the linear region, VDS begins to decrease, and IDS starts to rise from 0 to IDSMAX . In stages t2 to t3, the gate-source voltage remains unchanged, and the gate-source voltage charges the Miller capacitor CGD . During this stage, the MOSFET is still in the linear region, and the VDS continues to decrease to IDS × VGS(th) (ON) . From t3 to t4 stages, the gate-source voltage VGS continues to rise from the Miller plateau voltage. At this stage, the MOSFET exits the linear region and enters the fully saturated conduction stage. VDS is the product of the load current IDS and the conduction resistance RDS (ON) .

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Fig. 2. MOSFET conduction process VDS , VGS , and IDS waveforms

Fig. 3. High power current surge suppression circuit

By utilizing the the Miller plateau, a current surge suppression circuit can be designed, As shown in Fig. 3. R5 and R6 are voltage divider resistors with values of 100k, and D2 is a 15 V voltage regulator, which is used to reduce the voltage stress of capacitors C7 and M2. C8 is a large filter capacitor at the input terminal, the capacitance value of C8 is set to 470 µF. When the input is powered on, a voltage is established between the drain and the sources of MOSFET. The RC delay circuit composed of R5 and C7 makes the MOSFET gate voltage unable to step, the gate voltage rises slowly with the charging of C7. Using the Miller plateau effect of MOSFET, C8 is charged slowly, and the surge current is suppressed. By changing the values of R5 or C7, the required surge current suppression effect can be adjusted. The simulation and experimental results are shown in Figs. 4 and 5. In Fig. 4, the red line represents the MOSFET gate voltage waveform, while the purple line represents the current flowing through capacitor C8. After being powered on for 32 ms, the gate-source voltage is 3.5 V, and the MOSFET begins to conduct. After the gate-source voltage reaches 4.5 V, the MOSFET fully conducts at 43 ms. At the same time, the maximum surge current is suppressed at 3.7 A.

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Results of the experiments proved that the simulation analysis is correct, in the experiment, the maximum surge current was 3.4 A.

Fig. 4. Simulation result of high power current surge suppression circuit

Fig. 5. Experimental result of high power current surge suppression circuit

2.2 Surge Current Suppression Circuit Using NPN Transistor and Bandgap Reference The advantages of the method proposed in Sect. 2.1 is that the conduction time of MOSFET is adjustable, that is, the surge current suppression effect is adjustable. By replacing high-power MOSFET, it can be applied to high-power circuits. The disadvantage is that its surge current suppression effect is not accurately. For this reason, this paper proposes another surge current suppression circuit suitable for low-power, which can accurately suppress the maximum surge current. TL431 is a three-terminal adjustable shunt regulators. It can be used as a current amplifier, the input voltage is compared with the reference voltage, and then the comparison results are applied to adjust the output of current amplifier. According to this characteristic, a circuit that can accurately control the peak surge current can be designed, as shown in Fig. 6 A small resistance R3 is the current sampling resistance, and its resistance value is set to 1.5 . R3 is connected in parallel between REF and Anode of TL431. C3 is a large

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capacitor at the input terminal, the capacitance value of C3 is set to 2200 µF. When the 28 V bus is powered on, the NPN transistor Q1, Q2 are turned on, As the input current increases, the voltage at both ends of R3 increases. When the voltage is greater than 2.5 V, the cathode and anode of TL431 begin to conduct, resulting the current at the base of Q1 and Q2 to decrease, and then, the emitter current decreases.

Fig. 6. Surge current suppression circuit using NPN transistor and bandgap reference

Through the negative feedback regulation of TL431, the peak value of surge current is accurately suppressed at IMAX = 2.5/R2. After C3 charging is completed, the input current returns to the rated value. By changing R2, the maximum value of surge current limit can be adjusted. Q2 is a power transistor, and when selecting devices, it is necessary to choose a high-power transistor.

Fig. 7. Simulation result of low-power current surge suppression circuit

The simulation and experimental results are shown in Figs. 7 and 8. In Fig. 7, the maximum surge current is suppressed at 1.7 A. Results of the experiments proved that the simulation analysis is correct, in the experiment, the maximum surge current was 2.1 A. The power consumption of transistor Q1 equals UCE × IC , as the load current increases, Q1 power consumption increases. In high-power application scenarios, the transistor heats up severely, causing significant heat dissipation pressure and reducing the overall efficiency of the circuit. Therefore, this circuit is suitable for low-power applications that require accurate maximum surge current values.

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Fig. 8. Experimental result of low-power current surge suppression circuit

3 Design of Surge Voltage Suppression Circuit The description of overvoltage surges in GJB181B-2012 is as follows: Electrical equipment should withstand five overvoltage surges, with a time interval of 1 min between each surge. The operation method for each overvoltage surge test is as follows: first, the electrical equipment is powered at normal steady-state voltage, then the input voltage of the electrical equipment is increased to the surge voltage, and finally the input voltage is restored to normal steady-state voltage; The overvoltage surge of 28 V DC electrical equipment is set to 50 V, and after a continuous overvoltage surge of 50 ms, the electrical equipment should not experience any faults. The test waveform is shown in the Fig. 10. To suppress overvoltage surges, MOSFET and BOOST circuits are designed as shown in Fig. 1 (Figs. 9 and 11).

Fig. 9. Surge voltage suppression circuit

MOSFET conduction voltage VGS(th) = 4 V, the circuit boosts the input voltage to 36 V. When the input voltage is at a normal steady state of 28 V, the MOSFET conducts normally, and its drain and source voltage are also 28 V. MOSFET operates in the unsaturated region. When the surge voltage is 50 V, the drain voltage of MOSFET is 50 V. Due to the conduction conditions of MOSFET, the source voltage is clamped at 32 V. MOSFET operates in the saturation zone and withstand the surge voltage between the drain and source of MOSFET. At this time, the voltage applied between the drain stage and the source stage is 16 V. When the load current is large, the instantaneous

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Fig. 10. Surge voltage test waveform

Fig. 11. Surge voltage suppression effect

power consumption of MOSFET is equal to P = 16 × IMAX , which makes MOSFET vulnerable. It is necessary to select MOSFET with larger Safe operating area to ensure its voltage surge suppression function. Multiple MOSFETs can also be connected in parallel to reduce the power consumption borne by each MOSFET.

4 Conclusion The surge suppression circuit plays an important role in protecting back-end electrical equipment in the design of airborne equipment. The surge suppression circuit introduced in this article has a simple structure and low cost. Its basic working principle and design points are explained, and the working process is analyzed in detail. Simulation and experimental results show that the surge suppression circuit proposed in this article is feasible and effective.

References 1. Rao, Q., et al.: Study on the mode of surge current suppression in transformer turned into parallel operation. Gaoya Dianqi/High Volt. Appar. 53(7), 130–135 (2017)

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2. Zhong, W., et al.: Current overshoot suppression of wireless power transfer systems with on-off keying modulation. IEEE Trans. Power Electron. 36, 2676–2684 (2020) 3. Komori, K., Hirachi, K.: Surge voltage suppression by the secondary side short circuit for the full bridge type bidirectional DC/DC converter. J. Japan Inst. Power Electron. 41(0), 134–141 (2015) 4. Nahm, C.W.: Zinc oxide-praseodymia semiconducting varistors having a powerful surge suppression capability. Microelectron. Reliab. 55(11), 2299–2305 (2015) 5. Liu, J., Ruan, J., Wang, W.: Peng Ying research on electromagnetic interference and surge protection device for low voltage power supply. High Voltage Technol. 30(9), 47–48 (2004). (in Chinese) 6. Cao, H., Xiao, L.: A novel anti surge circuit for aviation DC power supply. J. Power Supply 7(3), 248–252 (2009). (in Chinese) 7. Yali, X., Wei, W.: Two stage connected high power surge voltage suppression circuit. Environ. Technol. 41(3), 58–62 (2023). (in Chinese) 8. Zhenni, M.: Design of regulated output circuit with wide voltage input and analysis of surge immunity. Sci. Technol. Innov. Appl. 12(34), 59–62 (2022). (in Chinese) 9. Wu, L., Li, G., Zhang, Z., Ma, H.: A wireless power transfer system topology with automatic switching characteristics of constant current and constant voltage output for electric vehicle charging. Trans. China Electrotech. Soc. 35(18), 3781–3790 (2020). (in Chinese) 10. Li, Z., Du, Y., Ji, J., Tao, T., Zhao, W.: Zero-sequence current suppressing strategy for dual three-phase permanent magnet synchronous machines connected with single neutral point. CES Trans. Electr. Mach. Syst. 6(4), 465–472 (2022). https://doi.org/10.30941/CESTEMS. 2022.00058

Speed Control of Ultrasonic Motor Based on Sliding Mode Control Boyang Ye, Long Jin, Zhike Xu(B) , Junyu Fan, and Qizhi Sui School of Electrical Engineering, Southeast University, Nanjing, China [email protected]

Abstract. Ultrasonic motor (USM) has the advantages of low speed and high torque, no interference from electromagnetic field, power off self-locking and so on. However, due to the special operating mechanism based on friction, the operating state of ultrasonic motor has obvious nonlinear characteristics. Therefore, the traditional analytical method is too complicated to construct the mathematical model of USM. In this paper, the second order model of USM is established by using system identification method based on Hammerstein model. In order to improve the speed stability of the USM, to overcome the speed fluctuations caused by temperature changes and frequency changes, the sliding mode control algorithm is applied to the design of the controller to improve the speed regulation performance and operation robustness of the USM. The control algorithm is designed based on the second-order mathematical model of the motor, and the robustness of the sliding mode control algorithm is verified by simulation. Design experiment based on DSP TMS320F28069 to observe the speed regulation performance of the proposed control algorithm. Experiments show that the algorithm has good control effect. Keywords: Ultrasonic motor · System identification · Sliding mode control

1 Introduction Unlike traditional electromagnetic motors, ultrasonic motors (USM) are driven by piezoelectric effects and frictional coupling. USM has the advantages of low speed large torque, power off self-locking, no electromagnetic interference and so on [1]. In recent years, USM have been widely used in surgical precision instruments [2], aerospace experimental components [3] and advanced camera lens zoom components [4]. Due to the operation characteristics of USM itself, its operation has a high nonlinear characteristic. This makes it difficult to create mathematical model of motor and speed regulation. Considering the application scenario of ultrasonic motor, the non-linearity and discontinuity of ultrasonic motor during operation will have negative impact on its application effect. In this paper, the motor speed regulation is carried out by changing the driving voltage frequency. Maintain the stability of the motor speed under the premise of ensuring the fast response of speed regulation.

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It is necessary to determine the mathematical model of USM before design speed controller. At present, there are several ways to create mathematical models of ultrasonic motors such as mathematical model based on friction mechanics, equivalent circuit model based on electronic components, finite element analysis based on mathematical derivation [5]. The models created by analytical method are deterministic and have a large number of undetermined parameters, which are quite difficult to determine and the process is extremely tedious, and cannot reflect the time variability of operating characteristics. The circuit model described by the electronic components is too rough to be used for high precision speed control. Finite element method cannot be used in many applications such as motor control because of its huge amount of computation. Now the USM can be treated as a black box, only through the voltage frequency input data and the speed output data for system identification, to get the motor mathematical model. Due to the operation characteristics of USM, some traditional control methods are not fully applicable. In recent years, more and more new controllers have been applied to USM such as fuzzy PID controller, Neural network controller [6] and H∞ robust controller [7]. Sliding mode control (SMC), also known as variable structure control, is essentially a nonlinear control. This kind of control can be purposefully changed according to the change of the control object during operation, and has the advantages of good robustness, fast response and simple structure. It is not sensitive to the disturbance of parameters, and can be suitable for the speed control of USM. The remaining contents of this paper are as follows: In Sect. 2, System identification method is applied to describe the motor speed model; In Sect. 3 and 4, The sliding mode controller is designed according to the speed model, and the speed control experiment is carried out based on the existing test platform to verify the control effect. In Sect. 5, the conclusion of this article will be explained.

2 USM Speed Model Based on System Identification 2.1 USM System Identification Features and Steady Speed Model The speed of the USM is affected by the amplitude, frequency and phase difference of the driving voltage. In this paper, the frequency modulation method is used to speed regulate the USM, which requires decoupling of the input conditions, that is, fixing the amplitude and phase of the drive voltage and changing its frequency only. The nonlinearity of ultrasonic motor operation characteristics leads to the nonlinear relationship between frequency and speed, so it is necessary to determine the operating frequency range of the ultrasonic motor. First, the ultrasonic motor should work on the right side of the resonant point. Second, when the drive frequency is too high, the motor speed is too low, which affects the recognition accuracy. It can be seen that the resonant frequency of the motor is 40 kHz. The test frequency range of this experiment is 40 kHz–43 kHz. In the frequency range determined above, the frequency-speed relationship of USM is tested, and it is measured every 500 Hz. The steady-state relationship between frequency and speed is shown in Fig. 1. The above models are fitted with cubic polynomials, As shown in formula (1). y(f ) = 3.289(43.5 − f )3 − 11.66(43.5 − f )2 + 18.74(43.5 − f ) + 2.918

(1)

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Fig. 1. Steady state speed model of ultrasonic motor

In formula (1), f is the drive frequency of the motor, kHz; y( f ) is the steady state speed of the USM, rad/min−1 . 2.2 Identification of Second-Order Systems Based on Step Response The speed characteristic process of ultrasonic motor is linearized, and a second-order model is selected to identify the parameters of step response image [8]. Due to friction and response delay, the second-order system has a delay link. The second-order model in this paper is shown in formula (2). G(s) = K

ωn2 e−τ s s2 + 2ζ ωn s + ωn2

(2)

Where K is the linear gain of steady-state speed, ωn is the natural frequency and ζ is the damping ratio. τ is the delay constant of the motor response. Record the transient process when the motor speed changes. According to formula (3), the speed of the motor step response is normalized. Y ∗ (t) =

y1 (t) − y0 (∞) y1 (∞) − y0 (∞)

(3)

In this formula, Y * (t) is the normalized speed response; y1 (t) is the real speed of the motor in the step response experiment; y0(∞), y1(∞) are the steady speed before and after the step response of the motor. The 41.4 kHz step response diagram of the motor after normalization is shown in Fig. 2. According to the figure above, the maximum value after overshooting and the time to reach the maximum value can be obtained. While M 1 = 1.8, M 2 = 1.58, t 1 = 0.00246, t 2 = 0.006166. The parameter calculation formula of the second-order system is shown

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Fig. 2. Normalized step response curve

in the following formula (4) and (5). ωn = ζ=

 4π 2 + (ln

M1 2 M2 )

t2 − t1 1

4π 2 + (ln

M1 2 M2 )

ln

M1 M2

(4) (5)

In practical engineering control, the delay of second-order system is 0.5ms. According to the steady speed curve, the steady speed gain of the motor K = 52.5. Then the natural frequency and damping ratio are calculated according to the above formula while ωn = 1511.973, ζ = 0.0135. The second-order system model of USM is obtained, as shown in Formula 6. Q(s) = 52.5

2286059.329 e−0.5s s2 + 40.85355s + 2286059.329

(6)

The structure of the second order system is simple and can be applied to the design of the subsequent motor controller. Although there are some errors, the difference between the second order system and the actual system is small.

3 Design of Motor Controller Based on Sliding Mode Control In this section, based on the mathematical model of ultrasonic motor obtained in the previous section, the sliding mode controller is designed in order to achieve fast dynamic response, eliminate steady-state error as much as possible, and reduce the influence of buffeting phenomenon to a certain extent.

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3.1 State Equation of USM System According to the analysis in Sect. 2, the ultrasonic motor system is a multi-input singleoutput system. Its equation of state can be expressed in the following form: x˙ (t) = Ax(t) + Bu y(t) = Cx(t)

(7)

In this formula, x(t) ∈ R3 is the state variable of the system; y(t) is the output speed of the system; u is the amount of input to be controlled. Expand e−τ s according to Taylor’s formula as follow. eτ s = 1 + τ s +

τ 3 s3 τ 2 s2 + + ··· 2! 3!

(8)

Then ignore remainder and take the reciprocal. e−τ s =

1 1 + τs

(9)

So the formula (2) can be transformed into formula (10). ω2

1 K s2 +2ζ ωn s+ω2 1+τ s = n

n

Kωn2 m√ τ [ s+ζ ω −ω 2 n n ζ −1

+

n √ s+ζ ωn +ωn ζ 2 −1

+

p s+1/τ ]

Transform formula (7) into formula (11). ⎤⎡ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ λ1 0 0 x1 (t) x˙ 1 (t) 1 ⎣ x˙ 2 (t)⎦ = ⎣ 0 λ2 0 ⎦⎣ x2 (t)⎦ + ⎣ 1⎦u 1 x˙ 3 (t) 0 ⎡0 λ3 ⎤ x3 (t)   x1 (t) y = Kωn2 p q r ⎣ x2 (t)⎦ x3 (t)

(10)

(11)

A non-singular linear transformation is performed on formula (7). x(t) = Tx(t) ⎡ ⎤ 1 0 −1 T = ⎣ 0 1 −1 ⎦ 00 1

(12)

Calculate the coefficients in Eq. (7). ⎡ A = TAT −1

⎤ λ1 0 λ1 − λ3 = ⎣ 0 λ2 λ2 − λ3 ⎦ 0 0 λ3

⎡ ⎤ 0   B = ⎣ 0 ⎦, C = CT −1 = Kωn2 p q r 1

(13)

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3.2 Determination of SMC Law and Stability Proof In order to improve the response speed of the system and reduce the impact of buffeting phenomenon, the exponential reaching law is used as the control law. The exponential reaching law is faster when it is far away from the target value, and slows down when it is close to the target value, which meets the control requirements. The exponential reaching law is expressed as Eq. (14). s˙ (t) = −ks(t) − εsgn(s(t))

(14)

In this formula, k > 0, ε > 0. εsgn(s(t)) is the switching part of sliding mode control rate. Through high-frequency switching, the system can gradually move towards the sliding mode control surface, and ensure that the system state slides along the sliding mode line to the stable point. When s tends to 0, its integral tends to 0 too. Combined with the equation of state obtained in the previous section, the sliding mode control rate can be solved as in formula (15). u(t) = −(MB)−1 [ks(t) + εsgn(s(t)) + MAx(t)]

(15)

The basic condition for the stability of the control law is s˙ s < 0. Formula (16) is the Lyapunov function chosen to prove the stability of the system. V =

s2 2

s = 0

(16)

Substitute formula (15) into formula (16). V˙ = s˙s = −s[εsgn(s(t)) + ks] < 0

(17)

It can be proved that the sliding mode control law designed in this paper is stable. 3.3 Modeling and Simulation of SMC The sliding mode controller is modeled by MATLAB/Simulink. The control effect of the controller is verified by the ability of simulation software, and compared with the existing PI controller. Figure 3 shows the control effect of sliding mode controller. As can be seen from the figure above, the sliding mode controller has a fast response speed, and tracks the target speed well, and the error is controlled in a small range after entering the steady state operation.

4 USM Speed Tracking Test The experimental platform used in this paper is composed of 60 mm traveling wave ultrasonic motor, photoelectric encoder and DSP chip TMS320F28069. The physical diagram of the experimental platform is given in Fig. 4. During the operation of the system, the control board outputs PWM voltage to the USM, receives feedback signals from the photoelectric encoder, and modifies the frequency of the output voltage through the control module. The system control flow chart is given in Fig. 5.

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Fig. 3. Simulation waveform of SMC

Fig. 4. Speed control experiment platform

Fig. 5. Control system flow chart

Based on the above experimental platform, the speed tracking test was carried out, and 75 rpm was set as the set speed to compare the effect of traditional PI control and the

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sliding mode control designed in this paper. Figure 7 shows the comparison of velocity measurement waveforms (Fig. 6). 90

PI controller SMC controller

85

speed/rpm

80

75

70

65

60

55

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

time/s

Fig. 6. Comparison of control effect. PI controller (red); SMC (blue)

As can be seen from the figure above, the fluctuation of motor speed is obviously smaller than that of traditional PI control algorithm after adopting sliding mode control algorithm. It shows that the control method used in this paper is effective and robust.

5 Conclusion In this paper, the step response test of traveling wave ultrasonic motor is carried out, and the second-order system model is used to describe the motor. A more accurate mathematical model which can be applied is constructed. Based on the mathematical model, a sliding mode controller is designed, and the controller is simulated by software. It is proved that the controller can realize fast response to the control signal and has a small steady speed error. The experimental platform based on TMS320F28069 was built to verify the effectiveness of the controller. Comparing with the traditional PI controller, we find that the controller designed in this paper has better speed stability and faster response speed. However, the chattering phenomenon caused by sliding mode control still exists, and different control laws can be tried to better eliminate the chattering phenomenon in the future.

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References 1. Deng, Y., Zhao, G., Yi, X., et al.: Comprehensively modeling and parametric identification for speed prediction of L1B2 ultrasonic motor, 012007 (9pp). IOP Publishing Ltd. (2020). https://doi.org/10.1088/1742-6596/1449/1/012007 2. Yamaguchi, D., et al.: Ultrasonic motor for sample spinning of solid-state nuclear magnetic resonance spectrometer in high magnetic field (2014) 3. Toyama, S., Yonetake, J.: Development of the ultrasonic motor-powered assisted suit system. In: 2007 IEEE/ICME International Conference on Complex Medical Engineering, CME 2007. IEEE (2007) 4. Zhou, T., Zhang, Y., Chen, Y., et al.: A nut-type ultrasonic motor and its application in the focus system. Chinese Sci. Bull. 54, 3778–3783 (2009). https://doi.org/10.1007/s11434-0090593-5 5. Frangi, A., et al.: Finite element modelling of a rotating piezoelectric ultrasonic motor. Ultrasonics 43(9), 747–755 (2005) 6. Lin, F.J., Shieh, P.H., Chou, P.H.: Robust adaptive backstepping motion control of linear ultrasonic motors using fuzzy neural network. IEEE Trans. Fuzzy Syst. 16(3), 676–692 (2008) 7. Garrido, R., Pineda, J.L.L.: Robust ultra-precision motion control of linear ultrasonic motors: a combined ADRC-Luenberger observer approach. Control. Eng. Pract. 111, 104812s (2021) 8. Yan, G.: Design of adaptive sliding mode controller applied to ultrasonic motor. Assembly Autom. 42, 147–154 (2022) 9. Ming, M., Liang, W., Feng, Z., Ling, J., Al Mamun, A., Xiao, X.: PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage. Mechatron. Sci. Intell. Mach. 76, 102543 (2021) 10. Delibas, B., Koc, B.: A method to realize low velocity movability and eliminate friction induced noise in Piezoelectric Ultrasonic Motors. IEEE/ASME Trans. Mechatron. 25, 2677– 2687 (2020) 11. Wenwen, H., Jingzhuo, S.: MISO nonlinear Gauss-Hammerstein model identification of ultrasonic motor. J. Control Autom. Electr. Syst. 32, 356–366 (2021). https://doi.org/10.1007/s40 313-020-00676-8 12. Lu, S., Jingzhuo, S.: Nonlinear Hammerstein model of ultrasonic motor for position control using differential evolution algorithm. Ultrasonics 94, 20–27 (2019) 13. Jingzhuo, S., Wenwen, H., Ying, Z.: T-S fuzzy control of travelling-wave ultrasonic motor. J. Control Autom. Electr. Syst. 31(2), 319–328 (2020)

The Fault Analysis and Performance Improvement of Pulse Reactors Wu Lizhou(B) , Liu Daqing, Geng Hao, Zhao Yingjie, Gao Bo, and Qiu Qunxian The 713 Research Institute of CSSC, Zhengzhou 450015, China [email protected]

Abstract. In capacitor energy storage pulsed power supplies, it is common to use a pulse inductor to adjust the discharge current waveform. To avoid magnetic saturation, hollow copper windings are typically employed for the pulse inductor. In this study, we utilized copper foil as the base material and adopted an epoxy casting method to manufacture an 80 µH pulse inductor. However, during experimentation, when the test current amplitude reached 45 kA, the pulse inductor suffered severe damage with the electrodes and epoxy core being detached, and the detachment area was heavily burnt. Through analysis, it was determined that the main causes of these issues were the inadequate design of the copper windings and electrode structure, as well as insufficient strength in the epoxy casting structure. To address these problems, we improved the epoxy core, copper windings and electrode structure, and fabricated an improved inductor by using epoxy glass around the copper windings. The improved inductor performed well without any abnormal occurrences under a pulsed current of 51 kA. This development process holds practical value for the research on pulsed power supplies. Keywords: Pulse reactor · pulse high current · fault analysis · pulse power supply

1 Introduction The discharge circuit of capacitor energy storage pulsed power supply module mainly includes pulse capacitor, high-power pulse thyristor, pulsed reactor, coaxial cable and copper bar [1–3]. By triggering the high-power pulse thyristor, the precharged capacitor discharges the load with a discharge pulse current of tens to hundreds of kilo amperes. The pulse capacitor, high-power pulse thyristor, coaxial cable and other equipment are usually mature industrial products. When selected with allowances and used correctly, they will generally do without problems. The pulsed reactor shall be customized according to the requirements of pulsed power supply index. The high current during discharge generates a strong electromagnetic expansion force on the multi-turn copper foil of the reactor, and also generates a large electromagnetic force on the electrodes near the copper foil and its lead structure, posing a big challenge to the structural strength of the pulsed reactor [4, 5] (Fig. 1).

© Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 250–258, 2024. https://doi.org/10.1007/978-981-97-1064-5_27

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Fig. 1. Principle of Pulsed Power Supply Module

The pulsed reactor, also known as wave modulating inductor, is generally made by copper foil winding or solenoid winding. Solenoid winding requires annealing of the copper tubes, which is a complex process especially in multi-layer winding [6]. Therefore, the pulsed reactor involved in this paper is of the copper foil winding type as shown in Fig. 2.

2 Structure and Test of Original 80 µH Pulsed Reactor 2.1 Structural Parameters of Original 80 µH Pulsed Reactor The original 80 µH pulsed reactor structure is shown in Fig. 2, which mainly consists of fixing rod, epoxy core, copper foil, upper and lower electrodes, positioning pin and outer sleeve. The fixing rod is used to fix the reactor. The epoxy core is mainly used to support the copper foil to be wound together with insulating paper. The outer diameter of the epoxy core is 100 mm, the cross section of the copper foil is 0.5 mm * 200 mm, and the number of turns is 40. The copper foil is connected with the external cable through upper and lower electrodes to form a conductive loop. The cross section of electrode is square and the side length is 12 mm. The locating pin is used to fix the upper and lower electrodes. The copper foil is wound together with insulating paper, and epoxy resin is poured for high-temperature curing after winding. The outer sleeve is made of epoxy bonded fiber-glass board material to function as a container. 2.2 Discharge Test and Fault Symptom In the test, the discharge current amplitude was increased by gradually increasing the voltage, and it was planned to discharge 3 times for each voltage. When the discharge current was increased to 8 kV, the first discharge did not show any abnormality. The waveform of the discharge current is shown in Fig. 3, and the amplitude of the current was 45.44 kA.

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Fig. 2. Structure of Original Pulsed Reactor

Fig. 3. 45 kA Discharge Current Waveform

In the second discharge, the discharge sound was loud and the current waveform was not captured. It was found in the inspection that the upper end of the pulsed reactor burst, the electrode fell off together with the epoxy core, the periphery of the fallen epoxy core was attached with black oil stains, and the cable connected externally to the electrode and its fixing device were seriously bent, as shown in the following figure. The test shows that the pulsed capacitor, high-current pulse thyristor, feeder copper bar and other equipment were not damaged by this discharge (Fig. 4).

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Fig. 4. Fault of Pulsed Reactor

3 Fault Cause Analysis and Simulation 3.1 Further Measurement and Simulation Calculation After the fault, the faulty reactor was removed for further observation and measurement. It was found that the welding between the upper electrode and the copper foil had been completely destroyed, and the width of the epoxy resin carried by the epoxy core as it came off varied from 8 to 11 mm. In order to clarify the condition of copper foil and insulating paper inside the reactor, the reactor was cut along the diameter. It was found that there was no problem with insulation between electrodes, but only the innermost insulating paper was burned out (Fig. 5).

Fig. 5. Anatomical View of Electrode Copper Foil

An electromagnetic field simulation model was established for the upper electrode and outgoing line structure of the reactor, and the axial electromagnetic force on the structure was calculated.

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The simulation showed that the maximum axial force of electrode and outgoing line structure is 10.64 kN, the electrode and epoxy core are connected as a whole by locating pins, and the shear strength of epoxy resin is 40 MPa. Simple electromagnetic force is not enough to destroy the resin around the epoxy core. The equivalent pressure of the electromagnetic expansion force on the copper foil in radial direction is 23.2 MPa, under which the welding strength between the electrode and the copper foil is greatly challenged [7, 8]. 3.2 Faulty Positioning The analysis shows that the main reason for reactor faulty positioning is that the radial electromagnetic expansion force of copper foil and axial electromagnetic force of electrode destroyed the welding structure. The specific destruction mechanism is as follows:

Fig. 6. Electrode Outgoing Line Structure

In the process of reactor processing, argon arc welding is selected to weld copper foil and electrode. The welding width of argon arc welding is only 2–3 mm wide. During each discharge, the copper foil and electrode will be deformed due to electromagnetic force. With the increase of discharge times, damage arcing occurs at the welding part between the copper foil and the electrode. At the same time, high-temperature arc ignites the insulating paper and cast epoxy resin to generate gas. With the increase of discharge current, the connection between copper foil and electrode changes qualitatively. The gas generated by arc increases rapidly in the reactor. Under the joint action of air pressure and electromagnetic force, the reactor electrode is separated from the copper foil and the epoxy resin explodes. In addition, as shown in Fig. 6, the secondary cause of this fault is also related to factors such as electrode outgoing line structure. (1) At the upper outgoing line end of the reactor, the electrode is connected to the small cable core bus bar through a copper hoop. The metal assembly structure at this location is not supported by a load-bearing structure on the outside, and the bus bar is responsible for both the flow passage and mechanical fixation, which is

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not in line with the general principles of designing for large electromagnetic force environments. (2) After casting, the length of outgoing line of the reactor electrode is short, and the copper hoop does not fully hold the electrode with sufficient length, resulting in slight bending of the electrode. (3) When a large current of tens of kilo amperes passes through the pulsed reactor, the conductor copper foil will generate heat. The transient current will cause excessive concentration of heat at the edge of the copper foil, and the resulting thermal stress concentration is also one of the causes for structural damage [9, 10].

4 Structural Improvement of Reactor 4.1 Simulation Calculation For the reason of faulty positioning, it is necessary to reduce the radial electromagnetic force of copper foil or enhance constraint, and reduce the axial electromagnetic force of electrode or strengthen the electrode and its connection structure during reactor design (Table 1). Table 1. Electromagnetic Expansion Force of Copper Foil Category

Original Reactor

Early-stage Reactor

Improved Reactor

Diameter of epoxy core

100 mm

150 mm

150 mm

Height of copper foil

200 mm

120 mm

120 mm

Current amplitude

45.4 kA

46.5 kA

51.5 kA

Simulated radial pressure

23.2 MPa

18.3 MPa

22.4 MPa

Test result

Damaged

Intact

To be tested

In the early stage, an epoxy inner core with a diameter of 150 mm and a copper foil cross section of 1 mm * 120 mm were used for a type of reactor. Other parameters and processes were the same. When a current of 50 kA was passed through, good test performance was demonstrated, and the corresponding simulated radial pressure was 18.3 MPa. As for the present test, the reactor was equipped with an epoxy core of 150 mm and a copper foil cross section of 0.5 mm * 200 mm, and damage occurred after a current of only 45.44 kA was passed in the test. It can be seen that the “short and thick” inductor is more conducive to the distribution of electromagnetic force. When the energizing current of a type of reactor in the early stage was increased to the presently required 58 kA, the corresponding simulated radial pressure was 24.7 MPa, and the same possibility of damage existed. Due to the limited installation space, the diameter of epoxy mandrel cannot be increased anymore, so it is still necessary to further optimize the structure.

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4.2 Structural Optimization According to the simulation results, the reactor structure was optimized in the following aspects. (1) The diameter of epoxy core was increased to reduce electromagnetic force. (2) The periphery of the copper foil was wet wound with high-strength fibers to apply pre-tightening force and strengthen the restraint on the copper foil. (3) The electrode height was increased to enlarge the distance between the electrode lead and the end face of copper foil, thus reducing the axial electromagnetic force. As shown in Fig. 7, The specific structure of the improved reactor adopted a mandrel with a diameter of 150 mm and a height of 140 mm. The electrode copper bar was made of copper-chromium alloy. The inner copper bar was fixed with pins. The copper foil and insulating paper were used for winding until the inductance reaches about 80 µH. After winding, it was necessary to ensure that the inductor entered and exited the copper bar at an angle of 180°. After the copper foil is wound, it shall be fixed to prevent loosening. The electrodes were made of copper alloy material and set at the same end, with a conductive cross section of 10 mm * 30 mm. Silver brazing electrodes were used for bilateral welding with copper foil. Glass fiber impregnated epoxy resin was used for pre-tightening winding of the copper foil periphery, with a fiber winding thickness designed to be 20 m and a peripheral diameter of 275 mm.

Fig. 7. Pre-tightening Winding

5 Improved Reactor Test The outgoing line corner of the original reactor electrode is only 60 mm away from the end face of copper foil of the reactor. The appearance of the improved pulsed reactor is shown in Fig. 8. The outgoing line corner of the electrode is 150 mm away from the end face of copper foil of the reactor, which better improves the electromagnetic force condition of the electrode outgoing line path.

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Fig. 8. Outline of Improved Inductor

The pulse discharge test was carried out on the improved pulsed reactor, and the current waveform is shown in Fig. 9. The pulse current amplitude was 51.3 kA, and the test was carried out twice. The reactor cover plate was disassembled for observation, and the reactor was in good condition.

Fig. 9. Test Current of Improved Pulsed Reactor

6 Conclusion In this paper, a large current fault of pulsed reactor is analyzed. The structure and manufacturing process of the reactor are optimized to improve its performance. (1) The main reason why the original pulsed reactor burst and fell off is that the radial electromagnetic expansion force of copper foil and the axial electromagnetic force of electrode together destroy the welding structure between them.

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(2) The small diameter of the epoxy core of the reactor leads to a large radial electromagnetic expansion force of the copper foil, and the small distance between the corner of the electrode outgoing line and the end face of the copper foil results in a large axial electromagnetic force of the electrode. (3) The structure and process of the reactor were optimized and improved: The diameter of the epoxy core was increased, the copper foil was fastened through glass fiber winding, the electrode corner was made away from the end face of the copper foil, high-strength electrode material was used, and the cross section of the electrode was enlarged. (4) The improved pulsed reactor passed 2 high-current impulse tests with an amplitude of 51.3 kA and showed good performance. It can be considered that the fault analysis is positioned accurately, the improvement measures are practical and in place, and the improvement effect is good. Acknowledgments. This work was funded by The Key Program of National Natural Science Foundation of China (No. 92266203).

References 1. Ma, W., Lu, J.: Research progress and challenges of electromagnetic launch technology. Trans. China Electrotech. Soc. 38(15), 3943–3959 (2023) 2. Fair, H.D.: Progress in electromagnetic launch science and technology. IEEE Trans. Magn. 43(1), 93–98 (2007) 3. Li, Z., Hao, S., Ma, F., et al.: Current situation and development of pulsed power supply module technology for electromagnetic gun. Acta Armamentar II 41(S1), 1–7 (2020) 4. Agostini, B.: State of the art of high heat flux cooling technologies. Heat Transf. Eng. 28(4), 258–281 (2007) 5. Yu, X., Dong, J., Wang, H., et al.: Measurement of stress in pulsed reactor structure. J. Nat. Univ. Defense Technol. 38(3), 124–128 (2016) 6. Peng, T., Li, L.: Influence of stainless steel cylinder on the magnetic field in pulsed magnet. Nucl. Tech. 34(6), 477–480 (2011) 7. Zhang, Y., Zhang, W., Yang, S., et al.: Mechanical property and manufacture technology of electromagnetic driving coil. High Voltage Eng. 40(4), 1186–1193 (2014) 8. Xiong, M., Zhang, Y., Gong, Y., et al.: Study on temperature rise of single-stage electromagnetic induction coil transmitter. Strong Laser Part. Beam 32(3), 114–121 (2020) 9. Li, S., Lu, J., Cheng, L., et al.: Research on inductance calculation for copper-skin pulse reactor. J. Naval Univ. Eng. 32(1), 38–43 (2020) 10. Liu, J., Dong, J., Zhang, X., et al.: Research on factors influencing temperature of pulse inductor of electromagnetic launch. J. Ballistics 26(2), 100–105 (2014)

Interval Prediction of Dynamic Line Rating of OHL Based on Improved Affine Arithmetic Hanru Li1 , Zhijian Liu1 , Tao xu1 , Liyong Lai1 , Lingyu Huang1 , Bin Xu2 , Ren Liu2(B) , and Tang Bo2 1 Guangzhou Power Supply Co. Ltd., Guangzhou 510006, China 2 China Three Gorges University, Yichang 443002, China

[email protected]

Abstract. Dynamic Line Rating (DLR) holds significant importance in fully tapping transmission potential of overhead transmission line and mitigating power shortage challenges compared to Static Line Rating (SLR). However, existing interval prediction methods based on affine arithmetic for DLR exhibit limitations such as excessively conservative prediction intervals and high computational burden. In order to tackle these challenges, the multiplication and division operations of affine arithmetic are improved by reducing the quadratic terms and introducing the interval Taylor formula in this paper. Based on these improvements, an interval prediction method for DLR is proposed by using the improved affine arithmetic. Finally, the computed results of the improved affine arithmetic, traditional affine arithmetic, and Monte Carlo algorithm are compared to validate the accuracy and practicality of the proposed method. Keywords: Dynamic line rating · forecasting · affine arithmetic

1 Introduction In the past few years, the remarkable growth of China’s national economy has led to an incessant increase in the societal requirement for electricity [1]. However, the static line rating (SLR) of overhead transmission line (OTL) have severely restricted the transmission capacity of the grid (The maximum permissible current of OTL is determined to be a static value which is calculated based on rigorous and conservative weather conditions) [2–4]. Consequently, the issue of power shortages has become increasingly prominent in some areas of China. Under this context, the construction of new OTL poses significant challenges, including substantial investment, lengthy timelines, and environmental constraints. However, practical engineerings have demonstrated that dynamic line rating (DLR) technology can fully tap the transmission potential of grid without the need to modify the existing grid structure or build new OTLs [5, 6]. This approach utilizes the surrounding meteorological conditions of the OTL to dynamically determine the maximum permissible current, thereby optimizing the transmission capacity of the grid. Currently, DLR for OTL has been piloted by both the State Grid Corporation of China and China Southern Power Grid Co., Ltd., however, there are still numerous challenges © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 259–268, 2024. https://doi.org/10.1007/978-981-97-1064-5_28

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to address in practical implementation for scheduling. Of particular significance is the accurate short-term forecasting of DLR, which represents a pivotal issue in developing scheduling plans grounded on DLR [7]. Based on existing research, the prediction methods for DLR can be categorized into point prediction, probability prediction, and interval prediction. Point prediction, as a deterministic approach, provides a specific numerical value as the predicted currentcarrying capacity of OHL. For instance, numerical weather prediction (NWP) was utilized to achieve point prediction of DLR up to 24 h ahead with a 1-h time resolution [8]. Similarly, the authors of [9] combined historical meteorological data with ensemble machine learning algorithms to achieve point prediction of DLR in the next 6 h with a 10-min resolution. However, these point prediction methods fail to consider the uncertainty associated with meteorological variables, thereby limiting the ability of transmission system operators (TSOs) to make reliable scheduling decisions based on these predictions. To address this limitation, some researchers have started exploring the probability prediction for DLR. For example, uncertain meteorological variables were modeled as Gaussian random variables, then Monte Carlo sampling method was employed to obtain probability distributions of current-carrying capacity up to 24 h ahead with a 1-h time resolution [10]. Similarly, [11] employs machine learning algorithms to construct a correlation model between NWP and micro-climate of OTL. Subsequently, an approach is proposed for probabilistic forecasting of DLR based on NWP. This approach enables the prediction of the probability distribution of DLR at 15-min intervals in the future. Moreover, in order to consider the correlation characteristics of probability distributions of DLR across multiple time periods, Ref. [12] introduced the Copula function to establish a dynamic dependence model. By doing so, the authors predicted joint probability density distributions of DLR in the next 72 h with a 1-h resolution. Nevertheless, probability prediction methods for DLR often necessitate a significant number of sampling calculations, leading to slow computational speeds. Particularly for large-scale power systems, it becomes challenging to achieve short-term prediction of DLR by using this method. To address this challenge, Ref. [13–15] proposed an interval prediction method for DLR based on affine arithmetic (AA). This approach converts the uncertainty of meteorological variables into affine form and solves the prediction interval of current-carrying capacity using affine arithmetic’s operational rules. This method not only accounts for the uncertainty of meteorological variables but also exhibits faster computation times. However, the approximation in affine arithmetic gives rise to computational errors during multiplication and division operations, leading to conservative predictions in DLR interval. Consequently, this poses challenges for TSOs to accurately identify potential overload scenarios through these prediction intervals. In this paper, the affine arithmetic is improved by reducing quadratic terms and introducing interval Taylor formula. These improvements achieve a more refined and less conservative prediction of DLR intervals, and the outcomes of this research establish a solid theoretical and technological basis for TSOs to formulate reliable scheduling decisions in subsequent stages.

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2 Modelling of Dynamic Line Rating Under the simultaneous impact of electric current and meteorological conditions, the OTL’s conductor temperature would reach a equilibrium state, as shown in the Fig. 1.

Fig. 1. Thermal balance of OHL.

This equilibrium state can be effectively characterized using the thermal balance equation of the conductor [16]: Qc + Qr = Qs + Qj

(1)

where Qc , Qr , and Qs correspond to the convective cooling, radiative cooling and solar radiation of the per unit length conductor, respectively. These quantities are related to the meteorological conditions, such ambient temperature, wind speed and solar radiation intensity. The detailed mathematical expressions for these quantities can be found in [16]. Qj represents the Joule heating of the conductor and is mathematically expressed as follows: Qj = I 2 R(Td )

(2)

where I represents the electric current transmitted through the OTL, and R(T d ) denotes the alternating current resistance value at temperature T d °C. By utilizing Eqs. (1) and (2), the formula for the ampacity of the OTL can be derived as follows:  Qc + Qr − Qs (3) I= R(Td ) where T d is set to the maximum permissible temperature of OTL, and the aforementioned equation yields the maximum allowable ampacity for the OTL.

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3 Interval Prediction of Dynamic Line Rating by Improved Affine Arithmetic 3.1 Basic Concepts of Affine Arithmetic Affine arithmetic, originally proposed by Comba and Stolfi in 1993, was initially developed to address computer graphics problems. This arithmetic not only enables the representation of relationships among uncertain variables but also quantifies the impact of uncertainty factors on these variables. In affine arithmetic, the uncertain variable x is represented by an affine form of a linear polynomial xˆ : xˆ = x0 + x1 ε1 + · · · + xn εn

(4)

Where x 0 denotes the central value within the range of numerical fluctuations; the variable Ei represents mutually independent noise elements used to characterize uncertain factors, with a value range of [−1, 1]; the coefficients x i corresponds to the noise elements, representing the extent to which the uncertainty factors influence the variable x. If a given affine number xˆ = x0 + x1 ε1 + · · · + xn εn is provided, it corresponds to an interval number as follows [17]: [x, x] = [x0 −

n 

n 

|xi |, x0 +

i=1

|xi |]

(5)

i=1

where x, x represent the lower and upper bounds of the interval number respectively. When provided with two affine numbers, xˆ = x0 + x1 ε1 + · · · + xn εn and yˆ = y0 + y1 ε1 + · · · + yn εn , as well as a real number k, the basic operations rules of affine arithmetic are as follows [17]: xˆ ± yˆ = (x0 ± y0 ) +

n 

(xi ± yi )εi

(6)

k × xˆ = kx0 + kx1 ε1 + · · · + kxn εn

(7)

k ± xˆ = k ± x0 + x1 ε1 + · · · + xn εn

(8)

i=1

xˆ × yˆ = (x0 +

n  i=1

= x0 y0 +

n  i=1

xi εi ) × (y0 +

n 

yi εi )

i=1 n 

(x0 yi + y0 xi εi ) + (

i=1

xi εi ) × (

n  i=1

(9) yi εi )

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3.2 Improved Affine Arithmetic In Sect. 3.1, it is evident from Eq. (9) that the multiplication process in AA gives rise to quadratic terms consisting of various noise elements. This is one of the key factors leading to the expansion of the prediction interval. However, simply discarding the quadratic terms would result in the incompleteness of affine operations. To address this issue, this paper introduces a new noise element εn + 1 ∈ [−1, 1] to simplify the quadratic terms. Consequently, an improved expression for the affine multiplication operation is deduced as follows: xˆ yˆ = x0 y0 +

n 

(x0 yi + y0 xi )εi + R(ˆx)R(ˆy)εn+1

(10)

i=1

where R(ˆx) =

n 

|xi | is the error term associated with xˆ ; R(ˆy) =

i=1

n 

|yi | is the error term

i=1

associated with yˆ . Due to the relatively slow computational efficiency of affine division, this paper convert the operation of affine division xˆ /ˆy into the operation of affine multiplication xˆ (1/ˆy). Additionally, the nonlinear operation in affine division introduces new noise elements, resulting in diminished computational efficiency and expanded prediction intervals of DLR. To address this issue, this paper introduces the interval Taylor formula to linearize the nonlinear operation of affine division. Finally, an estimated value for 1/ˆy can be obtained. Utilizing the second-order affine form of yˆ , the expansion of f (ˆy) around y0 yields the n-th order affine Taylor formula, accompanied by the Lagrange remainder term δ: f (ˆy) = f (y0 ) + f  (y0 )yd ε1 + · · · + f (n) (y0 )

(yd εn )n (yd εn + 1 )n+1 + f (n+1) (δ) n! (n + 1)!

(11)

By employing the Taylor series expansion on the given equation, the resulting expression of 1/ˆy can be represented as a linear polynomial. y2 y2 1 1 yd = + d3 − 2 ε1 + d3 ε2 = m0 + m1 ε1 + m2 ε2 yˆ y0 2y 2y y0

(12)

where y0 = (y + y)/2, yd = (y − y)/2. Finally, the operational expression for affine division is derived as:    xˆ = xˆ = x0 m0 + (x0 mj + m0 xi )εi + |xi | |mj |εn+1 yˆ n

2

i=1 j=1

n

2

i=1

j=1

(13)

To quantify the enhancement in the computational advantages of improved affine arithmetic (IAA), this paper proposes a improved accuracy index, g, by incorporating calculations of the upper and lower bounds of DLR prediction interval: g =1−

l IIAA − IIAA u − I1 IAA AA

(14)

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u , Il where IIAA IAA are the upper and lower bounds of the prediction interval of DLR u , I 1 are the upper and lower bounds obtained obtained by IAA respectively, while IAA AA by AA respectively.

3.3 Interval prediction of DLR To accurately forecast the interval of DLR, this paper initially acquires predicted values (T a0 , V w0 , θ 0 , J 0 ) for uncertain meteorological variables (ambient temperature T a , wind speed V w , wind direction angle θ, solar radiation intensity J) by using NWP for the area where the OHL is located. To align with the scheduling decisions of TSOs, a temporal resolution of 1 h is set (obtaining predicted values for the next 1 h of uncertain meteorological variables through NWP). Subsequently, the DLR prediction interval for the upcoming 1 h is calculated. Besides, the computational process of the proposed method for predicting the current-carrying capacity interval is depicted in the Fig. 2.

1

Fig. 2. The process of predicting DLR interval.

Considering the primary factors contributing to the uncertainty of meteorological variables as the errors in weather data acquisition and prediction model calculations, this paper introduces two noise elements εci and εyi separately to characterize the numerical fluctuations caused by these uncertain factors. Accordingly, based on the explicit expression of affine numbers, the affine forms of the uncertain meteorological variables (T a , V w , θ, J) can be formulated as follows: ⎧ Tˆ a = Ta0 + Ta1 εc1 + Ta2 εy1 ⎪ ⎪ ⎪ ⎪ ⎨ Vˆ w = Vw0 + Vw1 εc2 + Vw2 εy2 (15) ⎪ θˆ = θ0 + θ1 εc3 + θ2 εy3 ⎪ ⎪ ⎪ ⎩ˆ J = J0 + J1 εc4 + J2 εy4

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Next, by substituting the affine forms of the aforementioned meteorological variables into the calculation formulas for Qc , Qr , Qs , and R(T d ), and employing the ˆ r, Q ˆ s , and R(T ˆ c, Q ˆ d ) can IAA for computation, the corresponding affine forms of Q be derived.Subsequently, utilizing Eq. (3) yields the affine form of the ampacity for the OTL:  ˆc +Q ˆr −Q ˆs Q Iˆ = (16) ˆ d) R(T The linear polynomial expression for it is as follows: Iˆ = I0 +

4  i=

I1 εci +

4 

I2 εyi

(17)

i=1

Finally, by applying the transformation formula (5) between affine numbers and interval numbers, the predicted interval for the DLR is computed.

4 Case Study In order to validate the effectiveness of the proposed method, this section takes a 110kV OTL in Guangzhou, China as an example. IAA, AA, and Monte Carlo (MC) algorithm are employed to calculate the predicted intervals of DLR for each hour on July 2, 2022. The specific parameters of this OTL are presented in Table 1, while the historical meteorological data required for the calculations are obtained from the Guangzhou Meteorological Bureau. Table 1. Properties of the considered OTL. Property

Value

Conductor type

LGJ-300/40

Conductor section

338.99 mm2

Conductor diameter

27.3 mm

Nominal voltage

110 kV

Maximum allowableconductortemperature

70 °C

Resistance per km

92220 

Unit length weight

1133 kg/km

The MC algorithm employed in this paper utilizes a uniform distribution to randomly sample the changing range of uncertain meteorological variables (10,000 times). Subsequently, a substantial number of deterministic line rating calculations are performed using Eq. (3). Finally, the minimum and maximum values yielded from the ensemble of calculated results are considered as the lower and upper bounds of the DLR

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prediction interval. By simulating a diverse array of potential uncertain meteorology scenarios, MC algorithm provides a reliable estimation of the actual DLR uncertainty interval [15]. Thus, it can serve as a valuable benchmark for validating the accuracy and comprehensiveness of the proposed method. The ultimate outcomes of the three methods are presented in Fig. 3. It clearly illustrates that the Monte Carlo algorithm demonstrates superior computational precision, characterized by the narrowest prediction interval. In addition, both AA and IAA prediction intervals encompass the prediction interval of MC, thus underscoring the favorable comprehensiveness of the computed results obtained from AA and IAA. Moreover, The prediction interval of method AA entirely encompasses the prediction interval of method IAA, indicating that the conservatism of IAA’s calculations is lower. These findings serve to further substantiate the efficacy of the proposed approach expounded in this paper. To further illustrate the computational efficiency of the proposed method, Table 2 provides a statistical analysis of the computation times for the three methods. Based on Sect. 3, it can be inferred that the computational efficiency of AA decreases as the number of noise elements included in the affine form increases. Consequently, the computational advantages of IAA become more apparent. Conversely, the MC method necessitates tens of thousands of sampling computations during the solving process, rendering it the least computationally efficient approach.

1200

Upper Bound(MC) Lower Bound(MC)

Upper Bound(IAA) Lower Bound(IAA)

Upper Bound(AA) Lower Bound(AA)

1100

DLR[A]

1000 900 800 700 600 500 400

0

5

10

15

20

t[h]

Fig. 3. Prediction interval of DLR.

Table 2. The computation time of three methods. Method

Computation time

IAA

13.25 s

AA

20.21 s

MC

95.82 s

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According to Eq. (14), when g > 0 and approaches zero, it indicates lower conservatism in the prediction interval of DLR. Conversely, a higher value of g implies higher conservatism. As depicted in Fig. 4, all values of g are greater than zero. This signifies that, in comparison to AA, IAA generates narrower prediction intervals, particularly around 1:00 PM. Therefore, the IAA effectively reduces the conservatism of prediction interval, thereby augmenting the reliability of predictive outcomes. 0.8 0.75 0.7 0.65

g

0.6 0.55 0.5 0.45 0.4 0.35 0.3

0

5

10

15

20

25

t[h]

Fig. 4. Improved accuracy index g at different time.

5 Conclusion To account for the uncertainty in meteorological variables and address the issue of excessive conservatism in affine arithmetic computations, this paper proposes an improved affine arithmetic-based approach for the interval prediction of DLR. The following conclusions can be drawn based on the comparative analysis of the computational results: 1) This paper improves the multiplication and division operation rules of affine arithmetic by reducing quadratic terms and introducing interval Taylor formula. It effectively reduces the conservatism of DLR prediction intervals and enhances computational efficiency. 2) The analysis of the improved accuracy index, g, demonstrates that the proposed method achieves low conservatism in DLR interval prediction. This lays a solid theoretical and technical foundation for subsequent TSOs to develop reliable scheduling decisions. 3) While the IAA yields favourable computational results in predicting DLR intervals, there still exist certain computational errors during the square root operation. This area requires further efforts and exploration in future work. Acknowledgments. This work is supported by the technical project of Guangzhou Power Supply Co. Ltd. of China Southern Power Grid Co. Ltd. Under Grant 030166KK52222001.

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References 1. Ju, X., Cheng, Y., Yang, M., Cui, S., Liu, X.: Influence analysis of high frequency pulse voltage of SiC inverter on insulation safety of hairpin winding. Trans. China Electrotech Society 36(24), 5115–5124 (2021) 2. Nazemi, M., Dehghanian, P.: Powering through wildfires: an integrated solution for enhanced safety and resilience in power grids. IEEE Trans. Indust. Appl. 58(3), 4192–4202 (2022) 3. Jia, X., et al.: Static voltage stability assessment considering impacts of ambient conditions on overhead transmission lines. IEEE Trans. Indust. Appl. 58(6), 6981–6989 (2022) 4. Numan, N., Abbas, M F., Yousif, M., Ghoneim,S S M., Mohammad, A., Noorwali, A..: The role of optimal transmission switching in enhancing grid flexibility: a review. In: IEEE Access 11, 32437–32463 (2023) 5. Wang, M., Wang, S., Jin, X., Cui, M., Yang, M.: Prediction of intra-period minimum thermal rating of overhead conductors. In: IEEE Transactions on Power Delivery. 38(1), 564–574 (2023) 6. Jimada-Ojuolape, B., The, J.: Composite reliability impacts of synchrophasor-Based DTR and SIPS cyber–physical systems. IEEE Syst. J. 16(3), 3927–3938 (2022) 7. Cheng, Y., Liu, P., Zhang, Z., Dai, Y.: Real-time dynamic line rating of transmission lines using live simulation model and tabu search. IEEE Trans. Power Delivery. 36(3), 1785–1794 (2021) 8. Gao, Z., Hu, S., Sun, H., Wang, Z., Liu, S., Yang, F.: Day-ahead dynamic thermal line rating forecasting and power transmission capacity calculation based on ForecastNet. Electr. Power Syst. Res. 220, 109350 (2023) 9. Ahmadi, A., Nabipour, M., Mohammadi-Ivatloo, B., Vahidinasab, V.: Ensemble learningbased dynamic line rating forecasting under cyberattacks. IEEE Trans. Power Delivery 37(1), 230–238 (2022) 10. Muñoz, F., Torres, F., Martínez, S., Roa, C., García, L.: Case study of the increase in capacity of transmission lines in the Chilean system through probabilistic calculation model based on dynamic thermal rating. Electric Power Syst. Res. 170, 35–47 (2019) 11. Aznarte, J.L., Siebert, N.: Dynamic line rating using numerical weather predictions and machine learning: a case study. IEEE Trans. Power Delivery. 32(1), 335–343 (2017) 12. Wang, M., Wang, S., Jin, X., Cui, M., Yang, M.: Prediction of intra-period minimum thermal rating of overhead conductors. IEEE Trans. Power Delivery. 38(1), 564–574 (2023) 13. Piccolo, A., Vaccaro, A., Villacci, D.: Thermal rating assessment of overhead lines by Affine Arithmetic. Electr. Power Syst. Res. 71(3), 275–283 (2004) 14. Carlini, E.M., Pisani, C., Vaccaro, A., Villacci, D.: A reliable computing framework for dynamic line rating of overhead lines. Electric Power Syst. Res. 132, 1–8 (2016) 15. Coletta, G., Vaccaro, A., Villacci, D., Fang, D., Djokic, S.Z.: Affine arithmetic for efficient and reliable resolution of weather-based uncertainties in optimal power flow problems. Int. J. Electr. Power Energy Syst. 110, 713–724 (2019) 16. IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors. In: IEEE Std 738–2012 (Revision of IEEE Std 738–2006 - Incorporates IEEE Std 738–2012 Cor 1–2013), pp.1–72 (2013) 17. Pirnia, M., Cañizares, C.A., Bhattacharya, K.: A novel affine arithmetic method to solve optimal power flow problems with uncertainties. IEEE Trans. Power Syst. 29(6), 2775–2783 (2014)

Accurate Calculation Method for Radiation Field Generated by Lightning Waves Entering Substation Ninghui He1 , Xutao Wu1 , Yifan Lang2 , and Yangchun Cheng2(B) 1 Electric Power Research Institute of State Grid Ningxia Electric Power Co., Ltd.,

Yinchuan 750002, China 2 Beijing Key Laboratory of High voltage & EMC, North China Electric Power University,

Beijing 102206, China [email protected]

Abstract. The possibility of strong electromagnetic radiation caused by lightning waves invading substations has always been a concern. This article aims to introduce an accurate calculation method for evaluating the radiation field generated after lightning waves invade substations. This method combines the theory of traveling wave antennas and the theory of electromagnetic wave refraction and reflection, and can accurately analyze and predict the distribution and intensity of the radiation field. By deeply understanding the physical mechanism and mathematical model of lightning wave intrusion into substations, we can better address this challenge and ensure the safe operation of substations. Keywords: Lightning Wave · Substation · Traveling Wave Antenna Theory · Electromagnetic Field Calculation

1 Introduction The intrusion of lightning waves into substations is an important issue in the power system, which may cause serious equipment damage and safety risks. With the increasing scale and complexity of the power system, the problem of lightning wave intrusion faced by substations has become more prominent [1–3]. Therefore, in-depth research on the phenomenon, impact, and response measures of lightning wave intrusion into substations is crucial for ensuring the reliable operation of the power system. In the 1930s, American scholars began to study the characteristics of lightning intrusion wave traveling waves [4, 5]. Based on the measured waveforms of 15 lightning over voltages on 220 kV transmission lines, they proposed three representative lightning traveling wave characteristic parameters: 0.25/10 μs, 0.25/30 μs, and 0.25/90 μs. Subsequently, the American Electric Power Engineering Association determined three other traveling wave characteristic parameters based on relevant research: 0.5/5 μs, 1/10 μs, and 1.5/40 μs. In 1962, EC60060–1 specified a standard lightning traveling wave parameter of 1.2/50 μs. Although some scholars or associations have defined the characteristic parameters of lightning traveling waves, after nearly half a century of development, the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 269–275, 2024. https://doi.org/10.1007/978-981-97-1064-5_29

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power system has become more and more large-scale and complex in structure, and the characteristics of lightning Transient response will also change to some extent, which leads to more complex and diverse characteristics of lightning intrusion overvoltage traveling waves. Research on overvoltage caused by lightning intrusion waves. Due to the different mathematical models established, various methods are used. At present, the commonly used transient simulation program EMTP for power systems both domestically and internationally analyzes and calculates lightning over voltage [3]. In this type of analysis method, the main focus is on the traveling wave conduction of lightning waves, which is suitable for the coupling and propagation of lightning waves on multiple closely parallel wires, and cannot be used to analyze electromagnetic coupling on long-distance wires. In 2017, Nanjing University of Information Science and Technology established the lightning channel antenna model and the test model of cable receiving lightning Electromagnetic pulse, used the antenna, twisted pair and coaxial line coupling to simulate the lightning electromagnetic wave radiated from the lightning channel, and analyzed the voltage and spectrum characteristics of coupled lightning Electromagnetic pulse [6]. Based on the above research, this article proposes an accurate calculation method for the electromagnetic field generated by lightning wave intrusion into substations. By using this numerical calculation method, the intensity of electromagnetic interference caused by lightning waves invading substations can be evaluated, providing theoretical guidance for the design and optimization of substations.

2 The Propagation Mechanism of Lightning Waves in Substations In substations, the length of long conductors is limited, and branches may also occur at the end of the conductor, which is also connected to equipment such as transformers. Overall, the high-voltage conductors in the substation form a relatively complex network structure. For lightning intrusion waves, in the high-voltage wire network of the substation, due to the action of the lightning arrester at the line entrance, most of the lightning waves are limited to the outer side of the lightning arrester, and only the lightning waves corresponding to the residual voltage of the lightning arrester can continue to pass forward into the substation network [7].

Fig. 1. Model diagram of lightning wave intrusion into substation

As shown in Fig. 1, there is a detailed description of lightning waves invading the substation [8]. When lightning waves invade the substation, they will pass through the

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lightning arrester and reach the transformer along the wire. At the transformer, lightning waves will undergo total reflection and propagate along the wire to the lightning arrester. When the value of the lightning wave at the lightning arrester is greater than the operating voltage of the lightning arrester, the lightning arrester will act, and its action effect is equivalent to directly connecting the lightning arrester to the ground and releasing lightning current to the ground. The model used for lightning intrusion waves is a classic dual exponential model:   (1) U (t) = A e−α(t−τ ) − e−β(t−τ ) , t ≥ 0 According to the theory of traveling wave propagation, the above physical process can be conveniently transformed into the following calculation formula:



  ⎧ −α t−t1 − e−β t−t1 , k = 1 ⎪ ⎪ ⎪ U (t) = A e ⎪ ⎪



 



  ⎪ ⎪ ⎪ ⎪ U (t) = A e−α t−t1 − e−β t−t1 + e−α t−τ −t2 − e−β t−τ −t2 ,k = 2 ⎪ ⎪ ⎪ ⎪



 







   ⎪ ⎪ ⎪ −α t−t −β t−t −α t−τ −t −β t−τ −t 1 −e 1 + e 2 −e 2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎪ U (t) = A e ,k = 3 ⎪ ⎪ ⎪ ⎪ ⎧



 







 ⎫  ⎪ ⎪ ⎪ ⎨ e−α t−t1 − e−β t−t1 + e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎬ ⎪ ⎪ ⎪



  ⎪ U (t) = A ,k = 4 ⎪ ⎪ ⎩ −2 e−α t−td −τ −t2 − e−β t−td −τ −t2 ⎭ ⎪ ⎪ ⎨ ⎧ ⎫



 







  ⎨ e−α t−t1 − e−β t−t1 + e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎬ ⎪ ⎪ ⎪







 ⎪   U (t) = A ,k = 5 ⎪ ⎪ ⎩ −2 e−α t−td −τ −t2 − e−β t−td −τ −t2 + 2 e−α t−td −2τ −t1 − e−β t−td −2τ −t1 ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧



 







 ⎫  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ e−α t−t1 − e−β t−t1 + e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎪ ⎪ ⎪ ⎪ ⎬ ⎨  ⎪







  ⎪ ⎪ ⎪ ,k = 6 ⎪ U (t) = A −2 e−α t−td −τ −t2 − e−β t−td −τ −t2 + 2 e−α t−td −2τ −t1 − e−β t−td −2τ −t1 ⎪ ⎪ ⎪ ⎪



  ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ +2 e−α t−td −3τ −t2 − e−β t−td −3τ −t2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ••••••

(2) It is worth noting that the polarity of the current traveling wave is affected by the direction of the traveling wave propagation, so the current along the wire will be represented by formula (3): ⎧ ⎪ I (t) = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ I (t) = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ I (t) = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ I (t) = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨



 A  −α t−t

1 − e−β t−t1 , k = 1 e Z

 



 A  −α t−t

1 − e−β t−t1 − e−α t−τ −t2 − e−β t−τ −t2 ,k = 2 e Z

 







  A  −α t−t

1 − e−β t−t1 − e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ,k = 3 e Z ⎧



 







⎫  ⎪ −α t−t1 − e−β t−t1 − e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎪ ⎬ A⎨ e ,k = 4



  ⎪ Z⎪ ⎭ ⎩ +2 e−α t−td −τ −t2 − e−β t−td −τ −t2 ⎧



 







⎫  ⎪ −α t−t1 − e−β t−t1 − e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎪ ⎪ ⎬ ⎪ A⎨ e ⎪ ⎪ ⎪ I (t) = ,k = 5







   ⎪ ⎪ ⎪ ⎪ Z −α t−t −τ −t −β t−t −τ −t −α t−t −2τ −t −β t−t −2τ −t ⎪ ⎩ ⎭ 2 −e 2 +2 e 1 −e 1 d d d d ⎪ +2 e ⎪ ⎪ ⎪ ⎪

 







⎫  ⎪ ⎧  −α t−t

⎪ ⎪ 1 − e−β t−t1 − e−α t−τ −t2 − e−β t−τ −t2 − 2 e−α t−td −t1 − e−β t−td −t1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ e ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬





  ⎪ A ⎨  −α t−t −τ −t

⎪ −β t−td −τ −t2 + 2 e−α t−td −2τ −t1 − e−β t−td −2τ −t1 ⎪ 2 d ⎪ ,k = 6 I = (t) +2 e − e ⎪ ⎪ ⎪ ⎪ Z ⎪ ⎪ ⎪  ⎪ ⎪ ⎪



 ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ −α t−t −3τ −t −β t−t −3τ −t ⎪ 2 −e 2 d d ⎪ −2 e ⎪ ⎪ ⎪ ⎪ ⎩ • • • • ••

(3)

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The Theory of Traveling Wave Antennas

A current source is a very short linear current that is assumed to be extracted from the actual line current. Its length L is much smaller than the working wavelength, so the current at each point along the line can be considered the same (uniformly distributed), that is, I is a constant. Its total strength can be characterized by the electrical moment IL. The current distribution on the actual antenna can be seen as composed of many such current elements. Therefore, the current element is also known as an electric fundamental oscillator. Use the vector method to solve the electromagnetic field generated by the current source [9, 10].

Fig. 2. Electromagnetic field of current source

As shown in Fig. 2, place the current element at the coordinate circle point along the z-axis direction. The vector magnetic potential generated by it at any point in space only has a z-axis component:  Az =

L/2

−L/2

Ie−jkr  IL −jkr dz = e 4π r 4π r

Convert to spherical coordinates, as: ⎧ ⎪ cos θ −jkr ⎪ ⎪ Ar = Az cos θ = IL4π ⎪ r e ⎪ ⎨ sin θ −jkr Aθ = −Az sin θ = − IL4π r e ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Aϕ = 0

(4)

(5)

According to the basic theory of electromagnetic fields, there are:   =∇ ×A H

(6)

  − j 1 ∇(∇ • A)  = −jωμA E ωε

(7)

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Then use (6) and (7) to get the calculation formula of magnetic field intensity and electric field intensity distribution: ⎧ Hr = 0 ⎪ ⎨ Hθ = 0 (8)  ⎪ ⎩ H = j kIL sin θ 1 + 1 e−jkr ϕ 4π r jkr ⎧   ⎪ IL cos θ 1 −jkr ⎪ ⎪ E 1 + = η r ⎪ jkr e 2π r 2 ⎪ ⎨   kIL sin θ 1 1 (9) 1 + e−jkr E = jη − θ 2 2 4π r jkr ⎪ k r ⎪ ⎪ ⎪ ⎪ ⎩ Eϕ = 0   In the formula, η = μ ε. When kr > > 1 or r > > λ The region is called the far region or radiation region, and the higher-order term of kr in Eqs. (8) and (9) can be ignored and only the maximum term is retained. In this case, the field equation can be simplified as follows: ⎧ ⎪ ⎨ Eθ = jη kILsinθ e−jkr = j 60πIL sinθ e−jkr 4πr λr (10) ⎪ ⎩ H = j kILsinθ e−jkr = j IL sinθ e−jkr = Eθ ϕ 4πr 2λr 120π When a long wire is terminated with a matching resistor RL , there are no reflected waves, and the current on the wire is a traveling wave. To simplify the analysis and ignore the influence of the bottom, it is assumed that the radiation of the vertical section of the wire can be ignored, and the attenuation of the current along the line can be ignored. The simplified structure and coordinates of the long wire are shown in Fig. 3.

Fig. 3. Schematic diagram of row wavelength wire antenna

Assuming that the phase constant of the traveling wave propagation along the wire is equal to the phase constant k of the wave in free space, the current along the long wire can be expressed as: I (z) = I0 e−jkz

(11)

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According to the Superposition principle, the far field of a long wire can be obtained by superposition of the far field of each current element on it. From (8) and (9), it can be seen that when r > > λ The far field of the current source I (z) dz at z on the traveling wave length wire is: dEθ = j

60πI0 sinθ e−jkz e−jk(r−z cos θ) dz λr

(12)

In the formula, r is the distance from the source point to the field point at z = 0. The far-field of a row wavelength wire with a length of l is: 

 l 60π I0 sin θ e−jkr e−jkz(1−cos θ) dz λr 0 0   kl 60I0 −jkr sin θ kl = e sin (1 − cos θ ) e−j 2 (1−cos θ) r 1 − cos θ 2

Eθ =

l

dEθ = j

(13)

The direction function is:

    kl θ kl sin θ sin (1 − cos θ ) = cot sin (1 − cos θ ) f (θ ) = 1 − cos θ 2 2 2

(14)

4 Calculation Method For Electromagnetic Radiation Generated By Lightning Waves Invading Substations Substitute the current information of lightning wave invading the substation in Eq. (3) into the expression of the direct radiation of long conductor in Eq. (13), and the electromagnetic radiation generated by lightning wave invading the substation at a certain time and location in the substation can be easily calculated through mathematical methods such as Laplace transform.

5 Conclusion This article provides a detailed introduction to the propagation mechanism of lightning waves in the substation when lightning invades the substation. Based on the physical process, corresponding mathematical expressions are provided, which can conveniently calculate the magnitude of current and voltage on the wire at a certain time and location. Then, based on the theory of traveling wave antennas, the electromagnetic field intensity that the lightning current propagating along the line will radiate outward was analyzed. Finally, the combination of these two forms an accurate calculation method for the radiation field generated by lightning waves invading substations. Overall, this article has the following advantages in the field of lightning wave intrusion into substations. Firstly, it provides a detailed explanation of the entire process of lightning wave invasion into the substation, taking into account the complex and complete wave process in the calculation of lightning voltage and current wave propagation in the substation. At

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the same time, the propagation laws of intrusion waves were summarized and classified, greatly simplifying the difficulty of using the formula. Secondly, when borrowing the theory of traveling wave antennas, both the nearfield and far-field of electromagnetic radiation are considered simultaneously, that is, the calculation method proposed in this application serves as an unrestricted distance between the wire of the traveling wave antenna and the measurement point. It can accurately calculate the electromagnetic field in the entire domain. In the future, our research team will further study the modeling of electromagnetic radiation characteristics of long wires encountered in substations, as well as the impact and coupling characteristics of long wires, metal grid structures, and equipment metal shells on the electromagnetic radiation field. Ultimately, we will propose an accurate evaluation calculation method for evaluating the electromagnetic disturbance in the environment where the electrical equipment state perception sensors in substations are located. Acknowledgments. This work is supported by the Ningxia Natural Science Foundation project (2021AAC03498).

References 1. Jiang, K.: Lightning Monitoring and Fault Identification and Analysis of Corona Characteristic on Overhead Transmission Line, Chongqing University (2020) (in Chinese) 2. Zeng, R., Kang, P., He, J., et al.: Lightning transient performance analysis of substation based on complete transmission line model of power network and grounding systems. IEEE Trans. Magn. 42(4), 875–878 (2006) 3. Huangfu, Y.P., Wang, G W, et al. Modeling and insulation performance analysis of composite transmission line tower under lightning overvoltage. IEEE Trans. Mag. 51(3), 1–4 (2015) 4. Okabe, S., Takami, J., Tsuboi, T., et al.: Discussion on standard waveform in the lightning impulse voltage test. IEEE Trans. Dielectr. Electr. Insul. 20(1), 147–156 (2013) 5. Okabe, S., Takami, J.: Evaluation of breakdown characteristics of oilimmersed transformers under nonstandard lightning impulse waveforms method for converting nonstandard lightning impulse waveforms into standard lightning impulse waveforms. IEEE Trans.Dielectr.Insul. 15(5), 146–155 (2008) 6. Xiangchao, L.: Experimental Simulation Study on Radiation. Coupling and Suppression Method of Lightning Electromagnetic, Nanjing University of Information Science Technology (2017). (in Chinese) 7. Liu, Y.: Research on the response characteristics of lightning waves during the propagation of power systems. Electr. Equip. Econom. 04, 1–5 (2018) (in Chinese) 8. Xiangchao, L., Wen, O., Qiaoli, W.: Characteristic analysis of coupled lightning waves in multi-conductor transmission lines. Insulators Surge Arresters 06, 15–24 (2022). (in Chinese) 9. Hao, J.: Research on a new type of antenna based on traveling wave mechanism, Hangzhou Dianzi University (2021) (in Chinese) 10. Yang, Y., Qin, C., Zhao, Y., et al. Simulation design and analysis of traveling wave antenna of CFETR helicon wave. Nuclear Fusion Plasma Phys., 41(02), 138–142 (2021) (in Chinese)

Position and Speed Measurement Method for Segmented Long Primary Double-Sided Linear Motor Based on Polynomial Fitting Shijiong Zhou1,2

, Yaohua Li1,2 , Liming Shi1,2(B) , Manyi Fan1 , and Jinhai Liu1,2

1 Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering

Chinese Academy of Sciences, Beijing, China {Shijiongz,limings}@mail.iee.ac.cn 2 University of Chinese Academy of Sciences, Beijing, China

Abstract. To obtain the accurate motor position and speed feedback information, this paper presents a new position and speed measurement method of segmented long primary double-sided linear motor (SLP-DSLM). Considering that the SLPDSLM has a double-sided long primary and dynamic secondary structure, a grating sensor based on laser array to measure the position is used in this paper firstly. Then, a new position acquisition method based on polynomial fitting is proposed in this paper. Finally, the adaptive tracking differentiator (TD) is introduced to obtain the velocity of secondary. Compared with the conventional position accumulation method, the hardware-in-the-loop experiment proves the effectiveness of the proposed method. Keywords: segmented long primary double-sided linear motor (SLP-DSLM) · position acquisition method · grating sensor · polynomial fitting · tracking differentiator (TD)

1 Introduction Linear motors are widely used in the industrial transportation, maglev transportation, electromagnetic drive and so on. During the large thrust and high acceleration electromagnetic driving conditions, linear motors often adopt the form of segmented doublesided long primary, which can save the capacity of the inverters [1–3]. Stable control of linear motor cannot be separated from the accurate measurement system and effective control system. The speed closed-loop of segmented long primary double-sided linear motor (SLP-DSLM) is important to realize the high precision closed-loop control of motor drive. Especially in the case of high speed and long running distance of electromagnetic drive, an accurate position and speed measurement system of linear motor is needed to meet the requirements of position and speed control. The position and speed measurement technology of linear motor is developing constantly. The laser displacement sensor is used in [4], but with the increasing length of the primary, the laser signal intensity will be lower, the communication time will be © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 276–284, 2024. https://doi.org/10.1007/978-981-97-1064-5_30

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longer, which makes the cumulative error become larger. Inductive proximity switches [5] and eddy current sensors [6, 7] are used in position and speed measurement system of linear motors. But the accuracy of the position signal they have obtained is not accurate enough. Magnetic grid sensor [8, 9] can improve the measurement accuracy, but the magnetic head of this sensor is easy to demagnetize. The grating positioning sensor using laser array [10] has the high measurement accuracy, simple device and low cost. This kind of position measurement method is suitable for high accuracy and long distance electromagnetic drive occasions. The speed is usually obtained by differentiating the position signal. The ordinary differential processing mainly adopts the difference method, which is easy to magnify the noise caused by the measurement error. To solve this problem, the filter is usually added after the output signal of the speed, but this method will introduce a certain signal delay, which is not conducive to the closed-loop control under high speed motor operation [11, 12]. However, Han Jingqing, et al. proposed the tracking differentiator (TD) [13, 14], which can effectively suppress the noise amplification of differentiator and maintain the rapidity of speed measurement. This paper uses a laser array of grating sensor position and speed measurement system, which has the advantages of high precision, fast detection, relatively simple installation and non-electromagnetic interference. According to the position data points measured at each time point, the position of motor secondary is obtained by polynomial fitting method. The speed is then obtained by the TD. In comparison with the conventional position and velocity measurement systems based on the position accumulation, the effectiveness of the proposed method is verified.

2 Design of Speed and Position Measurement Method The brief system of position and speed measurement based on the grating sensor with laser array is shown in Fig. 1.

gggggg

gggggg

gggggg

gggggg

Fig. 1. Position and speed measurement system of SLP-DSLM.

In Fig. 1, the grating strip is installed on the moving secondary and is divided into the white transparent area and the black opaque area (with equal width that is set as D).

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d

d d d d d d 0

(a)

d d d d d d d d d 0

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Fig. 2. Position acquision methods: (a) conventional position accumulation (b) polynomial fitting.

The pulse counter module obtains the number of pulses produced by the motion of the grating strip and the position data (t k , d k ) of each time point t k (k = 0, 1, 2, …). The conventional method uses position accumulation to obtain secondary position, according to the number of pulses, which is shown as Fig. 2(a). When the secondary motion occurs, the pulse signal is generated which is as shown in Fig. 2 (a). The rising edge of the pulse is recorded at the same time. The conventional position accumulation calculation equation is as follows: dk = d0 + 2mD

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The fitting results of proposed method are shown in the Fig. 2 (b). It can be seen that the position information obtained by this method is almost the same as the reference position, which verifies the effectiveness of the proposed method. In Fig. 2 (b), the polynomial curve fitting method based on the least square method [15, 16] is used to obtain an approximate curve y = g(x) according to the given sample points of y = f (x), so as to minimize the deviation between g(x) and f (x), which g(x) can be expressed as: g(x) = a + bx + cx2 + ... + dxn

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where a, b, c, d is the coefficient, n = 0, 1, 2, …. The problem of position measurement problem is converted to the problem of finding a most suitable polynomial equation. Every position data (t k , d k ) can be obtained by the motion of the grating strip. In order to save the calculation time and improve the fitting accuracy, the sensor collects every 7 position data points to fit the position of the secondary. In addition, to prevent data jitter, it is necessary to remove a maximum value and a minimum value. Then, the fitting problem is shown as the following equation. ⎡ ⎤   g(tk , dk ) − f (tk , dk )   ⎢ g(tk+1 , dk+1 ) − f (tk+1 , dk+1 ) ⎥ ⎢ ⎥ (3) min : δ =  ⎣ g(tk+2 , dk+2 ) − f (tk+2 , dk+2 ) ⎦    g(t , d ) − f (t , d )  k+3 k+3 k+3 k+3 2 The coefficients can be obtained by using the partial derivatives of δ in (3) with respect to coefficients a, b, c, d, which is shown as: ⎧ 4  

⎪ ∂δ ⎪ a + bti + cti2 + dti3 − di ti3 = ⎪ ⎪ ∂a ⎪ i=0 ⎪ ⎪ ⎪ 4   ⎪

⎪ ∂δ ⎪ a + bti + cti2 + dti3 − di ti2 ⎨ ∂b = i=0 (4) 4  

⎪ ∂δ ⎪ ⎪ ∂c = a + bti + cti2 + dti3 − di ti ⎪ ⎪ ⎪ i=0 ⎪ ⎪ 4  ⎪ 

⎪ ∂δ ⎪ a + bti + cti2 + dti3 − di ⎩ ∂d = i=0

From (4), the coefficients of polynomial fitting are obtained, then the secondary position signal can be reconstruction. When n equals different values, the fitting results are shown in the following Fig. 3. In order to balance the accuracy of fitting and the speed of calculation, n is taken as 3.

3 Hardware-in-the-Loop Experiment To further validate the effectiveness of the position polynomial fitting based on least square method proposed in this paper, the experimental platform based on RTLabOP5607 is established, which is shown in Fig. 4. The experimental machine mainly includes a CPU board and a FPGA board of Xilinx Virtex7. The grating sensor position and speed detection system based on the laser array is built in the FPGA board, the conventional position accumulation and proposed polynomial fitting algorithms are built in the CPU control system. The TD discretization step is 500 ns.

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The reference position signal is shown in Fig. 5., indicating that the secondary accelerates for 2 s, then runs at the constant speed 100 m/s for 1 s, and finally decelerates for 2 s. In the experiment, according to the secondary position obtained by the above two methods in Fig. 2, this paper uses the adaptive TD to obtain the secondary speed. The

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Fig. 4. Hardware-in-the-loop simulation platform based on the RT-Lab OP5607. 350

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equation of adaptive TD is shown as (5). ⎧ x (k + 1) = x1 (k) + T · x2 (k) ⎪ ⎪ ⎨ 1 x2 (k + 1) = x2 (k) + T · fhan(x1 (k) −u(k), x2 (k), r(x2 , γ1 ), h(x2 , γ2 )) ⎪ ⎪ ⎩ y(k) = x2 (k)

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⎧ d =r·h ⎪ ⎪ ⎪ ⎪ ⎪ d0 = h · d ⎪ ⎪ ⎪ ⎪ y = x1− u + hx2 ⎪ ⎪ ⎪  ⎪ ⎨ a0 =⎧ d 2 + 8r|y| r(x2 , γ1 ) = Aarc tan( γx21 )  y x and |y| x + , ≤ d ⎨ − 1 ·( 2 )2 2 0 h ⎪ h(x2 , γ2 ) = γ12 e 2 γ2 ⎪ ⎪ a = x + 0.5 · (a − d )sgn(y) 0 ⎪ ⎪ ⎩ 2 ⎪ ⎪ |y| > d0 ⎪ ⎪  ⎪ ⎪ |a| > d −r · sgn(a), ⎪ ⎪  ⎩ fhan = −r · a d , |a| ≤ d x 2 (k) represents the speed of secondary, and γ 1 , γ 2 are the adjustable parameters. This TD is an adaptive tracking differentiator. α(x) increases rapidly with the increase of secondary speed, and β(x) decreases rapidly with the increase of secondary speed. The change rates of α(x) and β(x) can be changed by adjusting the values of γ 1 and γ 2 . α(x) is derived from a simple arctangent function, and β(x) is simplified from the standard normal distribution. α(x) and β(x) are used to fit the changes of speed factor r and filtering factor h. A and B are the variation range and initial value of the speed factor r respectively. The experimental results are shown as Fig. 6. It can be seen from Fig. 6 (a), the position obtained by the conventional position accumulation method has the obvious step shape, which is not conducive to motor position control. However, the position curve obtained by the proposed polynomial fitting algorithm is smooth and continuous. The maximum error of proposed position measurement method is 0.01 m. As can be seen from Fig. 6 (b), the speed obtained by the conventional method has the obvious fluctuation, which is obviously not conducive to motor control. The biggest error of speed is 2 m/s. However, the speed obtained by the proposed method has no fluctuation, and the error is small which is reduced by 80%, and the speed curve is smooth. Therefore, it is proved that this method can obtain accurate secondary position and velocity effectively.

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4 Conclusion In this paper, a new method of position and speed measurement is designed based on the grating sensor with laser array. This method uses the polynomial fitting method based on the least square method to obtain the position of secondary and the adaptive TD to obtain the speed of secondary. This method is simple, efficient, and has high fitting accuracy. Besides, the fitting accuracy can be improved by adjusting n. Compared with the conventional position accumulation method, the position and speed errors obtained by the proposed method are smaller and the accuracy is higher, which has been verified by the hardware in-the-loop experiments. The speed error caused by the proposed polynomial fitting method is 20% of that caused by the conventional position accumulation method.

References 1. Zhao, W., Zhu, J., Ji, J., Zhu, X.: Improvement of power factor in a double-side linear fluxmodulation permanent-magnet motor for long stroke applications. IEEE Trans. Ind. Electron. 66(5), 3391–3400 (2019)

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2. Fair, H.D.: Advances in electromagnetic launch science and technology and its applications. IEEE Trans. Magn. 45(1), 225–230 (2009) 3. Quesada, J.R., Charpentier, J.-F.: Finite difference study of unconventional structures of permanent-magnet linear machines for electromagnetic aircraft launch system. IEEE Trans. Magn. 41(1), 478–483 (2005) 4. Zhang, M., Shi, L.: Modeling and cooperative control of segmented long primary double-sided linear induction motor. IEEE Trans. Ind. Electron. 70(2), 1706–1716 (2023) 5. Wang, Q., He, N., Rui, W.: Study on the key technology of linear induction motor position detection system for electromagnetic emission. Proc. CSEE. 36(5), 1413–1420 (2016) 6. Wang, Q., Ma, W., He, N.: Sensitivity analysis of eddy-current sensor applied in grating-type displacement measurement system. In: Proceedings IEEE Conference Industrial. Electronics Applications., Auckland, New Zealand (2015) 7. He, N., Wang, Q., Rui, W.: Position measurement system for linear induction motor applied in electromagnetic emission system. Elect. Mach. Cont. 19(11), 10–16 (2015) 8. Hao, S., Liu, J., Hao, M., Song, B.: Design of high precision magnetic grid displacement sensor. In: IEEE International Conference on Mechatronics and Automation, Takamatsu, Japan, pp. 185–188 (2008) 9. Gong, Q., Jing, Y., Liao, Z., Qian, C., Hao, J., Kong, J.: Simulation research on structure optimization of maglev train gap sensor. In: 3rd International Conference on Electronic Information Technology and Computer Engineering (EITCE), Xiamen, China, pp. 1998–2001 (2019) 10. Zhou, S., Li, Y., Shi, L., Xu, F., Liu, J., Guo, K.: Research on the position-speed measuring system for high-speed long primary linear induction motor. In: 13th International Symposium on Linear Drives for Industry Applications (LDIA), Wuhan, China, pp. 1–4 (2021) 11. Salvatore, N., Caponio, A., Neri, F., Stasi, S., Cascella, G.L.: Optimization of delayed-state Kalman-filter-based algorithm via differential evolution for sensorless control of induction motors. IEEE Trans. Ind. Electron. 57(1), 385–394 (2010) 12. Gong, C., Hu, Y., Gao, J., Wang, Y., Yan, L.: An improved delay-suppressed sliding-mode observer for sensorless vector-controlled PMSM. IEEE Trans. Ind. Electron. 67(7), 5913– 5923 (2020) 13. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009) 14. Xie, Y., Long, Z., Li, J., Zhang, K., Luo, K.: Research on a new nonlinear discrete-time tracking-differentiator filtering characteristic. In: 7th World Congress on Intelligent Control and Automation, Chongqing, China, pp. 6750–6755 (2008) 15. Ni, Q., et al.: A new position and speed estimation scheme for position control of PMSM drives using low-resolution position sensors. IEEE Trans. Ind. Appl. 55(4), 3747–3758 (2019) 16. Feng, G., Lai, C., Han, Y., Kar, N.C.: Fast maximum torque per ampere (MTPA) angle detection for interior PMSMs using online polynomial curve fitting. IEEE Trans. Power Electron. 37(2), 2045–2056 (2022)

Sampling Analysis and Optimization Suggestions on Long Term Operation Metering Performance of Low Voltage Current Transformer Yicheng Bai1 , Shuai Gao1(B) , Lin Zhao1 , Zhengyu Jiang1 , Yuan Chi2 , Xuepeng Wei1 , and Yin Zhang1 1 State Grid Jibei Marketing Service Center (Metrology Center and Power Load Management

Center), Beijing, China [email protected] 2 Electric Power Research Institute, State Grid Beijing Electric Power Company, Beijing, China

Abstract. The operation quality of low-voltage current transformer directly affects the accuracy of electric energy measurement. This topic analyzes the metering performance of low-voltage current transformers in long-term operation, puts forward targeted optimization management suggestions, and guides the research on lean management optimization of low-voltage current transformers. This topic first investigates the characteristics of low-voltage current transformers that have been in operation for a long time. After that, this topic focuses on the research on the spot check of low-voltage current transformers, establishes a sampling plan based on Stratified sampling, completes the spot check analysis of 599 low-voltage current transformers, and analyzes and summarizes the influence law of multiple factors such as the unified recruitment mode, operating years, test current, transformation ratio, etc. on the measurement performance change of long-term operating low-voltage current transformers. At the same time, the targeted guiding opinions on the research of lean management optimization of low-voltage current transformers are proposed. Keywords: Low voltage current transformer · On site operating conditions · Sampling analysis · Lean optimization management suggestions

1 Introduction Low voltage current transformer is a kind of current conversion equipment that can convert the primary large AC current into the secondary small AC current. The primary rated current range is generally between 5 A and 1000 A, and the secondary current is usually 5 A. The accuracy level is generally 0.2S, 0.5S, 1, etc. The iron core used has undergone high vacuum heat treatment, and the shell is made of high impact flame-retardant ABS Science and technology project of State Grid Corporation of China (5700-202111201A-0–0-00). © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 285–292, 2024. https://doi.org/10.1007/978-981-97-1064-5_31

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material, which has good safety performance [1]. The manufacturing standards of lowvoltage current transformers are GB1207 and GB20840 series successively. At present, the influence of low-voltage current transformers on metering error is characterized by “large magnification” and the quality control means are relatively simple, which are mainly guaranteed through full performance test and full inspection acceptance test [2, 3]. However, after its operation, it is often difficult to achieve regular weekly inspections. Under complex on-site conditions, overcurrent, impulsive loads, etc. will accelerate the magnetic loss of the iron core, aging and deformation of insulation materials, which will cause compression or stretching of the iron core and winding, resulting in electric shock surface oxidation and an increase in contact resistance. Especially after replacing the secondary circuit and disassembling related circuit equipment, the increase in resistance is more obvious. Considering factors such as the harsh outdoor operating environment of the equipment, etc. The increase in resistance is becoming increasingly prominent, which cannot guarantee the metrological performance under long-term operation [4]. In addition, some low-voltage current transformers are user assets or not subject to centralized verification, so the metering performance after putting into operation cannot be guaranteed [5, 6]. Through the preliminary spot check analysis, it is found that the low-voltage current transformer in long-term operation has different degrees of wear, damage, cracking but not replaced in time. Therefore, it is urgent to study and put forward suggestions for optimizing the lean management of low-voltage current transformers based on the objective laws and actual operation.

2 Sampling Scheme of Low-voltage Current Transformer According to the requirements of DL/T 448–2016 Technical Management Regulations for Electric Energy Metering Devices, 1% –5% of the total amount of low-voltage current transformers should be sampled for subsequent verification every year since the 20th year of operation, and the statistical qualification rate should not be less than 98%; Otherwise, the sampling and verification should be doubled, and the pass rate should be counted until all are replaced. In order to better carry out the bottom-up analysis of the operation status of low-voltage current transformers, first of all, spot check the low-voltage current transformers in operation of a provincial power company. In order to comprehensively evaluate the factors affecting the metering performance of lowvoltage current transformers, Stratified sampling method is adopted according to GB/T 10111–2008 Generation of Random Numbers and Their Application in Product Quality Sampling Inspection, GB/T 4891–2008 Method of Selecting Sample Size for Estimating Average Quality of Batches (or Processes), etc., considering the characteristics of large quantity, different accuracy requirements, load characteristics, etc. of low-voltage current transformers in operation at present. The sampling implementation subject is a certain provincial power company participating in the project, and the basic unit selected for sampling is the subordinate city power company. For each basic unit (each city company), the sampling number of lowvoltage current transformers selected is 150 k (k is the expansion factor, k = 1–2, and the provincial company shall determine at least one city with representative environment or typical characteristics for expanded sampling). Stratified sampling is adopted as the main

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sampling method, and the service life and transformation ratio are layered, as shown in Table 1. Before conducting spot checks, it is necessary to conduct on-site inspections and check the marketing or collection systems to record equipment parameter information. Table 1. Specific Sampling Plan and Requirements Operating years Sample number Transformation ratio

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3 Analysis of Sampling Test Results of Low Voltage Current Transformer According to JJG1021–2007 “Power Transformer”, basic error verification was carried out for 599 sampled low-voltage CTs. The distribution of low voltage CT error (ratio difference) at 0.2S and 0.5S levels in various cities is shown in the figure: Out of the 599 sampled low-voltage CTs, approximately 60 had appearance defects such as nameplate wear, loss of secondary terminals (screws), and surface damage. After testing, the errors exceeded the standard, revealing issues such as lack of daily maintenance work and non-standard management of low-voltage CTs. The appearance is unqualified as shown in the figure: The results of sampling inspection of low-voltage current transformers are as follows: 1. The qualification rate of low-voltage current transformers under unified recruitment is significantly higher than that of low-voltage current transformers under non unified recruitment. The qualification rate of low-voltage CT purchased through the unified bidding method is 100%, while the qualification rate of low-voltage CT purchased through non unified bidding method is 60.98%. 2. With the increase of operating years, the qualification rate of transformers in operation shows a decreasing trend. The qualification rates of transformers operating for less than 5 years, 5–10 years, 11–15 years, and more than 15 years are 72.50%, 63.94%, 63.16%, and 65.52%, respectively. In ultra differential low pressure CT, the ratio difference and phase difference over differential multiples are distributed in the range of (−153.5, −51.2) and (−3.3, 8.3).

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Fig. 1. Distribution of error ratio of 0.2S low voltage CT

Fig. 2. Distribution of error ratio of 0.5S low voltage CT

3. As the ratio increases, the qualification rate shows an upward trend. The basic error qualification rate of large ratio current transformers is higher than that of small ratio current transformers. Small transformer ratio current transformers have fewer secondary turns, and under the same core size parameters, the error of the transformer is greater than that of large transformer ratio current transformers. Moreover, measures such as internal turn reduction compensation and magnetic shunt compensation for small ratio transformers will have an impact on the operational stability of the transformers.

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Fig. 3. Current Situation of Low Voltage CT with Unqualified Appearance

4. The out of tolerance of low-voltage CT detection is mostly concentrated in the area with small test current, such as 5% and 20% rated primary current percentage Test point. Among low voltage CT scans with out of tolerance, the measurement point with 20% out of tolerance accounts for the largest proportion, approximately 67.18%. In

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Fig. 4. Basic error qualification rate of low voltage CT operation years during spot check

Fig. 5. Qualification rate of basic error for different transformer ratios of low-voltage CT during sampling inspection

the out of tolerance verification results, the ratio difference and phase difference out of tolerance multiples are concentrated in the (1, 21) and (1, 2.4) intervals, respectively.

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Fig. 6. Current distribution ratio diagram of unqualified errors in low-voltage CT spot checks

4 Conclusion In combination with objective laws and operation practice, the following suggestions are proposed for low-voltage current transformers: 1. The low-voltage current transformer purchased through unified bidding can pass the full performance test and full inspection acceptance test to effectively ensure its metering performance. 2. After long-term operation under complex working conditions on site, overcurrent, impulsive loads, etc. will accelerate the magnetic loss of the iron core, and aging and deformation of insulation materials will cause squeezing or stretching of the iron core and winding, which may affect its measurement accuracy. It is recommended to conduct quality evaluation work on expired low-voltage CT in a timely manner. 3. For small transformer ratios, due to the small number of primary turns, it is difficult to meet the accuracy requirements [7, 8]. Each factory often designs compensation based on their own experience (usually using turns compensation and magnetic shunt compensation), but its long-term operating accuracy still lags behind that of large transformer ratio low-voltage CT. 4. Random inspection found that the transformer was damaged to varying degrees, cracked, and the nameplate was worn, but it was not operated and maintained in a timely manner. Suggest increasing efforts in operation and maintenance management and on-site verification. It is recommended to use image processing technology based on image duty cycle and circularity to detect surface cracks on the transformer. Firstly, the ROI of the transformer image is obtained, followed by extracting the relevant feature values of each connected domain in the ROI. Finally, the duty cycle and circularity of the connected domain are calculated to achieve surface crack detection on the water flow line. This method has high detection speed and accuracy [9, 10]. It is recommended to replace the damaged and cracked low-voltage CT in a timely manner.

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5. It is recommended to conduct a batch survey of transformers found to be out of tolerance in the same batch, age, and environment during spot checks, in order to timely grasp the actual operating conditions of the transformers.

References 1. Kong, X., Zhang, X., Lu, N., Ma, Y., Li, Y.: Online smart meter measurement error estimation based on EKF and LMRLS method. IEEE Trans. Smart Grid 12(5), 4269–4279 (2021) 2. Notice of the general office of the State Administration of market supervision on carrying out the special action of people’s livelihood measurement, 2021. https://gkml.samr.gov.cn/nsjg/ jls/202103/t20210329_327380.html 3. Li, Z., Zheng, Y., Abu-Siada, A., Lu, M., Li, H., Xu, Y.: Online evaluation for the accuracy of electronic voltage transformer based on recursive principal components analysis. Energies 13(21), 5576 (2020) 4. Dong, Y., Hui, Y.X.: The transformer accuracy on-line evaluation system. Int. Conf. Electr. Contr. Eng. 2011, 5030–5033 (2011) 5. Phadke, A.G., Thorp, J.S.: Synchronized Phasor Measurements and Their Applications[M]. Springer, 2017 6. Khandeparkar, K.V., Soman, S.A., Gajjar, G.: Detection and correction of systematic errors in instrument transformers along with line parameter estimation using PMU data. IEEE Trans. Power Syst. 32(4), 3089–3098 (2016) 7. Da Luz, M.V.F., Leite, J.V., Benabou, A., et al.: Three-phase transformer modeling using a vector hysteresis model and including the eddy current and the anomalous losses. IEEE Trans. Magn. Magn. 46(8), 3201–3204 (2010) 8. Hernandez, I., Olivares-Galvan, J.C., Georgilakis, P.S., et al.: Core loss and excitation current model for wound core distribution transformers. Int. Trans. Electr. Energy Syst. 24(1), 30–42 (2014) 9. Nogawa, S., Kuwata, M., Nakau, T., et al.: Study of modeling method of lamination of reactor core. IEEE Trans. Magn.Magn. 42(4), 1455–1458 (2006) 10. Zhu, J.G., Hui, S.Y.R., Ramsden, V.S.: A dynamic equivalent circuit model for solid magnetic cores for high switching frequency operations. IEEE Trans. Power Electron. 10(6), 791–795 (1995)

Design and Experiments of Voltage Sensor Based on Electric Field Coupling Principle and Differential Input Structure Jianghan Li, Qing Xiong(B) , Chen Zhang, Xiaoxiao Zhao, Tonghao Zhou, and Shengchang Ji StateKey Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an, China [email protected], {qingxiong,jsc}@xjtu.edu.cn, {qjwttc, zxxiao1998}@stu.xjtu.edu.cn, [email protected]

Abstract. Traditional voltage transformers often encounter problems such as large size, insulation damage, and core saturation. Voltage sensors based on the electric field coupling principle avoid these problems. In early research, the method of changing the mutual capacitance between differential electrodes had many problems and was difficult to apply in practice. This study uses multilayer ceramic capacitors to replace mutual capacitance to create a new voltage sensor. Tests have shown that the sensor has excellent linearity and phase accuracy, and performs superiorly in high-frequency response. In addition, it offers the advantages of cost-effectiveness, compactness, shape adaptability, and easily adjustable voltage divider ratio. Keywords: Differential input structure · Electric field coupling · Multi-layer ceramic capacitor · Non-contact voltage measurement · Instantaneous response

1 Introduction The voltage sensing measurements have significance in various areas in the power system, such as energy metering, relay protection, real-time overvoltage monitoring, smart device control, and power maintenance. As China accelerates its smart grid construction and elevates its grid’s digitalization, intelligence and automation levels, voltage and current sensors are designed toward digitalization, miniaturization, and user-friendliness [1]. Currently, inductive voltage transformers (IVTs) and capacitive voltage transformers (CVTs) are the mainstays for voltage measurements in the power systems. Despite its predominant usage, IVTs face challenges like bulkiness, high production costs, and susceptibility to insulation failures due to ferromagnetic resonance overvoltages [2–4]. CVTs, to some extent, address the shortcomings of IVTs. However, they exhibit subpar transient response characteristics, making them less favorable for transient overvoltage online-monitoring [5, 6]. By employing the electric field coupling technique, the noncontact voltage measurement method offers a promising approach. This method does not require direct contact with the target and has good insulation properties, simple structure, no resonant overvoltage, wide frequency band and fast response capability [7]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 293–302, 2024. https://doi.org/10.1007/978-981-97-1064-5_32

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For the electric field coupling, there are chiefly two sensor configurations for voltage measurement: the single-ended grounding setup and the differential input design. While the differential structure solves the problem of contact with the object being measured and grounding, it demands significant capacitance between its differential electrodes to satisfy the self-integration prerequisites and achieve an elevated voltage division ratio. Current studies have typically employed strategies like augmenting the electrodes’ equivalent surface area or inserting dielectrics between electrodes to boost their mutual capacitance [8]. However, these methodologies yield capacitance values that are not only diminutive but also lack precision. Such techniques also present challenges: amplified sensor dimensions, capacitance sensitivities to external conditions like temperature and moisture, instability of voltage division ratio, and a rather rigid sensor form factor. This study introduces a groundbreaking approach by incorporating a multi-layer ceramic capacitor as the mutual capacitance between the electrodes. Coupled with the dual bypass high-resistance grounding technique to amplify the input impedance of the differential signal processing circuit, this leads to the conceptualization of a novel voltage sensor. This innovative sensor has advantages of compact design, ease of voltage division ratio adjustments, a variable shape, and cost-effectiveness. Furthermore, both steady-state and transient tests are taken to investigate the sensor’s frequency response attributes and its precision levels.

2 Principle and Equivalent Model of Sensor 2.1 Principle of the Non-contact Wideband Voltage Sensor The schematic diagram of the non-contact wideband voltage sensor is shown in Fig. 1. As can be seen from the figure, the sensor mainly consists of two parts: the sensing electrode and the low-voltage arm. During application, the sensing electrode faces the high-voltage bus directly. Its working principle is similar to that of a capacitive divider. The high-voltage arm capacitance, C1 , represents the stray capacitance between the sensing electrode and the high-voltage bus. The low-voltage arm capacitance, C2 , is a capacitor made using insulating film or a surface-mount capacitor. Its two terminals are connected to the sensing electrode plate and reference ground, respectively. The required signal is connected from the sensing electrode through the front-end matching resistor and the coaxial cable to the data acquisition system. The value of the high-voltage arm capacitance, C1 , is affected by various factors such as the installation position and ambient temperature and humidity, making it difficult to maintain a constant value. Therefore, one can compare the sensor’s output with that of the existing voltage transformer at power frequency to achieve real-time calibration of the sensor’s ratio. 2.2 Equivalent Model of the Sensor For sensors with the same structural dimensions in the low-voltage arm, the stray inductance value L2 remains relatively constant. Hence, the key to improve the high-frequency characteristics of the sensor is reducing the capacitance value C2 of the low-voltage arm. Typically, data collection systems employ a high-resistance mode, with a fixed input

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Fig. 1. Schematic diagram of non-contact wideband voltage sensor

resistance of 1 M. Therefore, a larger capacitance C2 in the sensor’s low-voltage arm might compromise high-frequency response characteristics, while a lower value might not meet low-frequency response requirements. To address this problem, one solution is to introduce a resistor-capacitor voltage divider unit before the data collection system. This effectively heightens the input resistance of the data collection system. The equivalent circuit of the voltage sensor using the resistor-capacitor voltage divider unit is illustrated in Fig. 2.

Fig. 2. L 1 , L 2 ——Equivalent inductance and equivalent capacitance of sensor high voltage arm; L 1 , L 2 ——Equivalent inductance and equivalent capacitance of sensor low voltage arm; R— —Matching resistor; R3 , C 3 ——Resistor-capacitor voltage dividing unit RC-parallel resistor, RC-parallel capacitor; C 5 ——Resistor-capacitor voltage dividing unit compensation capacitor; R4 , C 4 ——Inlet resistance and inlet capacitance of data acquisition system. Equivalent circuit diagram of voltage sensor using resistor-capacitor voltage dividing unit

At this time, the low-frequency characteristics of the sensor are analyzed, and the calculation formula of the lower limit cutoff frequency can be obtained: fLow - cutoff =

1 1 ≈ 2π (R3 + R4 )(C1 + C2 ) 2π (R3 + R4 )C2

(1)

When the capacitance of the low-voltage arm of the sensor is small, the resistance at the entrance of the data acquisition system is not enough to make the lower limit

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cutoff frequency of the sensor meet the measurement requirements of power frequency voltage. Therefore, it is necessary to use a resistor-capacitor voltage dividing unit to increase the equivalent input resistance of the measurement system. When the resistorcapacitor voltage dividing unit is added, the equivalent input resistance value of the measurement system changes from the input resistance of the data acquisition system to the sum of the input resistance of the data acquisition system and the parallel resistance of the resistor-capacitor voltage divider unit. At low frequency, ignoring the parallel capacitance of the resistance-capacitance dividing unit and the inlet capacitance of the data acquisition system, the signal output 4 . At high by the sensor is divided by R3 and R4 , and the voltage dividing ratio is R3R+R 4 frequency, the parallel capacitance of the resistor-capacitor voltage dividing unit and the inlet capacitance of the data acquisition system cannot be ignored. Therefore, the parameters of the resistor-capacitor voltage divider unit and the data acquisition system 5 , so that the voltage dividing circuit has a consistent voltage need to satisfy RR43 = C4C+C 3 dividing ratio from low frequency to high frequency. 2.3 Design of Sensor This sensor mainly consists of two parts, namely the electrode and the differential processing circuit. The overall physical diagram is shown in Fig. 3. For the electrodes, to minimize the impact of the electrode shape on the coupling capacitance of the highvoltage arm, this paper uses a PCB board to manufacture the motor, and ensures that the two electrodes have the same position and shape in the design. In practice, during use, the shape of the electrode can be changed according to the actual application scenario.

Fig. 3. Physical picture of the sensor

This paper uses a two-stage amplification circuit for the design of the differential signal processing circuit, in which the first stage is a voltage follower circuit directly connected to two electrodes, and the second stage uses a differential processing circuit based on an operational amplifier. This circuit converts the floating potential to a potential relative to the processing circuit ground, which is key to eliminate the need for grounding for sensor measurements. OPA189 of Texas Instruments is used, which uses a doubleended 15 V power supply. It has the advantages of low temperature drift and small DC offset [9]. In addition, adding self-integrating modules to the two input ports of the circuit can not only ensure that the self-integrating conditions of the sensor are met, but also use integrated ceramic capacitors to replace the coupling capacitors between electrodes, which has the advantage of being more stable and less affected by the environment [10]. The signal processing circuit diagram is shown in Fig. 4.

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15V

Vin R1

C1 15V

R2

R3

15V

Vout 15V

R1

R2

C1

15V

R3

Vin 15V

Fig. 4. Diagram of differential processing circuit

3 Experimental Platform Two experimental platforms are used in this paper, i.e., the power frequency experimental platform and the sensor response characteristics experimental platform. The schematic diagram is shown in Fig. 5.

(a) Power frequency experimental platform

(b) Sensor response characteristics experimental platform

Fig. 5. Experimental platform.

4 Results and Result Analysis 4.1 Power Frequency Steady-State Experiments To study whether the voltage sensor have a stable voltage ratio under different voltage levels at a fixed position, power frequency platform was used to place the sensor at a position of 100 cm from the capacitive voltage divider and continuously increase the voltage. The results are as shown in the Fig. 6. It can be seen that the sensor has a stable voltage ratio and excellent linearity at a fixed position.

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Measurement points Fitted curve

Sensor output voltage(V)

1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

2

4

.

6

8

10

12

14

Transformer output voltage(kV)

Fig. 6. Result of distance experiment.

Figure 7 shows the comparison between the voltage measured by the high-voltage probe and the voltage curve measured by the voltage sensor produced in this paper. It can be seen that under power frequency conditions, when the integrating capacitance is 47 nF, a small phase difference can be guaranteed. The two figures in the figure. The phase difference between the two curves is only 19’. 12

2000

10 1500

CH1:Voltage sensor

6

1000

4 500 2 0

0 -2

-500 -4 -6 

-10



-12 -0.02

Sensor output voltage(V)

-1000

-8



Sensor output voltage(mV)

8

Transformer output voltage(kV)

Transformer output voltage(kV)

CH2:Capacitive voltage divider

Phase difference: 19' -1500





Time(s) 

-0.01

0.00

0.01

-2000 0.02

Time(s)

Fig. 7. Power frequency phase error of sensor.

4.2 Frequency Response Characteristics Experiments This paper produced sensors with low-voltage arm capacitance C2 of 15 nF and 220 nF respectively. The sensor with a low-voltage arm capacitance of 15 nF is used with a resistor-capacitor voltage dividing unit. The sensor with a low-voltage arm capacitance of 220 nF is directly connected to the data acquisition system. The coaxial cable lengths are selected from 1 m, 2 m and 10 m. The frequency response characteristics was tested using the platform shown in Fig. 5(b), and the experimental results are shown in Fig. 9 and Fig. 10.

Design and Experiments of Voltage Sensor 5.0

299

×104

4.5

Voltage division ratio

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 100

110

120

130

140

150

160

Distance(cm)

Fig. 8. Relationship between sensor voltage division ratio and distance.

It can be seen that when the low-voltage arm capacitance is 15nF, the cable length has a significant impact on the high-frequency response characteristics of the voltage sensor. When the cable length is 1 m, the high-frequency cutoff frequency of the voltage sensor is greater than 20 MHz, but the cable length is 2 m and 10 m, the frequency response of the voltage sensor changes significantly starting from 10 MHz, and resonance occurs. When the low-voltage arm capacitance is 220 nF, the cable length has little effect on the high-frequency response characteristics of the voltage sensor. When the cable length is 1 m and 2 m, the frequency response curves of the voltage sensor are almost the same, and the high-frequency cutoff frequency is about 2 MHz. When the cable length is 10 m, its high-frequency cutoff drops slightly to about 1.7 MHz. Therefore, the use of a resistorcapacitor voltage dividing unit combined with a smaller low-voltage arm capacitor can effectively improve the high-frequency response characteristics of the voltage sensor. When the low-voltage arm capacitance is small, its high-frequency response characteristics are easily affected by the cable length. However, compared to using a low-voltage arm capacitor with a larger capacitance, a voltage sensor using a smaller low-voltage arm capacitor still has a better high-frequency response characteristic.

(a) 1m

(b) 2m

(c) 10m

Fig. 9. Frequency response curve of voltage sensor with low voltage arm capacitance of 15 nF.

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(a) 1m

(b) 2m

(c) 10m

Fig. 10. Frequency response curve of voltage sensor with low voltage arm capacitance of 220 nF.

4.3 Transient Characteristics Experiments Using the setup in Fig. 5(b), the voltage sensor’s response to a standard 1.2/50 µs lightning double exponential wave, generated by an arbitrary waveform generator, is tested. The 1 m cable was used in the test. With a low-voltage arm capacitance of 15nF, a resistor-capacitor voltage dividing unit was used, whereas a 220 nF capacitance was directly linked to the data system. Results are shown in Fig. 11 and Fig. 12. The black curve represents the sensor output and the red curve is the metal plate voltage, measured by the voltage probe. Both sensors accurately captured the lightning wave, but the 220 nF sensor displayed oscillation at the wave’s head.

(a) Full wave diagram of lightning wave.

(b) Enlarged view of wave head

Fig. 11. Experimental results of the sensor’s lightning wave response capability when C2 = 15nF.

(a) Full wave diagram of lightning wave.

(b) Enlarged view of wave head

Fig. 12. Experimental results of the sensor’s lightning wave response capability when C2 = 220nF.

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5 Conclusion This paper designs a new type of non-contact wide-band voltage sensor and delves into its design, and testing procedures. Notably, it adopts a differential input structure grounded in the electric field coupling principle. The design innovatively incorporates multi-layer ceramic integrated capacitors in the differential signal processing circuit, replacing the self-integrating mutual capacitance between electrodes. In practical scenarios, the capacitance can be fine-tuned as per specific application needs. This ensures that mutual capacitance remains largely impervious to environmental factors, addressing several challenges prevalent in contemporary research. The sensor has excellent linearity and accuracy at power frequency, and can ensure a stable voltage division ratio when the position is fixed. It also proves that the high-frequency response characteristics can be enhanced by reducing the low-voltage arm capacitance. Realize effective measurement from power frequency to lightning impulse voltage. Given the existing coupling capacitance between the sensor and the non-measured phase, future research needs to strategize ways to mitigate the impact of the non-measured phase on sensor measurements. Acknowledgments. This work is supported by National Key Research and Development Program of China (No.2022YFB3205700).

References 1. Qing, Y., Shangpeng, S., Wenxia, S., Yanxiao, H., Mandan, L.: Research progress on advanced voltage and current sensing methods for smart grids. High Volt. Eng. 45(2), 349–367 (2019). https://doi.org/10.13336/j.1003-6520.hve.20190130002 2. Jahagirdar, A., Thosar, A., Dhote, V.P.: Study of high voltage inductive voltage transformer for transients and ferroresonance. In: 2018 International Conference on Power, Energy, Control and Transmission Systems (ICPECTS), Feb. 2018, pp. 174–180. https://doi.org/10.1109/ICP ECTS.2018.8521570 3. Kaczmarek, M., Brodecki, D.: Transformation of transient overvoltages by inductive voltage transformers. Sensors 21(12), Jan. (2021). https://doi.org/10.3390/s21124167 4. Arroyo, A., Martinez, R., Manana, M., Pigazo, A., Minguez, R.: Detection of ferroresonance occurrence in inductive voltage transformers through vibration analysis. Eng. Failure Anal. 134, 2022. https://doi.org/10.1016/j.engfailanal.2021.105979 5. Tajdinian, M., Allahbakhshi, M., Biswal, S., Malik, O.P., Behi, D.: Study of the impact of switching transient overvoltages on ferroresonance of CCVT in series and shunt compensated power systems. IEEE Trans. Industr. Inf. 16(8), 5032–5041 (2020). https://doi.org/10.1109/ TII.2019.2951332 6. Li, P., Guo, P.: Diagnosis of interturn faults of voltage transformer using excitation current and phase difference. Int. J. Electr. Power Energy Syst. 134(1), 294–300 (2018). https://doi. org/10.1016/j.ijepes.2018.10.011 7. Pouryazdan, A., Costa, J.C., Prance, R.J., Prance, H., Münzenrieder, N.: Non-contact long range AC voltage measurement. In: 2019 IEEE SENSORS, pp. 1–4 (2019). https://doi.org/ 10.1109/SENSORS43011.2019.8956724 8. Rostaghi-Chalaki, M., Haque, F., Yousefpour, K., Park, C.: Application of D-dot sensor for partial discharge waveform measurement. In: 2021 IEEE Electrical Insulation Conference (EIC), Jun. 2021, pp. 230–233 (2021). https://doi.org/10.1109/EIC49891.2021.9612343

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9. OPAx189 Precision, Lowest-Noise, 36-V, Zero-Drift, 14-MHz, MUX-Friendly, Rail-to-Rail Output Operational Amplifiers datasheet. Available online: https://www.ti.com/lit/ds/sym link/opa189.pdf. Accessed 27 September 2022 10. Xiong, Q., et al.: Series arc fault detection and localization in DC distribution system. IEEE Trans. Instrum. Meas. 69(1), 122–134 (2020). https://doi.org/10.1109/TIM.2019.2890892

In-Situ Detection of Thermal Runaway Gases of Lithium-Ion Batteries Based on Fiber-Enhanced Raman Spectroscopy Bing Luo1,2 , Dibo Wang1,2 , Qiang Liu3 , Tongqin Ran3 , and Fu Wan3(B) 1 United Laboratory of Advanced Electrical Materials and Equipment Support Technology,

CSG, Guangzhou 510663, People’s Republic of China {luobing,wangdb}@csg.cn 2 CSG Electric Power Research Institute CO., LTD, Guangzhou 510663, People’s Republic of China 3 State Key Laboratory of Power Transmission Equipment Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, People’s Republic of China {lq,fuwan}@cqu.edu.cn, [email protected]

Abstract. Gas detection is an effective early warning method of thermal runaway of lithium-ion battery (LIB). This paper proposes a method for in-situ detection of LIB thermal runaway gases based on Raman spectroscopy. Firstly, the detection platform is developed and the limit of detection (LOD) is obtained. According to the LOD, the sensitivity of gas Raman spectroscopy detection is significantly improved by fiber-enhanced technology. Next, a thermal runaway monitored by the platform is performed. Benefiting from the unique advantage of simultaneous and non-destructive analysis of Raman spectroscopy, real-time and in-situ detection of multiple gases generated during LIB thermal runaway is realized. A warning time of 526 s is achieved by the detection of CO2 in the early stage of thermal runaway, which provides sufficient time for battery safety management as well as personnel evacuation, and demonstrates the potential of gas Raman spectroscopy detection in LIB thermal runaway gas analysis and fault warning. Keywords: Raman Spectroscopy · Lithium-ion Battery · Thermal Runaway

1 Introduction Lithium-ion battery (LIB), an eco-friendly energy storage technology, has excellent performance such as high energy density and long cycle life, and thus has become a competitive energy storage technology for portable devices, electric vehicles, and stationary energy storage [1, 2]. However, the safety issues of LIB, especially the accidents caused by thermal runaway, have attracted extensive attention, and brought severe challenges to the battery management in recent years [3]. Various abuses [4] are the triggers of LIB thermal runaway, and when it occurs, internal temperature and pressure of LIB increase rapidly [5], with toxic and flammable gases generated and vented [6]; consequently, the LIB swells, ruptures or even explodes [7]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 303–311, 2024. https://doi.org/10.1007/978-981-97-1064-5_33

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Currently, the commonly used safety monitoring devices for commercial LIBs are based on temperature, voltage, smoke, and pressure measurement, etc., and relatively few researches involve gas detection [8]. Koch et al. [9] evaluated the thermal runaway detection capability of several different types of sensors, and the gas sensor showed the fastest and strongest response. Jin et al. [10] showed that the early safety warning method based on hydrogen detection was 639 s and 769 s earlier than smoke and fire detection, respectively. Liao et al. [11] achieved a warning time of 7.3 min by detection of C2 H4 , CH4 , and CO2 . Therefore, timely detection of thermal runaway gases is the key to achieve early warning of LIB thermal runaway. Methods for thermal runaway gas detection include gas chromatography-mass spectrometry (GC-MS) method [12], spectral analysis methods based on absorption effect (i.e., photoacoustic spectrometry, absorption spectroscopy, etc.) [11, 13], gas-sensitive transducers [14, 15], etc. GC-MS method features high sensitivity for multiple gases, but it requires gas sampling from cell before detection, which will affect the gas concentration inside the cell; additionally, the aging of chromatographic column is an inevitable problem. Spectral analysis methods based on absorption effect have high sensitivity for the gas whose absorption peak matches the wavelength of the incident laser, but these methods are not able to detect homonuclear diatomic thermal runaway gases such as H2 and O2 . Gas-sensitive transducers have cross-interference problems that limit the application in multiple gas detection, and the limited measuring ranges are not capable for high-concentration gas detection. Raman spectroscopy is based on scattering between the molecule and the photon [16]. The composition and concentration of the investigated substance are determined by direct measurement of Raman scattering signal, which is a non-invasive analysis method that does not require gas separation from cell. In addition, the unique feature of simultaneous detection of multiple gases (including homonuclear diatomic gases) with a single laser makes it suitable for in-situ analysis of thermally runaway gases. However, the insufficient detection sensitivity limits the application of Raman spectroscopy in early warning of thermal runaway [17]. Cavity-enhanced Raman spectroscopy (CERS) [18] and fiber-enhanced Raman spectroscopy (FERS) [19] are two methods to enhance the detection sensitivity. CERS is based on resonant cavity that increases the intensity of the excitation laser, thus enhancing the Raman scattering signal generated, but CERS needs a complex frequency-locking system to keep the resonance of excitation laser. FERS restricts the excitation laser, Raman scattering signal, and the gas to be detected within the hollow-core region of fiber, increasing the collection efficiency of Raman scattering signal on either terminal of fiber with a simpler detection platform compared to CERS. In addition, due to the µm-level diameter of hollow-core fiber, only approximately 10 µL of gas is needed for FERS detection, which is ideal for gas detection at early stage of LIB thermal runaway. In this paper, a FERS detection platform that significantly improves the sensitivity of gas detection is developed. Subsequently, the proposed platform is used to detect the gases generated by a thermal runaway fault of a ternary LIB. Taking advantage of simultaneous and non-destructive analysis of Raman spectroscopy, real-time and in-situ detection of multiple gases generated during LIB thermal runaway is realized and a warning time of 526 s is achieved.

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2 Experiment Based on the previously completed FERS detection platform reported in [20], the experimental setup of the in-situ gas detection platform is shown in Fig. 1(a). An excitation laser (Cobolt Samba series, HUBNER Photonics Inc., Sweden) of the key parameters listed in Table 1 is used. The beam size is adjusted by a coupling mirror to match the mode field of hollow-core fiber before entering the gas chamber. The fiber used in this platform is hollow-core anti-resonant fiber (HC-ARF) manufactured by Institute of Photonics Technology, Jinan University, China, as shown in Fig. 1(b), with key parameters listed in Table 2. The fiber is installed in the gas chamber that contains thermal runaway gases, as shown in Fig. 1(c). The Raman scattering signal, enhanced by the fiber, passes through the dichroic mirror, and then is guided into the spectrometer (HRS-300-S series, Princeton Inc., America) and CCD (PIXISTM 400B, Princeton Inc., America) as shown in Fig. 1(d). Finally, the Raman spectrum of the gases is obtained through the spectral analysis software. Unless otherwise noted, the key parameters of the platform listed in Table 3 are utilized.

Fig. 1. Experiment setup of the in-situ gas detection platform. (a) Schematic diagram of the in-situ gas detection platform; (b) Schematic diagram of HC-ARF; (c) The overall and decomposition structure of gas chamber; (d) Schematic diagram of the spectrometer and CCD.

Table 1. Key parameters of laser. Center wavelength

Pmax

Waist radius

Waist location

Beam quality

Emission angle

532 nm

200 mW

368 µm

+23.7 cm

M2 < 1.1

1.2 mrad

To obtain the limit of detection (LOD) for main LIB thermal runaway gases, first, the gas chamber is disconnected from the tank, purged with Ar and vacuumed. Then, Raman spectrum of background is obtained by detecting the vacuumed gas chamber to obtain and utilize the correction of background noise. Next, multiple-component calibration

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Core diameter

Length

Minimum attenuation at 532 nm

Wavelength range

26 µm

2m

0.08 dB/m

400–1200 nm

Table 3. Key parameters of in-situ gas detection platform. Plaser

Pressure of gas chamber

Slit width of spectrometer

Optical grating utilized

Spectral integration time

Volume for gas diffusion

200 mW

1 bar

50 µm

1200 g/mm

1 × 60 = 60 s

6L

gas (H2 , CH4 , C2 H2 , C2 H4 , C2 H6 : 80 ppm respectively; CO: 198 ppm; CO2 : 199 ppm; Ar: the remaining) is detected at 1 bar to determine the LOD. After the LOD is obtained, the thermal runaway of LIB is conducted in a sealed experimental tank as shown in Fig. 2, triggered by a heating rod whose heating rate is adjusted by the temperature control device. A commercial 18650 ternary LIB (3.7 V nominal voltage, 2600 mAh nominal capacity) is used in this experiment. The anode and cathode materials are graphite and lithium nickel cobalt manganese oxide (NCM), respectively, and the electrolyte is EMC, DMC, EC and LiPF6 mixture.

Fig. 2. (a) Sealed experimental tank; (b) 18650 ternary LIB; (c) Pressure sensor.

During the whole experiment, the surface temperature of battery and the pressure inside tank are measured by K-type thermocouple and pressure gauge, respectively, and recorded by paperless recorder. The tank is connected to the gas chamber through a valve, so the generated gases can be measured directly without separation. In addition, a filter is added to the air path to prevent the clogging of the fiber core by particulate matter ejected during thermal runaway.

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3 Results and Discussion The LOD of the detection platform is calculated based on concentrations of gases (c) and signal-to-noise ratio (SNR), as listed in Table 4, with LOD = 3 × c/SNR. It should be noted that due to the influence of background noise, the selected characteristic peak of CO2 is 1286 cm−1 rather than 1388 cm−1 which has a higher Raman intensity, though. According to the LOD, the platform is capable for ppm-level detection of main LIB thermal runaway gases. Table 4. LOD of main LIB thermal runaway gases. Component

Characteristic peak/cm−1

Raman intensity/a.u

Baseline for noise calculation/cm−1

Noise/a.u

LOD at 1 bar/ppm

H2

588

5022

640–710

88.0

4.2

CO2

1286

4835

1100–1200

61.5

7.6

C2 H2

1974

8550

1800–1900

54.8

1.5

CO

2143

3436

1800–1900

54.8

9.5

CH4

2918

15775

2500–2600

54.0

0.8

C2 H6

2955

4318

2500–2600

54.0

3.0

C2 H4

3022

9440

2500–2600

54.0

1.4

Before the thermal runaway experiment, the battery is pre-charged to 100% SOC, and the tank is connected to the gas chamber, purged with Ar and vacuumed. Figure 3 shows the variation of Raman intensity of gases during thermal runaway. At t = 0 s, the battery heating and the spectral data acquisition starts. As shown in Fig. 3(a), the concentration of O2 increases since t = 0 s due to the decomposition of NCM under high temperature, and reaches its maximum instantaneously before the thermal runaway. Then, the concentration of O2 decreases sharply because of the reaction between O2 and electrolyte (formula 1–2), which results in the rapid increase of the Raman intensity of CO2 . C2 H4 is detected in the meanwhile, generated by the reaction between lithium and the electrolyte (formula 3). H2 is detected last, generated by the reaction between lithium and the binder (formula 4). The following reactions are involved [3, 21, 22]: 2.5O2 + C3 H4 O3 → 3CO2 + 2H2 O

(1)

3O2 + C3 H6 O3 → 3CO2 + 3H2 O

(2)

2Li + C3 H4 O3 → Li2 CO3 + C2 H4

(3)

−CH2 − CF2 − + Li → LiF + −CH = CF − + 0.5H2

(4)

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Fig. 3. Changes in Raman intensity of the gases during thermal runaway: (a) O2 ; (b) CO2 , C2 H4 and H2 .

The changes in surface temperature of LIB and gas pressure during the thermal runaway process are shown in Fig. 4(a). The pressure rises slowly to about 0.3 bar, which is mainly caused by the generation of O2 . At t = 946 s, the pressure reaches a peak of 2.37 bar with jet flame, meaning the thermal runaway occurs. At the same time, the safety valve ruptures, releasing the gases inside the battery into the gas chamber. Later, the pressure gradually decreases to an equilibrium value of 1 bar. The peak temperature during thermal runaway is 620 °C, which occurs slightly later than the moment of peak pressure. As shown in Fig. 4(b), a trace of Raman signal of CO2 is detected at t = 7 min, which is 526 s earlier than the moment of thermal runaway, indicating that the detection of gas Raman signal, especially the Raman signal of CO2 , can be used for early warning of LIB thermal runaway. There is an inevitable time lag for gas diffusion before the equilibrium of gas concentration in the experimental tank and the hollow-core region of HC-ARF, especially when the gas concentration is low. For example, at 90–120 °C, a small amount of CO2 is generated by the breakdown of SEI layer [3], while in the thermal runaway experiment, CO2 is detected for the first time when the surface temperature of LIB is 140–152 °C. Though such a time lag is undesired for early warning of LIB thermal runaway based on gas Raman signal, and faster response can be achieved with smaller experimental tank and shorter HC-ARF, an excessively small experimental tank is unfavorable for the stability of optical path under rapid pressure rise due to thermal runaway, and short HC-ARF results in lower detection sensitivity. Therefore, the optimization of the FERS detection platform is an important problem that needs further investigation.

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Fig. 4. (a) Surface temperature of battery and pressure changes during thermal runaway; (b) Raman spectrum at t = 0 and 7 min.

4 Conclusion LIB thermal runaway gas detection is the key to achieve early warning of a thermal runaway fault. Aiming at the limitations of current methods for thermal runaway gas detection, firstly, a Raman spectroscopy platform for LIB thermal runaway gas detection is developed. The sensitivity of gas Raman spectroscopy detection is significantly improved by fiber-enhanced technique, realizing LOD of 4.2, 7.6, 1.5, 9.5, 0.8, 3.0, 1.4 ppm for H2 , CO2 , C2 H2 , CO, CH4 , C2 H6 , C2 H4 , respectively, with 60 s spectral integration time at 1 bar. Next, a thermal runaway fault experiment is performed. Benefiting from the unique advantage of simultaneous and non-destructive analysis of Raman spectroscopy, real-time and in-situ detection of O2 , CO2 , C2 H4 , H2 generated by LIB thermal runaway process is realized, and a warning time of 526 s is achieved based on the detection of trace CO2 in the early stage. The potential of gas Raman spectroscopy detection in LIB thermal runaway gas analysis and early warning is demonstrated. Acknowledgments. This work is supported by United Laboratory of Advanced Electrical Materials and Equipment Support Technology, CSG (No. 1500002022030103GY00040).

References 1. Masayoshi, W.: Research and development of electric vehicles for clean transportation. J. Environ. Sci. 21(6), 745–749 (2009). https://doi.org/10.1016/S1001-0742(08)62335-9 2. Tripathi, A.M., Su, W.-N., Hwang, B.J.: In situ analytical techniques for battery interface analysis. Chem. Soc. Rev. 47(3), 736–851 (2018). https://doi.org/10.1039/c7cs00180k 3. Wang, Q., Mao, B., Stoliarov, S.I., Sun, J.: A review of lithium ion battery failure mechanisms and fire prevention strategies. Prog. Energy Combust. Sci. 73, 95–131 (2019). https://doi.org/ 10.1016/j.pecs.2019.03.002

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4. Hu, X., Mousa, E., Annhagen, L., et al.: Complex gas formation during combined mechanical and thermal treatments of spent lithium-ion-battery cells. J. Hazard. Mater. 431, 128541 (2022). https://doi.org/10.1016/j.jhazmat.2022.128541 5. Chen, S., Gao, Z., Sun, T.: Safety challenges and safety measures of Li-ion batteries. Energy Sci. Eng. 9(9), 1647–1672 (2021). https://doi.org/10.1002/ese3.895 6. Sun, J., Li, J., Zhou, T., et al.: Toxicity, a serious concern of thermal runaway from commercial Li-ion battery. Nano Energy 27, 313–319 (2016). https://doi.org/10.1016/j.nanoen.2016. 06.031 7. Ping, P., Wang, Q., Huang, P., et al.: Study of the fire behavior of high-energy lithium-ion batteries with full-scale burning test. J. Power. Sources 285, 80–89 (2015). https://doi.org/10. 1016/j.jpowsour.2015.03.035 8. Wang, Z., Zhu, L., Liu, J., et al.: Gas sensing technology for the detection and early warning of battery thermal runaway: a review. Energy Fuels 36(12), 6038–6057 (2022). https://doi. org/10.1021/acs.energyfuels.2c01121 9. Koch, S., Birke, K.P., Kuhn, R.: Fast thermal runaway detection for lithium-ion cells in large scale traction batteries. Batteries 4(2), 16 (2018). https://doi.org/10.3390/batteries4020016 10. Jin, Y., Zheng, Z., Wei, D., et al.: Detection of micro-scale Li dendrite via H2 gas capture for early safety warning. Joule 4(8), 1714–1729 (2020). https://doi.org/10.1016/j.joule.2020. 05.016 11. Liao, Z., Zhang, J., Gan, Z., et al.: Thermal runaway warning of lithium-ion batteries based on photoacoustic spectroscopy gas sensing technology. Int. J. Energy Res. 46(15), 21694–21702 (2022). https://doi.org/10.1002/er.8632 12. Golubkov, A.W., Fuchs, D., Wagner, J., et al.: Thermal-runaway experiments on consumer li-ion batteries with metal-oxide and olivin-type cathodes. RSC Adv. 4(7), 3633–3642 (2014). https://doi.org/10.1039/c3ra45748f 13. Bertilsson, S., Larsson, F., Furlani, M., et al.: Lithium-ion battery electrolyte emissions analyzed by coupled thermogravimetric/Fourier-transform infrared spectroscopy. J. Power. Sources 365, 446–455 (2017). https://doi.org/10.1016/j.jpowsour.2017.08.082 14. Wang, D., Yang, J., Bao, L., et al.: Pd Nanocrystal sensitization two-dimension porous TiO2 for instantaneous and highly efficient H2 detection. J. Colloid Interface Sci. 597, 29–38 (2021). https://doi.org/10.1016/j.jcis.2021.03.107 15. Hjiri, M., El Mir, L., Leonardi, S.G., et al.: Al-doped ZnO for highly sensitive CO gas sensors. Sens. Actuators, B Chem. 196, 413–420 (2014). https://doi.org/10.1016/j.snb.2014.01.068 16. Raman, C.V., Krishnan, K.S.: The optical analogue of the compton effect. Nature 121(3053), 711 (1928). https://doi.org/10.1038/121711a0 17. Gerelt-Od, B., Kim, H., Lee, U.J., et al.: Potential dependence of gas evolution in 18650 cylindrical lithium-ion batteries using in-situ Raman spectroscopy. J. Electrochem. Soc. 165(2), A168–A174 (2018). https://doi.org/10.1149/2.0781802jes 18. Hippler, M.: Cavity-enhanced Raman spectroscopy of natural gas with optical feedback cwdiode lasers. Anal. Chem. 87(15), 7803–7809 (2015). https://doi.org/10.1021/acs.analchem. 5b01462 19. Knebl, A., Domes, R., Wolf, S., et al.: Fiber-enhanced Raman gas spectroscopy for the study of microbial methanogenesis. Anal. Chem. 92(18), 12564–12571 (2020). https://doi.org/10. 1021/acs.analchem.0c02507 20. Wan, F., Liu, Q., Kong, W., et al.: High-sensitivity lithium-ion battery thermal runaway gas detection based on fiber-enhanced Raman spectroscopy. IEEE Sens. J. 23(7), 6849–6856 (2023). https://doi.org/10.1109/JSEN.2023.3243213

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21. Liu, H., Wei, Z., He, W., et al.: Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: a review. Energy Convers. Manage. 150, 304–330 (2017). https://doi.org/10.1016/j.enconman.2017.08.016 22. Du Pasquier, A., Disma, F., Bowmer, T., et al.: Differential scanning calorimetry study of the reactivity of carbon anodes in plastic Li-ion batteries. J. Electrochem. Soc. 145(2), 472 (1998). https://doi.org/10.1149/1.1838287

Research on Power Accurate Control Method of Ramp-Type Gravity Energy Storage System Ming Li1 , YaXiaEr TuErHong1 , Zilin Hao2(B) , Jianwang Gao2 , Tian Gao2 , Linlin Dong2 , and Shuyang Fang2 1 State Grid Xinjiang Electric Power Corporation, Wulumuqi 830000, China 2 School of Electrical and Electronic Engineering, North China Electric Power University,

Beijing 102206, China [email protected]

Abstract. Presently, most of the ramp-type gravity energy storage devices through transport heavy blocks between the upper and lower stacking yards to switch between energy storage and energy release, but this method cannot regulate the energy output by changing the number of heavy blocks released in time, so it is difficult to quickly and accurately respond to the demand of the load, and it causes additional energy loss as the load demand changes. In this paper, we add auxiliary heavy block stacking yard on both sides of the ramp channel, and by controlling the release quantity of heavy blocks in the top stacking yard, selecting different heights of the ramp stacking yard to release the heavy blocks, and controlling the position of the grasping heavy blocks in the ramp stacking yard, we realize the precise control of the output energy of the gravity storage device, which improves the response speed of the gravity storage device and reduces the extra energy loss. Finally, based on Matlab/Simulink simulation, the correctness and effectiveness of the proposed method are verified. Keywords: Ramp-type gravity energy storage device · energy efficiency optimization · power control · power response

1 Introduction While more new energy generation provides a large amount of electricity for the power grid, it also brings a series of unstable factors, including intermittent power supply, system inertia reduction and other security risks [1]. Gravity energy storage technology is one of the key technologies in the development of new energy field because it has the characteristics of long time and large capacity, and compared with electrochemical energy storage technology, it does not cause environmental pollution and safety hazards. It can be widely used in many fields such as grid energy storage, power load balancing, photovoltaic power plants, wind farms, tidal energy, and hydro energy [2]. As an emerging energy storage technology, gravity energy storage is mostly in the theoretical research stage, and many theories and assumptions still lack a certain practical basis. A planning method for a capacity optimization model for wind-storage cogeneration was proposed in [3], which improves the ability to increase the consumption © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 312–319, 2024. https://doi.org/10.1007/978-981-97-1064-5_34

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of wind power. Energy Vault company of Switzerland proposed a gravity tower energy storage system with rubbish waste as the material [4]; and the Institute of Electrical Engineering of the Chinese Academy of Sciences proposed a multi-heavy climbing energy storage scheme based on mountain ramp [5]. In this paper, for the gravity energy storage system’s power response flexibility is poor, the response time is long, and it is difficult to make timely tracking of power changes when the system load changes, taking the discharge process of the ramp-type gravity energy storage system as the object of study, the effects of heavy block release height, grasping time and grasping position on the output power of the gravity energy storage system were analyzed, and a ramp-type gravity energy storage system configured with an auxiliary stacking yard was designed, and the method of releasing and grasping control of the heavy block with its auxiliary stacking yard was investigated.

2 Ramp-Assisted Gravity Energy Storage System The ramp-type gravity energy storage device is a device that uses gravitational potential energy as energy transmission and conversion, and its working principle is to use the potential energy change of the heavy block, the discharge will be placed in the high place of the heavy block release, according to the law of conservation of energy, the heavy block in the process of falling down to drive the generator to generate electricity, and the potential energy is converted into electrical energy to be fed back to the grid [6]. However, while increasing the system potential energy storage capacity by increasing the height of the heavy block, it will also increase the difficulty of system regulation and safety hazards [7]. Therefore, the design of the heavy block’s individual weight and shape also needs to take into account the actual application of the system, such as the existing building height, terrain conditions, system capacity, and usage scenarios, in order to achieve the optimal power output and conversion efficiency [8]. In order to achieve precise control of output energy by ramp-type gravity energy storage device, this paper proposes a ramp-type gravity energy storage device equipped with auxiliary stacking yards, which is configured with a number of auxiliary yards located on both sides of a conveyor chain ramp. The ramp-type gravity energy storage device mainly consists of a conveyor chain ramp, a top stacking yard, a bottom stacking yard, ramp ramp-assisted stacking yards, heavy blocks, travelling cranes, lifting claws, and other parts. The conveyor chain ramp is used to transport the heavy blocks; the heavy blocks are all squares of equal size; the top stacking yard and the ramp-assisted stacking yard are used to yard the heavy blocks transported by the conveyor chain ramp; the travelling crane and the lifting claw are located in the top yard and the ramp auxiliary stacking yard, respectively, and are used for gripping and releasing the heavy blocks in the respective yards. The ramp-assisted gravity energy storage device is shown in Fig. 1.

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Fig. 1. Structural diagram of ramp-assisted gravity energy storage device

3 Ramp-Assisted Conveyor Chain Structure Gravity Energy Storage Device Weight Block Release Control Method 3.1 Top Stacking Yard Heavy Block Release Control Method In the ramp-assisted gravity energy storage device, the top stacking yard is capable of releasing the most amount of energy. Therefore, the power generated by releasing the heavy blocks through the top stacking yard is the main power generation, while the ramp-assisted stacking yard plays the role of power regulation and energy saving control. From the instantaneous power of gravity it can be derived that the instantaneous mechanical power PF that can be emitted by the heavy block as it falls down the ramp of the conveyor chain is as in (1). PF = mgV0 sin(θ )

(1)

where the conveyor chain speed is V 0 , the weight of a single heavy block is m, the gravitational acceleration is g, and the ramp angle is θ. The transport speed is set to be constant on the conveyor chain ramp, in this case the mechanical power emitted by the ramp-assisted gravity energy storage device can only be changed by changing the number of heavy blocks on the conveyor chain. In order to reduce the energy loss of the gravity energy storage system, the instantaneous mechanical power emitted by the top stacking yard when releasing heavy blocks should maximise fulfil the load power demand Pt while not exceeding the load power demand, as shown in (2). X × PF ≤ Pt ≤ (X + 1) × PF

(2)

where X is the number of heavy blocks released from the top stacking yard. Since the descent of heavy blocks released from the top stacking yard along the conveyor chain to the bottom stacking yard cannot be done instantaneously, so a single heavy block will continue to emit mechanical power on the conveyor chain ramp. To cope with load fluctuations, the top yard adopts a heavy block release determination at intervals of sn seconds to determine whether to continue releasing heavy blocks and the number of heavy blocks to be released by comparing the energy emitted from the heavy

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blocks released from the top stacking yard on the ramp during the sn seconds to the electrical power consumed by the load.  sn Pt dt (3) Wt = 0

WF = PF × sn

(4)

where W t is the amount of electrical energy required in the grid in sn seconds, and W F is the amount of electrical energy that a single heavy block can produce in sn seconds. The number X of heavy blocks released from the top stacking yard on the ramp is given in (5) X × WF ≤ Wt ≤ (X + 1) × WF

(5)

When there are N heavy blocks on the ramp released from the top stacking yard: C =X −N

(6)

where C is the number of heavy blocks to be released from the top stacking yard. The top stacking yard does not perform the release of heavy blocks when C ≤ 0, and the top stacking yard releases C heavy blocks when C > 0. 3.2 Top Stacking Yard Heavy Block Release Control Method The height between two neighbouring layers of ramp-assisted stacking yards is the same, the ramp-assisted stacking yards are equally distributed on both sides of the conveyor chain ramp according to their heights, and the difference in height between each layer of the ramp-assisted stacking yards is h. The equation for the amount of energy that can be emitted from each ramp-assisted stacking yard can be obtained when the height of the whole ramp is H: h = H ÷ N

(7)

W = mg × h

(8)

where W is the additional amount of energy that can be emitted with each higher layer of the ramp-assisted yard; W n is the energy that can be emitted by releasing the heavy block from the nth level of the ramp-assisted stacking yard; N is the number of ramp-assisted stacking yards in the ramp-assisted gravity storage device; and n is the number of levels of the ramp-assisted stacking yard. The role of the ramp-assisted stacking yard is to make up the difference between the power emitted from top stacking yard and the load demand of the grid, and only can exist one heavy block that released by the ramp-assisted stacking yard on the conveyor chain ramp at the same time. The number of layers n of the ramp-assisted stacking yard selected for releasing heavy blocks should satisfy to (9). Wn−1 < Wt − C × PF ≤ Wn where if n < 1, take n = 1.

(9)

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3.3 Method of Controlling the Gripping Position of a Heavy Block in a Ramp-Assisted Yard By establishing a xyz-axis three-dimensional coordinate system, taking the volume of each heavy block as a square with unit 1, inputting the length, width, and height of the heavy blocks, as well as the maximum values of the boundaries of each layer of the yard space (x max , ymax , zmax ); and arranging the heavy blocks in a three-dimensional coordinate system by taking the coordinates of the origin to be (0, 0, 0), and the coordinates of each heavy block to be (x, y, z). As shown in Fig. 2. The initial position of the lifting claw right at the origin (0, 0, Z 0 ), and each time the lifting claw after grabbing the heavy block will return to the initial position.

2 1 2

3

1

1

23

Fig. 2. Three-dimensional coordinate diagram of ramp-assisted stacking yard

The lifting claw horizontal speed of movement for the V 1 , the lifting claw vertical speed of movement for the V 2 , to grab the heavy block located in the (x, y, z) need to move the distance of the horizontal for the L xy . Lxy = 2 × (x + y) x, y satisfy the constraints in (11).



x ≤ xmax y ≤ ymax

(10)

(11)

The distance travelled vertically is L z . Lz = (Z0 − z)

(12)

z ≤ Z0 ≤ zmax

(13)

z satisfies the constraint in (13):

The time t xyz required for the grab is as in (14) txyz = Lxy ÷ V1 + Lz ÷ V2

(14)

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The derivative of the power change curve P is curve f . The resulting curve f is segmented according to the unit time t, and the absolute value of the average value of the rate of change of power with time curve per unit time is taken as Dt . f =

Dt =

dP dt

   t+t  fdt   t t

(15)

(16)

Take the maximum value of Dt as Dtmax and the minimum value as Dtmin . Equally divide the interval between Dtmax and Dtmin into x max + ymax intervals (x max , ymax are the maximum number of heavy blocks stacked along the X-axis and Y-axis, respectively), the larger the Dt is, the faster the rate of change of the power per unit of time is, and in order to be able to satisfy the need for rapid response and meet the constraints, the grasping of the heavy blocks in the ramp-assisted stacking yard. The time t needs to be inversely proportional to the rate of change of power over time, that is, the average of the rate of change of power over time curves in different intervals is inversely proportional to the distance the heavy block needs to move. Lz V2

(17)

xmax + ymax Lz + Dt min V2

(18)

tmin = tmax =

tmin ≤ t ≤ tmax

(19)

where t min and t max are the minimum and maximum values of the grasping time, respectively.

4 Simulink Modelling and Simulation Verification According to the above formula, the corresponding Simulink simulation model can be built and its feasibility can be verified by simulating the number of heavy blocks released from the top stacking yard, the height of the ramp-assisted stacking yard selected for releasing the heavy blocks, and the location of the heavy blocks gripped in the ramp-assisted stacking yard. The system parameters of the ramp-assisted gravity energy storage system used in this paper are shown in Table 1. Figure 3 shows a plot of the load demand generated by the simulation model built by Simulink versus the mechanical power emitted by the online heavy blocks released from the top stacking yard. By observing Fig. 3, it can be found that in order to reduce the energy loss of the gravity energy storage system, the mechanical power emitted from the top stacking yard should be basically kept at a level that does not exceed the load power demand. In order to enable the system to track load fluctuations adaptive control is required, which can

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value

altitude difference

20 m

ramp angle

30°

ramp assisted yard elevation per level

2m

ramp speed

5 m/s

mass of the heavy block

0.1 t

number of layers of ramp-assisted stacking yard

9

travelling speed of the lifting claw

0.5 m/s

    





















Fig. 3. The top stacking yard releases the mechanical power emitted by heavy blocks

increase or decrease the number of released heavy weight blocks in time to meet the load demand. Figure 4 shows the simulation of the output power of the ramp-assisted stacking yard, and the output power is the average power issued within the whole process of the heavy block grasping from the ramp-assisted stacking yard to the completion of the descent. Comparing the variation between the mechanical power emitted by the rampassisted gravity energy storage device and the actual demanded load in Fig. 5, it can be determined that the ramp-assisted gravity energy storage device is able to follow the load demand to emit the required power and achieve a fast response. This means that the gravity energy storage system can achieve automatic adjustment under changing loads and can quickly adjust the energy output to meet current load demands, thus improving energy utilisation and system reliability.       





















Fig. 4. Mechanical power emitted from ramp-assisted stacking yard

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Fig. 5. Mechanical power emitted by ramp-assisted gravity energy storage device

5 Conclusions A novel ramp-assisted gravity energy storage system and its control method are proposed based on the operational characteristics of ramp-assisted gravity energy storage. The method is able to solve the problems of slow response speed and low energy conversion rate of the ramp-type gravity energy storage system to a certain extent by adding auxiliary heavy block yards on both sides of the ramp and by optimising the height of the auxiliary yards for releasing the heavy blocks and the grasping path within the auxiliary yards. This method realises that the gravity energy storage system can respond accurately with the load power change and reduce the energy loss as much as possible, and proved its correctness and feasibility by simulation. Acknowledgments. This work was funded by State Grid Corporation of China for Science and Technology Projects (5419-202240053A-1-1-ZN).

References 1. Newbery, D.: Shifting demand and supply over time and space to manage intermittent generation: the economics of electrical storage. Energy Policy 113, 711–720 (2018) 2. Zhiyong, S., Caixia, W., Ning, C., Xiaoning, Y., Si, W.: Policy requirements and economic affordability of energy storage for new energy. In: 2022 6th International Conference on Power and Energy Engineering (ICPEE), China, Shanghai, pp. 330–333 (2022) 3. Zhiyang, L., Hangxuan, S., Kuan, F.: Capacity optimisation of wind-storage co-generation system in alpine region relying on gravity energy storage. Heilongjiang Electric Power 45(01), 30–35 (2023). (in Chinese) 4. O’Grady, C.: Gravity Powers batteries for renewable energy. Science 372(6541), 446 (2021) 5. Xiao, L., Shi, L., Wai, T.: Energy storage system for railway rail vehicles: CN108437808A (2018). (in Chinese) 6. Berrada, A., Loudiyi, K., Garde, R.: Dynamic modeling of gravity energy storage coupled with a PV energy plant. Energy 134, 323–335 (2017) 7. Botha, C.D., Kamper, M.J.: Capability study of dry gravity energy storage. J. Energy Storage 23, 159–174 (2019) 8. Botha, C.D., Kamper, M.J.: Capability study of dry gravity energy storage. J. Energy Storage 23, 159–174 (2019)

Development of Contact Resistance Measurement Device for GIS Main Circuit Contacts Shuai Sun, Xingwang Li, Congwei Yao(B) , Bin Tai, Linglong Cai, Jianjun Li, and Xiaofeng Pang Guangdong Key Laboratory of Electric Power Equipment Reliability, Electric Power Research Institute of Guangdong Power Grid Co., Ltd., Guangzhou 510080, China [email protected]

Abstract. The contact resistance of GIS contacts is related to the stable operation of the power system. In this paper, a GIS contact resistance measurement device based on the pulse current method is developed on the FPGA platform, which accurately measures the time-domain curve of contact resistance by compensating for the influence of inductance, which is of positive significance for further evaluating the contact contact state. Keywords: Contact Resistance · Pulse Current · FPGA

1 Introduction Contacts are electrical contact connectors widely used in GIS to provide reliable connections between conductors. Due to the fully enclosed structure of GIS, once a contact failure occurs [1–5], it will cause long downtime and high maintenance cost in the substation. The contact resistance of a contact is the most direct parameter reflecting the contact state, so it is very important to measure the contact resistance accurately. Currently, the most commonly used method to measure contact resistance of contacts is to use a DC current of 100–200 A to measure the contact resistance and judge whether it is in normal contact according to the factory value. However, the voltage drop generated by the smaller current is very low, the lower signal-to-noise ratio is not conducive to the accurate measurement of contact resistance, and it is necessary to increase the test current to truly reflect the contact state [6–8]. In order to increase the test current, scholars have proposed the use of the pulse current method for contact resistance measurement. M. Runde used an electrolytic capacitor to apply a pulse current with a leading edge of 8 ms and an amplitude of 1–3 kA to the GIS circuit to detect the nonlinear behavior of degraded contact contact resistance [9]. R. Luo used supercapacitor discharge and pointed out that the pulse current method is more reflective of the actual circuit resistance value of the equipment than the DC voltage drop method [10]. L. Zhou proposed to evaluate whether the GIS contacts are in good electrical contact condition based on the magnitude of the rate of change of the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 320–329, 2024. https://doi.org/10.1007/978-981-97-1064-5_35

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contact resistance with the growth of pulse current [11]. However, due to the influence of inductance, all the above measurement methods only reflect the contact resistance at the peak of the current, but not the contact resistance in the time domain. In this paper, a GIS contact contact resistance measurement device based on the pulse current method is developed to compensate for the effect of inductance and obtain the time-domain change curve of the contact resistance, and the testing process is controlled by an FPGA system and the measurement results are automatically saved.

2 Introduction 2.1 Pulse Current Generation Circuit The use of capacitors as energy storage elements directly on the contact discharge can produce kA-level high current pulse, according to the test requirements, the construction of the circuit shown in Fig. 1, where C is a supercapacitor bank; D is a high-power thyristor; Rc and Lc for the contact resistance and inductance of the contact. 3XOVHFXUUHQWVRXUFH

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2.2 Contact Resistance Measurement Under Pulsed Current The contact voltage can be expressed as the pulse current flows through the contacts: u(t) = i(t)Rc (t) + (Lc + M )

di(t) d(t)

(1)

where M is the mutual inductance of the measurement circuit and the main circuit, Lc is the contact inductance. At this point, it is stated that the measured voltage is the contact resistance voltage drop superimposed on the inductive voltage drop, and the contact voltage is the actual contact resistance voltage only when the current peaks, i.e., when the rate of change of the current is zero when reading the contact voltage, and at this point the contact resistance can be calculated: Rc =

u(tpk ) i(tpk )

(2)

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However, under short pulse current, the skin effect is not negligible and is affected by the inductance, only the resistance at the peak current can be obtained, and the measurement results do not reflect the time-varying process of contact resistance. Using 12 supercapacitors with a rated voltage of 2.7 V and a capacity of 3000 F connected in series to form a capacitor bank, the time constant of the circuit is dominated by the supercapacitor, the inductance effect is very small, and the skin effect can be ignored. Figure 2 demonstrates the pulse currents of different amplitudes for supercapacitor discharging, varying the charging voltage U0 to 7.7 V, 13 V, 18.2 V, 23.3 V, and 28.4 V, respectively, which is capable of generating pulse current waveforms with amplitudes ranging from 1 to 5 kA directly on the contacts, and the time constant of the circuit is 1 s.

Fig. 2. Pulse current waveform waveform.

At the trailing edge of the pulse current, the inductive voltage drop (Lc + M)-di(t)/d(t) item is very small compared to the contact resistive voltage drop, so that the time-varying curve of the contact resistance under the pulse current can be obtained directly by Rc (t) = u(t)/i(t). 2.3 Long Loop Inductance Affects Compensation For longer GIS circuits, the inductive effect needs to be further removed, so long circuit inductive compensation is proposed. Based on the following two points: the voltage to current ratio read at the peak current is the contact resistance that is not affected by inductance; when the current is small, the thermal effect of the contact resistance is very small and the resistance value is basically unchanged. By changing the charging voltage of the capacitor, it is possible to obtain different sizes of current without changing the circuit parameters, there are:  ih (t) = kil (t) (3) uh (t) = kul (t)

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where the subscripts h and l denote the high and low capacitance charging voltages, respectively. From Eq. (2), there are for high and low currents: uh (t) ul (t) − = Rch (t) − Rcl ih (t) il (t)

(4)

This shows that the difference between the voltage to current ratio can reflect the change in contact resistance under pulse currents with different current amplitudes only, and does not include the inductance and mutual inductance of the main circuit, so the contact resistance under high currents can be obtained, there: Rch (t) =

uh (t) ul (t) − + Rcl ih (t) il (t)

(5)

3 Test Set Hardware Design The hardware part of the GIS main circuit contact resistance measurement device is mainly as shown in Fig. 3. The main components include constant current power supplies, capacitors, thyristors, Hall sensors, instrumentation amplifiers, analog-to-digital converters, relays, LCD screens and the FPGA system EP4CE10. First of all, after the FPGA charging signal control relay makes constant current power supply for capacitor charging, after reaching the set value to disconnect the relay, send a trigger signal to control the thyristor conduction, the voltage signal through the instrumentation amplifier and the current signal into the analog-to-digital converter and processed by the FPGA after the contact resistance and displayed on the LCD screen.

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3.1 Thyristor Driver Circuit Design Selected high-power flat plate thyristor KP2000A as the main switch, the maximum inrush current of 25 kA, fully able to meet the needs. Thyristor is a current-triggered device, requires a certain trigger power, KP2000A needs 40–300 mA trigger current to conduct reliably. In order to reduce the gate loss, the device adopts the pulse string triggering method to drive the thyristor, the circuit is shown in Figure. According to the high and low levels of io output to control the output pulse of NE555: when io is high, NE555 outputs a square wave with a frequency of 1 kHz, which triggers the thyristor conduction through the pulse transformer; when io is low, NE555 outputs a high level, and the thyristor doesn’t receive the trigger pulse (Fig. 4). GND

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Fig. 4. Thyristor driver circuit.

3.2 Relay Driver Design The charging of the capacitor is controlled using a relay, and a transistor 8050 is used to improve the driving ability of the io port charging control signal charge_crtl. When charge_crtl is high, the relay is attracted and the capacitor starts charging; when charge_crtl is low, the relay is disconnected and the capacitor stops charging. In order to suppress the interference of the switching power supply, the device uses a two-way relay, which is placed between the positive/negative poles of the switching power supply and the positive/negative poles of the capacitor (Fig. 5). D1 1N4148W

R1 Q1 SS8050

charge_crtl

+15V

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2 4

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Power+/-

GND

Fig. 5. Relay driver circuit.

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3.3 Relay Driver Design Contact contact resistance is generally only a few tens of µ, pulse current generated by the voltage drop is still small, in order to improve the voltage signal-to-noise ratio, the use of numerical gain instrumentation amplifier AD8253 contact voltage amplification, through A0, A1 control voltage amplification multiples of 1, 10, 100, 1000 to be able to obtain the highest signal-to-noise ratio within the scope of the range, D1–D4 and R7, R8 as the input protection (Fig. 6). RF2 HJ-SMA015

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3.4 Signal Acquisition Circuit Design In order to achieve accurate sampling of voltage and current, the analog-to-digital converter AD7606 is used, which has an eight-channel sampling rate of up to 200 Ksps, and is able to set a maximum of 64 times the oversampling multiplier, in order to maximize the signal-to-noise ratio of the voltage and current sampling (Fig. 7).

Fig. 7. Signal acquisition circuit.

4 Test Set Software Design The software design mainly adopts Verilog language and modularization, mainly realizes the charge/discharge control of the capacitor and calculates the contact resistance value of the contacts to be tested and displays it on the LCD screen (Fig. 8).

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Fig. 8. Test flowchart.

4.1 Charging and Discharging of Capacitors Capacitor charging is controlled by the relay, when touching the “start charging” button, fpga will control signal charge_crtl pull high, the capacitor starts charging; when touching the “stop charging”, charge_crtl pull low, the capacitor stops charging. When touching “stop charging”, charge_crtl is lowered and the capacitor stops charging. Capacitor discharge is controlled by the thyristor drive circuit, when touching the “enables pulse triggered” control signal trig_crtl pulls up 10 ms to provide enough drive energy to conduction thyristor. 4.2 Drivers for Analog-to-Digital Converters According to the datasheet of AD7606, the driver is written as follows: AD sampling process is as follows: pull down the CONVST signal to start the conversion; when the busy signal is low, enable the CS signal, and then transform the RD signal to read the data of each channel, and then disable the CS after the completion of the data reading of the eight channels, waiting for the next reading. 4.3 Data Storage and Display The FPGA calculates the collected voltage and current to get the contact resistance and stores it in the on-chip RAM, and finally displays the contact resistance curve on the screen by repeatedly reading the data in the RAM (Fig. 9).

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Fig. 9. Test interface.

5 Test Results The contact resistance of an SF6 circuit breaker with a voltage level of 126 kV is tested. Firstly, a 200 A DC circuit resistance tester was used to test the contact resistance, and the result was stable at 121.4 µ. The figure shows the results of the contact resistance measurement by the pulse current method, and the maximum contact resistance was 128.74 µ and the minimum contact resistance was 122.19 µ under the pulse current with a peak value of 2,100 A. Therefore, the developed device is able to accurately measure the contact resistance of the contacts and reflect the change of contact state of the contacts under high current. Under high current (Fig. 10).

Fig. 10. Circuit breaker contact resistance curve.

In addition, the dynamic contact resistance is an important parameter for assessing the life of the circuit breaker contacts, operating the circuit breaker to open the gate after triggering the pulse, the design device is also capable of obtaining the resistance change of the circuit breaker in the process of opening the gate, as shown in the figure, the circuit breaker is fully opened and closed after a series of bouncing process, this process is related to the contact surface state, which can be used to further study the circuit breaker contact condition (Fig. 11).

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Fig. 11. Dynamic contact resistance.

6 Concluding Remarks (1) A contact resistance measurement method based on the pulse current method is established, and the inductive influence is compensated for long circuits. (2) Based on the FPGA system, a GIS contact resistance measurement device based on the pulse current method is developed and tested on circuit breakers, which can accurately measure the contact resistance and reflect the contact state change of the contacts.

References 1. Xie, Z.: Analysis of GIS-to-ground fault caused by insufficient insertion depth of busbar conductor. High Volt. Electron. 45(3), 160–163 (2009). (in Chinese) 2. Li, G., Li, S., Liu, Z., Qu, Y.: Analysis on disconnector contacts burned in a 252kV GIS. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, China, pp. 204–208 (2023) 3. Yang, W., Hu, X., Zhang, G., et al.: Influence of contact resistance deterioration of contact finger on electrical thermal coupling field distribution in GIS. In: 2022 IEEE International Conference on High Voltage Engineering and Applications (ICHVE), Chongqing, China, pp. 1–4 (2022) 4. Li, M., Bai, J., Xia, H., Xu, L., Ding, D., Ren, C.: Test research on poor contact defect detection of GIS based on temperature and vibration. In: 2020 IEEE 1st China International Youth Conference on Electrical Engineering (CIYCEE), Wuhan, China, pp. 1–5 (2020) 5. Cheng, S., Gan, S., Zhang, P., et al.: Intelligent diagnosis method for heating defect of GIS disconnecting switch. In: 2023 Panda Forum on Power and Energy (PandaFPE), Chengdu, China, pp. 590–595 (2023) 6. He, L., Wang, H., Zhang, X., et al.: A case study of heating anomaly detection and disintegration analysis of 220 kV GIS equipment. High Volt. Electr. Appar. 54(6), 6 (2018). (in Chinese) 7. Yan, C., Ran, Y., Zhang, Y.: Analysis of DC resistance instability in the main circuit of GIS combination electrical appliances. Shandong Power Technol. 46(8), 6 (2019). (in Chinese) 8. Gao, K., Lu, Y., Xu, P., et al.: Characterization of GIS circuit resistance. High Volt. Electr. Appar. 56(8), 7 (2022). (in Chinese)

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9. Runde, M., Lillevik, O., Larsen, V., Skyberg, B., Mjelve, A., Tonstad, A.: Condition assessment of contacts in gas-insulated substations. IEEE Trans. Power Deliv. 19(2), 609–617 (2004) 10. Luo, R., Wang, Y., Huang, S., et al.: Research on Circuit resistance measurement method of conductive rod based on impulse current in GIS. High Volt. Electr. Appar. 49(10), 5 (2013). (in Chinese) 11. Zhou, L., Lu, T., Luo, R., et al.: Detection and evaluation method of contact state of gas insulated composite electrical apparatus. High Volt. Technol. 41(1), 8 (2015). (in Chinese)

Multi-criteria Integrated Early Warning of Thermal Runaway Risk Yaoming Chen(B) , Liguo Weng, Bingcheng Zhao, and Deqiang Lian State Grid Hangzhou Xiaoshan Power Supply Co. Ltd, Hangzhou 311200, Zhejiang, China [email protected]

Abstract. With the advancement of new energy storage technologies and their widespread industrial applications, the issue of thermal runaway in lithium battery energy storage systems has become increasingly significant. Thermal runaway in energy storage systems can not only result in equipment damage and extended downtime but also pose serious threats to personnel safety and the environment. Therefore, early warning of thermal runaway in energy storage systems has gained paramount importance and has garnered extensive research attention among domestic scholars. However, conventional methods for thermal runaway prediction primarily rely on empirical models, lacking a comprehensive analysis and profound understanding of operational data from energy storage systems. Data-driven approaches offer a fresh perspective on thermal runaway prediction, enabling the identification of potential risk factors from extensive historical data and providing accurate warning and prevention strategies. This paper first introduces the principles and methods of data-driven algorithms, while exploring how abundant historical data can be utilized to identify latent thermal runaway risk factors. A comparison with traditional warning methods is also provided, demonstrating that the approach proposed in this paper outperforms in terms of false alarms and missed warnings. Finally, the paper discusses the potential challenges and future directions in proactively addressing thermal runaway risks through data-driven prevention. Keywords: Lithium Battery · Energy Storage System · Data-Driven · Thermal Runaway Early Warning

1 Introduction Thermal runaway in lithium batteries is a critical safety concern within energy storage systems [1–3]. It poses risks of fire and explosions [4–6]. Current thermal runaway warnings primarily involve monitoring changes in battery voltage, current, internal resistance, internal pressure, temperature, and characteristic gases to predict whether a battery may undergo thermal runaway. Researchers have proposed numerous fault diagnosis, detection, and safety warning methods. Both domestic and international researchers and teams have conducted varying degrees of research on thermal runaway and its early causes. Some of the main approaches include: © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 330–338, 2024. https://doi.org/10.1007/978-981-97-1064-5_36

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1. Research using parameters such as battery body temperature, voltage, current, and discharge rate obtained through Battery Management Systems (BMS) as discrimination criteria [7, 8]. 2. Detection methods based on pressure strain in battery module. 3. Research on thermal runaway detection based on changes in internal resistance. 4. Methods for thermal runaway prediction involving gas collection during battery overcharging and heating experiments, followed by gas component and content analysis using chromatographic analysis [9, 10]. Among the mentioned methods, the approach involving pressure strain has drawbacks. Pressure sensors are rarely or even not deployed in the battery cells of energy storage systems, and their application would increase the overall cost of these systems. In large-scale energy storage stations, the identification of internal resistance in battery cells is time-consuming, making real-time application challenging and imposing higher demands on server hardware. The accuracy and effectiveness of gas component and content analysis are directly related to the distribution and quantity of sensors, requiring separate duct analysis for different energy storage systems. Due to the significant challenges associated with these methods, such as high data computational requirements, complex algorithms, poor universality (inability to apply to different battery types), and difficulties in online implementation, these approaches are challenging to widely deploy in practical systems [11]. Therefore, further research and development are necessary to create a practical and viable approach to enhance the availability and accuracy of thermal runaway prediction in batteries.

2 Battery Management System The Battery Management System (BMS) is a critical component that significantly impacts the operational cost and safety performance of lithium battery energy storage stations. Currently, BMS is in a phase of rapid development in terms of safety state monitoring, particularly in addressing the risk of thermal runaway in batteries. It commonly uses parameters such as State of Charge (SOC) and State of Health (SOH) to describe the safety and health status of energy storage systems. Research on BMS data analysis related to battery health, expected lifespan, and thermal runaway risk has attracted substantial attention from researchers. Data-driven techniques for lithium battery state identification and assessment represent a novel approach to battery management. This technology involves the creation of mathematical models that utilize data collected from devices such as BMS and environmental monitoring systems, including information like voltage, current, and temperature as model inputs. These models calculate parameters related to battery aging, expected lifespan, and overall health status. This data-driven modeling technique provides early warning signals for lithium battery safety management based on historical and current operational states, thereby helping to mitigate risks associated with battery aging, degradation, and thermal runaway due to battery misuse. Therefore, in the context of energy storage systems, research into data-driven thermal runaway warning algorithms holds particular significance for the safety assessment of lithium batteries.

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3 Challenges in Thermal Runaway Warning for Energy Storage Systems The thermal runaway warning in energy storage systems presents several challenges: 1. Data Acquisition Difficulty: Energy storage systems involve the monitoring of various parameters, such as battery voltage, current, temperature, etc., necessitating highprecision and high-frequency data collection and processing capabilities. 2. Data Processing Complexity: Energy storage systems generate a substantial volume of data that requires efficient processing and analysis to extract valuable information and features. 3. Algorithm Optimization Challenges: Early warning for energy storage systems demands the use of efficient algorithms for data analysis and prediction. 4. Accuracy of Warnings: Achieving precise early warnings for energy storage systems requires the accurate identification of battery health status and fault risks. However, due to the complexity and uncertainties inherent in these systems, achieving high accuracy in predictions is challenging. In addition to these challenges, the selection of parameters for thermal runaway warning is an area worth investigating. In contrast to traditional methods that rely on single warning parameters, this paper explores a multi-parameter approach to assess battery safety. It attempts to use parameters such as mean, range coefficient, standard deviation, and standard score in combination to detect anomalies. This approach aims to provide a more effective method for thermal runaway warning in energy storage systems, facilitating practical applications in real-world systems.

4 The Basic Principles and Methods of Data-Driven Early Warning Systems Coefficient of Range: A commonly used measure of dispersion in statistics. It is used to quantify the degree of variation between the maximum and minimum values in a dataset, indicating the dataset’s level of dispersion. A larger value indicates greater dispersion, while a smaller value indicates less dispersion. The formula for calculating the Coefficient of Range is as follows: CR =

xmax − xmin x

(1)

In the formula, CR represents the coefficient of range, xmax is the maximum value in the data, xmin is the minimum value in the data, and x is the mean of the data. Disadvantages: The coefficient of range only considers the difference between the maximum and minimum values and does not take into account the position and distribution of other data points. Standard Deviation: A commonly used measure of data dispersion in statistics. It measures the average distance of data values from the mean, describing the spread of data.

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The formula for calculating the standard deviation is as follows:  n 2 i=1 (xi − x) S= n−1

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(2)

In the formula, n represents the dimensionality of the data, and x represents the mean of the data. Standard Score: A commonly used method of data standardization in statistics, also known as the z-score or standardized value. It is used to transform the distribution of different data into a standard normal distribution for the purpose of comparison and analysis. The standard score indicates how much a raw data value deviates from the mean in terms of standard deviations. The mean of standard scores is 0, and the standard deviation is 1. A positive standard score indicates that the raw data value is above the mean, while a negative standard score indicates that it is below the mean. Larger standard scores indicate greater deviation from the mean, indicating that the data is relatively more extreme. The formula for calculating the standard score is as follows: (xi − x) (3) S In the formula, Z represents the calculated standard score, x is the mean of the data, and S is the standard deviation of the data. Converting data into standard scores allows for convenient comparison of the degree of deviation between different datasets and facilitates comparisons between different datasets. Applications of standard scores include: Z=

1. Data Comparison: It enables the comparison of distributions between different datasets, providing insights into the relative positions and dispersion of the data. 2. Data Analysis: It can be used for outlier detection to identify data points that deviate significantly from the norm. 3. Statistical Inference: It supports statistical inference between samples and populations, facilitating hypothesis testing and confidence interval estimation. It’s important to note that standard scores are suitable for data that approximately follows a normal distribution. For skewed or non-normally distributed data, other methods should be considered for data standardization and comparison.

5 Design of Multi-criteria Combined Early Warning Methods In recent years, algorithms in the data-driven direction have found extensive applications in thermal runaway early warning. While single-parameter early warning methods are commonly used in energy storage systems, their effectiveness in practical applications is limited. They often suffer from narrow parameter threshold ranges, leading to situations of false alarms and missed alarms. Multi-criteria combined early warning methods aim to ensure the accuracy of thermal runaway early warnings while reducing the computational workload. The workflow of multi-criteria combined early warning methods is illustrated in Fig. 1 and described as follows:

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Step 1. For an energy storage system, conducting statistical analysis on a batch of n data sequences collected at the i-th time point is represented as {xn }. Step 2. Calculate the mean, coefficient of range, and standard deviation for this batch of data, denoted as x, xCR , and xZ . Compare these three parameters with the predefined parameter thresholds of the energy storage system. If any of the above parameters exceed the threshold, an exception can be raised. Step 3. If no exception is raised in step 2, calculate the standard score for this batch of data, denoted as {xZn }. Find the maximum absolute value of the calculated standardized scores and compare it with the parameter threshold set for the energy storage system. If it exceeds the parameter threshold, an exception is raised. The index of the data is used to print the cell number where the abnormal value occurred. If the values are still within the parameter threshold range, it indicates good consistency among the cells in this batch, and there is currently no risk of thermal runaway.

Fig. 1. Algorithm Flowchart

6 Data Collection and Analysis Processing We applied the aforementioned thermal runaway early warning method to an actual energy storage system, collecting operational data from energy storage plants with different voltage differentials of the same type. We compared this method with traditional single-parameter early warning methods. During the use of lithium battery packs, there may be voltage differences among individual cells, which can potentially have adverse effects on battery performance. For instance, excessive voltage differentials can lead to overcharging of weaker cells while undercharging others, affecting the overall lifespan and capacity of the battery pack. Moreover, if the voltage differentials are excessively large and persist for a prolonged duration, it can exacerbate the increase in internal resistance of individual cells, ultimately leading to degraded battery pack performance or safety hazards, such as reduced charge-discharge efficiency and battery explosions.

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Therefore, to ensure the safety and performance of lithium battery packs, a series of measures need to be taken to screen, detect, and control voltage differences among individual cells. These measures include balancing the charging and discharging of battery packs and optimizing the design and assembly of the battery pack. Screening for voltage differentials among battery packs is of significant importance in preventing battery thermal runaway. In this study, we initially conducted experiments using data from battery packs with a 100 mV voltage differential.

Fig. 2. Lithium Battery Pack in Normal State

Based on the data shown in Fig. 2, it can be observed that under normal conditions of charge and discharge for lithium batteries, the voltage differentials among the batteries do not exceed 100 mV. Due to inherent variations in individual cells’ consistency, there is some fluctuation in the coefficient of range, standard deviation, and maximum standardized score of the battery voltages during charge and discharge states. In contrast, these parameters remain relatively stable when the batteries are in a static state.

Fig. 3. Lithium Battery Pack in Abnormal State

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Based on the data shown in Fig. 3, it can be observed that under conditions of inconsistency among lithium batteries during charge and discharge, the voltage differentials among the batteries have exceeded 100 mV. During charge and discharge, the coefficient of range, standard deviation, and maximum standardized score have also exceeded the preset thresholds. In a static state, these parameters exhibit significant outlier behavior. Using the multi-criteria combined standards approach, it is possible to quickly, effectively, and accurately identify the presence of inconsistency and screen out problematic cells, thus optimizing the assembly and future management of the lithium battery pack. Table 1. False Alarm Rate and Missed Alarm Rate for Various Metrics False Positive Rate

False Negative Rate

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0

0

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1.67%

0

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0.66%

0

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In comparison to energy storage batteries, the metric of missed alarm rate is relatively more important than the false alarm rate. The occurrence of missed alarms may lead to more severe accidents in lithium battery packs, whereas false alarms can directly impact the improper judgment and actions of operations and maintenance personnel. Therefore, in this experiment, conservative and cautious thresholds were chosen. From Table 1, we can observe that conducting experiments based on one or a few judgment metrics alone can lead to false alarms. By introducing the multi-criteria combined early warning method based on the maximum standardized score, false alarms can be effectively prevented, and cells with the worst consistency can be promptly identified. This approach holds significant potential for applications in the warning and safety systems of lithium battery packs. Through experiments in practical energy storage systems, we have identified several advantages of this warning method: 1. Multi-dimensional Screening: Using this method, data can be screened from multiple dimensions, improving the accuracy and reliability of screening. 2. Effective Screening: This method can efficiently eliminate outliers in the data, enhancing data quality and usability. 3. Broad Applicability: This method can be applied to different types of data, such as continuous and discrete data, demonstrating excellent adaptability and flexibility. 4. Strong Interpretability of Screening Results: This method provides specific numerical results, enabling the interpretation and analysis of data anomalies, facilitating further processing and application. Therefore, the method of jointly screening outliers based on mean, coefficient of range, standard deviation, and standardized score can improve data quality and usability

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standards, prevent the occurrence of false alarms and missed alarms in thermal runaway risk, and reduce the computational workload of energy storage systems. This is of significant importance for thermal runaway early warning.

7 Results In this paper, we have discussed the advantages and disadvantages of risk warning methods for energy storage systems, as well as relevant data characteristics. We have explored the potential direction of data-driven multi-criteria combined early warning for thermal runaway. Based on the accumulated data from existing energy storage systems, this method allows for a rapid and reliable assessment and warning of risks in energy storage systems. It offers clear advantages over single criteria methods and innovatively utilizes standardized scores as a key parameter, enabling the quick evaluation of abnormal situations and the screening of problematic cells. This presents a novel approach to ensuring the safe operation of energy storage systems. The quality and reliability of data are crucial for data-driven prevention of thermal runaway risks. Firstly, appropriate data collection methods and sensor configurations need to be determined to ensure data accuracy and completeness. Secondly, data storage and processing require corresponding technical support and resource allocation. The development of big data and cloud computing technologies has provided more flexible and efficient solutions for data collection and processing. In data-driven thermal runaway risk warning, the construction of accurate and reliable warning models is a critical step. Various deep learning and transfer learning algorithms [12], such as LSTM and MAML, can be used to build warning models.

8 Challenges and Developments in Data-Driven Prevention of Thermal Runaway Risks While data-driven approaches hold immense potential in preventing thermal runaway risks, there are still several challenges to address. Firstly, data quality and reliability are critical issues, with the accuracy and precision of sensors in energy storage systems directly impacting the credibility of early warnings. Secondly, acquiring and storing data require corresponding technical support and resource investments, especially in largescale energy storage systems, where considerations include data collection frequency, data loss, data privacy, and security. Future directions in thermal runaway warning systems will involve further improvements in data collection and processing technologies, enhancing the accuracy and interpretability of warning models, and addressing interdisciplinary cooperation. Collaborative efforts between domain experts and data-driven methods will better identify thermal runaway risk factors and provide effective prevention strategies. Additionally, as the Internet of Things and industrialization continue to advance, the connectivity and information exchange among energy storage system components will become more intricate, offering both greater opportunities and more stringent challenges for thermal runaway risk detection in these systems.

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References 1. Kim, T., Song, W., Son, D.-Y., Ono, L.K., Qi, Y.: Lithium-ion batteries: outlook on present, future, and hybridized technologies. J. Mater. Chem. A 7(7), 2942–2964 (2019). https://doi. org/10.1039/C8TA10513H 2. Lebrouhi, B.E., Khattari, Y., Lamrani, B., et al.: Key challenges for a large-scale development of battery electric vehicles: a comprehensive review. J. Energy Storage 44, 103273 (2021) 3. Yang, Z., Huang, H., Lin, F.: Sustainable electric vehicle batteries for a sustainable world: perspectives on battery cathodes, environment, supply chain, manufacturing, life cycle, and policy. Adv. Energy Mater. 12(26), 2200383 (2022) 4. Feng, X., Ouyang, M., Liu, X., et al.: Thermal runaway mechanism of lithium ion battery for electric vehicles: a review. Energy Storage Mater. 10, 246–267 (2017). S2405829716303464 5. Qiu, Y., Jiang, F.: A review on passive and active strategies of enhancing the safety of lithiumion batteries. Int. J. Heat Mass Transf. 184, 122288 (2022) 6. Zhang, Q., Niu, J., Zhao, Z., et al.: Research on the effect of thermal runaway gas components and explosion limits of lithium-ion batteries under different charge states. J. Energy Storage 45, 103759 (2022) 7. Xiong, J., Banvait, H., Li, L., et al.: Failure detection for over-discharged Li-ion batteries. In: Proceedings of the IEEE International Electric Vehicle Conference, F, (2012) 8. Mccoy, C.H.: System and methods for detection of internal shorts in batteries. WO 9. Liao, Z., Zhang, J., Gan, Z., et al.: Thermal runaway warning of lithium-ion batteries based on photoacoustic spectroscopy gas sensing technology. Int. J. Energy Res. 46(15), 21694–21702 (2022) 10. Golubkov, A.W., et al.: Thermal-runaway experiments on consumer Li-ion batteries with metal-oxide and olivin-type cathodes. RSC Adv. 4(7), 3633–3642 (2014). https://doi.org/10. 1039/C3RA45748F 11. Strozzi, F., Zaldívar, J.M., Kronberg, A.E., et al.: On-Line runaway detection in batch reactors using chaos theory techniques. AIChE J. 45(11), 2429–2443 (1999) 12. Noor, R.M., Ahmad, Z., Don, M.M., Uzir, M.H.: Modelling and control of different types of polymerization processes using neural networks technique: a review. Can. J. Chem. Eng. 88(6), 1065–1084 (2010)

Simulation Study on Temperature Rise Characteristics of 550 kV/8000 A Combined Electrical Apparatus Liuhuo Wang, Shuai Sun(B) , Rongchang Xie, and Qiang Sun Guangdong Power Grid, Corporation, Guangzhou 510000, China [email protected], {xierongchang,sunqiang}@gsbb.gd.csg.cn

Abstract. With the rapid development of national industry, the demand for power energy in all walks of life is increasing, which poses a major challenge and huge demand for the safe and stable operation of the power system. 550 kV/8000 A combined electrical appliances are representative of large-capacity power switchgear in the power system. The safe and stable operation of GIS is the key to the normal operation of power system. It is of practical significance to study the thermal distribution characteristics of GIS for improving the reliability and security of power system. This paper establishes an electromagnetic thermal coupling model for 550 kV/8000 A combined electrical appliance. Through multi-physical field coupling, electromagnetic loss is calculated and input into the thermal field as a load to calculate the temperature distribution. The results show that the contact resistance between the highest point of temperature rise and the intermediate conductor and the contact base is in line with the national standard, which provides a reference for the future optimization design of the product. Keywords: GIS · Temperature rise simulation · Harmonic frequency · Electromagnetic heat flow coupling simulation

1 Introduction With the rapid development of national industry, the increasing demand for power energy in all walks of life, which poses a major challenge and huge demand for the safe and stable operation of the power system, 550 kV/8000 A combined electrical appliances as a representative large-capacity power switchgear in the power system, its safe and stable operation is the key to the normal operation of the power system [1, 2]. The overheating of internal components is an important reason for the failure of GIS equipment, so it is of practical significance to study the heat distribution characteristics of GIS for improving the reliability and security of power system. With the rapid development of national industry, the increasing demand for power energy in all walks of life, which poses a major challenge and huge demand for the safe and stable operation of the power system, 550 kV/8000 A combined electrical appliances as a representative large-capacity power switchgear in the power system, its safe and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 339–352, 2024. https://doi.org/10.1007/978-981-97-1064-5_37

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stable operation is the key to the normal operation of the power system. Overheating of internal components is an important reason for the failure of GIS equipment [3], so it is of practical significance to study the thermal distribution characteristics of GIS for improving the reliability and security of power system. Scholars mainly calculate the temperature rise simulation of electric power equipment through hot path method and finite element method. With the development of computer technology, multi-physical field simulation through finite element method has become the main way to calculate temperature rise [15–17]. The multi-physical field coupling calculation is divided into electromagnetic heat and electromagnetic heat flow. The electromagnetic heat method calculates the electromagnetic loss under the operation of the equipment through the electromagnetic field analysis software, and input the loss into the thermal field as a load. The surface heat dissipation coefficient is applied to simulate the wall heat dissipation, and the electromagnetic heat flow further calculates the convective heat dissipation on the wall by calculating the flow velocity distribution of the fluid field [4–7]. Zhou Tian et al. [8–14] used the multi-field coupling simulation method to simulate the heat distribution characteristics of high voltage electrical equipment such as GIS and GIL. 1.1 550 kV/8000 A Combined Electrical Apparatus 3D Model The research object of this subject is a set of switchgear combination electrical apparatus, which consists of sleeve part, tee part, bus part, isolation switch part and current transformer part. The 3D temperature model of 550 kV 8000 A combined electrical apparatus was established by using 3D CAD software UG 1:1 according to the physical model, as shown in Fig. 1. The shell is filled with SF6 gas, and the whole is isolated by three insulated terminals into three gas chambers, one of which has an overflow hole. The air pressure of the sleeve chamber is 0.5 Mpa, and the air pressure of the other chambers is 0.4 Mpa. The original model is relatively complex and large in size, and there are many irregular shapes in the corners and corners of the model, which have little influence on the calculation of temperature rise and are not conducive to the convergence of the calculation results. Without proper treatment, the final iterative calculation results are easy to diverge, so it is necessary to properly simplify the model before simulation. For the electrical contact part that is focused on, it is necessary to model the contact resistance in each place. In order to carry out the simulation smoothly, based on the original three-position model, the corners which are not conducive to the convergence of the fluid field are simplified, and the contact resistance of all the watch band contacts is simplified into a ring entity. Figure 2 shows the calculation model of the casing. The SF6 pressure inside is 0.5 MPa. The casing consists of a wiring panel, a pressure balancing ring, a heat dissipation plate, a current carrying conductor, a ground shield, a support cylinder, and an insulating porcelain sleeve. The insulating porcelain sleeve is made of B2 ceramic material, and the rest is made of aluminum alloy castings. The basin insulator is epoxy resin.

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(a)Overall structure drawing

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(b) Part of the shell

(c) Part of diversion path

Fig. 1. Model of the combined electrical apparatus

(a) Casing section diagram

(b) casing structure diagram

Fig. 2. Casing model

As shown in Fig. 3, there is no insulating basin between tee and sleeve, and they belong to the same air chamber. The structure is divided into contact base, tee shield, tee inner conductor and transition conductor. The transition conductor is Cu-T2, and the rest

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are aluminum alloy castings. The contact resistance is one of the heating sources. The contact resistance model is simplified to a thin ring layer for convenience calculation.

(a) Tee section diagram

(b) Tee structure diagram Fig. 3. TEE model

As shown in Fig. 4 and Fig. 5, the insulating basin in the middle of this part has a flow hole, belonging to the same air chamber, and the internal SF6 pressure is 0.4 MPa. The structure is composed of the bus bar, DS shield, and moving contact, and the moving contact is connected with the contact base through the contact finger connector. The moving contact and contact material are copper, and the surface of the contact is silver plated; The rest are aluminum alloy castings.

(a)Bus section diagram

(b) Bus structure diagram Fig. 4. Bus model

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(a) Isolation switch structure diagram

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(b) Isolation switch model diagram

Fig. 5. Isolation switch model

Figure 6 shows the calculation model of the current transformer. The internal SF6 pressure is 0.4 MPa. This part consists of the transition conductor, the current carrying conductor, the current transformer shell, and the external shunt copper bar. The shunt copper bar is made of Cu-T2, and the rest are aluminum alloy castings.

(a)Current transformer section diagram

(b) Current transformer structure diagram

Fig. 6. Current transformer model

2 Establishment of Electromagnetic Thermal Field Model 2.1 Multi-physics Poupling Process This project uses ANSYS Workbench simulation platform to calculate and analyze the electromagnetic temperature field, and the simulation process is shown in the figure. The eddy current field and the steady-state temperature field share the model, and the boundary conditions, excitation, grid division, etc. are carried out separately before each calculation. Considering the influence of eddy current loss, proximity effect and skin effect, Maxwell was used to calculate the conduction path and the size and distribution of ohmic loss density of the shell, and Ansys heat module was introduced. The convection and radiation heat transfer processes were expressed in the steady-state temperature

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field by means of surface endowing convective heat transfer coefficient and radiation coefficient to complete the temperature rise analysis under long-term operation of the combined electrical apparatus. Figure 7 shows the calculation process.

Fig. 7. Electromagnetic thermal coupling simulation flow

2.2 Governing Equation of Electromagnetic Field The temperature field distribution of combined electric apparatus under 8000 A50 Hz alternating current is studied. When an alternating current flows through a conductor, the changing current generates a changing magnetic field, and the changing magnetic field generates a changing electric field, which affects the original flow of current in the conductor. This series of electromagnetic processes can be described by a set of Maxwell equations, including four laws: Ampere’s loop law, Faraday’s law of electromagnetic induction, Gauss’s law of electric flux and Gauss’s law of magnetic flux. Maxwell equations are differential forms: ∇ ×H =J+ ∇ ×E =−

∂D ∂t

∂B ∂t

(1) (2)

∇ ·D=ρ

(3)

∇ ·B=0

(4)

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∇ ×H =J ∇ ×E =−

∂B ∂t

345

(5) (6)

∇ ·B=0

(7)

J = σE

(8)

B = μH

(9)

Formula: H——magnetic Field Intensity Vector, a/m; J——Total Current Density Vector, A/m2 ; D——electric Displacement Vector, C/m2 ; E——electric Field Intensity Vector, V/m; B——Magnetic Induction Intensity Vector, Wb/m2 (T); t——time, s; ρ——Free charge density, C/m3 . For the quasi-stable electromagnetic field, the electrical flux density in maxwell equations can be ignored compared with the conduction current density, that is, the magnetic field generated by the change of electric field is not considered. The quasistable electromagnetic field, also known as eddy current field, containing conductive materials in the region is solved. The system of equations in differential form can be expressed as: μ——Magnetic permeability, H/m; σ ——Electric conductivity, S/m; In the normal operation of the combined electric device, there will be a large ohmic loss and a small part of eddy current loss. In these losses, the heat generated by the conductor can be solved by the differential form of Joule’s law. The relationship between the current density of the conductor and the electric field strength can be expressed as: − → − → p= J · E

(10)

− → − → J =σ× E

(11)

Formula: P——Thermal power density; σ——Electrical conductivity/S; E——Electric field strength V·m−1 . Based on the measured resistance values, the equivalent contact resistance parameters are calculated by the resistance calculation formula and Wedemann Franz formula. ρe =

Re · S l

(12)

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λc =

L·T ρe

(13)

ρ e ——Electrical resistivity/·m; Re ——resistance/; S——Cross-sectional area/m2 ; l——Altitude/m; λc ——Thermal conductivity/W·m−1 ·K−1 ; L——Lorentz coefficient/V2 ·K−2 , value is 2.4 × 10−7 V2·K−2 ; T ——Temperature/K (Fig. 8, Table 1).

Fig. 8. Contact resistance diagram

Table 1. Contact resistance equivalent conductivity and thermal conductivity Contact Resistance

Resistance (μ)

Electric Conductivity (s/m)

Thermal Conductivity (W/m·K)

R1, R5, R6, R14, R15

0.76

1.132 × 105

8.1504

R2, R3, R12, R13

1.2

1.256 × 105

9.0432

R4, R7, R8, R11, R16

0.5

3.109 × 105

22.3812

R9

0.5

6.920 × 105

49.824

R10

0.38

2.428 × 105

17.482

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3 Electromagnetic Thermal Field Calculation Above, the establishment of several types of heat sources and eddy current field models under long-term operation of the combined electrical apparatus is analyzed. 3.1 Loss Calculation Result Table 2 shows the losses in the electromagnetic field. Among them, the ohmic loss of the conductor accounts for 48.77% at most, followed by the loss caused by the contact resistance at the electrical contact point accounts for 13.72%. In addition to the energized conductor, due to the eddy current effect caused by the changing magnetic field caused by the alternating current of the conductor loop, the eddy current loss generated at the non-conductor shell accounts for 4.32%, which cannot be ignored. Table 2. The proportion of loss of each part Loss Part

Loss (W)

Proportion (%)

Shell

246.357

7.125

Terminal Plate

94.534

2.734

Voltage Balance

113.06

3.270

Cooling

127.553

3.689

Shield Can

15.504

0.482

Cylinder

19.187

0.555

Casing Conductor

1047.623

30.300

Three Internal Leads

54.859

1.587

Bus Conductor

455.671

13.179

DS Shield Can

234.984

6.796

Moving Side Contact

51.053

1.477

Transition Conductor

73.704

2.132

Basin Insert

40.534

1.172

Francois

8.168

0.236

Contact Resistance

503.8434

14.572

Total Loss

6358.87

100

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3.2 Thermal Field Calculation The heat source of the combined electrical apparatus includes the ohmic loss of the contact resistance between the current-carrying conductor and the electrical contact and the eddy current loss of the shell in the eddy current field, and a large part of these losses will be converted into heat, resulting in the heating and temperature rise of the diversion path, the shell and the insulation material. At the beginning, the temperature rises relatively fast, and as the temperature of each component rises, a certain temperature difference is formed between the heating body and the surrounding cooling medium, so that the heat is transferred to the surrounding medium. Subsequently, the temperature rise of each component slows down and gradually reaches equilibrium. There are three main forms of heat transfer in combined electrical appliances: heat conduction, heat convection and heat radiation. Heat transfer is simulated by adding thermal conductivity, convective heat transfer coefficient and radiant emissivity to each part of the combined apparatus. In order to facilitate the calculation, the following simplification is made: (1) GIS is in an infinite space without the influence of near heat source; (2) During the thermal analysis process, the ambient temperature remains unchanged; (3) Simulation model material isotropy; Therefore, the three-dimensional heat conduction equation at steady state is shown in Eq. (20): λ(

∂ 2T ∂ 2T ∂ 2T + + ) = −q ∂x2 ∂y2 ∂z 2

(14)

Formula: T ——Temperature; λ——Thermal conductivity; q——The amount of energy produced per unit volume/W·m−3 ; x, y, z——Rectangular coordinate; The form of criterion correlation is usually adopted, and through experimental research, the form of large space natural convection experimental correlation widely used in engineering calculation is obtained, as shown in equation: Nu = f (Gr , Pr ) = C(Gr Pr )n

(15)

According to the Nusselt similarity criterion: Nu =

αcon l = C(Gr Pr )n λ

(16)

Formula: N u ——Nussel number; λ——Thermal conductivity of gas /W·m−1 ·K−1 ; l——Feature length /m; C/n——The value of n is related to the state of the fluid, and the value of C is related to the heat dissipation surface according to experience;

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Gr ——Grashof number; Pr ——Prandtl number, gas is roughly between 0.6 and 0.7. By the Graschev criterion: Gr =

gβl 3 t ν2

(17)

Formula: g——Acceleration of gravity/m·s−2 ; β——Coefficient of volume expansion/K–1 ; t——Temperature difference between fluid and wall/K; ν——Kinematic viscosity of fluid/m2 ·s–1 . The characteristic length of the surface and the physical property parameters of the fluid are substituted into Eqs. (2–25) and (2–26) to calculate the corresponding convective heat dissipation coefficient αcon = C(Gr Pr )n λl Where the physical properties of the fluid are taken as the mean boundary layer temperature tm = (t0 + tf )/2’s value. The calculated total heat dissipation coefficient is shown in the table (Table 3): Table 3. Heat dissipation coefficient of each component position

Convection type

Convective heat transfer coefficient

Radiant heat transfer coefficient

Total heat transfer coefficient

Cooling fin

Large space natural convection

5.150

2.642

7.792

Porcelain sleeve Large space natural convection

4.176

7.045

11.221

Shell (horizontal)

Large space natural convection

3.523

2.642

6.165

Conductor (transverse)

Natural convection in limited space

3.165

2.642

5.807

Conductor (vertical)

Natural convection in limited space

2.617

2.642

5.259

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(a)Overall temperature distribution interface diagram

(b)Shell temperature distribution Fig. 9. Calculation results of the electromagnetic thermal field

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(c) current-carrying conductor temperature distribution Fig. 9. (continued)

4 Conclusion The calculation results of electromagnetic heat are shown in Fig. 9. The corresponding heat transfer coefficient is set on the surface of the shell and conductor to simulate convective heat transfer. The maximum temperature rise of the contact resistance between the two ends of the bus bar and the contact base is 60 K. The temperature of the conductor in the casing is higher, and the temperature rise is 57K. The cooling grid has obvious cooling effect, and the temperature rise is 20K. However, the heat transfer coefficient is calculated by empirical formula, which has a larger error than the fluid-structure coupling calculation of temperature rise, so the temperature field distribution is calculated by electromagnetic heat flow coupling next. Acknowledgments. This work is supported by China Southern Power Grid Science and Technology Projects (036100KK52210033(GDKJXM20210060)).

References 1. Chen, X., Zhao, T., Chen, L., Yao, Q., Miao, Y., Cao, Z.: Correlation characteristics of local overheat Fault Degree and SF6 decomposition of GIS Equipment. High Volt. Electr. Appar. 54(11), 109–115 (2018) 2. Yu, C., Yu, X.: Preliminary study on thermal analysis/thermal design/thermal test technology of electronic equipment. Microelectronics 30, 334–337 (2000) 3. Li, W., Xie, W., Gong, R., Qiao, S., Xie, B.: Simulation of Temperature field of 800 kV GIS isolated Switch based on thermoelectric coupling method. High Volt. Electr. Appar. 56(07), 44–49 (2020)

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4. Wang, Q., Qu, J., Wu, G., et al.: Multi-physics simulation and experiment on temperature rise characteristics of distribution switchgear. High Volt. Technol. 42(6), 1775–1780 (2016) 5. Niu, C., Jiao, L., Wang, X., Yang, A., Li, X.: Thermal characteristics analysis of environmental GIS based on multi-field coupling. Trans. China Electrotech. Soc. 35(17), 3765–3772 (2019) 6. Hou, G.: Simulation and experimental analysis of temperature rise characteristics of 126kVGIS based on multi-physical field coupling. Xi ’an Jiaotong University, Xi ’an (2019) 7. Wu, W., Yu, L., Zheng, Y., Wang, N., Zhang, M.: Analysis and test verification of internal fault arc of 800kV GIS bus. High Volt. Electr. Appar. 53(11):225–228+235 8. Zhou, T., Li, Z., Shen, Q., et al.: Multi-field Coupling Numerical Calculation and Analysis of temperature rise of GIS isolation Switch contacts. China Electr. Power 51(2), 13–20 (2018) 9. Yan, L., Zhang, Y.: Temperature rise calculation of high current closed bus. High Volt. Technol. 34(1), 20203 (2008) 10. Song, F., Shen, C., Lin, X.: Calculation and analysis of magnetic Field-temperature Field of 800kV GIS isolated switch. High Volt. Technol. 34(7), 1383–1388 (2008) 11. Song, F., Xu, J., Lin, X., et al.: Three-dimensional magneto-thermal fields analysis of 1100kV GIS disconnector. In: International Conference on High Voltage Engineering and Application, Chongqing, China, p. 53534. IEEE (2008) 12. Cheng, X., Han, S., He, Z., et al.: Design of air chamber Structure of 40.5kV Environmentfriendly Gas insulated switchgear. High Volt. Technol. 41(8), 2772–2779 (2015) 13. Wang, F., Kang, T., Rao, X., et al.: Calculation and analysis of three-dimensional magneticthermal Coupling Field of High voltage coaxial GIS bus. J. Hunan Univ. Nat. Sci. Edn. 41(8), 73–77 (2014) 14. Jin, H., Peng, Z., Wang, S., et al.: Research on temperature field distribution characteristics of 252kv three-phase common box GIS bus bar shell. High Volt. Electr. Appar. 53(12), 20–25 (2017) 15. Rong, M.: Electrical Contact Theory. China Machine Press, Beijing (2004) 16. Peng, D., Niu, H., Lin, T., et al.: Condensation study of GIS prefabricated cabin in severe weather based on thermal-fluid-humidity multiphysics field coupling simulation. Guangdong Electr. Power 36(1), 114–125 (2023) 17. Ke, H., Yu, Z., Yuan, J., et al.: Multi-physics coupling simulation research on temperature rise characteristics of medium voltage switchgear. Guangdong Electr. Power 35(10), 125–132 (2022)

A Data-Driven Method for Improving Voltage Quality of Large-Scale Distributed PV in Distribution Network Zhikun Xing1(B) , Haoran Lian1 , Fan Wang1 , Yabo Hu2 , Hao Wang2 , and Zhiyuan Chang2 1 State Grid Xiongan New Area Power Supply Company, Xiong An 071600, China

[email protected] 2 Pinggao Group Co., LTD, Pingdingshan 462500, China

Abstract. With the high-proportioned distributed PV supply connected to the distribution network, the voltage quality problem is particularly prominent. Firstly, a reactive voltage optimization model based on distributed PV reactive voltage regulation capability is established to improve the voltage quality by using PV reactive voltage regulation capability. At the same time, considering that the VVO model is nonlinear non-convex optimization model, the direct solution of the heuristic algorithm takes a long time, which is not conducive to the online VVO. In this regard, the SA algorithm is applied to obtain the distributed PV optimal output data set, and then the XGBoost model is trained according to the distributed PV optimal output data set, and the VVO of the distribution network is realized from the data-driven perspective, which significantly improves the solving speed of the distribution network optimization model. Finally, a typical distribution network example of IEEE 33 nodes is used to analyze the rationality of the proposed method. Keywords: PV supply · Reactive voltage optimization · Distribution network · Data-driven · The XGBoost model

1 Introduction Based on the global shortage of fossil energy and the aggravation of environmental pollution, all countries have taken clean energy power generation technology as an important response, and the installed capacity of renewable energy and its power generation have also shown an increasing trend year by year. With the policy support proposed by the Chinese government, the utilization rate of renewable energy has been improved, and the distributed power supply of renewable energy has been vigorously promoted and developed, and the wind power generation equipment has formed a complete industrial chain under the dual role of investment and policy. However, large-scale distributed power supply will cause problems such as voltage overshoot and the line current exceeds the limit, which will affect the voltage safety and then reduce the reliability of the safe operation [1, 2]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 353–359, 2024. https://doi.org/10.1007/978-981-97-1064-5_38

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The phenomenon of node voltage overlimit can be solved by the VVO method, which can be realized by adjusting the on-LVRT, static reactive compensator, and other reactive power regulating equipment [3–5]. Recently, the PV inverter has attracted more and more attention to realize VVO of distribution network. PV inverters have fast and flexible reactive power support capability, and there is no switching frequency limit of traditional mechanical regulation equipment, and the response speed is fast. PV inverter does not require additional equipment investment, and has better control economy and flexibility. In [6], a hierarchical voltage control method considering active and reactive power coordination of PV is proposed. The VVC strategy for a distribution system with PV is proposed [7]. A fully distributed VVO is applied to obtain the global optimum solution of nonconvex problems [8]. The VVO model contains a large number of nonlinear constraints, which can be solved by the genetic algorithm and simulated annealing algorithm [9, 10]. However, heuristic algorithms generally have problems such as a large amount of calculation, which is not convenient for the online operation of voltage/var optimization. Recently, deep learning and deep reinforcement learning method have been applied in the field of VVO. In [11, 12], the reinforcement learning method is adopted to realize the VVO. Inspired by the aforementioned issues, large-scale distributed PV supply access to regional voltage quality improvement model is established to improve the voltage quality by using PV reactive voltage output capability. Meanwhile, considering that the VVO model of the distribution network is nonlinear non-convex optimization model, the direct solution of the heuristic algorithm takes a long time, the SA algorithm is used to obtain the distributed PV optimal output data set, and then the XGBoost model is trained according to the distributed PV optimal output data set, and then the VVO is realized from the data-driven perspective, which significantly improves the solving efficiency of the distribution network optimization model. Finally, a typical distribution network example of IEEE 33 nodes is used to analyze the rationality of the proposed method.

2 Large-Scale Distributed PV Supply Access to Regional Voltage Quality Improvement Model The photovoltaic inverter can effectively improve the voltage quality by providing reactive power regulation capability. In this paper, the voltage quality model of large-scale distributed power supply connecting to distribution network is proposed. The loss of distribution network and voltage fluctuation of distribution network nodes are taken as targets, as shown in Eq. (1) f = min ω1 P net,loss + ω2

sum(|Vbus − 1|) n

(1)

where w1 is the first weight coefficient; w2 is the second weight coefficient; Pnet,loss is distribution network loss; V bus is the node voltage of the distribution network. The constraint conditions of the voltage quality improvement model of large-scale PV access area are shown in Eq. (2–9)     PV L 2 Pjk,t − rjk Ijk,t (2) Pk,t − Pk,t = Pkl,t − l∈L(k)

j∈J (k)

A Data-Driven Method for Improving Voltage Quality inv L Qk,t − Qk,t =



Qkl,t −

   2 Qjk,t − xjk Ijk,t

    2 2 2 2 2 Vk,t × Ijk,t = Vj,k − 2 rjk − Pjk,t + xjk Qjk,t + rjk + xjk =

2 + Q2 Pjk,t jk,t 2 Vj,t

Vmin ≤ Vk,t ≤ Vmax cap

0 ≤ Ijk,t ≤ Ijk  

PV Pk,t

2

(3)

j∈J (k)

l∈L(k)

2 Ijk,t

355

2  cap inv + Qk,t ≤ Sk

PV ,m PV 0 ≤ Pk,t ≤ Pk,t

(4) (5) (6) (7) (8) (9)

where, j, k, l are the bus index; J(k) and L(k) are parent and child nodes; Pjk,t , Qjk,t and I jk,t are the active power, reactive power and line current. r jk,t , x jk,t are the line resistance PV , Q inv , P L , V and line inductance; Pk,t k,t are the PV active power, PV inverter reactive k,t k,t power, active load, reactive load and bus voltage. The voltage quality improvement model of large-scale PV access area is a nonlinear non-convex optimization model. Meanwhile, the number of PV in distribution network is large, the variation range of decision variables is large, and the solution space is large, which cannot be directly solved by ergodic search method. Therefore, simulated annealing method is applied to solve the model. Simulated annealing algorithm was first proposed by Metropolis. In 1983, Kirkpatrick et al. introduced the results of simulated annealing algorithm into the field of combinatorial optimization. At present, the simulated annealing algorithm has been applied to solve the optimization problems of different occasions. The basis of the SA algorithm is the simulation of solid annealing process. The Metropolis criterion is used to control the process of the algorithm with the cooling schedule, and finally an approximate optimal solution is obtained. Solid annealing means that the solid is heated to a high enough temperature, so that the molecules show a random arrangement, and then gradually cooling to cool it, and finally the molecules are arranged in a low state, the solid to achieve a stable state. The SA algorithm is applied to solve the proposed optimization model, as shown in Table 1.

3 A Data-Driven Method for Improving Voltage Quality of Large-Scale Distributed PV in Distribution Network Considering that the heuristic algorithm such as simulated annealing is slow to realize the reactive VVO, the online operation of the VVO is limited. In this paper, the XGBoost model is adopted to realize VVO, and the solution efficiency of VVO is improved from the data-driven perspective.

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The simulated annealing algorithm Step1 Set the initial solution and related control parameters Step2 Determine whether the termination condition is met Step3 The power flow of distribution network is calculated, and the optimization model target is calculated according to the power flow result. And determine whether the constraints of the optimization model are satisfied. If the conditions are met, a random disturbance is performed on the current solution. If the conditions are not met, return to Step3 Step4 Compare two solutions, use the Metropolis criterion, and update the solution Step5 Determine whether the cooling stop condition is reached. If the condition is met, output the optimal solution; Otherwise, go back to Step3

The VVO of power system essentially reflects the internal relationship between the operating state of distribution network and the state of reactive power compensation equipment. The XGBoost model is used to establish the mapping relationship between the operating state of the distribution network and PV inverter, which is the VVO model based on the XGBoost model, as shown in Fig. 1. 1,

2,...

1, 1,

2

2,...

Fig. 1. XGBoost model training and use diagram.

In this paper, the XGBoost model is trained according to the operating state of the distribution network and the corresponding simulated annealing algorithm as the training set, the operating state data as the input, and the optimal distributed PV output as the output of the simulated annealing algorithm.

4 Case Study In this paper, the IEEE 33-node distribution network example is introduced to verify the effectiveness of the proposed strategy. The topology of the distribution network and the access of distributed PV are shown in the Fig. 2. The line parameters of the IEEE 33-node distribution system are detailed in reference [13].

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23 24 25

7 1

2

3

4

5

8 9

10 11 12 13 14 15 16 17 18

6

26 27 28 29 30 31 32 33

19 20 21 22

Fig. 2. Typical topology of IEEE 33-node distribution network.

Before the PV participates in the voltage regulation, the voltage of each node o is shown in the Fig. 3. The voltage of some nodes is out of bounds. After the distributed PV participates in the voltage regulation, the voltage of each node is shown in the Fig. 4. It can be seen that the voltage of each node has not crossed the boundary, and the fluctuation is small.

1.05

1

0.95

0.9 40 30 20 10 0

0

10

20

40

30

Fig. 3. PV does not participate in voltage regulation.

1.05

1

0.95 40 30 20 10 0

0

10

20

30

40

Fig. 4. PV participate in voltage regulation.

The network loss of operation is shown in Fig. 5. It can be seen that after the distributed PV participates in the voltage regulation, the network loss of the distribution network is reduced.

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on

0.15 0.1 0.05 0

0

5

10

15

20

25

30

35

40

45

Fig. 5. The network loss of the distribution network.

5 Conclusion Aiming at the problem of poor voltage quality caused by high-proportioned access of distributed power supply to distribution network, this paper proposes a large-scale distributed PV access to regional voltage quality improvement model. By means of distributed reactive power regulation capability, the problems of voltage overlimit and poor voltage quality of distribution network are effectively solved. At the same time, XGBoost model is applied to improve the solving efficiency of the optimization model. Acknowledgments. This work was supported by the Research on key technologies of low voltage DC power supply system for low carbon park (microgrid)(5204XQ230003).

References 1. Gebbran, D., Mhanna, S., Ma, Y., et al.: Fair coordination of distributed energy resources with Volt-Var control and PV curtailment. Appl. Energy 286, 116546 (2021) 2. Jabr, R.A.: Robust volt/var control with photovoltaics. IEEE Trans. Power Syst. 34(3), 2401– 2408 (2018) 3. Xu, R., Zhang, C., Xu, Y., et al.: Multi-objective hierarchically-coordinated volt/var control for active distribution networks with droop-controlled PV inverters. IEEE Trans. Smart Grid 13(2), 998–1011 (2022) 4. Wang, Y., Zhao, T., Ju, C., et al.: Two-level distributed volt/var control using aggregated PV inverters in distribution networks. IEEE Trans. Power Delivery 35(4), 1844–1855 (2020) 5. Nazir, F.U., Pal, B.C., Jabr, R.A., et al.: Distributed solution of stochastic Volt/VAr control in radial networks. IEEE Trans. Smart Grid 11(6), 5314–5324 (2020) 6. Xu, X., Li, Y., Yan, Z., et al.: Hierarchical central-local inverter-based voltage control in distribution networks considering stochastic PV power admissible range. IEEE Trans. Smart Grid 14(3), 1868–1879 (2023) 7. Yang, H.T., Liao, J.T.: MF-APSO-based multiobjective optimization for PV system reactive power regulation. IEEE Trans. Sustain. Energy 6(4), 1346–1355 (2015) 8. Zheng, W., Wu, W., Zhang, B., et al.: A fully distributed reactive power optimization and control method for active distribution networks. IEEE Trans. Smart Grid 7(2), 1021–1033 (2016)

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9. Ai, Y., Du, M., Pan, Z., et al.: The optimization of reactive power for distribution network with PV generation based on NSGA-III. CPSS Trans. Power Electron. Appl. 6(3), 193–200 (2021) 10. Qiao, F., Ma, J.: Voltage/var control for hybrid distribution networks using decompositionbased multiobjective evolutionary algorithm. IEEE Access 8, 12015–12025 (2020) 11. Wang, W., Yu, N., Gao, Y.: Safe off-policy deep reinforcement learning algorithm for volt-var control in power distribution systems. IEEE Trans. Smart Grid 11(4), 3008–3018 (2020) 12. Nguyen, H.T., Choi, D.-H.: Three-stage inverter-based peak shaving and volt-var control in active distribution networks using online safe deep reinforcement learning. IEEE Trans. Smart Grid 13(4), 3266–3277 (2022) 13. Baran, M.E., Wu, F.F.: Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Deliv. 4(2), 1401–1407 (1989)

Research on Classification Forecasting Method Based on Global Load Division of Typical day and Holiday Load Junwen He, Fang Zhijian(B) , Quanhui Li, and Ji Lv China University of Geosciences (Wuhan), Wuhan 43000, Hubei, China [email protected]

Abstract. The national holiday policy has a significant impact on the holiday load, and the curve’s shape differs from the regular daily load, making it challenging to directly anticipate the overall load. The categorization predicting approach presented in this research is based on the division of regular days and holidays. First, the load is divided depending on the date variable after an analysis of the characteristics of an ordinary day and a holiday load. The combined model based on similar day selection and generalized regression network is then utilized to forecast in accordance with the usual daily load. In order to predict the holiday load, a fusion model based on LightGBM and XGBoost is used. The experimental results demonstrate, using the data set provided by a power supply bureau in southern China as a practical example, that the classification forecasting method put out in this study increases the precision of global load forecasting. Keywords: Policy and Industry Factors · Typical Days and Holidays · Similar Day Selection · Machine Learning

1 Introduction The operation of the power grid and the enhancement of the overall dispatch of the power system are supported by short-term load forecasting [1]. Accurate load forecasting can directly impact the financial gains of power firms while also ensuring the dependability of energy consumption [2]. The electricity system’s load types are becoming increasingly complex as a result of the development of the smart grid, and different types of loads have varying sample sizes. Power load forecasting becomes more challenging in this situation [3]. In order to assure the best scheduling of the power system and achieve its cost-effective and secure operation, more efficient power load forecasting technology is required. Numerous forecasting techniques have been put forth by local and international experts due to the power load’s considerable nonlinearity and complexity. For load forecasting, literature [4–7] use the time series analysis method, while literature [8, 9] develops the gray forecasting model. These conventional forecasting techniques offer the advantages of simple modeling and low computational requirements but suffer from © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 360–369, 2024. https://doi.org/10.1007/978-981-97-1064-5_39

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significant mistakes and unstable predicting accuracy. In recent years, machine learning techniques have been able to somewhat make up for the drawbacks of conventional techniques. Literature [10, 11] proposes a short-term load forecasting method based on uplifting artificial neural network. The method is iteratively combined by a group of trained artificial neural networks. The optimal combination method can improve the prediction accuracy, but the prediction model adopted is single and the learning efficiency is low. Literature [12–14] uses optimization algorithms to train neural network model parameters, and uses combination models to improve prediction accuracy and accelerate learning efficiency. The accuracy of the predictions and the universality of the model are increased when multiple prediction networks are combined in parallel in literature [15– 17], with the former being used for feature extraction and the later for prediction. While the aforementioned combined forecasting techniques increase the model’s universality and fault tolerance, they neglect to consider the impact of regional policies and industrial factors on load forecasting, which leads to high forecasting accuracy for typical days with good data quality and extremely low forecasting accuracy for small samples and unstable time series, such as holidays. In this regard, literature [18, 19] uses the samples left over after excluding legal holidays as the forecasting samples to increase the system’s forecasting accuracy, but it ignores the holiday load forecasting, which cannot effectively address the issue of global load forecasting. In order to offer a combined model forecasting method based on the analysis of regional policies and industry characteristics, this research carefully weighs the benefits and drawbacks of the currently used approaches. The combined prediction approach of comparable day and GRNN is used in accordance with the normal daily load. Finally, a fusion forecasting model for holiday load is created using the pairing of LightGBM and XGBoost. The proposed approach effectively addresses the challenge of global load forecasting for various load categories.

2 Load Influencing Factor Analysis 2.1 Analysis of Regional Policy and Industry Factors Affecting Load The promulgation of the national transfer policy and the type of regional core industries are special factors that affect load, and the combined effect of the two leads to large differences in load characteristics on different dates across the region. The dataset provided by a power supply bureau in the southern region of China is used as an example for analysis. The global system load for the week before and after the New Year’s Day holiday in the area in 2022 is depicted in Fig. 1. Figure 1 (a) shows that the load curve is similar in the week leading up to New Year’s Day, with three peaks occurring daily at approximately 9:50 a.m., 5:30 p.m., and 6: 50 p.m. Additionally, the load peak-valley difference on New Year’s Day drops, the curve changes more subtly, and the amplitude of the significant decline is evident due to the national policy of shifting holidays and regular days, regardless of how it affects the load level. The load characteristics at the data collection site will be examined from the perspectives of several users, and the causes of the significant decline in holiday load amplitude will be examined from the viewpoint of users, in order to further explore the factors

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(a) Load before and after New Year's Day.

(b) Multi-load New Year's Day load.

Fig. 1. Holiday load characteristic analysis.

influencing the difference between holiday load and typical daily load. Figure 1 (b) shows that, compared to the industrial load on the working day the day before, the industrial load on the holiday day has a much lower amplitude, whereas the commercial and residential loads have not altered significantly. Therefore, it can be concluded that the withdrawal of some factory loads during the New Year’s Day holiday, which led to a large fall in the load level, is the main cause of the irregularity of the worldwide New Year’s Day load. This is true for other holidays as well. It can be seen that the complexity of the load characteristics of the whole area affected by social attributes such as vacation transfer policy is difficult to predict directly. Therefore, this paper sets up a date identification classification algorithm to classify typical days and holidays according to date variables, and classify and forecast loads of different sizes and characteristics. 2.2 Analysis of Other Factors Affecting Load Meteorological factors including temperature, humidity, wind speed, and weather type are common factors affecting load. The data from 2021.09 to 2022.06 months in a region in southern China were used to investigate Pearson correlation coefficients, and 10 external elements were chosen as influencing factors.Working days/holidays are quantified as 0/1, with quantified values 1–7 representing Monday to Sunday. The absolute values of the correlation coefficients of the temperature property indicators of meteorological factors, as shown in Table 1, are all greater than 0.6, and those of the date factors and historical load factors, as well as their absolute values, are all greater than 0.5. In general, significant correlation is indicated by correlation coefficients larger than 0.6, and moderate correlation is indicated by correlation coefficients greater than 0.4. This section’s important parameters impacting load characteristics are the seven variables having correlation coefficients greater than 0.5 in absolute value.

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Table 1. Correlation coefficients of influencing factors. Factor

Correlation coefficient

Weather Type

0.149

Maximum Temperature

0.686

Minimum Temperature

0.690

Average Temperature

0.698

Body Temperature

0.696 −0.073

Humidity Wind Speed

0.019

Holiday or not

0.672

Monday to Sunday

0.536

Peak of the previous day

0.537

3 Forecasting Method Based on the Division of Typical Days and Holidays The analysis in Sect. 2 shows that the influence of the national transfer policy leads to large differences in load characteristics under different dates. Therefore, based on the identification of load date types, the load of the whole area is divided into typical days and holidays. 3.1 Typical Daily Load Forecasting Method Based on Similar Day Selection Similar Day Selection Season, month, temperature (including body temperature, maximum temperature, minimum temperature, and average temperature), and peak load from the previous day were all chosen as the basis for clustering through the analysis in the previous section. Similar days were then chosen through K-mean clustering, and each cluster of the clustering results was the final set of similar days. For choosing the best clustering cluster K, the elbow approach is used. The elbow method, which is defined as follows, is achieved by observing the fluctuation of K with regard to the Sum of Squared Error (SSE): SSE =

k  

d (x, ci )2

(1)

i=1 x∈Ci

 x is the set D object, Ci is the cluster of items in i, ci is the center of Ci , ci = m1i x∈Ci x, and mi is the total number of data objects in the center of Ci . When K reaches the optimal cluster number, SSE declines as K increases, and it also declines gradually at the first key turning point.

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A Classification Modeling Approach Based on Generalized Regression Networks The clustering outcome separates the load data and its training-related influencing factors into several similar day sets. The temperature (including body temperature, the highest and lowest daily temperatures, and the daily average) and the load value at the same moment on the previous day are chosen as the model’s inputs, and the load value at the anticipated moment is used as the model’s output. The training dataset for each similar day set is used to create the generalized regression neural network prediction model. Donald F. Specht first suggested the generalized regression neural network (GRNN) in 1991. This artificial neural network is based on mathematical statistics. This network uses a probability density function to forecast the outcome and is ideally suited for tackling nonlinearity-related issues thanks to its powerful nonlinear mapping capacity and quick learning rate. The input, pattern, summation, and output layers are the four layers of neurons that make up the fundamental construction of a GRNN.The calculation formula is referred to literature [20], which will not be repeated here due to the limitation of space. 3.2 Holiday Load Forecasting Method Based on LightGBM-XGBoost Fusion XGBoost is an integrated learner that uses a gradient boosting framework based on decision algorithms [21]. Its prediction is equal to the sum of all base learners, which has the advantage of being highly accurate and less prone to overfitting. Given the normalized inputs, the formula for the final predicted value is as follows: yˆ i =

K 

fk (xi ), fk ∈ F

(2)

k=1

where fk denotes the k decision tree, K is the number of decision trees, and F is the set containing a set of decision trees. In addition, LightGBM [22] is a gradient boosting framework based on decision algorithms, and it differs from XGBoost in two ways: it uses independent feature merging and gradient one-sided sampling to avoid the influence of the long-tailed part of the low gradient, reduces the number of features by realizing feature bundling, and improves training speed and accuracy overall. Given that both models are tree models, the error inverse approach [23] can be used to combine the models, and MAPE is utilized as the model error value to obtain the model weights, as illustrated below: ε2 ε1 + ε2 ε1 w2 = ε1 + ε2 w1 =

(3) (4)

where w1 , w2 denote the weights of the two basic models and ε1 , ε2 denote the MAPE values of the single model. Accordingly, the predicted values of the fusion model can be obtained as follows: ft = w1 f1 + w2 f2

(5)

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3.3 Typical Day and Holiday Load Forecasting Process The process of building a typical day and holiday prediction model is shown in Fig. 2.

Fig. 2. Forecasting flowchart based on the division of typical days and holidays

4 Calculus Analysis The actual data of this power supply bureau from January 2019 to August 2022 are still used to validate the effectiveness of the approach provided in this research. The sampling interval of the data is 15 min, or 96 time points are sampled each day. 4.1 Experimental Evaluation Indicators The State Grid dispatching department’s official accuracy calculation formula, which is determined as the following evaluation index, is used to measure the total prediction effect.   T 1  dit2 ) × 100% (6) Ai = (1 −  T t=1

yˆ it − yit × 100% dit = yit

(7)

where T denotes the total number of load points on day i, dit the relative inaccuracy of point t on day i, yˆ it the predicted value of point t on day i, and yit the actual value of point t on day i. 4.2 Typical Day Forecast Results Analysis Similar day Selection Results The divided typical daily load data for the whole year 2021 is used as an example. The seven influencing factors from the previous correlation analysis results are selected as the clustering input features. The optimal number of clustering centers is selected by calculating the SSE values at different numbers of clusters, as shown in Fig. 3 (a). The number of clusters is set to 4, and the clustering results are shown in Fig. 3 (b). The overall load values of the load curves of category 1 and category 2 are larger, mostly

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(a) Cluster number selection analysis.

(b) Analysis of clustering results.

Fig. 3. Typical daily cluster analysis.

at the peak of electricity consumption in summer and fall. There is a partial overlap between category 3 and category 4, and the overlap is the transition period from winter to spring. It can be seen that the distribution of typical daily load curves after clustering has more obvious seasonal characteristics. Comparative Analysis of the Arithmetic Examples of Different Models A randomly selected 18 days in 2022 were utilized as the test set. In order to verify the effect of K-means-GRNN model for load forecasting in a power supply bureau, a comparison experiment is set up to analyze the results, and the comparison models are GRNN, K-means-BP, and K-means-XGboost. One day of forecasting results is selected for each category to draw a comparison graph as shown in Fig. 4.

(a) Different models predict curves.

(b) Prediction accuracy of different models.

Fig. 4. Analysis of typical day prediction results.

As illustrated in Fig. 4 (a), the prediction effect can be significantly enhanced by using the combination model and the K-means clustering technique to identify comparable days. The K-means-GRNN model is able to more closely resemble the real curve, although both the GRNN and the K-means-GRNN models can more accurately reflect

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the trend of the real curve. This demonstrates how the identical day screening data preparation method employing the K-means clustering algorithm for average daily loads may significantly increase the forecast accuracy. Quantitatively determining the daily load curve’s total prediction accuracy is also necessary for the performance assessment of daily load forecasting. In Fig. 4 (b), the comparison results are displayed.The graphs 1–18 represent the prediction accuracy for each day of the 18 days, and the 19th point indicates the average accuracy. From the prediction results, the K-means-BP model, which has a large prediction error on some prediction days, has very unstable prediction results. The K-means-XGboost model maintains a relatively stable prediction accuracy with good robustness, but the overall prediction accuracy is not high. In contrast, the K-means-GRNN model has a higher overall accuracy, resulting in an average prediction accuracy of more than 95% and good overall prediction results. 4.3 Analysis of Holiday Forecast Results Simulation experiments are conducted based on the divided 2019–2022 citywide legal holiday load data of a southern power supply bureau. The model training uses 2019–2021 holiday loads, and 2022 holiday loads are selected as the test set. As observed in Fig. 5, while the GRNN model, which is adequate for regular day prediction, has been unable to keep up with the variations in vacation loads, the XGBoost model prediction results fluctuate significantly. The model suggested in this study’s forecast results are the most in line with the actual load of the three, proving that the method used in this paper can better fit the features of the holiday load. Table 2 below displays the holiday prediction accuracy. 8000 Actual value GRNN XGBoost LightGBM XGBoost-LightGBM

7500 7000

Load(MW)

6500 6000 5500 5000 4500 4000 3500 3000

0

10

20

30

40

50

60

70

80

90

100

Time Step(15min)

Fig. 5. New Year’s Day forecast results comparison chart

The prediction accuracy of the LightBM-XGBoost fusion model is 93.81%; it is 4.6% more accurate on average than the single XGBoost model, 2.73% more accurate than the enhanced LightGBM model, and 3.15% more accurate than the day-appropriate GRNN model. It demonstrates that this approach has a positive impact on predicting holidays. The prediction accuracy is greater than 92% for short holidays like New Year’s

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Holiday

XGBoost-LightGBM

XGBoost

LightGBM

GRNN

New Year’s Day

94.53%

90.56%

91.23%

92.37%

Spring Festival

95.36%

89.90%

88.75%

90.54%

Qingming

92.31%

91.12%

93.84%

90.46%

May Day

93.89%

92.33%

92.68%

88.47%

Dragon Boat Festival

92.61%

87.65%

89.17%

90.79%

Mid-Autumn Festival

93.75%

90.30%

92.54%

91.42%

National Day

94.24%

82.63%

89.35%

90.54%

Average

93.81%

89.21%

91.08%

90.66%

Day, Qingming Festival, and Dragon Boat Festival, and greater than 94% for lengthy holidays like Spring Festival and National Day.

5 Conclusion This paper identifies the causes of the significant difference in load characteristics between typical days and holidays by examining the impact of regional policies and industrial factors on load forecasting. The global load is then divided into typical days and holidays by using dates that correspond to the load curve. The corresponding combined forecasting model is constructed in accordance with various forms of load. The experiment shows that the suggested strategy not only assures excellent prediction accuracy on regular days but also fundamentally resolves the issue of challenging prediction of various load types over the entire region during holidays.

References 1. Han, F.J., Wang, X.H., Qiao, J., et al.: A review of new power system load forecasting research based on artificial intelligence technology. Chin. J. Electr. Eng. 1–24 (2023). (in Chinese) 2. Qi, N., Cheng, L., Tian, L.T., et al.: Review and prospect of distribution network planning considering flexible load access. Autom. Electr. Power Syst. 44(10), 193–207 (2019). (in Chinese) 3. Hong, W., Khalid, A.A., et al.: Comprehensive review of load forecasting with emphasis on intelligent computing approaches. Energy Rep. 8, 13189–13198 (2022) 4. Liu, Y.N., Zeng, L.Q., Zhang, W.-S., et al.: Load time series prediction based on additive fuzzy system. New Tech. Electrengineering Electric Energy 20(04), 23–25+73 (2002). (in Chinese) 5. Pełka, P.: Analysis and forecasting of monthly electricity demand time series using patternbased statistical methods. Energies 16(2), 827 (2023) 6. Zhe, C., Chen, Y.B., et al.: A novel short-term load forecasting framework based on time-series clustering and early classification algorithm. Energy Build. 111375, 0378–7788 (2021)

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7. Zhang, F., Zhang, F., Zhang, S.W.: Power load Forecasting based on time series analysis of lifting wavelet. Electr. Autom. 39(03), 72–76 (2017). (in Chinese) 8. Tang, W., Zhong, S., Shu, J., et al.: Research on spatial load forecasting of distribution network based on GRA-LSSVM method. Dianli Xitong Baohu Yu Kongzhi/power Syst. Prot. Control 46(24), 76–82 (2018) 9. Feng, J.W., Yang, J.W.: Load forecasting of electric vehicle charging station based on grey theory and neural network. Energy Rep. 7(6), 487–492 (2021) 10. Tao, J., Zou, H.B., Zhou, D.: Short-term load forecasting model based on enhanced artificial neural network. Electr. Mater. 2021(02), 53–56 (2021). (in Chinese) 11. Kong, X.Y., Li, C., et al.: Short-term electrical load forecasting based on error correction using dynamic mode decomposition. Appl. Energy 261, 114368 (2020) 12. Cui, M.S.: District heating load prediction algorithm based on bidirectional long short-term memory network model. Energy 254, 124283 (2022) 13. Zhao, J.Y., Chi, Y., Zhou, Y.T.: Short-term power load forecasting based on SSA-LSTM model. New Technol. Electroengineering Electr. Energy 41(06), 71–79 (2022). (in Chinese) 14. Cheng, Z.Y., Ding, B.H., Yu, G.: Short-term load forecasting method based on IPSO-LSVM. New Technol. Electroengineering Electr. Energy 39(05), 41–48 (2019). (in Chinese) 15. Wang, Z.X., Yao, F., Zhang, L.: Short-term load forecasting with integrated machine learning forecasting algorithm. Electr. Autom. 45(02), 61–63 (2023). (in Chinese) 16. Wang, Y.: Short-term load forecasting for industrial customers based on TCN-LightGBM. IEEE Trans. Power Syst. 36(3), 1984–1997 (2021) 17. Bastian, D., Jessica, W., et al.: Machine learning based very short term load forecasting of machine tools. Appl. Energy 276, 115440 (2020) 18. Li, K., Li, W.J.: Research on Non-holiday load forecasting of electric power based on the fusion algorithm of BP neural networks and stacking model. J. Softw. 40(09), 176–181 (2019). (in Chinese) 19. Wu, M.G.: Power load short-term forecasting based on non-holiday Elman neural Network. Modern Commer. Ind. 39(03), 197–198 (2018). (in Chinese) 20. Bendu, H., et al.: Multi-objective optimization of ethanol fuelled HCCI engine performance using hybrid GRNN–PSO. Appl. Energy 187, 601–611 (2017). ISSN 0306–2619 21. Hou, H., Wang, Q., Zhao, B., et al.: Power load forecasting based on phase space reconstruction and machine learning with missing key information. Power Syst. Prot. Control 50(04), 75–82 (2022). (in Chinese) 22. Wu, T.H.: Optimization of LightBM-XGBoost model for power load forecasting based on genetic algorithm. Sci. Technol. Innov. 71–75 (2023). (in Chinese) 23. Dai, Y.M., Zhou, Q.Z.: Power load combination forecasting method based on improved BiLSTM and XGBoost. J. Univ. Shanghai Sci. Technol. 44(02), 138–147 (2022). (in Chinese)

Temperature Distribution Study of Armature and Guideway Under High-Speed Sliding Electrical Contact Hang Geng(B) , Li Zhang, Xu Jiang, and Yuanxin Teng School of Electrical Engineering, Shandong University, Jinan 250061, China [email protected]

Abstract. In electromagnetic launch systems, the sliding electrical contact formed by the armature and the rail poses challenges to track heat management research due to ultra-high-speed friction. To investigate the serious impact of armature-rail overheating under high-speed sliding electrical contact on the launch performance and service life of the launch system, researchers have established a transient simulation model of armature-rail launch system high-speed sliding electrical contact based on finite element analysis software. This model takes into account both the frictional heat and the Joule heat effect generated by contact resistance between the armature and the rail. Researchers have analyzed the current density, heating power, and temperature distribution between the armature and rail in the linear propulsion system and compared these data with the actual abrasion and burn conditions of the armature and rail obtained from actual launch experiments. Through these comparisons, researchers have identified the distribution rules of current density and temperature in the armature-rail launch system before and after the separation of the armature and rail, verifying the effectiveness of the simulation model. This study provides theoretical support for the subsequent modification design of armature materials and the preparation of abrasion-resistant materials. Keywords: High-speed sliding electrical contact · armature and rail launch system · transient analysis · temperature distribution

1 Introduction Electromagnetic launch technology represents a significant innovation in artillery launching techniques. Compared to conventional artillery launch methods, electromagnetic launch technology offers prominent advantages such as high controllability, rapid response, and high kinetic energy. These qualities make electromagnetic launch technology a disruptive equipment technology suited for adapting to the complexities of future battlefield environments [1, 2]. During the launch process, the armature experiences intense sliding electrical contact with the rail due to electromagnetic forces. This results in the generation of Joule heating and frictional heating, causing a substantial temperature rise in the armature-rail system. Complex interactions occur between magnetic, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 370–377, 2024. https://doi.org/10.1007/978-981-97-1064-5_40

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thermal, and mechanical processes, significantly impacting contact resistance, electrical conductivity, hardness, thermal conductivity, material properties, and mechanical characteristics [3, 4]. Therefore, studying the temperature distribution in the armature-rail system during the launch process is a crucial foundation for the design of such systems. Researchers both domestically and internationally have conducted relevant studies on the temperature distribution in armature-rail systems and the heating phenomenon in railguns. Hu Xinkai et al. [5] established a multi-field coupled model to study the thermal damage in different launch stages. Zhao Lingkang et al. [6] developed a heat conduction equation with internal heat sources to obtain theoretical solutions for armature-rail temperature distribution and analyzed the impact of non-Fourier heat effects on rail temperature. Klingenberg et al. [7] used experimental methods to measure parameters such as muzzle gas flow velocity, pressure, and temperature distribution in detail. Ruan Jinghui et al. [8] researched the current distribution in armature-rail systems and summarized measures for optimizing the armature-rail current distribution. Literature [9] analyzed the relationship between armature-rail temperature distribution, current density, launch velocity, and material parameters through numerical calculations. Literature [10, 11], by establishing a three-dimensional transient multi-field coupled computational model, studied the temperature distribution along the direction of armature motion on the rail. They found that changes in excitation current, launch structure, and material parameters led to variations in temperature distribution and concluded that the height of armature-rail temperature rise affects launch velocity, requiring forced cooling of the launch system to ensure normal operation. Existing research has primarily focused on the current distribution and thermal conduction effects in armature-rail systems, with relatively limited research on the comprehensive consideration of armature-rail temperature distribution during the launch process, taking into account both armature-rail friction and current thermal effects. This paper, based on the actual conditions of a linear propulsion mechanism, has established an electromagnetic launch armature-rail system model using the finite element analysis software ANSYS to conduct multi-field coupled simulations. It focuses on the study of the magnetic field, electric field, and temperature field between the armature and rail. Simultaneously, it analyzes the armature-rail temperature distribution from the perspective of current flow mechanisms. This research aims to provide effective ideas, suggestions, and reference value for the modification design of aluminum alloy armatures and the preparation of erosion-resistant materials.

2 Electromagnetic-Thermal Coupling Theoretical Analysis of the Armature-Rail System Electromagnetic rail launch system mainly consists of pulse power supply, rail, and armature, the strong pulsed current generated by the interaction between the rail and armature, along with the intense pulsed magnetic field, produces electromagnetic forces that drive the armature for high-speed launches, as shown in Fig. 1. The electromagnetic rail launch system exhibits extreme complexity under its operating conditions, with pulsed high currents reaching the MA level, operating times in the ms range, armature-rail contact pressures at the 100 MPa level, relative speeds of up to

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Fig. 1. Schematic diagram of the electromagnetic orbital launch system model.

2.5 km/s between the armature and rail, forming a high-speed sliding electrical contact friction pair [12]. In such an extreme service environment, complex interactions occur among physical processes like magnetism, heat, and force [13]. During the launch process of the armature-rail system, the armature undergoes accelerated motion along the rail under the influence of electromagnetic forces and is subsequently expelled from the muzzle [14]. The total heat generated during this entire process primarily consists of two components: one is the frictional heat produced by the translational motion of the armature along the rail, and the other is Joule heating generated as the current flows through the circuit composed of the rail, armature, and rail. These two components of heat distribution differ as follows: frictional heat mainly distributes along the rough surfaces where the armature contacts the rail, while Joule heating is distributed throughout the portions where current flows. Joule heating can be further subdivided into ordinary resistance heating and contact resistance heating, with ordinary resistance heating arising from the inherent resistance of the armature-rail system materials, and contact resistance heating primarily resulting from non-ideal contact between the rough surfaces of the armature and rail. This paper focuses on the theoretical analysis of contact resistance heating. During the launch process of the armature-rail system, there is relative motion between the armature and the rail, resulting in high-speed sliding friction [15]. This process generates a significant amount of heat, and the heat produced by high-speed sliding friction and the applied current load are described by Eqs. (1) and (2):  t2 μf FN vdt (1) Qf = t1

ϕf =

λQf t2 − t1

(2)

where “μf ” and “FN ” respectively represent the friction coefficient and contact pressure. When the rail and armature come into mutual contact and current flows through the circuit formed by the rail and armature, an additional voltage drop occurs at the contact region between the armature and the rail. This is because there is electrical resistance present at the armature-rail contact surface, which is referred to as contact resistance. When the surfaces of the armature and rail make contact with each other, only a small

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portion of the protruding points actually forms real contact, and current can only conduct through the spots in direct contact. The thermal effect generated by contact resistance and current can be expressed by the following equation: 1  ρ1 + ρ2 π H 2 (3) Rc (t) = 4 nηFc  t2 i2 Rc (t)dt (4) Qc = t1

where Rc , Fc , H , n, N, and η represent contact resistance, contact pressure, material hardness, the number of contact points, and the elastic deformation correction factor, respectively.

3 Simulation Model and Parameters A three-dimensional model of the armature-rail system was created for simulation analysis using the X-Y plane interface in ANSYS. The rail length was set to 500 mm, with rail dimensions of 30 mm × 30 mm, and a 90 mm gap between the rails. Initially, a simplified model of the launch rail and armature was built using the Magnetostatic module in ANSYS. This allowed for obtaining the magnetic field distribution at the interface between the rail and armature by applying a specified current load. The magnetic field distribution was then exported for further analysis. Subsequently, the electromagneticthermal coupling of the armature-rail system was analyzed using the Structural Dynamics simulation module. This involved incorporating the motion of the armature and the obtained magnetic field distribution. Multiple-field coupling simulations, including electrical-thermal, structural, and temperature analyses, were performed by configuring the armature-rail contact model. Finally, the simulation results were observed, and subsequent analysis and processing were carried out (Fig. 2).

Fig. 2. Simulation model of pivotal orbit launch system.

Due to the symmetry of the launch system and for the sake of simplifying computations, only half of the model was constructed. After performing basic operations such as grid partitioning and refinement, a high-pulse current was applied to obtain the magnetic field distribution of the armature-rail system. According to the principles of heat generation, simulating temperature requires considering Joule heating from the current, frictional heating, and heat conduction from high-temperature objects. For the contact surface between the armature and rail, factors like friction, current conduction, and appropriate thermal resistances were considered to conduct a simulation analysis of the heating situation in the armature-rail system.

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4 Analysis of Armature-Rail Temperature Distribution Calculation The total launch time for the armature-rail system is 51 ms. Recordings of the armaturerail system were taken at moments t = 8, 19, 35, and 51 ms. An analysis of the current density, heat generation power, and temperature distribution in the armature-rail system was conducted at these specific time points. 4.1 Analysis of Simulation Results

Fig. 3. Distribution of pivotal rail current density at different moments.

Figure 3 shows the current density distribution at different times in the armature-rail system. It can be observed that, before the armature separates from the rail, the current density remains nearly constant. This is because the current flows through the path of rail-armature-rail, and the cross-sectional area at the top of the armature is smaller than that of the rail, resulting in a more concentrated current density distribution at the top of the armature. However, during the separation of the armature from the rail, the contact area between the armature and rail decreases, leading to a rapid increase in current density at the contact portion between the rail and the armature at the end of the rail.

Fig. 4. Heat power distribution of pivotal rail current at different moments.

Figure 4 displays the distribution of armature-rail heating power at different time points. Taking into account both the heat generated by friction between the armature and rail and the Joule heating due to the current, it can be observed that the heating power distribution aligns with the overall current density distribution. Before the separation of the armature and rail, the top of the armature exhibits a higher heating power, consistent with the current density distribution. At the moment of

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separation, there is a dramatic increase in heating power between the contact surfaces of the armature and rail. The heating power distribution map reveals that the rear part of the armature, due to its smaller cross-sectional area, experiences significantly higher heating power compared to the other parts.

Fig. 5. Distribution of pivot rail temperature at different moments.

Figure 5 presents the armature-rail temperature distribution at different time points. It can be observed that the contact surface between the armature and rail exhibits significantly higher temperatures than the rest of the components. The highest temperature point, as measured by a probe, is at the rear part of the armature where it contacts the rail, reaching a maximum temperature of 1544 °C. Comparing this with the distribution of current heating power discussed earlier, it becomes evident that in the established armature-rail launch system, the rear part of the armature experiences significantly higher temperatures than the top of the armature. This is because the rear part not only experiences frictional heating due to the friction but also Joule heating effects from the current.

(a) Maximum heating power of pivot rail system.

(b) Maximum temperature distribution of pivot rail system.

Fig. 6. Maximum heating power and temperature distribution of pivot rail system.

Based on the analysis conducted earlier, the maximum heating power of the armaturerail system during high-speed sliding electrical contact and the highest temperature data for both the armature and rail during the launch process were extracted and graphed, as shown in Fig. 6. During the period when the rail and armature are in full contact, the overall heating power of the armature remains nearly constant, and its temperature rise

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is relatively gradual. However, during the separation process, the contact area between the armature and rail is reduced, resulting in a sharp increase in heating power, and correspondingly, the armature temperature rapidly rises. 4.2 Analysis of Launch Test Results The condition of the armature and rail after launch is depicted in Fig. 7, allowing for a clear observation of their erosion and wear. As seen in the figures, the entire contact surface between the armature and rail has suffered severe erosion. The armature exhibits noticeable deformation and melting, while the inner side of the rail also shows significant wear and erosion due to high-speed sliding friction and Joule heating from the current.

(a) Armature damage map for launching experiments. (b) Rail damage map for launching experiments.

Fig. 7. Maximum heating power and temperature distribution of pivot rail system.

5 Conclusions This paper established a transient armature-rail launch system and a simulation model that comprehensively considers the effects of high-speed sliding electrical contact friction and Joule heating from the current to analyze the temperature distribution in the armature-rail system. The following conclusions were drawn: (1) In the armature-rail launch system, the temperature at the contact surface between the armature and rail is significantly higher than in other areas. The highest temperature point, measured by a probe, is at the rear part of the armature where it contacts the rail, reaching a maximum temperature of 1544 °C. Compared to the Joule heating generated by current conduction, frictional heating plays a dominant role in elevating the temperature of the armature-rail system. (2) Based on simulation design and experimental verification, it can be concluded that under the impact of high current, the temperature rise effect in the electromagnetic launch system causes the armature and rail to reach temperatures higher than their respective melting points. This results in severe wear, melting, and even vaporization of the armature and rail materials. These findings provide a theoretical foundation for subsequent modifications and the development of erosion-resistant materials for armatures and rails in electromagnetic launch systems. Acknowledgments. This work was funded by NSFC (No. 92166110).

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References 1. Ma, W.M.: Thoughts on the development of frontier technology in electrical engineering. Trans. China Electrotechnical Soc. 36(22), 4627–4636 (2021). (in Chinese) 2. Mcnab, I.R.: Large-scale pulsed power opportunities and challenges. IEEE Trans. Plasma Sci. 42(5), 1118–1127 (2014) 3. Konchits, M.B.V.V., Myshkin, N.K.: Electrical Contacts Fundamentals, Applications, and Technology. China Machine Press, Beijing (2010). (in Chinese) 4. Karhi, R.W., Mankowski, J.J., Dickens, J.C., et al.: Secondary arc formation within a distributed energy railgun. IEEE Trans. Plasma Sci. 36(5), 2738–2746 (2008) 5. Li, B., Lu, J.Y., Tan, S., et al.: Effect of interfacial roughness of sliding electrical contact on the melting characteristics of armature. Trans. China Electrotechnical Soc. 33(07), 1607–1615 (2018). (in Chinese) 6. Zhao, L.K., Tian, Z.G., Jin, L.Y.: Temperature field and non-fourier heat effect of launching electromagnetic Rail. J. Ordnance Equip. Eng. 41(03), 57–61,66 (2020). (in Chinese) 7. Klingenberg, G., Mach, H.: Investigation of combustion phenomena associated with the flow of hot propellant gases-i: spectroscopic temperature measurements inside the muzzle flash of a rifle. Combust. Flame 27, 163–217 (1976) 8. Ruan, J.H., Chen, L.X., Xia, S.G., et al.: A review of current distribution in electromagnetic railguns. Trans. China Electrotechnical Soc. 35(21), 4423–4431 (2020). (in Chinese) 9. Cao, B., Guo, W., Ge, X., et al.: Analysis of rail erosion damage during electromagnetic launch. IEEE Trans. Plasma Sci. 45(7), 1263–1268 (2017) 10. Lin, L.S., Yuan, W.Q., Zhao, Y., et al.: Thermal analysis on electromagnetic launcher under transient conditions. IEEE Trans. Plasma Sci. 45(7), 1476–1481 (2017) 11. Lin, Q.H., Li, B.M.: Numerical Simulation of transient temperature field in the electromagnetic railgun. J. Eng. Thermophys. 38(1), 149–154 (2017). (in Chinese) 12. P P. Du, J Y. Lu, J H. Feng, et al.: Numerical simulation of dynamic launching process of electromagnetic rail launcher with electromagnetic and structural coupling. Trans. China Electrotechnical Soc. 35(18), 3802–3810 (2020). (in Chinese) 13. Li, X.P., Lu, J.Y., Zhang, X., et al.: Analysis of distribution characteristics of electromagnetic launcher projectile muzzle magnetic field. Trans. China Electrotechnical Soc. 36(03), 525–531 (2021). (in Chinese) 14. Weimer, J.J., Singer, I.L.: Temperatures from spectroscopic studies of hot gas and flame fronts in a railgun. IEEE Trans. Plasma Sci. 39(1), 174–179 (2011) 15. Gao, Y., Xiao, H., Ni, Y., et al.: Simulation and analysis of the railgun muzzle flow field considering the arc plasma. IEEE Trans. Plasma Sci. 47(5), 2242–2249 (2019)

Improved Pre-synchronization and Grid Connection Strategy Based on Virtual Synchronous Generator Haihong Huang, Xiaoyi Qu(B) , and Haixin Wang School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China [email protected]

Abstract. To enhance the inertia and damping of power grid, enhance the support ability of voltage and frequency, virtual synchronous generator (VSG) technology is widely applied. An improved pre-synchronous grid connection strategy is proposed to address the issues of large power oscillations and current surges during VSG off grid switching. Under the coordinate αβ axis, a method similar to reactive power calculation is used to obtain the adjustment amount of VSG output voltage, and through control, fast and accurate synchronization with grid voltage is obtained to achieve smooth switching of VSG off grid. Finally, the effectiveness of the proposed improved pre-synchronization grid connection strategy is verified through simulation and a 50 kV/A prototype is built to prove the feasibility of proposed method. Keywords: Virtual synchronous generator · power calculation · Pre-synchronization · grid connection

1 Introduction The penetration rate of distributed new energy such as wind power and photovoltaic in power industry is increasing. A large amount of distributed new energy is connected to power grid through power electronic inverters, improving response speed and control flexibility, while reducing power grid stability. To increase inertia and damping of power grid and enhance robustness, virtual synchronous generator (VSG) control method is proposed. Based on synchronous generator, inertia and damping with enough value for power grid are obtained, furthermore frequency and voltage to power grid are supported through active and reactive power [1]. Supporting properties of VSG determine its output characteristics as a voltage source. For the point of common coupling (PCC) with small impedance, if voltage difference on both sides of VSG is relatively large when connected to grid, power oscillation and current surge will occur. Therefore, when grid-connected mode switched to grid-off mode, pre-synchronization control (PSC) is required to ensure that the phase, frequency, and output voltage amplitude meet grid connected requirements, to achieve smooth grid connection. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 378–384, 2024. https://doi.org/10.1007/978-981-97-1064-5_41

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At present, various pre-synchronization methods are used for controlling the phase: output voltage phase information and grid voltage through two phase-locked loops are obtained in [2, 3], and the difference between the two is defined as input for PI regulation. Voltage on output phase tracking the grid voltage is realized through output frequency compensation. However, delay issue is brought by its complex structure. Power grid voltage phase through a single phase-locked loop method is obtain in [4–6], which is used for coordinate transformation of voltage on output end. But the phase-locked loop is prone to dynamic interaction with other control loops, reducing synchronization stability of the system [7]. Phase of output voltage on VSG is used for grid voltage coordinate transformation [8, 9]. Based on coordinate transformation value, VSG output voltage leads the grid voltage value, and the difference between VSG output voltage and grid voltage value is used as the input for PI regulation. VSG angular frequency compensation is obtained from PI control, achieving frequency and phase synchronization. But there are also issues with phase lag and inaccurate control. PSC based on virtual power is performed in [10], assuming that there is a virtual impedance at the PCC point. By calculating virtual active power, compensating amount for VSG output angular frequency is obtained. However, work process is relatively cumbersome to realize power calculation and reasonable assuming about virtual impedance. This article intends to improve the method of pre- synchronization phase, and utilizing Clark transform in αβ axis, a method similar to reactive power calculation is used to obtain the adjustment amount of VSG output voltage. Through control, fast and accurate synchronization with the grid voltage is achieved, realizing smooth grid-off mode to grid-connected mode switching process.

2 VSG Control Principle 2.1 Establishment of VSG Mathematical Model The rotor of traditional synchronous generators stores a large amount of kinetic energy, exchanging with the power grid when connected to it. VSG is precisely connected to power grid through virtual synchronous machine control, providing support for power grid. In actual control, the primary frequency and voltage regulation functions based on droop control are added to active and reactive power control loops to better support voltage frequency and amplitude. VSG active frequency regulation and reactive voltage regulation can be described as follows: Pref + Kw (w0 − wt ) Pe dwv + KD (wv − w0 ) − =J w0 w0 dt  U = Uref + KQ (Qref + Ku (U0 − Ut ) − Qe )dt

Tm − Te =

(1) (2)

where T m and T e are the rotor parameters, Pref and Qref are references of active and reactive power, U and U ref are actual voltage and given voltage, Pe and Qe are actual active power and reactive power, w0 and U 0 are rated angular frequency and rated voltage amplitude, wv is frequency of VSG rotor angular, wt and U t are angular frequency and amplitude of AC bus voltage, K w and K u are primary regulation coefficients of frequency and voltage, J is rotational inertia, and K D is damping coefficient.

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2.2 Topology Overall control structure of VSG is shown in Fig. 1. Udc is ideal DC power source, L, C, and Lg are filtering inductance, filtering capacitance, and grid impedance, respectively. Uabc is three-phase output voltage of inverter, iabc is three-phase output current, ilabc is three-phase bridge side current, ugabc is grid voltage, and uref is VSG output voltage command value. ila

L

ilb

U dc

ia

ua

Lg

uga

ib

ugb

uc ic

ugc

ub

ilc

PCC

C

uabc

i abc

PWM Pe

uref

Qe P ref Q ref

Fig.1. VSG overall control structure

An ideal DC power supply is adopted in power circuit, IGBT three-phase full bridge topology structure is used in power switch. LC filter is used to filter out high-order harmonics. PCC point is equipped with an electronic switch. Before closing of switch, VSG is in an off grid operation state. After pre-synchronization, frequency, phase, and amplitude of voltage meet the grid connection conditions, and switch is closed, and VSG is connected to power grid. At this time, power circuit is in a grid connected operation state. VSG power control is adopted in control outer loop to output voltage command values, while voltage and current dual closed-loop control is adopted in inner loop to improve dynamic performance of power system. Power calculation and control are based on the dq coordinate system.

3 Improved Pre Synchronization Control Strategy Let the vector representations of voltage on VSG output, current, and voltage of grid are as follows: Uabc = [ua ub uc ]

(3)

Iabc = [ia ib ic ]

(4)

Ugabc = [ uga ugb ugc ]

(5)

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Perform equal power Clark transformations on VSG output voltage, current, and grid voltage, a matrix representation is as follows: ⎤⎡ ⎤  ⎡ ⎤ ⎡ 1 1 1 − uα iα ugα ua ia uga 2 −√2 √ 2 ⎢ ⎥ 3 ⎣ uβ iβ ugβ ⎦ = − 3 ⎦⎣ ub ib ugb ⎦ (6) ⎣ 0 3 √1 √21 √12 u0 i0 ug0 u i u c c gc 2 2 2 Calculate instantaneous reactive power based on equal power transformation values can be expressed as: Q = uβ iα − uα iβ

(7)

When Q = 0, output voltage and current are in phase. iα and iβ are replaced with ugα and ugβ respectively, and define γ as the phase difference between VSG output voltage and grid voltage. When controlling uβ ugα -uα ugβ = 0, γ = 0, the compensation amount for output angular frequency is output by PI control in VSG active frequency control. Output voltage of VSG is in phase with grid voltage to complete phase PSC. The phase PSC diagram is shown in Fig. 2.

Fig.2. Phase pre-synchronization block diagram

4 Simulation and Experimental Verification 4.1 Comparison with PLL Pre-synchronization According to above proposed PSC method, simulation is done, and simulation parameters are shown in following (Table 1). Proposed improved PSC is compared with traditional dual phase-locked loops PSC. A-phase waveform in output end is observed, and the initial phase difference between the output voltage and the grid voltage is given to be 50°. The PCC point switch is not closed during off-grid operation. The pre-synchronization voltage tracking waveform of the phase-locked loop is shown in Fig. 3. From Fig. 3, at t = 0.06s, output voltage basically coincides with voltage on grid. The improved PSC voltage tracking waveform is shown in Fig. 4. At t = 0.005s, the output voltage coincides with voltage on grid end. According to above comparison, improved PSC is faster and simpler than the traditional dual phase-locked loop PSC. The use of phase-locked loops and simplifies in the control structure is omitted in proposed method.

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Value

DC side voltage U dc /V

770

Rated frequency f c /Hz switching frequency f k /kHz

50 9

filter inductance L/mH

0.8

filter capacitor C/uF

55

Grid impedance L g /mH

2

Effective value of grid phase voltage ug /V

220

Rotational inertia J/kg.m2

10

Damping coefficientK D /N.m.s.rad−1

100

Primary frequency modulation coefficient K w

3000

Primary voltage regulation coefficient K u

0.02

Given value of active power Pref /kW

6

Given value of reactive power Qref /Var

0

Fig. 3. Phase locked loop pre-synchronization

Fig. 4. Improved pre-synchronization

4.2 Mode Switching and Grid Connection Operation By using an improved PSC for grid connection, the PCC point switch is closed at t = 0.2s, and grid-off mode is switched to grid-connection mode of VSG for operation. The output voltage and current waveforms of VSG before and after grid connection are shown in Fig. 5. Before grid connection, due to no load, the VSG output active and reactive power was 0. After grid connection, VSG injects power into the grid based on the given active and reactive power. Due to the inherent inertia and damping of synchronous generators, the output power will not be fully injected into the grid immediately after grid connection at t = 0.2s, but will slowly rise to the given value at t = 0.75s, and then inject smoothly. The output power waveform of VSG before and after grid connection is shown in Fig. 6.

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Fig. 5. VSG output voltage and current simulation waveform

Fig. 6. VSG output power simulation waveform

4.3 Experimentation Experimental platform based on simulation model is built, as shown in Fig. 7. The left prototype is a 50 kV/A virtual synchronous generator, and the right prototype is a rectifier. The rectifier input is connected to the AC power grid, and outputs a stable DC voltage of 770V to supply power to virtual synchronous generator. Virtual synchronous generator output is connected to AC power grid, and after pre-synchronization is completed, it is connected to the grid to provide voltage and frequency support for the power grid. The waveform of the A-phase output voltage and bridge side current during the grid connection process are shown in Fig. 8.

Fig. 7. Experimental prototype

Fig. 8. Output voltage and bridge side current

From Fig. 8, it is clear that after improving PSC before grid connection, voltage on VSG output end and grid end are almost synchronized, and there is no significant

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oscillation in the voltage and current when grid connection. Instead, the transition is smooth and finally stabilizes.

5 Conclusion An improved pre-synchronization grid connection method is proposed to address some issues arising from the application of traditional pre-synchronization control strategies to VSG controlled voltage source inverters. The use of phase-locked loop is not required and computing of virtual power is avoided, resulting in a simpler control structure and simpler calculation. Through simulation and experiments analysis, the proposed control strategy is verified with good control ability and simple feasibility.

References 1. Zhan, C., Wu, H., Wang, X.: An overview of stability studies of grid-forming voltage-source converters. Proc. CSEE 43(06), 2339–2359 (2023). (in Chinese) 2. Li, M., Zhang, X., et al.: The control strategy for the grid-connected inverter through impedance reshaping in q-axis and its stability analysis under a weak grid. IEEE J. Emerg. Sel. Top. Power Electron. 9(3), 3229–3242 (2021) 3. Li, M., Zhang, X., Yang, Y., et al.: The grid impedance adaptation dual mode control strategy in weak grid. In: 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), pp. 2973–2979 (2018) 4. Fang, J., Li, X., Li, H., Tang, Y.: Stability improvement for three-phase grid-connected converters through impedance reshaping in quadrature-axis. IEEE Trans. Power Electron. 33, 8365–8375 (2018) 5. Yuqi, W.U., Yuqing, Y.E., Xiao, M.A., et al.: Pre-synchronization scheme with voltage fluctuation suppression and frequency out-of-limit avoidance for grid connection of islanded microgrid. Autom. Electr. Power Syst. 45(14), 56–64 (2021). (in Chinese) 6. Zhang, X., Danni, X., Zhichao, F., et al.: An improved feedforward control method considering PLL dynamics to improve weak grid stability of grid-connected inverters. IEEE Trans. Ind. Appl. 54(5), 5143–5151 (2018) 7. Cespedes, M., Sun, J.: Adaptive control of grid-connected inverters based on online grid impedance measurements. IEEE Trans. Sustain. Energy 5(2), 516–523 (2014) 8. Ciobotaru, M., Teodorescu, R., Blaabjerg, F.: A new single-phase PLL structure based on second order generalized integrator. In: Power Electronics Specialists Conference, pp. 1–6 (2006) 9. Li, M., Zhang, X., Guo, Z., Wang, J., Li, F.: The dual-mode combined control strategy for centralized photovoltaic grid-connected inverters based on double-split transformers. IEEE Trans. Industr. Electron.Industr. Electron. 68(12), 12322–12330 (2021) 10. Gao, Y., Sun, X., Zhou, Z.: Grid-connected pre-synchronization control based on virtual impedance power without PLL.Power Electron. 55(04), 99–102 (2021). (in Chinese)

Analysis of Electromagnetic Characteristics of Dual-Rotor Induction Machines Based on Modularization Hao Luo(B) , Kunshuo Zhu, Yifan Xiao, Xijun Ni, and Gang Wu School of Electric Power Engineering, Nanjing Institute of Technology Nanjing, Nanjing, China {luohao,nxj}@njit.edu.cn

Abstract. In order to solve the manufacturing, transportation, installation and repair problems of the giant fan, on the basis of the traditional one-piece dualrotor induction machine, the two rotors of the fractional-slot centrally wound dual-rotor induction machine (15-slot 7-pair poles versus 24-slot 11-pair poles) are modularized separately, and the use of the T-type modular structure, which is equivalent to inserting a rotor gap in the yoke part of the rotor, thus changing the rotor magnetic circuit. According to the machine principle of this machine, the analytical method is used to derive the winding coefficients of the rotor for the T-type modular structure, and it is analytically obtained that the modular rotor structure reduces the amplitude of the winding coefficients of the non-operating subharmonics to a certain extent, and reduces the amplitude of the air-gap magnetism of the non-operating subharmonics. And through the finite element analysis on the traditional dual-rotor induction machine and modular dual-rotor induction machine no-load and load simulation, the results of comparative analysis, theoretical analysis and simulation results basically match. The modular rotor structure effectively improves the performance of the machine and increases the operating efficiency of the machine. Keywords: Fractional-slot centralized winding · Modular structure · Modularization structure · Electromagnetic characteristics · Finite-element analysis

1 Introduction In 2021, the installed capacity of wind power generation in China once again reached a new high, with a total of 15911 additional wind turbines added, reaching a capacity of 55.92 million kilowatts, a year-on-year increase of 2.7%. As of the end of 2021, hoisting fans accounted for more than half of the installed capacity of all fans, reaching 50.8%. It can be seen that the hoisting of wind turbines has gradually become the mainstream of wind turbine types [1–3]. Fraction-slot Concentrated Winding (hereinafter referred to as FSCW) induction machine has a lot of advantages, mainly including small size, high power density, high efficiency, its winding factor is large, self-inductance is large, mutual inductance is low, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 385–392, 2024. https://doi.org/10.1007/978-981-97-1064-5_42

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the torque pulsation is small, the tooth slot torque is small, and at the same time, it has a stronger weak magnetic speed expansion and fault-tolerance ability. It has been more and more used in the field of large-scale wind power engineering, especially in the field of offshore wind power generation. Therefore, FSCW machines have become an important direction in the development of wind power generation technology today. Most of the studies on FSCW focus on the general expression of winding coefficients, magnetomotive potential distribution, pole-slot fit, harmonic loss suppression, and calculation of parameters such as inductance [4–6]. At present, most of the induction machine stator-rotor cores are made of whole silicon steel sheets laminated together. However, it will cause large losses in the production process, in addition, when processing large-size machines, it is difficult to make the whole stamping sheet integrally, and it is necessary to use specialized stamping equipment. In order to overcome this problem, most of the machines are made of rare-earth-free materials [7–9], which has the disadvantage of lower power density. By individually winding and assembling the machine on each module, mechanized winding improves the slot fullness rate, reduces labor costs, and has a low machine production error rate; at the same time, rotor windings of different phases can be connected in parallel to form a multi-circuit system for power generation. When the machine needs to be repaired, only the faulty module is removed from the modular machine, and does not affect the normal work of other modules, which greatly improves the fault tolerance of the machine. In addition, in order to dissipate the heat generated inside the casing of the operating time as soon as possible, the modular structure of the machine can be added in the stator-rotor module gap water-cooled heat dissipation piping or magnetic isolation materials, effectively reducing the internal heat of the machine resulting in the machine cannot run normally and uneven distribution of the air gap magnetic density and other issues, thereby improving the service life of the machine, a comprehensive analysis of the use of the modular machine structure to increase the machine’s power density and operating efficiency [10–12]. In this paper, a modular machine is designed to adopt axial magnetic field machine structure based on the FSCW structure with pole-slot ratio close to 1. The calculation of winding coefficients in the basic theory of FSCW is summarized, and using this theory, it is extended to the modular FSCW induction machine by using a pair of dominant components in the pole-logarithmic spectrum of the stator’s magnetomotive force for dual-rotor AC excitation. The design of such modular machines has advantages: modular structure machines can reduce the amplitude of air-gap flux density of the non-operating harmonics, at the same time can increase the fault-tolerance of the machine, improve the electromagnetic performance of the machine, solve the problem of manufacturing, transportation, installation, and repair of the giant wind turbine. It is of significant significance to develop a new type of wind power transmission system with light weight, low cost, high efficiency and high reliability.

2 Machine Structure and Working Principle The FSCW dual-rotor induction machine model studied in this paper is shown in Fig. 1. The stator core is unified in a modular structure with equal size and trapezoidal shape of each module, aluminum alloy brackets with non-conductive materials are used on both

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sides of the stator, and the centralized windings are wound sequentially on each tooth. Figure 1(a) shows a conventional dual-rotor induction machine and Fig. 1(b) shows a modular dual-rotor induction machine. In the modular machine, the two rotor cores are each constructed using a T-shaped modular structure that cuts the rotor yoke between two adjacent teeth, a gap exists in the middle of the dual core modules that can be used to fill with magnetically insulating material, the slots are oriented towards the stator side, the ratio of teeth to slots is 1:1, and the centralized windings are wound on each tooth.

1#

1#

(a) Conventional induction machine

(b) Modular induction machines

Fig. 1. Machine topology

The parameters of the dual-rotor induction machine are shown in Table 1. The stator winding coefficients are maximum at pole pair numbers 7 & 11. Using the stator harmonic pole-pair spectrum of a pair of dominant poles 7 and 11, respectively, with the 1#rotor dominant pole-pair 7 and 2#rotor dominant pole-pair 11 for the magnetic field coupling, at this time, the mutual inductance between the 1#rotor and the stator is mainly through the 7-pair poles flux turn chain, and the mutual inductance between the 2#rotor and the stator is mainly through the 11-pair poles flux turn chain.

3 Magnetic Circuit Model and Winding Coefficients for Modular Machines After the modularization of the two rotors, the rotor gap leads to a corresponding change in the equivalent magnetic circuit model of the machine and the winding coefficients of the two rotors. Therefore, it is necessary to reanalyze the equivalent magnetic circuit model of the machine after modularization, modify the winding coefficients of the two rotors, and compare the differences before and after modularization. 3.1 Magnetic Circuit Model Assuming that the ferromagnetic material of the machine is linear and the permeability is infinite, the equivalent magnetic circuit of the modular machine follows the “principle of minimum reluctance” in the same way as the equivalent magnetic circuit of a conventional dual-rotor induction machine. The magnetic circuit model of the modular machine is shown in Fig. 2.

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Parameters

Value

Machine outer circle

100 mm

Radius of inner circle of yoke

60 mm

Radius of inner circle of tooth

50 mm

Length of air gap

1 mm

1#Rotor pole number/slot number

7/15

1#Rotor rated speed

3000/7 rpm

2#Rotor pole number/slot number

11/24

2#Rotor rated speed

3000/11 rpm

Pole number/slot number of stator

7/18

Number of parallel branches

1

Number of coils

56

For a conventional dual-rotor induction machine, the main magnetic flux generated by the stator excitation only passes through two air gaps and two rotor cores to form a circuit. After the modularization of the two rotors, as shown in the equivalent magnetic circuit schematic in Fig. 2(a), the main magnetic flux generated by the stator coil excitation passes through each stator-rotor core, air gap and rotor gap sequentially to form a closed magnetic circuit. In Fig. 2(b), F S , Rag1 , Rag2 , Rw1 , Rw2 , Rδs are the stator magnetomotive force, 1#air gap reluctance, 2#air gap reluctance, 1#rotor gap reluctance, 2#rotor gap reluctance, and leakage equivalent reluctance, respectively, which are compared with the equivalent magnetic circuit schematic diagram of the conventional machine, and the gap reluctance of two more rotors, Rw1 and Rw2 , leads to a different rotor magnetic density in the modular machine compared with that of the conventional machine is different, which causes the harmonic content of the rotor air-gap magnetism to change, which in turn affects the electromagnetic performance of the machine. Rw1 Rag1

FS

Rag1

R

S

R

Rag 2

FS

S

Rag 2

Rw 2

(a)Structural diagram

(b)Schematic diagram

Fig. 2. Equivalent magnetic circuit model of modular dual-rotor induction machine

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3.2 Winding Factor The winding coefficient k wυ of a conventional FSCW induction machine is further divided into the short pitch coefficient k yυ and the distribution coefficient k qυ . The expression of the distribution coefficient of 1#rotor is obtained according to the coil arrangement law and the magnetic potential vector distribution of 7 pairs of poles and 15 slots as Eq. (1), in which the number of slots of 1#rotor is Q, N = Q/3, n = (N-1)/2, and α 0 = 2π/Q. The expression of the distribution coefficient of 2#rotor is obtained according to the coil arrangement law and the magnetic potential vector distribution of 11 pairs of poles and 24 slots as Eq. (2), in which N = Q/6. Rotor slot number is even, the even harmonic magnetic potential is 0, so only the odd harmonics need to be considered when calculating the winding coefficients of 2#rotor. The presence of the rotor gap in the modular machine does not change the relative position of the individual coils in the rotor and the direction of the coil magnetomotive potential remains constant in each phase, so the distribution coefficients of the modular machine do not change.   n  1 n n−i (−1) cos iυα0 (1) (−1) + 2 kqν_1 = N i=1

kqυ_2 =

N /2 2  1 (−1)N /2−i sin υ(i − )α0 N 2

(2)

i=1

where, is the number of harmonics, y is the slot spacing of the rotor of the conventional dual-rotor induction machine, and γ is the radian of the rotor gap. The schematic structure of the modularized two rotors is shown in Fig. 3.

(a) 1#Rotor

(b) 2#Rotor

Fig. 3. Modular dual-rotor induction machine structure diagram

For the conventional machine, the period of change of the winding factor of 1#rotor is 15, and the minimum winding factor in one cycle is 0, which corresponds to the number of harmonics of 15, and none of the other sub-harmonics of the winding factor is 0 except for the 15th , and the maximum winding factor is 0.952, which corresponds

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to the number of harmonics of 7 and 8. After the modularization of the rotor, in the 1st ~7th harmonics, the existence of rotor gap reduces the slot spacing y, resulting in a decrease in the short pitch coefficient of the modular machine; whereas, in the 8th ~14th harmonics, the short pitch coefficient of the modular machine is instead increased due to the presence of the rotor gap which reduces the slot spacing.

4 Comparative Analysis of Electromagnetic Performance of Machines Before and After Modularization 4.1 Air-Gap Magnetic Density The dual-rotor induction machine is an axial flux machine, so only the axial flux is considered and the radial flux is ignored when analyzing the air gap magnetism. The synthesized magnetic kinetic potential of the three-phase winding acts on both sides of the air gap to produce the air gap magnetism, which is expressed as Eq. (3), where μ0 is the vacuum permeability, lag is the length of the air gap, and N S (α) is the winding function of the three-phase winding of the stator. Bs (t, α) =

μ0 is (t)Ns (α) lag

(3)

The Fourier decomposition of the air gap densities of airgap 1 and air gap 2 is performed to obtain the magnitude of each harmonic of the airgap densities, and the airgap densities with the largest magnitude of the first 50 magnitudes are extracted in accordance with the magnitude size as shown in Fig. 4. For the 15-slot 7-pole machine, the 7th harmonic amplitude of the air gap magnetization is the largest, followed by the 11th harmonic, and the two sets of harmonic magnetization are used to generate the load torque of the two rotors. 0.045

0.05

0.040 0.04

0.035

11

11

/T

/T

0.030 0.025

0.03

0.020 0.02

0.015 0.010

0.01

0.005 0.000 0

5

10

15

20

25

30

35

40

45

50

0.00 0

5

10

15

20

25

(a) Air gap 1

30

35

40

45

50

v

/v

(b)Air gap 2

Fig. 4. The first 50 air gap magnetic density amplitude

For the modular machine, the presence of rotor gap changes the air gap permeability of the machine and the magnetic circuit in the rotor core, resulting in a larger lag, which makes the air gap magnetic density smaller on both sides of the stator.

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The air gap magnetization of the modular machine is reduced compared to the conventional machine because the rotor module gap increases the air gap width, making the air gap magnetization smaller on both sides of the stator. 4.2 Inductors The inductance waveforms of the modular rotor structure machine and the conventional machine are shown in Fig. 5. The amplitude of the mutual inductance waveforms between the stator and rotor of the machine changes with the rotor structure under different slot-pole configurations. The amplitude of the mutual inductance waveform between the stator and rotor is mainly affected by 2 factors: winding factor and no-load air gap magnetization. For modular machines, the rotor gap reduces the machine winding factor, so the amplitude of the mutual inductance waveform between stator and rotor of modular machines is reduced.

Fig. 5. Inductance waveform

5 Conclusion In this paper, a rotor modular FSCW dual-rotor wound induction machine with T-tooth is designed. The traditional one-piece rotor structure machine is modularized by inserting a rotor gap in the rotor, and the magnetic circuit model, winding coefficients, and electromagnetic characteristics of two modular rotor structure machines with 15 slots and 7 pairs of poles and 24 slots and 11 pairs of poles are investigated. The above theories are verified by using finite element model. The use of modular structure machine can reduce the amplitude of air-gap magnetism of non-operating harmonics, and also improve the fault-tolerance of the machine, improve the electromagnetic performance of the machine, reduce the cost of machine manufacturing, and reduce the difficulty of the machine fabrication process. In addition, modularized machines also have problems of reduced mechanical strength of the rotor structure and difficulty in fixing each rotor module, which can be solved by installing removable fixing housings on the outer surfaces of the rotor modules.

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References 1. Luo, H., Xu, X., Shi, Z., et al.: Analysis of electromagnetic coupling characteristics of direct drive doubly-fed machine based on multi-frequency magnetic field coupling. Electr. Power Autom. Equip. 41(02), 159–165 (2021) (in Chinese) 2. Xu, Z., Yu, Q., Zhang, F.: Design and analysis of asymmetric rotor pole type bearingless switched reluctance motor. In: China Electrotechnical Society Transactions on Electrical Machines and Systems, vol. 6, no. 1, pp. 3–10 (2022) 3. Guo, F., Chu, Q., Li, C., Meng, T.: Research on influence f motor parameters on the negativesalient permanent magnet synchronous motor. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 6(1), 77–86 (2022) 4. Aimeng, W., Yi, T.: Performance analysis of modular stator fractional-slot concentrated windings machines. Micromotor 53(01), 35–42 (2020). (in Chinese) 5. Bian, C., Liu, S., Xing, H., et al.: Research on fault-tolerant operation strategy of rectifier of square wave motor in wind power system. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 5(1), 62–69 (2021) 6. Zheng, J., Zhao, W., Ji, J.: Review on design methods of low harmonics of fractional-slot concentrated windings permanent magnet machine. In: Proceedings of the Chinese Society of Electrical Engineering, vol. 40(S1), pp. 272–280 (2020). (in Chinese) 7. Liao, H., Zhang, X., Ma, Z.: Robust dichotomy solution-based model predictive control for the grid-connected inverters with disturbance observer. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 5(2), 81–89 (2021) 8. Paul, S., Chang, J.: Fast model-based design of high performance permanent magnet machine for next generation electric propulsion for urban aerial vehicle application. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 5(2), 143–151 (2021) 9. Lee, J.S., Choi, G.: Modeling and hardware-in-the-loop system realization of electric machine drives - a review. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 5(3), 194–201 (2021) 10. Zhang, Y., Yin, Z., Li, W., et al.: Finite control set model predictive torque control using sliding model control for induction motors. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 5(3), 262–270 (2021) 11. Huang, X., Lin, Z., Xiao, X.: Four-quadrant force control with minimal ripple for linear switched reluctance machines. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 4(1), 27–34 (2020) 12. Li, W., Cheng, M.: Investigation of influence of winding structure on reliability of permanent magnet machines. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 4(2), 87–95 (2020)

Research on Identification Method of Subsynchronous Oscillation Parameters Based on FSST and STD XiaoBiao Fu1 , Peng Zhang2 , XiaoZhe Song1 , Changjiang Wang2(B) , and Hao Ding1 1 State Grid Jilin Electric Power Company Limited, Princeton University, Changchun, China 2 Department of Electrical Engineering Northeast, Electric Power University, Jilin, China

{zhangpeng980926,cjwang17}@aliyun.com

Abstract. With the aim of double carbon in China, the incorporation of a significant quantity of novel energy devices and dynamic compensation devices and dynamic compensation devices into the grid has caused many instances of sub-synchronous oscillation (SSO) incidents, which have a considerable impact on the secure and stable operation of the power system. Rapid identification of SSO parameters can provide characteristic parameters for suppression measures, real-time warning, and analysis of SSO. Therefore, this paper proposes a timefrequency analysis approach based on the Short-Time Fourier Transform (STFT) and incorporates it with the Sparse Time Domain (STD) technique for the identification of sub-synchronous oscillation parameters. The proposed method first applies the SST time-frequency domain transformation to the oscillation data collected by Phasor Measurement Unit (PMU) at key nodes in the power grid, decomposing a set of signals with multiple modes into different modal components. Subsequently, an improved ridge extraction method is employed to reconstruct the time-frequency domain signals of each mode. The STD method is subsequently employed to precisely identify the modal parameters of SSO. Finally, through the analysis and verification of ideal examples and real-world power grid data, the identification results demonstrate the accuracy, robustness, and computational efficiency of the proposed method, thus satisfying practical engineering applications. Keywords: Sub-synchronous oscillation · Short-Time Fourier Transform · PMU · Sparse Time Domain

1 Introduction As the energy reform progresses further, the level of power electronics employed in different sections of the “source-grid-load” continuum within the power system has been progressively escalating with each passing year 1. As power systems develop, the ability to enhance the transmission capacity of the power grid, improve system stability, and establish a basis for the large-scale integration of renewable energy is employed 2. However, they have also led to an increase in weak links in the power © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 393–400, 2024. https://doi.org/10.1007/978-981-97-1064-5_43

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system, resulting in the increasingly prominent problem of sub-synchronous oscillation (SSO). SSO can cause damage to new energy devices and large-scale disconnection of new energy, which may trigger regional power grid chain accidents 3. Therefore, prompt detection of oscillation phenomena within power system and precise identification of oscillation parameters, such as frequency and damping characteristics, may provide theoretical basis for online localization of SSO weak links or SSO disturbance sources through data analysis [4, 5]. Time-frequency analysis methods combine the advantages of both time and frequency domains, comprehensively reveal the time-varying characteristics of different frequency components in non-stationary mixed signals based on the two-dimensional time-frequency distribution of signals. They accurately capture the characteristic information in the signals. They are suitable for analyzing non-stationary signals [7]. Commonly used time-frequency analysis methods based on wide-area measurement information include STFT [8] and Continuous Wavelet Transform (CWT) [9]. However, the distribution of energy of various frequency bands in the resulting time-frequency spectrum of these methods is spread over a wide range around the center frequency, leading to energy leakage, spectral blurring, frequency band overlap. Therefore, this paper proposes a sub-synchronous oscillation identification technique based on FSST-STD. Firstly, the PMU measurement signals are transformed into the time-frequency domain using SST. Then, an improved ridge extraction algorithm is introduced to reconstruct the signals of each mode from the time-frequency domain. Furthermore, by combining STD with the reconstructed single-mode signals, the oscillation parameters are identified. Finally, the proposed method is analyzed and validated through synthetic test signals and measured signals from a specific subsynchronous oscillation in a wind power plant.

2 Methods 2.1 Principle of Fourier Synchrosqueezing Transform Due to the wide range of energy dispersion in the time-frequency bands produced by STFT, post-processing synchronous compression technique is employed, concentrating the energy in a certain interval around the central frequency of each time-frequency band to the true center frequency. The steps are as follows [10]: Step 1. The original signal can be modeled as: s(t) = A(t)eiϕ(t)

(1)

Apply Taylor’s theorem to expand A(t) and ϕ(τ ). The signal can be expressed as: 

s(t) = A(τ )ej2π [ϕ(τ )+ϕ (τ )(t−τ )] By applying STFT to Eq. 2, we obtain:  +∞  G(t, ω) = g(u − t)s(u)e−iω(u−t) du=A(t)eiϕ(t) g(ω − ϕ  (t)) −∞

(2)

(3)

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Step 2. From the equation above, it can be observed that the STFT of the signal (1) is composed of a series of time-frequency coefficients, where each coefficient represents a specific mode of the signal with a certain instantaneous amplitude and phase. The frequency components of the coefficients decrease as the distance from the instantaneous frequency trajectory increases. Additionally, the instantaneous phase of the coefficients is equivalent to the instantaneous phase of the original signal. Using this property, we can calculate the derivative of G(t,ω) with respect to time τ. 

∂t G(t, ω) = ∂t (A(t)eiϕ(t) g(ω − ϕ  (t))) = G(t, ω)iϕ  (t)

(4)

The estimation of instantaneous frequency can be expressed as: 

ω(t, ω) =

∂t G(t, ω) iG(t, ω)

(5)

Step 3. Since the estimated instantaneous frequency value can be regarded as an approximation of the true instantaneous frequency of the signal, the FSST can be expressed as follows:  +∞  Ts(t, η) = G(t, ω)δ(η − ω(t, ω))d ω (6) −∞

Step 4. Since synchronous compression only reallocates operators for compression in the frequency domain without any information loss, the FSST theoretically allows for perfect signal reconstruction.  +∞  +∞  +∞ Ts(t, η)d η = G(t, ω)δ(η − ω(t, ˆ ω))d ωd η = 2π g(0)s(t) (7) −∞

−∞

−∞

2.2 Principle of Improved Ridge Wave Extraction To reduce computational burden, we divide the time-frequency plane composed of K mode signals into F sub-time-frequency planes [11]. We select local maxima as the starting points from each individual sub-time-frequency plane. After screening multiple instantaneous frequency trajectories, it is necessary to select the optimal instantaneous frequency trajectory based on the time-frequency energy from these trajectories. Finally, based on the FSST equation derivation, the signal reconstruction can be performed as follows: 2.3 Principle of Sparse Time-Domain Identification Step 1. The response matrix and delay matrix are constructed ⎡ ⎤ ⎤ ⎡ x1 (t2 ) x1 (t3 ) · · · x1 (tN +1 ) x1 (t1 ) x1 (t2 ) · · · x1 (tN ) ⎢ x2 (t2 ) x2 (t3 ) · · · x2 (tN +1 ) ⎥ ⎢ x2 (t1 ) x2 (t2 ) · · · x2 (tN ) ⎥ ⎢ ⎥ ⎥ ⎢

=⎢ . ⎥,  = ⎢ . ⎥ . . .. .. .. .. ⎦ ⎣ .. ⎦ ⎣ .. . . xr (t1 ) xr (t2 ) · · · xr (tN )

xr (t2 ) xr (t3 ) · · · xr (tN +1 )

(8)

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By selecting the measured data, sampled at equal time intervals t, we can obtain N + 1 data. The upper type is satisfied: = ψ and  = ψα = ψα. Step 2. There exists the following linear relationship between the two delayed matrices:  = B

(9)

Step 3. B is a Hessenberg matrix with only the last column elements unknown. To solve for the unknown elements in the last column, we can use Eq. (9) which implies:

b = . Using the least squares to find the pseudo-inverse, we can get B, which can be inferred from the upper formula: B−1 = −1 α

(10)

Step 4. Clearly, Eq. (10) represents a standard eigenvalue equation. The i-th order eigenvalue of matrix B is λi. Therefore, by obtaining the eigenvalues of matrix B, by solving the eigenvalue equation, we can obtain the frequencies fi and damping ratios ξ i corresponding to the oscillation modes of the system, expressed as follows: λi | fi = |ln 2π t (11) 1 ξi = √ 2 1+(Im(ln λi )/Re(ln λi ))

3 Experimental Validation and Results Comparison 3.1 Validation Using Synthesized Simulated Signals The sub-synchronous oscillation signal can be modeled as: x(t) =

n

Ai e−λi t cos(2π fi t + ϕi )

(12)

i=1

The sampling frequency is set at 100 Hz, and a total of 400 sampling points were taken during the signal acquisition. The waveform of the synthesized signal is shown in Fig. 1.

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Fig. 1. Time-domain waveform of a self-synthesized analog signal

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To validate the rationality of using synchronous compression Short-Time Fourier Transform (STFT) in this invention, the synthesized simulated signal is subjected to STFT, synchronous compression STFT, as well as second-order and fourth-order synchronous compression transforms. The corresponding time-frequency plots are shown in Figs. 2. 50 40

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Fig. 2. Analog signal time-frequency diagram (a) STFT result, (b) local enlargement, (c) FSST result (d) local enlargement.

From Fig. 2(a), it is evident that the time-frequency representation obtained through STFT exhibits a coarse resolution and lacks precise time-frequency localization. This limitation hinders the direct identification of frequency characteristics for the signal modes from the time-frequency plot. FSST employs synchronous compression to reaggregate the dispersed time-frequency coefficients around the true frequencies. As shown in Fig. 2(c), FSST effectively improves the blurring issue of the STFT curve, with frequencies converging at 16 Hz, 34 Hz, and 40 Hz. Applying a method with high time-frequency concentration in the time-frequency domain transformation can provide a more reliable guarantee for subsequent signal reconstruction and parameter identification. After applying FSST, the improved ridge extraction algorithm is used on the resulting time-frequency plot to find the instantaneous frequency trajectories and depict the true frequency trends. Finally, the signal is reconstructed based on the theoretical derivation of FSST. The reconstructed signals for each mode are shown in Fig. 3. 5

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Considering the significant influence of noise in practical working scenarios, it is important for the proposed method to have robustness. Therefore, tests are conducted using white noise signals with signal-to-noise ratios (SNR) of 30dB, 45dB, and 60dB, respectively (Tables 1 and 2). Table 1. Comparison of frequency identification results of FSST-STD for subsynchronous oscillations in different noise environments Model 1

Model 2

Model 3

Frequency/Hz

Error/%

Frequency/Hz

Error/%

Frequency/Hz

Error/%

60dB

16.0001

0.0006

34.0001

0.0002

39.9987

0.0033

45dB

16.0005

0.0031

34.0003

0.0008

39.9980

0.0050

30dB

16.0006

0.0037

34.0017

0.0050

39.9979

0.0052

Table 2. Comparison of damping ratio identification results of FSST-STD for subsynchronous oscillations in different noise environments Model 1

Model 2

Model 3

Damp/%

Error/%

Damp/%

Error/%

Damp/%

Error/%

60dB

0.1293

0.0077

0.0938

0.1923

0.1379

1.8313

45dB

0.1314

1.6163

0.0940

0.4059

0.1387

2.4221

30dB

0.1356

4.8643

0.0940

0.4059

0.1418

4.7113

The above results illustrate the accurate and effective parameter identification of subsynchronous oscillations in power systems using the proposed method, demonstrating its feasibility and accuracy. 3.2 Validation of Measured Data Between 2012 and 2013, the North China region experienced over 58 oscillation events, with their occurrence attributed to the interplay between Type-3 wind turbines and the 500kV series-compensated transmission lines that connect the Gu Yuan Substation to the Inner Mongolia and North China power grids. For analysis, the voltage data from the JLQ monitoring point during one of the oscillation events was selected. The recorded waveform is shown in Fig. 4(a). The sampling frequency of the PMU recording this waveform was 50 Hz, and a total of 400 data points. Figure 4(b) displays a segment of the recorded A-phase current waveform on the PCC bus. The original signal was processed using the FSST method, and the resulting timefrequency representation is shown in Fig. 5. The improved ridge extraction algorithm was employed to extract the individual component signals, enabling the reconstruction of the mode components. Finally, the

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Fig. 4. (a) Actual recorded waveform of phase A voltage at the monitoring point. (b) Waveforms of 400 sampling points in the extracted actual recorded waveform data. 25 20 15 10 5 0

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parameters of each mode component, including frequency and damping, were identified using the STD algorithm applied to each individual component signal. Table 3. Measured data identification result Oscillation mode

Frequency/Hz

Damping ratio/%

Model 1

6.5935

0.1332

Model 2

13.1059

0.0289

The results from Table 3 validate the consistency between the identification results obtained using the FSST-STD method and the reports from the State Grid Corporation of China regarding subsynchronous oscillation incidents in the local region. This validation further confirms the effectiveness of the proposed method.

4 Conclusion In this paper, a FSST-STD-based subsynchronous oscillation identification method is proposed, and the method is analyzed and validated using simulated and measured data. The FSST-STD-based oscillation identification utilizes the time-frequency aggregation of FSST and the accurate reconstruction of the improved ridge extraction method to assist the STD to accomplish the identification task. The above results demonstrate that the FSST-STD method applied to wide-area PMU measurements achieves accurate identification results and exhibits strong noise robustness, making it highly practical for engineering applications.

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Acknowledgment. This work was supported by State Grid Jilin Electric Power Co., Ltd.: Research on the key technology of evaluation and improvement of new energy carrying capacity of power grid with dynamic stability constraints (No. SGJL0000DKJS2200369).

References 1. Cheng, Y., Fan, L., Rose, J., et al.: Real-World sub-synchronous oscillation events in power grids with high penetrations of inverter-based resources. IEEE Trans. Power Syst. 38(1), 316–330 (2023) 2. Ma, N., Xie, X., He, J., et al.: Review of wide-band oscillation in renewable and power electronics highly integrated power systems. Proc. CSEE 40(15), 4720–4732 (2022) 3. Li, Y., Fan, L., Miao, Z.: Wind in weak grids: low-frequency oscillations, subsynchronous oscillations, and torsional interactions. IEEE Trans. Power Syst. 35(1), 109–118 (2022) 4. Fan, L., Miao, Z., Shah, S., et al.: Real-world 20-Hz IBR subsynchronous oscillations: signatures and mechanism analysis. IEEE Trans. Energy Convers. 37(4), 2863–2873 (2022) 5. Shair, J., Xie, X., Yang, J., et al.: Adaptive damping control of subsynchronous oscillation in DFIG-based wind farms connected to series-compensated network. IEEE Trans. Power Delivery 37(2), 1036–1049 (2022) 6. Xu, Y., Cheng, Y., Liu, H., et al.: Subsynchronous oscillation frequency extraction and oscillation source identification method based on instantaneous power. Trans. Chin. Electrotechnical Soc. 38(11), 2894–2907 (2023). (in Chinese) 7. Wu, X., Chen, X., Lu, W., et al.: Review of detection and online localization technology of sub-synchronous oscillation in power system. Electr. Power Autom. Equip. 40(9), 129–141 (2020). (in Chinese) 8. Estevez, P.G., Marchi, P., Galarza, C., et al.: Non-stationary power system forced oscillation analysis using synchrosqueezing transform. IEEE Trans. Power Syst. 36(2), 1583–1593 (2021) 9. Ma, J., Liu, F., Wu, M., et al.: Wind farm sub-synchronous oscillation mode identification based on wavelet decomposition of ambient noise signals. Power Syst. Technol. 43(4), 1294– 1300 (2019). (in Chinese) 10. Yu, G., Wang, Z., Zhao, P.: Multisynchrosqueezing transform. IEEE Trans. Industr. Electron. 66(7), 5441–5455 (2019) 11. Meignen, S., Pham, D.-H., McLaughlin, S.: On demodulation, ridge detection, and synchrosqueezing for multicomponent signals. IEEE Trans. Sig. Process. 65(8), 2093–2103 (2017)

Induction Motor Fault Diagnosis Based on SSA-SVM Manqiang Liu(B) and Jie Wu Lanzhou University of Technology University, Lanzhou 730000, China [email protected]

Abstract. In response to the problem of low fault identification rate of induction motor, An induction motor fault diagnosis method based on the combination of fast overall average empirical modal decomposition (FEEMD) and support vector machine (SSA-SVM) optimized by sparrow search algorithm is proposed. First, the stator current is decomposed into intrinsic modal components (IMFs) of sequentially decreasing frequency by FEEMD, and then the IMF components with larger correlation coefficients are selected by correlation coefficient method and the energy entropy and sample entropy are calculated as the eigenvectors, which are then inputted into the SSA-SVM model in order to receive the diagnosis results. The results show that the fault diagnosis accuracy of SSA-SVM model reaches 96.7%, which has higher accuracy and shorter time compared with the two models of Grey Wolf Algorithm (GWO) optimized SVM and Particle Swarm Algorithm (PSO) optimized SVM, which verifies that the method is a reliable method for fault diagnosis of induction motors. Keywords: Sparrow Search Algorithm · Support Vector Machine · Induction Motor

1 Introduction Induction motors are widely used field through their simple structure, easy maintenance and reliable operation. Induction motors work in harsh environments and frequent startups lead to failures. Common faults of induction motors include turn-to-turn shortcircuit, rotor breakage, air gap eccentricity, etc. If the fault is not detected in time, it will further aggravate. When the motor failure occurs if not found in time, the fault will be further aggravated, resulting in serious consequences. Early state detection of induction motors to detect abnormalities in time is of great practical significance [1]. Support vector machine (SVM), for monitored learning, can effectively dissolve the problem of classification of the data in the field of pattern recognition and is widely used for fault identification [2, 3]. Huang Yufei et al. [4] A wind turbine gearbox fault diagnosis method will be the basis for the proposal of the principal component regression analysis into combination with SVM, which has a better classification effect. But, the performance of SVM is limited by selecting kernel function parameters and penalty factors, so the optimization of its parameters is crucial. Agasthian A et al. [5] optimize the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 401–409, 2024. https://doi.org/10.1007/978-981-97-1064-5_44

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SVM penalty factors and kernel function parameters through cuckoo search algorithm, effectively improve the model diagnostic accuracy, and realize the accurate diagnosis of wind turbine gearbox faults. Wu Zhenghao et al. [6] used a method for fault diagnosis based on the following the variational modal decomposition and gray wolf optimization SVM for planetary gearbox fault identification, and achieved good diagnostic results. Qiu haifeng et al. [7] proposed to combine SVM and bacterial foraging algorithm for power transformer fault diagnosis, improvement of diagnosis accuracy. Wang et al. [8] proposed optimization of SVM parameters with particle group optimization algorithm to complete the high-speed aero-engine bearing fault diagnosis. In summary, By optimizing the parameters of SVM using intelligent algorithms can greatly improve the accuracy of SVM fault identification, and improve the reliability of fault identification. FEEMD decomposition method for stator current handling, the IMF components screened according to the correlation coefficient will be used to calculate its energy entropy sample entropy as the feature vector, and the feature vector will be input into the SSA-SVM model to get the fault diagnosis results, and the experiments have proved that the method can be effective in the identification of motor faults.

2 Sparrow Search Algorithm Optimization SVM Theory 2.1 Sparrow Search Algorithm SSA is a new optimization algorithm for population intelligence that was proposed by Xue and Shen. [9] in 2020, which was proposed with reference to the foraging and anti-predatory behaviors of subjected sparrows, which can be specifically abstracted as a discoverer-follower model and incorporate a detection and warning mechanism. The mathematical model followed by the discoverer to update the location is as follows: ⎧   ⎪ −i ⎨ X t · exp , R2 < ST i α·iter max (1) Xit+1 = t ⎪ ⎩ X t + Q · L, R ≥ ST 2 i where: Xit is the position of the i-th sparrow at the t-th iteration; itermax is the maximum number of times the, iterations; α is a (0,1) random number; R2 ∈ [0, 1] is the warning value, if it reaches the warning value, it means that the sparrow population is in danger and measures need to be taken; ST ∈ [0.5, 1] is a safe value, i.e., if the sparrow population is free to move within the safe value range; L is a 1*d matrix with each element 1. The follower position update formula is as follows: ⎧  t t  ⎪ ⎨ Q · exp Xworst2−Xi , i > n 2 i t+1 (2) Xi = ⎪ ⎩ X t+1 + X t − X t+1 · A+ · L, otherwise p p i t where: Xpt+1 is the position of the optimal discoverer at the t + 1 st iteration; Xworst denotes the global worst position at the t th iteration; A is a 1 ∗ d 1*d matrix with each element of the matrix randomly assigned a value of −1 or 1.

Induction Motor Fault Diagnosis Based on SSA-SVM

The updated formula for Vigilante locations is as follows: ⎧ ⎪ ⎨ X t + β · X t − X t , fi > fg best best i t+1 Xi =   t ⎪ | ⎩ X t + K · |Xit −Xworst , fi = fg i fi −fw +ε

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(3)

where: Xbest is the current global optimal location; β is a random number that follows a standard normal distribution; K is a [−1, 1] random number expressing the direction of the sparrow’s movement and the step size; fi is the fitness of the optimal parameters for the current sparrow individual; fg is the current globally optimal fitness value; fw is the current global worst fitness value; ε is an infinitesimal quantity, avoiding zero in the denominator. 2.2 Optimizing SVM Based on SSA SVM has many unique benefits including solving small sample, non-linear and highdimensional pattern recognition, and is in widespread use in the field of fault diagnosis.SSA has the advantages of high solution accuracy, good stability, and fast convergence speed in dealing with the optimization problem. In this paper, SSA is used to optimize SVM penalty coefficient and kernel function parameters to improve the accuracy of SVM fault detection and reduce the running time of the model. In order to verify the following the superiority of the sparrow optimization algorithm the following are proposed in this paper, two test functions are selected for simulation and comparison with the PSO and GWO, and the algorithms are set with the same parameters during the test, and the test functions are shown in the following Eqs. (4) and (5): f1 (x) =

n

xi2

(4)

i=1

f2 (x) =

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|xi + 0.5|2

(5)

i

The converging curves of the three algorithms are shown in Figs. 1 and 2. From the figure, shows that SSA can quickly find the global optimum, and it has a faster rate of convergence and higher convergence precision, while the other two algorithms converge slower and fall into the local optimum.

3 SSA-SVM Asynchronous Motor Fault Diagnosis In this paper we will, the SSA-SVM method is used for fault diagnosis of squirrelcage three-phase induction motors, which consists of three main parts: stator current data acquisition, FEEMD decomposition of stator currents to extract fault features, and inputting the feature vectors into the SSA-SVM model for the identification of fault types. The fault diagnosis process is shown in Fig. 2:

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(a) The first test function

(b) The second test function

Fig. 1. Test the function convergence curve

Fig. 2. Troubleshooting flowchart

The specific steps are: (1) Build an induction motor fault simulation test bench, and collect stator current data from four states of motors: normal motor, rotor broken bar, turn-to-turn short circuit, and air gap eccentricity. (2) Perform FEEMD decomposition of the gathered stator currents, take a series of IMF components obtained from the decomposition, calculate the correlation coefficients

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between any IMF component and the original signal, and screen out the IMF features with larger correlation coefficients. (3) Calculation of energy entropy and sample entropy of the filtered IMF components to form the eigenvectors. (4) Select appropriate parameters for setting up SSA-SVM classification model, divide the feature vectors into training sentence and test sentence, and use the training kit and test set for training and testing the SSA-SVM type to ultimately obtain the fault diagnosis results of asynchronous motor.

4 Experimental Verification 4.1 Current Data Acquisition For verification of the effectiveness of the method in this document, a motor fault simulation experimental bench is constructed to collect the stator current data during the stable operation of the motor for verification. The motor fault simulation test bench is shown in Fig. 3, which mainly includes power supply, three-phase asynchronous motor, DC generator load, current transformer, data acquisition card and other parts.

Fig. 3. Motor failure simulation test bench

The experiment simulates three fault states of three-phase induction motor: stator turn-to-turn short-circuit, rotor broken bar, and mixed air gap eccentricity. The rotor broken stripes simulate the faults by turning holes in the guide strips, the turn-to-turn short circuits simulate the faults by drawing out a tap in the stator winding and connecting a resistor in series with the tap, and the mixed air gap eccentricity simulates the faults by changing the type of the bearings and installing eccentric bushings. The sampling frequency is 5 kHz, sampling time is 60 s, and the number of stator current points is 300000 when the motor is running at rated load data points.

5 Fault Feature Extraction The fast overall average empirical modal (FEEMD) decomposition optimizes the stopping criterion criterion, shortens the time by reducing the number of screening [10], improves the feature extraction efficiency, and can better extract the fault Induction

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motor stator current characteristics. Information entropy, as a measure of the degree of signal uncertainty, can reflect the change of stator current under different states of the motor, energy entropy, as a feature extraction method [11], can effectively reveal the change of signal characteristics from the perspective of energy change, sample entropy is a time series complexity measure [12], this paper combines the FEEMD decomposition method with the energy entropy sample entropy for the stator current of the motor. Fault feature extraction. Due to the limitation of space, this paper takes the rotor broken bar data as an example to carry out FEEMD decomposition, the amplitude of the white noise is 0.2 times that of the original signal, and the number of decompositions is N = 100. The results are shown in Fig. 4:

Fig. 4. FEEMD Decomposition chart

As shown in the figure above, a series of IMF components are generated after the motor current data is decomposed by FEEMD method, although FEEMD method can improve the phenomenon of modal aliasing, there still exists some IMFs overlapping with each other after decomposition, in order to avoid the interference of modal aliasing when extracting the fault characteristics, the Pearson’s correlation coefficients of the individual IMF components with originals are usually used to determine whether the IMF components are valid or not. The following table lists the time-domain correlation coefficients between individual IMF constructs as well as the original current after the FEEMD disintegrating of one of the current signals of each state motor, and the specific values is presented in Table 1. According to the correlation coefficient, noise components can be effectively identified, usually the smaller the correlation coefficient between the IMF component and the original signal, the higher the possibility that the component is a noise component. When extracting noise features, the components with correlation coefficients less than 0.1 times the maximum coefficient are eliminated. Table 2 shows that the maximum

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Table 1. Correlation coefficients between each state signal and the original signal State of motor

IMF component 2

3

4

5

6

7

Normal motor

0.0074

0.1607

0.9995

0.8773

0.1497

0.0599

Rotor broken strip

0.0069

0.1765

0.9996

0.9126

0.1036

0.0324

Short circuit between turns

0.0148

0.1934

0.9991

0.8742

0.1098

0.0223

Air gap eccentricity

0.0202

0.2316

0.999

0.8766

0.1442

0.0363

coefficient of each state of the motor signal is about 0.999, and the correlation coefficients of the decomposed three, four, five and six components in each state are all greater than 0. 099, so the above four components are selected to calculate the energy entropy and sample entropy to form an 8-dimensional feature vector.

6 Fault Feature Extraction For each of the four state motors, 100 groups of data are extracted, totaling 400 groups of data, each of which is an 8-dimensional vector. A total of 280 groups of 70 groups are randomly selected from thedata of each state motor as training samples, and the remaining 120 groups of data are used as test samples. During training, the normal motor signal is selected as label 1, the rotor broken bar fault signal as label 2, the stator turn-to-turn short-circuit fault signal as label 3, and the air gap eccentricity fault signal as label 4. The number of wolf packs in the SSA-SVM model is configured as 20, and the number of iterations to be completed is 100, with fivefold cross-validation, and the search range of the penalty coefficient C and the kernel function parameter g are both between 0.01 and 100. The fitness curves of the SVM parameter search are shown in Fig. 5 above, and the test set classification results of the SSA-SVM model are shown in Fig. 6.

Fig. 5. Adaptation curve

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Fig. 6. SSA-SVM test set classification

Meanwhile, to demonstrate the superiority of the SSA-SVM model in identifying engine faults, it is compared with two models, GWO-SVM and PSO-SVM, with the same parameter settings of the three models. The obtained detection the table shows the results below: Table 2. Three model identification results Classification Accuracy/% Time/s method Normal state Rotor broken Short circuit Air gap Average Strip between turns eccentricity SSA-SVM

100

93.3

93.3

100

96.7

6.02

GWO-SVM

100

83.3

93.3

90.0

92.5

10.89

PSO-SVM

100

76.7

90

96.7

90.8

20.83

Table 2 compares the classification accuracy of the three fault identification models, and from the identification results, it can be seen that the SSA-SVM fault identification accuracy is the highest at 96.7%, and the SSA-SVM model not only has the highest diagnostic accuracy, but also has the shortest running time compared to the other two models, which verifies the conclusion that the SSA has the best optimisation performance among the three algorithms, and proves the effectiveness and feasibility of the SSA-SVM model in electric motor fault diagnosis.

7 Conclude Aiming at the problem that the fault identification accuracy of induction motor is not high, this paper proposes a fault diagnosis method combining FEEMD and SSA-SVM. Firstly, the stator current during stable operation is decomposed by the FEEMD algorithm, and

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then the energy entropy and sample entropy are calculated as feature vectors by selecting the effective IMF components according to the correlation coefficients, and inputted into the SSA-SVM model for fault identification.The experimental results show that this diagnostic method has a certain degree of superiority and higher accuracy compared with the GWO-SVM and PSO-SVM methods. Acknowledgments. This work was supported by the National Natural Science Foundation of China, grant number 62203196.

References 1. Li, R.Y., Liu, F., Liang, L., et al.: Fault identification of broken rotor bars the variable frequency AC motor based on parameter optimized variational mode decomposition. Trans. China Electrotechnology Soc. 36(18), 3922–3933 (2021). (in Chinese) 2. Chen, P., Yuan, L., He, Y., et al.: An improced SVM classifier based on double chains quantum geneticalgorithm and its application in analogue circuit diagnosis. Neurocomputing 211, 202–211 (2016) 3. Shi, L.P., Wang, P.P., Hu, Y.J., et al.: Broken rotor fault diagnosis of induction motor based on bare-bone particle swarm optimization and support vector machine. Trans. China Electrotechnology Soc. 29(01), 147–155 (2014). (in Chinese) 4. Huang, Y.F., Shi, X.F., He, S.Z.: A wind power gearbox fault diagnosis method based on principal component analysis and support vector machine. Therm. Power Eng. 37(10), 175– 181 (2022). (in Chinese) 5. Agasthian, A., Pamula, R., Kumaraswamidhas, L.A.: Fault classificationand detection in wind turbine using Cuckoo-optimized support vector machine. Neural Comput. Appl. 31(5), 1503–1511 (2019) 6. Wu, Z.H., Bai, H.J., Yan, H., et al.: Gearbox fault diagnosis based on variational state decomposition and gray wolf optimization support vector machine. Sci. Technol. Eng. 23(16), 6881–6888 (2023). (in Chinese) 7. Qiu, H.F., Su, N., Tian, S.L.: Research on the application of improved support vector machine in power transformer fault diagnions. Electr. Measure. Instrum. 59(11), 48–53 (2022). (in Chinese) 8. Wang, B.J., Zhang, X.L., Sun, C., et al.: A quantitative intelligent diagnosis method for early weak fault of aviation high-speed bearings. ISA Trans. 93, 370–383 (2019) 9. Xue, J., Shen, B.: A novel swarm intelligence optimization approach: sparrow search algorithm. Syst. Sci. Control Eng. 8(1), 22–34 (2020) 10. Wang, Y.H., Yeh, C.H., Young, H.W.V., et al.: On the computational complexity of the empirical mode decomposition algorithm. Phys. Stat. Mech. Appl. 400(2), 159–167 (2014) 11. Yang, Z.S., Kong, C.R., Rong, X., et al.: Fault diagnosis of mining asynchronous motor based on EEMD energy entropy and ANN. Micro Motor. 54(08), 23–27+61 (2021). (in Chinese) 12. Huang, X.H., Tian, K.C., Rong, X., et al.: Fault diagnosis method of asynchronous motor under variable frequency environment. Mach. Tools Hydraulics 50(18), 165–171 (2022). (in Chinese)

Study on Design and Feasibility of Acrylic-Based Repair Liquid for Buffer Layer Ablation Failure Mengdi Qian1 , Shiyi Zhou1 , Jing Cai1 , Yongli Wang1 , Wei Guo1 , and Zhou Ge2(B) 1 State Grid Beijing Electric Power Research Institute, Beijing 100075, China 2 Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China

[email protected]

Abstract. In recent years, the frequent occurrence of high-voltage cable buffer layer ablation faults seriously threatens the safe and stable operation of the power system. In order to eliminate the hidden danger of high-voltage cable ablation, a kind of buffer layer ablation fault repair liquid with acrylic resin as the matrix was designed in this paper. The influence of the repair liquid on the electrochemical corrosion of aluminum sheath was analyzed, and the application performance of the repair liquid was tested. The results shown that the repair liquid prepared with acrylic resin as the matrix, ethyl acetate as the solvent, and carbon black as the conductive filler adhered well to the buffer layer. In addition, the repair liquid formed an acrylic resin-carbon black coating in the ablative buffer layer. The corrosion current density of aluminum in the mixed liquid of water-blocking powder and acrylic resin was about 9.72 × 10–4 µA/cm2 . Therefore, the acrylicbased repair liquid did not cause new electrochemical corrosion problems in a short time after injection into the cable. The repair liquid, at low viscosity, was able to reduce the volume resistivity of the ablative buffer layer, and cured quickly at a certain temperature by evaporating. The study provided a reference for the repair of high voltage cable ablation fault. Keywords: High voltage cable · buffer layer ablation · acrylic resin · electrochemical

1 Introduction With economic development and urbanization, the demand for high-voltage cables is increasing year by year. High-voltage cross-linked polyethylene (XLPE) insulated cables, which have the advantages of excellent performance, mature manufacturing process, and convenient installation and maintenance, had been widely used in the power transmission system, and they are one of the core equipment in the construction of urban power grids [1]. The reliable operation of high-voltage cables is crucial for maintaining the safety and stability of power grids and ensuring the normal operation of urban functions [2]. In order to maintain the reliable operation of high-voltage cables, the discovery and elimination of hidden dangers and failures of high-voltage cables in the process of long-term operation have become a common concern of researchers. Particularly, high-voltage XLPE cable buffer layer ablation faults are currently the focus of attention. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 410–419, 2024. https://doi.org/10.1007/978-981-97-1064-5_45

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In recent years, high-voltage cable body breakdown accidents due to water-resistant buffer layer ablation faults have occurred frequently in major cities such as Beijing, Shanghai, Guangzhou, etc., which has become one of the main hidden dangers threatening the safe and stable operation of high-voltage cables [3–5]. The main performance of high-voltage cable buffer layer ablation faults include: buffer layer surface fiber damage, and accompanied by a large number of white high-resistance powder generation, part of the region appeared the ablation hole, the buffer layer resistance abnormally increased; in the aluminum sheath and the buffer layer on the contact surface, the aluminum sheath inside the valley of the white powder adherence and the existence of corrosion traces; corresponding to the area of ablation, the insulation shielding shows traces of white spots and there are traces of damage to the insulation shield layer after the insulation shield layer in the severely ablated area [3, 4]. According to statistics, most of the faulty cables are corrugated aluminum sheathed high-voltage cables, and the service time is much lower than design service life [5]. At present, there are still many corrugated aluminumsheathed high-voltage cables in operation, and there are plenty of latent ablation faults unexposed, which is a serious safety hazard and increases the operation and maintenance cost. Therefore, the study of high-voltage cable buffer layer ablation fault repair technology, to eliminate ablation fault hidden danger, ensure the safe operation of high-voltage XLPE cable and reduce operation and maintenance costs is of great significance. Researchers have initially carried out research on repair techniques for ablation defects in the buffer layer of high-voltage cables. The current study mainly takes to the cable buffer layer injected into the conductive powder or conductive liquid method, to restore the conductive properties of the buffer layer. Song Pengxian et al. [6] proposed a graphite powder injection based XLPE cable buffer layer repair device and repair method, using high-pressure airflow to carry graphite powder injected into the crosslinked polyethylene cable buffer layer, so that the resistivity decreased by 9 orders of magnitude, the dielectric properties have changed significantly. Chen Peiyun et al. [7] proposed a liquid repair agent for the ablation defects of water-resistant buffer layer as well as a repair liquid filling device, and the main components of the liquid repair agent were polydimethylsiloxane, graphite, silica, and silane coupling agent. The liquid repair agent effectively reduces the overall resistance between the aluminum sheath and the shielding layer. Huang Jasheng et al. [8] prepared a curable conductive repair fluid for cable buffer layer ablation faults by using a two-component AB-added silica gel as a substrate filled with suitable conductive nano-fillers. However, it is difficult for the powder to be firmly attached to the buffer layer, and the liquid may cause electrochemical corrosion of the aluminum sheath. Although the current repair method realizes the repair of the conductivity of the buffer layer, the reliability of the repair of ablation faults has not been effectively verified. In this paper, an acrylic-based high-voltage cable buffer layer ablation fault repair liquid is designed with acrylic resin as the matrix and filled with conductive carbon black. Combined with electrochemical workstation testing, the electrochemical corrosion of the repair fluid on the aluminum sheath was analyzed. Repair experiments were carried out using the repair liquid on the actual faulty cable disassembled ablative buffer layer, to verify the repair effect of the repair liquid on the ablative buffer layer, and to study the effect of different ratios of the repair liquid on the performance of the repair liquid. The

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study proved the feasibility of high-voltage cable ablation fault repair technology, which provides support for the development of high-voltage cable ablation fault repair work.

2 Experimental Content 2.1 Buffer Layer Repair Experiments Ablative buffer layer specimen is obtained from the actual cable disassembly, the ablative buffer layer is placed in a constant temperature drying cabinet for 24 h, the temperature is 25 °C, after removing for made into a round piece of ablative buffer layer specimen, the diameter of 100 mm. The ablative buffer layer will be immersed in different ratios of the repair liquid, to be sufficiently moistened, and then taken out into the drying of 50 °C oven to make the repair of buffer layer specimen. 2.2 Microcosmic Characterization Optical microscopy (OM) was used to represent the change in microtopography before and after buffer repair. 2.3 Electrochemical Corrosion Analysis A PARSTAT MS electrochemical workstation was used for electrochemical testing. In a standard three-electrode system electrolytic cell, the auxiliary electrode was a platinum (Pt) electrode, the reference electrode was a saturated calomel electrode (SCE) and the working electrode was a 1060 aluminum sheet. The electrolyte used was a water-resistant powder-acrylic resin solution. The open-circuit potential test was carried out until the open-circuit potential stabilized, followed by dynamic potential polarization curve test with a scan rate of 1 mV/s and a potential scan range of −400 mv to −1400 mv. The polarization curves were analyzed at the end of the test. 2.4 Buffer Layer Resistivity Testing The volume resistivity of the buffer layer was tested according to the method specified in JB/T 10259. The test apparatus includes brass rod electrode (weight 2 kg, diameter 50 mm); brass plate electrode (100 mm × 100 mm × 10 mm); multimeter; and rubber cushion (300 mm × 300 mm). During the test, the specimen was placed on the copper plate electrode, the copper rod electrode was pressed on the specimen, and a 4.5 V DC voltage was applied between the two electrodes, and the volume resistance value was read by a multimeter after 1 min, and then the volume resistivity of the buffer layer was calculated by combining the electrode area with the buffer layer thickness. The average value of 3 valid data for each specimen was taken as the measurement result. 2.5 Repair Liquid Viscosity Test The dynamic viscosity of the liquids was determined using a rotational viscometer (NDJ-8S) with a measurement error of ± 2.0% and a measurement speed of 60 r·min−1 .

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2.6 Solvent Evaporation Time Test Place the specimens soaked in the repair liquid in a constant temperature oven, remove them every 5 min, weigh the mass of the buffer layer with a precision balance, and record the evaporation time when the mass remains unchanged. Repeat the test 5 times for each group of specimens and take the average value as the test result.

3 Design of Repair Liquid The buffer layer is located between the wrinkled aluminum sheath and the insulation shield, which is a structure designed to maintain the electrical contact between the wrinkled aluminum sheath and the insulation shield, weaken the distribution of electric field strength, longitudinal water resistance, and mechanical buffer. The mechanism of buffer layer ablation failure is still inconclusive, and existing studies have proposed two causes of ablation failure, namely, current thermal effect ablation and partial discharge ablation [9]. In the model of current thermal effect-induced ablation, the thermal effect of cable capacitive current or circulating current in the crumpled aluminum sheath of the cable leads to a significant increase in the temperature of the buffer layer, the conductive fibers of the buffer layer fuse at high temperatures, and the resistance of the buffer layer rises [10, 11]. In the model of local discharge-induced ablation, the buffer layer is subjected to moisture, the water-resistant powder absorbs water and precipitates, and the aluminum sheath undergoes electrochemical corrosion, which generates a white powdery highresistance substance, forming a white spot in the contact area between the buffer layer and the trough of the crumpled aluminum sheath, and destroying the conductive channel inside the buffer layer. The local resistance of the buffer layer increases significantly, resulting in the formation of suspended potentials between the insulation shielding layer and the aluminum sheath, triggering partial discharges [12]. The decrease in electrical contact capability between the buffer layer and the aluminum sheath is the main reason for the development of buffer layer ablation faults. Buffer layer ablation continues to accumulate to a certain extent, will further damage the insulation shielding layer and the main insulation, and ultimately lead to cable breakdown. In order to prevent the further development of the ablation fault, in the early stage of the ablation fault, by injecting the conductive repair liquid into the buffer layer of the ablation cable, the conductive ability of the buffer layer can be restored, thus eliminating the suspended potential, and repairing the ablation fault. In the manufacturing process of the buffer layer, aqueous acrylic resin emulsions are used as the substrate of the semiconductive adhesive on the composition of the buffer layer of fluffy cotton and nonwoven fabrics for ginning and dyeing, after drying, the formation of a conductive coating on the surface of the fibers, so that the buffer layer has a conductive performance [13]. Acrylic resin, as a widely used coating, has a bonding and film-forming effect, the polyester fibers of the buffer layer have a good adhesion ability, to which the conductive filler can be doped to form a conductive coating on the surface of the buffer layer fibers. Therefore, in this paper, an acrylic resin-based restorative was prepared. The preparation of acrylic-based repair liquid and buffer layer repair process is shown in Fig. 1. The water-based acrylic resin emulsion contains water, which can be fully dried

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Fig. 1. Preparation of acrylic-based restorative liquid and buffer layer repair process

during the buffer layer manufacturing process, but it is difficult to be completely removed during the ablative buffer layer repair process. Therefore, the repair liquid uses highly volatile ethyl acetate as the solvent. The acrylic resin is dissolved in it to form a solution, and the acrylic resin used in the repair liquid takes methyl methacrylate as the main body to maintain the hardness of the coating, and copolymerizes with the appropriate amount of ethyl acrylate, butyl acrylate, etc. to make the coating flexible. Carbon black as a conductive filler, through the dispersant uniformly dispersed in the liquid. The repair liquid is injected between the wrinkled aluminum sheath and the shielding layer, the repair liquid impregnates the buffer layer, and after the volatilization of ethyl acetate, the molecular chains of the acrylic resin entangle with each other to form a film on the surface of the fibers of the buffer layer, and attach the carbon black to the fibers, forming a composite conductive coating of acrylic resin - carbon black, and the conductivity of the buffer layer is repaired. The cross-sectional morphology of the buffer layer before and after repair was observed using an optical microscope. The cross-sectional morphology of the ablated buffer layer under optical microscope is shown in Fig. 2 (a). The fibers of the ablated buffer layer were fluffy and there were traces of fiber fusion; the carbon black coating was unevenly distributed, and the carbon black coating on the surface of some polyester fibers was detached; and there were white flocculent particles in the fibers. As shown in Fig. 2 (b), the repair buffer layer was repaired by injecting repair liquid, and the internal fibers were covered by acrylic resin-carbon black coating.

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(a) ablation buffer layer

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(b) repair buffer layer

Fig. 2. Cross-sectional morphology of buffer layer under optical microscope

4 Effect of Repair Liquid on Electrochemical Corrosion Electrochemical corrosion of aluminum sheaths to generate high resistance substances is considered to be one of the main causes of buffer layer burnout failures. Therefore, it should be avoided to cause new electrochemical corrosion after the repair liquid is injected. The cross-linked sodium polyacrylate water-resistant powder in the buffer layer is a polyanion electrolyte. When sodium polyacrylate is dissolved in water, it dissociates to produce polymer ions and many low molecular ions [9]. The repulsion of the anions on the backbone of the main chain network generates the driving force for network expansion, causing it to swell in volume. The concentration of cations inside the network is greater than outside, generating osmotic pressure inside and outside the network, and due to the fact that the polyelectrolyte itself has highly hydrophilic groups, water can enter the network in large quantities in a very short period of time. Due to the further penetration of water, some cations from the molecular chain to the water diffusion, resulting in a decrease in osmotic pressure, which makes the polymer chain with a net charge, due to electrostatic repulsion, caused by the expansion of the polymer chain, the polymer chain expansion leads to the elasticity of the molecular network contraction, which several roles to reach an equilibrium when the water absorption is completed. Therefore, sodium polyacrylate will ionize a large number of free-migrating Na+ and OH− ions after absorbing water, and the aluminum sheath, electrolyte liquid, and semiconducting fibers in the buffer layer will constitute an electrochemical battery, and electrochemical corrosion of the aluminum sheath will occur, and the equation of the reaction is as follows [9]: NaPA + H2 O ↔ HPA + Na+ + OH−

(1)

Al3+ + 3OH− = Al(OH)3 ↓

(2)

2Al3+ + 3H2 O + 6e− = Al2 O3 ↓ + 3H2 ↑

(3)

2H+ + 2e− = H2 ↑

(4)

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The reaction generates high resistance substances such as Al2 O3 and Al(OH)3 , which block the conductive path of the buffer layer and form a suspension potential. Therefore, new electrochemical corrosion caused by the repair liquid should be avoided. It is generally believed that sodium polyacrylate is soluble in water and polar solvents, and ethyl acetate is a moderately polar organic solvent. Excess aluminum sodium polyacrylate was dissolved in ethyl acetate liquid of acrylic resin to form a mixed liquid of water-blocking powder-acrylic resin, which was used as an electrolyte liquid, and the polarization curve of the kinetic potential of the aluminum in which was obtained by using an electrochemical workstation test as shown in Fig. 3.

Fig. 3. Dynamic potential polarization curve

The Tafel straight line extrapolation method was used to solve the self-corrosion current icorr, when the polarization potential is large enough, two straight lines tangent to the strong polarization zone can be obtained by Tafel extrapolation method. The value of anodic or cathodic current at the intersection point is the value of corrosion current, and the self-corrosion current density of aluminum in the water-blocking powder-acrylic resin liquid was found to be 9.72 × 10−4 µA/cm2 , which is a very small value, and it can be assumed that the repair liquid will not have an effect on the electrochemical corrosion.

5 Application Properties of Repair Liquid In the acrylic-based repair fluid on the buffer layer ablation fault repair process, need to pay attention to the following several properties: 1) repair liquid on the buffer layer conductivity repair ability. The buffer layer needs to have a lower volume resistivity after repair. This is a measure of the main performance of the repair effect of the ablation fault. 2) the viscosity of the repair fluid itself. In the actual repair work, the buffer layer is tightly filled in the wrinkled aluminum sheath and shielding layer between the need for low viscosity conductive repair fluid, in order to be able to infuse into the buffer layer. 3) short curing time. Repair liquid solvent needs to have a short evaporation time, can be cured in a relatively short period of time in the buffer layer for the conductive coating. In the repair liquid solvent volatilization will form acrylic resin - carbon black conductive coating, in which carbon black as a conductive filler, carbon black and acrylic resin ratio is the main factor affecting the performance of the coating. The variation of volume resistivity of the repair buffer layer with the mass fraction of carbon black in the

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coating is shown in Fig. 4. The volume resistivity of the repaired buffer layer gradually decreased with the increase of the mass fraction of carbon black in the coating. When the mass fraction of carbon black in the coating is between 5 wt% and 10 wt%, the volume resistivity of the repaired buffer layer samples decreases rapidly; when the mass fraction of carbon black is between 10 wt% and 20 wt%, the decrease tends to slow down; when the mass fraction of carbon black is more than 20 wt%, the volume resistivity tends to stabilize. This phenomenon is in line with the “seepage effect”, when the critical value of seepage is reached, the conductive particles are in contact with each other to form a conductive network, and the resistance of the coating decreases significantly. After the formation of a complete conductive network in the coating, the resistance of the coating is mainly determined by the conductivity of the conductive carbon black itself, at this time to increase the content of carbon black, the conductive properties of the coating had less impact. At the same time, when the proportion of carbon black exceeds 20 wt%, the volume resistivity of the repair buffer layer meets the standard of JB/T 10259, and meets the repair requirements. Therefore, the subsequent experiments are prepared with this ratio.

Fig. 4. Effect of carbon black mass fraction in coating on resistivity of repaired buffer layer

The solvent in the repair liquid is used to dissolve the acrylic resin matrix and also serves as a bridge between the acrylic resin matrix and the conductive filler. As shown in Fig. 5 (a), the viscosity of the repair liquid gradually decreases as the proportion of solvent in the repair liquid increases. The lower viscosity of the repair liquid is favorable for the actual repair work to inject the repair liquid into the cable. However, with the increase of the solvent mass fraction in the repair liquid, the repair effect of the repair liquid on the electrical conductivity of the buffer layer decreased slightly. As shown in Fig. 5 (b), the volume resistivity of the repaired buffer layer gradually increased with the increase of the solvent fraction in the repair liquid. As the amount of solvent is too much to reduce the solid content of the repair liquid, the viscosity of the repair liquid decreases at the same time, reducing the conductivity of the coating. At the same time, the increase of solvent in the repair liquid will prolong the volatilization time, as shown in Fig. 5 (c). However, ethyl acetate is a highly volatile organic solvent, so increasing the ambient temperature can significantly shorten the volatilization time of the solvent, as shown in Fig. 5 (d).

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(a) Effect of solvent ratio on the viscosity

(c) Effect of solvent ratio on evaporation time

(b) Effect of solvent ratio on volume resistivity

(d) evaporation time at different temperatures

Fig. 5. Effect of repair fluid ratios on performance (20 wt% carbon black in the solid)

In summary, acrylic-based ablative failure repair fluids with reduced resistance of the ablative buffer layer, fast evaporation curing, and low viscosity can be produced with different ratios of carbon black, acrylic resin, and solvent.

6 Conclusion The main conclusions of this paper are as follows. (1) A high voltage cable buffer layer ablation fault repair liquid was prepared using acrylic resin as the matrix, ethyl acetate as the solvent and carbon black as the conduc-tive filler. The acrylic resin matrix has good adhesion to the buffer layer and can form an acrylic resin-carbon black coating in the ablative buffer layer. (2) The self-corrosion current density of aluminum in the water-blocking powder-acrylic resin mixed solution was extremely low, about 9.72×10−4 µA/cm2 , so the acrylicbased repair solution would not cause new electrochemical corrosion problems within a short time after injection into the cables, and it was feasible for practical application. (3) The application performance of the repair solution was changed by adjusting the ratio of carbon black, acrylic resin and solvent. The repair solution can reduce the volume resistivity of the ablative buffer layer to meet the industry standard; fast volatilization and curing at a certain temperature; and low viscosity. The study provides a reference for the practical application of the restoration fluid.

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References 1. Chen, W., Zhou, M., Yan, X., Li, Z., Lin, X.: Study on electromagnetic-fluid-temperature multiphysics field coupling model for drum of mine cable winding truck. CES Trans. Electr. Mach. Syst. 5(2), 133–142 (2021) 2. Wei, G., et al.: Simulation of the critical time of XLPE cable insulation. Electr. Power Eng. Technol. 42(01), 178–184 (2023). (in chinese) 3. Yekun, M., et al.: Dynamic conductive characteristics and mechanism of high-voltage XLPE cable buffer band. Electr. Power Eng. Technol. 41(6), 163–171 (2022). (in chinese) 4. Ren, Z., et al.: The influence of force inhomogeneity on the development process of high voltage cable buffer fault. Insul. Mater., 1–7. (in chinese) 5. Chen, Y., et al.: Failure investigation of buffer layers in high-voltage XLPE cables. Eng. Fail. Anal. 113, 104546 (2020) 6. Song, P., et al.: Repair device and repair method of XLPE cable buffer layer based on graphite powder injection (2022). (in chinese) 7. Chen, P., et al.: The liquid repair agent and its preparation method, filling equipment and filling method of high voltage and ultra-high voltage cables (2022). (in chinese) 8. Huang, J., et al.: A conductive repair solution used for ablation failure of cable buffer layer and its preparation method and application (2023). (in chinese) 9. Chen, Y., et al.: Hydrogen evolution and electromigration in the corrosion of aluminium metal sheath inside high-voltage cables. High Voltage 7(2), 260–268 (2022) 10. Chen, W., et al.: Study on electromagnetic-fluid-temperature multiphysics field coupling model for drum of mine cable winding truck. CES Trans. Electr. Mach. Syst. 5(2), 133–142 (2021) 11. Wen, H., et al.: Electromagnetic-thermal coupled analyses and joint optimisation of electrically-excited flux-switching linear machines. CES Trans. Electr. Mach. Syst. 6(4), 368–377 (2022) 12. Tang, J., Wang, L.: Research on the discharge between high - voltage cable metal sheath and insulation shield. IEEE (2019) 13. Yang, H., Yu, F.: Semi-conductive adhesive and its preparation method, semi-conductive fiber, semi-conductive copper wire shielding strip and its preparation method and cable (2020). (in chinese)

Infrared Image State Evaluation of Power Cables Based on Mask R-CNN and BP Joint Algorithm Yang Zhao1 , Yingqiang Shang1(B) , Jun Xiong1 , and Xuehan Li2 1 Beijing Electric Power Company, State Grid Cooperation China, Beijing 100022, China

[email protected] 2 Shanghai University of Electric Power, No. 2588 Changyang Road, Shanghai 200090, China

Abstract. In order to solve the problems of traditional image processing algorithms in handling precise target detection and condition monitoring of power cable, this paper proposes an improved infrared image-based condition diagnosis scenario of power cable based on Mask R-CNN and BP joint algorithm. Mask R-CNN is used to solve the problem of refined image segmentation when the background of cable infrared image is complex. And BP neural network algorithm is used to classify and identify the key features of power cable. The results show that the proposed method has a good detection effect on the operation status of cables in infrared images with an average accuracy rate of 87.63%, which presents a good solution to the problem of infrared image identification of substation equipment and its status assessment. Keywords: Power Cable · Mask R-CNN · BP Neural Network · Infrared Image · State Diagnosis

1 Introduction The power cable is widely used in electric power system as an alternative to overhead transmission line, with superior electrical and mechanical properties, and saving of occupying spaces [1–3]. However, as the cable is put into operation for an increased period, it can lead to abnormal operating conditions due to the heat generated by the current flowing through it, the laying environment, and other factors [4, 5]. The abnormal operating condition of power cables would cause power outage or fire accidents to the transmission system, leading serious economic losses to the power system. According to statistics, the temperature of cables with defects is often higher than that of cables in normal condition, and the proportion of thermal faults for power cables can reach 25%. Therefore, the accurate assessment of the cable operating condition, particular thermal state monitoring, plays a vital role in ensuring the safe operation of power equipment. When a thermal fault occurs in a cable, its manifestation is usually characterized by an abnormal change in temperature, from which the operating status of the cable can be judged [6]. To improve the intelligence level in fault detection, a lot of research on © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 420–427, 2024. https://doi.org/10.1007/978-981-97-1064-5_46

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the condition diagnosis technology based on infrared (IR) thermal imaging has been carried out. For example, Lin Ying et al. [7] used the super pixel segmentation method combined with chromaticity information for temperature anomaly region extraction, but this method only works well when the IR image background is simple. Niu Haiqing [8] et al. used Random and Fourire-Mellin transforms to extract IR image features for IR image identification of cable terminals, but did not involve the state diagnosis after extracting overheated regions. To solve the problems of unable detecting cable faults from IR images by previous research, when the image background is complex and the clustering algorithm is missing, this paper proposes a new infrared image state diagnosis method of power cables based on Mask R-CNN and BP joint algorithm. Firstly, the Mask R-CNN model improved from Faster-RCNN is proposed to realize the recognition and mask segmentation of cables in complex backgrounds for the influence of other interference information in infrared images on cable target recognition; secondly, the BP neural network is used to classify and recognize cable features; finally, the feasibility and accuracy of the method are verified in practical applications.

2 Methodology 2.1 Working Principles of Mask R-CNN Mask R-CNN is obtained by combining Faster R-CNN and classical semantic segmentation network by Kaiming He et al. Mask R-CNN not only has the segmentation speed of Faster R-CNN but also adds mask branches on top of it, which can further realize the refined mask segmentation of the target based on ensuring good recognition [9]. Mask R-CNN is mainly divided into four parts, which are: feature extraction module (ResNet50-FPN feature pyramid network), candidate region generation module (RPN region suggestion generation network), region of interest aggregation module (ROI Align) and output prediction module, and the structure of Mask R-CNN is shown in Fig. 1.

Mask

FC layers

Rol Align

Input

FC layers

bbox reg

Box Regression

FC layers

feature map

softmax

Classification

3×3 conv softmax

bbox reg

Regional proposal

Fig. 1. Structure of Mask R-CNN

Wherein the feature extraction module can be used to obtain a feature map of the input image, which contains location information and semantic information [10]. RPN

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is a network used to identify the set of target candidate regions on feature images, and the generated regions of interest are filtered using a non-maximal suppression method, which removes the regions of interest with high overlap and finally obtains the candidate ROI with high quality. ROI Align is a normalization process for different size ROIs, using bilinear interpolation to make the algorithm more accurate for localization and identification of small targets [11]. Finally, the output prediction module is used for classification, position prediction and mask generation. 2.2 Working Principles of BP Neural Network BP neural network is widely used in state diagnosis because of its self-learning ability, nonlinear mapping ability and strong fault tolerance, and is a feed-forward neural network with the input layer, hidden layer and output layer as the main structure [12, 13], and the structure is shown in Fig. 2.

W

W ij

jk

Yi

Xi

Input Layer

Hidden Layer

Output Layer

Fig. 2. Structure of BP neural network

Where X i is used as the input of the BP neural network, W ij and W jk are the connection weights before the neuron vectors in the input and hidden layers and the hidden and output layers, respectively, and Y i is used as the output of the neural network. The basic working principle of the BP neural network is that the input quantity is sent to the hidden layer through the input layer, which is processed and transmitted to the output layer to get the error between the desired output and the output before, and the error is propagated backwards along the neural network, and the weights between the network neurons are continuously corrected until the error in the output layer of the network is less than the set value or the training reaches a predetermined number of iterations. 2.3 Cable Condition Diagnosis Algorithm In this paper, we realize the recognition and refinement of mask segmentation of power cables based on Mask R-CNN to extract the fault region; by feature extraction of cable segmentation images, we use BP neural network to realize the state diagnosis of cables. The overall flow chart of this paper is shown in Fig. 3.

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Infrared image to be detected Mask R-CNN

Image preprocessing

Cable recognition and segmentation in infrared background

Feature extraction

Power cable status diagnosis

BP neural Network

Fig. 3. Power cable condition diagnosis flow chart

3 Results and Discussion 3.1 Target Recognition and Segmentation In this paper, the collected cable infrared images are organized into a dataset, and some of the cable infrared images are shown in Fig. 4, but the data samples obtained directly are small, and the data need to be data augmented to ensure the balance between the data. By processing the original images by rotating, scaling and adding and subtracting noise, the amplification results are shown in Fig. 5 and Table 1, and they are divided into training and testing sets in the ratio of 8:2 for training and testing of Mask R-CNN.

(a) Faulty joints

(b) Cable body heating

(c) Ground fault

Fig. 4. Partial cable infrared diagram

The constructed dataset is trained using Mask R-CNN, and the initial learning rate is set to 0.001, and it is trained for 30 and 50 rounds respectively, and the change curve of the loss function is shown in Fig. 6, from which it can be seen that the loss value of the network gradually decreases as the number of training increases, representing the more accurate training of the network. The loss value after 50 rounds of training is significantly lower than that of 30 rounds of training under the same conditions, and the loss value can reach 0.1192.

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Increased noise

Rotation

Brighten up

Rotati Rotation

Increased noise

Brighten up

Rotation

Increased noise

Brighten up

Fig. 5. Data Augmentation

Table 1. Number of images after data augmentation Fault Type

Number of original images

Number of amplifications

Total

Faulty joints

10

90

100

Cable body heating

10

90

100

Ground fault

10

90

100

Total

30

270

300

After iterative training of Mask R-CNN, the model was used for target segmentation tests on the images in the test set, and the segmentation results of some of the cables are shown in Fig. 7. The results show that Mask R-CNN can effectively localize, identify and segment power cables accurately and distinguish them from the feature information of complex backgrounds. 3.2 Cable Condition Diagnosis After Mask R-CNN accurately identifies and segments power cables, it is necessary to use BP neural network to diagnose their states. In this paper, we extract the feature values from the segmented cable images, use the feature values as input and the state diagnosis results as output to establish a BP neural network state diagnosis model.

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Fig. 6. Loss map

Fig. 7. Segmentation result graph

To extract the feature values and perform grayscale processing on images, the weighted average method is one of the commonly used methods. The gradient color image in RGB color gamut is reduced to a grayscale image by (1), and the floating-point calculation method is used in this paper for the calculation of: Gray = 0.299R + 0.587G + 0.114B

(1)

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where Gray represents the grayscale value, and R, G, and B represent the colors of red, green, and blue channels, respectively. Meanwhile, according to the characteristics of BP neural network algorithm, the data set is divided into training set and test set according to 7:3, 10 representative gray values are selected as the input features of BP neural network, and the BP network is trained until the error of the network output layer is less than the set value or the training reaches a predetermined number of iterations. Finally, the accuracy test of cable infrared image fault diagnosis is conducted using the test set, and the results are shown in Fig. 8.

Fig. 8. BP network algorithm prediction results

4 Conclusions In this paper, we propose infrared image condition diagnosis of power cables based on Mask RCNN and BP joint algorithm and illustrate the application of both in substation equipment condition assessment. Firstly, for the influence of other interference information in infrared images on cable target recognition, the Mask R-CNN model is proposed to realize the recognition and mask segmentation of cables in complex backgrounds; secondly, BP neural network is used to classify and recognize cable features with 87.63% state recognition accuracy, which presents a solution for the problem of infrared image recognition of substation equipment and its state assessment. Acknowledgement. This work is funded by the science and technology project from State Grid Beijing Electric Power Company on research and application of key technologies for intelligent inspection of large-scale urban cable tunnels based on panoramic lidar technology (Project No: 520246230002).

References 1. Orthon, H.: Power cable technology review. High Voltage Eng. 41(4), 1057–1067 (2015)

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2. Cui, J., et al.: Improved Faster R-CNN method and its application in recognition of cable tunnel water accumulation. Electr. Power Autom. Equipment 39(07), 219–223 (2019) 3. Zhao, J., et al.: Influence of insulation ageing on electric field distribution at interface defects of cable joints. Insul. Mater. 54(07), 67–74 (2021) 4. Huanan, W., et al.: Study on closing over-voltage simulation of 110 kV cable intermediate joint. High Voltage Apparatus 57(07), 127–134 (2021) 5. Wang, W.G., et al.: Research on the identification of UAV patrol image based on R-CNN. J. Earth Inf. Sci. 19(2), 256–263 (2017) 6. Qi, C., et al.: Infrared monitoring system for substation based on intelligent visual internet of things. Power Syst. Prot. Control 46(15), 135–141 (2018) 7. Li, Y., et al.: Convolutional-recursive network based current transformer infrared fault image diagnosis. Power Syst. Prot. Control 43(16), 87–94 (2015) 8. Niu, H.Q.,et al.: Identification of infrared images of cable terminal based on radon transform and fourier-mellin transform. J. South China Univ. Technol. 44(08), 47-52+59 (2016) 9. Wei, X.Z., et al.: Target detection method for external damage of a transmission line based on an improved mask R-CNN algorithm. Power Syst. Prot. Control 49(23), 155–162 (2021) 10. Lin, G., et al.: Multi-target detection and location of transmission line inspection image based on improved faster-RCNN. Electr. Power Autom. Equipment 39(05), 213–218 (2019) 11. Peng, Q.C., Song, Y.X.: Mask R-CNN-based object recognition and localization. J. Tsinghua Univ. 59(02), 135–141 (2019) 12. Hu, K., et al.: Fault diagnosis on clutch brake based on firefly optimization BP neural network. Forging Stamping Technol. 48(06), 124–129 (2023) 13. He, H.Y., et al.: Contamination grades recognition of insulators under different humidity using infrared image features and RBPNN. Proc. CSEE 8, 117–123 (2006)

Research on Stability of a 4-Channel Amplifier in Engineering Applications Kai Dong(B) , Xuejian Wang, Zhifei He, Guofei Teng, and Qing Lin Xi’an Aeronautics Computing Technique Research Institute, AVIC, Xi’an 710065, China [email protected]

Abstract. With the increasing application of computers, various analog signals (such as fire alarm/cabin door/fuel volume/control valve, etc.) need to be collected and calculated in the field of electromechanical control of aircraft. The conditioning circuit in these signal acquisition circuits is essential, and a large number of high-speed or low-speed amplifiers are used in the conditioning circuit. The stability of the amplifier determines whether the signal acquisition is stable, reliable, and accurate, Therefore, the stability analysis of amplifiers, as well as the gain and noise figure, are necessary factors to consider in the design of amplifier conditioning circuits. Based on these factors, an amplifier that can work stably and reliably in various harsh environments, such as gain, bandwidth, and noise, can be designed, truly reflecting the real-time changes of the input signal in the previous stage. Keywords: Amplifier · Stability · Analysis method

1 Introduction Since the concept of negative feedback was proposed, it has become the foundation of control theory. Negative feedback can improve various performance, including gain instability caused by external and environmental changes, reduction of distortion caused by component nonlinearity, frequency band changes, and impedance transformation. Especially when negative feedback is added to the operational amplifier, the advantages and effects brought by negative feedback are particularly evident. However, improper introduction of negative feedback can also cause oscillations in the system. When the system maintains a signal on the loop that is independent of the input being added, oscillation occurs. The generation of oscillation is caused by a phase shift in the loop, which changes the increased negative feedback into positive feedback. At the same time, it has enough Loop gain to keep the output oscillation without any input. Only when there is no oscillation in the circuit and it is stable [1], can negative feedback truly realize its advantages. The negative feedback system model of the amplifier is shown in Fig. 1. When the amplifier detects an input error Vd , it attempts to reduce it. However, there is a delay in the output response of the amplifier feedback back to the input through the feedback network [2]. Delay will cause the amplifier to tend to overcorrect input errors. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 428–435, 2024. https://doi.org/10.1007/978-981-97-1064-5_47

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Fig. 1. Schematic diagram of the system with unilateral Negative-feedback amplifier

If the overcorrection exceeds the original error, negative feedback will become positive feedback, and the amplitude of input error Vd will diverge, resulting in instability.

2 Stability Description 2.1 Gain Margin The stability of a system depends on the relationship between Loop gain T and frequency. For the purpose of proof, let T be at a certain frequency f−180° the phase angle is −180°. So the feedback changes from negative feedback to positive feedback, and T (jf −180° ) is a negative real number, such as −0.5, −1, −2, indicating that the feedback has changed from negative feedback to positive feedback. The following assume three main scenarios. If | T (jf −180° ) | 1, assume to change T (jf −180° ) from −1 to a more negative value, such as −1.2. This indicates that each time the signal passes through the loop, it will increase by 20% compared to the original amplitude, resulting in vibration. The vibration will continue to increase until the circuit exhibits inherent nonlinear phenomena, such as the saturation of the operational amplifier output causing T to approach −1, at which point the vibration will also tend to stabilize [3]. The gain margin provides a measure of stability. The definition is as follows: GM = 20log

1 |T(jf−180◦ )|

(2)

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GM refers to the number of decibels that can be increased √ before | T (jf −180° )| becomes unstable due to “1”. For example, when T (jf ) = 1/ 10, its GM −180° √ √ = 20 × Log10 10 = 10 dB, which is a reasonable margin; When T (jf −180° ) = 1/ 2, its GM = 3d B, this margin is very small: as long as the circuit parameters change or external environmental changes cause gain a slight change in may lead to instability [4]! Fig. 2 shows the changes in GM.

Fig. 2. Gain margin GM and Phase margin φm Graphical representation diagram

2.2 Phase Margin Another more commonly used method is to use phase to measure stability. Note that T is at the crossover frequency f x the phase angle T(jf x ). By definition, there is | T |=1 at the crossover frequency. Define Phase margin φm is the degree that can be reduced before T(jf x ) reaches −180°, leading to instability. Have φm = T(jf x )- (−180°), i.e. φm = 180◦ + T(jfx )

(3)

T(jfx ) =φm − 180◦

(4)

T(jfx ) = lexp[jφm −180◦ ] = −lexp(jφm )

(5)

obtained:

so:

euler’s theorem expansion and utilization of identities cos2 φm + sin2 φm = 1, obtained: 1 D(jfx ) = √ 2(1 − cos φm )

(6)

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Engineering generally requires systematic φm ≥ 45°, considering that there are power rise, power fall and transient conditions in the actual circuit [5], in which the change of Loop gain curve may lead to transient oscillation. In addition, due to the parasitic capacitance and PCB layout parasitic effect, this experience also considers using additional phase margin in the Loop gain bandwidth to consider the additional phase shift in the actual circuit. In addition, when φm ≤ 45°, it can cause unnecessary spikes and even oscillations in the closed-loop transmission function.

3 Stability Analysis Methods Calculate based on Fig. 3 using the return ratio method: (a) Set all input sources to zero; (b) Disconnect the output terminal of the non independent source on the right side of the circuit; (c) Applying an AC test voltage downstream of a non independent source vt ; (d) Calculate the voltage returned by the power supply vr ; (e) Obtain the negative value of T as the ratio of the return voltage to the test voltage used (referred to as the return ratio). T=

vr vt

(7)

In Fig. 3, the “X” in (a) indicates that the circuit is disconnected, while (b) modifies the circuit in (a) using a non independent voltage source to calculate the return ratio.

Fig. 3. Schematic diagram of feedback circuit for voltage gain

The Loop gain of the operational amplifier can be expressed as follows: T = aβ

(8)

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or |Tdb | = 20 log10 |T| = 20 log10 |a| − 20 log10 |1/β|

(9)

|T|db = |a|db − |1/β|db

(10)

or

The bode plot of T can be calculated through the drawing method, which is α and 1/β the difference between the respective bode plots [6]. In the return ratio analysis of operational amplifiers, the frequency curve of T is usually not directly calculated, but rather separately calculated first α and 1/β the frequency curve of T is obtained by adding these two curves together. This separation method can be considered separately α and 1/β the frequency response characteristics facilitate the analysis of factors affecting stability.

Fig. 4. Schematic diagram of Loop gain amplitude

To draw the Loop gain amplitude diagram shown in Fig. 4, first use the return ratio method to calculate the open-loop gain curve, that is a = vr /vx , next find β = vx /vt . Take its reciprocal 1/β, Then draw the graphics of |1/β|. Usually there are |β| ≤ 1v/v, i.e. |β| ≤ 0 dB, can obtain |1/β| ≥ 1v/v, then |1/β| ≥ 0 dB, the |1/β| curve is located above the 0 dB axis. Although this |1/β| curve is flat in most frequency domains, but there are usually several turning points. Its low-frequency and high-frequency Asymptote are recorded as |1/β0 | and |1/β∞ |. Finally, |T| is|a| curve and |1/β| the difference between the curves, as shown in the lower half of Fig. 4 is the |T| curve. The frequency at the intersection of two curves fx is called the crossover frequency. |T(jfx )|dB = 0dB or |T(jfx )| = 1. When f  fx , there is |T| 1, indicating that the

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closed-loop characteristic is close to ideal here; When f > fx , there is |T|dB < 0 dB, or | T | 0 (7) φ(r) = 0, r = 0 Construction of Mixed Surrogate Model The mixed surrogate model [9] is composed of weighted linear superposition of multiple meta-surrogate models, which can be expressed as ⎧ N  ⎪ ⎪ ⎪ y (x) = ωi yi (x) ⎪ ⎪ ⎨ e i=1 (8) N ⎪  ⎪ ⎪ ⎪ ωi = 1 ⎪ ⎩ s.t.



i=1

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where yˆ e is the predicted response value of the sample point corresponding to the mixed surrogate model, N is the number of meta-models of the surrogate model, ωi and yˆ i (x) are the weight coefficient and predicted response value of i th surrogate model. In this paper, the prediction sum of squares (PRESS) [9] is used as an indicator to measure the accuracy of the single metamodel. Leave-one method cross-validation is used to calculate PRESS. Assume that there are N points in the sample point set, the real model response value at sample point i is yi , the predicted value is yˆ i , and the PRESS of the j th surrogate model is Pj . Then the specific calculation can be carried out according to the following process: Step1: The surrogate model is constructed for N-1 sample points except the i th point. Step2: The i th point is taken as the prediction point of the surrogate model, and the corresponding prediction error as ei = yi − yˆ i , then the PRESS value of the

is calculated 2. e j th surrogate model is Pj = N i=1 i Step3: The weight coefficient of the j th surrogate model is calculated using the inverse proportional averaging method: ωj =

1 Pj

N

1 j=1 Pj

.

4.2 Model Accuracy Check and Improvement It is necessary to consider the accuracy of the model both globally and locally. In this paper, the coefficient of determination (R square) and root mean square error (RMSE) are used to measure the global accuracy, and mean absolute error (MAE) is used to measure local accuracy. The K-fold cross-validation method is used to check the global accuracy of the surrogate model constructed from the initial point set in a similar way to the leave-one method. 198 initial points are randomly divided into 20 disjoint subsets, each subset is taken as a test set in turn to calculate R square and RMSE. After 20 calculations, the prediction accuracy of the three surrogate models was obtained, as shown in Table 2. On the whole, the mixed surrogate model is more accurate in predicting the torque characteristics of the machine, it can maintain relatively good prediction accuracy even if the sample points are not ideal, which shows that the mixed surrogate model has better prediction stability. The mixed model can achieve better prediction effect and save the finite element simulation time. The function relationship between the torque ripple ratio and optimization variables is complex, so the accuracy of the model needs to be improved by increasing the sample points. Under the condition of uniform spatial distribution of sample points, the validation of local minima on the response surface will be helpful to better obtain the global optimal solution. In this paper, DDS algorithm [10] is used to achieve the point. The new sample points solved by the DDS algorithm are used as the test set, and the MAE values of the predicted values of the test set and the actual simulation results are calculated. The termination conditions are taken as the MAE of the test set is less than 2.5 and the average R-square of the sample point set is greater than 0.9. By adding points to the DDS algorithm, the sample size was increased from the initial 198 to 291, and the process of each round of adding points was shown in Table 3.

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Table 2. Average prediction accuracy for the three surrogate models Prediction target

Prediction model

R-square mean

RMSE mean

Average torque (N.m)

Combinatorial surrogate model

0.989

0.345

Kriging model

0.984

0.352

RBF model

0.982

0.368

Combinatorial surrogate model

0.725

5.406

Kriging model

0.669

6.057

RBF model

0.655

6.183

Torque ripple ratio (%)

Table 3. Point adding process based on DDS algorithm Number of rounds

Number of add points

MAE of the test set

R-squared of the sample point set

1

28

29.10

0.775

2

23

17.84

0.804

3

16

12.05

0.827

4

11

7.06

0.868

5

9

5.97

0.885

6

6

2.37

0.907

4.3 Multi-Objective Optimization Algorithm In this paper, a swarm intelligence heuristic algorithm: the moth-flame optimization algorithm [11] is used to solve the surrogate model. This algorithm simulates the movement of moths towards the flame to achieve iterative optimization. The position update rule of moth in this algorithm can be expressed as  S Mi , Fj = Dij · ebt · cos(2π t) + Fj (9) where M i represents the i th moth, F j represents the j th flame, S represents the path function of the moth to the flame, D represents the distance between the moth and the flame, b is the defined logarithmic spiral shape function, path coefficient t is the random number in [r,1]. The population was set to 150. After 100 iterations, the Pareto frontier was obtained, as shown in Fig. 6. The two terms of average torque and torque ripple ratio in the obtained Pareto set were normalized respectively, and both were constrained between [0, 1]. If the two normalized items are f 1 and f 2 respectively, the following formula is performed. f = 0.3(1 − f1 ) + 0.7f2

(10)

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Fig. 6. Pareto frontier based on multi-objective moth-flame algorithm

Choose the point corresponding to the minimum value as the final optimization result. The final point is (20.32746, 7.53024). The average torque and torque ripple ratio after finite element simulation of corresponding parameters are shown in Table 4. After optimization, the average torque of the external rotor synchronous reluctance machine is 20.28 N.m, which is 13.36% higher than the initial design. The torque ripple ratio is 7.63%, which is 43.9% lower than the initial design. Table 4. Design parameter optimization results Structural parameters and optimization objectives

Initial value

Optimized value

kq

0.43

0.51

k q1

0.33

0.47

kq2

0.33

0.34

k w1

0.25

0.21

k w2

0.25

0.38

k w3

0.25

0.29

e

1.5 mm

0.96 mm

Average torque

17.89 N.m

20.28 N.m

Torque ripple ratio

13.6%

7.63%

5 Conclusion This paper presents an optimal design method for external rotor synchronous reluctance machine based on the mixed surrogate model. In this method, the parameters to be optimized are determined by grouping parametric finite element analysis, and the initial samples are obtained by using Latin Hypercube test design with linear constraints. Based on Kriging and RBF surrogate models, a two-objective mixed surrogate model of mean torque and torque ripple ratio of Ex-SynRM is established. Furthermore, an

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addition criterion based on DDS is added to ensure the local accuracy and global accuracy of the model. Combined with the multi-objective moth-flame algorithm, the torque characteristics of the external rotor synchronous reluctance machine are optimized. Compared with the traditional optimization design method using a single surrogate model, the mixed surrogate model proposed in this paper has higher prediction accuracy, better prediction stability, improved sample utilization, reduced simulation cycle, and the addition criterion adopted is not dependent on the specific surrogate model and has universal applicability. Acknowledgments. This work is supported by National Natural Science Foundation of China (52177040), and by Natural Science Foundation of Hunan Province (2021JJ30107).

References 1. Özçelik, N.G., Do˘gru, U.E., Gedik, H., ˙Imeryüz, M., Ergene, L.T.: A multi-parameter analysis for rotor design of synchronous reluctance motors. In: 2016 XXII International Conference on Electrical Machines (ICEM), Lausanne, Switzerland, pp. 664–670 (2016) 2. Hadi, A., et al.: Sizing and detailed design procedure of external rotor synchronous reluctance machine. IET Electr. Power Appl. 13(8), 1105–1113 (2019) 3. Chengcheng, L., et al.: Shape analysis and optimization design of magnetic barrier of low torque ripple synchronous reluctance machine. Electr. Mach. Control 26(12), 38–47 (2022). (in Chinese) 4. Chengcheng, L., et al.: Design of synchronous reluctance machine based on asymmetric rotor structure and sequential Taguchi robust optimization method. Trans. China Electrotech. Soc. 37(S1), 50–61 (2022). (in Chinese) 5. Xia, B., et al.: Multi-modal optimization design of permanent magnet synchronous machine based on improved firefly algorithm. Electr. Mach. Contr., 1–8 (2023). (in Chinese) 6. Li, X., et al.: Optimization design of thrust characteristics of flat plate permanent magnet linear synchronous machine. Trans. China Electrotech. Soc. 36(05), 916–923 (2021). (in Chinese) 7. Matthieu, P., et al.: Latin hypercube sampling with inequality constraints. AStA Adv. Stat. Anal.: J. Ger. Stat. Soc. 94(4) (2011) 8. Regis, R.G., Shoemaker, C.A.: Improved strategies for radial basis function methods for global optimization. J. Glob. Optim. 37, 113–135 (2007) 9. Goel, T., et al.: Ensemble of surrogates. Struct. Multidisc. Optim. 33, 199–216 (2007) 10. Tolson, B.A., Shoemaker, C.A.: Dynamically dimensioned search algorithm for computationally efficient watershed model calibration. Water Resour. Res. 43(1) (2007) 11. Mirjalili, S.: Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl.-Based Syst. 89 (2015)

Analysis and Improvement Measures for a 66 kV Shunt Capacitor Fault Jianying He1(B) , Qingyang Tian2 , and Zhiyu Liu2 1 State Grid Liaoning Electric Power Research Institute, Shenyang 110000, China

[email protected]

2 State Grid Liaoning Electric Power Supply Co., LTD., Shenyang 110000, China

{tqy,lzy}@sgcc.ln.com.cn

Abstract. The fault of the shunt capacitor device in a 220 kV substation led to the 66 kV bus outage and the total shutdown of six 66 kV substations. In order to find out the specific cause of the fault and avoid the recurrence of similar problems, analysts conducted a comprehensive analysis and judgment on the capacitor fault process and causes from various aspects such as protection action, setting calculation, disassembly inspection and harmonics. Through analysis, it is determined that the reason for the expansion of the accident is the mismatch between the shunt capacitor bank unbalance protection current transformer and the protection device. In view of this accident, the corresponding measures and suggestions are put forward from the aspects of optimization protection setting principle, bridge difference current transformer transformation, etc., which is of great significance to improve the operation reliability of this type of shunt capacitor device. Keywords: Shunt capacitor · Unbalanced current protection · Bridge differential Voltage protection · Fault

1 Introduction 1.1 A Subsection Sample Shunt capacitor device is an important reactive power compensation equipment in substation, which is mainly used for on-site reactive power compensation and power factor improvement in substation to reduce loss, improve power quality and stabilize voltage [1]. With the increase of various nonlinear loads and new energy plants in the power system, the switching of shunt capacitor devices in substations is becoming more and more frequent. Due to the aging of the dielectric and insulation in the capacitor, the breakdown of the dielectric in the capacitor may occur during the switching process [2]. If the protection configuration of the capacitor is unreasonable, the accident will be further expanded, and serious accidents such as group explosion will occur [3], which will affect the safe and economic operation of the power grid [4]. This paper makes an in-depth analysis of the 66 kV bus outage accident caused by group explosion of 66 kV shunt capacitor device in a 220 kV substation, and finally puts forward corresponding measures and suggestions to prevent the accident from happening again [5]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 446–456, 2024. https://doi.org/10.1007/978-981-97-1064-5_49

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2 Fault Event Introduction 2.1 Fault Process Description At 6:54 on May 27, 2020, the #1 capacitor bank of a 220 kV substation failed to catch fire, the #1 capacitor bank switch refused to operate, the #1 main transformer low backup protection action, the #1 main transformer secondary switch tripped, the 66 kV east bus line was cut off, and the load loss was about 39 MW, resulting in the complete shutdown of 6 66 kV substations and the shutdown of 2 66 kV photovoltaic substations. 2.2 Operation Mode Before Failure Before the accident, the #1 and #2 main transformer of the 220 kV system were running side-by-side, the #1 main transformer neutral point was directly grounded, and the #2 main transformer neutral point gap was grounded. 66 kV system 66 kV east and west busbars are running separately, busbar switch is hot standby, 66 kV busbar is prepared for self-input, 66 kV line is prepared for self-input, 66 kV busbar differential protection is enabled, fault #1 capacitor is running on 66 kV east busbar. 2.3 Basic Information About the Faulty Device The station #1 capacitor bank model TBB66-20040AQW, a total of 60 capacitor units, model BAM10.5-334-1W, reactance of 6%, using a single star connection. #1 Capacitor bank single-phase connection form is 5 and 4 strings, the bridge arm is 2 + 3 unequal capacity unbalanced current (bridge difference current) protection, the capacitor unit is an internal fuse structure, the internal component connection form is 11 and 5 strings. The complete set of capacitors was manufactured in 2011 and put into operation on July 13, 2011. #1 Capacitor bank protection configuration overcurrent protection, unbalanced current protection (bridge difference current protection), overvoltage protection, undervoltage protection, zero sequence current protection [6]. The ratio of bridge difference current transformer is 50/5, and the setting range is (0.05–20) In .

3 Fault Check Situation 3.1 Field Inspection After on-site inspection, the main damaged equipment is as follows: phase B 19 capacitor units “bulge”, 1 capacitor unit is completely burned out, internal bus is burned out, bridge difference current transformer and 8 support insulators are burned out and broken; In phase C, 17 capacitor units “bulge”, 3 capacitor units burned out, internal bus burned out, bridge difference current transformer and 8 support insulators burned out and broke; The external insulation of A-phase bridge difference current transformer is burned out, and the capacitor is affected less, only several shells are blackened. A, B, C three-phase series reactors all have fire blackening marks, and the A phase is relatively light. The burning condition is shown in Fig. 1.

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(a) t#1 Capacitor bank.

(b) C-phase bridge difference current transformer.

Fig. 1. Capacitor bank burn condition.

3.2 Protection Action Condition At 6:44 min 35 s 204 ms, 66 kV #1 capacitor bank internal fault, unbalanced current protection action, unbalanced current value 5.75 A when starting, the maximum value of 31.17 A (set value 5 A, 200 ms), #1 capacitor bank 66 kV circuit breaker refused, the fault was not removed, continued to develop into B, C phase fault. During the duration of the fault, the #1 capacitor bank current I protection action 562.48 A (fixed value of 520 A, 0.1 s); Current phase II protection action 562.48 A (set to 256 A, 0.5 s) consecutively. At 6:44 min 51 s 459 ms, the first set of the #1 main transformer protection high voltage side revoltage overcurrent III section starts, the first time exit jumps 66 kV busbar switch, the fault current of B and C phase 525.12 A (fixed value of 480 A, 3.2 s), the actual site is separate operation, 66 kV busbar switch has been in the fraction before, the second time limit has not reached the setting time (4.0 s) and has not been exported. At 6:44 min, 51 s, 849 ms, the T1 time outlet of the low-voltage side overcurrent phase II jumps the #1 low-voltage switch of the main transformer, the fault is 1884.3 A (the fixed value is 1560 A, 3.6 s), jumps the #1 main transformer secondary switch, the fault is removed. At 6:44 min 51 s 448 ms, #1 main change the second set of protective action, consistent with the first set of protective action behavior. Because the #1 primary transformer backup protection action blocks the busbar backup and self-throws, the #1 primary transformer busbar backup self-throws does not operate.

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3.3 Disassembly Inspection A total of 7 capacitor units with shell bulge deformation and shell integrity (slight blackening) were selected to return to factory for disassembly inspection. The test capacitance value of the unit with shell bulge deformation is “0” before disintegration. After disintegration, it is found that most of the internal components have been charred and carbonized, the internal fuse is broken, and the film is melted. The disassembly inspection of the shell bulge deformed capacitor unit is shown in Fig. 2.

(a) The inner fuse is blown.

(b) Component film melting.

Fig. 2. Disassemble and check the shell bulge deformed capacitor unit.

The shell is intact (slightly blackened) capacitor unit, and the measured capacitance value has no significant change from the factory value before disintegration (factory value 9.71 μF, measured value 9.69 μF), there is no internal oil, the film is not overheated, all components are intact and not damaged, and the disintegration inspection of the shell bulge deformation capacitor unit is shown in Fig. 3.

4 Fault Cause Analysis 4.1 Harmonic Analysis Harmonic Monitoring Data. In order to analyze the influence of harmonics on the capacitor, the #2 capacitor bank was inverted to the 66 kV east bus. The power quality tester monitored the power quality of the #1 main transformer high voltage side, the #1 main transformer low voltage side, the 220 kV inlet line and the 66 kV outlet line, and found that the harmonic source was located on the two 66 kV outlet lines, and the harmonic source was traced to the above two lines. The monitoring points are the first line of 10 kV load and the second line of 10 kV load [7, 8].

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Fig. 3. Capacitor unit with intact housing disassembly inspection.

According to the national standard GB/T 14549–1993 “Power quality Public Grid Harmonics”, the limit of total harmonic distortion rate of 10 kV public grid voltage is 4.0%, of which the limit of odd harmonic content is 3.2%, and the limit of even harmonic content is 1.6%. The 10 kV load line is monitored, the characteristic harmonics are 3 times, 11 times and 13 times, the 95% probability maximum value of Uab is 6.62%, there is a shortterm instant exceeding phenomenon, the national standard limit value is 4%, but the 95% probability maximum value is not exceeding the standard. The maximum value of Ucb is 5.14%, the phenomenon of short-term instantaneous exceedance occurs, and the national standard limit value is 4%, but the 95% probability of the maximum value is not exceeded. The total distortion rate curve of 10 kV load first-line voltage is shown in Fig. 4. The harmonic voltage curve of the first line of 10 kV load is shown in Fig. 5.

Fig. 4. Total distortion rate curve of 10 kV load line voltage.

The second line of 10 kV load is monitored, and the characteristic harmonics are 5, 7, 11, 13, 17 and 19 times. The 95% probability maximum value of Uab is 3.97%, and the national standard limit value is 4%, which is close to exceeding, but not exceeding. The maximum 95% probability of Ucb is 4.12, and the national standard limit is 4%, exceeding the standard. The total distortion rate curve of line two voltage of 10 kV load

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Fig. 5. 10 kV load line each harmonic voltage curve.

is shown in Fig. 6. The harmonic voltage curve of the second line of 10 kV load is shown in Fig. 7.

Fig. 6. Total distortion rate curve of 10 kV load line two voltage.

Fig. 7. 10 kV load line two harmonic voltage curve.

Test Conclusion. (1) The harmonics on the high voltage side of the #1 main transformer did not exceed the standard. (2) The total distortion rate of 10 kV load first-line harmonic voltage is 95% probability that the maximum value is not exceeded. However, the total distortion rate of harmonic voltage exceeds the threshold instantaneously, and the characteristic harmonics are 3, 11 and 13. (3) The total distortion rate of second-line harmonic voltage of 10 kV load has a 95% probability of exceeding the standard, and the characteristic harmonics are 5 times, 7 times, 11 times, 13 times, 17 times, 19 times. (4) The long-term impact of the 11 characteristic harmonics on the low-pressure side of the main transformer is easy to aggravate the aging of the equipment, and the higher the harmonic number, the more obvious the impact. (5) The moment the capacitor bank is switched, the harmonic current will be amplified. The amplified harmonic current is easy

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to increase the capacitor current, increase the temperature rise and shorten the capacitor life [9].

4.2 Calculation and Analysis of Capacitor Setting Unbalanced Current Protection. The capacitor unit of the capacitor bank is an internal fuse structure, the internal components of the unit are 11 and 5 strings, and the internal wiring of each phase is 4 strings and 5 strings, and the bridge arm is protected by 2 + 3 unequal capacity unbalance current (bridge difference current). The single-phase wiring diagram is shown in Fig. 8.

Fig. 8. #1 Capacitor bank single-phase wiring diagram.

When the capacitor unit has a single component failure, the internal fuse action excises and isolates the faulty component. When the component breakdown occurs, the internal fuse cannot be reliably fused and the arc time is longer than the unbalanced current protection action trip setting time, the unbalanced protection will act and remove the faulty capacitor bank. When multiple components fail, the fuse acts, causing the overvoltage of the intact component to exceed the allowable value, and the unbalanced current protects the action to remove the faulty capacitor bank. Protection Set Value Check. In order to further analyze the fault cause of the capacitor bank, the output current of the unbalanced protection action of the capacitor group is checked, and the calculation of the output current of the unbalanced protection action of the internal fuse (asymmetric wiring) is calculated by referring to the formula in DL/T 1415–2015 “Protection Guidelines for High Voltage Shunt Capacitor Devices” [10]. The overvoltage multiple and unbalance protection current of different cutting elements are obtained, as shown in Table 1. The unbalanced current protection setting principle is implemented in accordance with DL/T 1415–2015 “High voltage Shunt Capacitor Device Protection Guidelines”, “the overvoltage multiple of the intact capacitor unit shall not exceed 1.1 times and the overvoltage multiple of the intact capacitor unit shall not exceed 1.3 times” [10]. After calculation, when the number of damaged components in a parallel section inside

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Table 1. Over voltage multiple and unbalanced protection current calculation value for different number of cutting elements. Number of damaged components in a unit

Multiple of intact element overvoltage

Overvoltage multiple of intact unit

Unbalanced current primary value (A)

1

1.08

1.00

0.125

2

1.18

1.01

0.273

3

1.3

1.02

0.451

4

1.44

1.02

0.668

9

3.25

1.12

3.39

10

4.34

1.18

5.02

the capacitor unit reaches 3 (that is, the maximum of k is 3), the primary value of the unbalanced current is 0.451A, which is converted to the secondary value of 0.0451A, the overvoltage multiple of other intact components will reach 1.3, and the overvoltage multiple of the unit is 1.02. At this time, the unbalanced current protection should start. It is consistent with the unbalance protection current (0.451A) provided by the capacitor manufacturer. The transformer ratio of the #1 capacitor bank in the substation is 50/5. When the primary value of the unbalanced current is 0.451A, the secondary value of the unbalanced current protection is only 0.0451A, which does not meet the minimum setting range of the protection device (0.1A). In fact, the field one-time setting value is 5A, which is set according to the capacitor protection of the external fuse before the capacitor transformation, resulting in the bridge differential protection not acting in time. 4.3 Cause Analysis of Capacitor Bank Failure Fault Initiation Device Analysis. On-site inspection found that the B-phase 34 unit, C-phase 52 unit and C-phase bridge current transformer of #1 capacitor bank were seriously damaged, but the expander of C-phase bridge current transformer was not expanded, the upper cap was complete and the oil level indication was normal, and the internal coil shape of the current transformer was complete (the insulation resistance of each phase current transformer in the maintenance test in April 2019 was greater than 10000 M, , The dielectric loss and capacitance comparison historical data do not change significantly, within the qualified range), eliminate the possibility of the bridge difference current transformer fault first. Therefore, it is judged that the fault starts from the capacitor unit. By looking at the protection action waveform diagram, unbalanced current appears first in phase B, and the initial starting point is confirmed as unit 34 of phase B. #1 capacitor unbalanced current protection action waveform is shown in Fig. 9. Damage Analysis of B-phase 34 Capacitor Unit. The #1 capacitor group has been in operation for 9 years. In the early stage of the accident, due to the operation of a smelting enterprise user, the reactive power demand increased greatly, and the number of operations switching of its circuit breaker in the past year was 421 times, which

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Fig. 9. #1 Capacitor unbalanced current protection action waveform.

was more than the #2 capacitor group. In addition, the harmonic test load contains 11 harmonics, the capacitor bank in the station is equipped with a reactance of 6%, the device will amplify the 11 harmonics, the capacitor is in a long-term overvoltage operation state, and the internal components of B-phase 34 unit have weak insulation, which will aggravate the aging of the film in the overvoltage environment, and then reduce the insulation, resulting in the breakdown of the internal components. The corresponding internal fuse is blown [11]. The first value of the unbalanced current protection action of the group of capacitors is 5A, which is calculated according to the formula in DL/T 1415–2015. When the unbalanced current protection action is performed, the internal fault components of the B-phase 34 capacitor unit have reached 10, and the overvoltage multiple of the components is 4.34 times. After the fuse of the components inside the capacitor unit is blown to a certain amount, other intact components will withstand overvoltage. If the trip is not removed in time, the intact components will break down one after another, which will lead to internal discharge overheating, and the high temperature will cause the capacitor insulation oil to vaporize, causing the capacitor belly or even oil leakage. Fault Expansion Cause Analysis. The unbalanced current of the faulty capacitor during the unbalanced protection action reached 31.17A, far exceeding the 5A set by the protection device. Later, due to the switch rejection, the failure time lasted 16.8 s before the fault was removed after the main transformer backup protection action. Capacitor long time overvoltage, and accompanied by discharge corona phenomenon, capacitor imbalance current reached 31.17A when tripping, has exceeded the capacitor components can withstand the range, capacitor components have been broken down, high temperature caused insulation oil and gas, resulting in capacitor “bulge”, explosion resistance decreased (capacitor bursting energy is proportional to the square of voltage, In the overvoltage operation, its blasting energy is much larger than the explosion-proof energy 15kJ), at this time, the capacitor breakdown causes the shell to burst or the dip mouth to crack, and the fire after contact with the air. The capacitor oil (benzyl toluene) has a flash point of 136 degrees and an ignition point of 300 degrees,

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and if there are successive breakdown diffusion discharges during this process, the fire will be expanded. The capacitor unit No. 34 of phase B first caught fire, which caused the support insulator to burst after the fire. The four capacitor units and support of the upper layer of phase B as a whole reversed to the C phase bridge difference current transformer, thus developing into a short circuit between B and C, and the transformer oil overflow expanded the fire range. After the short-circuit current continues to develop and reaches the value of the backup protection action of the main transformer, the secondary switch of the #1 main transformer will trip and the east bus will lose power.

5 Conclusions Through the analysis of the capacitor device failure, the following suggestions and measures are put forward: (1) Capacitor bank unbalanced current protection setting problem. Capacitor bank unbalanced current protection setting should be provided by the capacitor manufacturer reference value, while considering the impact of the initial unbalanced current, when the capacitor is modified, the setting value should be recalculated [12]. (2) Capacitor bridge difference current transformer secondary coil wiring selection problem. The accuracy level of the internal fuse capacitor bank bridge difference current transformer should be 0.5. In this case, 5p30 coil is selected according to the conventional protection, which does not meet the accuracy requirements. (3) The current transformer ratio matches the setting range of the protection device. The ratio of current transformer for unbalance protection should be compatible with the setting range of the protection device. In this case, the bridge difference current transformer ratio is selected as 50/5, the secondary value of the unbalanced protection action current is 0.05A, and the minimum setting range of the protection device is 0.1A, which cannot be set. It is recommended to reduce the bridge difference current transformer ratio and use 10/5 transformer or 1/1 transformer. (4) Capacitor production process problems. The aging period of the film or insulation oil is short, the outer cover of the dip hole is not tightly sealed, cracks and leaks oil. You are advised to improve the performance of the insulation medium (film or oil) and replace the inner cover of the oil injection hole with a silicone rubber plug.

References 1. Bin, H., et al.: Reason analysis and precautionary measures for a 35 kV shunt capacitor bank explosion. Power Capacitor React. Power Compensation 39(01), 23–27 (2018). (in Chinese) 2. Song, B.: A method of coordinated reactive power loss reduction for power capacitors under the influence of harmonics. Power Capacitor React. Power Compensation 35(11), 7–12 (2019). (in Chinese) 3. Daiyong, Y., et al.: Study on fault development characteristics of shunt compensation capacitor bank in 66 kV substation. Power Capacitor React. Power Compensation 42(02), 5–11 (2021). (in Chinese)

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4. Bin, L., et al.: Fault analysis on 35 kV shunt capacitor device. Power Capacitor React. Power Compensation 35(11), 7–11 (2022). (in Chinese) 5. Ruming, F., et al.: Analysis and study on internal insulation fault of 35kV shunt capacitor. Power Capacitor React. Power Compensation 42(05), 14–20 (2021). (in Chinese) 6. Zhang, M., et al.: Research on the implementation scheme of shunt capacitor protection and monitoring. In: 2017 International Electrical and Energy Conference, pp. 448–451. IEEE, China (2017) 7. Lei, G., et al.: Damage fault analysis on high voltage shunt capacitor. Power Capacitor React. Power Compensation 41(05), 23–28 (2020). (in Chinese) 8. Yuqiang, O., et al.: Review of the relationship between harmonic and parallel capacitor fault. Adv. Mater. Res. 3530(1044), 507–514 (2014) 9. Aleksander, K., et al.: Analysis of the impact of nonlinear loads on capacitor banks for reactive power compensation in MV/LV substations. Przeglad Elektrotechniczny 89(10), 172–175 (2013) 10. Bo, Z., et al.: Analysis of protective action cause and improvement measures for 35kV assembled capacitor. Power Capacitor React. Power Compensation 41(02), 38–41 (2020). (in Chinese) 11. Shi, H., et al.: Research on the parallel capacitor series reactance rate parameter design. In: 2012 Asia-Pacific Power and Energy Engineering Conference, pp. 2076–2079. IEEE, China (2012) 12. Hangtao, C., et al.: Unbalanced protection and fault analysis of frame shunt capacitor banks. Electr. Switchgear 61(02), 60–62 (2023). (in Chinese)

A New Safety System Architecture and Design for High-Speed Trains Xin Zhou1,2(B)

, Guangwu Chen1,2

, Yongbo Si1,2 , and Pengpnge Li1,2

1 Institute of Automation, Lanzhou Jiaotong University, Lanzhou, Gansu, China

[email protected], [email protected] 2 Key Laboratory of Traffic Information Engineering and Control in Plateau, Lanzhou Jiaotong

University, Lanzhou, Gansu, China

Abstract. In order to address the large amount of data interaction during highspeed train operation and the high reliability of data security, this paper designs a new type of security system based on FPGA+DSP as the main framework. The system adopts XINIF parallel interface in DSP to achieve interconnection with FPGA, which accelerates the data transmission speed. At the same time, on the base of the original double 2-vote-2, two-way redundancy system is added to improve the safety and reliability of the computer interlocking system. Analysed by simulation experiments, the new safety system has a certain degree of improvement in reliability and safety compared with the traditional double 2-vote-2 system. Keywords: FPGA · DSP · Double 2-Vote-2 · Security Systems

1 Introduction In recent years, with the comprehensive construction of high-speed railway and the further development of railway speed upgrading, the railway industry has put forward higher requirements for the reliability and safety of computer interlocking control system [1]. As the more popular computer interlocking control system in the railway industry at present, double 2-vote-2 computer interlocking is a kind of interlocking control system based on computer technology, control technology and communication technology to achieve the interlocking control system of the station signalling equipment [2]. The system often consists of two functionally identical subsystems, the two subsystems can constitute a mutually complementary system, strict synchronisation, time to time comparisons, only when the two subsystems are running in unison, only when the external output results. Double 2-vote-2 system to a certain extent can effectively avoid the system in real-time operation of the misoperation, reduce the chance of accidents, its reliability and safety is directly related to the safety of traffic and railway operation efficiency [3]. Although the double 2-vote-2 computer interlocking system has made great progress in recent years, it still suffers from the shortcomings of insufficiently timely data transmission, insufficient data storage space, insufficiently reasonable comparison structure and insufficiently clear judgement mechanism. Under this background, many scholars have carried out more indepth research and improvement on the double 2-vote-2 system. Chen G et al. proposed © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 457–467, 2024. https://doi.org/10.1007/978-981-97-1064-5_50

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the 2-vote-2 system and the full electronic computer joint application of the approach to achieve the integration of the signal control, monitoring, supervision, so that the 2-vote2 system applied to the railway station from the theory into reality [4]; Yang L et al. developed a set of train computer interlocking simulation system on the existing the double 2-vote-2 system, which can achieve the simulation of the train control centre and wireless occlusion centre and other signal safety control equipment, and introduced in detail the system structure and features [5]; Yan L [6] and Yang Y [7] from the practical application of the system, using Markov model and fuzzy model, fully considering the influence of fault coverage, maintenance rate and other factors, the reliability and safety of the system are analysed in depth, and the performance of the two-by-two-take-two system and two-machine hot-standby system are compared by MTTF value and reliability and safety curves, which verifies that the two-by-two-take-two computer interlocking system has higher safety and reliability than the two-machine hot-standby computer interlocking system; Wang B combined with the design concept of fault-safe circuits, a design method of a single-chip multi-soft-core system is proposed, and the FPGA-based two-by-two take-two safety system design scheme is given to complete the two-by-two take-two function [8]; Gao Y suggested a hierarchical synchronisation mechanism by setting up two-way timed supervisory monitors between different levels, and realising the synchronisation process of a two-by-two-take-two computer interlocking system by adopting a task-cyclic scheduling control and a two-module communication method [9]. However, the existing research does not take into account that with the rapid development of high-speed railway, the computer interlocking system requires more and more real-time and fast communication data, and it becomes an urgent problem to improve the space storage capacity and data transmission capacity of the double 2-vote-2 system. This paper adopts a new safety system architecture design method based on FPGA and DSP to overcome the deficiencies of the existing double 2-vote-2 system. Based on the traditional double 2-vote-2 computer interlocking control system, this paper adopts the CPCI board to connect the two FPGA and the two DSP data fusion processing boards, and combines the data output boards of the FPGA and the DSP to achieve hardware comparison and software comparison of the collected data. The Markov model is used to compare and analyse the security and reliability of the system. After analysing, the new security system architecture system has higher security and reliability compared with the single circuit system and the double 2-vote-2 system.

2 New Safety System Structure In this paper, a new security system architecture based on FPGA and DSP is designed to solve the problems of untimely and insecure data transmission and insufficient storage space. Using the FPGA module to complete the hard comparison of the two data boards, using the DSP module to complete the soft comparison of the two data boards, the same will output the value of 1, different will output the value of 0 and the alarm, and then the hard comparison and soft comparison of the output value of the contingency comparison, and then complete the whole process of the new security system design.

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2.1 A Subsection Sample FPGA and DSP are mainly used in the design process of the new security system. Among them, FPGA is a kind of highly integrated semi-customised circuit, and the internal chip adopts parallel sending and streaming structure, which greatly improves the speed and efficiency of the data throughput [10]; DSP is a kind of microprocessor dedicated to the rapid implementation of digital signal processing algorithms, which has the characteristics of fast computing speed and high numerical processing accuracy [11]. At the same time, the security system in the process of designing has fully considered the shortcomings of the existing security system data transmission is not timely, using the parallel input interface XINIF interface in the DSP, XINIF interface adopts the mode of non-multiplexed asynchronous bus, which can be connected with multiple external memories and allow it to access different rates of the external storage device, thus ensuring that the two data acquisition boards in this paper have the same Timing. In order to complete the normal data transfer function of the XINIF interface, 24 pins between the DSP and the FPGA need to be connected. Among which, the pins in the DSP include 13 address bus pins from XA0 to XA12, 8 data bus pins from XD0 to XD7, the XZWE write operation select pin, the XZRD read operation select pin, and the XZCS6 area 6 chip select signal pin. The XINIF interface is mapped to 3 fixed memories in the DSP respectively (area 0, area 6, area 7), here We choose area 6 as the data storage processing area, so the XZCS6 pin should be set low. As for the FPGA, due to its hardware programming characteristics, its corresponding pins do not specify a specific function, in this paper, we have selected a total of 24 pins from T2 to T14 and R4 to R14 to be connected to the DSP pins, and the specific connections are shown in Table 1 below. Table 1. XINIF interface wiring. DSP pin

FPGA pin

DSP pin

FPGA pin

XA0

R9

XA12

T2

XA1

T8

XD0

R11

XA2

R8

XD1

T11

XA3

T7

XD2

R12

XA4

R7

XD3

T12

XA5

T6

XD4

R13

XA6

R6

XD5

T13

XA7

T5

XD6

R14

XA8

R5

XD7

T14

XA9

T4

XZWE

T10

XA10

R4

XZRD

T9

According to the above table sequential wiring, and the two chips for power and ground pin resource allocation, in the actual design process, this system is embedded

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in the train integrated positioning system to obtain better experimental results. Figure 1 shows the block diagram of the double 2-vote-2 system structure based on FPGA and DSP, and the system is mainly composed of a multi-channel power safety board, a one-way data acquisition board, two-way data fusion boards A and B, and data output boards, etc. Among them, the data acquisition board contains the data fusion board A and B, and the data output board. Among them, the data acquisition board contains GNSS discrete devices and IMU discrete devices; the data fusion board is a two-channel redundant structure, and the data output board implements all the processes of data hard comparison and soft comparison.

Multiple Safety Power Boards

One 12V power input

Data Acquisition Board

Four 5V power outputs

Data Fusion Board

Data Fusion

Output Fusion Board B FPGA

DSP

Data Process Dual-port RAM Serial Port

Data Solution

XINTF

Optocoupler Isolation

DSP Software Comparison

CPCI Connector

Serial Port Converter

Serial Port

DSP

Data Solution

XINTF

GNSS Serial Interface

CPCI Connector

GNSS Discrete Device

Data Process Dual-port RAM

Output Board

DSP

FPGA IMU Serial Interface

Data Output Board

Fusion Board A

Acquisition Board IMU Discrete Device

One 12V power output

XINTF

Data Fusion

FPGA FPGA Hardware Comparison

Fig. 1. Block diagram of the new security system.

2.2 A Subsection Sample 2.2.1 FPGA Hardware Comparison FPGA hardware comparison part for the use of Exclusive-OR gate design of the comparison circuit, the circuit adopts redundant design, it is mainly on the two data fusion board sends out the data to compare the judgement, to ensure that the system can be normal operation, and DSP software comparison synchronous, its circuit structure is shown in Fig. 2. Comparison loop works as follows: FPGA on-chip registers obtain data information from two FPGA+DSP data fusion boards, respectively, and are judged by the ExclusiveOR gate modules OE1 and OE2 according to Eq. 1 and Eq. 2, which control the output of

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1

Fig. 2. FPGA Hard Compare Circuit Structure.

the data latches, respectively, and work with the clock signals to control the synchronous output of the latches. OE1 = A1 ⊕ A2

(1)

OE2 = B1 ⊕ B2

(2)

Latch from the further output of the data after processing or circuit to form a comparison result, if the comparison result confirms the data fusion board A, B output results are consistent, the system normal output, and send the value of 1; if the comparison circuit confirms that the data fusion board A, B output results are inconsistent, then re-operate and send out an alarm signal and the value of 0. 2.2.2 DSP Software Comparison After completing the hardware comparison of the data and the output value is 1, the DSP is further used to complete the software comparison of the data. In view of the DSP has excellent computing ability, this paper uses the CRC checksum to complete the software comparison of data fusion board A, B. CRC algorithm is a kind of original data into a checksum formula to generate a certain length of the checksum code, and then add the checksum code to the back of the original data, the composition of the new data checksum method. The process of calculating CRC to compose new data is encoded, and then decode the data in the same way, you can find out whether the data changes, and then determine whether the results of the two data is consistent, to complete the soft comparison part of the new security system. In this paper, we choose the structure of the simpler serial software calculation method, due to the data fusion board for the 16-bit data output, the checksum formula to choose the 16-bit checksum code, the form shown in Eq. 3. CRC − 16 : x16 + x15 + x2 + 1

(3)

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When the data output from data fusion boards A and B are simultaneously CRCchecked, the result of the decoding mode operation is 0. If the result is not 0, it means that the data has been changed after encoding. When the outputs of the two data fusion boards result in 0 after decoding, the data is output to the outside and the value 1 is sent; if the result is not 0, an alarm signal is issued and the value 0 is sent to the outside. Subsequently, the value of the DSP output and the value of the FPGA output are again compared with an or gate, and the data is output normally if the result is 0. If the result is 1, an alarm signal is issued. The soft comparison process is shown in Fig. 3 below.

Fig. 3. DSP software comparison.

3 Experimental Analyses 3.1 Reliability and Safety Analysis of New Safety Systems To verify the reliability and safety of the novel safety system proposed in this paper, experiments based on a integrated on-board GNSS/INS positioning system are designed. The reliability of the system is set as R(t) and the safety as S(t), and three parameters, namely, the failure rate λ, the fault coverage c, and the repair rate μ, are introduced to examine the effects on the reliability and safety of the system. The failure of the system occurs mainly in three places, respectively, the discrete device of GNSS in the data acquisition card, and the conditional probability of its failure is set as λG ; a discrete device of IMU in the data acquisition card, and the conditional probability of its failure is set as λI ; and the last is the system data fusion card, and the conditional probability of its failure is set as λR . The system is also designed to be redundant in each subsystem, and the failure rate a, failure coverage b, and repair rate c are introduced to examine the impact on the system reliability and safety. As each subsystem is set up with redundancy, the working state table of the system can be derived based on the failure probability of each system, with a total of eight states, as shown in Table 2 below. The subsystem failures in Table 2 refer to the subsystem failures of this redundancy configuration, not just the failure of a single sensor, and the failure of any one of the data fusion boards A and data fusion boards B will lead to the failure of the data fusion board subsystems.

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Table 2. Table of operating states of new safety systems. Mode

Meaning

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0

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Since the method of calculating the failure probability of the subsystems separately is adopted, only the overall working state of each sensor subsystem is analysed in the state transfer diagram. Under the precondition of meeting the above requirements, this paper can nearly get the Markov state transfer diagram of the system according to the above table, and the curves between each state transfer are marked in the diagram, and the specific process is shown in Fig. 4 below.

Fig. 4. System Markov operating state transfer diagram.

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According to the Markov operating state transfer diagram the transfer matrix P can be obtained as shown in Eq. 4.

(4)

According to Table 2 and Fig. 3, combined with the general sensor failure probability can be approximated to obey the Poisson distribution, as shown in Eq. 5. P(t) =

(λt)x · exp(−λt) x!

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Then the probability of failure of the GNSS discrete device can be approximated as: P(G) =

2 λG 3

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The probability of failure of the IMU separation device is: P(I ) =

12 λI 13

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The probability of a data fusion board sending a fault is: P(R) =

5 λR 6

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Further, the expressions for the reliability and safety of the system can be obtained      2 12 5 R(t) = exp − λG t + exp − λI + λR t (9) 3 13 6 S(t) = R(t)μ(1 − c)

(10)

3.2 Reliability and Safety Analysis of New Safety Systems When the expressions for the safety and reliability of the system are obtained, the Laplace transform method can be used to compute the analytical solution of the expressions for the reliability and safety, and then the reliability and safety of the system can be obtained. Considering that the variation of the system’s safety degree is small and not easy to observe and analyse, this paper then chooses to observe the system’s insecurity U(t), which indicates the probability of the system to produce a dangerous output and sums up with the system’s safety degree S(t) as 1.

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The length of the simulation experiment is 10,000 h, due to the low probability of system failure, it is assumed here that the system failure rate λ is 0.0001 times/h, and the failure coverage c = 0.95, and the effect of different repair rates μ on the reliability and insecurity of the single-circuit system, the two-by-two-take-two system, and the new safety system is examined, and the transformation trend of the system reliability is shown below in Figs. 5, 6, and 7, and that the system insecurity transformation trends are shown in Figs. 8, 9 and 10 below. c=0.95 u=0.95 effect on system reliability

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The figure above shows that the new safety system is better than the single circuit system and the traditional double 2-vote-2 system in terms of both safety and reliability. At the same time, the new safety system can reduce the disturbance to the system caused by the decrease of repair rate A to a certain extent.

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4 Conclusion This paper designs a new type of security system based on FPGA+DSP as the main architecture, using the parallel serial port XINIF interface in DSP to complete the data interaction with FPGA, which effectively improves the data transmission capability. At the same time, the simulation experiment verifies and analyses that the system’s safety and reliability as well as anti-jamming ability have a greater degree of improvement compared with the single-circuit system and the traditional two-by-two-take-two system during the long-time operation. Acknowledgements. This research is supported by Gansu Youth Science and Technology Fund Programme (21JR7RA323) and Gansu Provincial Science and Technology Programme Funding (23JRRA846& 22JR5RA323).

References 1. Cao, Y., Yang, Y., Ma, L., et al.: Research on virtual coupled train control method based on GPC & VAPF. Chin. J. Electron. 31(5), 897–905 (2022) 2. Feng, H.: Design and research on all electric computer interlocking system for urban transit. J. Railw. Sci. Eng. 18(08), 2145–2155 (2021). (in Chinese) 3. Chen, F., Yun, Z., Yan, L., et al.: Reliability and safety evaluation of autonomous computer system of intelligent CTC in high speed railway. Acta Automatica Sinca 46(03), 470 (2020). (in Chinese) 4. Chen, G., Fan, D., Wei, Z., et al.: All electronic computer interlocking system based on double 2-vote-2. China Railw. Sci. 31(04), 138–144 (2010). (in Chinese) 5. Yang, L., Yao, Y., Cheng, J., et al.: Design of simulation system based double 2-vote2 computer-based interlocking system. In: 2019 International Conference on Information Technology and Computer Application (ITCA), pp. 279–284. IEEE (2019) 6. Yan, L., Zhang, T., Gao, Y., et al.: Reliability analysis of station autonomous computer system based on fuzzy dynamic fault tree and Markov model. Eng. Rep. 3(8), e12376 (2021)

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7. Yang, Y., Chen, G., Qu, R., et al.: Markov model based multi-sensor combination localization reliability assessment. J. Railw. Sci. Eng. 14(12), 2689–2696 (2017). (in Chinese) 8. Wang, B., Zhang, C., Wang, Y.: Design of 2-vote-2 safety control system based on FPGA for railway train operation. In: 2nd International Conference on Computer Engineering, Information Science & Application Technology (ICCIA 2017), pp. 465–468. Atlantis Press (2016) 9. Gao, Y., Ma, L., Cao, Y.: The research of hierarchical synchronization mechanism about 2-vote-2 safety computer. In: 2018 International Conference on Control, Automation and Information Sciences (ICCAIS), pp. 536–541. IEEE (2018) 10. Fu, H., Li, P., Fu, X., et al.: A resource optimisation allocation approach for multi-FPGA real-time emulators. Autom. Electr. Power Syst. 47(11), 88–100 (2023).(in Chinese) 11. Hu, X., Li, X., Huang, H., et al.: TiNNA: a tiny accelerator for neural networks with efficient DSP optimization. IEEE Trans. Circuits Syst. II Express Briefs 69(4), 2301–2305 (2022)

Harmonic Voltage Effect on Partial Discharge Characteristics of Oil-Paper Insulation Under Non-uniform Electric Field Weiju Dai1 , Zhihu Hong1 , Shan Wang1 , Guochao Qian1 , Jie Wu2(B) , and Ruochun Xia2 1 Electric Power Research Institute Yunnan Power Grid Co., Ltd., Kunming, China 2 State Key Laboratory of Power Transmission Equipment and System Security and New

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

Abstract. In the new power system, the harmonic source and the content increase, which puts forward a new test to the oil-impregnated paper insulation performance of the transformer. Therefore, this paper carries out the research on the effect of harmonic voltage on oil-impregnated Paper insulation partial discharge (PD) by means of the partial discharge platform under the action of harmonic voltage, and analyses the influence law of harmonic voltage frequency on partial discharge parameters. The results show that the harmonic voltage changes the partial discharge inception situation for the oil-impregnated paper due to the differences in harmonic polarity at different frequencies from the 50 Hz-industrial voltage. The split-peak phenomenon appears in all of the PD patterns of the oil-impregnated paper under the action of harmonic voltages and it is more obvious in the higher harmonic frequency. The harmonic voltage causes the maximum and average discharge magnitude increases, whereas the number of discharge pulses and discharge repetition rate decreased under the positive and negative discharge. Keywords: Harmonic Voltage · Oil-impregnated Paper · Partial discharge · Insulation Characteristic

1 Introduction The harmonics problems in the new power system have become more prominent, due to the high proportion of renewable energy and the high proportion of power electronic equipment characteristics [1]. It is manifested by the increase of harmonic components, the uncertainty of harmonic flow and the complexity of harmonic propagation mechanism. The harmonic voltage can increase the electrical and thermal stresses on equipment insulation, accelerate equipment ageing and shorten equipment life. It brings a significant impact on the operational safety of power equipment finally [2]. However, the research on harmonics problems of new power systems is still in the initial stage. Several studies have shown that harmonics can cause no-load losses and full-load losses in power transformers to rise [3–5]. These losses cause a significant increase in © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 468–476, 2024. https://doi.org/10.1007/978-981-97-1064-5_51

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power transformer hot spot temperature and the effect of high-frequency harmonics on the temperature is more severe than that of low-frequency harmonics [6, 7]. Harmonics cause more power loss in the insulating material and have a serious accelerating effect on the material aging process, especially the effect of higher frequency harmonics is more obvious [8]. The significant effect of harmonics on the insulation of power transformers is reflected in the partial discharge (PD) characteristics of the oil-impregnated paper insulation. Another research shows that high-frequency harmonics accelerate PD and affect the effective discharge time of a single cycle [9]. High harmonic frequency increases the rate of voltage rise, which increases the frequency of partial discharge within the insulating material [10, 11]. Similarly, there is a correlation between the amplitude of harmonics for the number of PD [12]. In addition, the increase in harmonic distortion rate makes the suspended discharge voltage decrease and change the PD pattern [13]. The frequency and content of harmonic voltage have an important effect on the insulation characteristics of oil-impregnated paper, but the research on the effect of harmonic voltage on the insulation characteristics of oil-impregnated paper is still in the initial stage. There is a lack of deep analysis of the effect of harmonic voltage frequency on the electric field distribution of oil-impregnated paper insulation. To analyze the effect of the harmonic voltage on the oil-impregnated paper insulation properties in a new power system with a high proportion of renewable energy sources and power electronic equipment, this paper performs an experimental study of the partial discharge characteristics at different frequencies of harmonic voltages. Firstly, this paper designs an experimental platform for partial discharges under the harmonic voltages, which outputs harmonic voltage with different frequencies superimposed on the industrial frequency voltage. Then the effect of harmonic voltage on the discharge characteristics of oil-impregnated paper is analyzed by the discharge patterns of harmonics with different frequencies and the discharge parameters including the partial discharge inception voltage, the discharge magnitude and the discharge number.

2 Experimental Set-Up The PD test platform of oil-impregnated paper under the harmonic voltage is mainly composed of the power supply unit, the electrode and the PD measuring system, as shown in Fig. 1. The power supply is composed of a voltage generator and a voltage amplifier. The voltage generator can output voltage signals with industrial frequency (50 Hz) superimposed any frequency harmonics. The PD measuring system is composed of high-frequency CT, PD pulse analyzer and computer. The copper spherical electrode is used in this experiment, and its structure and size are shown in Fig. 2. The insulating paper is cut into 10 cm × 10 cm square paper. Then the insulating oil and paper are dried at 90 °C and in vacuum for 24 h. After drying, the paper is mixed with the insulating oil and dried at 60 °C, in vacuum for 48 h. The moisture content of the dried oil-impregnated paper is measured to be 0.87%, which meets the requirements of partial discharge experiment.

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The voltage amplitude and discharge volume are calibrated using a high-frequency pulse generator before the test started. The fitting results in the calibration coefficient k0 = 7.61231, as shown in (1). k0 =

q0 u0

(1)

where the k0 is the calibration coefficient; q0 is the amount of charge (pC); u0 is the voltage (mV). 100 pC is chosen for the inceptive partial discharge capacity. According to the calculation of calibration coefficient, when the partial discharge capacity reaches 100 pC, the voltage amplitude of discharge reaches 0.0131 V.

Fig. 1. Schematic diagram of partial discharge test platform

Fig. 2. Diagram and dimension of electrode structure

3 Results and Discussing The partial discharge inception voltage (PDIV) of oil-impregnated paper at different frequencies and different contents of harmonics is shown in Fig. 3. 3%, 5%, 10%, 15%, 20% represents harmonic content respectively. The horizontal straight line in Fig. 3. Indicates the PDIV of oil-impregnated paper at the industrial frequency (50 Hz) voltage, the value of which is 10.7 kV. The result shows that 250 Hz and 650 Hz harmonic voltages decrease the PDIV of oil-impregnated paper, whereas 350 Hz and 550 Hz increase the PDIV of it. It means the harmonics changes the original partial discharge inception

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situation. When the applied voltage is superimposed with 250 Hz and 650 Hz harmonic voltages, the voltage peak value does not decrease, and the voltage change rate increases around the voltage peak value, so the PDIV of the oil-impregnated paper decreases. For 350 Hz and 550 Hz harmonic voltages, the voltage polarity of the harmonic voltage at the peak of the 50 Hz voltage is opposite to that of the 50 Hz voltage. It results in a decrease in the voltage peak, and thus an increase in PDIV of the oil-impregnated paper.

Fig. 3. PDIV of oil-impregnated paper under harmonic voltages of different frequencies and contents

In order to adequately describe the effect of harmonic frequency on the PD characteristics of the oil-impregnated paper, the PRPD results with the harmonic content of 20% are selected for analysis, as shown in Fig. 4 to Fig. 8. These PRPD patterns show that the PD characteristic patterns of the oil-impregnated paper, all produce a split-peak phenomenon under the action of harmonics. Specifically, the discharge pattern under the 650 Hz harmonic voltage shows a peak-splitting phenomenon from 12 kV onwards. After the applied voltage reaches 16 kV, the peak splitting phenomenon occurs at all frequencies of the harmonic voltage. As the applied voltage increases, the peak splitting phenomenon becomes more obvious, and the amount of discharge and the number of pulses in the main peak gradually increase.

Fig. 4. PRPD pattern of oil-impregnated paper under the 100% 50 Hz harmonic voltage (a) 12 kV, (b) 14 kV, (c) 16 kV

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Fig. 5. PRPD pattern of oil-impregnated paper under the 80% 50 Hz and 20% 250 harmonic voltage (a) 12 kV, (b) 14 kV, (c) 16 kV

Fig. 6. PRPD pattern of oil-impregnated paper under the 80% 50 Hz and 20% 350 harmonic voltage (a) 12 kV, (b) 14 kV, (c) 16 kV

Fig. 7. PRPD pattern of oil-impregnated paper under the 80% 50 Hz and 20% 550 harmonic voltage (a) 12 kV, (b) 14 kV, (c) 16 kV

The characteristic parameters of PD are calculated from the PD patterns of oilimpregnated paper, and further, the effects of harmonic voltages on the characteristic parameters of PD under different applied voltages are analyzed. The maximum positive and negative discharge magnitude of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages are shown in Fig. 9. With the increase of the applied voltage, the positive maximum discharge magnitude under different frequency harmonic voltages increases gradually, whereas the negative maximum discharge magnitude under different frequency harmonic voltages shows a tendency of first increasing and then decreasing. Specifically, with different applied voltages, the maximum value of the negative maximum discharge under the 250 Hz, 350 Hz, 550 Hz and 650 Hz harmonic voltages is 2.7 times, 2.6 times, 2.7 times and 2.4 times of that under the 50 Hz voltage, respectively. It shows harmonic voltage frequency has a greater effect on the negative maximum discharge.

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Fig. 8. PRPD pattern of oil-impregnated paper under the 80% 50 Hz and 20% 650 harmonic voltage (a) 12 kV, (b) 14 kV, (c) 16 kV

Fig. 9. Maximum discharge magnitude of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages (a) positive discharge, (b) negative discharge

The average positive and negative discharges magnitude of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages are shown in Fig. 10.

Fig. 10. Average discharge magnitude of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages (a) positive discharge, (b) negative discharge

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With the increase of applied voltage, the positive average discharge magnitude under different frequency harmonic voltages increases gradually. The positive average discharge magnitude is larger than the average discharge magnitude under 50 Hz voltage. The difference between the negative average discharge under harmonic voltages and that under 50 Hz voltage is small. The pulse number and pulse repetition rate of positive and negative discharge of oilimpregnated paper under different applied voltages and different frequencies of harmonic voltages are shown in Fig. 11 and Fig. 12, respectively.

Fig. 11. Discharge pulse number of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages (a) positive discharge, (b) negative discharge

Fig. 12. Pulse repetition rate of oil-impregnated paper under different applied voltages and different frequencies of harmonic voltages (a) positive discharge, (b) negative discharge

Under different applied voltages and frequency harmonic voltages, the pulse repetition number of positive discharge is lower, whereas the pulse repetition number of negative discharge is not much different from that under 50 Hz voltage. The pulse repetition rate of positive and negative discharge under different applied voltages and frequency harmonic voltages is not much different from that under 50 Hz voltage. Under the spherical electrode structure, the effect of harmonic voltage frequency on the pulse number and pulse repetition rate is small.

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4 Conclusion To analyze the effect of the harmonic voltage on the oil-impregnated paper insulation properties in a new type of power system with a high proportion of renewable energy sources and power electronic equipment, this paper performs an experimental study of the partial discharge characteristics at different frequencies of harmonic voltages. There are three conclusions. Firstly, the harmonic voltage changes the original partial discharge inception situation for the oil-impregnated paper. Due to the differences in harmonic polarity at different frequencies from the 50 Hz voltage, harmonic voltages have opposite effects on PDIV at different frequencies. Secondly, the split-peak phenomenon appears in all of the PD patterns of the oil-impregnated paper under the action of harmonic voltage. Moreover, the peak-splitting phenomenon is more obvious as the harmonic frequency is higher. Finally, the harmonic voltage causes the maximum and average discharge magnitude under the positive and negative discharge pulse increases, whereas positive and negative polarity of the number of discharge pulses and discharge repetition rate decreased. Acknowledgments. This work was supported by “Research on insulation life prediction of key components of equipment under the effect of the harmonic coil in power system and the transformer trial scale test device production with typical defects” of the Electric Power Research Institute of Yunnan Power Grid Co, Ltd., China Southern Power Grid (No. 056200KK52210034, No. YNKJXM20210186).

References 1. Yang, P., Liu, F., Jiang, Q.R., Mao, H.Y.: Large-disturbance stability of power systems with high penetration of renewables and inverters: phenomena, challenges, and perspectives. J. Tsinghua Univ. 61(5), 403–414 (2021). (in Chinese) 2. Zheng, Z., Miao, S.H., Li, C., Zhang, D., Han, J.: Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy internet. Trans. China Electrotech. Soc. 37(1), 192–207 (2022). (in Chinese) 3. Yazdani, A.M., Mirzaei, M., Akmal, A.: No-load loss calculation of distribution transformers supplied by non-sinusoidal voltage using three-dimensional finite element analysis. Energy 50, 205–219 (2013) 4. Taher, M.A., Kamel, S., Ali, Z.M.: K-factor and transformer losses calculations under harmonics. In: IEEE Eighteenth International Middle East Power Systems Conference, Cairo, Egypt, pp. 978–984. IEEE (2016) 5. Tan, Y.B., Yu, X.L., Zang, Y., Wang, H.T., Li, J.H.: The influence of harmonic current on the loss and temperature distribution characteristics of a converter transformer winding. Trans. China Electrotech. Soc. 38(2), 542–553 (2023). (in Chinese) 6. Ebnezer, M., Ramachandralal, R.M., Sarasamma, C.: Study and analysis of the effect of harmonics on the hot spot temperature of a distribution transformer using finite-volume method. Electr. Power Compon. Syst. 43(20), 2251–2261 (2015) 7. Jie, Z., Lin, C., Hao, W., Cong, L., Jian, H., Zhiwei, L.: Simulation analysis of the influence of harmonics current on the winding temperature distribution of converter transformer. In: 2021 6th Asia Conference on Power and Electrical Engineering (ACPEE), Chongqing, China, pp. 1566–1571. IEEE (2021)

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8. Yaghoobi, J., Alduraibi, A., Martin, D., Zare, F., Eghbal, D., Memisevic, R.: Impact of high-frequency harmonics (0–9 kHz) generated by grid-connected inverters on distribution transformers. Int. J. Electr. Power Energy Syst. 122, 1–9 (2020) 9. Wang, J., Li, Q., Liu, S.: Characteristics of partial discharge in oil-paper insulation system under high frequency voltage. In: 2017 IEEE 19th International Conference on Dielectric Liquids (ICDL), Manchester, UK, pp. 1–5. IEEE (2017) 10. Li, X.N.., Cui, Y.J., Ji, S.C., Zhu, L.Y., Sun, J.T.: Partial discharge characteristics of needleplane defect in oil-paper insulation under actual stress in converter transformers. In: 2017 IEEE Conference on Electrical Insulation and Dielectric Phenomenon (CEIDP), New York, US, pp. 397–400. IEEE (2017) 11. Azizian, F.M., Reid, A.J., Hepburn, D.M.: Analysis of HVDC superimposed harmonic voltage effects on partial discharge behavior in solid dielectric media. IEEE Trans. Dielectr. Electr. Insul. 24(1), 7–16 (2017) 12. Florkowski, M., Florkowska, B.: Distortion of partial-discharge images caused by highvoltage harmonics. IEE Proc. Gener. Transm. Distrib. 153(2), 171–180 (2006) 13. Sarathi, R., Archana, M.: Investigation of partial discharge activity by a conducting particle in transformer oil under harmonic AC voltages adopting UHF technique. IEEE Trans. Dielectr. Electr. Insul. 19(5), 1514–1520 (2012)

Effect Mechanism of Ambient Temperature and Humidity on Polyimide Partial Discharge Under High Frequency Electrical Stress Yiwei Wang(B) , Li Zhang, and Huangkuan Xu School of Electrical Engineering, Shandong University, Jinan 250061, China [email protected]

Abstract. The high frequency power transformer faces some problems such as partial discharge and premature insulation failure due to the effect of electrothermal coupling stress. In order to study the coupling effect of ambient temperature and humidity on the characteristics of polyimide partial discharge, this paper studied the characteristics of polyimide partial discharge at four temperature points of 75–150 °C and three humidity points of 40–80%. The initial partial discharge voltage, the maximum and average discharge amplitude and characteristic parameters were counted to observe the surface morphology. The test results show that temperature is proportional to the maximum discharge amplitude, humidity is proportional to the maximum discharge amplitude when the temperature is less than 100 °C, and the maximum discharge amplitude increases first and then decreases when the temperature is greater than 100 °C. For the average discharge amplitude and the number of discharge per unit time, with the increase of temperature, the first increase and then decrease, the temperature is less than 100 °C and the humidity is less than 60%, the temperature is more than 100 °C and the humidity is more than 60%, and the temperature is more dominant. Keywords: High-frequency power transformer · Polyimide · Partial discharge · Temperature-humidity coupling effect

1 Introduction The development of the current power system presents new features such as large-scale distributed power supply grid-connection and extensive application of power electronic equipment [1]. Power Electronic Transformer (PET) has been widely used due to its advantages such as AC side reactive power compensation, harmonic control, DC access of renewable energy/energy storage equipment [2]. High-frequency power transformer is the core component of PET to achieve electrical isolation and voltage level transformation, and its operating frequency is usually between 400 and 40 kHz [2], and its voltage is high-frequency square wave or high-frequency class sine wave [3] the local temperature can reach more than 150 °C, which is worse than the traditional power frequency transformer. Polyimide (PI) has been widely used in various power equipment because of its excellent electrical properties and heat resistance [4] With the increase © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 477–485, 2024. https://doi.org/10.1007/978-981-97-1064-5_52

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of capacity, voltage level and operating frequency, its insulation problem will become more prominent, and the insulating medium is prone to partial discharge leading to aging breakdown and loss of insulation effect. Studies have shown that the factors affecting partial discharge of insulating medium mainly include the applied electrical stress parameters (amplitude, frequency, etc.) and the applied environmental stress parameters (temperature, humidity, etc.). The combined effect of many factors affects the aging rate of insulation, and then affects the insulation life of materials. Most studies focus on the mechanism of partial discharge under the action of a single factor, without considering the synergistic effect of temperature and humidity. With the increase of temperature, the average discharge and discharge times increase, and the insulation life decreases [5, 6]. According to literature [7], polyimide hydrolyzes with water molecules, resulting in insulation deterioration. Literature [8] shows that at low humidity, with the increase of humidity, the repetitive partial discharge inception voltage (RPDIV) of the film decreases, and the average discharge number and average discharge amplitude increase. In the high humidity environment, the RPDIV of the film increased with the increase of humidity, and the average discharge times and average discharge amplitude decreased. There is a critical value of the influence of humidity on the insulation life of the film, but the experimental temperature reached the highest 90 °C, and the study of temperature and humidity on the characteristics of polyimide partial discharge at 100 °C and above was not taken into account. Aiming at the research on the coupling effect of temperature and humidity in the working environment of high frequency power transformer at 100 °C and above, this paper relies on the electro-thermal accelerated aging experimental platform to carry out partial discharge experiments of polyimide samples under high frequency sinusoidal electrical stress under different experimental conditions of temperature and humidity, and carries out statistical analysis on the characteristics of partial discharge starting voltage, discharge amplitude and discharge number. The surface morphology of polyimide samples in different aging periods was analyzed. The effect of temperature and humidity on polyimide partial discharge is described. The research results can provide reference for insulation protection of high-frequency power transformer under high temperature and high humidity working environment.

2 Experimental Apparatus and Sample The experimental platform is a high-frequency partial discharge test platform, as shown in Fig. 1. The high frequency and high voltage power supply is mainly composed of a power supply case, a frequency modulation inductor box, a transformer tank and various connecting lines, which can output a high frequency sinusoidal voltage with a peak value of 0–20 kV and a frequency of 5–50 kHz. The frequency can be continuously adjustable through the frequency modulation unit. The constant temperature range of the aging box is 20–200 °C. In order to ensure uniform heating, an internal circulation air duct is set. ETS-93686 high frequency pulse current sensor with measuring bandwidth of 10 kHz–100 MHz was selected to collect PD signals. Tektronix P6015A high voltage probe was used to measure real-time voltage on the ball electrode. The probe attenuation multiple was 1000:1. The digital oscilloscope model is Tektronix MDO3024 four-channel

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oscilloscope with a sampling rate of up to 2.5 GS/s and a sampling bandwidth of up to 200 MHz. The relative humidity is defined as the percentage value of the actual moisture vapor density in the air and the saturated water vapor density at the same temperature. The ambient relative humidity of the sample is measured by the DT-625 hygrometer. Due to the slightly uneven electric field between the ball-plate electrode and the normal and tangential electric field components, the ball-plate electrode was selected to simulate the actual electric field subjected to the insulation sample. The diameter of the ball electrode was 20 mm, the thickness of the plate electrode was 10 mm, and the diameter was 75 mm. The 75 µm polyimide film of DuPont was selected as the sample, which was a polymer formed by polycondensation reaction of dianhydride of homophthalic acid and 4,4’-diaminodiphenyl ether in solvent. The heat resistance temperature was greater than 220 °C.

Fig. 1. High frequency partial discharge test platform

3 Experimental Scheme Kapton 75 µm polyimide film was used as the sample in the experiment. In order to avoid the interference of contamination and moisture on the surface of the sample to the experimental results, the polyimide sample under test should be treated with alcohol before the experiment and dried in a drying oven at 60 °C for 2 h. After drying, the sample is cut into a size of 50 mm × 50 mm and placed between the upper and lower electrodes to ensure that the upper and lower electrodes are in close contact with the sample. In order to study the influence of ambient temperature and humidity on the partial discharge of polyimide, the high frequency and high voltage power supply was set to 3 kV and 30 kHz to simulate the electrical stress of polyimide in the actual working environment. 75 °C was selected as a reference, and three temperature points of 100 °C, 125 °C and 150 °C and three humidity values of 40%, 60% and 80% were selected for the experiment. First, the aging box is heated to the set temperature, and the voltage is applied after 30 min of stability. 200 V/s is selected as the voltage boost speed, and the voltage is applied under different temperature and frequency conditions until the initial repetitive discharge pulse is generated. Observe and record the Voltage amplitude, namely Partial Discharge Inception Voltage (PDIV) [9]. Then the accelerated insulation aging test was carried out at three temperature points and three humidity points respectively until the

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insulation breakdown, and the experiment was repeated. The experiment was repeated 5 times in each group of experimental conditions. The oscilloscope displayed the highfrequency sine waveform of the power supply and the induced voltage waveform of the pulse sensor, and the computer was connected to the Labview program for continuous recording of partial discharge data. The EO-VMD partial discharge denoising algorithm is used to denoise the signal obtained by the high-frequency pulse sensor, and the discharge signal obtained after denoising is used to draw the PRPD spectrum [10] to obtain the corresponding maximum discharge amplitude, total discharge amplitude, total discharge frequency and average discharge frequency. The changes of discharge morphology of polyimide in different stages of aging were determined. The surface morphology of the samples at different aging stages was observed with a German ZEISS SmartZoom 5 optical microscope, and the section aging depth of the samples was observed.

4 Results and Discussion 4.1 Partial Discharge Morphology Under Different Temperature-Humidity Conditions The accelerated aging experiment of polyimide with different temperature and humidity was carried out. The voltage boost rate was 200 V/s, and the pressure was first pressed to start partial discharge. PDIV is slightly different under different temperature and humidity, and decreases with the increase of temperature and increases slightly with the increase of humidity. The initial voltage of local discharge under different conditions is shown in Table 1. Table 1. PDIV at different temperature and frequency temperature

PDIV/kV

/°C

40%

60%

80%

75

1.29 kV

1.28 kV

1.30 kV

100

1.26 kV

1.27 kV

1.28 kV

125

1.21 kV

1.25 kV

1.24 kV

150

1.20 kV

1.22 kV

1.25 kV

Pressure to 2 times of PDIV, that is, 3 kV, is used as the partial discharge test voltage under different temperature and humidity conditions [11]. Each group of experiments is carried out 5 times to eliminate accidental errors. The partial discharge waveform is collected through Labview control program and post-denoising is carried out. The resulting signal is mapped as a Phase Resolved Partial Discharge (PRPD). As shown in Fig. 2, Fig. 3 and Fig. 4, different colors represent the density of partial discharge points, with red representing the densest area and blue representing the sparsest area.

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Fig. 2. Partial discharge characteristics at different temperatures at 40% humidity

Fig. 3. Partial discharge characteristics at different temperatures at 60% humidity

Fig. 4. Partial discharge characteristics at different temperatures at 80% humidity

It can be seen from Fig. 2 that partial discharge mainly concentrates on the voltage rising edge of the positive and negative half waves in the single cycle wave, and there is also a small amount of discharge along the voltage falling edge. With the increase of temperature, the discharge quantity increases along the voltage drop. At 40% humidity, the partial discharge pattern appeared in the “cluster” pattern. With the increase of temperature, the partial discharge phenomenon on the surface of polyimide sample became more and more intense, and the discharge phase range became larger and larger. The “cluster” pattern disappeared at 125 °C, and the discharge phase range further diffused. From the point of view of the partial discharge frequency distribution, the discharge phase distribution of different amplitudes is more regular, showing a blue-red-blue “stratification” phenomenon along the direction of the amplitude increase. As can be seen from Fig. 3, the “clustering” form is weakened when 60% humidity is compared with 40% humidity, and the “clustering” form disappears when the temperature is greater than 100 °C. With the increase of temperature, the discharge amplitude moves to the direction of small amplitude, indicating that the discharge amplitude decreases gradually. When the discharge phase range increases, the voltage drops along with the discharge times, and the discharge phase range reaches more than 300° at 150 °C. As can be seen from Fig. 4, the discharge phase is relatively dispersed at 80% humidity, and the “clustering” form disappears from 75 °C. In addition to the voltage rising edge of 0°–90° and 180°–270°, partial discharge also occurs along the voltage falling edge of 140–180° and 300–360° in the discharge phase, but the discharge amplitude at the voltage falling edge is small. The phenomenon of “stratification” of discharge with different amplitude is obvious. With the increase of temperature, the number of discharges decreased significantly, and

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when the temperature was 150 °C and the humidity was 80%, the insulation life was too severe, and the data points in the PRPD diagram were the least. The influence of different temperature and humidity on the maximum discharge amplitude is shown in Fig. 5 (1). Under the same humidity condition, the maximum discharge amplitude increases with the rise of temperature, and the rise amplitude becomes larger when the temperature is greater than 100 °C. Under the same temperature condition, the action law of humidity is divided into two parts from the temperature of 100 °C: When the temperature is less than 100 °C, the higher the humidity, the greater the maximum discharge amplitude; when the temperature is greater than 100 °C, the maximum discharge amplitude reaches the peak value when the humidity is 60%; and the maximum discharge amplitude when the temperature is 80% is greater than the humidity 40%

Fig. 5. Influence of temperature and humidity on maximum discharge amplitude, average discharge amplitude and discharge times per unit time

The influence of different temperature and humidity on the average discharge amplitude is shown in Fig. 5 (2). When the humidity is less than 60%, the average discharge amplitude increases, reaches a peak value at 100 °C, and then decreases. When the humidity is greater than 60%, the average discharge amplitude decreases with the increase of temperature. At 75 °C, the average discharge amplitude in 80% humidity environment is twice that in other humidity environment. At 80% humidity environment, the average discharge frequency decreases with the increase of temperature. When the temperature is greater than 100 °C, the average discharge amplitude in 40% humidity environment is the largest, and the difference between the three is small. The influence of different temperature and humidity on the number of discharge per unit time is shown in Fig. 5 (3). Under the same humidity condition, the number of discharge per unit time first increases and then decreases with the temperature, reaching the peak value at 100 °C. When the temperature is less than 100 °C, 60% humidity has the largest discharge times per unit time. When the temperature is greater than 100 °C, the number of discharge per unit time at 40% humidity is the largest, and it decreases with the increase of humidity. It can be seen that the increase of humidity has an inhibitory effect on the number of discharge per unit time in high temperature environment. 4.2 Surface Topography Observation and Analysis The influence of different temperature and humidity on the breakdown surface morphology of polyimide samples is shown in Fig. 6. The upper left is low temperature and low humidity, the upper right is low temperature and high humidity, the lower left is high temperature and low humidity, and the lower right is high temperature and high

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humidity. It can be seen from the figure that the increase of temperature and humidity can lead to the increase of the breakdown point, the breakdown position gradually moves to the outside, and the ablative carbonization near the breakdown point is similar. The increase of humidity is conducive to the increase of breakdown point, and the increase of temperature increases the intensity of partial discharge. It can be seen from the figure on the lower left that other substances produced by polyimide pyrolysis or reaction in high temperature environment.

Fig. 6. Breakdown surface morphology of polyimide samples

4.3 Mechanism of Influence of Ambient Temperature and Humidity According to Richaedson-Schottky law, the probability of initial electron generation by field-assisted thermal electron emission is [10]: h(t) = Nsc (t)v0 e−

ψ−(e[E(t)]/4π ε0 )0.5 KT

(1)

where, electron emission probability of electrode surface; The number of electrons on the surface at time t that can be used for detrapping; Is the escape work function; Is the electric field strength in the defect at time t. With the increase of temperature, the metal electrons of the electrode obtain great kinetic energy, the emission energy of the electrode is increased, the impact ionization and photoionization are increased, and the frequency and intensity of partial discharge are promoted. In addition, since the bulk conductivity of insulation is proportional to the discharge repetition rate [12], the increase in temperature increases the bulk conductivity and increases the number of discharges of insulation per unit time. The discharge quantity and the maximum discharge amplitude increase with the increase of temperature. The destructive effects of discharge on materials mainly include cracking of molecular chains by impact, melting or degradation of polymers caused by temperature rise, and corrosion of polymer bases such as ·H and ·O with high chemical activity caused by partial discharge [13–15]. When the temperature is less than 100 °C and the humidity increases, water molecules will form tiny water droplets on the surface of polyimide samples, which can adsorb the charge generated by local discharge and increase the charge retention effect [7], making partial discharge become intense. Therefore, the average discharge amplitude increases with the increase of humidity at 75 °C, and the maximum discharge amplitude also shows

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an upward trend. Liquid water begins to vaporize at 100 °C under normal pressure and becomes water vapor, so there is no surface liquid water droplets in the environment above 100 °C. When the humidity increases, the water molecules in the air show weak electronegativity, adsorb the electrons generated by the discharge, and weaken the discharge intensity. At the same time, the hydrolysis of polyimide in humid environment will reduce the molecular weight of polyimide [16], and the active groups/ions -NO2, -COOH, ·O, ·H, etc. generated by partial discharge may enhance the charge transport capacity of polyimide medium [17, 18]. The increase of temperature increases the emission energy of hot electrons, increases the conductivity, and promotes the maximum discharge amplitude of partial discharge. With the increase of temperature, the pyrolysis reaction is severe, and the average discharge amplitude and frequency decrease. When the temperature is less than 100 °C, the number of water droplets on the surface of the polyimide sample increases and the partial discharge becomes intense. When the temperature is greater than 100 °C and the humidity is greater than 60%, the water molecules in the air adsorb the electrons generated by the discharge and weaken the discharge intensity.The coupling effect of temperature and humidity on the discharge characteristic quantity is as follows: for the maximum discharge amplitude, temperature is proportional to it; when humidity is less than 60%, temperature and humidity have a synergistic effect, and the increase of temperature and humidity will increase the discharge amplitude; when humidity is greater than 60%, temperature plays a leading role. For average discharge amplitude and discharge times per unit time, temperature less than 100 °C and humidity less than 60% have a synergistic promoting effect, temperature greater than 100 °C and humidity greater than 60% have a synergistic weakening effect, and other conditions temperature plays a dominant role.

5 Conclusion This paper studied the characteristics of polyimide partial discharge under different temperature and humidity conditions under high frequency sinusoidal electrical stress, expounded the law of the influence of temperature and humidity on the characteristic quantities such as the initial voltage, discharge amplitude and discharge times of partial discharge, and explained the mechanism of temperature and humidity from the perspective of polyimide molecular explanation. The surface morphology of polyimide samples under different experimental conditions was observed and analyzed. The experimental results show that temperature makes partial discharge more intense, but the average discharge amplitude and discharge times decrease with the increase of temperature above 100 °C due to the pyrolysis reaction of polyimide. Humidity can increase the discharge phase range and the discharge region on the sample. For the average discharge amplitude and discharge times, when humidity is less than 60%, the temperature is less than 100 °C, and when humidity is more than 60%, the temperature is more than 100 °C, the temperature is more decisive.

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References 1. Zhang, J., Huang, L., Shu, J., et al.: The impact of distributed generation on the stability of the large power grid under high penetration rates. New Energy Prog. 4(5), 379–385 (2016). (in Chinese) 2. Li, Z., Gao, F., Zhao, C., et al.: A comprehensive review of power electronic transformer technologies. Chin. J. Electr. Eng. 38(5), 1274–1289 (2018) 3. Aggeler, D., Biela, J., Kolar, J.W.: A compact, high voltage 25 kW, 50 kHz DC-DC converter based on SiC JFETs. In: IEEE Applied Power Electronics Conference (APEC), Austin, TX, USA (2008). (in Chinese) 4. Xue, W., Zheng, L., Gao, Y., et al.: Design methods for high-frequency transformers in power electronic transformers. Electr. Meas. Instrum. 52(23), 117–121+128 (2015). (in Chinese) 5. Cao, K., Wu, G., Luo, Y., et al.: Partial discharge characteristics of traction motor insulation under high-frequency pulse excitation. High Volt. Eng. 38(6), 1376–1382 (2012). (in Chinese) 6. Luo, Y., Wu, G., Wang, P., et al.: Influence of temperature on the partial discharge characteristics of polyimide films under continuous square-wave pulse voltage. Chin. J. Electr. Eng. 32(19), 154–160 (2012). (in Chinese) 7. Zou, C., Fothergill, J.C., Rowe, S.W.: The effect of water absorption on the dielectric properties of epoxy nanocomposites. IEEE Trans. Dielectr. Electr. Insul. 15(1), 106–117 (2008) 8. Luo, Y., Yang, X., Shi, C., et al.: Mechanisms of the influence of environmental humidity on partial discharge characteristics of PI Films under pulse voltage. Insul. Mater. 49(5), 65–73 (2016). (in Chinese) 9. Fard, M.A., Farrag, M.E., McMeekin, S.G., Reid, A.J.: Partial discharge behavior under operational and anomalous conditions in HVDC systems. IEEE Trans. Dielectr. Electr. Insul. 24(3), 1494–1502 (2017) 10. Xu, H., Zhang, L., Ayubi, B.I., et al.: Study on the temperature-frequency characteristics of partial discharge in polyimide under high-frequency electrical stress based on improved variational mode decomposition denoising. Trans. China Electrotech. Soc. 38(03), 565–576 (2023). (in Chinese) 11. Zhang, K., Zhang, L., Zhao, T., et al.: Influence of high-frequency sinusoidal electrical stress on gas-solid insulation partial discharge. High Volt. Eng. 45(12), 3879–3888 (2019). (in Chinese) 12. Yu, Q., Yin, C.: Research on DC partial discharge in oil-paper insulation. Transformer 35(5), 17–20 (1998). (in Chinese) 13. Peter, H.F.M.: Degradation of solid dielectrics due to internal partial discharge: some thoughts on progress made and where to go now. IEEE Trans. Dielectr. Electr. Insul. 12(5), 905–913 (2005) 14. Mayoux, C.: Degradation of insulating materials under electrical stress. IEEE Trans. Dielectr. Electr. Insul. 7(5), 590–601 (2000) 15. Xu, S.Z., Li, X., Wang, F.P.: Synthesis and spectroscopic properties of five novel polyimides. J. Kunming Inst. 44(03), 116–120 (2022). (in Chinese) 16. Xia, Z., Zhu, Z., Howe, D.: Analytical magnetic field analysis of Halbach magnetized permanent magnet machines. IEEE Trans. Magn. 37(4), 2827–2830 (2001) 17. Li, Y., Qu, C., Xia, Y., et al.: Under the action of electric charge traps and the microcosmic characteristics of polyimide insulation. High Volt. Technol., 1–11 (2023). (in Chinese) 18. Wang, F., Li, X., Yang, Y., et al.: Synthesis and optical properties of seven polyimides. Yunnan Chem. Ind. 49(10), 20–23 (2022). (in Chinese)

Research on Intrinsic Shaft Voltage in Permanent Magnet Synchronous Wind Generators with Sectionalized and Overlapped Stator Laminations Yali Hao1 , Ruifang Liu1(B)

, Liangliang Zhang2 , Weili Li1 , and Lei Jia1

1 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China

{23121414,rfliu,wlli,20121446}@bjtu.edu.cn

2 Jing-Jin Electric Technologies Co., Ltd., Beijing 100015, China

[email protected]

Abstract. The stator laminations of large permanent magnet synchronous wind generators are often sectionalized and overlapped, which will cause the magnetic circuit asymmetry. The resulting asymmetric magnetic flux around the shaft yields intrinsic shaft voltage along the shaft. The shaft voltage will cause electric corrosion of the bearing and endanger the security of system. In this paper, the shaft voltage of a 5.57 MW permanent magnet synchronous wind generator with sectionalized and overlapped stator laminations is calculated through analytical method and finite element method. The results show that when the number of overlapped layers is the same, the voltage amplitude with symmetrical overlapping is much smaller than that of asymmetrical overlapping. It is necessary to properly match the sectionalized stator and the number of overlapped layers combination. In a certain range, the larger the rotating speed, the larger the shaft voltage amplitude; The shaft voltage amplitude of the generator under loaded condition is larger than that under no-loaded condition. Keywords: Permanent magnet synchronous wind generator · stator lamination · sectionalization and overlap · Intrinsic low-frequency shaft voltage

1 Introduction In order to accelerate the global energy low-carbon transition, renewable energy generation has been the general trend. Among them, wind power has become the fastest growing clean energy in emerging industries [1]. With the advantages of high efficiency and low cost, permanent magnet synchronous generator has become the first choice of current wind power generation system [2]. Practical experience shows that shaft voltage is the main factor leading to bearing electrical corrosion and then bearing damage [3], threatening the normal operation of the whole system, so it is very necessary to analyze and suppress intrinsic low-frequency shaft voltage. Shaft voltage can be divided into high frequency and low frequency according to frequency. When the generator is driven by a converter or switched transmission, the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 486–495, 2024. https://doi.org/10.1007/978-981-97-1064-5_53

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common-mode voltage is coupled to the inner and outer rings of the bearing through stray capacitance to induce high-frequency bearing voltage [4], The high-frequency shaft voltage induced by the common mode current and the intrinsic low-frequency shaft voltage caused by the asymmetry of the magnetic circuit inside the motor are at both ends of the shaft [5]. At present, there are many researches on common mode shaft voltage. For example, reference [6] uses capacitor network model to study the influence of driver and parameters on common-mode voltage. The suppression of common-mode shaft voltage is mainly based on the software suppression of common-mode voltage on the frequency converter side [7] and the use of insulated bearings and grounded carbon brushes on the electric motor side [8, 9]. At present, there are relatively few researches on the intrinsic low-frequency shaft voltage of permanent magnet generators, which mainly focus on the model of permanent magnet generators and its own parameters [10, 11], and the researches on suppression measures are also relatively scattered. At present, there is a lack of comprehensive researches on the sectionalizing of stator lamination under different conditions and the symmetric and asymmetric overlapping of permanent magnet synchronous wind generators in practical occasions. On this basis, the low-frequency shaft voltage of permanent magnet synchronous wind generator caused by sectionalized and overlapped stator is studied in this paper. The shaft voltage under different conditions of sectionalization, symmetric and asymmetric overlap is verified by analytic derivation, ANSYS simulation and some experiments. Finally, the measures to weaken the intrinsic shaft voltage are proposed, aiming at providing some reference for the design of permanent magnet generators.

2 Analysis of Low-Frequency Shaft Voltage 2.1 Mechanism of Low-Frequency Voltage Generated by Sectionalized Stator The outer diameter of large permanent magnet synchronous wind generator is large, and the stator laminates are usually sectionalized and overlapped. Therefore, the resulting air gap will destroy the symmetry of the primary magnetic field. Figure 1 shows the diagram of symmetrical and asymmetrical flux when the stator is divided into two sections. When the rotor rotates, only the asymmetrical magnetic flux encircles the rotating shaft, thus producing intrinsic shaft voltage V sh along the shaft.

Fig. 1. Magnetic flux diagram of a generator with two sections

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2.2 Analytic Derivation of Low-Frequency Shaft Voltage In order to predict or suppress the shaft voltage, it is necessary to analyze the air-gap magnetic field generated by the sectionalized stator. The magnetic reluctance of the iron core is assumed to be zero, the end effects of winding are not considered, and factors other than stator lamination that may cause shaft voltage are ignored. From the ideas of permeance λ, Magnetic-motive-force (MMF) F → magnetic density B → magnetic flux Φ → shaft voltage V sh , the low-frequency shaft voltage formula of sectionalized and overlapped stator is derived [12]. 2.2.1 Shaft Voltage with Sectionalized Stator The F is expressed as follows [10]:    F2n−1 cos (2n − 1)pθr F=

(1)

n

where θ r is angular variable in rotor’s coordinate, p is the pole pair number, the F 2n-1 is the (2n − 1)th order harmonic component of the Magnetic-motive-force. Among them,   (2n − 1)αp π 4Bc (2) lm (θr ) sin F2n−1 = μ0 (2n − 1)π 2 where Bc is the density of remanence in a permanent magnet, lm (θ r ) is the thickness function of the magnetizing direction of the permanent magnet, μ0 is the air permeability, αp is the pole-arc coefficient.  λm cos(mDθs ) λf = λ0f + (3) m

where λ0f is the equivalent joint air gap permeance of the fundamental wave, λm is the mth order harmonic component of the the equivalent joint air gap permeance, D is the number of stator sections per layer. The sector is stacked on the stator side, θ s − ωr t = θr

(4)

where θ s is angular variable in stator’s coordinate. According to the principle of magnetic circuit, the Br_f is as follows: Br_f = λf F

(5)

And by bringing (1), (2), (3), (4) into (5), (6) can be obtained, Br_f = λf F = Br_f0 + Br_f1 + Br_f2 Br_f0 = λ0f



  F2n−1 cos (2n − 1)pθr

(6) (7)

n

Br_f1 =

  F2n−1 λm n

m

2

   cos mDθs + (2n − 1)pθs − (2n − 1)pωr t

(8)

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Br_f2 =

  F2n−1 λm n

2

m

   cos mDθs − (2n − 1)pθs − (2n − 1)pωr t

489

(9)

Since the trigonometric function is orthogonality, only Eq. (9) may not be zero. When mD = (2n − 1)p, that is, D/p = (2n − 1)/m, the Φ is as follows: Φ = BS =

  F2n−1 λm n

2

m

  cos (2n − 1)pωr t SL

(10)

where S L is the unit area which magnetic lines of flux pass through. Vsh = −N

  d    F2n−1 λm = (2n − 1)pωr SL sin (2n − 1)pωr t dt 2 n m

(11)

where N is 1, since the shaft of rotation is regarded as a conductor. Therefore, if the numerator whose ratio of D/p is reduced to the simplest fraction is odd, the shaft voltage with corresponding odd multiples will be generated, as illustrated in Table 1. In Table 1, p is 12. When D is 9, the simplest fraction of D/p is 3/4, so the shaft voltage mainly composed with third harmonics will be generated. Table 1. Theoretical analysis of shaft voltage with sectionalized stator. Joints number D

pole pairs p

D/p

Harmonic number

8

12

2/3

0

9

12

3/4

3

12

12

1

1

2.2.2 Shaft Voltage with Symmetric-Overlapped Stator The expression of the permeance λf* is as follows:  λ∗f = λ0f + λm cos[mD(θs + cδ)]

(12)

m

where δ is the overlapped angle of the two layers, δ = 360°/DQ; Q is the number of layers of overlapped stator; c is the overlapped layer of the lamination. The magnetic density Br_fc = λ∗f F = Br_f0∗ + Br_f1∗ + Br_f2∗, Br_f0∗ = λ0f



  F2n−1 cos (2n − 1)pθr

(13)

n

Br_f1∗ =

  F2n−1 λm n

m

2

   cos mD(θs + cδ) + (2n − 1)pθs − (2n − 1)pωr t (14)

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Br_f2∗ =

  F2n−1 λm n

2

m

   cos mD(θs + cδ) − (2n − 1)pθs − (2n − 1)pωr t (15)

The air gap magnetic density will not be zero only when mD = (2n − 1)p, so: Φ = BS =

  F2n−1 λm n

Vsh =

m

  F2n−1 λm n

m

  cos (2n − 1)pωr t + (2n − 1)pcδ SL

(16)

  pwr SL sin (2n − 1)pωr t + (2n − 1)pcδ

(17)

2 2

Therefore, if the numerator whose ratio of DQ/p is reduced to the simplest fraction is odd, the shaft voltage with corresponding odd multiples will be generated. In Table 2, when the number of p and the number of joints D are both 12 and the number of overlapped layers Q is 3, the shaft voltage dominated by third harmonics will be generated. Table 2. Theoretical analysis of shaft voltage with symmetric-overlapped stator D

p

Q

DQ/p

Harmonic number

12

12

2

2

0

12

12

3

3

3

12

12

5

5

5

3 Finite Element Analysis of Shaft Voltage with Sectionalized Stator 3.1 Finite Element Modeling In order to verify the correctness of the above theoretical analysis, the finite element simulation model of 1/12 permanent magnet synchronous wind generator is established, as shown in Fig. 2. The power of the permanent magnet synchronous wind generator is 5.57 MW, the rated speed is 410 rpm, the number of stator slots is 216, the frequency of the generator is 82 Hz, and the pole pair number p is 12, the outer diameter of the rotor is 1893 mm, the outer diameter of the stator is 2240 mm and the inner diameter of the stator is 1900 mm. 3.2 Simulation of Sectionalized Sector at Different Positions Joints widths of 0.4mm at the position of 10°, 15°, 20° and 30° respectively are simulated, and the speed of generator is 410 rpm under loaded condition. In Fig. 2, the stator is sectionalized at a position of 10°, and then the presence of a shaft-encircling flux can

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Fig. 2. Model of generator

be clearly observed in Fig. 3. Spectrum analysis of shaft voltages generated at different positions was performed, as shown in Fig. 4(a) and (b). It can be found that the peak shaft voltage at different locations is about 274 mV, only the difference in phase. As can be seen from the spectrum distribution diagram, it is mainly the first harmonics of 82 Hz, which is completely consistent with the analytic derivation.

Shaft-encircling magnetic field lines Fig. 3. Distribution of magnet field lines of sectionalized stator at 10° position

X: 3.794 Y: 137.3

X: 1.762 Y: 137

150

X: 5.827 Y: 137.9

Single-Sided Amplitude Spectrum of X(t)

X: 9.892 Y: 131.1

10° 15° 20° 30°

70 X: 82.31 Y: 70.34

100

shaft voltage/mV

shaft voltage/mV

60 50

0

-50

50 40 30 20 10

-100

0 1

2

3

4

5

6

time/ms

7

8

9

10

11

0

200

400

600

800

1000

1200

f (Hz)

(a) Time domain waveform diagram (b) Spectrum characteristics distribution diagram Fig. 4. Shaft voltage of sectionalized stator at different positions under loaded condition

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3.3 Simulation of Sectionalized Stator Under Different Loads and Different Rotating Speeds Set the current drive of the generator to 0, perform the same thing as Sect. 3.2. It can be seen from Fig. 5 that the peak value of shaft voltage with sectionalized stator at the four positions of 10°/15°/20°/30° under no-loaded condition is smaller than that under loaded condition. X: 0.271 Y: 132.4

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X: 2.304 Y: 132

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/mV

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50

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Fig. 5. Time domain waveform diagram of shaft voltage with sectionalized stator at different positions under no-loaded condition

In addition, taking the sectionalized stator at 10° position under no-loaded as an example, the simulation was carried out at 200 rpm/300 rpm/410 rpm (rated speed) respectively, as shown in Fig. 6. It can be found that with the increase of speed of the generator, the amplitude and frequency of shaft voltage are increasing, but it is still mainly the first harmonics of 82 Hz. Therefore, the speed of the generator should be limited in a proper range. 150

410rpm 300rpm 200rpm

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4 Finite Element Analysis of Shaft Voltage with Overlapped Stator 4.1 The Shaft Voltage with Symmetric-Overlapped of Stator The simulation is a two-dimensional field, and the method of superposition is needed to study the overlapped stator in three dimensions. In the case of three-layer symmetricoverlapping, the shaft voltage obtained by 10°/20°/30° sectionalized stator is superimposed and divided by 3, and the same is true for two layers and five layers. Their time-domain waveform and spectrum distribution are shown in Fig. 7 and 8. As can be seen from the figure, the peak value of shaft voltage is very small and almost 0 when two layers are overlapped. When three layers and five layers are overlapped, the peak value of shaft voltage is about 75 mV and 37 mV respectively, which are dominated by third and fifth harmonics respectively. They are consistent with analytic derivation. Therefore, the more the number of overlapped layers, the smaller the shaft voltage amplitude. But processing time and cost need to be carefully considered. X: 1.762 Y: 37.94

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20 10

X: 3.523 Y: 6.395

0 -10 -20 -30

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Fig. 7. Time domain waveform diagram of shaft voltage with 2, 3 and 5 layers overlapped Single-Sided Amplitude Spectrum of X(t) X: 82.31 Y: 1.761

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Fig. 8. Spectrum characteristics distribution diagram of shaft voltage of overlapped stator

4.2 The Shaft Voltage with Asymmetric-Overlapped of Stator In order to explore the influence of symmetric and asymmetric overlapped stator on shaft voltage, it is necessary to keep other conditions unchanged for comparative analysis. Take

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the two layers overlapped as the example, the asymmetric-overlapped of cross angle 10° and the symmetric-overlapped of cross angle 15° are simulated. The simulation results are shown in Fig. 9. The results show that the shaft voltage waveform and harmonic composition of asymmetric-overlapped are no longer regular. The peaking value is 10.83 times that of symmetric-overlapped, and the main harmonics are fundamental and third. Therefore, asymmetric-overlapped greatly increases the amplitude of shaft voltage. 40

80 60

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X: 5.827 Y: 68.2 shaft voltage/mV

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Fig. 9. The shaft voltage with asymmetric-overlapped stator

4.3 Experimental Verification In order to verify the correctness of the simulation results of asymmetric-overlapped stator, the low-frequency shaft voltage of the above 5.57 MW permanent magnet synchronous wind generator was measured. The experimental data show that the peak shaft voltage of two-layer symmetric-overlapped is 0.84 V, and that of two-layer asymmetricoverlapped is 4.89 V. It can be found that the peak-to-peak value of shaft voltage is much larger when asymmetric-overlapped is adopted than that with symmetric-overlapped, which verifies the correctness of the above simulation conclusions.

5 Conclusions (1) In this paper, the finite element model of permanent magnet synchronous wind turbine is established and the shaft voltage of the generator is actually analyzed. It is found that the low-frequency shaft voltage with asymmetric-overlapped stator is smaller than which with symmetric-overlapped for the same number of layers. (2) The low-frequency shaft voltage formula is derived and the simulation analysis is carried out. It is found that when the number of sectionalization D, the number of asymmetric-overlapped layers Q and the pole pair number p meet the requirement that the molecule after DQ/p is reduced to the simplest fraction is odd, the corresponding odd times of shaft voltage harmonics will be generated.

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(3) In order to suppress the low-frequency shaft voltage, the stator laminates should be symmetric-overlapped. The D and Q combinations should be coordinate rationally. In a proper range, the speed of the generator should be limited; The amplitude of shaft voltage under no-loaded condition is smaller than that under loaded condition. Acknowledgments. This work was funded by Beijing Natural Science Foundation (3222055) and 2021 High Power and High efficiency Electric Drive assembly system Development and Industrialization Project (TC210H02Q).

References 1. Tan, Y.: Application of new energy power generation technology in power system. Light Sour. Light. 175(12), 240–242 (2022). (in Chinese) 2. Zeng, Y.: Application and development of permanent magnet motor in wind power generation system. Urban Constr. Theory Res. (Electron. Ed.) 338(20), 11–12 (2019). (in Chinese) 3. Li, W., Wang, Y., Li, J.: Optimization scheme of electric corrosion and insulation performance of traction motor bearing. Bearing 521(04), 26–31 (2023). (in Chinese) 4. Zhao, Q., Yang, E., Liu, R., et al.: A high frequency shaft current modeling method for variable frequency powered induction motor. Proc. CSEE 41(23), 8139–8148 (2021). (in Chinese) 5. Zhao, F.: Study on Shaft Voltage Analysis and Weakening Measures of Built-in Permanent Magnet Synchronous Motor. Shandong University (2021). (in Chinese) 6. Wang, F.: Motor shaft voltages and bearing currents and their reduction in multilevel mediumvoltage PWM voltage-source-inverter drive applications. IEEE Trans. Ind. Appl. 36(5), 1336– 1341 (2000) 7. von Jauanne, A., Zhang, H.: A dual-bridge inverter approach to eliminating common-mode voltages and bearing and leakage currents. IEEE Trans. Power Electron. 14(1), 43–48 (1999) 8. Liu, R., Chen, J., Zhu, J., et al.: Study on effect of bearing insulation on high frequency shaft voltage and shaft current of doubly-fed induction generator. Trans. China Electrotech. Soc. 35(S1), 212–219 (2019). (in Chinese) 9. Ammann, C., Reichert, K., Joho, R., et al.: Shaft voltages in generators with static excitation systems-problems and solution. IEEE Trans. Energy Convers. 3(2), 409–419 (1998) 10. Peng, B.: Research on Shaft Voltage Generation Principle and Suppression Method of Permanent Magnet Motor. Shandong University (2019). (in Chinese) 11. Zhao, J.: Analysis and Weakening of Shaft Voltage of Surface Mounted Permanent Magnet Synchronous Motor. Shandong University (2021). (in Chinese) 12. Raymond, O.K.J.: An investigation of Shaft Current in a Large Sleeve Bearing Induction Machine. McMaster University (1999)

A Robust H∞ CKF-Based Dynamic State Estimation Method for Distribution Networks Su Zicong1(B) , Liu Min1 , Wang Kai2 , and Man Yanlu1 1 School of Electrical Engineering, Guizhou University, Guiyang 550025, Guizhou, China

[email protected] 2 China Southern Power Grid Company Limited, Guangzhou 550025, China

Abstract. Due to the development of new power systems, the impact of stochastic loads, demand response participation, distributed voltage randomness and volatility and the variety of measurement devices lead to the complexity of the distribution network structure and the aggravation of the state estimation task, which may lead to a decrease in the estimation accuracy of the dynamic state estimation algorithm in some scenarios. In this paper, the dynamic state estimation method for distribution networks based on improved H∞ volumetric Kalman filtering is firstly combined with volumetric Kalman filtering and H∞ filtering to robust the model error uncertainty problem, and then finally combined with a noise valuer to estimate the parameters in the process noise online and to reduce the impact of noise on the prediction error. Simulations are carried out by the IEEE69-node system, and the results show that the method maintains a relatively high estimation accuracy under normal system operation, after the demand response is involved in peak shaving, and when the load undergoes sudden changes. Keywords: Cubature Kalman Filter · H-infinity · noise statistic estimator · demand response · cut the peak to fill the valley (idiom); fig. to reduce peaks and fill valley

1 Introduction Power system state estimation, as one of the keys of energy management system [1], improves the data accuracy based on the accessible volume measurements, screens out the error information due to abnormal power system disturbances and thus obtains the state of the power system afterwards. The emergence of demand response [2], electric vehicle uncertainty [3], distributed power supply volatility and stochastic output [4] and external disaster factors in the distribution network increases the network size and system volatility, as well as the difficulty of maintenance of the distribution system, which brings new challenges to state estimation. The current state transfer function model commonly used in CKF is the Holt twoparameter linear smoothing parameter prediction model [5], but the model obtained by Holt’s method not only has a large modeling error in this model, but also still has obvious nonlinearity in the actual system [6]. Due to the volatility of load and DG in © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 496–503, 2024. https://doi.org/10.1007/978-981-97-1064-5_54

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distribution networks, the statistical parameters of process noise are time-varying and difficult to obtain. Also the estimation accuracy tends to degrade if the measured data is anomalous. Literature [7] describes the dynamic state estimation of generators improved by interpolation and H∞ filter based on EKF. Literature [8] introduces the noise valuer with the aim of reducing the effect of process noise on the estimation results. Literature [9] describes the inclusion of H∞ filter on top of UKF, which is useful in terms of uncertainty in the system. Literature [10] describes an improvement on the EKF with the aim of allowing the extended Kalman filter to improve on the model error. Aiming at the nonlinearity and measurement noise error characteristics of the distribution network in the power system machine, this paper proposes a new method of state estimation based on the noise estimator H∞ volumetric Kalman filter. Firstly, the H∞ (H-infinity) filter is used to be robust to uncertainty problems such as modeling error, and finally the noise statistic estimator (NSE) is used to estimate the process noise parameter online, which improves the prediction error and improves the state estimation accuracy in distribution networks by reducing the noise to solve the problems such as modeling error and process noise. Problems. Simulations show that the method in this paper can effectively reduce the modeling error and maintain high estimation accuracy when the state undergoes sudden changes and peak shaving occurs.

2 Dynamic State Estimation Model for Distribution Networks 2.1 Distribution Network State Estimation Model The dynamic state estimation model for distribution networks is basically composed of 2 equations, the state equation and the measurement equation, and is often a nonlinear system:  xk = f (xk−1 ) + wk (1) zmk = h(xk ) + ek Where xk is the state quantity of the distribution network; xk and xk−1 are the state quantities at moments k and k-1, respectively; f (x) and h(x) are expressed as equations of state and measurement equations of the distribution network, respectively. The Eq. (1) and Holt’s two-parameter smoothing method are coupled to give the equation of state as: ⎧ ⎨ xk|k−1 = Sk−1 + bk−1 (2) S = αH xk−1 + (1 − αH )xk−1|k−2 ⎩ k−1 bk−1 = β H (Sk−1 − Sk−2 ) + (1 − β H )bk−2 Where Sk−1 is the horizontal component; bk−1 is the vertical component; αH and β H are smoothing parameters, the value is usually from 0 to 1, the size of its value has a significant impact on the model prediction effect, in this paper, through experiments, to choose the optimal parameter values, αH = 0.8, β H = 0.29.

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2.2 H∞ Capacitive Kalman Filter CKF has low estimation accuracy in some scenarios. The estimation performance of the CKF algorithm is tied to the system model uncertainty, and the filter can constrain the maximum estimation error and make it smaller, which can effectively complement the RCKF filtering. The filter has two advantages, namely, improved estimation accuracy and robustness. The filter guarantees a finite upper bound on the estimation error, which can be achieved by satisfying the following inequality if the measured sequence values are provided before time N: N

  xk − xk|k−1 2 −1 Pκ|κ

≤ γ2 N 2 2 + k=0 qk  −1 + rk  −1 

k=0

sup



2 x0 − x0|0 P 2

{x0 ,vk ,wk } 



0|0

Qk

(3)

Rk

2 will be the initial state quantities and their covariance matrices respecWhere x0 and P0|0 tively; γ is a positive scalar parameter that qualifies the uncertainty. The process is as follows: T T P k|k = {I − P k|k−1 [H Tk I]R−1 e,k [H k I] }P k|k−1

 Re,k =



T  Rk + H k P k|k−1 H Tk P k|k−1 H Tk P k|k−1 H Tk −γ 2 I + P k|k−1

(4)

(5)

Where I is the unit matrix; H k = ∂h/∂x|x=ˆx k|k−1 is the Jacobi matrix. In order to be able to perform state estimation, P k|k must be guaranteed to be positive definite, so we introduce a tuning coefficient γ . To ensure the positivity of the error covariance matrix, it is necessary to fulfill: −1  −2 + H Tk R−1 I>0 P xx k|k−1 k Hk − γ

(6)

  −1  T −1 γ 2 ≥ max eig P −1 + H R H k k k k|k−1

(7)

Where eig(A)−1 for finding the eigenvalues of the A matrix. 2.3 Noise Statistics Estimator The value of the process noise variance matrix tends to affect the filtering performance of the CKF algorithm, and its inaccuracy can seriously affect the accuracy of the estimation. In this regard, this paper introduces the noise valuer NSE to improve the algorithm on the basis of CKF:   Qk+1 = (1 − d k )Qk + d k K k εk εkT + P k

A Robust H∞ CKF-Based Dynamic State Estimation Method

 T 1  i i χk|k−1 − xk|k−1 χk|k−1 − xk|k−1 2n

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2n

−





(8)

i=0

Where εk is the residual difference between the real-time measure and the predicted measure at moment k; b is the forgetting factor, taking the value from 0 to 1, when the value is larger, the system changes more, in this paper the value is taken as 0.995. The subtraction operation appearing in the process noise tends to change its semipositive definiteness, and the process noise not satisfying the semipositive definiteness condition will seriously affect the estimation accuracy and even lead to dispersion. In this paper, the CKF algorithm is improved by adding fault-tolerant NSE, which can guarantee that it belongs to the semipositive definite matrix, and the fault-tolerant NSE is combined by biased and unbiased NSE respectively.  Qk+1

if Qk+1 is semipositive (9) Qk+1 = (1 - dk )Qk + dk K k εk εkT K Tk other In cases where the process noise obtained by the unbiased noise estimator is not a semipositive definite matrix, the biased NSE is utilized to recalculate to guarantee that the process noise satisfies the condition. Unlike the adaptive factor, the introduced SageHuse noise estimator identifies the model error covariance matrix online, optimizing the system model and the estimation results in multiple scenarios.

3 Arithmetic Simulation In this section, the effectiveness of the proposed RHCKF method is simulated and verified using 69 nodes [11] and analyzed in comparison with EKF and CKF.The 69 node distribution system is shown in Fig. 1 below.

Fig. 1. 69 node power distribution system.

PMUs are configured at nodes 1, 9, 27, 35, 46, 50, 57 and 65 to provide node voltage magnitude and voltage phase angle measurements. Assuming that all nodes have data from the SCADA system, node injected power and branch power quantity measurements can be obtained. Firstly, the distribution system is allowed to be in normal operation and the MATPOWER [12] software is utilized to calculate the tidal flow calculations to obtain the node state quantities, node injected power and line parameters. Secondly, Gaussian

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white noise is added to the quantity measurements to compare the superiority of the DSE method for distribution networks. It is assumed that the Gaussian white noise parameters of the quantity measurement are as follows, the voltage magnitude measurement error of PMU obeys the distribution of mean 0 and standard deviation 0.005, while the voltage phase angle measurement error obeys the distribution of mean 0 and standard deviation 0.002; and obeys the distribution of mean 0 and standard deviation 0.02 in the SCADA system [13, 14]. The system noise variance matrix is set to 10–4 . 3.1 Normal Operation of the System The simulation of EKF, CKF, and RHCKF is carried out for 100 moment points under normal operation of the system, and the comparison of the voltage magnitude estimation results of the three methods are shown in Figs. 2 and 3, and the related estimation accuracy indexes are shown in Table 1.

Fig. 2. 56 node voltage amplitude.

Fig. 3. 56 Node voltage phase angle

Table 1. Indicators of different DSE methods during normal operation. Method

EKF

Relative error of voltage amplitude(%)

Relative error of voltage phase angle (°)

average

Max

average

Max

0.1659

1.1661

0.001208

0.009572

CKF

0.1213

0.8606

0.000651

0.005421

RHCKF

0.1086

0.7343

0.000481

0.003618

The H∞ Kalman filter based on robust control ensures that the maximum variance of the dynamic state estimation is minimized, thus suppressing the effects of various measurements and model uncertainties on the estimation results and improving the robustness of the DSE algorithm. 3.2 DGs and Charging Post Access In order to simulate the sudden changes in the load and DGs of the distribution system, DGs are set up at nodes 18 and 33, and EV charging piles are set up at nodes 19 and 23.

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The load at node 18 and node 33 is reduced by 70% for 20 moments due to the activation of the DG at the 10th moment point. At the 20th moment point, the load at node 19 and node 23 increases by 50% for 20 moments due to the activation of the charging pile. For the joint simulation test of the three methods EKF, CKF, and RHCKF (Figs. 4, 5 and Table 2).

Fig. 4. 56 node voltage amplitude.

Fig. 5. 56 Node voltage phase angle

Table 2. Indicators of different DSE methods. Method

Relative error of voltage amplitude(%)

Relative error of voltage phase angle (°)

average

Max

average

Max

EKF

0.1522

1.001

0.001206

0.007195

CKF

0.1226

0.9239

0.000518

0.003165

RHCKF

0.1135

0.7580

0.000478

0.002698

Based on the above graphs and tables, it is known that among the three methods, EKF, CKF, and RHCKF, RHCKF effectively and efficiently reduces the average value of the relative error in voltage magnitude and phase angle and is effective in terms of the maximum value of the error in the case of DG access and sudden load change. 3.3 Participation in Peak-Shaving and Valley-Filling Scenarios With the development of new power systems, demand response needs to be involved in order to make the power system operation more reliable. Due to the randomly changing characteristics of demand response, the distribution network is often affected. Considering that there are more ways of demand response participation, it is now simulated when the load changes after the demand response participation in peak shaving and valley filling. In order to simulate the load change of the distribution network system, the energy storage is installed at nodes 27, 35, 46, 50, 65 and the electric vehicle charging pile is installed at nodes 31, 38, 47, 53. The grid connection of the energy storage starts from the 10th moment and continues until the 40th moment point, i.e., during this period the load at nodes 27, 35, 46, 50, and 65 drops by 80% for peak shaving. The EV charging pile is connected to the grid from the 60th moment and continues charging until the 90th

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moment, i.e., the loads at nodes 31, 38, 47, and 53 increase by 60% during this period for peak shaving. The variation diagram for the case of participating in constant power peak shaving and valley filling is shown in Fig. 6 (Fig. 7).

Fig. 6. Load change.

Fig. 7. 56 Node voltage amplitude and phase angle

Faced with this type of scenario, the RHCKF method also produces relatively good estimation results, and compared to the normal case, the RHCKF still provides a good improvement in estimation results due to the relatively flat load.

4 Conclusion Aiming at the Holt’s two-parameter model for CKF, which may have a large model error in some application scenarios and a large process noise error, this paper proposes a RCKF algorithm based on the RCKF algorithm applied in the dynamic state estimation of the distribution network, which is based on the volumetric Kalman filtering algorithm plus the combination of the filtering, and finally combined together with a noise valuer, which can effectively reduce the model error, ensure that the process noise parameter is effectively estimated, and improve the performance of the volumetric Kalman filtering in different scenarios.

References 1. Zhao, J., et al.: Roles of dynamic state estimation in power system modeling, monitoring and operation. IEEE Trans. Power Syst. 36(3), 2462–2472 (2021). https://doi.org/10.1109/TPW RS2020.3028047 2. Cui, Y., Gu, C., Fu, X., et al.: Low-carbon economic dispatch of an integrated energy system with carbon capture power plant considering generalized electric heat demand response. Chin. J. Electr. Eng. 42(23), 8431–8446 (2022). https://doi.org/10.13334/j.0258-8013.pcsee. 211942 3. Yu, D., Yang, C., Jiang, L., et al.: A review of electric vehicle charging safety protection research. Chin. J. Electr. Eng. 42(06), 2145–2164 (2022). https://doi.org/10.13334/j.02588013.pcsee.210274 4. Li, Z., Tian, B., Yin, X., et al.: Active distribution network protection containing distributed power sources and random loads. High Volt. Technol. 43(04), 1231–1238 (2017). https://doi. org/10.13336/j.1003-6520.hve.20170328021 5. Silva, A., Filho, M., Queiroz, J.: State forecasting in electric power systems. IEE Proc. CGener. Transm. Distrib. 130(5), 237–244 (1983) 6. Kong, X., Zhang, X., Zhang, X., Wang, C., Chiang, H.-D., Li, P.: Adaptive dynamic state estimation of distribution network based on interacting multiple model. IEEE Trans. Sustain. Energy 13(2), 643–652 (2022). https://doi.org/10.1109/TSTE.2021.3118030

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7. Ai, M., Sun, Yh., Wang, Y., et al.: Dynamic state estimation of generator based on interpolated H_∞ extended Kalman filter. Chin. J. Electr. Eng. 38(19), 5846–5853+5942 (2018). https:// doi.org/10.13334/j.0258-8013.pcsee.172039 8. Wang, Y., Xia, M., Liet, P., et al.: A dynamic state estimation method for distribution networks based on improved robust adaptive UKF. Power Syst. Autom. 44(01), 92–100 (2020) 9. Zhao, J., Mili, L.: A decentralized H-infinity unscented Kalman filter for dynamic state estimation against uncertainties. IEEE Trans. Smart Grid 10(5), 4870–4880 (2019). https://doi. org/10.1109/TSG.2018.2870327 10. Zhao, J.: Dynamic state estimation with model uncertainties using H ∞ extended Kalman filter. IEEE Trans. Power Syst. 33(1), 1099–1100 (2018). https://doi.org/10.1109/TPWRS. 2017.2688131 11. Sahoo, N.C., Prasad, K.: A fuzzy genetic approach for network reconfiguration to enhance voltage stability in radial distribution systems. Energy Convers. Manag. 47(18–19), 3288– 3306 (2006) 12. Zimmerman, R.D., Murillo-Sanchez, C.E., Thomas, R.J.: MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26(1), 12–19 (2011) 13. Qu, Z., Zhang, J., Wang, Y., et al.: Improved affine state estimation for distribution networks considering distributed power uncertainty. Power Syst. Autom. 45(23), 104–112 (2021) 14. Bai, X., Zheng, X., Ge, J.L., et al.: Adaptive UKF dynamic state estimation for distribution networks based on event triggering mechanism. High Volt. Technol. 47(07), 2312–2321 (2021). https://doi.org/10.13336/j.1003-6520.hve.20201771

Detection of Bearing Fault in Induction Motor Based on Improved Adaptive Chirp Mode Decomposition Wei Li, Chidong Qiu, Ruihan Liu, and Zhengyu Xue(B) College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China {happiness54934,qiuchidong,liu990711,xuezy}@dlmu.edu.cn

Abstract. Bearing fault detection based on stator current signals has the characteristics of non-invasive and easy to implement, but weak fault features are submerged by strong background noise, posing a great challenge. Although adaptive chirp-mode decomposition (ACMD) has achieved good results in processing non-stationary signals in many fields, it requires some prior information to initiate, which limits its widespread application. Therefore, an improved ACMD method is proposed. First, the instantaneous frequency of initial estimation is obtained based on general linear chirplet transform. Then, the instantaneous frequency is used as the iterative condition, and the motor current signal will be decomposed into several modes. Finally, use power spectrum analysis to determine if it is faulty. The experimental results indicate that the improved method proposed in this paper is feasible for bearing fault detection. Keywords: Induction motor · Bearing · Fault · Adaptive chirp mode decomposition

1 Introduction Induction motors play an important role in many industrial and on-board applications because of their low cost, simple construction, and high reliability [1]. Rolling bearings are a very important component in induction motors, and accurate and effective fault detection is the key to the stable operation of motors. At present, most motors in the industrial field operate under harsh conditions such as high noise and heavy loads. Therefore, non-invasive methods using current signals are one of the effective choices for diagnosing bearing faults [2]. According to the differences in the implementation forms of signal decomposition methods, time-domain decomposition, frequency-domain filtering, and time-frequency domain reconstruction are currently widely used methods for bearing fault feature extraction [3]. Time-domain decomposition mainly involves conducting data statistical analysis. At present, these analysis methods mainly extract signal components directly in the time-domain through iterative algorithms. Time-domain method only provides a simple description of bearing operation, but early bearing fault signals are often very weak and © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 504–511, 2024. https://doi.org/10.1007/978-981-97-1064-5_55

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easily submerged by strong background noise [4]. It is very challenging to operate only in the time-domain to effectively obtain fault information. The frequency domain filtering method separates these signal components in the frequency domain through a filter and then performs spectral analysis [5], but the limited processing ability for nonlinear and non-stationary signals has affected its wide application. The time-frequency domain reconstruction method can transform the signal from 1-D time domain into the 2-D timefrequency domain [6], and the obtained time-frequency distribution function has great significance for non-stationary nonlinear signal processing. For example, methods such as continuous wavelet transform (CWT) and nonlinear mode decomposition (NMD). Empirical mode decomposition (EMD) is a very famous fully data-driven method, which can adaptively decompose signals into several simple intrinsic mode functions (IMF) [7]. However, its sensitivity to environmental noise and lack of effective mathematical theory support make it more suitable for analyzing quasi stationary signals with high signal-to-noise ratios. Dragomiretskiy proposed variational mode decomposition (VMD) [8]. This method has a good mathematical theoretical foundation, and estimates various signal modes by solving variational optimization problems. However, for broadband frequency modulation signals, the decomposed modes often exhibit frequency band aliasing. Inspired by VMD, CHEN extended narrowband signals to broadband signals under conditional constraints and proposed a new decomposition method called adaptive chirp mode decomposition (ACMD) [9]. It has good results in weak feature extraction and noise suppression [10]. Compared to VMD, there is no need to set the number of modes. However, a key problem in the application of ACMD is the need to preset the instantaneous frequency (IF) of initial estimation in advance, and the estimation of the initial IF will directly affect the subsequent decomposition effect. It is one of the effective ways to obtain IF by using time-frequency representation method with high resolution. Therefore, this article proposes a method mainly used to solve the above problems.

2 Proposed Approaches 2.1 Review of ACMD A non-stationary signal containing multiple components can be modeled as an amplitude and frequency modulation signal, so the non-stationary signal g(t) containing M components can be represented as: g(t) =

M 

M 

gm (t) =

m=1

⎡ Am (t) cos⎣2π

m=1

t

⎤ fm (τ )d τ + θm ⎦

(1)

0

where, Am > 0, fm (t) > 0 and θ m are respectively the instantaneous amplitude (IA), instantaneous frequency (IF) and initial phase of the m-th signal component. Demodulation technology can be used to convert a broadband signal into a narrowband signal. Equation (1) can be expressed as: g(t) =

M  m=1

⎡ pm (t) cos⎣2π

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 ⎪ ⎪  ⎪ ⎪ ⎦ ⎣ q f = −A sin 2π − f d τ + θ (t) (t) (τ ) (τ ) ⎪ ⎪ m m m m m ⎪ ⎪ ⎩ ⎭

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where, f˜m (τ ) is the frequency  t function of two orthogonal demodulation operators t sin[2π 0 f˜m (τ )d τ ] , cos[2π 0 f˜m (τ )d τ ] ; pm (t) and qm (t) are corresponding demodulation signals which are used to recover the instantaneous amplitude (IA) of each component signal.  2 (t) + q2 (t) Am (t) = pm (4) m According to Eq. (3), when f˜m (τ ) is close to the true IF, the m-th signal component will become a pure AM signal with the narrowest sideband. ACMD obtains target signal components by solving the following constraint problems:       (t)2 + p (t)2 + μg(t) − g (t)2 arg min pm m m 2 2 2 pm ,qm, fm     (5) t t s.t.gm (t) = pm (t) cos 2π  fm (τ )d τ + qm (t) sin 2π  fm (τ )d τ 0

0

where, gm (t) is the m-th extracted signal component, · representing the l2 norm; g(t) − gm (t)22 is the remaining energy after removing the estimated component, μ is the weight factor. 2.2 Improved ACMD It can be concluded that the ACMD method requires a pre-set initial iteration condition, which is the initial IF. Finding the time-frequency distribution (TFD) of the original signal and extracting the initial IF through ridge extraction is an effective method. Therefore, the resolution of time-frequency representation becomes a key factor affecting the initial IF. So it is important to get more valuable initial IF by obtaining higher precision TFD. This work proposes the method to drive ACMD based on the initial IF calculated by general linear chirplet transform (GLCT). The well-known linear chirp variation formula can be represented by: +∞ −jc(τ −t)2 h(τ − t)g(τ )e−jωτ e 2 d τ S(t, ω, c) =

(6)

−∞

where, c represents the chirp rate, h represents the window function, g(τ ) represents the 1 2 current signal. The demodulation operator e− 2 ·jc(τ −t) will generate a rotation effect of

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arctan(-c) on the time-frequency plane. GLCT effectively solves the problem of determining tuning operators. For the current signals, the sampling time T and sampling frequency F s are determined. The chirp rate c can be determined by:  π π Fs tan(β) c= ,β ∈ − , (7) 2T 2 2 Equation (6) can be written as: S(t, ω, β) =

+∞ tan(β)(τ −t)2 dτ h(τ − t)g(τ )e−jωτ e−j· 4T

(8)

−∞

Subsequently, the number of segments represented by parameter K is used to determine β. It can be expressed as: β = {−π/2 + 1 · π/(K + 1) − π/2 + 2 · π/(K + 1) . . . − π/2 + K · π/(K + 1)} (9) c˜ = arg maxc |S(t, ω, c)| Equation (8) and (9) illustrate the main features of GLCT, which uses a series of demodulation operators instead of parameterization analysis to identify the IF characteristics of signals, and obtain high-quality time-frequency readability. The specific steps of the proposed method are as follows: First, based on the existing experimental platform, obtain the current signal of induction motor with faulty bearing. Secondly obtain the time-frequency distribution of current signal based on GLCT, and extract the IFm of m-th component by ridge detection. Next, start ACMD to decompose the signal and obtain information of the m-th component. Then, subtract the m-th component from the original signal to obtain the remaining signal, and use the remaining signal as the original signal for the next iteration. Finally determine whether to stop decomposition. When the energy ratio is less than the threshold, stop decomposition, and select the appropriate mode for fault diagnosis. The flowchart of the proposed method is shown in Fig. 1.

Fig. 1. The flowchart of the proposed method

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3 Experimental Verification 3.1 The Experiment Verification Platform The bearing fault experimental verification platform constructed mainly consists of the main circuit system, FPGA driver system, and current signal collection system. The SPWM signal generated by FPGA is transmitted to the IPM for controlling the induction motor. The experimental verification platform is shown in Fig. 2.

Fig. 2. Experimental platform

The induction motor used in the platform is Y100L1-4T, which rated voltage, current, power and speed are 380 V, 5.03 A, 2.2 kW, 1430 rpm, respectively. FPGA is an Altera Cyclone IV E device EP4CE15F17C8. IPM is a Mitsubishi intelligent power module PM50CSD120. The stator current is measured by Hall current sensor LEM IT60-S, with measuring range of 60 A, linearity error of 20 ppm. The faulty bearing used for the experiment is SKF6206 whose number of balls is 9; The pitch diameter and ball diameter are 46 mm and 9.6 mm, respectively. Using discharge technology to generate pitting corrosion faults in outer raceway of the experimental bearing. 3.2 Experimental Result Resonance occurs in the motor body at a power frequency of 20 Hz, where the fault characteristic frequency is most pronounced [11]. Therefore, the power frequency of experimental motor is set as 20 Hz, correspondingly the fault characteristic frequency f c is 35 Hz. Install the faulty bearing with outer raceway defect into the experimental motor. In order to have reasonable comparisons, all the following spectrum are generated using Welch spectral analysis and same parameters: sampling frequency F s = 2000, sampling point N = 10000, NFFT = 4096.

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Firstly, directly analyze the raw current signal, as shown in Fig. 3. It can be clearly seen that the fundamental frequency f s , secondary harmonic 2f s and third harmonic 3f s . The fault characteristic frequencies fs ± fc are almost submerged in strong noise. Then, use ACMD to analyze the current data, as shown in Fig. 4. The initial IF is set to 20 Hz. In order to ensure consistency with subsequent improved methods, use relatively concentrated energy mode after decomposition to compare. The first mode is selected for power spectrum analysis. In Fig. 4, compared to the spectrum without ACMD processing, it can be seen that the fault feature frequencies f s + f c and f s − f c are relatively enhanced. Other fault feature frequencies can also be found such as 2fs-fc and 3fs-fc. In addition to the above frequencies, we can also find some other frequency information, such as f s + f r and 2f s + f r , which are related to eccentricity. The spectrum using the improved ACMD is shown in Fig. 5. Compared with Fig. 4, the amplitude of fault characteristic frequency is more prominent. Especially for f s + f c , except for the fundamental frequency and second harmonic, its amplitude is the highest. That is because the improved ACMD uses GLCT to obtain the initial IF, and GLCT can obtain more precise time-frequency resolution, which can reduce the accuracy error caused by presetting the initial IF. This provides convenience for subsequent decomposition algorithms. The analysis results indicate that the improved ACMD has more advantages than the original ACMD method. Reinstall the healthy bearings into the experimental motor, obtain the stator current signal under the same conditions, and decompose it using an improved ACMD. The analysis results are shown in Fig. 6. Compared with Fig. 5, there is a significant difference at fault characteristic frequency (nf s + f c ) between faulty bearing and the healthy bearing. It shows that it is very convenient to identify faulty bearings and healthy bearings based on the proposed method.

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4 Conclusion In this article, an improved adaptive chirp mode decomposition method is proposed. One time-frequency method is used to estimate the initial instantaneous frequency instead of manual setting, which reduces the limitations of the original method and increases the accuracy. Experimental verification shows that this method can make weak fault features more prominent and achieve the purpose of fault detection. Acknowledgments. This work is supported by the National Natural Science Foundation of China under Grant 51279020.

References 1. Qiu, C., Wu, X., Xu, C., et al.: An approximate estimation approach of fault size for spalled ball bearing in induction motor by tracking multiple vibration frequencies in current. Sensors 20(6), 1631(2020) 2. Immovilli, F., Cocconcelli, M.: Experimental investigation of shaft radial load effect on bearing fault signatures detection. IEEE Trans. Ind. Appl. 53(3), 2721–2729 (2017) 3. Lv, M., Li, H.: Nonlinear chirp component decomposition: a method based on elastic network regression. IEEE Trans. Instrum. Meas. 70, 1–13 (2021) 4. Dalvand, F., Dalvand, S., Sharafi, F., et al.: Current noise cancellation for bearing fault diagnosis using time shifting. IEEE Trans. Ind. Electron. 64(10), 8138–8147 (2017) 5. Kang, M., Kim, J., Jeong, I.-K., et al.: A massively parallel approach to real-time bearing fault detection using sub-band analysis on an FPGA-based multicore system. IEEE Trans. Ind. Electron. 63(10), 6325–6335 (2016) 6. Xu, L., Yin, X., Zong, Z., et al.: Synchrosqueezing matching pursuit time-frequency analysis. IEEE Geosci. Remote Sens. Lett. 18(3), 411–415 (2021) 7. Wang, J., Li, J., Wang, H., et al.: Composite fault diagnosis of gearbox based on empirical mode decomposition and improved variational mode decomposition. J. Low Freq. Noise Vib. Act. Control 40(1), 332–346 (2021)

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8. Dragomiretskiy, K., Zosso, D.: Variational mode decomposition. IEEE Trans. Signal Process. 62(3), 531–544 (2014) 9. Chen, S., Yang, Y., Peng, Z., et al.: Detection of rub-impact fault for rotor-stator systems: a novel method based on adaptive chirp mode decomposition. J. Sound Vib. 440, 83–99 (2019) 10. Wang, X., He, Y., Wang, H., et al.: A novel hybrid approach for damage identification of wind turbine bearing under variable speed condition. Mech. Mach. Theory 169, 104629 (2022) 11. Patel, V.N., Tandon, N., Pandey, R.K.: Vibration studies of dynamically loaded deep groove ball bearings in presence of local defects on races. Procedia Eng. 64, 1582–1591 (2013)

Detection of Bearing Fault in Induction Motor Based on Improved Adaptive Local Iterative Filtering Guomin Wang, Chidong Qiu, Shuai Hong, and Zhengyu Xue(B) College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China {wgm,qiuchidong,hongshuai,xuezy}@dlmu.edu.cn

Abstract. The stator current of induction motor is not affected by environmental interference, so it is widely used in the motor bearing fault detection. But weaker fault features are easily masked by strong noise, and are difficult to detect. Therefore, an improved adaptive local iterative filtering fault detection method is proposed. Aiming at the problem of poor noise reduction effect of adaptive local iterative filtering, a method for screening data is proposed, which solves the problem of excessive noise components, and improves the accuracy of fault identification. Experimental results show that the proposed method is very effective for bearing fault detection and has better performance than the original method. Keywords: Induction motor · Bearing · Fault · Adaptive local iterative filtering

1 Introduction Induction motors are widely used in household life, industrial manufacturing and intelligent machine industries. Its low cost and ability to work in harsh conditions are reasons for its prominence compared to other types of electric motor [1]. It is no exaggeration to say that the development of induction motors has promoted the development of technology in today’s world [2]. Bearing failure accounts for the highest proportion of motor failure types, and almost 50% of motor failures are related to bearing failure [3]. Therefore, it is very important to research the bearing fault diagnosis. Empirical mode decomposition (EMD) is an adaptive non-stationary nonlinear signal processing method [4]. As one of the most widely used bearing fault diagnosis methods, due to the lack of rigorous mathematical theoretical derivation of its own algorithm, the modes generated by signal decomposition have serious mode aliasing problems. Inspired by EMD, iterative filtering (IF) is proposed by Lin [5]. This method mainly uses the global extremum scale of the signal to construct the filter, replaces the mean curve in EMD by convolution of the filter function and the signal, and decomposes the signal through iterative screening. A reliable proof of mathematical reasoning is put forward for the convergence of the decomposition process. However, because the method constructs the filter according to the global extremum scale of the signal, the analysis result of the non-stationary signal is unsatisfactory. Therefore, Cicone [6] et al. proposed © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 512–519, 2024. https://doi.org/10.1007/978-981-97-1064-5_56

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a new time-frequency analysis method: Adaptive local iterative filtering (ALIF), which is developed from the IF method. The adaptive filter function is mainly constructed by using the basic solution system of Foller-Planck differential equation, and its signal decomposition ability is better than EMD. Zhang [7] et al. have successfully applied the ALIF method to signal processing of generator rotors. However, ALIF method also has the problem of mode aliasing when processing signals, so it needs to be further improved. Li Xiaobin [8] et al. have studied the orthogonality of intrinsic mode functions (IMF) and obtained the theory that IMF is not aliasing with the orthogonal index discriminant method. Therefore, to avoid aliasing, it is necessary to ensure that the decomposed IMF is orthogonal. The Principal component analysis (PCA) [9, 10] can convert correlation data into orthogonalized data. Therefore, in this paper, ALIF is improved by the orthogonality of PCA to achieve the effect of signal fault feature frequency enhancement.

2 Proposed Approaches 2.1 Review of Adaptive Local Iterative Filtering The ALIF method is developed on the basis of the IF method, so its decomposition process is similar to the EMD method. Finally, the signal is decomposed into a series of IMF components and a decomposition margin. The IMF component satisfies two conditions: • The number of the extrema and zero-crossings of an IMF must be equal or differ at most by one. • At any point of an IMF, the mean value of the envelopes defined by the local extrema is zero. For signal f (x), x ∈ R, the specific steps of the ALIF method are as follows: (1) Calculate the sliding operator L(f (x)) of the signal:  L(f (x)) =

l(n)

−l(n)

f (x + t)ω(t)dt

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(1)

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where the steady-state coefficient η is 1.6, k represents the number of extreme points in the sequence, N represents the signal length, and [·] represents the integer function. (2) Calculate the volatility operator F(f (x)): F(f (x))=f (x) − L(f (x))

(3)

(3) If the wave operator F satisfies the inner cycle condition, then the first IMF is c1 = F. If the condition is not met, continue to execute Step (1~2) until it is satisfied.

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(4) A total of m IMFs are obtained from the signal f (x) and the remaining components r(t) are obtained: r(t) = f (t) −

m 

ci (t)

(4)

i=1

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m 

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(5)

i=1

The filter ω(t) in Step (1) is given by the solution of the Fokker-Planck differential equation as follows:   ∂ 2 f 2 (x)p ∂p ∂(k(x)p) = −α +β (6) ∂t ∂x ∂x 2 The p(x) obtained from the solution is the filter and satisfies: 

b

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(7)

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Fi,n − Fi,n−1 2 Fi,n−1 2

(8)

where RSD value reaches the set threshold, the iteration stops to get an IMF component. 2.2 Improved Adaptive Local Iterative Filtering Principal component analysis (PCA) is a multivariate statistical method proposed by Hotelling. Its main purpose is to orthogonalize the original data and reduce the dimensionality. Under the condition of retaining as much information of the original variables as possible, the method mainly derives a few orthogonal principal components and recombines them into a new set of unrelated variables to replace the original variables. Therefore, inspired by the PCA, the ALIF method is improved, and a series of correlated IMFs are transformed into mutually orthogonal IMFs, thereby improving the effect of signal processing. The algorithm of improved ALIF is shown in Fig. 1. The flow of proposed approaches is as follows: (1) The original signal x(t) is decomposed into m IMFs through ALIF, and each component takes n sampling points.

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Fig. 1. Improved Adaptive Local Iterative Filtering

(2) Let the IMF components be x1 , x2 , · · · , xm , and the value corresponding to the sampling point be aij , and centralize the data: a˜ ij = aij − μj i = 1, 2, · · · , n; j = 1, 2, · · · , m 1 aij n

(9)

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(10)

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where μj represents the mean of the j-th IMF component. ∼

(3) Calculate the correlation coefficient matrix R of a ij : n ˜ fi · a˜ fj f =1 a rij = i, j = 1, 2, · · · , m n−1   R = rij m×n

(11) (12)

(4) The eigenvalue λ and eigenvector u of the correlation coefficient matrix R are obtained. The eigenvectors form m new orthogonal principal component variables yi (i = 1, 2, · · · , m): ⎧ y1 = u11 x˜ 1 + u21 x˜ 2 + · · · + um1 x˜ m ⎪ ⎪ ⎪ ⎨ y2 = u12 x˜ 1 + u22 x˜ 2 + · · · + um2 x˜ m (13) .. ⎪ ⎪ . ⎪ ⎩ ym = u1j x˜ 1 + u2j x˜ 2 + · · · + umj x˜ m

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(5) Select q orthogonal principal component variables, and calculate the information contribution rate cj and cumulative contribution rate θq of the principal component variables respectively: λj cj = m

f =1 λf

j = 1, 2, · · · , m

(14)

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f =1 λf

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where cj is the information contribution rate of the j-th orthogonal principal component, λj is the j-th eigenvalue. (6) Select the combination of orthogonal principal components with a cumulative contribution rate of θq above 85%, and perform signal reconstruction to generate a new signal x (t). (7) Perform ALIF decomposition on the new signal x (t) to obtain a new IMF component.

3 Experimental Verification 3.1 Experiment Platform The induction motor bearing fault experiment platform consists of the motor control system and the current signal acquisition system, which is shown in Fig. 2. The FPGA generates SPWM signals to the IPM for controlling the induction motor. Then, the current signal is collected by Hall sensor IT60-S, the data acquisition card is NI-6356. Motor parameters are as follows: rated power 2.2 kW; rated voltage 380 V; rated current 5.03 A; rated speed 1430 r/min; pole pairs is 2. The bearing is SKF6206, the balls is 9, the diameter of the balls is 9.6 mm, and the diameter of the pitch circle is 46 mm. 3.2 Experimental Result Analysis According to the literature [11], when the power frequency is 20 Hz, the feature frequency of the bearing fault is easier to identify. Therefore, the power supply is set as 20 Hz.The bearing fault feature frequency is 35 Hz. For a reasonable comparison, the following spectrum analysis uses the same parameters: the sampling frequency is 2000 Hz, the sampling points is 10000, and the length of the fast Fourier transform is 4096. After the current data is processed by traditional ALIF, the modes with fault feature information are listed here, as shown in Fig. 3, x2 contains second and third harmonics, and the fault feature frequency fc − fs can be seen. There is a lot of noise around the fault feature frequency fc − fs in x7 , the effect is not obvious. Overall, the identification of fault feature frequencies are weak. In order to identify the fault frequency more effectively, an improved adaptive local iterative filtering method is used for signal processing. The information contribution rate of the principal component variable y1 , y2 , · · · , y8 is obtained through the proposed algorithm, as shown in Table 1.

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Fig. 2. Experimental platform

Table 1. Principal component information contribution rate yi

y1

y2

y3

y4

y5

y6

y7

y8

cj

35.99

26.27

22.27

11.02

3.82

0.29

0.25

0.1

It can be seen in Table 1 that the information contribution rate of the first four principal component variables has reached 85%, so the first four principal components are used to reconstruct the signal to obtain an orthogonal signal x (t). Then, the new IMFs component decomposed by ALIF is compared with the previous IMFs. The spectrum of the new IMF component is shown in Fig. 4. It can be seen in Fig. 4 that noise is well eliminated in x1 , and the fault feature frequency fc +fs is strengthened in x2 ,and clearly highlight the fault feature frequency fc − fs is highlighted in x7 and x8 . By comparing Fig. 3 and Fig. 4, the improved ALIF method has better performance in extracting fault features.

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4 Conclusion In this paper, an improved adaptive local iterative filtering method is proposed. Based on the original method, the orthogonality selection of the mode is carried out. Through the orthogonality selection, the noise in the signal is eliminated partly, and the fault features is highlighted. Experimental results show that the proposed method is effective for bearing fault detection. Acknowledgment. This work is supported by the National Natural Science Foundation of China under Grant 51279020.

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References 1. Barnett, R.D.: Induction motors: early development [History]. IEEE Power Energy Mag. 20(1), 90–98 (2022) 2. Sawma, J., Khatounian, F., Monmasson, E., Ghosn, R.: Induction motor parameters identification in noisy environment. IEEE Ind. Electron. Soc., 1–6 (2021) 3. Kudelina, K., Vaimann, T., Rassõlkin, A., Kallaste, A., Asad, B., Demidova, G.: Induction motor bearing currents - causes and damages. In: Improving Reliability of Electric Drives (IWED), pp. 1–5 (2021) 4. Ye, X., Hu, Y., Shen, J., Chen, C., Zhai, G.: An adaptive optimized TVF-EMD based on a sparsity-impact measure index for bearing incipient fault diagnosis. IEEE Trans. Instrum. Meas. 70, pp. 1–11 (2021) 5. Huang, C., Yang, L., Wang, Y.: Convergence of a convolution-filtering-based algorithm for empirical mode decomposition. Adapt. Data Anal. 1(4), 561–571 (2009) 6. Cicone, A., Liu, J., Zhou, H.: Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis. Appl. Comput. Harmonic Anal. 41(2), 384–411 (2016) 7. Zhang, W., Min, J., Wang, Y., et al.: Application of adaptive local iterative filtering in axis trace purification of turbine generator rotor. J. Mech. Sci. Technol. 36(6), 2721–2728 (2022) 8. Li, X.: Study of the orthogonality of EMD methods in HHT. Kunming Univ. Sci. Technol., 27−45 (2010). (in Chinese) 9. Liu, B., Fu, A., Yao, Z., et al.: SO2, concentration retrieval algorithm using EMD and PCA with application in CEMS based on UV-DOAS. J. Technol. Sci. 158, 273–282 (2018) 10. Javed, E., Faye, I., Malik, A.S., et al.: Removal of BCG artefact from concurrent fMRI-EEG recordings based on EMD and PCA. J. Neurosci. Methods 291, 150–165 (2017) 11. Patel, V.N., Tandon, N., Pandey, R.K.: Vibration studies of dynamically loaded deep groove ball bearings in presence of local defects on races. Procedia Eng. 64, 1582–1591 (2013)

Detection of Bearing Fault in Induction Motor Using Multi-parameter Optimized Resonance Sparse Signal Decomposition Meitao Li, Chidong Qiu, Shuai Hong, and Zhengyu Xue(B) College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China {muzili,qiuchidong,hongshuai,xuezy}@dlmu.edu.cn

Abstract. When the induction motor bearing fails, the stator current signal not only has weak fault features related to fault information, but also includes plenty of strong background noise, which increases the difficulty of fault detection. In order to effectively extract the fault features, this paper proposes a multi-parameter optimized resonance sparse signal decomposition (RSSD). The proposed method does not depend on frequency range, but divides the spectrum through resonance, and overcomes the limitation of traditional RSSD methods that rely on manual experience to set important parameters such as quality factors. The novelty of this method lies in the introduction of gorilla troops optimizer (GTO) algorithm to automatically select quality factor Q, weight factor A and Lagrange multiplier μ. Firstly, with the minimum fitness function as the goal, GTO is used to optimize the selected parameters. Secondly, RSSD is used to obtain the best resonance component and power spectral density (PSD) carried out to extract the bearing fault feature frequency. The experimental results show that the proposed method is more effective in detecting bearing faults than the traditional method. Keywords: Induction motor · Bearing · Fault · Resonance sparse signal decomposition

1 Introduction The motor is a vital driving force in modern industrial society, playing a significant role in social development. However, harsh environments and complex working conditions may damage key components, leading to equipment failures and major accidents. According to relevant statistics, bearing failures account for about 40% of motor failures [1]. While using vibration signals as fault feature carriers offers unique advantages, it often requires expensive sensor and is susceptible to environmental interference, resulting in poor detection performance. Meanwhile, the non-intrusive current signals with less interference from the operating environment are still the ideal choice for detecting bearing faults [2]. The research on current signal mainly takes extracting and enhancing the fault frequency in current signal as the starting point, and weakens fundamental frequency and higher harmonics [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 520–527, 2024. https://doi.org/10.1007/978-981-97-1064-5_57

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He Q, Ren X et al. [4] introduced empirical mode decomposition (EMD) for adaptively decomposing motor current into intrinsic mode functions (IMFs) with multiple vibration frequency segments. The best-performing IMF is selected for fault feature detection. However, both EMD and multi-wavelet transform methods suffer from spurious pulses in the resulting IMFs, limiting their ability to fully decompose fault features caused by motor bearing faults. Overcoming this limitation requires a signal decomposition approach not reliant on frequency range [5]. Selesnick proposed the resonance sparse signal decomposition (RSSD) based on the tunable quality factor wavelet transform (TQWT) [6]. RSSD divides the quality factor Q, reflecting the signal’s resonance feature, into high resonance component Qh and low resonance component Ql according to the persistence of the resonance component. Morphological component analysis (MCA) is used to establish the objective function model. Then the split augmented lagrangian shrinkage algorithm (SALAS) is used to increase the signal sparsity to minimize the objective function and effectively separate complex signals. The signal decomposition of RSSD is not reliant on frequency band division, surpassing limitations of traditional methods. In [7, 8], researchers applied RSSD to successfully detect bearing faults in vibration signals. The results demonstrate that RSSD can be introduced into motor fault detection. In recent years, metaheuristic optimization algorithms have gained popularity in bearing fault detection. Particle swarm optimization (PSO) was proposed based on the collective behavior of animals in nature. Gong and Xiao successfully applied PSO to the fault diagnosis of rotating machinery based on RSSD, achieving effective separation of resonance components [9]. Karaboga proposed an algorithm based on the collective behavior of bees called the artificial bee colony (ABC) algorithm. Na Chai, Ming Yang et al. successfully decomposed the sparse motor current signal into high and low resonance components by using ABC [5]. The early algorithms provide a feasible research direction for global optimization problems, but these algorithms have a weak ability to approximate the spatial optimal solution, resulting in slow convergence speed, large computation amount and low efficiency in each iteration of wavelet decomposition. In addition, the optimization of only a single parameter can not give full play to its global optimization performance. Inspired by the social intelligence of gorilla troops in nature, Benyamin Abdollahzadeh proposed a new meta-heuristic algorithm called GTO [10], which can be used as a robust metaheuristic algorithm to solve global optimization problems. To address these challenges, this paper proposes a multi-parameter optimized RSSD, using the Q-factor of wavelet basis, weight coefficients A, and Lagrange multipliers μ as optimization targets. The method employs GTO-optimized RSSD for decomposing the optimal signal, followed by power spectral density (PSD) to extract fault feature frequencies. Experimental results validate the method’s effectiveness in motor bearing fault detection.

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2 Proposed Approaches 2.1 Review of RSSD The RSSD considers the difference in resonance degree, separating the complex signal x(n) into high resonance components x 1 (persistent oscillations) and low resonance components x 2 (non-oscillating transients), effective separation of signals with different quality factors and close frequencies is achieved. The Q reflects the resonance feature of the signal. A higher value of Q express better frequency aggregation of the signal, while a lower value of Q express better time aggregation of the signal. The Q is defined as ratio of center frequency to bandwidth, and as follows: Q=

fc BW

(1)

Where f c is signal center frequency; BW is pulse signal bandwidth. RSSD achieves signal decomposition through a two-channel decomposition filter bank as shown in Fig. 1, where high pass scaling (HPS) β and low pass scaling (LPS) α are as follows: β=

β 2 ,α = 1 − Q+1 γ

(2)

Fig. 1. Analysis and synthesis filter bank for TQWT

H h (ω) and H l (ω) in Fig. 1 represent the frequency response of HPS and LPS respectively, which can be represented by: ⎧ ⎪ |ω| ≤ (1−β)π ⎨ 0, ω+(β−1) ), (1−β)π < |ω| < απ θ ( (3) Hl (ω) = α+β−1 ⎪ ⎩ 1, απ ≤ |ω| ≤ π ⎧ ⎪ |ω| ≤ (1−β)π ⎨ 0, απ−ω ), (1−β)π < |ω| < απ Hh (ω) = θ ( α+β−1 (4) ⎪ ⎩ 1, απ ≤ |ω| ≤ π Where ω is angular frequency; the θ (ω) is given by: √ θ (ω) = 0.5(1 + cos ω) 2 − cos ω, |ω| ≤ π

(5)

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Assuming x 1 , x 2 can be sparsely expressed in bases K 1 , K 2 , respectively, they can be estimated by minimizing the objective function.The equation can be expressed as: J (ω1 , ω2 ) = x − K1 W1 − K1 W1 22 + A1 W1 1 + A2 W2 1

(6)

where Ai=1,2 is the weight coefficient, which can directly affect the energy of x 1 , x 2 . If A1 is fixed and A2 is increased, the energy of the x 2 is reduced. If A1 and A2 is increased, the energy of the x 1 and x 2 will be reduced. It can be seen that the selection of Ai=1,2 is an important factor, affecting the effect of RSSD. 2.2 Multi-parameter Optimized Resonance Sparse Signal Decomposition The GTO is a new intelligent optimization algorithm [10]. The algorithm has three solutions for the position optimization of Silverback gorillas, namely the development stage and the exploration stage. The exploration stage is further divided into the following Silverback gorilla mechanism and the competition adult female mechanism. Correlation kurtosis is a new component evaluation index first proposed by GeoffL McDonald [11]. Compared with the traditional kurtosis index, correlation kurtosis synthesizes the feature of correlation function and can represent the oscillation change of resonance signal more clearly. The equation can be expressed as: CKM (T ) =

N   ( M m=0 xn−mT )

n=1

(

N  n=1

(7) xn2 )M +1

Where x n is signal sequence; N is sampling length; T is period of the pulse signal of interest; M is the number of cycles shifted. In order to avoid the problem that resonant signals in current are accompanied by many same components when RSSD is executed, cross-correlation constraints are introduced. For any signal e and g, the correlation coefficient can be expressed by: n 

C=



(ei −e)(gi −g)  n n   (ei −e)∗ (gi −g)2 n=1

i=1

(8)

i=1

Where the value range of C is [0, 1]. A larger C indicates a higher correlation between the two signals; otherwise, the correlation is small. Combined with the feature of correlation kurtosis and correlation number, the minimum value of the ratio of low resonance signal CK M to high and low resonance signal C is taken as the fitness function F, which is given by: F=

C CKM

(9)

The selection of Q, A, μ in the objective function constructed using MCA has a great influence on the decomposition results. Therefore, combining the advantages of GTO, a optimized RSSD is proposed. The final process is as follows:

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Step 1. Initialize the number of iterations T, population size N and some basic properties of the GTO algorithm. Step 2. Define the range of extreme values of the target parameter POP(Q), POP(A), and POP(μ), which is to be optimized. Step 3. Enter the exploration phase and calculate the fitness value, setting the best solution as the “silverback” location. Step 4. Enter the development phase and intelligently determine algorithmic mechanisms for following Silverback gorillas or competing adult females, then calculating the fitness value and setting the best solution as the “silverback” location. Step 5. Repeat Steps 3 and 4 until the number of iterations reaches the maximum T. Step 6. Current signal is decomposed by using optimal parameter combination.

3 Experimental Verification 3.1 The Experiment Platform The fault characteristic frequency f c is as follows [12]: fc = 0.5N fr [1 − (Db cos α)/Dc ]

(10)

Where f r is the mechanical rotor frequency, N is the number of balls, Db is sphere diameter, α is the contact angle of ball to raceway and Dc is the bearing pitch diameter.

Fig. 2. Experiment platform

The Fig. 2 is the induction motor bear fault experiment platform. The intelligent power module (IPM) is Mitsubishi PM75CL1A120, with collector current of 50 A, collector-emitter voltage of 1200 V and maximum switching frequency of 20 kHz. The three-phase induction motor is Y100L1-4T, which rated voltage, current, power and speed are 380 V, 5.03 A, 2.2 kW, 1430 rpm, respectively. The stator current is measured by Hall current sensor LEM IT60-S, with measuring range of 60 A, linearity error of 20 ppm.

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Power/frequency (dB/Hz)

50

525

3fs

2fs 0

fc+fs

fc-fs -50

20 40 Frequency(Hz)

60

Fig. 3. Spectrum of raw signal

3.2 Experimental Result Analysis Because the mechanical resonance frequency of the motor is the most sensitive at 20 Hz, the power frequency of experimental motor is set as 20 Hz, correspondingly, the fault characteristic frequency f c is 35 Hz,. Firstly, the raw signal is directly processed.Setting the sampling number N = 16384 and sampling frequency F s = 1024, we use PSD to get the result shown in Fig. 3. It shows that the fault characteristic frequencies f c ± f s are completely buried by noise and harmonics, only the fundamental frequency f s , second harmonic 2f s and third harmonic 3f s are obvious. 60

fs

40

fs+fr

20

2fs

3fs 4fs

fc-fs

0

fs-fr

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60

fs

40

3fs+fr-fc 2fs

20

0 2fs-fc fc-fs 3fs-fc fs-fr fs+fr -20

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fc-fs+5fr 4fs-fc fc+fs 3fs

-40

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Fig. 4. Spectrum based on traditional RSSD

0

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Fig. 5. Spectrum based on improve RSSD

Secondly, using manual parameter selection with Q1 = 19, Q2 = 3, A1 = 0.6, A2 = 0.3 and μ = 0.9, the traditional RSSD method is applied to process the original signal. As shown in Fig. 4, besides f s , 2f s and 3f s , there are f c ± f s and eccentric frequencies f s − f r , f s + f r and 3f s + f r . Compared with Fig. 3, the processing effect has been improved but it is still not ideal. Finally, with the improved RSSD and adaptive parameter selection Q1 = 10, Q2 = 2, A1 = 0.7, A2 = 0.1, and μ = 2, the processed results is shown in Fig. 5. Unlike Fig. 4, Fig. 5 not only shows clear fs, 2fs, and 3fs, but also exhibits relatively prominent fault characteristic frequencies such as f c ± f s , 2f s − f c , 3f s − f c , and 4f s − f c . The results show that the improved RSSD is more effective than the traditional RSSD.

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Because multi-parameter optimized RSSD can select the optimal parameters, it fundamentally avoids the shortcomings brought by manual experience, and the experiment results verify that the algorithm is more effective than the original algorithm.

4 Conclusion This paper proposes a multi-parameter optimized RSSD approach that divides the spectrum based on resonance rather than relying on frequency range. It overcomes the limitations of traditional frequency band division filters and addresses the randomness inherent in the traditional RSSD method, which requires manual selection of important parameters like quality factors. The proposed method breaks through these limitations and offers a more robust approach for bearing fault detection.The experimental results show that this proposed method is more effective in detecting bearing faults. Acknowledgement. This work is supported by the National Natural Science Foundation of China under Grant 51279020.

References 1. Song, X., Sun, W., Liu, G., Zhao, W., Wang, Z.: Deep subdomain adaptive network motor rolling bearing cross-condition fault diagnosis. Trans. China Electrotech. Soc. 38, 1000–6753 (2023). (in Chinese) 2. Immovilli, F., Cocconcelli, M.: Experimental investigation of shaft radial load effect on bearing fault signatures detection. IEEE Trans. Ind. Appl. 53(3), 2721–2729 (2017) 3. Li, R., Liu, F., Liang, L.: Fault identification of broken rotor bars for the variable frequency AC motor based on parameter optimized variational mode decomposition. Trans. China Electrotech. Soc. 36(18), 3923–3933 (2021). (in Chinese) 4. He, Q., Ren, X., Jiang, G., Xie, P.: A hybrid feature extraction methodology for gear pitting fault detection using motor stator current signal. Insight Non-Destruct. Test. Cond. Monit. 56(6), 326–333 (2014) 5. Chai, N., Yang, M., Ni, Q., Xu, D.: Gear fault diagnosis based on dual parameter optimized resonance-based sparse signal decomposition of motor current. IEEE Trans. Ind. Appl. 54(4), 3782–3792 (2018) 6. Selesnick, I.W.: Wavelet transform with tunable Q-factor. IEEE Trans. Signal Process. 59(8), 3560–3575 (2011) 7. Lu, Y., Du, J., Tao, X.: Fault diagnosis of rolling bearing based on resonance-based sparse signal decomposition with optimal Q-factor. Meas. Control 52(7–8), 1111–1121 (2019) 8. Yu, G.: Feature enhancement method of rolling bearing acoustic signal based on RLS-RSSD. Measurement 192, 110883 (2022) 9. Gong, Y., Xiao, H.: Application of resonance sparse decomposition to particle swarm optimization in bearing fault diagnosis. Mach. Des. Manuf. 4(21–25), 1001–3997 (2017). (in Chinese) 10. Abdollahzadeh, B., Soleimanian Gharehchopogh, F., Mirjalili, S.: Artificial gorilla troops optimizer: a new nature-inspired metaheuristic algorithm for global optimization problems. Int. J. Intell. Syst. 36(10), 5887–5958 (2021)

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11. Zhu, J., Zhang, Y., Wang, X.: Research on rolling element bearing fault diagnosis based on empirical mode decomposition and correlated kurtisos. J. Wuhan Univ. Technol. Transp. Sci. Eng. 38(2), 367–370 (2014). (in Chinese) 12. Qiu, C., Wu, B., Xu, C., Qiu, X., Xue, Z.: An approximate estimation approach of fault size for spalled ball bearing in induction motor by tracking multiple vibration frequencies in current. Sensors 20(6)(2020)

Chopping Compensation Control and Low Frequency Pulse Suppression Strategy of DC Side Current in Lithium Battery Energy Storage System Yiyang Liu, Weichao Li, Liang Zhou(B) , and Jinyang Han National Key Laboratory of Electromagnetic Energy, Naval University of Engineering, Wuhan 430033, China [email protected] Abstract. To resolve the issue of lithium-ion batteries in electromagnetic emission work environments experiencing voltage drop at the battery output due to high rate discharge, which in turn cannot meet the DC voltage requirements of the load converter. Therefore, this article proposes an N+1 level dynamic chopping structure energy storage system topology to compensate and stabilize the DC bus voltage. Meanwhile, in order to improve DC bus voltage compensation performance, this paper adopts a composite compensation control strategy of LADRC+PI. In response to the problem of negative saturation caused by initial feedback in the LADRC controller, this article uses the method to start the observer feedback by judging the DC bus voltage and the reference voltage. Secondly, in order to reduce the three fold fundamental frequency ripple on the DC side caused by the modulation strategy of the load inverter, the bus voltage feedback value filtered by a notch filter is used for feedback to suppress the DC side current ripple. Finally, the above strategies were validated through the RT-LAB experimental platform. Keywords: Lithium ion battery · High rate discharge · DC/DC converter · Bus voltage · ADRC · Current ripple

1 Introduction As a new type of launch technology, electromagnetic launch has broad application prospects in the military and civilian fields [1, 2]. However, the high instantaneous power required during the operation of electromagnetic emission loads (from 100 MW to GW), traditional power systems cannot provide the required power requirements. Therefore, energy storage equipment is needed to achieve energy storage and power regulation [3]. Lithium iron phosphate batteries have excellent electrochemical performance and long cycle period, and is an excellent choice for energy storage equipment [4]. In fact, the electromagnetic emission condition requires lithium batteries to discharge at a high rate, but this will lead to a drop in the terminal voltage of the lithium battery, which cannot meet the bus voltage requirements of the later stage inverter. In response to this issue, this article proposes a N+1-Level Dynamic Chopping (N+1-LDC) energy storage topology, specific as shown in Fig. 2. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 528–538, 2024. https://doi.org/10.1007/978-981-97-1064-5_58

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Fig. 1. Entire system structure diagram.

Figure 1 shows the entire system structure diagram of this article. Considering the electromagnetic emission conditions, due to the wide range fluctuations of motor load and the voltage drop characteristics of lithium battery packs, classical PI control is difficult to balance the system’s fast response and anti-interference characteristics. In contrast, the active disturbance rejection control (ADRC) proposed by Han has strong disturbance suppression ability and robustness [5]. However, the traditional ADRC components are composed of nonlinear functions, which makes the design process more complex and cumbersome. Therefore, based on this, Gao proposed linear active disturbance rejection control (LADRC),which simplified parameter configuration and verified its effectiveness through experimental methods in DC/DC transformation [6, 7]. After nearly 20 years of development, LADRC has been widely used in various industries, from motor control [8, 9], grid connected inverters [10], DC/DC converters [11], flight control [12], to bus voltage control [13], and so on. In addition, when the load inverter adopts the SVPWM modulation strategy, there will be three times the fundamental frequency ripple on the DC bus [14, 15], which will be transmitted to the DC side current, resulting in three times the fundamental frequency ripple on the DC side current. This pulsation information will increase the loss of power devices, accelerate the aging of lithium batteries, affect the estimation of battery SOC by lithium-ion BMS, and endanger the safe operation of batteries [16]. In summary, the work of this article is as follows: 1) Aiming at the voltage sag characteristics of lithium batteries, which can not meet the bus voltage requirements, an N+1-LDC energy storage system topology is proposed to meet the bus voltage requirements. In response to the shortcomings of classical PI double closed-loop control, LADRC+PI composite control is adopted to improve the performance of bus voltage compensation. 2) Due to the characteristics of the controlled object in this paper, the LADRC controller appears negative saturation phenomenon. In view of this problem, the observer feedback operation mode is activated by judging the DC bus voltage and the given value to suppress the initial negative saturation phenomenon of the control quantity. 3) To reduce the triple low-frequency pulsation on the DC side caused by load characteristics, a notch filter is introduced at the reference current to achieve suppression of DC side current pulsation.

2 Structural Analysis and Modeling of N+1-LDC Figure 2 shows the topology of an energy storage system with N+1 level dynamic chopping structure, where V Libat is the open circuit voltage of a single group of lithium batteries, Rrx (x = 1, 2) is the equivalent internal resistance of a single group of lithium

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batteries and N groups of lithium batteries, respectively, and Rload is the equivalent load at full load. When the DC bus voltage cannot be maintained at the reference voltage, VT is turned on and a single set of lithium batteries are put into operation, dynamically compensating the DC bus voltage to the reference voltage.

Fig. 2. N+1-LDC energy storage system topology.

When modeling and analyzing the lithium battery energy storage system, the following assumptions are made: 1) The parameters of individual lithium batteries are consistent; 2) The system has been operating in a stable state; 3) Power devices are all ideal switching devices, ignoring conduction voltage, power device losses, and dead time; Based on state averaging and small signal disturbance injection, the transfer function model can be obtained as shown in Eqs. (1–3). (1) (2) (3) where, a1 = Lf Cbus (Rload + RC ), a2 = Lf + (DRr1 + Rr2 + RL )Cbus (Rload + RC ) a3 = DRr1 + Rr2 + RL + Rload , + Cbus Rload RC , D = (Vbus + (Rr2 + RL )IL − V1 )/(V2 − IL Rr1 ).

3 N+1-LDC Bus Voltage Compensation Control Strategy Considering the shortcomings of classical PI control and low-frequency pulsation of DC side current, according to Eqs. (1–3), a LADRC+P bus voltage composite control block diagram can be established as shown in Fig. 3(a). The outer loop is a voltage stabilizing

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loop, and the inner loop is a current pulsation suppression loop. According to Fig. 3(a), the closed-loop transfer function of the current inner loop is shown in Eq. (4). To ensure the dynamic characteristics of the system, the cut-off frequency of the inner loop is set at around 500 Hz, and the inner loop PI controller parameter is k ip = 0.0035, k ii = 5. Gicl =

Gi Gpwm Gid 1 + Gi Gpwm Gid

(4)

0

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-5

Gicl

-10 -15 -20 -25

Phase (deg)

-30 0

-45

-90 100

101

102

103

104

105

Frequency (rad/s)

(a) System control block diagram.

(b) Bode diagram of Gicl.

Fig. 3. Control block diagram and bode diagram of transfer function of Current loop.

According to the Bode diagram of the current closed-loop transfer function shown in Fig. 3(b), the current inner loop closed-loop transfer function can be approximately simplified as a first-order system. Therefore, the controlled plant of the voltage outer loop is simplified as Eq. (5). (5) Convert the plant shown in Eq. (5) to obtain the first-order LADRC control paradigm of Eq. (6), where the input is the given inductance current and the output is the bus voltage.     v˙ bus = f f vbus , iLref , δ + b0 (6)     Let x1 = vbus , x2 = f (f vbus , iLref , δ), f (f vbus , iLref , δ) is the lumped disturbance of the system, According to Eq. (6) and x 1 and x 2 , LESO can be obtained as shown in Eq. (7), where L0 is the observer gain. z˙ = Az + Bu + L0 (vbus − yˆ ) yˆ = Cz  where, A =

       01 b β1 . , B 0 , C = 1 0 , L0 = 00 0 β2

(7)

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When z1 ≈ x 1 and z2 ≈ x 2 , the control law shown in Eq. (8) can be adopted, and the parameters can be configured by bandwidth method as shown in Eq. (9). ⎧ ⎨ e = r − z1 (8) u = kp e ⎩ 0 u = (u0 − z2 )/b0 ⎧ ⎨ β1 = 2ωo (9) β = ωo2 ⎩ 2 kp = ωc

Control input

2550

2500

2450

Disturbance observation

Bus voltage observation/V

Generally, the larger the observer gain and the controller gain, the faster the system response speed. However, in reality, due to the influence of noise, the larger the observer gain, and the system may experience oscillation or overshoot. Under the electromagnetic emission condition, the bus voltage has initial energy storage and is greater than the reference voltage, which makes the initial error negative and is amplified after the control law.  Secondly, because the gain matrix L0 is too large, the high-order state (f (f vbus , iLref , δ)) appears a large short-term “peaking”, which makes the synthesized reference current appear negative saturation, and then makes the initial drop of DC bus voltage larger. Therefore, this article proposes an operation method of starting observer feedback by judging the DC bus voltage and the given value to suppress the initial negative saturation phenomenon of the control quantity. Specifically, when the DC bus voltage is higher than the given value, LESO only observes and does not enter the feedback channel, and the control quantity is 0 at this time; When the DC bus voltage drops below the given value for the first time, LESO observes and also enters the feedback loop for duty cycle calculation.

0 4

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Fig. 4. Negative saturation suppression simulation waveform.

As can be seen from Fig. 4, when negative saturation control is not introduced, the observed value of disturbance has a large “peaking” phenomenon, which leads to a large negative saturation of the synthesized control quantity and reduces the bus voltage compensation performance. Using the negative saturation suppression method, the negative saturation suppression of the control quantity can be realized without affecting the performance of the observer.

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4 Suppression Strategy for Triple Frequency Ripple Current of DC Side Inductance In the introduction, it is mentioned that the adoption of SVPWM modulation strategy in the load will lead to three low-frequency fluctuations in the midpoint potential, so that the pulsation information will be transmitted to the DC side through the bus capacitor current. At the same time, the feedback link introduces the information of cubic pulsation, which further intensifies the current pulsation on the DC side. Considering that the notch filter can greatly weaken the gain at a specific frequency, this paper introduces the notch filter into a given current to suppress the gain of the system loop at the third frequency, so as to achieve the effect of suppressing the third low-frequency pulsation. Its expression is shown in Eq. (10), where ωr is the characteristic frequency, ξ is the quality factor. Here, the characteristic frequency ωr set to three times the fundamental period, ξ Take 0.1, 0.5, 0.75, and 2 respectively, and draw the frequency characteristics of the notch filter as shown in Fig. 5(a). It can be seen that with the ξ With the increase of, its bandwidth gradually decreases, and its notch ability becomes stronger, but its adaptability to frequency is poor. Therefore, in practical applications value of ξ needs to be considered in a compromise. Gnotch =

S 2 + ωr2 S 2 + ωr /ξ S + ωr2

(10)

=0.1

=0.75

100

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0 -50

=0.5 =2

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106

(a) Bode diagram of notch filter.

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102 Frequency (rad/s)

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(b) Bode diagram of Goc1 and Goc2.

Fig. 5. Block diagram of notch filter and open-loop transfer function.

According to [17], the open-loop transfer function under LADRC+PI control can be obtained as Eq. (12), Eq. (11) is the open-loop transfer function with notch filter under PI control. According to Eqs. (11) and (12), the Bode diagram shown in Fig. 5(b) can be obtained. From Fig. 5(b), the introduction of notch filter does not affect the dynamic characteristics and stability of the system, and at the same time, the gain at the third frequency is greatly suppressed, so that the current low-frequency ripple can be suppressed. Goc1 = Gv Gp Gnotch

(11)

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Goc2 = C1 C2 Gp Gnotch

(12)

5 Experimentation To verify the feasibility of the above analysis, an experimental platform was built using RT-LAB and a digital controller, as shown in Fig. 6. The main loop of N+1-LDC converter and inverter is simulated by RT-LAB real-time simulator. The converter controller and N+1-LDC controller were composed of DSP and FPGA, with DSP used for calculation, sampling, and duty cycle output, and FPGA used for generating interrupt and pulse signal output. The experimental data are saved in the event loop memory. After the experiment is completed, the experimental waveform is exported and drawn using MATLAB. The model parameters and controller parameters are shown in Table 1, where f s1 is the switching frequency of the N+1-LDC converter, f s2 is the switching frequency of the load converter, Rx and L x are the AC side load parameters (x = A, B, C). Table 1. Simulation Parameters and Controller parameters. Parameter

Value

Parameter

Value

V1

268 V

Lf

0.3 mH

V2

2546 V

RL

3.2 m

Rr1

20 m

C bus

44 mF

Rr2

190 m

RC

2 m

Rx

50 m

f s1

2 kHz

Lx

46 0µH

f s2

2.5 kHz

k vp

7.989

ft

50 Hz

k vi

600

ωo

1000 rad/s

k ip

0.0035

ωc

250 rad/s

k ii

5

b0

45.26

Figure 7 show the experimental waveforms of DC bus voltage compensation and DC side current ripple under load current peak of 5000 A and bus set value of 5000 V. From Fig. 7(b), it can be seen that when compensation is not applied, the voltage of the lithium battery pack drops between 4800 V and 4850 V, which cannot meet the DC bus voltage requirements of the subsequent stage converter of 5000 V. Under traditional PI control, the initial drop in bus voltage is 4966 V; The initial drop in bus voltage of the control strategy proposed in this article is 4981 V. In steady state, the bus voltage ripple values of the two are basically the same. Secondly, From Fig. 7(c), it can be seen that the dynamic response time of the LADRC+PI composite control strategy has been improved by 10 ms. From Fig. 7(d), it can be seen that the current pulsation on the DC side of PO and ON before the introduction of a notch filter is about 550 A. After introducing a

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Fig. 6. RT-LAB real-time simulation platform.

notch filter at 1.3 s, the current pulsation on the DC side decreases to about 378 A, and the current pulsation value on the DC side decreases by about 31.2%.

Fig. 7. Experimental waveform.

Figure 8 show the experimental waveforms of DC bus voltage compensation and DC side current ripple under the conditions of load current peak of 7000 A and bus set value of 5000 V. Figure 8(b) shows that as the current demand of the post load converter increases, the voltage drop of the pre stage energy storage system also increases. The voltage drop

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falls between 4500 V and 4600 V, which cannot meet the DC bus voltage demand of the post stage converter. Secondly, the initial bus voltage drop difference between the traditional PI double closed-loop control strategy and the LADRC+PI composite control strategy is about 21 V. In contrast, From Fig. 8(c) it can be seen that the dynamic response time under LADRC+PI control has been improved by 30 ms, and the steady-state voltage ripple values of the two are basically the same. From Fig. 8(d), it can be seen that the current ripple on the DC side of PO and ON before the introduction of a notch filter is about 260 A. After introducing a notch filter at 1.3 s, the current ripple on the DC side decreases to about 196 A, and the current ripple value on the DC side decreases by about 24.6%.

Fig. 8. DC side voltage and current waveform.

6 Conclusion (1) In the case of electromagnetic emission, the lithium battery pack can’t meet the bus voltage requirement of load converter due to large-rate discharge. Using N+1-LDC energy storage topology can reduce the economic cost of the system on the premise of meeting the bus voltage compensation.

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(2) According to the characteristics of electromagnetic emission, the LADRC+PI compound control appears negative saturation. The simulation and experimental results show that by judging the DC bus voltage and the given value to start the observer feedback, the initial negative saturation of the control quantity can be suppressed. (3) In view of the modulation strategy of three-level parallel converter, the low-frequency ripple of DC side current is caused three times, and the notch filter is introduced into the current control loop. The experimental results show that the low-frequency ripple of DC side current can be greatly suppressed. Acknowledgments. This work is supported by the National Key Laboratory of Electromagnetic Energy Fund (614221722050501).

References 1. Ma, W., Lu, J.: Research progress and challenges of electromagnetic launch technology. Trans. China Electrotech. Soc. 38, 1–17 (2023). (in Chinese) 2. Ma, W., Xiao, F., Nie, S.: Applications and development of power electronics in electronmagnetic launch system. Trans. China Electrotech. Soc. 31(19), 1–8 (2016). (in Chinese) 3. Long, X., Lu, J., Wei, J., et al.: Application on lithium batteries for electromagnetic launch. J. Natl. Univ. Def. Technol. 41(4), 66–71 (2019). (in Chinese) 4. Li, J., Lai, Q., Wang, L., et al.: A method for SOC estimation based on simplified mechanistic model for LiFePO4 battery. Energy, 1266–1276 (2016) 5. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009) 6. Gao, Z.Q.: Scaling and bandwidth-parameterization based controller tuning. In: Proceedings of the American Control Conference, Denver, Colorado, pp. 4989–4996. IEEE (2003) 7. Sun, B.S., Gao, Z.Q.: A DSP-based active disturbance rejectioncontrol design for a 1-kW H-bridge DC-DC power converter. IEEE Trans. Ind. Electron. 52(5), 1271–1277 (2005) 8. Xu, Y., Lin, C., Xing, J.: Transient response characteristics improvement of permanent magnet synchronous motor based on enhanced linear active disturbance rejection sensorless control. IEEE Trans. Power Electron. 38(4), 4378–4389 (2023) 9. Wang, R., Wu, Z., Lin, P., et al.: Speed and voltage controllers design for the permanent magnet starter/generator. IEEE Trans. Ind. Electron. 70(8), 8314–8322 (2023) 10. Lin, Y.: Research on Active Disturbance Rejection Control of Three Level Photovoltaic Inverter, pp. 1–73. South China University of Technology, Guangzhou (2019). (in Chinese) 11. Łakomy, K., Madonski, R., Dai, B., et al.: Active disturbance rejection control design with suppression of sensor noise effects in application to DC–DC buck power converter. IEEE Trans. Ind. Electron. 68(1), 816–824 (2022) 12. Sun, C., Liu, C., Feng, X., et al.: Visual servoing of flying robot based on fuzzy adaptive linear active disturbance rejection control. IEEE Trans. Circuits Syst. 68(7), pp. 2558–2562 (2021) 13. Lang, X., Yang, T., Bai, G., et al.: Active disturbance rejection control of DC-Bus voltages within a high-speed aircraft electric starter/generator system. IEEE Trans. Transp. Electrif. 8(4), 4229–4241 (2022) 14. Pou, J., Pindado, R., Boroyevich, D., et al.: Evaluation of the low-frequency neutral-point voltage oscillations in the three-level inverter. IEEE Trans. Ind. Electron. 52(4), 1582–1588 (2005)

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15. Jiang, W., Wang, Q., Shi, X., et al.: Low frequency oscillation of neutral point voltage of neutral-point-clamped three-level VSI under SVPWM control. Proc. CSEE 29(3), 49–55 (2009). (in Chinese) 16. Chang, F., Roemer, F., et al.: Influence of current ripples in cascaded multilevel topologies on the aging of lithium batteries. IEEE Trans. Power Electron. 35(11), pp. 11879–11889 (2020) 17. Makeximu: Active Disturbance Rejection Control of Lean Pre-mixed Combustion Oscillation. Tsinghua University, pp 1–115 (2017). (in Chinese)

Research on Preliminary Integrated Design of Electric Ducted Fan Ye Li1

, Qi Li1,2(B) , Tao Fan1,2 , and Xuhui Wen1,2

1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

[email protected] 2 University of Chinese Academy of Sciences, Beijing 100190, China

Abstract. Electric ducted fans are widely used in hybrid aircraft, electric aircraft, and VTOL vehicles. The future development of ducted fans will focus on achieving high power density, higher cruise speeds, longer battery life, and increased task load capacity. Under the conditions of specified tension and motor power constraints, the ratio of hub to blade tip and the ratio of inner and outer diameters of the motor stator are introduced to analyze the performance of the propulsion system in this paper. And this article mainly studies the relationship between the static thrust of the fan, motor power, and motor temperature rise, and proposes the direction for optimizing the design of duct fans based on the relationship between these three factors. Keywords: Electric aircraft · ducted-fan · motor · thermal model · design method

1 Introduction The application of ducted fans in electric aircraft provides Vertical Takeoff and Landing (VTOL) capability, Short Takeoff and Landing (STOL) and slow-speed flight capabilities, noise reduction, and improved energy efficiency [1]. These features make ducted fans highly promising in the field of electric aircraft. As electric aircraft technology continues to advance, ducted fans will play a vital role in driving the application and development of electric aircraft in various domains [2, 3]. Electric ducted fans are widely used in hybrid aircraft, electric aircraft, and VTOL vehicles. The future development of ducted fans will focus on achieving high power density, higher cruise speeds, longer battery life, and increased task load capacity. A ducted fan consists of several main components, including the motor, blades, and housing. The motor is typically located at the center of the fan and rotates the blades to generate the airflow. The blades are usually made of lightweight metals or plastics, and their shape and angle can affect the flow rate and velocity of the air. The housing guides the airflow and provides structural support and protection for the motor and blades. This article mainly focuses on ducted fan motors. Many researchers have paid attention to ducted fan n motors. Jin introduces a motor design model based on the fan hub-to-tip ratio, which demonstrates the significant potential of the thermal coupling effect between fan aerodynamic design and motor cooling © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 539–546, 2024. https://doi.org/10.1007/978-981-97-1064-5_59

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design in enhancing motor power density in electric propulsion systems. A smaller hubto-tip ratio is preferred, ensuring power and cooling balance [4]. Hu introduces a novel air-cooling system specifically designed for the electrical machine in an electric ducted fan propulsion system. The innovative cooling system incorporates a cooling guide vane with a heat pipe (CGVHP), strategically positioned downstream of the rotating blades within the ducted fan assembly [5]. To seek reliable methods for calculating the characteristics of ducted propellers, a modified momentum theory model for ducted propellers considering the rotational flow effect was developed based on the momentum theory of propellers [6]. By introducing the axial power coefficient, the model accounts for the rotational flow induced by the propeller. The influence of parameters such as the thrust coefficient was analyzed in relation to the overall characteristics of the lift system. In [7] an efficient design method for ducted fan propellers is proposed based on the modification of design using CFD calculations and the momentum theory. In the design process, the accuracy is improved by modifying the inflow angle and angle of attack, and the correction coefficients are obtained by back-solving from the CFD results. After the preliminary design, an iterative process involving solving the correction coefficients and redesigning is performed to quickly obtain a ducted fan propeller that meets the design requirements. The relationship between the blade diameter and thrust of an axial flow fan is influenced by multiple factors. The shape, number, and angle of the blades, blade material and its quality, motor power, rotational speed of the fan can impact the thrust of the axial flow fan. Under the conditions of specified tension and motor power constraints, the ratio of hub to blade tip and the ratio of inner and outer diameters of the motor stator are introduced to analyze the performance of the propulsion system in this paper. And this article mainly studies the relationship between the static thrust of the fan, motor power, and motor temperature rise, and proposes the direction for optimizing the design of duct fans based on the relationship between these three factors.

2 Modeling Description By calculating the static thrust power, motor power, and motor temperature rise of the duct fan, combined with the constraints of the geometric dimensions, thrust demand, and other parameters of the duct fan motor, the specific calculations are as follows. 2.1 Theoretical Minimum Aerodynamic Power The ducted fan is an electrically driven propeller enclosed within a duct shows in Fig. 1. The propeller is a device that converts the power of an engine into a pulling force. The momentum theory regards a propeller as a disc with an infinite number of advancing blades, and the distribution of tension generated on the disc is uniform. There is a pressure difference front and back of the disc, but the axial velocity before and after the disc is equal (because it is assumed that the disc has no thickness). There is no twisting on the disc, and the airflow passing through the disc does not rotate. In addition, for the convenience of solving, it is also assumed that the gas is ideal compressible fluid. According to the Bernoulli equation, the tension of the propeller can be obtained; In

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addition, according to the momentum theorem, the force exerted by the propeller on the airflow (equal to the pulling force of the propeller, opposite in direction) should be equal to the incremental momentum of the propeller disk.

Fig. 1. Schematic diagram of ducted fan.

The static thrust of a ducted fan can be calculated using the following formula: Dm,out = kout Dtip

(1)

Dm,inner = kd Dm,out

(2)

A=

 π 2 2 Dtip − Dm,out 4

Tc = Avout ρair vout

(3) (4)

where Dtip is outer diameter of propeller hub, k out is the ratio of the outer diameter of the motor to the outer diameter of the propeller hub, k d is the ratio of the inner diameter of the motor stator to the outer diameter of the motor, Dm,out is the outer diameter of the motor, Dm,inner is the inner diameter of the motor stator, A is the effective area of duct, T c is the static thrust of ducted fan, vout is outlet flow velocity of duct, ρair is air density. Pc =

 1  2 2 m vout − vin 2

(5)

where Pc is the theoretical minimum aerodynamic power.It’s important to note that the calculation of static thrust for an axial flow fan is based on an idealized model, and in practical situations, it can be influenced by various factors such as air density, fan efficiency, motor efficiency, etc. This formula serves as a basic calculation method. 2.2 Motor Output Power The power is proportional to the torque and speed of the motor. Therefore, the power output of the motor can be written as: 2 Le kw Pm,out = ωm Tm ∝ nBg AI Dm,inner

AI =

Qns Is π Dm,inner

(6) (7)

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where Pm,out is the motor output power, ωm is motor speed (rad/s), T m is motor torque, n is motor speed (r/min), Bg is based on the amplitude of the fundamental wave of air gap magnetic density, AI is line load, L e is effective axial length of iron core, K w is winding factor, Q is number of slots, ns is number of conductors per slot, and I s is the current. 2.3 Motor Thermal Calculation The heat generated inside the motor is the sum of all losses, including iron losses, copper losses, etc. The heat generated by the ducted fan motor must be dissipated through the convective heat transfer between the motor casing and the air. The component that generates the most heat for a motor is the winding. The thermal network model is commonly used to calculate the temperature distribution in an electric motor. This model divides the motor into several thermal elements representing different parts of the motor, such as the stator, rotor, core, and winding. The heat transfer paths and thermal resistances between these elements are considered to determine the temperature rise.This article analyzes the heat transfer of individual copper losses. Therefore, the thermal circuit model can be simplified to a certain extent, and temperature rise analysis of the motor can be carried out quickly and conveniently. The simplified thermal circuit model is shown in Fig. 2. Rconv is the resistant of the convection of the motor housing, R2 is the resistant between winding and stator teeth, R3 is the resistant between stator yoke and outer wall of stator, R5 is the resistant stator teeth and stator yoke. According to different electromagnetic designs, the copper loss of the motor varies, and the lumped thermal circuit of the motor is a highly correlated numerical value with the geometric size of the motor, which together represent different electromagnetic designs.

Fig. 2. Geometry of the machine fraction and thermal circuit of the machine

According to Eqs. (8)–(9). The heat that can be carried away through convective heat transfer is shown in Eq. (10). Ploss,cu ∝ AI J J =

Is = Sn

π 4

Qns Is   2 2 Dm,out − Dm,in kslot

(8) (9)

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Qout = hAmotor (Twall − Tair )

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(10)

where Ploss,cu is the copper loss, h is the surface average convective heat transfer coefficient, k slot is the spacer factor, Amotor is the external surface area of the motor, and T wall is the average temperature of the outer surface wall of the motor, T air is the temperature of air. In the lumped thermal circuit, the loss can be calculated by Eq. (8). The thermal resistance is calculated according to the theoretical formula and empirical formula, as shown in Eqs. (11)–(14). The relationship between motor temperature rise, copper loss, and thermal resistance can be obtained through calculation, as shown in Eq. (15). Rconv =

1 hAmotor

wt ws + 8λcu,jz ht Le Q 8λfe ht Le Q Dm,out − Dm,in R3 = 4λfe wt QLm hy R5 = Dm,out +Dm,y 2λfe π 2

R2 =

T ∝ Ploss,cu (R2 + R3 + R5 )

(11) (12) (13) (14) (15)

where Ploss,cu is the copper loss, h is the surface average convective heat transfer coefficient, k slot is the spacer factor, Amotor is the external surface area of the motor, and T wall is the average temperature of the outer surface wall of the motor, T air is the temperature of air.

3 Modeling Description Assumptions and Limitations Based on the previous section, a coupling model was established between the static thrust of the fan, motor power, and motor temperature rise. However, in order to simplify the preliminary design phase of pipeline fans. The model makes the following assumptions: firstly, the heat exchange between the motor and the ambient air is considered in the model, and only forced thermal convection is considered. Secondly, the temperature of the motor winding is the most limiting factor, as the motor winding is the weak point of heat exchange in the motor. The temperature rise calculation of the motor was only carried out in the case of pure copper loss, as the copper loss of the motor is the largest heating unit of the motor. Finally, in this model, it is assumed that the efficiency of the motor and fan is constant. Therefore, this model is more suitable for obtaining approximate results during the preliminary design stage, which still need to be verified and modified through 3D simulation and experiments. The design requirements of this article require the static thrust of ducted fan is 500N, the outer diameter of propeller hub varying from 200 to 800 mm, the ratio of hub to blade tip varying from 0.3 to 0.6, and the ratio of outer diameter to inner diameter of the motor core ranging from 0.5 to 0.8. The optimization design is carried out under the above requirements.

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4 Calculation Results and Discussion Calculate according to the parameter requirements and parameter variation range specified in Sect. 3. 4.1 Different Propeller Hub Diameters Figure 3 show the changes in motor temperature rise and motor power when the outer diameter of propeller hub is 570, 400 mm. Due to the fact that the copper loss of the second section motor is a proportional coefficient, the temperature rise of the motor is corrected here. Identify optimization points in the diagram. It can be seen that when the ratio of the outer diameter of the motor to the outer diameter of the propeller hub (k d ) is about 0.73, and the ratio of inner diameter to outer diameter of the motor (k out ) is 0.25, the temperature rise of the motor is small. But the power increases with the increase of k out . From the figure, it can be seen that k d is about 0.72–0.74, and k out is between 0.25 and 0.4. The temperature rise of the motor is relatively small and the power increases with the increase of k out .

Fig. 3. The change of relative temperature rise and power with the outer diameter of propeller hub is 570 mm and 400 mm (The point with the lowest temperature rise of the motor is taken as the reference, and the relative temperature rise is 1).

4.2 Fixed kd When the k d value is around 0.72, the results are shown in Fig. 4. When k out is fixed, the temperature rise gradually decreases with the increase of Dtip , but after reaching a certain value, the improvement of Dtip on temperature rise remains basically unchanged. And the power decreases with the increase of Dtip. Fix the Dtip to 390 mm. When k out is less than 0.33, the temperature rise of the motor decreases with the increase of k out . When k out is greater than 0.33, the temperature rise of the motor increases with the increase of k out . As the k out increases, the power increases. The k out where both power and temperature rise are met is at about 0.26. 4.3 Simulation Verification Therefore, we are optimizing a duct fan motor with a Dtip of 390 mm. Dmout is 100 mm, k d is 0.7. In order to simplify the model calculation time and save computational resources, this simulation adopts the method of calculating flow conditions and heat transfer of the

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Fig. 4. The change of temperature rise and power with k d is 0.72.

motor body separately. According to the principle of heat transfer, under convective heat transfer conditions, there is a temperature difference between the mainstream and the wall. In a thin layer near the wall, the fluid temperature undergoes a drastic change in the normal direction of the wall, while outside this thin layer, the temperature gradient of the fluid is almost zero. Assuming that all the heat generated by the motor is transferred through the wall in the form of Forced convection heat transfer, set the outer surface of the motor as a surface heat source, intercept the average temperature of the motor surface through the flow field calculation, and calculate the flow heat transfer coefficient of the outer wall of the motor. The obtained convective heat transfer coefficient is attached to the outer wall of the motor using the third type of boundary condition, which specifies the surface heat transfer coefficient h between the boundary and the surrounding fluid and the temperature T air of the surrounding fluid. The temperature field calculation of the motor is performed using Fluent. After numerical calculation, this duct fan motor can provide a static thrust of 553.37 N (meet design requirements 500N), the fan power is 49.7 W and motor temperature rise of 96.85K (the incoming temperature is 273.15K). h=

Qloss,cu π Dm,outer Le (Twall − Tair )

(16)

Fig. 5. Simulation model and calculation results.

5 Conclusion The ratio of the outer diameter of the motor to the outer diameter of the propeller hub is a key parameter for duct fans and motors. This article establishes a model based on k out and k d of the motor, revealing the electromagnetic and thermal coupling effects between the fan and the motor. This model can be used for preliminary optimization design of

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duct fan motors. Under the constraints of this article, the following conclusions can be drawn: (1) The value of k d of the motor is better at around 0.72–0.74; (2) When k out is fixed, the temperature rise gradually decreases with the increase of Dtip , but after reaching a certain value, the improvement of Dtip on temperature rise remains basically unchanged. (3) When k out is fixed, the power decreases with the increase of Dtip. Acknowledgment. This work was supported by Youth Innovation Promotion Association CAS (2022135).

References 1. Qian, Y., Luo, Y., Hu, X.: Improving the performance of ducted fans for VTOL applications: a review. Sci. China Technol. Sci. 65, pp. 2521–2541 (2022) 2. Akturk, A., Camci, C.: Experimental and computational assessment of a ducted-fan rotor flow model. J. Aircr. 49, 885–897 (2012) 3. Vratnya, P.C., Hornunga, M.: Sizing considerations of an electric ducted fan for hybrid energy aircraft. Transp. Res. Procedia 29, 410–426 (2018) 4. Denisenkoa, P.V., Chernyshova, P.S., Volkovb, K.N.: Numerical simulation of the flow around the ducted fan. Russ. Aeronaut. 64, 224–232 (2021) 5. Wand, K., Zhou, Z., Ma, Y.: Development and trend analysis of vertical takeoff and landing fixed wing UAV. Adv. Aeronaut. Sci. Eng. 13, 1–13 (2022) 6. Guo, J., Zhou, Z.: An efficient blade design method of a ducted fan coupled with the CFD modification. Aerospace 9, 1–17 (2022) 7. Jin, Y., Qian, Y., Zhang, Y.: Modeling of ducted-fan and motor in an electric aircraft and a preliminary integrated design. SAE Int. J. Aerosp. 11, 1–12 (2018) 8. Hu, X., Qian, Y., Dong, C.: Thermal benefits of a cooling guide vane for an electrical machine in an electric ducted fan. Aerospace 583, 1–17 (2022) 9. Fu, J., Zhou, Z.: Research on the characteristics and computational methods of ducted fan system of VTOL UAV fine particles, thin films and exchange anisotropy. Sci. Technol. Eng. 12, 1671–1815 (2012) 10. Jiaohao, G., Zhou, Z., Li, X.: An efficient design method for blade of ducted propeller. Acta Aeronaut. Astronaut. Sin. 43, 1–11 (2022)

Analysis of Restraining Circulating Current with Parallel H-bridge Power Supply Current Sharing Reactor Haihong Huang, Guang Yang(B) , and Haixin Wang School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China [email protected]

Abstract. Fast and stable tracking of reference signals for each branch is an essential indicator for the output current control of a parallel H-bridge power supply system. Due to parallel structure of multiple inverters used in parallel H-bridge power supply, inconsistent output voltage parameters and line impedance coefficients for each branch can lead to circulating current effects. Excessive circulating current will lead to poor tracking stability for branch current. In response to circulating current problem for parallel branches of parallel H-bridge power supply, the causes of circulating current in parallel branches are analyzed, and the role of current sharing reactor in suppressing circulating current is studied, as well as the corresponding relationship for parameters of current sharing reactor and circulating current. A calculation method for electrical parameters based on current sharing reactors is proposed based on operating effects of parallel H-bridge power supply systems under different current sharing reactors are simulated and experimentally verified. The results verified that the proposed design method for current sharing reactors has good reliability and practicality. Keywords: Parallel H-bridge power supply · Inverter parallel structure · Circulation · Current sharing reactor

1 Introduction With the progress and development of science and technology, the requirements for the output power of the power supply are constantly increasing in the practical application of the project. The modular parallel H-bridge converter has been proved to be an effective and feasible power supply design method to achieve high output voltage and large output current, and good application results have been obtained in the project. This kind of circuit structure has been successfully used in full superconducting Tokamak fusion experimental device (Experimental Advanced Superconducting Tokamak, EAST). The parallel H-bridge power supply is composed of multiple similar H-bridge inverter circuits in parallel. However, the different output voltage parameters of each branch and the inconsistency of the output impedance of the line caused by the differences in the characteristics of the power devices will lead to the circulation between the branches of © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 547–554, 2024. https://doi.org/10.1007/978-981-97-1064-5_60

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the parallel system, which greatly reduces the safety of the system [1]. Therefore, the circulation should be suppressed to realize the stable operation of the parallel H-bridge power supply. In terms of hardware, the mainstream circulation suppression method is to series the current sharing reactor (that is, the inductor) at each inverter output. The basic structure of the fast control power supply (fast control power supply) in EAST is a parallel module power supply formed by six H-bridge inverter branches in parallel. The stable operation of the EAST fast control power supply can be realized by installing the current balancing reactor between the H-bridge branches. For the circulation suppression of H-bridge inverter power supply, relevant research contents have been published in the literature. The causes of H-bridge inverter circulation is discussed in [2]. The influence of circulation on the operating performance of H-bridge power supply is verified in [3]. The method of external equipment or redesigning the inverter structure topology to suppress the circulation is adopted in [4–6], which requires high hardware. In [7–10], software suppression method is adopted to improve control accuracy by introducing control links and parameter prediction, which has a good effect on solving circulation problems but a more complex control algorithm. Most of the existing literatures consider the effect of current balancing reactor on restraining current circulation, but there are few studies on the corresponding relationship between current balancing reactor and current circulation, resulting in the lack of reliable theoretical basis for the calculation of current balancing reactor parameters of parallel H-bridge power supply. To solve the above problems, this paper starts with the topology of the EAST fastcontrol power supply, establishes a transfer function model by analyzing the parallel circulation between the inverter modules in the parallel inverter system, studies the correlation between the parallel circulation and the impedance value of the currentsharing reactor, and obtains the value range of the inductance of the current-sharing reactor through the closed-loop transfer function of the single branch of the parallel H-bridge power supply and the stability criterion. The practicability and reliability of the algorithm are verified by MATLAB simulation and experimental analysis, which provides a certain reference for the parameter selection of the current sharing reactor of parallel H-bridge power supply.

2 Parallel H-Bridge Power Supply Structure The main circuit of EAST fast control power supply is shown in Fig. 1, which consists of six branches in parallel, and each branch can be cascaded by multiple H bridges. Among them, HB1~n (n = 3) is H-bridge inverter circuit, E is DC voltage of each branch Hbridge, uHi (i = 1 ~ 6) is AC voltage of each branch H-bridge, R is the sum of equivalent resistance of inductance on load side, L is load inductance, and L Hi is current-sharing reactor. It can be seen from Fig. 1 that current-sharing reactor is connected for each parallel H-bridge branch. In order to facilitate analysis of circulation in parallel, Fig. 1 is simplified and the H-bridge is represented by an AC voltage source, and its equivalent circuit diagram is shown in Fig. 2. In Fig. 2, U 1~6 is output voltage of each inverter, U 0 is parallel bus voltage, Z 1~6 is impedance of current-sharing reactor of each branch, and Z 0 is load impedance.

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Fig. 1. EAST fast control power supply structure diagram.

Z6 I6 U 6 Z1

Z0

I0

I1

U0

U1

Fig. 2. Equivalent circuit diagram of six inverters in parallel system.

3 Value Analysis of Current Sharing Reactor 3.1 Derivation of Circulation Expression As shown in Fig. 2, according to Thevenin’s equivalence theorem, for branch 1 and branch 2, there are: •

•

U0 = U1 • I1

• I2

• Z0 //Z2 Z0 //Z1 + U2 Z1 + Z0 //Z2 Z2 + Z0 //Z1 •

=

(1)

•

Z0 U1 U2 − · Z1 + Z0 //Z2 Z2 + Z0 //Z1 Z1 + Z0 •

(2)

•

Z0 U1 U2 =− · + Z1 + Z0 //Z2 Z2 + Z0 Z2 + Z0 //Z1

(3)

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By extending formula (2) and (3) to six branches, current can be expressed as:

I1

6

Z1 i 0 i 1

1 Ui 5

6

U1 1 Zi

i 1 i

6

Zi j

M 6

U6

I6

6

Z6 i 0 i 1

1 Zi

i 1 i 6

Z0 6

1 Z0 Z 0 j

j

1 Z 0 j

(4) 1 Ui 5 6

Zi j

Z0

1 Z0 Z 0 j

6 j

1 Z 0 j

The circulation between branch x and branch y is defined as: • I xy

•

=

•

Ix − Iy 2

(5)

Then the total circulation is: 6

6

IH

I xy

(6)

x 1y 1

Assuming that Z 1 = Z 2 = Z 3 = Z 4 = Z 5 = Z 6 = R + jX, substitute Eqs. (2) and (3) into Eq. (5) to get the circulation between the two branches: • I xy

•

=

•

Ux − Uy 2(R + jX )

(7)

Substitute Eq. (4) into Eq. (6) to get the total circulation: • I xy

•

•

Ux − Uy = 2(R + jX )

(8)

It can be seen from Eq. (5) that the size of parallel circulation between each inverter branch is related to output voltage difference of inverter branch and the impedance of current-balancing reactor. The size of circulation is proportional to output voltage difference of inverter branch and inversely proportional to the impedance of currentbalancing reactor. 3.2 Requirements of Parallel H-Bridge Power Supply for Current Balancing Reactors The cost and volume of current sharing reactor usually need to be considered comprehensively. With the increase of current sharing inductance, satisfactory circulation

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suppression can be obtained, but the cost and volume will be greatly increased. Therefore, it is significant in engineering practice to obtain the minimum value of current-sharing reactor under the condition of system stability. Closed-loop proportional adjustment is adopted in each branch separately. The single-branch equivalent current control block diagram is shown in Fig. 3.

ui

u1

K1

K2

1 ( R Ls )

io

Fig. 3. Single branch equivalent current control block diagram

In Fig. 3, K 1 is preamplifier gain, K 2 is inverter gain, (R + Ls) is equivalent impedance of a single branch, α is current feedback coefficient. Closed-loop transfer function of a single branch is as follows: G(s) =

ui K1 K2 = αK1 K2 + R + Ls io

(9)

From Eq. (7) and (8), the expression form of total circulation and circulation between two branches is the same. In order to simplify calculation, circulation between two branches is taken as the analysis object. According to Eq. (5), the circulation is as follows: • IH

•

•

Ux − Uy = 2αK1 K2 + R + Ls

(10)

According to Eqs. (9) and (10), after the closed-loop negative feedback is added, output impedance of a single branch changes from R + Ls to αK 1 K 2 + R + Ls, where imaginary part remains unchanged, and the real part increases. When αK 1 K 2 is much larger than R, the output circulation is mainly affected by α, and the DC and low frequency circulation are significantly inhibited, but too high αK 1 K 2 will increase the instability of the system. In practical engineering, due to the influence of switching frequency and sampling frequency, there will be a delay in the output current of the system. Assuming that the delay time is τ, the actual closed-loop transfer function of the system is: G(s) =

K1 K2 e−τ s αK1 K2 e−τ s + R + Ls

(11)

Since τ s 0, and because delay time τ is less than a carrier period t, the parameters of the current-balancing reactor must meet: L > αK1 K2 t

(13)

Therefore, according to the carrier frequency and open-loop gain of the system, combining Eqs. (8), (12) and (13), and considering the stability and cost control of the system, the size of current sharing reactor can be reasonably selected.

4 Experimental Verification To further verify the correctness of the calculation method, a 2H bridge cascade prototype is built shown in Fig. 4.

Fig. 4. Experimental prototype

According to circuit control structure, the parameters are set as follows: carrier frequency is 5 kHz, current feedback coefficient is 1. By calculation, K 1 K 2 = 3.9, t = 2 × 10−4 s, α = 1, and substituting into Eq. (11), L > αK 1 K 2 t = 8 × 10−4 H. (I) The nominal parameter of current-sharing reactor in the first group of steady-state tests is 0.4 mH, and the experimental waveform is shown in Fig. 7. At this time, the branch output current generates a circulation with obvious amplitude due to the instability of the system. As can be seen from Fig. 5, output of the common load current io is stable, but the output current i1 of branch 1 and output current i2 of branch 2 have circulation oscillations, which reduces the tracking current accuracy of branch.

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Fig. 5. Experimental waveforms of each branch output when the inductance is 0.4 mH

Fig. 6. Experimental waveforms of each branch output when the inductance is 1 mH

(II) Select a current sharing reactor with nominal parameter 1mH. The experimental waveform is shown in Fig. 6. It can be seen from Fig. 6 that the tracking currents of branch 1 and branch 2 rapidly follow the reference values, and enter the flat topping stage soon despite the short overshoot process, and there is no circulation in the flat topping stage.

5 Conclusion In order to improve the circulation for different branches of the parallel H-bridge power supply, a calculation method based on parameters of the equalizing reactor is proposed to calculate parallel circulation for branches of the inverter power supply. Theoretical basis is obtained for parameter selection of equalizing reactor. Effectiveness of the proposed method is verified by experimental analysis. The results show that there are obvious differences in parallel circulation for inverter branches under different current sharing reactor parameters, and the parallel circulation can be effectively suppressed by current sharing reactor selected according to proposed method. Compared with conventional current-sharing reactor analysis, the proposed method quantifies the selection range of parameters more precisely. Theoretical reference for the parameter selection of current equalizing reactor in EAST fast control power supply is provided.

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Acknowledgments. This work was supported by Regional Innovation and Development Joint Fund of National Natural Science Foundation of China (No.U22A20225).

References 1. Huang, H.-H, Fu, P., Gao, G., et al.: Paralleling inverters analysis of EAST fast control power supply. Power Electron. 44(03), 57–59 (2010). (in Chinese) 2. Lv, J., Zhu, J., Yuan, J., et al.: Interaction mechanism and modelling of capacitor voltage unbalance and circulating current of single-phase NPC H-Bridge Cascaded Inverter 48(08), 81–89 (2021). (in Chinese) 3. Chen, J., Hu, Y., Wang, Y., et al.: Study on harmonic interaction between paralleled STATCOMs with cascaded H-bridge topology in wind farm clusters. IET Renew. Power Gener. 15(11) (2021) 4. Srikanth, I., Pradeep. K., Amit, K., et al.: Power quality analysis by H-bridge DSTATCOM control by Icosθ and ESRF SOGI-FLL methods for different industrial loads. Smart Cities 5(4) (2022) 5. Xinyu, Z., Xiao, L., Kaiyue, G., et al.: Negative sequence control for DC voltage balancing in three-phase cascaded H-bridge rectifiers considering DC-port failures. J. Power Electron. 22(12) (2022) 6. Zhao, Z., Shaojun, X., Xiaofeng, S., et al.: Circulating current suppression method for paralleled current-fed bidirectional DC-DC converters. Trans. China Electrotechn. Soc. 37(S1), 181–189 (2022). (in Chinese) 7. Wei, Z., Zhaolong, S., Baolong, L.: Sliding mode predictive current control for single-phase H-bridge converter with parameter robustness. Energies 16(2) (2023) 8. Ning, W., Zhen-zhen, W., Jian-zhong, Z.: Cause and suppression method of circulating current for parallel operation of power electronic transformer. Power Electron. 56(12), 21–24 (2022). (in Chinese) 9. Ting, H., Junqiang, Q., Yong, C.: Paralle control of photovoltaic grid connected inverter based on model prediction control. Chin. J. Electron Dev. 45(05), 1187–1194 (2022). (in Chinese) 10. Chun, W., Wenxu, Y., Wenyuan, W., et al.: The suppression of modular multi-level converter circulation based on the pir virtual impedance strategy. World Electric Veh. J. 14(1) (2023)

Simulation Analysis of the Electrical and Thermal Characteristics of Water Ingress Defects Within High-Voltage Direct Current Cable Terminals Yang Zhao1 , Tian Guo1 , Boxiang Ma1 , Yingqiang Shang1(B) , and Yaogang Wang2 1 Beijing Electric Power Company, State Grid Cooperation China, Beijing 100022, China

[email protected] 2 Shanghai University of Electric Power, No. 2588 Changyang Road, Shanghai 200090, China

Abstract. For maintaining the stable operation of power systems, there is an urgent need to master the electro-thermal characteristics of DC cables. This paper establishes a three-dimensional electric-thermal coupling simulation model of 220 kV cable terminals, and simulates three kinds of operating conditions (no defects, small amount of water intake, and large amount of water intake) of the cable terminals respectively. Based on the simulation results, the electrical-thermal characteristics of cable terminals under defects are analyzed and summarized. The results show that the water ingress defects mainly affect the localized electrical and thermal characteristics of the cable terminal, with less influence on the overall affectivity. Slight increase in average temperature in the area around the defect, accompanied by a distorted electric field with a higher field strength (10% increase for small amounts of water intake, 15% increase for large amounts of water intake). The results of this paper can provide a reference for temperature rise phenomena and insulation design of DC cable terminals. Keywords: Cable terminals · Simulation studies · Electro-thermal field distribution

1 Introduction With the development of long-distance power transmission technology, the demand for high-voltage cables is gradually increasing [1]. As an essential connecting part of high voltage cables, cable terminals play a key role in the stable transmission of electricity. However, defects within the terminal will severely distort the temperature and electric field distribution of the cable, thereby weakening its insulation properties [2]. Therefore, it is of great practical importance to study the electrical-thermal characteristics of terminal defects [3]. Currently, there have been some advances in research related to the electrical-thermal characteristics of cable defects [4, 5]. Xu et al. established a three-dimensional electric field model for cable terminals based on Maxwell’s system of equations, analyzed the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 555–562, 2024. https://doi.org/10.1007/978-981-97-1064-5_61

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influence of impurities, scratches, and bubble defects on the electric field distribution of the intermediate joints, and pointed out that the magnitude of the distorted electric field is related to the defect size [6]. Liu et al. investigated the discharge characteristics of cable terminals in the presence of air defects, noting that the presence of air gaps will lead to localized discharges in the defect areas [7]. Aldo Canova et al. constructed a thermal network model of cable terminals to simulate the thermal behavior of cable system operation [8]. Literature [9] simulated 132 kV oil-immersed cable terminals and obtained the distribution characteristics of electric and thermal fields inside the cable terminals. However, most of the current studies are focused on electric field characteristics or temperature characteristics alone, with fewer studies on electro-thermal coupling. Based on the above analysis, this paper establishes a three-dimensional electricthermal coupling model of cable terminal, and calculate the operation state of cable terminal under different degrees of water ingress defects, aiming to investigate the electricthermal field characteristics of localized water ingress defects in cable terminal, with a view to providing a reference for the insulation design of high-voltage direct-current cable accessories.

2 Simulation Model 2.1 Geometric Model This paper takes the porcelain-sleeved XLPE outdoor cable terminal of model YJZWC4, rated voltage 127/220 kV, as an example [10]. The 3D cable terminal geometric model was built in COMSOL Multiphysics 6.0 according to its actual size, and the model and internal structures are shown in Fig. 1. The specific geometric parameters are as follows: conductor diameter is 26.6 mm; cross-linked polyethylene diameter is 61.2 mm, reinforced insulation (silicone rubber) maximum diameter is 140.0 mm, silicone oil maximum diameter is 194.4 mm, epoxy sleeving diameter is 211.0 mm, silicone rubber sheath average diameter is 227.8 mm, large umbrella arc radius is 74 mm, small umbrella arc radius is 51 mm. 2.2 Electro-thermal Multiphysics Field Coupling Model Electromagnetic Field According to Maxwell’s system of equations, the vector magnetic potential A is introduced, and for the current region in the presence of an excitation source, the governing equation for the vector magnetic potential is: (∇ ·

1 ∇)A = −Js + jωσ A μ

(1)

where ω is the angular frequency, rad/s; μ and σ are the magnetic permeability (H/m) and electrical conductivity (S/m) of the material respectively Js is the conduction current density, A/m2 .

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(a) structure and parameters

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(b) geometric model l built in COMSOL

Fig. 1. Structure and parameters of the cable terminal model YJZWC4.

In the current region without an external excitation source, the vector magnetic potential equation is satisfied: (∇ ·

1 ∇)A = 0 μ

(2)

Thermal Field In practice, the core in a porcelain-sheathed cable terminal will generate Joule heat under the action of the applied voltage, which makes the internal temperature higher than the temperature on the surface of the terminal. The presence of a temperature difference will result in the transfer of heat between the structures in contact, also known as heat conduction. The process of heat transfer satisfies the equation of conservation of energy and Fourier’s theorem: ρc

∂ ∂ ∂T ∂T ∂T ∂ ∂T = Qv + (λx ) + (λy ) + (λz ) ∂t ∂x ∂x ∂y ∂y ∂z ∂z

(3)

where ρ and c are the density (kg/m3 ) and specific heat capacity (J/(kg·K)) of the material, respectively; T is the cable terminal temperature, K; t is the time, s; Qv is the heat source generated by electromagnetic induction, W/m3 ; λ1 , λ2 , and λ3 are the thermal conductivities of the material along the coordinate axes (x, y, and z) in units of W/(m·K). Electro-lhermal Coupling The external heat source is equal to the impedance heat generated by the electromagnetic field when no other heat source is considered: Qex = J · E

(4)

J =σ ·E

(5)

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The cable core will generate heat in response to external excitation, which in turn leads to variable temperature gradients throughout the system. The conductivity of the insulating material in the system has a strong temperature dependence, and the conductivity distribution of the material will change with the temperature gradient. The relationship between the conductivity of the material and the temperature satisfies the following equation: σs =

σ0 1 + α(T − 293.15K)

(6)

where σ s is the conductivity of the material at the current temperature, σ 0 is the conductivity of the material at 293.15 K, α is the sensitivity coefficient of temperature, and T is the current temperature. 2.3 Boundary Conditions and Settings Based on the above physical model, the simulation model can be solved by setting reasonable boundary conditions. The conductor is loaded with a current of 400 A at industrial frequency. All the material parameters required for the simulation calculations were obtained from the literature [10]. Electromagnetic Field When farther away from the cable core, the vector magnetic potential is infinitely close to 0. Therefore, a forced boundary condition is set at the outer boundary of the cable terminal: A|1 = 0

(7)

The magnetic field direction at the outer boundary is set to be all parallel to the boundary surface, i.e., the magnetically insulating boundary is satisfied: n × A|2 = 0

(8)

Thermal Field Assuming a constant ambient temperature, the external boundary can be considered to satisfy the forced boundary conditions: T |1 = 0

(9)

Assuming that there is no heat exchange between the system and the external environment, the external boundary can be considered to obey thermal insulation: −λ ·

∂T |2 = 0 ∂n

(10)

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3 Results and Analysis In this section, cable terminals operating under different scenarios are simulated separately. The three scenarios are no defects within the system, minor defects (little water in the insulating oil), and major defects (massive water in the insulating oil). And the temperature distribution as well as the electric field distribution inside the terminal in each case are compared to summarize the law of temperature distribution change caused by defects. 3.1 Temperature Characteristics The overall temperature distribution of the terminal under the three operating conditions is shown in Fig. 2. Through comparison, it can be seen that there is no obvious difference in the overall temperature distribution under the three conditions, the maximum temperature reaches 305 K, mainly distributed in the reinforced insulation region as well as XLPE insulation, while the minimum value is 295.15 K, and the low temperature is mainly distributed in the shielding cover as well as the flange region. Figure 3 shows the temperature distribution in and around the silicone oil defect region for each of the three scenarios. As the water content increases, the average temperature in the system increases and the temperature maximum decreases. When there are no defects in the silicone oil, the temperature distribution is relatively more uniform, but there is a higher temperature maximum with a value of 304.219 K. When a large amount of water is present in the silicone oil, the maximum value of the temperature in the oil is lower with a value of 304.197 K. In this scenario, the temperature gradient in the defective region is smaller compared to other regions, and the overall temperature is relatively high. The average temperature at this defective region is calculated to be 303.74 K, which is higher than the other two scenarios. When there is less water in the silicone oil, the maximum value of its temperature is between the other two cases and is 304.216 K. This shows that the water in the silicone oil pulls down the maximum value of the local temperature of the terminals, but increase the overall temperature inside the system 3.2 Electrical Characteristics Figure 4 presents the overall electric field distribution inside the terminal for the three cases. As shown, there is little difference in the overall electric field distribution among the three cases, and all of them generate distorted electric fields at the top and bottom of the stress shields. However, the distortion electric field of the case with defects has a slightly higher electric field strength, such as 0.149 V/m in Fig. 4(b) and (c). Figure 5 presents the local electric field distribution in the vicinity of the defect for the three cases. In the scenario without defects, the maximum value of the electric field strength occurs close to the cable core and is 3.62 × 10−2 V/m. The electric field decreases gradually from the cable core to the outer shell and is uniformly distributed. As the water intake increases, the degree of distortion of the electric field increases and the maximum value gradually rises, as shown in Fig. 5(b) at 3.93 × 10–2 V/m and in Fig. 5(c) at 4.17 × 10–2 V/m. It is noteworthy that the distortion electric fields all appear at the junction of the defects and the silicone oil.

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(a) defect-free

(b) small amount of water intake

(c) large amount of water intake

Fig. 2. Overall temperature distribution under three operating conditions.

(a) defect-free

(b) small amount of water intake

(c) large amount of water intake

Fig. 3. Temperature distribution in a localized region near a defect.

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(a) defect-free

(b) small amount of water intake

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(c) large amount of water intake

Fig. 4. Overall electric field distribution.

(a) defect-free

(b) small amount of water intake

(c) large amount of water intake

Fig. 5. Electric field distribution in a localized region near a defect.

4 Conclusion This paper establishes a three-dimensional electric-thermal multi-physical field coupling model of 220 kV high-voltage cable terminals, and carries out simulation calculations for cable terminals under three operating conditions, and analyzes the internal electricthermal characteristics of cable terminals under the water ingress defects. The results show that water ingress defects will reduce the maximum temperature in the silicone oil and increase the average temperature inside the terminals. Compared to the defect-free condition, the maximum temperature inside the silicone oil with a large amount of water ingress was reduced by 0.022 K, but the average temperature was increased by 0.02 K. The effect of the water intake defect on the electric field distribution is reflected in two aspects, one is to produce a distorted electric field located in the defectoil junction region, and the other is to increase the maximum electric field strength in the

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silicone oil. And the degree of influence of both mechanisms increases with the increase of water intake. Acknowledgement. This work is funded by the science and technology project from State Grid Beijing Electric Power Company on research and application of key technologies for intelligent inspection of large-scale urban cable tunnels based on panoramic lidar technology (Project No: 520246230002).

References 1. Ye, H., Fechner, T., Lei, X., et al.: Review on HVDC cable terminations. High Voltage 3(2), 79–89 (2018) 2. Albertini, M., Bononi, S.F., Giannini, S., et al.: Testing challenges in the development of innovative extruded insulation for HVDC cables. IEEE Electr. Insul. Mag. 37(6), 21–32 (2021) 3. Chimunda, S., Nyamupangedengu, C.: A reliability assessment model for an outdoor 88 kV XLPE cable termination. Electric Power Syst. Res. 177, 105979 (2019). https://doi.org/10. 1016/j.epsr.2019.105979 4. Bora, A., Mehmet Aytac, C., Yunus Berat, D., Adem, I.N.C.E.: Evaluation of the effect of structural defects in the heat-shrink cable terminal on electric field distribution. Eng. Failure Anal. 132, 105920 (2022). https://doi.org/10.1016/j.engfailanal.2021.105920 5. Teyssedre, G., Thi Thu Nga, V., Le Roy, S.: Insulating materials for HVDC cable accessories: effects on the electric field in nonstationary situations. IEEE Electric. Insul. Magaz. 38(5), 6–17 (2022). https://doi.org/10.1109/MEI.2022.9858038 6. Xu, S., Huang, X., Yang, S., et al.: Three-dimensional simulation analysis of electric field distribution at the middle joint of 110 kV cable with typical defects. In: IOP Conference Series: Earth and Environmental Science (2021) 7. Liu, G., Chen, Z.: 10kV cross-linked polyethylene cable terminal main insulation containing air gap defect test. High Voltage Eng. 38(3), 6 (2012) (In Chinese) 8. Canova, A., Freschi, F., Giaccone, L., et al.: The high magnetic coupling passive loop: A steady-state and transient analysis of the thermal behavior. Appl. Therm. Eng. 37(none), 154–164 (2012) 9. Zachariades, C., Peesapati, V., Gardner, R., et al.: Electric field and thermal analysis of 132 kV ceramic oil-filled cable sealing ends. IEEE Trans. Power Delivery 99, 1 (2020) 10. Guo, W., Sun, Z., Men, Y., et al.: Analysis of high-voltage cable terminal defects based on COMSOL electrical-thermal-fluid field distribution simulation. Electric. Measure. Instrument. 1–8 (2023) (In Chinese)

Research on Electric Load Forecasting Considering Node Marginal Electricity Price Based on WNN Xiaolu Li1 , Jun Li1 , Shijun Chen1 , Mingli Li1 , Bangyong Pan2 , Jie Luo2(B) , and Min Liu2 1 Southern Power Grid Guizhou Power Exchange Center, Guizhou 550025, China 2 School of Electrical Engineering, Guizhou University, Guizhou 550025, China

[email protected]

Abstract. This research suggests an electric load forecasting method that takes into account the marginal price of electricity in order to further increase the forecasting accuracy for electric loads. By including the marginal electricity price, the approach creates the training and test sets for the electric load. The establishment of an electric load prediction model using a Wavelet Neural Network (WNN) is followed by load prediction using the local power grid’s current data. By comparing the evaluation indicators with the electric load forecasting case without considering the marginal electricity prices of nodes, the results show that considering marginal electricity prices can improve the accuracy of electric load forecasting. Keywords: Electric load forecasting · wavelet neural network · node marginal price

1 Introduction Given the continuous growth of the energy system and the escalating need for energy, the precision of electric load prediction becomes increasingly vital. Relevant research has demonstrated that enhancing the accuracy of load forecasting is essential for the smooth and effective operation of the power system, as well as for the advancement of long-term strategic planning [1]. In order to make precise and scientific predictions of future power usage within a specific timeframe, power system load forecasting studies the patterns of electric load changes. Its main objectives are to improve the economy, security, and stability of the power grid system, as well as the accuracy and management efficiency of power dispatch, and to reduce the power gap and power loss [2]. Power system load forecasting is not only of significant importance to the planning, operation, and decision-making of the power system, but it’s also the cornerstone of the economic operation of the power system [3]. By accurately predicting the demand for electricity, it not only assists power companies in better planning their equipment and manpower resources, but also when the demand for electricity is effectively and accurately met, it © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 563–571, 2024. https://doi.org/10.1007/978-981-97-1064-5_62

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can realize the stable supply of electricity for communities, cities, or countries, thereby improving the stability of society [4]. Simultaneously, it can help the power department balance supply and demand. Through multi-faceted analysis of relevant load forecasting data, the power supply department can formulate corresponding unit maintenance and output plans, improve the operational efficiency and economic efficiency of the entire power system, and provide a guarantee to meet users’ reliable, high-quality electricity needs [5]. Node marginal electricity price refers to the change in the marginal generation cost of the entire system caused by a unit change in electricity at a certain node. Its significance lies in the optimization and scheduling of the power grid. Currently, there is no study considering the impact of node marginal price factors on electric load forecasting. The Wavelet Neural Network (WNN) is an innovative neural network based on wavelet analysis. Wavelet transformation effectively extracts the signal’s local information through multi-scale analysis, avoiding nonlinear optimization problems like local optimum in Backpropagation (BP) neural networks [6]. Hence, this study explores how to utilize WNN to consider node marginal prices for electric load forecasting to enhance prediction accuracy.

2 WNN WNN utilizes wavelet space for pattern recognition, achieving signal feature extraction through the weighted sum of the inner product of wavelet basis and signal vector. It integrates the self-learning function of traditional neural networks and the excellent time-frequency localization properties of wavelet transformation, resulting in powerful approximation and fault tolerance capabilities. The structure of WNN is akin to that of a single-hidden-layer BP network. The difference lies in the activation function of the hidden layer, with WNN using a wavelet transformation function instead of a sigmoid function [7]. The network topology structure is depicted in Fig. 1.

Fig. 1. WNN topology structure diagram.

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The specific steps for WNN training are as follows [8]: (1) Using wavelet transformation, the wavelet basis function undergoes contractiondilation and shifts, followed by taking the inner product with the signal under analysis. The mathematical expression is as follows [9]:    ∞ t−τ 1 dt, a > 0 (1) fx (a, τ ) = √ x(t)ψ a a −∞ (2) Calculate the equivalent frequency domain. The mathematical expression is as follows:  ∞ 1 fx(a, τ ) = √ x(ω)ψ(aω)ejω dt, a > 0 (2) a −∞ where τ represents the translation scale, and a represents the contraction-dilation scale. (3) Compute the network output yi (t). The mathematical expression is as follows:  n    ωij ψa,b netj , i = 1, 2, . . . , N (3) yi (t) = σ i=1

The Morlet wavelet basis function is often used for time-frequency analysis, and its general mathematical expression is [10]: ψ(t) = cos(μt)e−t

2 /2

(4)

where μ is a constant factor, generally taking the value of 1.75. (4) Use the following error target function to correct parameters, reducing the error gradually until the network reaches the convergence conditions [11]. 1 yi − oi 2 2 N

E(ω) =

(5)

i=1

where oi is the output vector predicted by the network; ω is the weight vector composed of all the connection weights of the network. (5) According to the gradient method, the expression of the network’s target error is as follows: 1  p p oi − yi 2 P

E=

N

(6)

p=1 i=1

p

p

where oi and yi are the i th expected output and predicted output of the p th data group in the training samples, respectively; P is the given data sample; η is the learning rate.

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During the initial network adjustment period, the learning pace can be increased to speed up the learning process. If the network is approaching the optimal solution, an overly high learning rate should not be chosen to prevent severe fluctuations in the weight vector and, thus, affect the convergence of the network. Generally, the adjustment of the network learning pace follows a principle: during the iterative optimization process, if the new error of the modified network exceeds the old error, the learning speed should be reduced; otherwise, the learning pace can be increased to improve network learning efficiency [12].

3 Electric Power Forecasting 3.1 Evaluation Metrics Measuring prediction error is key to solving practical prediction problems. The electric load sequence is essentially a time series, and the electric load prediction problem is a time series prediction problem. Therefore, the methods of evaluating time series predictions are often used to evaluate the accuracy of electric load predictions. The calculation of its relative error is as follows:   Ppi − Pi · 100% (7) η= Pi To further gauge the accuracy of forecasting performance, the ultra-short-term electric load forecasting values obtained from the testing process will be compared with the actual values. The following indicators will be used to evaluate the accuracy of the forecasting model [13, 14]. The specific indices are as follows. The details are as follows. (1) Mean Absolute Error (MAE) The larger the value of MAE, the greater the error, and vice versa. The calculation formula is as follows: MAE =

n

1 

Ppi − Pi

n

(8)

i=1

where, Ppi and Pi are the predicted load power and actual load power at sampling time i, respectively, and n represents the sampling step size. (2) Mean Absolute Percentage Error (MAPE) The smaller the value of MAPE, the higher the accuracy of the model prediction. If MAPE is 0, then the model is a perfect model. The calculation formula is as follows:



n  1 

Ppi − Pi

(9) MAPE =

· 100%



n Pi i=1

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(3) Mean Squared Error (MSE) The larger the value of MSE, the greater the error, and vice versa. The calculation formula for MSE is as follows: 2 1  Ppi − Pi n n

MSE =

(10)

i=1

(4) Root Mean Squared Error (RMSE) The larger the value of RMSE, the greater the error, and vice versa. The calculation formula for RMSE is as follows:   n   Ppi − Pi 2

RMSE = (11) n i=1

(5) Coefficient of Determination (R) R represents the degree of model fitting, and its range is between [−∞, 1]. The calculation formula for R is as follows [14]:   n     Ppi − P p Pi − P

R= 

i=1 n  i=1



  2 Ppi − P p

·

   2 i=1 Pi − P

n

(12)

where, the value range of P˙ p and P˙ is from 0 to 1. 3.2 Data Description and Model Structure The data in this paper comes from actual power data of a certain area in the real power grid. Figure 2(a) and Fig. 2(b) depict the changes in electric load data and nodal marginal price data (with a sampling point every 1 h, 24 points per day, totaling 768 time points, with units of MW and ¥/MWh respectively) for a total of 32 days from October 2, 2020 to November 2, 2020. The WNN topology structure is designed according to the characteristics of the electrical load, as shown in Fig. 2. It includes an input layer, a hidden layer, and an output layer. The number of neurons in the hidden layer is determined by the following equation [15]:  (13) L < (m + n) + c

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(a) Change in electric load.

(b) Change in nodal marginal electricity price.

Fig. 2. 32 days of data from a certain power grid.

3.3 Data Processing In order to enhance prediction accuracy, an initial screening of data samples is performed to eliminate outliers. It’s crucial to eradicate the scale differences among data across all dimensions, thereby avoiding errors in network prediction [16]. All data samples are subjected to preprocessing and normalization, transforming them into numerical values within the [0, 1] range. This necessary process paves the way for accelerated learning and improved outcomes. The associated calculation formula is as follows [14]. xiT =

xi − Xmin Xmax − Xmin

(14)

The training set is first composed of data points from the electric load power of the previous seven days, and the subsequent day’s electric load data forms the target set. The Wavelet Neural Network (WNN) is then trained using this training set. The trained WNN is finally used to predict the electric load power for November 2, 2020. Therefore, it’s understood that the number of neurons in the input and output layers of the WNN are 336 and 24, respectively. With C = 9 chosen in this study, the hidden layer consists of 27 neurons. 3.4 Results and Discussion To evaluate if considering nodal marginal prices can improve the effectiveness of electric load forecasting, this study compares it with the predictive performance of electric load forecasting without considering nodal marginal prices. The forecast results are shown in Fig. 3(a), and the relative error line of the forecast is depicted in Fig. 3(b). From Fig. 3(a), it can be observed that the electric load forecasting considering marginal prices is better and closer to reality compared to the one without considering marginal prices. Figure 3(b) shows that the relative error of electric load forecasting considering marginal prices is smaller and fluctuates within a smaller range compared to the one without considering marginal prices. The maximum relative errors of the electric load forecasts with and without considering marginal prices are approximately −22.6874% and -14.0506%, respectively.

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(a) Prediction result graph.

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(b) Prediction relative error line chart.

Fig. 3. Prediction result.

The MAE, MAPE, MSE, RMSE, and R values for predictions considering different factors are given in Table 1. Table 1. Prediction and evaluation results of different factors. Model

MAE

Ignoring Marginal 134.4197 Price Considering Marginal Price

84.4219

MAPE

MSE

RMSE

R

14.4810%

20107.5494

141.8011

0.99828

9.0474%

7949.5184

89.1601

0.99943

From Table 1, it can be observed that the four evaluation indicators of electric load forecasting considering marginal prices, namely MAE, MAPE, MSE, and RMSE, are all smaller than those of electric load forecasting without considering marginal prices. Therefore, compared to not considering marginal prices, electric load forecasting that does consider marginal prices has higher predictive accuracy and better performance. Additionally, relative to not considering marginal prices, the R-value of electric load forecasting considering marginal prices is larger and closest to 1, indicating a strong correlation between the forecast results and the actual electric load. Thus, electric load forecasting that takes into account marginal prices is the most reliable compared to that which does not. To better intuitively assess the reliability of prediction models considering different factors, related scatter plots have been drawn, as shown in Fig. 4. Figure 4(a) and Fig. 4(b) show that compared to the prediction model that does not consider marginal prices, the scatter of the prediction model that does consider marginal prices is more concentrated around the linear regression line. This suggests a strong linear relationship between the predicted electric load and the actual electric load in the model that considers marginal prices, with a correlation degree far greater than the model that does not consider marginal prices. All the above analysis illustrates that, compared to not considering marginal prices, considering marginal prices in electric load forecasting can predict the electric load more accurately and effectively.

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(a) Without considering marginal price.

(b) Considering marginal price.

Fig. 4. Scatter plot.

4 Conclusion Electric load forecasting is an important subject in power grid dispatch research. Incorporating nodal marginal price influence factors into electric load forecasting can enhance its accuracy and precision. The feasibility of the method model and input data used in this paper is not complex, thus it can be extended to other fields. Acknowledgments. This work was funded by the Science and Technology Project of Guizhou Power Exchange Center, Southern Power Grid of Guizhou Province, China (No. 0682002023080201JY00001).

References 1. Chae, Y.T., Horesh, R., Hwang, Y., et al.: Artificial neural network model for forecasting sub-hourly electricity usage in commercial buildings. Energy Build. 111, 184–194 (2016) 2. Li, K., Huang, W., Hu, G., et al.: Ultra-short term power load forecasting based on CEEMDAN-SE and LSTM neural network. Energy Build. 279, 112666 (2023) 3. Yang, Y., Li, S., Li, W., et al.: Power load probability density forecasting using Gaussian process quantile regression. Appl. Energy 213, 499–509 (2018) 4. Li, X., Wang, Y., Ma, G., et al.: Electric load fore-casting based on Long-Short-Term-Memory net-work via simplex optimizer during COVID-19. Energy Rep. 8, 1–12 (2022) 5. Li, Y.C., Hong, S.H.: BACnet–EnOcean Smart Grid Gateway and its application to demand response in buildings. Energy Build. 78, 183–191 (2014) 6. Feng, Q., Qian, S.: Research on the prediction of short-term wind power based on wavelet neural networks. Energy Rep. 8, 553–559 (2022) 7. Duan, M., Yang, J., Li, P.: Research on power load forecasting based on wavelet and radial basis function neural network. J. Yunnan Univ. (Natl. Sci. Edn.) 42(S2), 18–25 (2020) (in Chinese) 8. Ong, P., Zainuddin, Z.: An optimized wavelet neural networks using cuckoo search algorithm for function approximation and chaotic time series prediction. Dec. Anal. J. 6, 100188 (2023) 9. Kushwaha, V., Pindoriya, N.M.: A SARIMA-RVFL hybrid model assisted by wavelet decomposition for very short-term solar PV power generation forecast. Renew. Energy 140, 124–139 (2019)

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10. Masood, A., Ahmad, K.: A review on emerging artificial intelligence (AI) techniques for air pollution forecasting: Fundamentals, application and performance. J. Clean. Prod. 322, 129072 (2021) 11. Yang, Z., Mourshed, M., Liu, K., et al.: A novel competitive swarm optimized RBF neural network model for short-term solar power generation forecasting. Neurocomputing 397, 415– 421 (2020) 12. Sideratos, G., Hatziargyriou, N.D.: A distributed memory RBF-based model for variable generation forecasting. Int. J. Electr. Power Energy Syst. 120, 106041 (2020) 13. Zhang, L., He, S., Cheng, J., et al.: Research on neural network wind speed prediction model based on improved sparrow algorithm optimization. Energy Rep. 8, 739–747 (2022) 14. Zhang, C., Zhang, M.: Wavelet-based neural network with genetic algorithm optimization for generation prediction of PV plants. Energy Rep. 8, 10976–10990 (2022) 15. Yu, L., Xie, L., Liu, C., et al.: Optimization of BP neural network model by chaotic krill herd algorithm. Alex. Eng. J. 61(12), 9769–9777 (2022) 16. Sarshar, J., Moosapour, S.S., Joorabian, M.: Multi-objective energy management of a microgrid considering uncertainty in wind power forecasting. Energy 139, 680–693 (2017)

Distribution Characteristics of Electric Field Under Defect State of Large Shielding Ball in Valve Hall of Converter Station Yitao Zhang1(B) , Lingjiang1 , Yongsheng Zhang2 , Yu Su3 , Chenglei Zhang1 , and Shengcheng Dong1 1 Electric Power Research Institute, State Grid Qinghai Electric Power Company,

Xining 810008, China [email protected] 2 State Grid Qinghai Electric Power Company, Xining 810001, China 3 China Electric Power Research Institute, Beijing 100192, China

Abstract. The structure of valve hall fittings in UHV DC converter station directly affects the reliability and stability of each system in the converter station, surface defects will inevitably occur in the process of processing, transportation and installation of large size fittings, and the existence of these surface defects will reduce the switching impulse voltage of air gap. In this paper, the simulation model of shielding ball with three kinds of surface defects including screw protrusion, burr and scratch under ±800 kV and ±1100 kV is established, and the influence law of different defects on the surface electric field of shielding ball is analyzed. Keywords: shielding ball · large size fittings · converter station · electric field distribution

1 Introduction In the study of a series of key technologies in UHV DC power transmission project, the structure of valve hall fittings in UHV DC converter station directly affects the reliability and stability of each system in the converter station. China has done a lot of research on the valve hall fittings for ±500 kV DC transmission projects, and has been able to design and manufacture the valve hall fittings for ±500 kV DC transmission projects, but the valve hall fittings for ±660 kV and above UHV DC converter stations have been imported from abroad in the past, which directly affects the cost and progress of the project. Valve fitting not only determines the operating reliability of the equipment, but also directly determines the headroom size of the whole valve hall, and its switching impulse discharge characteristic is a key technical problem. The valve hall shielding ball fittings is generally larger in size, and the air gap composed of it and the surrounding grounding body is closer to the slightly uneven electric field, and its discharge characteristics are very different from the rod-plane, rod-rod and tower head gap of the transmission line. The electrode size and surface defects have great influence on it. With the increase of voltage level, the © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 572–585, 2024. https://doi.org/10.1007/978-981-97-1064-5_63

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size of the equipment end fittings in the valve hall of the converter station also increases [1, 2]. Surface defects are unavoidable in the process of machining, transportation and installation of large electrodes, and the existence of these surface defects will reduce the impact discharge voltage of gap operation [3, 4]. Whether the maximum surface electric field intensity of the fittings can reach the corona field intensity is an important basis for judging whether corona discharge occurs. Due to the variety of DC valve hall voltage equalizing shielding fittings, the variety of shapes and structures, the complex interaction between different potential fittings, and the difficulty of true shape test, most of the current research on its electric field distribution law adopts the numerical simulation research method. By establishing an equivalent model of electric field calculation that is the same or similar to the object of study, using numerical simulation method and combined with certain input conditions, the electric field distribution law on the surface of the fittings in the valve hall can be obtained through simulation calculation, and the anti-corona characteristics can be evaluated by comparing the control value of the surface field intensity designed by the fittings [5–10]. The electric field distribution characteristics of the shielding ball with screw protruding, burr and scratch on the surface of the large shielding ball in the valve hall of the converter station are obtained by simulation.

2 Effect of Surface Defects on Electric Field Distribution Characteristics of Shielding Ball 2.1 Simulation Model The radius of the shielding ball was 2 m, the protrusion height of the screw/burr was 0 mm, 1 mm, 2 mm and 5 mm, and the gap distance was 1m, 4 m, 6 m and 9 m. The vertical line A of the shielding ball, B of 45° below the horizontal line of the center, and C of the horizontal line of the center were selected as the typical protrusion positions, and 72 operating conditions of ±800 kV and ±1100 kV reference voltage were applied; the radius of the shielding ball is 2 m, the distance from the ground is 1 m, 4 m, 6 m and 9 m respectively, two scratch lengths of 63 mm and 130 mm and three scratch depths of 1 mm, 1.5 mm and 2 mm, and 64 simulation conditions of ±800 kV or ±1100 kV reference voltage are uniformly applied to the ball electrode (Fig. 1).

(1) Screw protrusion (2) Surface burr projection (3) Surface scratch Fig. 1. Simulation model

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2.2 The Screw Protrudes on the Shielding Ball Surface The shielding ball is generally assembled by the upper and lower hemispheres, and the connection is fixed with a set screw. If the screw is not installed in place or loose, the screw protrusion will exceed the spherical surface, which will shorten the effective distance of the air gap, which may lead to gap discharge. In this paper, the typical height of screw projection was 1 mm, 2 mm and 5 mm. The installation orientation of the shielding ball is not fixed, so the position of the tightening screw is also different. The vertical line A of the shielding ball, the horizontal line B of 45° below the horizontal line of the center, and the horizontal line C of the center are selected as typical raised positions, as shown in Fig. 2. The distance d from the bottom of the shielding ball to the ground is 1 m, 4 m, 6 m and 9 m respectively. The simulation applied ±800 kV and ±1100 kV voltages (Fig. 3).

Fig. 2. Screw projection position diagram

Fig. 3. Screw projection shielding ball submodel

The simulation results are as follows (Tables 1, 2, 3 and 4):

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Table 1. The electric field intensity of screws with different protrusion heights at different gap distances under ±1100 kV(kV/cm) Gap distance

Protrusion height 0 mm

1 mm

2 mm

5 mm

1m

19.27

62.64

66.75

79.93

4m

9.34

30.31

32.52

38.79

6m

7.22

23.21

25.05

30.39

9m

5.33

17.52

18.94

22.19

Table 2. The electric field intensity of screws with different protrusion heights at different gap distances under ±800 kV(kV/cm) Gap distance

Protrusion height 0 mm

1mm

2 mm

5 mm

1m

14.01

4 5.56

48.54

58.13

4m

6.79

22.04

23.65

28.21

6m

5.25

16.88

18.21

22.10

9m

3.88

12.74

13.77

16.54

Table 3. The electric field intensity of different protrusion positions of screws at different gap distances at 4m gap distances at ±1100 kV(kV/cm) Screw position

Protrusion height 0 mm

1 mm

2 mm

5 mm

A

9.34

30.31

32.52

38.79

B

9.34

15.38

16.60

20.34

C

9.34

11.66

12.58

14.95

The electric field intensity distribution law of the screw protruding surface: (1) With different applied voltages, the protruding height of the screw affects the variation law of the surface electric field intensity: Under the applied voltage of ±800 kV and ±110 0kV, the field intensity increases gradually with the increase of the protruding height of the screw, and the increase amplitude is basically the same. Under the voltage of ±800 kV, the screw projection height

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Table 4. The electric field intensity of different protrusion positions of screws at different gap distances at 4m gap distances under ±800 kV(kV/cm) Screw position

Protrusion height 0 mm

1 mm

2 mm

5 mm

A

6.79

22.04

23.65

28.21

B

6.79

19.75

21.18

25.21

C

6.79

14.81

15.84

18.94

increases by 1 mm, the maximum field intensity increases by 7.45%, the screw projection height increases by 3 mm, the maximum field intensity increases by 20.13%; under the applied voltage of ±1100 kV, the screw protrusion height increased by 1 mm, the maximum field intensity increased by 7.47%, the screw protrusion height increased by 3 mm, the maximum field intensity increased by 19.38%. Therefore, the increase in the field intensity of the shield ball surface caused by the screw projection height is independent of the applied voltage, and the maximum field intensity increases by 7.5% for every 1mm increase in the screw projection height, and 20% for every 3 mm increase in the screw projection height (Fig. 4 and Table 5).

Fig. 4. The maximum surface field intensity of the screw protruding shield ball with 4m gap

Table 5. Maximum and increase of surface field intensity under different protrusion heights of screws Screw length(mm)

add 1 mm

add 3 mm

±1100 kV-Maximum electric field intensity(kV/cm)

7.47%

19.38%

±800 kV- Maximum electric field intensity(kV/cm)

7.45%

20.13%

(2) The influence of screw projection height on surface electric field intensity under different gap distances:

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Taking the screw at the position A in Fig. 5 as an example, when the ball surface is clean (screw projection height 0 mm) and the applied voltage is ±1100 kV, at 1 m gap distance, the maximum field intensity of the shielded ball surface at 1 mm, 2 mm and 5 mm projection height increases by 225.0%, 246.4% and 314.8%, respectively, compared with the clean state; At 4 m gap distance, the height of the three kinds of protrusion increases by 224.5%, 248.2% and 315.3%; At 6m gap distance, the increase is 221.4%, 247.0% and 320.9%, respectively; At 9m gap distance, the increases by 228.7%, 255.3% and 316.3% respectively. It can be seen from the above that with the increase of the protrusion height of the screw, the increase of the surface field intensity gradually increases, and the maximum surface field intensity also presents an increasing trend when the screw is in position B and position C. When screws with the same protrusion height are placed at different gap distances, the increase of field intensity on the surface of the ball decreases with the increase of gap distances. As shown in Fig. 6, the increase of electric field intensity of 5 mm screws with protrusion height at 1 m, 4 m, 6 m and 9 m gap distances is 257.5%, 257.8%, 251.3% and 250.6%.

Fig. 5. The electric field intensity of the ball surface varies with the height of the screw under ±1100 kV

Fig. 6. The electric field intensity of the ball surface varies with the height of the screw under ±800 kV

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(3) The effect of different screw positions on the surface electric field intensity: When the gap distance is constant, the influence of screw position on the surface field intensity of the shielded ball is analyzed. Taking 4m gap as an example, its surface field intensity variation characteristics are shown in Fig. 7:

Fig. 7. Effect of screw position on electric field intensity of ball surface under ±800 kV

It can be seen from Fig. 7 that the field intensity on the surface of the shielded ball will increase regardless of the position of the screw, and the position with the most obvious influence is located at the middle vertical line A. 2.3 The Surface of the Shielding Ball Contains a Burr Burr defect is the most likely and most common defect type of shield ball. Due to the short burr length, 1 mm, 2 mm and 5 mm are set as the typical analysis lengths, and the simulation applied voltages of ±800 kV and ±1100 kV. Burrs are arranged in the same position as screws.

Fig. 8. Burr model

Because the burr has a sharp tip, the burr head model is cylindrical with a radius of 0.5 mm and a chamfer of 0.1 mm, as shown in Fig. 8. Simulation results are as follows (Fig. 9): The field intensity distribution law of burr projection surface: (1) Influence of burr length on surface electric field intensity (Figs. 10 and 11).

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Fig. 9. Simulation results of shield ball with 1 mm projection burr at 4m gap distance under ±800 kV

Fig. 10. The variation of electric field intensity with burr length under ±1100 kV

Fig. 11. The variation of electric field intensity with burr length under ±800 kV

When burr defects appear on the surface of the shielded ball, the field intensity of the surface of the ball increases to different degrees and is positively correlated with the burr length. Taking position A (at the middle vertical line) shown in 12 as an example, compared with the clean state of the ball surface (burr length 0 mm), when the applied voltage is ±1100 kV, at 1m gap distance, the field intensity of the ball surface increases by 486.4%, 874.8% and 661.2% when the length of 1 mm, 2 mm and 5 mm burrs are present. The burr in position B and position C also increased gradually; when burrs of the same length are at different gap distances, the increase of field intensity decreases with the increase of gap distances. The increase of surface field intensity of 2mm burrs at

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1m, 4m, 6m and 9m gap distances is 874.8%, 853.1%, 819.7% and 715.5%, respectively, and the influence of burr length is gradually weakened. When the applied voltage is ±1100 kV and ±800 kV, the increase of the maximum field intensity of the burr protruding is basically the same as that in the clean state. For example, when the applied voltage is ±800 kV and the gap distance is 1m, the field intensity of the ball surface increases by 486.1%, 874.5% and 1660.7% respectively when the length of 1 mm, 2 mm and 5 mm burrs are present. Compared with ±1100 kV, the increases are 0.24%, 0.30% and 0.52% respectively, and the increases are basically synchronous, which verifies the rationality of the model. (2) Influence of burr position on surface electric field intensity When the gap distance is constant, the influence of burr position on the surface field intensity of shielded sphere is analyzed. When the applied voltage is ±1100 kV, taking 4 m gap as an example, the surface field intensity variation characteristics are shown in Fig. 12:

Fig. 12. Effect of burr position on surface electric field intensity (±1100 kV & 4 m gap)

Fig. 13. Effect of burr position on surface electric field intensity (±800 kV & 4 m gap)

As can be seen from Figs. 12 and 13, regardless of the position of the burr, the field intensity on the surface of the shielded ball will increase significantly with the burr protrusion, among which the position with the most obvious influence is the midvertical line A.

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2.4 Effect of Surface Scratches on Electric Field Intensity of Shielding Ball The scratch has two parameters: length and depth. In this paper, two scratch lengths of 63 mm and 130 mm and three scratch depths of 1 mm, 1.5 mm and 2 mm are set, Simulation voltage ±800 kV and ±1100 kV, simulation results are as follows (Fig. 14 and Tables 6, 7):

Fig. 14. Simulation model of shield ball surface scratch

Table 6. The electric field intensity of 130 mm long scratches at different depths and at different gap distances(±1100 kV) (kV/cm) Gap distance

Scratch depth

The maximum increase of electric field intensity

0 mm

1 mm

2 mm

5 mm

1 mm

2 mm

5 mm

1m

19.23

29.31

32.14

31.53

52.4%

67.2%

63.9%

4m

9.32

13.47

15.42

16.16

44.5%

65.4%

73.3%

6m

7.22

11.14

11.79

12.41

54.3%

63.3%

71.9%

9m

5.36

7.91

8.56

9.28

47.6%

59.6%

73.2%

Table 7. The electric field intensity of 130 mm long scratches at different depths and at different gap distances(±800 kV) (kV/cm) Gap distance

Scratch depth

The maximum increase of electric field intensity

0 mm

1 mm

2 mm

5 mm

1 mm

2 mm

5 mm

1m

13.99

21.33

23.39

23.81

52.4%

67.2%

70.2%

4m

6.78

9.81

11.26

11.75

44.6%

66.1%

73.3%

6m

5.25

8.21

8.61

9.05

56.4%

63.9%

72.4%

9m

3.90

5.76

6.23

6.76

47.7%

59.8%

73.4%

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Table 8. The electric field intensity of 63 mm long scratches at different depths and at different gap distances(±1100kV) (kV/cm) Gap distance

Scratch depth

The maximum increase of electric field intensity

0 mm

1 mm

2 mm

5 mm

1 mm

2 mm

5 mm

1m

19.23

28.70

31.21

31.32

49.2%

62.3%

62.9%

4m

9.32

13.19

13.61

14.94

41.6%

46.0%

60.3%

6m

7.22

10.49

11.04

11.79

45.3%

53.0%

63.3%

9m

5.36

7.64

8.20

8.96

42.5%

53.0%

67.2%

Table 9. The electric field intensity of 63 mm long scratches at different depths and at different gap distances(±800kV) (kV/cm) Gap distance

Scratch depth

The maximum increase of electric field intensity

0 mm

1 mm

2 mm

5 mm

1 mm

2 mm

5 mm

1m

13.99

20.89

22.70

22.79

49.3%

62.3%

62.9%

4m

6.78

9.59

9.90

10.87

41.5%

46.0%

60.4%

6m

5.25

7.65

8.05

8.61

45.8%

53.3%

63.9%

9m

3.90

5.57

5.97

6.52

42.7%

53.1%

67.2%

The field intensity distribution law of scratch surface: (1) The influence of scratch depth on surface field intensity. When the scratch length remains unchanged at 63mm, the influence of scratch depth on the surface field intensity is analyzed, and the analysis results are shown in Tables 8 and 9. Taking the field intensity under clean ball surface as the basis (scratch depth 0 mm), when the gap distance of 1 m and the applied voltage is ±800kV, the maximum field intensity at the depth of 1.0 mm, 1.5 mm and 2.0 mm is 20.89 kV/cm, 22.70 kV/cm and 22.79 kV/cm, respectively. The surface field intensity increases by 49.3%, 62.3% and 62.9%, respectively. When the applied voltage is ±1100kV, the maximum field intensity at the depth of 1.0 mm, 1.5 mm and 2.0 mm is 28.70 kV/cm, 31.21 kV/cm and 31.32 kV/cm, respectively. In the clean state, the increase of surface field intensity is 49.2%, 62.3% and 62.9%, respectively. The scratch depth is positively correlated with the surface field intensity of the shielded ball. It can also be seen from Fig. 15 that the surface electric field of the dented part of the scratch decreases, while the electric field intensity at the edge of the scratch increases by about 50%. (2) The influence of scratch length on surface field intensity

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Fig. 15. The electric field distribution on the surface of the shielding ball with 2 mm scratch

The scratch depth was set to 1 mm, and the surface field intensity when the scratch length was 63 mm and 130 mm was compared and analyzed, as shown in Table 10. Table 10. Surface field intensity at different scratch lengths(kV/cm) Gap distance

Voltage

Scratch length

The increase of electric field iintensity

0 mm

63 mm

130mm

±110 kV

19.23

28.70

29.31

49.23%

52.44%

±800 kV

13.99

20.89

21.33

49.31%

52.44%

4m

±110kV

9.32

13.19

13.47

41.56%

44.54%

±800 kV

6.78

9.59

9.81

41.46%

44.65%

6m

±110 kV

7.22

10.49

11.14

45.27%

54.29%

±800 kV

5.25

7.65

8.21

45.76%

56.36%

±110 kV

5.36

7.64

7.91

42.47%

47.59%

±800 kV

3.90

5.57

5.76

42.74%

47.72%

1m

9m

As can be seen from Table 10, with the increase of the gap distance, the surface field intensity at the scratch length of 63 mm and 130 mm gradually decreases compared with the increase in the surface clean state. The surface field intensity with a scratch length of 63 mm is higher than that with a scratch length of 130 mm, and the increase of the field intensity is somewhat reduced. For example, if the reference voltage of ±1100 kV is applied with a gap distance of 9 m, the surface field intensity with a scratch length of 63 mm and 130 mm is 7.64 kV/cm and 7.91 kV/cm. Compared with the surface clean state, the value increased by 42.47% and 47.59%, respectively; When the reference voltage of ± 800kV is applied, the surface field intensity of the scratch length of 63mm and 130 mm is 5.57 kV/cm and 5.76 kV/cm, which is 42.74% and 47.72% higher than that of the surface clean state, respectively. Under 9 m gap distance, the surface field intensity of the shielded ball is affected by the length of the scratch. When the scratch

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length is 63 mm, the surface field intensity increases by 42%. When the scratch length is 130 mm, the surface field intensity increases by 47%.

3 Conclusions In this paper, a simulation model of shielding ball with surface defects and installation process deviation under ±800 kV and ±1100 kV was established to analyze the variation rule of surface electric field, and the following conclusions were reached: (1) When the screw/burr defect appeared on the surface of the shielded ball, the field intensity of the surface of the ball increased to different degrees and was positively correlated with the screw/burr length. With the increase of screw/burr projection height, the field intensity of the shield ball surface gradually increased, and the maximum field intensity was located at the end of the screw/burr. When screws/burrs with the same protrusion height are at different gap distances, the increase of field intensity on the ball surface decreases with the increase of gap distances. Regardless of the position of the screw/burr, the surface field intensity of the shielded ball will increase, and the most obvious position is located at the midvertical line. (2) When the surface of the ball is scratched, the depth of the scratch is positively correlated with the surface field intensity of the ball. When the length of the scratch remains unchanged, the field intensity of the shield ball surface gradually increases with the increase of the scratch depth. The surface electric field of the dented part of the scratch decreases, while the electric field intensity at the edge of the scratch increases by about 50%. With the increase of gap distance, the surface field intensity of the shielded ball decreases gradually when the scratch length is 63 mm and 130 mm. Under 9 m gap distance, the surface field intensity of the shielded ball is affected by the length of the scratch. When the scratch length is 63 mm, the surface field intensity increases by 42%. When the scratch length is 130 mm, the surface field intensity increases by 47%. Acknowledgments. This work was funded by State Grid Qinghai Electric Power Company, China.(“Research on key technology of external insulation of high altitude ±800kV (±1100kV) DC UHV transmission and transformation equipment(NO.522807210005)”).

References 1. Jia, L., Wang, G., Li, E., Tu, H., Liu, L., Fang, Y.: Experimental investigation of discharge characteristics of a sphere-plane long air gap under switching impulse voltage. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), pp. 3913–3917. Hefei, China (2023) 2. Ding, Y., Yao, X., Wang, S., Quda, Z., Li, X.: Altitude correction and selection of air gap discharge voltage in converter stations in high altitude areas. In: 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), pp. 1–4. Beijing, China (2020)

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3. Shiling, Z., Liangjun, D., Baojia, D., Ziqi, L.: Altitude correction of surface control field strength of converter valve hall fittings based on ultraviolet spectrum image analysis. In: 2022 7th International Conference on Image, Vision and Computing (ICIVC), pp. 818–824. Xi’an, China (2022) 4. Li, Z., et al.: Experiment and simulation of high current temperature rise of valve hall fittings. In: 22nd International Symposium on High Voltage Engineering (ISH 2021), Hybrid Conference. Xi’an, China (2021) 5. Zhou, H., Wang, D.J.: Over-voltage protection and insulation coordination of ±1100 kV UHV DC converter Station. Power Grid Technol. 36(9), 1–8 (2012). (in Chinese) 6. Zhang, Y.B., et al.: Study on shield ball structure of valve hall in converter station. Sci. Technol. Eng. 15(4), 229–233 (2015). (in Chinese) 7. Wang, L.G., Yang, J.G.: Hardware design of Valve Hall in Gaoling back-to-back Converter Station. Electric Power Construct. 30(9), 31–35 (2009). (in Chinese) 8. Du, Z.Y., Zhu, L., Ruan, J.J., et al.: Solution of surface electric field of ±800kV UHV valve hall fittings based on instantaneous potential loading method. High Voltage Technol. 40(06), 1809–1815 (2014). (in Chinese) 9. Ji, D.Q., Liu, Z.H., et al.: Electric field analysis in high-end valve hall of UHVDC system during steady operation. High Voltage Technol. 39(12), 3000–3008 (2013). (in Chinese) 10. Wang, J.L., Peng, Z.R., et al.: Surface Electric Field Analysis of Pressure equalizing shield hardware in Valve Hall of ±1100kV UHV Converter Station. High Voltage Technol. 41(11), 3728–3736 (2015). (in Chinese)

Research on Fault Diagnosis of Neural Network Power Transformer Based on Dung Beetle Optimization Algorithm Song Xiaofei(B) , Dang Cunlu, Wang Weiwei, and Yao Dengyin School of Electrical Engineering and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China [email protected]

Abstract. In this study, a fault diagnosis method for power transformers based on dissolved gas analysis (DGA) was proposed. Firstly, nuclear principal component analysis (KPCA) is used to preprocess the collected fault data to remove the interference data, and KPCA is used to perform feature extraction on the mixed DGA data. Then, the dung beetle optimization algorithm (DBO) was used to optimize the neural network algorithm (BP), and an improved dung beetle optimization algorithm (DBOBP) was formed to achieve better optimization accuracy and convergence speed. Since tent diagrams are used instead of traditional population initialization methods, this method improves population diversity. Simulation examples verify the superior performance of the proposed method, including high diagnostic accuracy, short diagnosis time, strong significance and effectiveness. This study provides a feasible research idea for solving practical engineering problems in the field of power transformer fault diagnosis. Keywords: Power transformer · fault diagnosis · nuclear principal component analysis · neural network · dung beetle optimization algorithm

1 Introduction Dissolved argon gas analysis (DGA) is the most extensively used conduct in power transformer difficulty examinations [1–4]. Most circumstances however, rely on the experiences of individuals and information from history. Many innovative approaches, including, but not limited to, (ANN) [5, 6], (SVM) [7, 8], ambiguous theory [9, 10], have been suggested and widely employed in the field of power transformer defect diagnosis [11]. As a result, we present a transformer failure diagnosis technique based on the dung beetle optimization algorithm and neural network modeling (DBOBP).

2 DBO Optimizer On the twenty-seventh of November, 2022, Instructor Shen Bo’s team at Donghua Academy proposed Dung the Volkswagen Beetle Scheduler (DBO), a novel artificial intelligence optimization strategy that [12] predominantly propagates the animal’s dung © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 586–593, 2024. https://doi.org/10.1007/978-981-97-1064-5_64

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beetle’s moving ball, performing, foraging, stealing, and breeding behavior. DBO optimizer has the benefits of quick search speed, high accuracy, and great flexibility when compared to other algorithmic approaches to optimization, and it has been extensively used in tackling issues such as functionality optimization, neural network optimization, and combinatorial optimization. 2.1 Dung Beetles Rolling Ball The animal dung beetle’s rolling the environment requires it to shift its position in a certain direction across the hunting arena. The geographical location of the picking dung beetle is constantly changing periodically throughout the rolling operation and may be stated as follows: xi (t + 1) = xi (t) + a × k × xi (t − 1) + b × x   x = xi (t) − X w 

(1)

The dung beetle has managed to set a new direction and it should keep moving. Therefore, the motion position update and dedefinition is shown in the following equation: xi (t + 1) = xi (t) + tan(θ )|xi (t) − xi (t − 1)|

(2)

In this paper, θ ∈ [0π ], |xi (t) − xi (t − 1)| is the difference in position of the i rd dung beetle after the tth and t − 1th iterations. His location updates are closely related to current and historical information. If θ equals 0, π2 or π the position will not change. 2.2 Dung Beetles Breed A boundary selection strategy to simulate the mathematical model of dung beetle breeding area is as follows: Lb∗ = max(X ∗ × (1 − R), Lb) Ub∗ = min(X ∗ × (1 + R), Ub)

(3)

Of these, X ∗ are currently the best locations locally, Lb∗ and Ub∗ are the upper and lower limits of the spawning area, Tmax are the maximum number of repetitions, and Lb and Ub are the upper and lower limits, respectively, optimal dung beetles to choose spawning grounds. Each dung beetle can only produce one ball per iteration [12]. From (3), it can be seen that the boundary range of the spawning zone is dynamic, which is mainly determined by R. Therefore, the breeding position is also dynamic during the iteration process, and the mathematical model of the dynamic position of the chick is as follows: Bi (t + 1) = X ∗ + b1 × (Bi (t) − Lb∗ ) + b2 × (Bi (t) − Ub∗ )

(4)

Bi (t) is the location of the tth egg in the ith another iteration, where b1 and b2 represent two separate from random vectors with D dimensions that and the location of the egg is strictly limited, as shown in Fig. 1, where the large circle represents the top X* local most effective locations, the small circle represents the fledgling, and the small red circle represents the upper and lower limits of the boundary.

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Fig. 1. A conceptual model of a boundary selection strategy

2.3 Dung Beetles Forage Occasionally, adult humans emerge from the ground in order to nourish themselves. Through this behavior, dung beetles are led to seek sustenance through the development of maximum browsing zones, and the borders of the best scavenging regions for these dung caterpillars while scavenging for food in the wild can be determined as follows: Lbb = max(X b × (1 − R), Lb) Ubb = min(X b × (1 + R), Ub)

(5)

Since and are the northern and southern boundaries of the ideal foraging area, correspondingly, the place of residence of the animal’s dung beetle infestation in the computational model has been changed as illustrated in the remainder of the equation: xi (t + 1) = xi (t) + C1 × (Bi (t) − Lbb ) + C2 × (xi (t) − Ubb )

(6)

where xi (t) represents the position information of the ith dung beetle in the tth iteration, C1 represents the random number that follows the normal distribution, and C2 represents the random vector belonging to (0,1). 2.4 Dung Beetle Stealing As pointed out in (6), it is the highest-quality food source. As a consequence of this, we may assume that the surrounding community is the ideal area to experience food competition. During the iteration, the attacker’s position information is updated and may be classified according to the mathematical model that is provided listed below:      (7) xi (t + 1) = X b + S × g × xi (t) − X ∗  + xi (t) − X b 

3 DBOBP 3.1 Improve The DBO’s Approach The difference between the expected result and what actually happens with the value of the neural network’s BP neural network after DBO maximizing efficiency, as shown in Fig. 6, demonstrates that the model’s diagnostic success rate is actually quite high

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and that the actual amount of vulnerability has been very close to the expected value of DBOBP. As shown in Fig. 7, the projected value and true worth of the BP neural network, which is the one that has been utilized by the DBO of 60 distinct sets of assurance data are particularly close by, as are the true size of the origin of the issue and the anticipated effect of DBOBP (Fig. 2).

Fig. 2. DBO optimizes the flowchart design of BP neural network

4 Analysis of Simulation Results When determining the type of transformer fault, the concentration of typical fault characteristic gas can be selected as the input basis. Since the content of faulty gas in oil varies greatly, in order to reduce simulation errors, preprocessing such as Eq. (8) is required before substituting into the algorithm. x =

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Formula: xi is the volume fraction of a gas. 4.1 Simulation Data Processing Power transformer faults can be divided into five types [13]; low-energy discharge, medium-low temperature overheating, high-energy discharge, high-temperature overheating, and partial discharge. For transformer fault classification and diagnosis, the

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code corresponding to the above fault type can be used as the output value. The specific fault types and their corresponding codes are shown in Table 1 (Table 2). Table 1. Power transformer fault types and their corresponding codes Failure normal Low-energy Low High High Partial Medium type discharge temperature energy temperature discharge temperature overheating discharge overheating overheating Fault code

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The present investigation retrieved problems information concerning 360 sets of gases present in power oil for transformers from a power grid firm and published literature from previous decades for the purpose to confirm the accurateness of the information being analyzed. We chose 300 of these individuals at random to serve as the instructional set and the additional 60 as the evaluation set. In the following table the precise population subdivision is provided. Calculated lines representing the information’s distribution of the three-dimensionally decreased and automated generator information on faults is depicted in Fig. 3. 4.2 Comparison of Simulation Results The data were trained by the failure model, and the DBOBP training model was obtained and 60 sets of validation data were verified, and the fluctuation curve of DBOBP prediction error was obtained as shown in Fig. 4. As you can see from the figure, the

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prediction error of the model is small. Figure 5 shows the adaptation curve. The DBOBP optimization algorithm has high search efficiency and convergence speed. 1.45 0.04

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The difference between the expected result and what actually happens with the value of the neural network’s BP neural network after DBO maximizing efficiency, as shown in Fig. 6, demonstrates that the model’s diagnostic success rate is actually quite high and that the actual amount of vulnerability has been very close to the expected value of DBOBP. As shown in Fig. 7, the expected value and true worth of the BP neural network that has been maximized by the DBO of 60 different sets of confirmation data are extremely close, as are the actual magnitude of the source of the problem and the expected outcome of DBOBP. 1

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We compare the real value of the fault data, the diagnostic value of the BP neural network and the diagnostic value after DBOBP optimization, as shown in the simulation curve shown in Fig. 8. Comparing the test set error of DBOBP neural network and the test set error of BP neural network, it can be seen that the test set error and error fluctuation of DBOBP neural network are also very small. As shown in Fig. 9, the performance of the DBOBP optimization algorithm compared to the BP neural network

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5 Summary In this paper, five typical gases dissolved in 360 groups of faulty power transformer oil are selected as the basis for diagnosis, and the improved DBOBP optimization algorithm power transformer fault diagnosis method is faster, and the single iteration operation speed of DBOBP is faster than BP with the classical neural network algorithm, indicating that the improved algorithm has higher efficiency, faster speed and higher accuracy for power transformer fault classification.

References. 1. Zhang, P., Qi, B., Li, C., et al.: Quantitative analysis of influencing factors of dissolved gas characteristics in power transformer oil. Proc. CSEE 41(10), 3620–3631+3686 (2021). (in Chinese)

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2. Kari, T., He, Z., Rouzi, A., et al.: Power transformer fault diagnosis using random forest and optimized kernel extreme learning machine. Intell. Autom. Soft Comput. 37(1) (2023) 3. Li, P., Hu, G.: Transformer fault diagnosis method based on data-enhanced one-dimensional improved convolutional neural network. Power Syst. Technol. 47(07), 2957–2967 (2023). https://doi.org/10.13335/j.1000-3673.pst.2022.1902. (in Chinese) 4. Engin, B., Varbak, S.N., Erkan, D.: Hybrid condition monitoring system for power transformer fault diagnosis. Energies 16(3) (2023) 5. Taha, I.B.M., Ibrahim, S., Mansour, D.A.: Power transformer fault diagnosis based on DGA using a convolutional neural network with noise in measurements. IEEE ACCESS 9 (2021) 6. Jia, L., Zhang, J., Wang, C., et al.: Fault diagnosis of power transformer for differential evolution support vector machine based on DGA. High Voltage Apparat. 51(04), 13–18 (2015). (in Chinese) 7. Li, G., Meng, K., He, S., et al.: Fault diagnosis method of Bi-LSTM transformer considering feature coupling. Electric Power 56(03), 100–108+117 (2023). (in Chinese) 8. Zhou, J., Hou, H., Sheng, G., et al.: Transformer fault diagnosis algorithm based on state parameter correlation rule mining and deep learning fusion. High Voltage Apparat. 59(03), 108–115 (2023). https://doi.org/10.13296/j.1001-1609.hva.2023.03.015. (in Chinese) 9. Wang, X., Yi, Y., Li, T.: An optimization method of convolutional neural network for transformer fault diagnosis. Electron. Sci. Technol. 1–9 (2023). (in Chinese) 10. Zhang, B., Wu, J., Luo, W.: Evaluation of transformer insulation aging state based on fuzzy theory and evidence theory. Guangdong Electric Power 32(08), 109–118 (2019). (in Chinese) 11. Wang, J., Li, X., Shu, Y., et al.: Review of intelligent fault diagnosis technology of power transformer. J. Shanghai Univ. Electric Power 38(05), 518–522 (2022). (in Chinese) 12. Xue, J., Shen, B.: Dung beetle optimizer: a new meta-heuristic algorithm for global optimization. J. Supercomput. (2023) 13. Merve, D., Haluk, G., Cengiz, M.T.: Improvement of power transformer fault diagnosis by using sequential Kalman filter sensor fusion. Int. J. Electric. Power Energy Syst. 149 (2023)

A New Secondary Frequency Control Method for Distributed VSGs in Island Operation Yuting Teng1,2 , Wei Deng1,2(B) , Guoju Zhang1,2 , Shiyi Zhang3 , and Wei Pei1,2 1 Institute of Electrical Engineering Chinese Academy of Sciences, No.6, Zhongguancun North

2nd Road, Beijing, China [email protected] 2 University of Chinese Academy of Sciences, No.19, Yuquan Road, Beijing, China 3 State Grid, Shanxi Marketing Service Center, Shanxi, China

Abstract. Virtual synchronous generator (VSG) control technology is widely used in off-grid control of distributed power supply by simulating the characteristics of synchronous generator, increasing the inertia of the system, realizing the advantages of frequency regulation and voltage regulation. In the multi-VSGs islanded operating system, the damping function of VSG can play a role of primary frequency modulation similar to droop control. The load increment is distributed according to the damping coefficient. When the system frequency crosses the line due to sudden load change, the droop characteristic can be changed to bring the system’s frequency back to the normal range. The secondary frequency modulation characteristics of translation droop curve method and changing damping coefficient method are analyzed, and a joint adjustment method combining translation droop curve and changing damping coefficient is proposed. Finally, simulation experiments are carried out on Matlab/Simulink platform to verify the effectiveness of the proposed method. Keywords: Distributed generation · virtual synchronous control · grid-forming inverter · secondary frequency control · droop control

1 Introduction In recent years, with the continuous development of new energy power generation technology, the proportion of new energy in the global power generation capacity will rise from 26% in 2020 to 57% in 2030, and reach 86% in 2050. Literature [1] points out that by 2050, new energy can meet more than 60% of China’s primary energy demand and more than 85% of its electricity demand. At the same time, the traditional synchronous generator as the dominant mode of power system synchronization has been broken, can independently establish voltage and frequency grid control has become a research hotspot. Virtual synchronous generator (VSG) is a kind of grid-forming control strategy which directly simulates the internal and external characteristics of synchronous generator by using the mathematical model of synchronous motor in the control link [2–5]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 594–601, 2024. https://doi.org/10.1007/978-981-97-1064-5_65

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Literature [6] proposes a secondary frequency modulation method based on consistency algorithm to compensate the frequency signal, reduce the amount of communication between inverters, and improve the dynamic performance of the system. Literature [7] proposes to adopt the algorithm based on deep learning, define the long-term performance function to obtain the optimal control strategy, adjust the control parameters in real time, and realize the frequency modulation control; Literature [8] designed a method based on distributed optimal quadratic control for the secondary regulation of frequency voltage, so that the system frequency automatically recovers after disturbance. Literature [9, 10] improves the tracking accuracy and anti-winding performance of micro-grid inverter at each harmonic frequency, and improves the voltage control accuracy of the secondary frequency. Literature [11, 12] uses a distributed consistency algorithm to restore the frequency to the rated value on the premise of ensuring the active power sharing accuracy by using the communication between adjacent inverters. The power distribution among the parallel inverters is mostly based on the droop characteristics of frequency - active power. Therefore, in the aspect of active frequency control, changing its droop characteristics can also effectively improve the frequency level of the system. A large number of literatures have carried out research on this aspect. Literature [13, 14] proposes to add an integral advance compensation item to the active frequency sag control loop to carry out secondary frequency modulation, which can eliminate the static frequency difference and improve the stability of the multi-parallel inverter system. In literature [15, 16], an S-type sagging control enables the inverter to increase output when the frequency is close to the rated value, and reduce output when the frequency is far from the rated value. On the other hand, in view of VSG multi-machine parallel operation, literature [17] proposes a simplified VSG virtual inertia control model and establishes multi-VSGs small signal model, which can effectively realize the function of primary frequency modulation. Based on this, a virtual inertia matching method of multi-paralleled VSGs is proposed. Literature [18] establishes the small signal model of multi-VSGs grid-connected system, analyzes the influence of different parameters on the system characteristic root. Literature [19, 20] proposes improved VSG, which dynamically adjusts virtual inertia and damping coefficient to achieve coordinated control of virtual inertia and damping coefficient, suppress power frequency oscillation, shorten regulation time, and improve system stability. The above studies mostly fail to consider the power shortage of the system and the power limitation of the inverter; In addition, for the island system composed of multiparallel VSG grid control unit, the analysis of active frequency droop characteristics and the study of secondary frequency modulation performance are still lacking. In this paper, to solve the problem of frequency crossing in the first frequency modulation of multiple VSG islanding system due to the large amplitude of load change, the characteristics of the system are analyzed by simplifying the VSG frequency control model. Considering the power balance of the system and the output power limit of each generating unit, the second frequency modulation method of translation sag curve method and changing damping coefficient method is analyzed, and the variable sag characteristic method combining translation sag curve and changing damping coefficient is proposed to realize the function of secondary frequency modulation. Finally, three parallel VSGs islanding operating system is built on Matlab/Simulink platform.

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2 VSG Control Technology Figure 1 is a typical VSG control block diagram. Usually, the droop control is added to the active and reactive power control loops to achieve the functions of primary frequency and voltage regulation, similar to synchro.

Fig. 1. VSG control block diagram

Fig. 2. Simplified block diagram of VSG active power control

VSG’s active frequency control block diagram can be simplified as Fig. 2, in addition to the active power-frequency droop characteristics, k p = 2πf 0 *2πDp .

3 Analysis of Secondary Frequency Regulation Characteristics For secondary frequency control, in the case that the system power does not produce a gap, the frequency can be adjusted without difference, but in the case of active power gap, the traditional integral based secondary frequency control will be limited. This chapter will discuss three kinds of secondary control methods that can achieve frequency improvement. According to the local measurement, the imbalance between the system frequency level and power is calculated in real time, and the sag control parameters of the inverter participating in the secondary frequency modulation control are automatically adjusted, so as to make full use of its active power margin and maintain the system frequency within the safe range. 3.1 Translation Method Changing the system power set point Pset can make the up and down translation of the P-f characteristic curve of the system. When the total load power is P, the system frequency exceeds the allowed interval [ωmin , ωmax ], set the i inverter as the frequency modulation inverter, the frequency modulation inverter needs to adjust the input power

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set value Pseti to P’seti , so that the frequency works at the frequency set value ωn , set the system power deficit as P can be obtained: P = Pm − Pset = ωn (ωn − ωm )Dp

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If the maximum power is not emitted, the system frequency is continuously adjustable between [m ω, e ω], and Pseti ‘is the value between [Pmaxiseti , P]. When the power limit of the frequency-modulated inverter meets the system power deficit, the operating point is located in the triangle region composed of A-B-C, and when the power deficit is not met, the operating point is located in the triangle region composed of B-D-E. When there are multiple frequency-modulated inverters in the system, the missing power can be allocated in proportion to the rated power. In summary, the control principles of the available translation method are as follows:   = P + Pseti , Pmax i > P + Pseti Pseti (2)  Pseti = Pmax i , Pmax i ≤ P + Pseti

3.2 Rotation Method The rotation method only changes the Dpi of the frequency modulation inverter, so that the P-f characteristic curve rotates around the rated operating point, and the deviation between the system frequency and the rated value can be reduced under the premise of ensuring the total output power is unchanged. Set the adjusted sagging control factor to D’pi . Obtained by power conservation: n  i=1

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If the maximum power is not emitted, it ism continuously adjustable between [ω, ωe ]. By changing the damping coefficient, the rotation method can effectively improve the frequency level of the system and increase the damping coefficient, reduce the overshoot of the system and shorten the adjustment time. The operating point is located in the triangle area composed of B-D-E. However, this method is differential regulation, no matter how the damping coefficient is changed, the system frequency cannot be returned to the rated frequency.

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3.3 Joint Adjustment Method According to the above analysis, only changing the power setting value can make the system frequency return to the rated level without changing the dynamic response characteristics of the system when the power output of the adjustable inverter meets the system power deficit. Only changing the damping coefficient can change the slope of the P-f characteristic curve of the adjustable inverter, which can effectively improve the system frequency level, increasing the damping coefficient can reduce the system overshooting and shorten the adjustment time, but can not make the system frequency back to the rated frequency. The combined regulation method combines the advantages of both, and changes the power set value and the damping coefficient at the same time to increase the frequency regulation flexibility of the island system. Set a as the adjustment coefficient, in the state of primary frequency modulation a = 1, in the process of secondary frequency modulation, change a can change Pseti and Dpi at the same time, and then change the output power. Obtained from the above formula a=

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In summary, the control principle of the combined regulation method changes the power set value and damping coefficient at the same time when the system power deficit is met, and the maximum output power is not met when the power deficit is not met.

4 Simulation According to the VSG model obtained from the above analysis, a distributed power island operating system simulation model with 3 VSG converters is built, and the characteristics of primary frequency modulation and secondary frequency modulation are analyzed. The schematic diagram of the simulation system structure is shown in Fig. 1, and the system parameters are shown in Table 1. The permissible frequency range is 49.5–50.5 Hz. Before 1.5 s, the system runs at rated state, and each inverter outputs power according to the set value of active power, and the system frequency stabilizes at 50 Hz. At 1.5 s, the system suddenly increases 120 kW load. At this time, the system frequency drops to 49.47 Hz, which exceeds the allowable value of the frequency range, and secondary frequency modulation control is required. At 4 s, by changing the droop characteristic of the adjustable inverter to adjust the output power for frequency regulation.

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4.1 Single VSG Participates in SFR When the maximum power output Pmax1 of the frequency modulation inverter VSG1 is 170 kW, it can be seen from the analysis in Sect. 2 that the converter can restore the rated frequency of the system under the condition of changing the power set value. The simulation verification is shown in Fig. 3(a). In the case of only changing the damping coefficient, there will be frequency deviation, but it will reduce overshoot and improve the response speed. The simulation verification is shown in Fig. 3(b); At the same time, changing the power set value and damping coefficient can realize the frequency adjustment without difference, and can also reduce the adjustment time. Its simulation verification is shown in Fig. 3(c). As can be seen from the simulation, both the translation method and the joint regulation method can realize the non-difference regulation of frequency under the condition of meeting the power gap, and the combined regulation method can realize the rapid adjustment of frequency better than the translation method, reduce overshooting, and effectively improve the frequency safety of the system. When the maximum power output Pmax1 of the adjustable inverter VSG1 is 130kW, the frequency deviation of the primary frequency modulation is reduced, but it will not return to the rated value. At this time, the maximum power of the frequency modulation inverter is output. Figure 3(e) and 3(f) are the simulation diagrams of the system using the joint regulation method. 50.2

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5 Conclusions In this paper, the simplified VSG control method is adopted, and the droop with damping characteristics of VSG converter are shown simultaneously by using the equivalent droop coefficient. The use of joint adjustment algorithm, while changing the power set value of VSG in the island system and the equivalent droop coefficient, increase the system damping at the same time, can realize the rapid and stable adjustment of the secondary frequency control of the multi-VSGs islanding system, improve the frequency safety level of the island distributed power generation system. The effectiveness of the proposed method is verified by simulation. The control algorithm in this paper can provide an effective method for multi-VSGs paralleled operation of island system, the analysis and optimization of secondary frequency control. Acknowledgements. This work is supported by the National Natural Science Foundation of China (52177122) and S&T Program of Hebei (22292101Z).

References 1. Energy Research Institute, NDRC. Study on Scenarios and approaches of High Proportion renewable Energy development in China 2050. 2050 (2018). (in Chinese) 2. Yun, Y., Fei, M.: Collaborative adaptive control strategy of moment of inertia and damping coefficient for virtual synchronous generator. Electric Power Autom. Equip. 39(03), 125–131 (2019). (in Chinese) 3. Dong, S., Chen, Y.C.: Adjusting synchronverter dynamic response speed via damping correction loop. IEEE Trans. Energy Conv. 32(2), 608–619 (2016) 4. Unruh, P., Nuschke, M., Strauß, P., et al.: Overview on grid-forming inverter control methods. Energies 13(10), 2589 (2020) 5. Teng, Y., Deng, W., Pei, W., et al.: Review on grid-forming converter control methods in highproportion renewable energy power systems. Global Energy Interconnect. 5(03), 328–342 (2022) 6. Dong, J., Gong, C.: Distributed secondary frequency modulation Method for island-operated multi-inverter microgrid systems based on Event Triggered improved consistency Algorithm. Proc. CSEE 2023, 1–15 (2023). (in Chinese) 7. Adibi, M., Woude, J.V.D.: Secondary frequency control of microgrids: an online reinforcement learning approach. IEEE Trans. Autom. Control 67(9), 4824–4831 (2022)

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8. Khayat, Y., Naderi, M., Shafiee, Q., et al.: Decentralized optimal frequency control in autonomous microgrids. IEEE Trans. Power Syst. 2019(3), 2345–2353 (2019) 9. Babayomi, O., Li, Z., Zhang, Z.: Distributed secondary frequency and voltage control of parallel-connected VSCS in microgrids: A predictive VSG-based solution. CPSS Trans. Power Electron. Appl. 5(4), 342–351 (2020) 10. Li, Z., Zeng, J., Huang, J.: Time-frequency voltage control strategy of microgrid inverter based on linear active disturbance rejection control. Autom. Electric Power Syst. 44(10), 145–154 (2020). (in Chinese) 11. Li, Z., Cheng, Z., Liang, J., et al.: Distributed event-triggered secondary control for economic dispatch and frequency restoration control of droop-controlled AC microgrids. IEEE Trans. Sustain. Energy 11(3), 1938–1950 (2019) 12. Liu, Y., Zhuang, X., Zhang, Q., et al.: A novel droop control method based on virtual frequency in DC microgrid. Int. J. Electr. Power Energy Syst. 2020(119), 105946 (2019) 13. Dong, J., Gong, C., Chen, H., et al.: Secondary frequency regulation and stabilization method of islanded droop inverters based on integral leading compensator. Energy Rep. 2022(8), 1718–1730 (2022) 14. Dong, J., Wang, Z., Zhu, G., et al.: Secondary Frequency modulation method of Gudao Operating droop Inverter. Electric Power Autom. Equip. 42(05), 40–46 (2022). (in Chinese) 15. Li, J., Li, F., Li, X., et al.: S-shaped droop control method with secondary frequency characteristics for inverters in microgrid. IET Gener. Trans. Distrib. 10(13), 3385–3392 (2016) 16. Vijay, A.S., Dheer, D.K., Tiwari, A., et al.: Performance evaluation of homogeneous and heterogeneous droop-based systems in microgrid—Stability and transient response perspective. IEEE Trans. Energy Conv. 34(1), 36–46 (2018) 17. Bo, Z., Xi, Y., Yi, H.: Transactions of china electrotechnical society 32(10), 42–52 (2017). (in Chinese) 18. Lu, S., Zhu, Y., Dong, L., et al.: Small-signal stability research of grid-connected virtual synchronous generators. Energies 15(19), 7158 (2022) 19. Chen, M., Zhou, D., Wu, C., et al.: Characteristics of parallel inverters applying virtual synchronous generator control. IEEE Trans. Smart Grid 12(6), 4690–4701 (2021) 20. Zhang, L., Zheng, H., Cai, G., et al.: Power-frequency oscillation suppression algorithm for AC microgrid with multiple virtual synchronous generators based on fuzzy inference system. IET Renew. Power Gener. 16(8), 1589–1601 (2022)

Research on the Early Warning Method of Thermal Runaway of Lithium Battery Based on Strain Detection of Explosion-Proof Valve Hangyu Luo, Tao Cai(B) , Aote Yuan, and Song He State Key Laboratory of Strong Electromagnetic Engineering and New Technology, Huazhong University of Science and Technology, Wuhan 430074, Hubei Province, China [email protected]

Abstract. Overcharging and runaway of lithium batteries is a highly challenging safety issue in lithium battery energy storage systems. Choosing appropriate early warning signals and appropriate warning schemes is an important direction to solve this problem. This research proposes a battery overcharge warning scheme based on the hard case lithium battery explosion proof valve Strain gauge. Starting from the external strain mechanism of the lithium battery, the strain change of the lithium battery explosion proof valve under normal conditions and overcharge is studied. Based on the comparison of the two conditions, an online warning scheme using sliding window and data standard deviation is proposed. The experimental results show that: (1) under normal charging and discharging conditions, the strain of the safety valve of the lithium battery will monotonically increase with the increase of SOC and battery temperature; (2) Under overcharging conditions, the inflection point of the strain change of the explosion-proof valve occurs earlier than the characteristic gas, at most about 600 s earlier; (3) The online warning method using sliding windows and data standard deviation can advance the warning of characteristic gases by about 500 s and improve the generalization ability of the method. This study proposes a cheap and reliable early warning scheme for lithium battery energy storage systems, greatly improving the safety of battery systems. Keywords: Li-ion energy storage · strain · safety warning · multi-physical model

1 Introduction With a large number of energy storage containers on the market, as well as the pursuit of high energy density by developers and consumers, the frequent occurrence of safety accidents in lithium-ion energy storage batteries has become a bottleneck restricting its further development. Lithium-ion battery storage power station in the event of thermal runaway and lead to fire or explosions, which are unimaginable. Therefore, early warning is the most important function in the safety and security system of the energy storage plant [1, 2]. Currently existing energy storage engineering applications are not well warned, partly due to the lack of physical quantities other than voltage, current and temperature to characterize the state of the battery [3]. When a battery undergoes thermal runaway, © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 602–614, 2024. https://doi.org/10.1007/978-981-97-1064-5_66

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a series of side reactions occur inside the battery, some of which generate gases. These gases can build up inside the battery case before the explosion-proof battery valve opens, causing the battery to bulge and changing the pressure inside the battery [4–6]. Therefore, early warning can be carried out by detecting the pressure inside the battery, and the validity of this data is limited to before the explosion-proof valve is opened. A more accurate method is to use embedded optical fiber to detect the pressure inside the battery [7, 8], however, this solution is more costly and complicated, and it is difficult to achieve engineering applications at present. Instead, the internal pressure changes are reflected by detecting the stress-strain on the surface of the cell. By analyzing the thermal stress of lithium-ion Shi [9] concluded that the thickness of the battery becomes thicker during charging, the thickness decreases during discharging, and the thickness change is reversible. Mei [10] established a forcethermal model at the cell scale and investigated the thermal stress and expansion behavior due to the temperature difference, and found a good correlation between the temperature difference, thermal stress, thermal strain and expansion behavior of the battery, which provides sufficient theoretical support to explore the internal chemical processes of lithium batteries from external strains. Ren et al. [11] installed strain gauges at different locations in the axial-radial direction of 18650 batteries. By analyzing the strain changes in charging and discharging at 0.5 C, it was found that the strains during charging and discharging had different tendencies but all of them showed monotonous relationships with SOC. Chen et al. [12] used an external heat source heating to make the battery thermal runaway, to study the stress change of a single cell with different capacity externally subjected to thermal runaway and the stress change of the thermal runaway propagation of a group of cells, and concluded that there will be a trend of three stages of strain change in the process of thermal runaway, and at the same time, the strain can be realized earlier than the electrical signals to achieve the early warning, at most, 500s ahead of the time. Numerous studies have shown that the mechanical signal changes inside the battery can be reflected by the strain changes outside the battery, and the current research still has the following problems: (1) The use of external fixtures to detect the external strain of the battery is costly and has no engineering value. (2) Current research mostly uses full-stage data for analyses, which are computationally complex and poor in real time, making it impossible to realize the requirements of online early warning. (3) Separate consideration of the effects of SOC and temperature rise T on the external strain, while in fact the relationship between them is complex and strongly coupled. (4) The use of external heat sources to heat the static battery resulting in thermal runaway, without considering the dynamic process of thermal runaway faults, such as overcharging. In order to solve the problems above, this study proposes a method for estimating the safety state of lithium batteries based on the change of external strain of the battery by detecting the strain of the explosion-proof valve of the battery due to the change of internal pressure during the battery charging and discharging process, which can be used to reflect the change of the internal pressure of the battery by installing sensors on the outside and detecting the deformation of the outer surface of the battery due to the internal pressure, and then realize the early safety warning of lithium batteries.

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2 Strain Mechanism of Explosion-Proof Valve for Li-ion Battery Lithium-ion batteries are accompanied by de-embedded lithium in the electrode material and temperature increase during the charging and discharging process, which generates internal stresses and leads to internal pressure changes. Lithium-ion batteries are accompanied by temperature changes during use, which causes thermal stress. The hard-shell Li-ion battery is a coiled structure, due to the different coefficients of thermal expansion between the layers of the coiled, the thermal expansion of each layer of material to constrain each other will also produce thermal stress. Lithium-ion batteries are accompanied by the expansion and contraction of the electrodes during use, which is manifested in the change of electrode thickness with the change of charging and discharging states, thus changing the volume size of the internal void of the hard-shell battery. At the same time, the temperature rises during the charging and discharging process will cause the gas inside the battery to expand by heat, which will change the internal pressure of the battery [13–21]. As lithium battery internal pressure relief channel, the battery explosion-proof valve than other parts of the battery for the internal pressure is more sensitive, at the same time, lithium battery storage system in the battery is mostly placed in groups, tightly arranged, other parts of the battery will be subjected to strain limitations, and explosion-proof valve above the free space, more conducive to the transfer of stress. The expansion and contraction of the coils inside the cell produced by internal stresses changes the volume of the internal void of the cell, denoted as V. Assuming that the change in the thickness of the cell due to charging and discharging is hpole , and assuming that the internal temperature of the cell remains constant, that the lithium-ion cell expands without constraints, and that the diaphragm and collector are not compressed and deformed, the change in the thickness of the electrodes, hpole , changes monotonically with the amount of change in the SOC [19]:   ω− α− − ω+ α+ · hpole SOC (1) hpole = 1+β where the hpole is the initial thickness of the electrode, ω− is the volume fraction of the negative material, ω+ is the volume fraction of the positive material, α− is the volume expansion coefficient of the negative material, α+ is the volume expansion coefficient of the positive material, and β is the negative excess coefficient [4], and set the initial SOC be 0, then there are SOC = SOC

(2)

Similarly, assuming SOC is constant, we have [18–20]: α=

htemp hpole T

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where htemp is the change in thickness during the resting phase, T is the change in temperature, and α is the coefficient of thermal expansion. The combination of the above equations can be obtained [22–26]:   ω− α− − ω+ α+ · hpole SOC + αhpole T (4) hpole = 1+β

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We also set the volume change of the internal void of the cell be V , then we have V = hpole Spole

(5)

V  = V − V

(6)

where V is the altered cell interstice, V is the original cell internal void, and S pole is the surface area of the unfolded electrodes, which remains constant as the internal strain change. The explosion-proof valve pressure is internal stress is generated by the gas inside the cell acting on the explosion-proof valve, according to the ideal gas equation of state: Pin V = nRT

(7)

Fin = Pin Svalve

(8)

and

and Generalized Hooke’s law ⎧ 1 ⎪ ε1 = (σ1 − μ(σ2 + σ3 )) ⎪ ⎪ ⎪ E ⎪ ⎨ 1 ε2 = (σ2 − μ(σ1 + σ3 )) ⎪ E ⎪ ⎪ ⎪ ⎪ ⎩ ε = 1 (σ − μ(σ + σ )) 3 3 1 2 E

(9)

where Pin is the internal pressure of the battery; n is the amount of gas; R is the mole gas constant; σvalve is the battery explosion-proof valve stress, which direction is perpendicular to the surface of the explosion-proof valve, Fin is the pressure inside the cell acting on the explosion-proof valve; Fout is the pressure outside the battery on the explosion-proof valve, usually Fout = P0 Svalve , P0 is the standard atmospheric pressure; Svalve is the area of the valve; E is the modulus of elasticity; μ is the Poisson’s ratio; ε1 is the strain in the same direction as the metal strain gauges, and σ1 is the strain in the same direction as the metal strain gauges, σ2 is the stress in the direction perpendicular to the surface of the explosion-proof valve, it can be considered that σ2 = σvalve ; σ3 is the stress in the direction perpendicular to both σ1 and σ2 ; in the safe state of the battery, it is approximated that the explosion-proof valve has a primary strain in only one direction, so we get ε2 = ε3 = 0. Integrating the above equations, we get ⎞ ⎛   1 1 − μ − 2μ2 ⎝ nR(T0 + T )

  ε1 = − P0 ⎠ − α− E μ V − ω1+β − ω+ α+ · hpole SOC + αhpole T · Spole

(10)

Equation (10) reflects the normal charging and discharging conditions of the battery explosion-proof valve strain trend with the battery SOC and the battery temperature rise T between the relationship between the coefficients before the SOC and T are

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negative numbers, it can be seen that the explosion-proof valve strain changes with the SOC and T monotonically increasing and safe state with the charging and discharging cycle and cyclic changes [27]. When the lithium battery overcharge condition occurs, the battery internal gas production [28–30], the battery explosion-proof valve pressure will increase dramatically until the explosion-proof valve to open the internal pressure relief, at this time there will be the generation of characteristic gases, and through the detection of the explosion-proof valve to withstand the pressure of the sudden increase in the stage of the theoretically achievable earlier than the characteristics of the gas detected to the occurrence of the battery overcharging.

3 Experimental Methods and Analyses 3.1 Setting Up the Experimental Environments The Everest Lithium 50 Ah lithium iron phosphate hard shell battery LF50F was selected as the experimental object, and the experimental instruments included: Neware CT4008-5V60A-NTA charge/discharge tester, BFH120-2AA-R1-P300 strain gauge with temperature compensation, and MOT500-D-H2 on-line gas detector. Firstly, the battery was discharged to 2.8 V, and then the battery was allowed to fully rest at a constant temperature of 25 °C. According to Fig. 1, two metal strain gauges are tightly pasted on the explosion-proof valve; use the Wheatstone bridge and differential amplifier circuit shown in Fig. 2 as the conditioning circuit to process the signals from the metal strain gauges; and then set up the experimental environment in accordance with Fig. 3: place the battery and the conditioning circuit together in a dry and airtight explosion-proof box at a constant temperature of 25 °C, connect the output of the charging instrument to the battery, and then connect the sensors on the battery and to the computer. Then connect the sensor and the battery to the computer, put the sensor and the battery into the explosion-proof box, arrange the gas detector at the upper end of the explosion-proof box to accurately detect the gas, only the charging cable and the data cable lead out.

Fig. 1. Installation diagram of strain gauge.

3.2 Strain Test of Explosion-Proof Valves Under Normal Operating Conditions Battery charging and discharging experiments under 0.3 C constant current condition were first carried out to verify the trend of explosion-proof valve strain with SOC and

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Fig. 2. Strain gauge conditioning circuit.

Fig. 3. Schematic diagram of experimental environment and equipment connection.

temperature rise as reflected in Eq. (10). The change of explosion-proof valve pressure and battery charging curves were recorded, and the curves of battery charging and discharging time and cell explosion-proof valve strain were plotted as shown in Figs. 4 and 5. The explosion-proof valves strain curve first decreases and then shows a slow rising trend. Since the coefficients before SOC and T are negative numbers, it can be seen that the strain of the explosion-proof valve increases monotonically with SOC and T . In the charging process, the explosion-proof valve strain due to the increase in SOC and the trend of increasing, but also with the increase in the trend of increasing. At stage t0–t1, the battery temperature changes and SOC changes in the joint role of the battery explosion-proof valve pressure, this time by the temperature dominated by the changes

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in the battery explosion-proof valve pressure, the extent of the explosion-proof valve strain was a rapid increase in the trend; t1–t2 of the battery’s internal heat generation gradually tends to dissipation, the temperature increases slowly, this time the explosionproof valve strain by the SOC and the joint effect of temperature, showing a slow increase in the trend. After t2 the temperature is no longer increased, the battery heat and heat to reach equilibrium, this time the battery in the role of the SOC changes, due to the SOC at this time is larger, the battery charging process began to be accompanied by a small amount of gas production, in the SOC and the chemical reaction under the joint effect of gas production, the battery explosion-proof valve pressure is still increasing faster, for the irreversible process, but in the battery charging and discharging process, this process is not dominant. However, with the increase in the number of battery cycles and the occurrence of overcharge, the impact of this irreversible process cannot be ignored.

Fig. 4. Experimental curve of 0.3C charge

In the discharge process, the explosion-proof valve strain changes due to the decrease in SOC and produce a decreasing trend, while with the increase in the trend of increasing. At stage t0–t1, the battery temperature changes more rapidly, at this time by the temperature dominated by the change in the battery explosion-proof valve strain, explosion-proof valve strain changes in the trend of increasing; At t1–t2 moments of the battery’s internal heat production is equal to the dissipation of heat, the temperature is no longer increasing, at this time, the explosion-proof valve strain by the SOC dominated, showing a decreasing trend; after t2 moments of temperature is slowly increasing again, at this time the battery changes under the dual role of the SOC and the temperature. SOC dominated, showing a decreasing trend; After t2 moments the temperature is slowly increasing, this time the battery changes under the dual role of SOC and temperature. 3.3 Strain Test of Explosion-Proof Valve Under Overcharging Condition The battery was charged according to 0.5 C constant current from 80% SOC until the explosion-proof valve was opened, and the experimental results are shown in Fig. 6.

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Fig. 5. Experimental curve of 0.3 C discharge

At t1 moment explosion-proof valve strain appeared the first obvious inflection point, when the battery voltage is about 4.4 V, overcharge leads to irreversible chemical processes occurring within the battery; at t2 moment the second inflection point, this time the extent of strain on the explosion-proof valve may be due to the gas generated by the chemical reaction within the rapid increase; at t3 moment the third inflection point, this time, the battery sidewalls began to bulge deformation, resulting in an internal cavity The third inflection point at t3, when the battery side walls began to bulge deformation, resulting in the internal cavity gradually become larger, so that the internal pressure of the battery decreased; at t4 moment gas detector detected a sharp increase in gas,

Fig. 6. Experimental curve of 0.5 C overcharge.

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explosion-proof valve strain rises sharply, at this time, due to the internal pressure of the battery, explosion-proof valve burst open, a large number of internal gas leakage.

4 Online Early Warning Method Based on Battery Strain Signal Explosion-proof valve strain is capable of overcharging warning, but due to the installation process of strain gauges and the variability of different batteries, it is not possible to directly use the threshold value as a judgement, so the original strain data is processed first before safety warning. For overcharging conditions and normal conditions of the explosion-proof valve strain change, it is easy to see that the normal charging and discharging conditions of the explosion-proof valve strain change range of about 0.01, while in the overcharging of the conditions, the explosion-proof valve strain change range of about 0.1, the two difference of an order of magnitude, and the overcharging conditions of the explosion-proof valve strain change more quickly. In order to achieve effective online warning, it is proposed to use a sliding window to obtain the standard deviation of the data in the window, and then set the judgement threshold for the standard deviation, so as to make full use of the trend of the strain change of the explosion-proof valve to judge the safety status of the battery in different working conditions, and at the same time, it can rule out the interference brought by the variability of the battery and strain gauges, and save the computational resources. The data processing method is shown in Fig. 7, where the window size is 5. The window slides when new data is collected, and the corresponding standard deviation Si at that moment is obtained, and the warning is carried out by setting the standard deviation threshold.

Fig. 7. Data processing methods

The strain data under normal charging and discharging and overcharging conditions are processed as above, as shown in Fig. 8. The standard deviation under normal charging and discharging conditions is nearly a straight line with a slope of zero, while the standard deviation under overcharging conditions has obvious fluctuations, and a larger threshold is chosen in order to reduce false alarms as well as to further improve the generalization capability.

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(c) Fig. 8. Standard deviation curves under different operating conditions. (a) 0.3 C charging. (b) 0.3 C discharging. (c) 0. 5 C over-charging.

Figure 9 shows the hydrogen detector data, explosion-proof valve strain raw data and standard deviation data warning curve, the standard deviation of the data to reflect the rate of change of the strain, while eliminating the impact due to the different initial values. The standard deviation curve of the two obvious peaks S1 and S2 correspond to the battery sidewall bulging and explosion-proof valve open process; set the standard deviation warning threshold of 0.01, the threshold, the method in advance of the characteristic gas about 500s to send out an alarm signal.

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5 Conclusion Aiming at the safety of lithium battery warning in energy storage power stations, this study proposes a lithium battery safety warning method based on explosion-proof valve strain gauges from the mechanism of explosion-proof valve strain, which provides a guarantee for the safe and stable operation of lithium battery energy storage systems, and summaries the conclusions as follows: (1) Explosion-proof valve strain changes with the change of SOC and temperature rise of the battery, the explosion-proof valve strain changes with the SOC and monotonically increasing respectively, and with the charging and discharging cycle in the safe state and cyclic changes. (2) Battery overcharging process explosion-proof valve strain will appear three inflection points, in order to symbolize: overcharging began to occur, the battery began to produce a large amount of gas inside the battery, the battery side wall of the bulge; and these three inflection points are earlier than the explosion-proof valve open, up to about 600s ahead of time. (3) Based on the change rule of explosion-proof valve stress in normal condition and overcharging condition, an online early warning scheme based on explosion-proof valve strain gauges is proposed, in order to improve the accuracy of the early warning system, sliding window and data standard deviation are used to process the raw data, which can achieve the early warning of the characteristic gases about 500s ahead of the time, and has good generalization ability. Acknowledgments. This work was funded by National Natural Science Foundation of China (NSFC) Smart Grid Joint Fund Project "Safe and High Specific Energy Low-cost Lithium-Ion Phosphate Energy Storage System (U1966214)".

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References 1. Deng, Q.X.: Safety state of the art of Lithium-Ion battery energy storage system. Sino Foreign Energy 27(11), 93–99 (2022). (in Chinese) 2. Lai, Y.L., Yang, K., Liu, H., et al.: Review of safety warning methods for lithium-ion batteries. Energy Storage Sci. Technol. 9(6), 1926–1932 (2020). (in Chinese) 3. Scrosati, B., Garche, J.: Lithium batteries: status, prospects and future. J. Power Sources 195(9), 2419–2430 (2010) 4. Li, J., Wang, Q.S., Kong, D.P., et al.: Progress in safety evaluation of lithium-ion battery energy storage. Energy Storage Sci. Technol. 1–18 (2023). (in Chinese) 5. Wang, Z.J.: Research on the inflation problem of liquid soft packaged lithium-ion batteries. Tianjin University (2009). (in Chinese) 6. Huang, L., Jin, M.G., Cai, H.Q., et al.: Research on gas generation in polymer lithiumion batteries under different formation voltages. Electrochemistry 9(4), 387–392 (2003). (in Chinese) 7. Micael, N., Susana, N., Markus, S.D., et al.: Internal strain and temperature discrimination with optical fiber hybrid. J. Power Sources 410–411, 1–9, 15–31 (2019) 8. Sommer, L.W., Kiesel, P., Ganguli, A., et al.: Fast and slow ion diffusion processes in lithiumion pouch cells during cycling observed with fiber optic strain sensors. J. Power Sources 2015(296), 46–52 (2015) 9. Shi, Q.T.: Thermal stress analysis and thickness variation of lithium-ion batteries. Beijing Institute of Nonferrous Metals Research (2014). (in Chinese) 10. Mei, W.X.: Electrochemical force thermal coupling modeling and safe application of lithiumion batteries. University of Science and Technology of China (2022). (in Chinese) 11. Ren, W., Zheng, T., Piao, C., et al.: Characterization of commercial 18,650 Li-ion batteries using strain gauges. J. Mater. Sci. 57(28), 13560–13569 (2022) 12. Chen, S.Q., Wei, X.Z., Zhang, G.X., et al.: Mechanical strain signal based early warning for failure of different prismatic lithium-ion batteries. J. Power Sources 580 (2023) 13. Liu, B., Jia, Y., Yuan, C., et al.: Safety issues and mechanisms of lithium-ion battery cell upon mechanical abusive loading: A review. Energy Storage Mater. 24, 85–112 (2020) 14. Zhang, N., Tang, H.: Dissecting anode swelling in commercial lithium-ion batteries. J. Power Sources 218, 52–55 (2012) 15. Yamada, A., Chung, S.C., Hinokuma, K.: Optimized LiFePO4 for lithium battery cathodes. J. Electrochem. Soc. 148(3), A224–A229 (2001) 16. Cai, T., Valecha, P., Tran, V., et al.: Detection of Li-ion battery failure and venting with Carbon Dioxide sensors. eTransportation 7, 100100 (2021) 17. Zhang, X., Hao, F., Chen, H., et al.: Diffusion-induced stresses in transversely isotropic cylindrical electrodes of lithium-ion batteries. J. Electrochem. Soc. 161(14), A2243–A2249 (2014) 18. Sethuraman, V.A., Chon, M.J., Shimshak, M., et al.: In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation. J. Power Sources 195(15), 5062–5066 (2010) 19. Fu, R., Xiao, M., Choe, S.Y.: Modeling validation and analysis of mechanical stress generation and dimension changes of a pouch type high power Li-ion battery. J. Power Sources 224, 221–224 (2013) 20. Wu, B., Lu, W.: A battery model that fully couples mechanics and electrochemistry at both particle and electrode levels by incorporation of particle interaction. J. Power Sources 360, 360–372 (2017) 21. Xiao, X., Wu, W., Huang, X.: A multi-scale approach for the stress analysis of polymeric separators in a lithium-ion battery. J. Power Sources 195(22), 7649–7660 (2010)

614

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22. Li, W.T., Huang, B.H., Bi, Z.B.: Analysis and Application of Thermal Stress Theory, pp. 75– 76. China Electric Power Press, Beijing (2004). (in Chinese) 23. Xia, Q., Ren, Y., Wang, Z., et al.: Safety risk assessment method for thermal abuse of lithiumion battery pack based on multiphysics simulation and improved bisection method. Energy 75–76 (2023) 24. Wu, Y.K., He, J., Yang, L., et al.: Theoretical model and calculation method of Multiphysics simulation and multi-scale deformation of lithium-ion battery. Energy Storage Sci. Technol. 1–16 (2022). (in Chinese) 25. Ma, D.Z.: Multiphysics simulation coupled stress analysis of lithium-ion battery. Shanghai University of Engineering Science (2021). (in Chinese) 26. Gritton, C., Guilkey, J., Hooper, J., et al.: Using the material point method to model chemical/mechanical coupling in the deformation of a silicon anode. Model. Simul. Mater. Sci. Eng. 25(45005) (2017) 27. Sauerteig, D., Ivanov, S., Reinshagen, H., Bund, A.: Reversible and irreversible dilation of lithium-ion battery electrodes investigated by in-situ dilatometry. J. Power Sources 342, 939–946 (2017) 28. Shi, S., Lv, N.W., Ma, J.X., et al.: Comparison of effectiveness of different types of gas detection for overcharge safety warning of lithium-ion phosphate battery energy storage cabin. Energy Storage Sci. Technol. 11(08), 2452–2462 (2022). (in Chinese) 29. Wang, M.M., Sun, L., Guo, P.Y., et al.: Overcharge Thermal runaway characteristics of Lithium iron phosphate energy storage battery module based on online gas monitoring. High Voltage Technol. 47(1), 279–286 (2021). (in Chinese) 30. Huang, W.S., Feng, X.N., Yue, P., et al.: Early warning of battery failure based on venting signal. J. Energy Storage 59, 106536 (2023)

Research on High-Speed Uniaxial Stretching Method Based on Magnetic Pulse Drive Hao Shi(B) , Weihao Li, Shiyu Hao, Qiancheng Hu, Chengcheng Li, Ran An, Li Chen, and Xingwen Li State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China [email protected]

Abstract. During the launch of electromagnetic railguns, the deformation of high strain rate materials in armature and orbit will affect the orbital launch performance, and it is of great significance to study the instability mechanism of electromagnetic energy materials under high strain rate. This paper presents a novel approach for evaluating the high-speed behavior of metallic materials through the utilization of magnetic pulse drive. The proposed method involves employing the magnetic pressure generated by the magnetic pulse driver (MPD) to apply stress input pulses, enabling uniaxial tensile deformation of the material. To measure the stress-strain relationship of the specimen, the study utilizes high-speed cameras and digital image correlation (DIC) systems. High-speed cameras and digital image (DIC) systems are used to measure the stress-strain relationship of the specimen. At the same time, by establishing a finite element model, it was found that the strain rate can reach 2000 s−1 within a short time and maintain relative stability. Additionally, a tensile experiment was carried out under a charging voltage of 35 kV. The results demonstrated great consistency between the calculation results and the experimental values, which confirming the effectiveness of the proposed method. Keywords: Magnetic Pulse Method · High Strain Rate · Dynamic Tensile Testing · Electromagnetic Energy Materials

1 Introduction During the launch process of an electromagnetic railgun, vibrations occur between the armature and the rail, resulting in high-strain-rate plastic deformation of the armaturerail material interface. This degradation of the contact condition between the armature and rail can lead to material failure [1]. Therefore, studying the mechanical properties of electromagnetic materials under high strain rates is of significant importance for analyzing material instability during electromagnetic launch, placing higher demands on testing techniques for armature-rail materials under high strain rates. In the process of high-speed deformation, the mechanical properties of materials significantly differ from those under low-strain-rate conditions [2–4], indicating the strain © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 615–625, 2024. https://doi.org/10.1007/978-981-97-1064-5_67

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rate effect. Meyers [5] classified the strain rate range of 103 –104 s−1 as high-strain-rate deformation. Correspondingly, there are various types of dynamic mechanical testing methods. Tinius Olsen, a Norwegian company [6], invented a universal testing machine in the 19th century for testing the strength of concrete and metals, which has now evolved to provide testing strain rates as high as 1000 s−1 . Bruce et al. [7] proposed a novel tensile platform using servo-hydraulic specifically designed, it’s strain rate can reach 500 s−1 . High-speed tensile machines, widely used for material dynamic behavior testing, can perform tensile measurements under 1000 s−1 . Nonetheless, when these devices are used at near maximum speeds, the cost of conducting high-speed tensile tests on individual specimens is high. Theodore Nicholas [8] developed a split Hopkinson tension bar (SHTB) based on the Hopkinson pressure bar for higher strain rate tensile testing, which enables uniaxial stretching at strain rates of 1000 s−1 . Rammohan et al. [9] reviewed that the Hopkinson bar is typically applied for the mechanical property test of metals within strain rates exceeding 1000 s−1 . Nonetheless, conventional Hopkinson bars encounter challenges related to specimen mounting and immobilization, stress wave overlap, as well as slow triggering response [10, 11]. To ensure precise trigger regulate, Nie et al. [12] developed a novel electromagnetic split Hopkinson bar in which electromagnetic energy can be accurately triggered within microseconds. However, this method is challenging to implement as the strain gauges are susceptible to electromagnetic interference. Therefore, obtaining stable and accurate stress-strain relationships through Hopkinson bars remains complex. Zhang et al. [13] studied the dynamic behavior of 7075-T6 Al under ultra-high strain rates. They used an electronic universal testing machine and a split Hopkinson tension bar (SHTB) to achieve strain rates of 103 s−1 and extrapolated to obtain stress-strain relationships at higher strain rates. Therefore, for dynamic behavior testing of metallic materials at high strain rates, the experimental input load response is slow, the experimental cost is high, and it is not easily scalable, which hinders the study of dynamic instability mechanisms in electromagnetic materials. The objective of this paper is to introduce a methodology for evaluating the dynamic behavior of metallic materials under ultra-high speeds, enabling high-speed uniaxial tensile experiments on electromagnetic materials with strain rates ranging from 103 to 104 s−1 to evaluate the mechanical properties of armature-rail materials. The magnetic pulse method is a technique for generating controlled pressure pulses of microsecond duration. By connecting a pulse current generator (PCG) and a magnetic pulse driver (MPD) as an RLC circuit, the MPD generates magnetic pressure as a repulsive force acting on the specimen within an extremely short time, driving the tensile deformation of the specimen. This method has been widely used since the 1980s to reveal the high-speed dynamic behavior and fracture processes of brittle materials [14–16]. The limitation in strain rates is related to the design of the pulse current generator and the magnetic pulse driver. This method features fast, controllable, low-cost, and easily implementable input responses, providing experimental parameters for studying the dynamic instability mechanisms of electromagnetic materials at high strain rates. Therefore, this paper designs a magnetic pulse-driven high-speed tensile apparatus for metallic materials, records plastic deformation using high-speed cameras and a digital image processing

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system, and obtains strain and strain rate parameters of the materials. Numerical simulations are conducted using LS-DYNA to analyze and assess the variation of strain rate in the deformation history of the material and verify the accuracy of the apparatus.

2 Experimental Setup and Testing Method 2.1 Tensile Testing Apparatus The tensile testing apparatus is illustrated in Fig. 1. It primarily consists of a pulse current generator (PCG), magnetic pulse generator (MPD), tensile specimen, and fixtures for fixation and measurement. The right side of the elongated dumbbell specimen is fixed onto an insulated base using a clamping device. The left side is connected to a POM block (indicated in black), which is secured to the base with a groove to accommodate the MPD. Epoxy resin is filled between the MPD and the groove to ensure electrical insulation and act as a medium. The pulse current generator discharges current through a capacitor bank. When the current flows through the MPD, a magnetic field is generated around it, and the interaction between the current and the magnetic field produces magnetic pressure, which acts on the polyoxymethylene block, causing deformation in the tensile specimen. It is crucial to ensure uniform current distribution into both sides of the MPD. To prevent the non-planar motion of the free end on the left side from affecting the tensile region, the fixture above the specimen is made of smooth, insulated, and high-strength hard plastic board. The lower surface of the fixture is lubricated to minimize friction while maintaining contact with the specimen. The magnetic pressure can be estimated using Eq. 1 [13, 17]: Pm = kp

μ × 2

 2 I b

(1)

In the equation, μ is the magnetic permeability, I is the current flowing through the conductor, w is the width of the conductor, and k is a correction factor related to the geometry of the driver. As the frequency increases, the current distribution becomes non-uniform. The relationship between k and the ratio of the MPD width to the distance between them is shown in Fig. 2. [14] for the considered frequency. If the ratio is, then. Here, d is the distance between the MPDs. The thickness of the dielectric between the MPDs must be taken into account, as it affects the coefficient k and, consequently, the magnetic pressure. In our apparatus, the thickness of the dielectric is approximately 0.7 mm, and kp ≈ 0.85. The core of the pulse current generator is a high-voltage capacitor bank consisting of 3 capacitors connected in parallel, with a total capacitance C of 16 μF. The self-inductance L is 720 nH, and the maximum discharge energy is 20 kJ. The MPD has a thickness of 0.3 mm and a width of 10 mm. The discharge current is measured using a Rogowski coil, and its waveform is depicted in Fig. 3. The discharge current waveform exhibits strong damping, resembling a damped sinusoidal wave with a period of approximately 10 μs. By varying the charging voltage of the capacitors, the amplitude of the current can be adjusted, thereby affecting the magnetic pressure.

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Fig. 1. High strain rate tensile platform structure based on MPD.

2.2 Sample Design and Measurement Methods The designed sample dimensions are shown in Fig. 4. The central region of the sample is the tensile region, with a width of 2 mm, length of 6 mm, and rounded corners with a radius of 15 mm. The width of the other regions is 22 mm. The force measurement region is used to quantify the uniaxial tensile force. While undergoing the uniaxial tensile procedure, the tensile force is equal on any cross-section along the direction of tension. Therefore, the measurement of the tensile force (F) can be converted to the measurement of elastic strain in the force measurement region. Firstly, the elastic stress (σ) is calculated using Eq. 2. Then, the tensile force (F) is calculated using Eq. 3. Finally, by combining with the cross-sectional area of the tensile region, the stress in the tensile region can be calculated. σTure = εTure E

(2)

FTure = σTure Af

(3)

3 Tensile Experiment and Numerical Model To verify the efficacy of the developed high-speed tensile approach, a numerical model was constructed to analyze the distribution of strain and strain rate. Additionally, a magnetic pulse tensile test was conducted on AA7075 (1 mm) material.

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Fig. 2. Dependence of kp on ratio of MPD width to distance between its legs.

Fig. 3. Current waveforms of different discharge voltages of the pulse generator.

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3.1 Experimental Setup The experimental configuration comprises of a pulse current generator, a digital image correlation (DIC) measurement system, and a tensile platform, as shown in Fig. 5. The DIC measurement system includes a high-speed camera, a non-stroboscopic LED light, and a host computer. The high-speed camera captures speckle patterns from different regions to measure the plastic strain in the dumbbell region and the elastic strain in the force measurement region. The camera operates at a frame rate of 200,000 frames per second with an exposure time of 4.67 μs. To prevent damage to the experimental platform and measurement instruments caused by inertia after sample fracture, a cover plate is added above them as a recovery device. Multiple tensile experiments were conducted with a charging voltage set at 35 kV, resulting in a discharge energy of 10 kJ.

Fig. 4. Specimen dimension.

Fig. 5. Magnetic pulse high-speed stretching device.

3.2 Numerical Simulation Model To verify the viability of the magnetic pulse tensile method, finite element simulation was performed using LS-DYNA R11 to analyze the mechanical behavior of the sample under magnetic pulse-driven tension. Figure 6 illustrates the geometric structure and configuration of the finite element model used in the simulation. To simplify the calculations, zero displacement conditions

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were applied to the fixed portions. The pressure pulse P was calculated using Eq. 1, and its waveform is shown in Fig. 7. The AA7075 specimen was modeled using the Johnson-Cook material model, considering the effects of strain rate, strain, and strain hardening:  • •    (4) σy = A + B · εn 1 + C · ln ε / ε0 •

where: represents the strain rate, ε represents the reference strain rate, A is the initial yield 0

stress at the reference strain rate and reference temperature, B is the strain hardening modulus and n is the hardening exponent of the material, C is the strain rate hardening parameter. Specific parameter settings are shown in Table 1. Table 1. AA7075 specimen material parameters Sample material parameters. Parameters

Values

Density (kg*m−3 )

2770

Poisson’s ratio

0.33

Young’s modulus (GPa)

71

Reference strain rate (s−1 )

0.001

A (MPa)

473

B (MPa)

210

n

0.3813

c

0.033

Fig. 6. Numerical model of dynamic tensile

4 Results and Analysis For the designed tensile apparatus, the strain and strain rate during the stretching process play a crucial role in verifying its effectiveness. We processed the high-speed camera data using DIC (Digital Image Correlation) system to obtain the strain and strain rate curves during the tensile process of the specimens.

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Figure 8 presents the strain-time curves obtained from both simulations and experimental measurements during the tensile process. The simulation results show a high level of agreement with the experimental results. The simulation demonstrates that as the voltage increases, the accumulated strain decreases, and the ultimate strain decreases as well, which is consistent with the phenomenon observed in the tensile experiments mentioned in reference [18]. This is because with the increase in voltage, the amplitude of the magnetic pressure pulse increases, thereby increasing the strain rate during stretching. For aluminum alloys, they exhibit strain rate sensitivity, meaning that at high strain rates, as the strain rate increases, the material strength and hardness typically increase, but the toughness and ductility decrease, resulting in a decrease in the ultimate strain.

Fig. 7. Output pressure pulse by MPD.

A well-designed tensile apparatus should ensure that the strain rate of the specimen remains relatively stable during the stretching process for a certain period of time. Figure 9 illustrates the relationship between strain rate and time obtained from simulations and experiments with a charging voltage of 35 kV, showing excellent consistency between the two. From Fig. 9, we can observe that plastic strain starts to accumulate at around 100 μs and ends at approximately 200 μs. During this period, the strain rate remains relatively stable at around 2000 s−1 .

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Fig. 8. Strain-time curve.

Fig. 9. Strain rate-time curve.

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5 Conclusion This article presents a method for dynamically stretching metal materials at high strain rates using the magnetic pulse technique, providing an effective experimental approach for analyzing the mechanical properties of electromagnetic materials under ultra-high strain rates. Experimental results demonstrate that controlled stress input can be achieved by utilizing the magnetic pulse method, enabling the testing of metal materials at relatively stable high strain rates within a short period of time. The strain, strain rate, and other relationships during the stretching process can be obtained. The use of high-speed cameras and DIC (Digital Image Correlation) systems ensures accurate measurements while avoiding electromagnetic interference. Finite element analysis results show good agreement between the strain, strain rate, and experimental results. Under a charging voltage of 35 kV, a stable strain rate of 2000 s−1 can be achieved, meeting the requirements for uniaxial tensile testing. The strain rate can be controlled by adjusting the discharge energy of the pulse current generator. Moreover, the small and easily implementable design of this apparatus allows for future application of current loading during the stretching process, creating an equivalent extreme multi-physical field environment for electromagnetic emission. This enables research on the constitutive relationships of electromagnetic materials under coupled multi-field conditions and provides data support for the study of failure mechanisms of railgun materials under extreme electromagnetic emission environments.

References 1. Ma, W., Lu, J.: Research status and challenges of electromagnetic emission technology. Trans. China Electrotech. Soc. (2023). (in Chinese) 2. Yan, S., Yang, H., Li, H., Yao, X.: A unified model for coupling constitutive behavior and micro-defects evolution of aluminum alloys under high-strain-rate deformation. Int. J. Plast. 85, 203–229 (2016) 3. Mirone, G., Barbagallo, R.: How sensitivity of metals to strain, strain rate and temperature affects necking onset and hardening in dynamic tests. Int. J. Mech. Sci. 195, 106249 (2021) 4. Nagarajan, S., Gurao, N.P., Parameswaran, V.: On the kinetics of texture development in Al-Mg alloy under high strain rate tension. Mater Charact 163, 110303 (2020) 5. Meyers, M.A.: Dynamic Behaviors of Materials. Wiley, Manhattan (1994) 6. Baumgartner, H.: Tinius olsen and his little giant. Mech. Eng. 119(2), 80–81 (1997) 7. Bruce, D.M., Matlock, D.K., Speer, J.G., et al.: Assessment of the strain-rate dependent tensile properties of automotive sheet steels. SAE Technical Paper (2004) 8. Nicholas, T.: Tensile testing of materials at high rates of strain: an experimental technique is developed for testing materials at strain rates up to 103 s− 1 in tension using a modification of the split Hopkinson bar or Kolsky apparatus. Exp. Mech. 21(5), 177–185 (1981) 9. Rammohan, Y.S., Pradeep, M.S.: Split Hopkinson pressure bar apparatus for compression testing: a review. Mater. Today Proc. 5(1), 2824–2829 (2018) 10. Wang, S., Flores-Johnson, E.A., Shen, L.: A technique for the elimination of stress waves overlapping in the split Hopkinson pressure bar. Exp. Tech. 41, 345–355 (2017)

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11. Ma, H., Mao, W., Su, H., et al.: Rate-related study on mechanical properties and fracture characteristics in aluminium alloy via electromagnetic ring expansion test. Int. J. Mech. Sci. 209, 106712 (2021) 12. Nie, H., Suo, T., Wu, B., et al.: A versatile split Hopkinson pressure bar using electromagnetic loading. Int. J. Impact Eng 116, 94–104 (2018) 13. Fengge, Z., Jinhua, C., Guangwei, L., et al.: Analytical solution of magnetic field for surfacemounted permanent magnet machines with anti-rotation dual rotors. Trans. China Electrotech. Soc. 26(12), 28–36 (2011) 14. Magazinov, S.G., Krivosheev, S.I., Adamyan, Y.E., et al.: Adaptation of the magnetic pulse method for conductive materials testing. Mater. Phys. Mech. 40(1), 117–123 (2011) 15. Krivosheev, S.I., Magazinov, S.G.: Irreducible specific energy of new surfaces creation in materials with crack-type macro defects under pulse action. J. Phys. Conf. Ser. 774(1), 012049 (2016) 16. Kanel, G.I., Razorenov, S.V., Fortov, V.E.: A failure wave phenomenon in brittle materials. Joint 20th AIRAPT–43th EHPRG, Karlsruhe/Germany (2005) 17. Ostropiko, E., Krivosheev, S., Magazinov, S.: Uniaxial high strain rate tension of a TiNi alloy provided by the magnetic pulse method. Appl. Phys. A 127, 1–7 (2021) 18. Wu, J.: Study on the effect and mechanism of electro-heat-high-speed effect on the deformation behavior of aluminum alloy in electromagnetic forming. Huazhong University of Science and Technology (2021). (in Chinese)

Research on Variable Droop Control Method for Improving Stability of Low-Voltage DC Distribution System Yantao Liu1,2 , Wei Deng1,2(B) , Xuekui Mao3 , Shiyi Zhang4 , and Wei Pei1,2 1 Institute of Electrical Engineering, Chinese Academy of Sciences, No. 6, Zhongguancun

North 2nd Road, Beijing 100190, China [email protected] 2 University of Chinese Academy of Sciences, No. 19, Yuquan Road, Beijing 100049, China 3 State Grid Beijing Haidian Power Supply Company, Beijing, China 4 State Grid Shanxi Marketing Service Center, Taiyuan, China

Abstract. Low voltage multi-terminal DC system is one of the important forms of future power grids, and its commonly used control method is droop control. This article proposes a variable droop control mode based on traditional droop control and applies it to low voltage multi-terminal DC systems. Variable droop control has a larger operating boundary and better stability compared to traditional droop control. Similar to traditional droop control, the variable droop control strategy and key system parameters are closely related to the small signal stability of the system. In order to verify the stability of low voltage multi-terminal DC system based on variable droop control, this paper constructs a Small-signal model of low voltage multi-terminal DC system based on variable droop control, and uses the analysis method of dominant eigenvalue to study its stability and operating boundary. Validate through Matlab/Simulink simulation models, and compare the low voltage multi-terminal DC system based on variable droop with the low voltage multi-terminal DC system based on traditional droop. The results indicate that the variable droop control proposed in this paper has higher stability compared to traditional droop control. Keywords: Multi-terminal flexible DC · Variable droop control · Small signal stable · Eigenvalue analysis

1 Introduction As environmental problems have become increasingly severe and traditional energy sources have gradually been exhausted, distributed energy systems have become one of the directions for energy transformation with their advantages of high primary efficiency, strong complementarity, and nearby consumption. Distributed energy sources connected to the large power grid through DC can reduce commutation links and improve efficiency. [1] However, since the current power grid system is still dominated by AC loads, AC-DC © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 626–633, 2024. https://doi.org/10.1007/978-981-97-1064-5_68

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hybrid will still be one of the important forms of the power grid in the future. Multiterminal DC systems generally use VSC (Voltage Source Converter) to connect the DC system and AC network. Various types of loads within the DC system are connected to the DC bus by DC-DC converters. Compared with traditional AC power grids, multi-terminal DC systems have a high degree of power electronics, and the interaction mechanism between power electronic devices and networks is also more complex. Aiming at the stability problem of multi-terminal DC systems, relevant scholars have carried out a series of research work. Droop control is the most typical and widely used multi-terminal VSC (Voltage Source Converter) power coordination control method. It has received a lot of attention and application in recent years. Literature [2] proposes an active power balancing control strategy, which reduces the VSC transmission power deviation in traditional linear droop control. Literature [3] proposes a droop control strategy that can realize voltage adjustment without difference, and realizes voltage control without difference in low-voltage multi-terminal DC systems under different operating conditions. Literature [4] proposed a load current sharing control strategy based on active voltage disturbance for parallel operation of multiple VSCs to achieve the purpose of power distribution and voltage control of DC microgrid. Literature [5] studied the influence of system parameters on the stability of DC microgrid systems under different network structures. The small signal stability of multi-terminal DC systems based on variable droop control remains to be studied. The improved control method may have negative effects on the stability of the power grid. Therefore, the small signal stability problem of relevant optimized control methods needs to be studied urgently. This article will study the impact of the introduction of variable droop control on the stability of multi-terminal DC systems, use the eigenvalue analysis method to draw the root locus, and analyze the key factors and parameters that affect system stability. Finally, the validity of the relevant research results is verified through Matlab/Simulink simulation.

2 Variable Droop Control Method This paper proposes an optimization method of variable droop control based on droop control. A variation factor is introduced, which combined with the droop factor allows the droop coefficient to change in real time with the total system load. Its specific control principle diagram is shown in Fig. 1. P is the DC side power value, and Pref is the power reference value. U dci is the DC side voltage value, and U ref is the DC voltage reference value. V sd is the d-axis component of the three-phase AC grid voltage. k i is the droop coefficient, k p1 , k i1 , k p2 , k i2 are the outer loop proportional coefficient, outer loop integral coefficient, inner loop proportional coefficient and inner loop integral coefficient respectively. idref , V cdref are respectively the reference value of the inner loop controller and the modulation signal output by the controller under the dq coordinate axis [6]. Ps is the introduced variable factor, and its specific calculation value is shown in Eq. 1. Ps =

Pload Pref

(1)

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Fig. 1. Schematic diagram of variable droop control

Pload is the total DC bus load of the system, which is the dispatch signal of the total power demand of the DC bus. The introduction of this value can dynamically adjust the droop coefficient through dispatch instructions, that is, variable droop control. ki = −

Uref − Umin Pref − Pmax

(2)

Equation (2) is the calculation formula for the droop coefficient of droop control. U min is the minimum DC voltage allowed by the system; Pmax is the maximum active power transmitted by each station [7, 8]. The droop coefficient of DC variable droop control used in this article is to add a coefficient based on power scheduling instructions to the droop coefficient of traditional droop control, as shown in Eq. (3). kiv =

ki Uref − Umin = Ps (Pref − Pmax )Ps

(3)

In the above formula, k iv is the variable droop coefficient of the i-th VSC. The voltage and power of each converter station satisfy Eq. (4). Udci − Uref = kiv (P − Pref )

(4)

The PWM control signal of the variable droop control output above acts on VSC, and the VSC topology is shown in Fig. 2.

Fig. 2. Topology of VSC

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According to the above VSC topology, its mathematical model under the dq coordinate axis can be constructed as [6] dXi = Ai Xi + Bi Ui dt

(5)

X i , U i are the state vector and input vector of VSC respectively, X i = [U dci idi wp wd ], U i = k i .

3 Research on System Stability Improvement Under Variable Droop Control 3.1 System Analysis Model The research object of this article is a low-voltage multi-terminal DC system based on variable droop control [6].

Fig. 3. Topology diagram of mult-terminal DC system

In terms of circuit modeling, this article uses the equivalent circuit of type π. The corresponding small signal model can be obtained as 1 dIi = (Um − ri Ii − Un ) dt li

(6)

The total load mathematical model of the DC bus in Fig. 3 can be expressed as Cdc

dUdc Pbess + Pload − PDG = idc1 + idc2 + idc3 − dt Udc

(7)

By linearizing Eq. (7), the small signal model can be obtained as dUdc 1 Pbess0 + Pload0 − PDG0 = (idc1 + idc2 + idc3 + Udc ) 2 dt Cdc Udc0

(8)

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By combining the above small signal models of VSC, DC branch, and DC bus load, the global small signal model of the multi-terminal DC system can be obtained. dX = AX + BU (9) dt In the formula, the state variable of the system is X = [X 1 X 2 X 3 U dc idc1 idc2 idc3 ]; the input variable U = [k 1 k 2 k 3 ]. 3.2 Dominant Characteristic Root Analysis Table 1 lists the system parameters. Calculate all characteristic values of the system when the total load is 80kW, as shown in Table 2. Table 1. System basic parameters parameters

value

parameters

value

r line /(/km)

0.091

L line /(mH/km)

0.245

l 1 /km

0.5

l 2 /km

0.5

l 3 /km

0.5

U ref /V

800

P1ref /kW

40

P2ref /kW

50

P3ref /kW

60

Pbess /kW

10

C 1 /mF

1

C 2 /mF

1

C 3 /mF

1

C dc /mF

0.5

Rs /m

0.001

L s /H

0.002

PDG /kW

10

k1

2.5 × 10–3

k2

2.5 × 10–3

k3

2.5 × 10–3

Table 2. System eigenvalues (80 kW) eigenvalues

real part

imaginary part

eigenvalues

real part

imaginary part

λ1, λ2

−61.41

± 7.57 × 103

λ3, λ4

−49.24

± 1.10 × 103

λ5, λ6

−48.37

± 3.11 × 103

λ7, λ8

−48.37

± 3.11 × 103

λ9

−171.90

0

λ10

−501.27

0

λ11, λ12

−501.27

0

λ13, λ14

−15.22

0

λ15, λ16

−124.82

0

3.3 Stability Improvement Research The research goal of this paper is to compare the stability of multi-section DC systems based on variable droop control and traditional droop control. It is necessary to compare

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the maximum load at which the two systems can maintain small signal stability under the same line parameters, that is, the stable operation boundary of the system. For this system, we can change Pload and observe the changes in the dominant eigenvalues. When the eigenvalues cross zero, Pload is the stable operating boundary of the system [9]. Calculate the eigenvalues and stable operation boundaries based on the line parameters in Table 1, using the gradual increase Pload method, 200 sets of dominant eigenvalues can be obtained. By observing the eigenvalues Part of the specific numerical value to judge the stability of the system. In order to facilitate observation, the load-eigenvalue real part curve can be drawn [10]. System Eigenvalue Trajectories and Operating Boundaries for Variable Droop Control It has been known above that the pole that plays a dominant role in the stability of the system is λ1 ~ λ8 . Figure 5 (a) shows the moving trajectories of the eight eigenvalues when Pload changes. It can be seen from the changing trend of the eigenvalues in the figure that as Pload continues to increase, the dominant eigenvalue of the system moves along the real axis toward the positive semi-axis. When Pload increases to a certain value (stable operation boundary), the real part of the eigenvalue will crossing zero. However, this figure can only observe the operating trend of the eigenvalues, and cannot quantitatively observe which eigenvalue crosses zero first, so the load-eigenvalue real part curve can be drawn as shown in Fig. 5 (b) (Fig. 4).

(a)

(b)

Fig. 4. Variable droop control (a) Eigenvalue trace (b) Load-Eigenvalue Real Part Curve

It can be clearly observed that the first eigenvalue to cross zero is λ5 ~ λ8 . The stable operation boundary of the system can be obtained as Pload = 110 kW. System Eigenvalue Trajectories and Operating Boundaries of Traditional Droop Control The real part of λ3 , λ4 first crosses the imaginary axis, and its operating boundary is 100 kW. It can be clearly seen from the comparison between Fig. 5 (b) and Fig. 6 (b) that when the other line parameters are the same, compared with the droop control, the change of the droop factor in the variable droop control causes the change speed of the real parts of the two poles λ3 , λ4 of the system to slow down, corresponding to the slope of the

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(a)

(b)

Fig. 5. Droop control (a) Eigenvalue trace (b) Load-Eigenvalue Real Part Curve

load-real part curve of the two eigenvalues becomes smaller, which in turn causes the zero-crossing point to shift to the right.

4 Simulation The above calculation of the operating boundary shows that under the same line parameters, variable droop control has a larger load variation range than traditional droop control, so the small signal stability of the multi-terminal DC system using variable droop control is better. In order to verify the accuracy of the above analysis, this article built a simulation model on the Matlab/Simulink platform for verification based on the line parameters in Table 1. The two systems are stably operated at 90 kW, and a small signal disturbance is added to the system at t = 0.3 s, that is, the power rises to 105 kW. The DC bus voltages of the two systems are observed as shown in Fig. 6.

(a)

(b)

Fig. 6. DC Bus Voltage (a) variable droop control (b) droop control

Observing the DC bus voltage change curves when variable droop control and droop control are used under the same line parameters, it can be clearly seen that the system is in a stable state before 0.3 s. After adding a small signal disturbance at 0.3 s, the droop control is adopted. The system cannot withstand this disturbance and the voltage becomes unstable. Multi-terminal DC systems using variable droop control can still maintain stable operation after small signal disturbances.

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5 Conclusion This paper proposes an optimization strategy based on droop control. By establishing its small signal model, the matrix is obtained, and the dominant eigenvalues are determined based on the analysis of participating factors. The operating boundary is calculated through the dynamic analysis of the characteristic values and compared with the droop control. Theoretically, it shows that it has higher stability than the droop control. With the help of Matlab/Simulink simulation, it is verified that the multi-terminal DC system using variable droop control has higher stability than the multi-terminal DC system using droop control. The variable droop method proposed in this article is analyzed at the small signal stability level of the system, and is of great value for improving the VSC control method of multi-terminal DC systems. Acknowledgments. This work is supported by National Natural Science Foundation of China (52177122).

References 1. Xu, D., Liu, Y., Wu, J.: Transactions of China Electrotechnical Society 30(17), 1–12 (2015). (in Chinese) 2. Li, Z., Li, Z., Lu, Y., et al.: Multiterminal flexible dc power active power balance coordination control strategy. Automation of electric power systems, Lancet (17), 117–124 (2019). (in Chinese) 3. Zhu, H., Li, Y., Wang, Z., et al.: MMC-MTDC coordinated sag control strategy considering DC voltage differential regulation. Electric Power Automation Equipment 38(7), 196–199 (2018). (in Chinese) 4. Tong, Z., Wu, J.-W., Ma, S., et al.: Transactions of China Electrotechnical Society 34(24), 5199–5208 (2019). (in Chinese) 5. Zhu, X., Li, Z., Meng, F.: Stability analysis of DC microgrid based on different grid structures. Chin. J. Electr. Technol. 36(1), 166–178 (2021) 6. Wu, Q., Deng, W., Tan, J., et al.: Stability Analysis of Multi-terminal DC System Based on Sag Control. Transactions of China Electrotechnical Society (2021). (in Chinese) 7. Kapat, S.: Small-signal analysis of parallelly connected buck converters and nonlinear droop control design for ultra-fast transient performance in DC microgrids. In: 2022 IEEE 1st Industrial Electronics Society Annual On-Line Conference (ONCON), Kharagpur, India, pp. 1–6 (2022) 8. Conte, F., D’Agostino, F., Massucco, S., Silvestro, F., Grillo, S.: Small-signal stability analysis of a DC shipboard microgrid with droop-controlled batteries and constant power resources. In: 2021 IEEE Power & Energy Society General Meeting (PESGM), Washington, DC, USA, pp. 1–5 (2021) 9. Tabari, M., Yazdani, A.: A mathematical model for a droop-controlled DC distribution system with a large number of DC-DC converters. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE), Montreal, QC, Canada, pp. 3367–3371 (2015) 10. Braitor, A.-C., Konstantopoulos, G.C., Kadirkamanathan, V.: Power sharing of parallel operated DC-DC converters using current-limiting droop control. In: 2017 25th Mediterranean Conference on Control and Automation (MED), Valletta, Malta, pp. 528–533 (2017)

Electromagnetic Performance Analysis of PM Linear Synchronous Motor with Star-Delta Windings Ma Mingna(B) , Wang Lei, and Zhang Xin School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230000, China [email protected]

Abstract. In order to achieve high thrust density and dynamic performance, this study investigates design criteria and electromagnetic characteristics of a permanent magnet (PM) synchronous linear motor with star-delta winding. Firstly, analytical model of armature magnetic potential harmonics and winding inductance is established. Next, electromagnetic characteristics are calculated by finite element method. Simultaneously, inductance waveform characteristics considering end effects with different pole-slot combinations are analyzed respectively, and then design criteria for hybrid windings are summarized. Finally, experiment of 14-pole, 12-slot linear motor is carried out to validate analysis results. Keywords: Star-delta winding · inductance · thrust · end effect

1 Introduction PM linear motors have the advantages of high thrust density, high efficiency, and good dynamic performance, so they have been widely applied in industrial automation, manufacturing equipment, and new energy fields [1–5]. The constantly expanding application fields have put forward higher performance for linear motors, so new materials and structure are emerging. As well known, motor performance is largely determined by armature winding, hence more efficient windings are being explored. A novel unequal turn winding technology was proposed in [6], and the finite element simulation results showed that it can eliminate specific order magnetomotive force harmonics. In [7], an asymmetric stator slot is present to suppress the first order winding tooth harmonic. Reference [8] a star-delta hybrid winding is discussed and the results show that this winding can effectively eliminate stator magnetomotive force harmonics. The armature magnetic potential harmonics with Y-delta connection winding are analyzed in [9]. Meanwhile, according to [10], it can be seen that multi-layer star delta hybrid windings can increase torque density. However, star-delta windings can only be fully utilized in specific pole-slot combination [11]. Due to finite length of primary and secondary, magnetic field distribution of armature winding is different from that of

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rotating motors. The applicability of star-delta winding in PM linear motors should be examined in details. In this paper armature magnetic potential harmonics of star-delta winding and inductance considering end effects are analyzed theoretically. Subsequently, thrust performance of star-delta winding linear motor with different pole-slot combinations discussed by finite element method. A comparative study of inductance parameters was conducted to summarize the design criteria for hybrid windings. Finally, experiment on prototype to verify the effectiveness of analysis conclusions.

2 Topological Characteristics of Star-Delta Winding The traditional winding connection methods can be divided into two types: star connection and delta connection, and the star-delta hybrid connection winding can also be divided into two types: internal star external delta and internal delta external delta, as shown in Fig. 1.

(a) Internal star external delta

(b) Internal delta external delta

Fig. 1. Two forms of star-delta windings.

If three-phase current in star part winding is expressed as: √ ⎧ ⎨ IAX = √ 2I sinωt  IBY = √2I sinωt − 23 π  ⎩ ICZ = 2I sin ωt − 43 π According to Kirchhoff’s law, the current in delta part can be expressed as: ⎧  2 1/2   1 ⎪ ⎨ IXY = I 3  sin ωt + 6 π  1/2 IYZ = I 23 sin ωt − 23 π + 16 π ⎪     ⎩ 1/2 IYZ = I 23 sin ωt − 43 π + 16 π

(1)

(2)

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3 Armature Magnetic Potential Harmonics and Winding Inductance Model 3.1 Harmonic Analysis of Armature Magnetic Potential If the total number of slots is Z, and the number of pole pairs is p, then the slot number per phase per poles is q=

Z c q =b+ = 2pm d d

(3)

where, m is the number phases, c and d are coprime integers, and q’ is the equivalent number of slots per phase per pole. It satisfies q = qd = bd + c

(4)

If there is a maximum common divisor t between Z and p. t = Z/p = Z0 /p0

(5)

where Z 0 is an integer multiple of m, the slot number Z 0 and pole number P0 is called a unit motor, and the proposed motor consists of t unit motors. When the star-delta windings is adopted, the equivalent number of slots per phase per pole is divided into two parts as q = qY + q

(6)

The fundamental distribution factor at this time is calculated as follows Kd

sin qY2α1 + sin q2α1 = (qY + q ) sin α21

(7)

According to (1) and (2), the amplitude of the star part winding current and the delta part winding current satisfy as √ IiY = 3Ii (8) The phase advance π/6 electrical angle of delta part winding current to star part winding current. To ensure the consistent of magnetic electromotive force amplitude, it can be satisfied. NY IiY = N Ii

(9)

Therefore, the number of turns of the two parts of the winding needs to meet √ N = 3NY (10) The A-phase winding is divided into two parts: A1 and A2. The coil turns of A1 are Nc1, and that of A2 are Nc2. According to the theory of winding functions, the Fourier series of windings functions of phases A1 and A2 can be expressed as   ∞ π

kπ kπ 4Nc1 x = sin sin x (11) NA1 τ kπ 12 τ k=1,3,...

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NA2

∞ π

x =− τ

k=1,3,...

  kπ x 1 4Nc2 sin sin kπ − kπ 12 τ 6

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(12)

Here, x is windings position, τ is pole pitch, the 5th harmonic is a negative value used to explain the harmonic sequence. Similarly, the magnetic electromotive force generated by armature winding can be expressed as ∞

F1p (x, t) = −

k=1,−5,7,... ∞

F2p (x, t) = −

k=1,−5,7,...

  kπ kπ 6Nc1 Im1 sin · cos x − ωt kπ 12 τ

(13)



   kπ kx 1 π 6Nc2 Im2 sin · cos π − − ωt − (14) kπ 12 τ 6 6

The total magnetomotive force is obtained as Ftp (x, t) = F1p (x, t) + F2p (θ, t) =





 kπ kπ 12Nc1 Im1 (k − 1)π (k − 1)π sin · sin · sin x − ωt − kπ 12 12 τ 12

∞

k=1,−5,7,...

(15)

Based on the above analysis, Taking 14 pole, 12 slot as an example, in star connection, q’ = 2,k d = 0.9659, k p = 0.9659, k w = 0.9330.While in star-delta connection, qY = qΔ = 1, k’d = 1, k p = 0.9659, k w = 0.9330.The fundamental wave distribution factor has increased by 3.5%. Meanwhile, it can be seen from (15) that the star-delta winding can eliminate harmonics of υ = ±12k + 1(k = 0, 1, 2, ...). 3.2 Inductance Analysis Model Considering End Effect Based on the above analysis, inductance parameters are analyzed by a multi loop model. The multi-loop model of PM linear motor has its particularity: (1) This motor with less than 1 slot per phase per pole. A single slot spans two magnetic poles. (2) Due to longitudinal end effects, mutual inductance of coils at both ends of primary is very small, which results in asymmetric three-phase mutual inductance. Therefore, it is necessary to multiply it by a coil inductance weakening coefficient when inductance coefficient is calculated. The coefficient calculation process is as shown in Fig. 2. The coils in region c are located below the S pole, while the coils in regions a and b are located below the N pole. The areas of region b and c are equal, and the magnetic flux in the two regions cancel out each other, ultimately equivalent to only the magnetic flux in region a. Self-inductance coefficient L AΦ is derived as LAφ =

   

4 4 2N 2 τ l kyk kyj λdkj + λqkj cos(k − j)(γ + θm ) − jθ (m, n) A n) (m,    LA m n Pπ 2 kj + λdkj − λqkj cos(k + j)(γ + θm ) + jθ (m, n) k

j

(16)

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a

b

S

15

Fig. 2. Calculation of coil inductance weakening coefficient.

In Eq. (16), λdkj and λqkj is the air gap permeability coefficient of the k-th harmonic magnetomotive force on the d-q axis, which generates the j-th harmonic magnetic flux density, m and n represent the m and n coils of the phase winding from left to right, and ALA (m, n) is the inductance weakening coefficient of A-phase winding coils. θ m is electrical angle of the first coil in phase band, and θ (m,n) is the electrical angle at which the m coil leads the n coil. Table 1 lists ALA (m, n) with m and n. Similarly, the mutual inductance coefficient MAB and MAC are derived as shown in Table 2 and 3. Due to end effects, mutual inductance between AB phase at both ends is very small. Table 1. Coil mutual inductance weakening coefficient AMAB . n

m 1

2

3

4

1

10/14

−8/14

−10/14

8/14

2

−8/14

6/14

8/14

−6/14

3

−10/14

8/14

10/14

−8/14

4

8/14

−6/14

−8/14

6/14

Table 2. Coil mutual inductance weakening coefficient AMAB . n

m 1

2

3

4

1

−8/14

6/14

8/14

−6/14

2

10/14

−8/14

−10/14

8/14

3

0

−6/14

−8/14

6/14

4

0

0

10/14

−8/14

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Table 3. Coil mutual inductance weakening coefficient AMAC . n

m 1

2

3

4

1

6/14

6/14

−6/14

−6/14

2

−4/14

−4/14

4/14

4/14

3

−6/14

−6/14

6/14

6/14

4

4/14

4/14

−4/14

−4/14

4 Electromagnetic Performance 4.1 Analysis of Thrust Characteristics A 2D finite element model is established, and thrust characteristics of proposed motor with star-delta windings were analyzed.

(a) Comparison of electromagnetic thrust.

(b) Magnetic potential harmonics.

Fig. 3. Analysis results.

Figure 3(a) shows thrust waveform of traditional star and star-delta windings motors. It can be seen that average thrust with hybrid windings increased by 2.79%, and the thrust fluctuation decreased by 21.7%. The magnetic potential harmonic distribution of the motor under different connection methods is shown in Fig. 3(b).

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4.2 Inductance Parameters The end magnetic field using star connection and star-delta connection with different pole-slot combinations is shown below; The waveform diagrams of winding selfinductance and interphase mutual inductance of a 14 pole 12 slot linear motor are shown in Fig. 4 and Fig. 5 under two different conditions. The three-phase self- and mutual inductance with star connection and star-delta connection are shown in Table 4.

(a) Star connected

(b) Hybrid connection

Fig. 4. Magnetic density distribution at the end of 10 pole 12 slot motor

(a) Star connected

(b) Hybrid connection

Fig. 5. Magnetic density distribution at the end of 14 pole 12 slot motor.

Table 4. Inductance parameters (mH) Item

P14Z12S (star)

P1412S (star-delta)

P10Z12 (star)

P10Z12 (star-delta)

LA

8.91

8.68

8.61

8.58

LB

8.91

8.89

8.83

8.80

LC

8.71

8.57

8.52

8.47

M AB

−298.40

−281.08

−279.90

−275.75

M BC

−597.22

−541.99

−580.37

−529.07

M AC

−597.80

−542.47

−579.28

−530.60

Max./min.deviation of L

1.47% 0.79%

2.07% 0.34%

2.08% 0.50%

2.12% 0.43%

Max./min.deviation of M

40.06% 19.97%

38.25% 19.07%

41.60% 20.95%

38.05% 18.85%

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Table 5. Main design parameters of prototype.

Fig. 6. Experimental measurement of inductance

From Table 4, it can be seen that three-phase self- and mutual inductance are asymmetric, and the asymmetry of mutual inductance is greater than that of self-inductance. With the same pole slot coordination, the asymmetry using star connection are greater than that using star-delta connection. Small inductance parameters can improve the dynamic response ability of the motor, so using a hybrid winding connection for the motor can quickly adapt to external interference and load changes.

5 Prototype and Experiment Table 5 shows the main design parameters of prototype, while Fig. 6 shows the prototype and testing platform. A flat drive controller is used to provide AC power to the prototype, and the static thrust is tested using a locked mover method. The static thrust with calculation and compared in Fig. 7. They are in good agreement. The dielectric performance tester GCSTD-D from Crown Test Company was used to measure self-inductance, as shown in Table 6. The results indicate that the multi loop model with coil inductance weakening coefficient is more accurate in calculating phase winding inductance. Table 6. Comparison of inductance

(b) Inductance

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0

5

10

15

20

(a) Thrust vs current.

Fig. 7. Static thrust characteristic curve of the prototype

6 Conclusion The star-delta winding can increase winding factor for PM linear motor and suppress some magnetic electromotive force harmonics. By introducing a coil inductance weakening coefficient, inductance of linear motor can be accurately calculated. Through FEM and experiments, it is verified that star-delta windings can improve thrust density and the asymmetry of three-phase inductance. Acknowledgments. The work was supported by the National Natural Science Foundation of China under Grant 51977056 and Grant 51507043.

References 1. Sun, Y., Zhao, W., Ji, J., et al.: Overview of multi-star multi-phase permanent magnet machines with high torque performance and its key techologies. Trans. China Electrotech. Soc. 38(06), 1403–1420 (2023). (in Chinese) 2. Hong, J., Wang, S., Sun, Y., et al.: The influence of high-order force on electromagnetic vibration of permanent magnet synchronous motors. Trans. China Electrotech. Soc. 37(10), 2446–2458 (2022). (in Chinese) 3. Kou, B., Ge, Q., Zhang, H., et al.: Design and analysis of double-sided dislocated high speed permanent magnet linear synchronous motors. Trans. China Electrotech. Soc. 36(06), 1149–1158 (2021). (in Chinese) 4. El Refaie, A.M.: High speed operation of permanent magnet machines. The University of Wisconsin-Madsion, USA (2005) 5. Carraro, E., Bianchi, N., Zhang, S., Koch, M.: Design and performance comparison of fractional slot concentrated winding spoke type synchronous motors with different slot-pole combinations. IEEE Trans. Ind. Appl. 54(3), 2276–2284 (2018) 6. Chen, X., Wang, J.: Magnetomotive force harmonic reduction techniques for fractional-slot non-overlapping windings configurations in permanent magnet synchronous machines. Chin. J. Electr. Eng. 3(2), 102–113 (2017) 7. Ishak, D., Zhu, Z.Q., Howe, D.: Permanent-magnet brushless machines with unequal tooth widths and similar slot and pole numbers. IEEE Trans. Ind. Appl. 42(1), 584–590 (2005) 8. Abdel-Khalik, A.S., Ahmed, S., Massoud, A.M.: Low space harmonics cancelation in doublelayer fractional slot winding using dual multiphase winding. IEEE Trans. Magn. 51(5), 8104710 (2015)

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9. Chen, Z., Tang, J., Ma, H., et al.: Harmonic magnetomotive force analysis of multilayerwinding FSCW-PM machine with star-delta hybrid connection. Chin. J. Electr. Eng. 41(17), 6060–6071 (2021). (in Chinese) 10. Abdel-Khalik, A.S., Ahmed, S., Massoud, A.M.: Effect of multilayer windings with different stator winding connections on interior PM machines for EV applications. IEEE Trans. Magn. 52(2), 8100807 (2016) 11. Vansompel, H., Sergeant, P., Dupre, L., Bossche, A.: A combined wye-delta connection to increase the performance of axial-flux PM machines with concentrated windings. IEEE Trans. Energy Convers. 27(2), 403–410 (2012)

Design of Portable Rechargeable Plasma Generator Zicheng Wang, Zhongbo Hou, Jiayang Zhang, Qiaojue Liu(B)

, and Zhanhe Guo

School of Automation, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China [email protected]

Abstract. In order to meet the urgent needs of high-reliability portable plasma generators in many fields, this paper designs a portable atmospheric pressure air discharge plasma generator and tests its discharge performance. By using a high-voltage package to amplify the low-voltage pulse generated by the micro-arc lighter, and then multi-stage amplification by the voltage-doubling rectifier circuit, a high-voltage pulse generator with low input, high output, compact structure and repeatable charging is realized, which can effectively break through the air to form a blue-purple plasma arc. The purpose of this paper is to provide a convenient and rechargeable plasma generation scheme, which is oriented to industrial applications and can meet the needs of plasma applications in material insulation detection, short-time discharge, confined space discharge and other occasions. Keywords: Plasma generator · portable · atmospheric pressure discharges · voltage-doubling rectifier circuit

1 Introduction In recent years, plasma, as a new type of molecular activation means, has not only achieved good application results in the fields of exhaust gas treatment [1], material surface modification [2–4], but also been widely used in the fields of energy conversion, cancer treatment, and bacterial inactivation, which has received keen attention from researchers of various disciplines. Among them, the generation of plasma arc under atmospheric pressure [5] has the characteristics and advantages of simple generation device and easy operation, which has become a research hotspot at home and abroad in recent years. At present, the research on plasma arc mainly focuses on the two aspects of discharge mechanism and practical application, as shown in Fig. 1. The former is mainly carried out in four aspects, namely, plasma excitation power supply, plasma generating device, experimental diagnostic technology and numerical simulation; the latter is mainly concentrated in the fields of material processing, energy conversion, environmental treatment, biomedicine, aerospace and so on, focusing on the cross-fertilization between plasma and multidisciplinary disciplines [6]. At present, there are more in-depth studies on the principle design and practical application of plasma generators at home and abroad. In 2023, Aero environment Ltd. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 644–655, 2024. https://doi.org/10.1007/978-981-97-1064-5_70

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conducted research on a DC double-tube arc plasma generator [7], which has a simpler structure and wider range of application compared to a single-tube generator; in 2011, Jia Xianghong’s team at the Chinese Academy of Sciences studied a plasma generator applied to active protection against space radiation [8] design, the use of spiral waves to generate high-density plasma, successfully triggering the expansion of the magnetic field. At the same time, foreign groups have done a series of studies on the application of plasma generators in fields such as nanomaterial processing [9] and biomedical engineering [10]. However, domestic and foreign researches mainly focus on the plasma generator design for specific application scenarios as well as the design of high-power plasma generators, with less attention paid to the design of portable and rechargeable plasma generators, and even fewer researches on their load characteristics.

Fig. 1. Research hotspots in discharge mechanisms and practical applications of atmospheric pressure plasma.

This paper studies the plasma integrated generator device design program for the current plasma pulse excitation power supply generally exists in the large volume, discharging time is short and thus lead to bottlenecks like the use of power supply efficiency is low. The use of compact modular design significantly reduces the size of the power supply device. Meanwhile, the use of easy to replace the rechargeable module further improves the efficiency of the use of power supply. The plasma generator has the

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advantages of convenience, portability, rechargeability, integration, and etc., which can provide feasible solutions and technical support for the plasma discharge needs under space constraints, repeated discharges and other applications.

2 Device Design The structural design of the device part of the device body is shown in Fig. 2. As seen in the figure, the circuit part of the device adopts the acrylic glass hole plate as the circuit bottom plate to ensure the insulation of the device security; device support fixed part of the selection adopts the thickness of 4 mm acrylic side panels and 8 mm acrylic base plate to ensure the stability of the device; device switch and line part use hot melt adhesive on the line and the pulse generating circuits and the triggering switches for the limitation of the safety of the insulation distance to ensure that the device is to further ensure the reliability of the device. In the overall process of device design, under the premise of ensuring the stability of the device, insulation safety and the complete function of each module of the circuit, the volume of the device is minimized to the greatest extent to highlight its portability and integration.

(a) Front view

(b)dimensions of side

(c)bottom panels

Fig. 2. Front view of portable rechargeable plasma generator and dimensions of side and bottom panels of the unit.

The circuit design part of this device design is modularized as shown in Fig. 3, with the following three modules: pulse source generation module, boosting module, charging and discharging module.

Fig. 3. Circuit module diagram.

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The overall design of the circuit part seeks to meet the design objectives of the plasma generator device with minimized volume and portable integration, and its specific design parameters and indexes are shown in Table 1. Among them, the pulse source generation circuit is obtained by splitting the JOBON ZB-310 arc lighter, which mainly includes the pulse generation circuit, protection circuit, power supply circuit, and charging circuit. The power supply is provided by a 3.7 V lithium battery with a peak pulse output voltage of 3.28 kV, and the Micro-USB charging interface can be directly charged using a standard cell phone charger with 5 V/1 A. A single charge can be filled in 2 h, and the full state can be triggered 100 to 120 times, with a maximum discharging time of 15 s each time. Table 1. Main parameters of portable rechargeable plasma generator. Parameters

Numerical value

Device Size

12 × 17 × 26 cm

Charging Time

2h

Output Voltage Amplitude

30 kV

Average value of discharge current

50 mA

High voltage pulse frequency

14.7 kHz

Battery full state discharge times

100–120 times

Maximum discharge time

15 s

The high-voltage part is realized by a modified voltage doubling rectifier circuit, and the components used are shown in Table 2. Table 2. Models of components used. Typology

Model number

Quantity/pc

Diodes

2CLB15 kV-450 mA

18

1nF Capacitor

CT81-15 kV-2D4-102K

18

Considering the output voltage of this device, economic cost and device volume and other factors, a 9-stage voltage doubling rectifier circuit is finally adopted to realize voltage doubling. The improved voltage doubling rectifier circuit used in this paper differs from the traditional voltage doubling rectifier circuit by replacing the spark gap with a high-voltage power diode, which is equivalent to the traditional voltage doubling rectifier circuit, i.e., through the parallel charging and series discharging of high-voltage capacitors, the target output voltage with a peak value of about 30 kV is generated. In the actual experiments, the final measurement of the output voltage is 17.27 kV, which is lower than the target output voltage. According to the analysis, this is due to the

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design of the target output voltage of 30 kV is the no-load output voltage of the power supply, while the actual measurement of the resistive voltage divider measured for the load voltage. From the external characteristics of the power supply, it can be seen that there is a corresponding gap between the two due to the different loads. Among them, the voltage drop of the components used in the circuit and the partial pressure of the equivalent capacitance of the medium are also important factors.

3 Simulation Verification Based on Multisim software, the simulation verification of the improved voltage doubling rectifier circuit module of the device is shown in Fig. 4. As can be seen from the figure, 2CLB15 kV-450 mA diode and CT81-15 kV-2D4-102K 1nF capacitor are used to build the circuit, which constitutes a 9-stage voltage doubling rectifier circuit and the output voltage is measured by an oscilloscope, the results are shown in Fig. 5. As can be seen from the figure, the slope of the output voltage increase gradually slows down, and eventually tends to stabilize at about 29 kV, which is the theoretical output voltage stabilization value.

Fig. 4. Improved voltage-doubling rectifier circuit simulation circuit.

In order to obtain better experimental results, in the design of the peak output voltage, due to the room temperature conditions of the breakdown of 1cm of air requires a voltage of about 30 kV, taking into account the experimental demand and experimental conditions, the final device selected 30 kV for the desired peak output voltage. Obviously, the number of stages of the voltage doubling rectifier circuit will significantly affect the output voltage amplitude, so the same devices and circuit structure were used in the design of the 3-stage, 6-stage, 9-stage, 12-stage amplifier circuits were simulated and analyzed, and the simulation results are shown in Fig. 6. As can be seen from the figure, the peak output voltages of about 9 kV, 19 kV, 29 kV and 39 kV are obtained respectively. It can be seen that the simulation results obtained corresponding to the multiplication of the number of stages changed by multiples, and voltage doubling rectifier circuit with the increase in the number of stages, the doubling effect is affected by the capacitance and diode parameters, and the increase in its output voltage will gradually tend to saturation, in line with the simulation results, verifying the correctness of the boosting module

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Fig. 5. Improved voltage-doubling rectifier circuit simulation result.

circuit [11]. Therefore, in this paper, the amplifier circuit with 9 amplification stages is selected as the generator.

Fig. 6. Output voltage simulation results of different stages voltage-doubling rectifier circuit.

It is worth noting that the capacitance value used in the simulation circuit is also a key parameter of the output voltage [12], which can significantly affect its waveform, so this paper explores the effect of capacitance value on the output waveform based on the simulation circuit model using the control variable method. While keeping the rest of the conditions the same, the capacitance values of 0.1nF, 1nF and 10nF are selected respectively, and the 6-stage amplifier circuit is taken as an example to be simulated and analyzed in Multisim. As shown in Fig. 7, the magnitude

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of the output voltage tends to be stable and equal over time, and there is a significant difference in the time to saturation. It can be observed that the selection of capacitance of 10nF, the output voltage saturation time is the shortest, the selection of capacitance of 0.1nF, the output voltage saturation time is the slowest, in order to take into account the speed of boosting as well as security considerations, this paper ultimately selected the capacitance of 1nF for the design of the device.

Fig. 7. Output voltage simulation results of voltage-doubling rectifier circuits with different capacitance values.

According to the conclusions obtained from the simulation experiments, i.e., the effects of different number of stages and capacitance values on the magnitude of output voltage amplitude, transient process length, saturation degree, etc., the circuit model with different output voltage requirements can be designed. Overall, the circuit simulation results preliminarily verify the correctness of the design scheme.

4 Output Characteristics 4.1 Measuring Platforms In order to further measure the output characteristics of this plasma generator, a laboratory oscilloscope, a resistive-capacitive voltage divider, a high-voltage isolation probe, and a Roche coil are used to construct a comprehensive measurement platform for testing, as shown in Fig. 8. As can be seen from the figure, the output characteristics measurement platform can be divided into two parts: the discharge circuit and the measurement circuit. Among them, the measurement loop consists of an oscilloscope, a high-voltage isolation probe, a Roche coil and a resistive divider; the discharge loop consists of the main body of the plasma generator and a lithium battery. In voltage measurement, the device uses a resistive voltage divider (divider ratio of 1000:1) to measure the peak value of the

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output voltage, and uses a high-voltage isolation probe (model Tektronix P6015A) for voltage acquisition, and records the waveforms through the channels of a multi-channel oscilloscope (model RIGOL DS1104Z Plus); in the current measurement, it is only when the Roche coil (Model Pearson 6585) was used for current measurement to collect the discharge current and record the waveform through the oscilloscope channel.

Fig. 8. Schematic diagram of output characteristic measurement platform.

4.2 Output Voltage For better circuit design, an oscilloscope and a high-voltage isolation probe were first used to measure the output voltage waveform of the pulse generator chip, and the measured waveform is shown in Fig. 9(a), which produces a positive pulse with a frequency of 14.7 kHz, a peak pulse value of 3.28 kV, and a duty cycle of 10%, which is in line with theoretical expectations. Due to the high output voltage of the plasma generator, in order to prevent it from damaging the test instrument, a resistive voltage divider (model FRC-100 kV) was used to measure the output voltage, and the size of the peak output voltage was measured to be 17.27 kV, which is the voltage at both ends of the load. After considering the parasitic parameters existing in the actual device and the external characteristics of the power supply is basically consistent with the theoretical analysis of the target no-load voltage of 30 kV. In order to facilitate the observation of the output waveform, the output voltage is attenuated by a 1000x high-voltage isolation probe and displayed by an oscilloscope, and the results are shown in Fig. 9(b), where the peak voltage of each pulse fluctuation is about 7.4 kV and the average voltage is 6.5 kV.

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(a) Pulse generation circuit output waveform (yellow).

(b) Output voltage waveform (yellow).

Fig. 9. Output Waveforms.

It is worth noting that the peak output voltage measured using a resistive voltage divider is 17.27 kV, and the peak output voltage measured using an oscilloscope is 7.4 kV, and the results are inconsistent, which are analyzed for the following possible reasons: (1) The voltage measured by the resistive-capacitive voltage divider is an instantaneous voltage, and it takes time for the capacitor in the voltage doubling circuit to charge and discharge, so there is a transient measurement error. (2) The use of oscilloscope measurements, the output voltage through the cable into the oscilloscope, so that the impedance in the line can not be ignored, the measured voltage is less than the theoretical calculated value after voltage divider. 4.3 Discharge Current The discharge current of this plasma generator was measured with a Roche coil, and the waveform presented the pulse characteristics as shown in Fig. 10, which indicated that a number of discharge filament channels were generated when the plasma generator pierced the air, with an average current value of about 50 mA. Among them, the amplitude of each discharge current pulse was approximately the same, and the time intervals between the largest pulses were basically the same, which were between about 66 ms and 71 ms.

5 Load Effect The device uses a typical single dielectric blocking discharge structure when testing the load effect, as shown in Fig. 11. The output voltage of the discharging part of the device is connected to the high-voltage electrode and the ground electrode. The polyimide dielectric material with a thickness of 0.54 mm is placed on the ground electrode, and an electric field will be generated between the two metal flat plates after starting the device. Then the load characterization tests (1) and (2) are carried out separately to study the load effect under different dielectric blocking situations.

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Fig. 10. Discharge current waveform (blue).

Fig. 11. Single dielectric barrier discharge structure.

The load characterization experiment (1) used polyimide material with a thickness of 0.54 mm as an insulating dielectric, which was placed in the discharge platform. From Fig. 12(a), it can be clearly observed that a plasma flow injection discharge was formed between the upper and lower electrodes [13], and the discharge channel was brighter and accompanied by a clearer discharge sound. The polyimide material was penetrated by the discharge channel. Load Characterization Experiment (2) used a glass material with a thickness of 1 mm to replace the polyimide material as the insulating medium as shown in Fig. 13. The plasma was generated at the center of the glassmedium, and the discharge path developed along the surface of the glass plate and formed an ionic wind, which was ultimately bent at the edge of the glass plate, connecting the high-voltage and the ground electrode [14]. The experimental results are shown in Fig. 12(b), where it can be observed that as the electrode approaches the edge of the glass plate, a discharge along the surface occurs.

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(a) Polyimide material breakdown.

(b) Glass plate discharge along the surface.

Fig. 12. Load discharge effect.

Fig. 13. Surface discharge of glass dielectric [15].

6 Conclusions This device is designed as a portable rechargeable plasma synthesis generator composed of pulse voltage generating circuit, improved voltage doubling rectifier circuit composed of capacitor and diode, with charging and discharging circuit, which meets the needs of plasma application in the occasions of material insulation testing, short time discharge, and restricted space discharge, etc. The device is designed with innovative design features such as obtaining atmospheric pressure arc plasma, rechargeable battery renewal or replacement, discharge protection, portability, etc. Through the study of its loading characteristics, adjusting the gap and other operations to obtain atmospheric pressure arc plasma, the device has a high value of the application. The charging module provides Micro-USB charging interface, which can charge the 3.7 V lithium battery in real time, while the device is equipped with a two-terminal plug-in lithium battery interface, which can be used to replace the battery capacity according to the application occasions to cope with the sudden battery problems. The circuit design of the power switch and the protection switch meets the realization of the protection function of the discharge, which effectively improves the safety of the device. And the mechanical structure is designed to be smart and ensure the insulation safety performance, which is also easy to carry. The design of this device can be discharged many times in a limited space, with the advantages of small size, long endurance, easy to replace the battery and can be better adapted to the application scenarios. It is expected to be widely used in material

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insulation testing, heating and de-icing, water purification, etc. For example, it can be used as a simple material insulation testing device, which can flexibly adjust the number of effective voltage doubling and rectification circuit levels according to the target test voltage level. And it can be used as a simple arc plasma generator for laboratory use, which can flexibly adjust the parameter range, so that it is easy to cope with the experiments of different needs. Also, it is smart, safe and low-cost, which is very suitable for many applications in life. Acknowledgments. This work was funded by Central Universities’ Basic Research Operating Expenses Program (NS2023013) & National Natural Science Foundation of China Youth Program (51907089) &Youth Program of Natural Science Foundation of Jiangsu Province (BK20190421).

References 1. Ouyang, F., Wu, S., Liu, X., Guo, Y., Zhang, C.: Study of electric field diagnosis and propagation process of helium plasma in a tube. Chin. J. Electr. Eng. 41(17), 6116–6127 (2021). https://doi.org/10.13334/j.0258-8013.pcsee.201978. (in Chinese) 2. Zhu, Z., Wu, S., Bian, W., Gu, Y., Zhang, C.: Effects of transformer parasitic parameters and load characteristics on high-voltage pulse waveforms. Intense Laser Particle Beam 33(06), 65–73 (2021). (in Chinese) 3. Tang, S., Liu, Q., Wang, S., Guan, Y., Mu, H., Li, Q.: Advances in atmospheric pressure pulsed dielectric barrier discharge plasma research. Safety Health Environ. 19(07), 70–74 (2019). (in Chinese) 4. Zhang, X., Huang, G., Wu, S., Ouyang, F., Zhang, C.: Experimental study of discharge characteristics and induced gas flow in a three-electrode coplanar dielectric barrier discharge. Gas Phys. 6(02), 28–37 (2021). https://doi.org/10.19527/j.cnki.2096-1642.0840. (in Chinese) 5. Liu, X., Zhao, X., Liu, L., Wang, X., He, J.: Characteristics of the discharge channel during the relaxation process in the long air gap. Trans. China Electrotech. Soc. 36(2), 380–387 (2021). (in Chinese) 6. Mei, D., Fang, Z., Shao, T.: Current status of research on atmospheric pressure lowtemperature plasma characteristics and applications. Chin. J. Electr. Eng. 40(04), 1339– 1358+1425 (2020). https://doi.org/10.13334/j.0258-8013.pcsee.191615. (in Chinese) 7. Guo, Z., Liu, Z., Wang, S.: Performance study of a DC twin-tube arc plasma generator. Fusion Plasma Phys. 1–7 (2023). http://kns.cnki.net/kcms/detail/51.1151.TL.20230613.1609.008. html. (in Chinese) 8. Jia, X., Xu, F., Wan, J., et al.: Design of a plasma generator for active protection against space radiation. J. Vacuum Sci. Technol. 31(04), 481–484 (2011). (in Chinese) 9. Appl. Phys. A Mater. Sci. Process. 126(9), 1–29 (2020) 10. IEEE Trans. Plasma Sci. 48(9), 3054–3060 (2020) 11. Wu, S., Liu, X., Ouyang, F., Luo, Y., Guo, Y., Zhang, C.: Effects of applied voltage waveform on the uniformity of a microplasma array confined inside polydimethylsiloxane microchannels. Plasma Process. Polym. e2100164 (2021) 12. Chen, Y., Cai, Y., Shi, Y., Fan, R., Ji, L., Wang, W.: Influence of measured capacitance on discharge parameters of DBD reactors. High Voltage Technol. 46(08), 2960–2967 (2020) 13. Syssoev, V.S., et al.: Streamer discharge plasma generator. Inorganic Mater. Appl. Res. 13(5) (2022) 14. Dariusz, K., Daniel, N., Stefan, N.: Generation of negative air ions by use of piezoelectric cold plasma generator. Plasma 4(3) (2021) 15. Kogelschatz, U.: Dielectric-barrier discharges: their history, discharge physics, and industrial applications. Plasma Chem. Plasma Process.sma Process. 23(1), 1–46 (2003)

Research on Improved Disturbance Observation Method for Photovoltaic MPPT Control Haoran Li1 , Yupeng Xiang1 , Junhong Chen1 , Shitao Hao1 , Xiaopin Yang1(B) , Cui Wang1,2 , Bing Zeng1 , and Fanxing Rao1 1 Nanchang Institute of Technology, Nanchang 330099, China

[email protected], [email protected] 2 Jiangxi Engineering Research Center of High Power Electronics and Grid Smart Metering,

Nanchang 330099, China

Abstract. For the purpose of addressing the issue that the maximum power point tracking (MPPT) perturbation method of observation cannot realize both speed and accuracy, an improved perturbation observation method based on duty cycle is proposed in this paper, which tracks the maximum power point more quickly and accurately through the optimization of step size. It is minutely introduced the principle and implementation process of the revised algorithm and the viability of the proposed method can be seen from the simulation results. The improved disturbance observation method based on duty cycle can obviously have higher tracking accuracy than the traditional disturbance observation method on the basis of ensuring the tracking speed of the maximum power point, and can play a better role in ensuring the stability, accuracy and rapidity of the system, and achieve better results. Keyword: Duty cycle Maximum power point Perturbation observation method

1 Introduction As the requirement for renewable energy rises steadily, people’s environmental awareness is also rising. As a pollution-free, green and clean new energy, solar energy is favored by people. In terms of solar energy utilization, photovoltaic power generation is one of the best ways to use it, because of its convenient installation, no noise and low maintenance costs, so more and more People’s concerns. Due to external factors such as the weather, the voltage and current output of the power generation system will fluctuate, leading to unstable system operation. The main use of photovoltaic MPPT (maximum power point tracking) technology is to improve the stability of the system, in which the disturbance observation rule is one of the most used methods in photovoltaic MPPT. In recent years, more intelligent algorithms have been applied to the perturbation observation method, but the intelligent algorithms have obvious deficiencies in the calculation speed. Based on the concept of the duty cycle, the traditional interference observation method is improved in order to make the method both fast and accurate. From the simulation results, it can be seen that the improved disturbance observation method has a great convergence effect, which can provide a good basis for system control and loss reduction [1–3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 656–663, 2024. https://doi.org/10.1007/978-981-97-1064-5_71

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2 Perturbation Observation Method The basic principle of the PV MPPT disturbance observation method is that by applying disturbance to the input voltage of the PV cell and the maximum power point can be found by observing the change process of the output power [4, 5]. The flowchart of the algorithm is shown in Fig. 1. Among them, U and I are the output voltage and current measurements of the PV array, P is the output power, k and k-1 are the current measured value and the last measured value, respectively. The principle of operation is to periodically perturb the output voltage U of the photovoltaic cell, for example, by applying a small fluctuating voltage signal U to the reference voltage Vref, PV battery output power P will also change accordingly. By sampling and processing P, a power value with periodic fluctuations is obtained, and by measuring and analyzing the fluctuations of the power value, it is possible to identify the voltage value, which is equivalent to the maximum power point, and then to adjust it by constant photovoltaic cell output voltage U, the power can be brought infinitely close to the point of maximum magnitude. Finally, the voltage U of the photovoltaic cell is controlled, it can always be maintained at the maximum power point. Therefore, the efficiency of photovoltaic power generation systems can be maximized [6–8].

Fig. 1. Traditional perturbation observation method

2.1 Duty Cycle Disturbance Observation Method The duty cycle perturbation observation method, which is improved by the traditional perturbation observation method, is to regard the applied small-amplitude fluctuation voltage signal as the duty cycle signal. By changing the duty cycle to control the IGBT turn-on and turn-off signal, thus, The output voltage of the photovoltaic cell is controlled to optimize the efficiency of the photovoltaic power generation system. In a complete

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cycle, the proportion of time occupied by the active signal is the duty cycle.. The duty Ton cycle is calculated as D = Ton+T × 100%, where Ton , Toff are the IGBT on and off off times in a cycle, respectively.Fig. 2 shows the flow chart of the duty cycle disturbance observation method [9, 10].

Fig. 2. Duty cycle perturbation observation method

The duty cycle perturbation observation method, whose advantages are simple to implement and easy to control, is an improvement of the traditional perturbation observation method. However, it still has its own shortcomings, for example, the step length of the duty cycle perturbation observation method is fixed and cannot be changed, which will cause too much energy loss [11]. 2.2 Improvement of Duty Cycle Perturbation Observation Method The flowchart of the improved duty cycle perturbation observation method used in this paper is shown in Fig. 3. The main improvement is made in the duty cycle step size, changing the fixed step size to one that can be converged gradually. With the increase of time, the step length decreases gradually, and the lost energy decreases gradually [12–14]. The working principle is as follows: The relationship between the voltage and current of the cell output of the PV photovoltaic array at 25° and the power and voltage, and the V-I characteristic curve and Fig. 4 shows the P-V characteristic curve. As shown in the figure, the power can reach the maximum power point when the voltage reaches a certain value. The improved duty cycle perturbation observation method used in this paper is to dP of the P-V characteristic curve and the slope monitor whether the tangent K = dV monitors whether the output power reaches the maximum power point in real-time, If the maximum power point to the left is the output power of the system, then k >

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0 is obtained, and the duty cycle D needs to be reduced; If the output power lies to the right of the maximum power point, then k < 0 is obtained, and the duty cycle D needs to be increased. When the product of the previous measured slope K(k − 1) and the new measured slope K(k) is negative, it means that the maximum power point has been passed once, and the system will get a waveform infinitely close to the maximum power point by decreasing the number of duty cycle increase/decrease steps L each time dK = K(k − 1) ∗ K(k) is measured negative.

Fig. 3. V-I and P-V characteristic curves

Fig. 4. Improved duty cycle disturbance observation method

The characteristic curve of the step L using the function L = M1 is shown in Fig. 5, and with each increase in the horizontal axis M, L gradually decreases and approaches 0, so that the duty cycle gradually approaches the value to be output at the maximum power point.

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Fig. 5. L-M characteristic curve

3 Simulink Simulation Model and Result Analysis The Boost boost circuit controlled by the MPPT-perturbation observation method is shown in Fig. 6, where the output voltage of the PV array is 29 V and the current is 7.35 A. The traditional disturbance observation method has the same initial step size as the improved duty cycle disturbance observation method.

Fig. 6. Boost circuit simulation model

A comparison plot of the duty cycle D of the output of the conventional and the modified perturbation observation method after MPPT control is shown in Fig. 7, and it can be seen from the figure that, in the case of the same initial step size, the duty cycle of the traditional perturbation observation method can only fluctuate between 0.4–0.7 and each fluctuation of the inverse time with the same numerical value, while the improved perturbation observation method fluctuates to show the convergence state, and the time of convergence is gradually decreasing, and the accuracy is gradually increasing and the stability is better. The improved perturbation observation method shows a convergence state, the convergence time gradually decreases, the accuracy gradually increases and the stability is better. This brings the duty cycle close to the optimal duty cycle point required for the maximum power point. Figure 8 shows the waveform variation of the output power P of the PV array under the two methods, i.e., the traditional and the improved perturbation observation method.

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Fig. 7. Duty cycle simulation results

As illustrated in Fig. 8, Output power derived from conventional perturbation observation methods generally oscillates between 140–230 W, the fluctuation inverse time and numerical magnitude are fixed, and as the output power of the improved perturbation observation method with the increase of time, the power gradually converges to the optimal maximum power point and the convergence speed is gradually accelerated.

Fig. 8. Output power simulation results

The output voltage of the Boost boost circuit controlled by the perturbation observation method is shown in Fig. 9, from which it can be seen that the output voltage of the Boost boost circuit controlled by the traditional perturbation observation method fluctuates between 45–75 V and the amplitude of the fluctuation with the increase of time does not shrink while the improved perturbation observation method gradually approaches the optimal voltage output at the maximum power point under the rapid convergence of the fluctuation. From the analyses in Fig. 7, 8 and 9, it can be seen that the improved duty cycle perturbation observation method has better speed, accuracy, and precision than the unimproved former. The improved duty cycle perturbation observation method is far superior to the unimproved former in terms of tracking accuracy and tracking speed.

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Fig. 9. Output voltage simulation waveform

4 Conclusion In this paper, the perturbation observation method based on the duty cycle is improved, through the simulation comparison results, it can be seen that the improved method makes the duty cycle D, the output power P, and the load voltage U are gradually close to the result of the maximum power point, with better convergence and faster convergence, which illustrates the superiority of the improved duty cycle perturbation observation method. Acknowledgment. This work was funded by the Natural Science Foundation of Jiangxi under Grant (No. 20224ACB204016), and the Science and Technology Plan of Jiangxi Provincial Department of Education under Grant (No. GJJ211918, GJJ211942).

References 1. Gupta, A., Pachauri, R., Maity, T., et al.: Effect of various incremental conductance MPPT methods on the charging of battery load feed by solar panel. IEEE Access 9, 90977–90988 (2021) 2. Mandourarakis, I., Gogolou, V., Koutroulis, E., et al.: Integrated maximum power point tracking system for photovoltaic energy harvesting applications. IEEE Trans. Power Electron. 37(8), 9865–9875 (2022) 3. Osman, M., Ahmed, M., Refaat, A., et al.: A comparative study of MPPT for PV system based on modified perturbation & observation method. In: IEEE Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus), pp 1023–1026 (2021) 4. Ghislain, D., Li, X.: Combination result of two MPPT techniques (fuzzy logic and perturb and observe method): comparison with the conventional perturb and observe method. In: IEEE Conference on Energy Internet and Energy System Integration (EI2), pp. 4323–4327 (2021) 5. Cheng, H., Li, S., Fan, Z., et al.: Intelligent MPPT control methods for photovoltaic system: a review. In: IEEE Chinese Control and Decision Conference (CCDC), pp 1439–1443 (2021) 6. Tahiri, F., Harrouz, A., Colak, I., et al.: Comparative study of the MPPT methods applied to the PV system; perturbation & observation technique, sliding mode control and fuzzy logic control. In: IEEE International Conference on Smart Grid (icSmartGrid), pp 1–6 (2023) 7. Liu, Y., Liu, D., Chen, F., et al.: Research on MPPT control method of IoT terminal photovoltaic power generation system based on disturbance self-optimization and fuzzy algorithm. In: IEEE Sustainable Power and Energy Conference (iSPEC), pp. 2644–2648 (2021)

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8. Siddiqui, N., Verma, A., Srivastava, D.: Perturb and observe algorithm for MPPT of bifacial photovoltaic module. In: IEEE International Power and Renewable Energy Conference (IPRECON), pp. 1–6 (2022) 9. Sun, Z., Jang, Y., Bae, S.: Optimized voltage search algorithm for fast global maximum power point tracking in photovoltaic systems. IEEE Trans. Sustain. Energy 14(1), 423–441 (2022) 10. Mbarki, B., Chrouta, J., Farhani, F., et al.: Comparative evaluation of three maximum power point tracking algorithms for photovoltaic systems using quadratic boost-converter. In: IEEE International Conference on Control, Decision and Information Technologies (CoDIT), vol. 1, pp. 1244–1249 (2022) 11. Wang, D., Zhang, P., Cao, X., et al.: Power adaptive low-voltage ride-through control strategy of two-stage photovoltaic inverter with improved disturbance observation algorithm. In: IEEE International Conference on Power Electronics and ECCE Asia (ICPE 2023-ECCE Asia), pp. 2398–2403 (2023) 12. Mishra, J., Das, S., Kumar, D., et al.: A novel auto-tuned adaptive frequency and adaptive step-size incremental conductance MPPT algorithm for photovoltaic system. IEEE Int. Trans. Electr. Energy Syst. 31(10), e12813 (2021) 13. Feng, H., Chen, Y., Ma, X.: A variable step sizes perturb and observe MPPT method in PV system based on flyback converter. In: IEEE China Automation Congress (CAC), pp. 186–190 (2021) 14. Yixuan, C., Yanping, W.: MPPT tracking technique based on fuzzy controlled disturbance observation of variable step length. In: IEEE International Conference on Electronics Technology (ICET), pp. 704–709 (2023)

Study on the Effect of Sand on the DC Discharge Character Curve of Air Gap in an Altitude of 3500 m Xudong Ma(B) , Shengfu Wang, Guangxiuyuan Zhu, Chenglei Zhang, Yuan Li, and Taohui Yang Electric Power Research Institute of State Grid Qinghai Electric Power Company, Xining, China [email protected]

Abstract. Sand weather often occurs in areas with an altitude of 3500 m, which affects the insulation character curve of transmission line gaps. Therefore, so as to investigate the impact of sand on the typical gap discharge character curve of rod and rod plane in high-altitude areas, gap discharge tests were conducted using a simulated wind and sand test device at an altitude of 3500 m in Nachitai under DC voltage conditions. The single variable method was used to obtain the impact of different wind speeds, sand grain charges, and sand grain sizes on the discharge character curve. The results show that in a high altitude area of 3500 m, the effect of sand parameters, including wind and sand conditions, wind speed, sand grain charge, and sand grain size, on the DC discharge voltage of typical gaps between rods and planes is within 3.2%. Keywords: High altitude · sand dust · Discharge character curve · Air gap · DC

1 Introduction Due to the unique geographical layout of China, a lot of DC transmission projects will pass through the northwest of China, and a large number of ultra-high voltage transmission line [1] corridors will pass through high-altitude deserts or even desert areas. The harsh environment will have a certain impact on transmission lines [2, 3], Transmission line failures caused by large-scale sandstorms have occurred both domestically and internationally. Therefore, there are significant insulation hazards in lines operating in dusty environments, and further research is needed through relevant experiments. There are also relevant studies both domestically and internationally [4–15], and scholars such as M.I. Qureshi and A.A. Al Arainy from Saudi Arabia have conducted relevant experiments on the impact of wind and sand discharge character curve of typical gaps under operational and lightning impacts. Deng Heming and others from Huazhong University of Science and Technology in China studied the effect of sand on gap breakdown voltage under short gaps. Cheng Hao and others from Chongqing University studied the effect of sand on the AC surface flashover character curve of insulators. He Bo from Xi’an Jiaotong University conducted tests on the power frequency breakdown © Beijing Paike Culture Commu. Co., Ltd. 2024 Q. Yang et al. (Eds.): ACCES 2023, LNEE 1167, pp. 664–670, 2024. https://doi.org/10.1007/978-981-97-1064-5_72

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voltage character curve of plane-plane gaps under different wind speeds and dust concentrations. Chongqing University has conducted research on air gap breakdown and surface flashover under different wind speeds, sand charge, sand deposition amount, and sand moisture content under sand conditions. According to the project research plan, the research team conducted relevant northwest wind and sand research, and conducted wind and sand discharge tests with different wind speeds, charges, and grain sizes based on the research results.

2 Test Preparation 2.1 Test Device Typical air gap: The rod to rod gap test uses a 3 m long rod with a cross-section of 20 mm × 20 mm, stainless steel square tube is used as the upper electrode, and another 2 m long and a cross-section of 20 mm × 20 mm is used as the lower electrode, with the end of the rod electrode being a flat surface and the plane electrode having an area of 5 m × 5 m iron plane with clearance distances of 1, 2, and 2.5 m, respectively (Fig. 1 and Table 1).

Fig. 1. Field Test Photo at an Altitude of 3500 m

Table 1. DC Generator Parameters Parameter

value

Setting range:

0~ ±1600 kV

Measurement display range

0~ ±199.9 mA

Current display accuracy

0.1 mA

Adjustment accuracy

1 kV

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Before the experiment, typical values of key parameters of sand were obtained through wind and sand research in the northwest region, as shown in Table 2. In order to better understand the impact of key parameters of sand on the discharge character curve of sand, the single variable method is adopted. 2.2 Parameter Settings Before the experiment, typical values of key parameters of sand were obtained through wind and sand research in the northwest region, as shown in Table 2. In order to better understand the impact of key parameters of sand on the discharge character curve of sand, the single variable method is adopted. Table 2. Typical parameter values of northwest sandstorms parameter

Specific value

wind speed

5 m/s, 15 m/s, 25 m/s

Sand grain size

0.125 µm, 0.25 µm, 0.5 µm

Sand charge

−100 µC/kg, −200 µC/kg, −300 µC/kg

3 Test Results and Analysis 3.1 Study on the Effect of Wind Speed on Air Gap Discharge Character Curve

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