The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023): Volume III (Lecture Notes in Electrical Engineering, 1160) 9819708648, 9789819708642

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Lecture Notes in Electrical Engineering 1160

Chunwei Cai · Xiaohui Qu · Ruikun Mai · Pengcheng Zhang · Wenping Chai · Shuai Wu   Editors

The Proceedings of 2023 International Conference on Wireless Power Transfer Volume III

Lecture Notes in Electrical Engineering

1160

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

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Chunwei Cai · Xiaohui Qu · Ruikun Mai · Pengcheng Zhang · Wenping Chai · Shuai Wu Editors

The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023) Volume III

Editors Chunwei Cai Harbin Institute of Technology Weihai, Shandong, China

Xiaohui Qu Southeast University Nanjing, Jiangsu, China

Ruikun Mai Southwest Jiaotong University Chengdu, Sichuan, China

Pengcheng Zhang Tsinghua University Beijing, China

Wenping Chai Harbin Institute of Technology Weihai, Shandong, China

Shuai Wu Harbin Institute of Technology Weihai, Shandong, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-97-0864-2 ISBN 978-981-97-0865-9 (eBook) https://doi.org/10.1007/978-981-97-0865-9 © 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

Design and Simulation Analysis of Curved Coupler in Wireless Power Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qi Li, Jiacheng Li, Ziyu Wang, Bo Pan, Yun Tian, and Feng Wen Design of Control System for Electron-Beam Diagnostic Equipment Based on Electrical Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hongjie Xu, Yifeng Zeng, Tongning Hu, Xiaofei Li, Feng Zhou, and Kuanjun Fan Electromagnetic Sensitivity Analysis of Radio Frequency Front-End Module in Wireless Intelligent Sensors Subjected to Nanosecond Electromagnetic Pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin Zhang, Linghan Xia, Qishen Lv, Chengye He, Zhijiang Yan, Zhanhua Huang, Ying Yu, Yuting Yan, and Guodong Meng Dielectric Constant Characterization of Artificial Electromagnetic Materials for Ultra-high Field Magnetic Resonance Radio Frequency Field Manipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Gao, Long Li, and Xiaotong Zhang A Power-Enhanced Large-Space Wireless Charging System with Relay Energy Conversion Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yaju Yuan, Zhuangsheng Xiao, Xingpeng Yu, Yanzhao Fang, and Siqi Li A Practical Method for Calculating Indirect Carbon Emissions of Electricity Users in Large Power Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sirui Zhang, Jing Zhang, Fanpeng Bu, Ling Cheng, Zhanbo Wang, and Zihan Gao

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Design of Wind Turbine Speed Control System Based on Permanent Magnet Synchronous Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhifei He, Xinyao Li, Kai Dong, and Fei Feng

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Improved Fractional-Order Sliding-Mode Voltage Controller-Based MPDPC Strategy for PV Grid-Connected . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaoying Zhang, Zixuan You, and Lingzhi Qian

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Research on the Key Technologies of Control and Protection for Static Frequency Converter (SFC) Valve Group of Pumped Storage Units . . . . . . . . . . . Xu Hao, Zhang Xuejun, Ma Jiayuan, Tian Anmin, Liang Shuaiqi, and Wang Jiayu A Carbon Emission Prediction Model Based on PSO and Stacking Ensemble Learning for the Steel Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yingqiu Wang, Chenguan Xu, Chenyang Zhao, Meng Zhao, and Runze Tian Approximate Analytical Calculation of Magnetic Shielding of Double-Layer Conducting Plates with Periodic Apertures . . . . . . . . . . . . . . . . . Jiancheng Huang, Xingxin Guo, Yang Wang, and Chongqing Jiao

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A Novel Method for Electric Energy Substitution Technology Evaluation Based on the Cloud-TOPSIS Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Hang Xu, Xingong Cheng, Shengnan Zhao, Minjiang Xiang, Xu Zhang, and Biao Fu Reluctance Torque Optimization of Dual Rotor Permanent Magnet Reluctance Motor Reluctance Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Xiaoguang Kong, Yaowen Zhang, and Zhuo Yang Research on Temperature Characteristics Based on Optical Magnetic Field Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Yiming Xie, Qifan Li, Yi Zhao, Tao Wen, Xingwang Wu, Haitao Yang, Jie Wu, and Xiaoyu Hu Active Distribution Network Optimal Dispatch Model Considering Day-Ahead-Intraday Scale Demand Side Response . . . . . . . . . . . . . . . . . . . . . . . . . 127 Changbin Hu, Zhicheng Yang, Shanna Luo, and Yu He Design of a Vibration Energy Harvester for Power Transformers Monitoring . . . 137 Li Zheng, Wenbin Zheng, Jiekai Pan, and Qianyi Chai Substation WSN Coverage Optimization Technology Based on Improved Dragonfly Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Donglei Zhang, Jianding Fu, Hongjian Gao, Longwei Wang, and Fei Du Application of Flexible Control Devices in Typical Scenarios of the Hebei South Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Peng Yang, Jiahui Tian, Xudong Li, Yubin Li, and Yanhui Xu

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Short-Circuit Fault Section Location Method of Flexible Interconnected Distribution Network Based on Transient Component Similarity . . . . . . . . . . . . . 169 Hongxu Yin, Liang Song, Zhitong Xing, Wencong Chen, Ning Chu, and Chenxu Mao Thermal Layout Optimization of Power Devices on PCB . . . . . . . . . . . . . . . . . . . . 181 Dan Luo, Yao Zhao, Zhiqiang Wang, and Guofeng Li Calculation of Dead Time in Full-Bridge Converters Considering MOSFET Parasitic Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Lei Xu, Fuchao Lu, and Zhenquan Zhang Optimal Configuration of Hydrogen Energy Storage in Park Integrated Energy System Considering Medium/Long-Term Electricity and Carbon Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Yixing Ding, Yun Gu, Jun Chen, and Jilin Cai Development of Wearable Pulsed Magnetic Field Generation Device . . . . . . . . . . 205 Chuncheng Zhao, Pingping Wang, Donglin Si, and Ming Wang Comparative Study on Flexible Power Sources for Renewable Energy Bases in High Altitude Arid Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Zhan Shen, Xingyun Li, Weining Bao, Jun Wang, Ruiqing Zhang, Pengfei Zhang, and Shunchao Wang Calculation Model of Green Power Offset Carbon Baseline Based on Cluster Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Xu Lin, Jiaao Zu, and Yanling Wang Based on LMP to Help New Energy to Avoid Market Risk CFD . . . . . . . . . . . . . . 231 Jiaao Zu, Qiu Li, and Yanling Wang Research on SVPWM Optimized Modulation Algorithm Based on ANPC Five-Level Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Shizhou Xu, Jinhai Chang, Jingsheng Fan, and Xinxin Jia Research on Output Ripple Suppression of Two-Phase Interleaved Parallel Buck Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Chuanren Chen, Yinghui Gao, Xu Cao, and Ping Yan Suppression of Broadband Forced Torsional Vibration of Doubly-Fed Wind Turbine Shaft System Based on RBFNN-MRAC . . . . . . . . . . . . . . . . . . . . . . 263 Zhaohui Li, Xiaolan Wang, Tenfei Wei, Rui Hao, Jiarui Wang, Lixin Wang, and Meng Yue

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Research on Integrated Energy System Planning for Typical Scenarios Considering Demand Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 Chao Gai, Kai Zhang, Jia Chen, Xiangwen Chi, Yi Liu, and Wenzhang Zheng Demand Response of Load Aggregator Based on Game Theory and Potential Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Kun Gao, Chenghao Li, Mingyang Liu, Chunsun Tian, Ze Gao, Yucui Wang, and Di Zhang Operation Optimization Strategies for Power System Considering High Wind Power Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Tingxu Pu, Li Zhang, Juguang Ren, Li Jin, and Xiaobing Liu Optimal Control of Integrated Losses in Dual Active Bridge DC-DC Converters Under Extended Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Rui Hao, Xiaolan Wang, Tengfei Wei, Jiarui Wang, Lixin Wang, Meng Yue, and Zhaohui Li The Interval Dynamic Model of the DAB Converter is Used for Robust Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Jiarui Wang, Xiaolan Wang, Rui Hao, Zhaohui Li, Lixin Wang, and Meng Yue Fabricate and Test of Superconducting Dipole Magnet for FRIB . . . . . . . . . . . . . . 326 Tao Zhou, Chao Li, Wei Liu, Chuan Chen, Wei Gao, Fengtai Li, and Tao Zhang Low-Carbon and Economical Orderly Charging Strategy for Electric Vehicles in Residential Area Based on Dynamic Charging Prices . . . . . . . . . . . . . 334 Nan Yang, Xizheng Zhao, Xiaodong Li, Yuanzhi Zhao, and Songnan Yu Distribution Network Reactive Power Optimization Method with Distributed Power Sources Based on Improved Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 Jing Wang, Jinshan Li, Jinlong Gao, Ning Su, Dong Zhao, and Yanwen Wang Cascading Failure Propagation of Modular Cyber-Physical Power Systems Under Information Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Xingle Gao, Xing Xu, Yuping Lai, Ji Zhang, Hongmei Zhang, Ming Gao, and Minfang Peng

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Green and Low Carbon Assessment for Substation Based on Fuzzy Comprehensive Evaluation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 Chunli Wang, Jingxuan Lin, Yan Yan, Zhen Xie, Xiaomin Chen, Xilong Chen, Zheyuan Gao, and Ming Meng Low-Carbon Technology in Transmission Engineering . . . . . . . . . . . . . . . . . . . . . . 371 Xiaolin Shi, Benzhao Fu, Xianri Wang, Xingyun Chen, Jianping Cheng, Jiyao Huang, Ming Meng, and Xiping Wang Low-Carbon Technology in Power Transformation Engineering . . . . . . . . . . . . . . 379 Chunli Wang, Xiaomin Chen, Jingxuan Lin, Xilong Chen, Zhen Xie, Yan Yan, Jun Wang, and Ming Meng Study on the Control Strategy of Cascaded H-Bridge Photovoltaic Grid-Connected Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 Xinzhao Liang and Fenghuang Cai A PWM Fixed-Frequency and Constant Opening Time (COT) Hybrid Control Strategy for a Quasi-Resonant Forward-Flyback DC/DC Converter . . . . 395 Zihe Li, Zhenyu Zhao, Xinyu Gao, Dong Gao, and Xuejian Wang Credibility Evaluation of Renewable Energy Comprehensive Capacity Based on Recursive Function Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Yinsheng Su, Hongyue Zhen, Qian Ma, Ligang Zhao, Runzhi Mu, Tinghui Zhou, and Yuan Xu Error Location Analysis of Wind Power Prediction Based on EMD-LSTM . . . . . 414 Jieyi Sun, Yangwu Shen, Heping Jin, Hong Wu, and Shuaihu Li Research on Current Measurement Technology Based on Ring Point Hall Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 Zhenyu Zhao, Xinyu Gao, Zihe Li, and Fei Feng Review of Tuning Methods in Wireless Power Transfer Systems . . . . . . . . . . . . . 434 Jianghua Lu, Shixiong Sun, Haojie Ke, and Guorong Zhu A High Step-Up DC–DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Shili Guan and Zhilei Yao Real-Time Carbon Emission Monitoring System for Coal-Fired Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 Wangpei Yan, Baoling Liu, Jun He, Huidong Liang, Zhengwen Zhang, Xiaocui Yuan, Xinguang Liu, and Yongtao Wang

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A Capacitor Voltage Balancing Strategy Based on Improved Group-Sort Algorithm for MMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 Yongli Fang and Kui Chen Research on Low-Carbon Operation of Substation Power Supply System Based on Microgrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 Chunli Wang, Xiaomin Chen, Jingxuan Lin, Yan Yan, Xilong Chen, Xuezhi Tao, Siyuan Ma, and Ming Meng Coordinated Control of Engine-Load-Storage for Marine Micro Gas Turbine Power Generation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Yueming Li, Zemin Ding, Youhong Yu, and Yongbao Liu Finite Element Analysis-Based Impedance Calculation of GIS Station Horizontal Pipeline Considering Magnetization Curve . . . . . . . . . . . . . . . . . . . . . . 493 Yu Wang, Zhiming Huang, Shenggui Pan, Jingdong Yan, Kelin Fu, Bowen Li, and Yumin He Energy Harvesting Device Based on Magnetic Levitation Magnetic Spring and Friction Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 Haoran He, Yanbin Liu, Haoxiang Huo, and Jun Wu In Situ Conduction Current Extraction of SiC MOSFET Modules in Switching Transient Based on Second-Order Passive Filtering . . . . . . . . . . . . . 509 Jingwei Zhang, Dahan Deng, Zhikang Guo, and Guojun Tan Fast Calculation of the Impedence Using Tensor-Based FEM for Evaluating Very Fast Transient Overvoltage in GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518 Li Zhang, Ran Zhuo, Shenggui Pan, Yan Luo, Kelin Fu, Junjie Zhang, and Yu Wang Design of a Train Storage Battery Balancing Equipment . . . . . . . . . . . . . . . . . . . . 527 Zhaojing Tong, Peng Wu, Lingqiang Meng, and Jinhao Tang Research on Cyclic Ampacity Computational Model of High Voltage AC Submarine Cables Under Typical Load Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Chengxiang Li, Zhaoxiao Wu, Yan Zhou, Dan Chen, and Xinyue Zhang A Virtual Synchronous Generator System and the Control Technology Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548 Zhongming Yu, Yu Zhang, Ketong Lu, and Keyu Chen

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Summary of Distributed Photovoltaic Hosting Capacity Analysis and Improvement Measures for Distribution Network . . . . . . . . . . . . . . . . . . . . . . . 556 Jinzhi Guo, Feng Zhao, Chao Sun, Youzhong Miao, Jie Zhou, Yi Wang, and Zongmin Yu Three-Dimensional Simulation of the Erosion in Solid Armatures . . . . . . . . . . . . 564 Suna Yan, Yeping Huang, Qiming Chen, Ming Li, Dong Chen, Junsong Yu, Liyan Chen, and Wanyu Zhao Phase Shift Regulation Method of Electric-Field Coupling Bidirectional Wireless Power Transfer Under Variation of Coupling Capacitance . . . . . . . . . . . 574 Min Sun, Xin Dai, Yugang Su, Yue Sun, and Xueying Wu Improved Space Vector Modulation of Single-Phase ANPC Three-Level Converter with Balanced Loss Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Xiao Yang, Weiwei Li, Chunping Guo, and Dandan Qiang A Biphase Low-Loss Narrow-Rail System with Uniform Output Power for EV DWPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 Xingjian Zhou, Xin Gao, Dongxue Li, and Chunbo Zhu Research on Double Closed-Loop Control System of NPC Cascaded H-Bridge Photovoltaic Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 Ningzhi Jin, Jing Yang, Jiaxin Jiang, Fanshun Meng, and Dongyang Sun Design of Biological Weak Magnetic Field Detection System Based on TMR Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 Xuelei Jiao, Sinan Zhang, and Chuanfang Chen Short-Term Load Forecasting Model Considering Multiple Time Scales . . . . . . . 625 Dan Li, Jian Tang, Yawen Zhen, and Ke Zhang Research Progress and Application Prospect of Perovskite Solar Cells . . . . . . . . . 633 Genmi Zhang, Xingyu Zhao, Hui Ling, Jiexin Zhang, Yongli Yi, Yao Zhou, Huasen Xie, Wenjie Liu, and Yi Ding Modeling and Fault Characteristics Analysis of Ultra High Voltage Direct Current Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644 Yaoqi Xu, Cui Tang, Qi Xu, and Jian Liu How Does Current Establish in Transient Electromagnetic Field . . . . . . . . . . . . . . 653 Shuqi Liu and Dezhi Chen

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Thermal Resistance Measurement Methods for Double-Sided Heat Dissipation IGBTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 Yuqing Zhang and Zhibin Zhao Analysis of EIT Effect Under Different Fine Level Selections of Cesium D2-Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Chao Ding, Baoshuai Wang, Zengxing Pu, Dongping Xiao, Hongtian Song, Shanshan Hu, Huang Yu, and Xutao Wei Frequency Calibration Method Based on Cesium Atom nDJ Rydberg State Laser Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Baoshuai Wang, Chao Ding, Hongtian Song, Zengxin Pu, Shanshan Hu, Huaiqing Zhang, Yu Huang, and Wenyu Lin Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

Design and Simulation Analysis of Curved Coupler in Wireless Power Transmission System Qi Li1 , Jiacheng Li1,2(B) , Ziyu Wang1 , Bo Pan2 , Yun Tian2 , and Feng Wen3 1 College of Electrical Engineering and Control Science, Nanjing Tech University,

Nanjing 211816, China [email protected] 2 Jiaxing Guodiantong New Energy Technology Co. Ltd., Jiaxing 314031, China 3 College of Electrical Engineering and Control Science, Nanjing University of Science and Technology, Nanjing 210094, China [email protected]

Abstract. The magnetic coupling resonant transmission method has been widely concerned due to its high transmission efficiency, reliability, convenience, and effectiveness. In this paper, the application of magnetic coupling resonance type wireless power transmission technology in the rocket power supply scenario is studied, and the influence of the operating frequency, the number of transmitter receiver coil turns and the transmission distance changes on the parameters and performance of the curved coupling coil is analyzed. The coupling structure model of the rocket ground Wireless power transfer system is established, and the scheme of curved coupler Wireless power transfer system for the Long March 8 carrier rocket is proposed, which is verified through simulation analysis. Keywords: Wireless power Transmission · Curved Coil · Carrier Rocket · Rocket ground Wireless charging

1 Introduction In recent years, China’s rocket launch frequency has increased year by year, ranking among the world’s top. China broke its historical record and executed 55 launch missions, ranking first in the world, indicating that China’s aerospace has entered a stage of highdensity launch normalization. The instruments and electromechanical equipment on the carrier rocket require a power supply system to provide stable and reliable electrical energy [1, 2]. Currently, the arrow-to-ground power transmission method used is a wired transmission method. The power supply interface, control interface, and measurement interface of the rocket ground test system are all connected to the rocket body through plug-and-play connections. This method of supplying power to the rocket through the ground power source requires complex cable laying, which is labor-intensive and costly. Before the rocket completes its ground charging preparation and enters the launch phase, the cables

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 1–8, 2024. https://doi.org/10.1007/978-981-97-0865-9_1

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connected to the rocket need to be cut off, which is contrary to the goal of developing low-cost and reusable rockets [3, 4]. Traditional wired power transmission relies on wire and metal contact to transmit electrical energy, which inevitably brings problems such as medium loss, aging of the line, and insulation damage. Moreover, the insulation material on the surface of the medium will fall off from the wire due to aging, compression, wear and other reasons, exposing the wire to the air, which poses a short-circuit risk and is prone to accidents. This greatly reduces the safety and service life of electrical equipment. However, wireless power transmission technology uses new methods of power transmission that are detached from electrical contact, such as high-frequency electromagnetic fields, electromagnetic waves, lasers, microwaves, and ultrasonic waves to transmit energy between the transmitting and receiving ends. Compared with the traditional wired power transmission method, wireless power transmission technology can cross a certain spatial distance and transmit electrical energy from the power source end to the load end without direct electrical contact, providing an extremely flexible transmission method and achieving efficient transmission and utilization of electrical energy [5, 6]. It is currently a very active research direction in the field of electrical engineering and has broad application prospects. By analyzing the research progress of the wireless power supply system for carrier rockets before launch at home and abroad and combining with the existing conditions in China, a new design scheme for the wireless power supply system for rocket launch sites has been proposed. The theoretical and experimental research has been conducted on the main problems that may exist in the system. The magnetic-coupled resonance transmission mechanism with medium transmission distance in wireless power supply technology has been studied for its transmission mode, transmission characteristics, and coupling structure, which promotes the research of wireless power supply system for arrow-to-ground before the launch of carrier rockets. In 2020, Wang Guohui and Li Yaqun from China Academy of Launch Vehicle Technology proposed a patent for an arrow-to-ground interface that uses composite bus full regulation technology, which is suitable for power supply systems that require high bus voltage stability. The system has the advantages of being unaffected by battery voltage changes, stable power output voltage and good load stability, especially suitable for centralized power supply systems and can realize autonomous charging and discharging management of the power supply on the rocket [7]. Combined with the wireless energy transmission ground power interface, wireless transmission between the arrow and the ground and between different modules of the rocket can be realized. In 2021, a research team from Nanjing University of Science and Technology studied the application of non-planar coils in rocket fairings, missile cones and missile bodies. According to the structural characteristics of military equipment such as rockets and missiles, conical coils and curved coils are used as receivers in the WPT system [8]. By studying the curvature of the receiving coil, a method to avoid curvature angle splitting is obtained. Under the condition of reasonable adjustment of the transmission distance, the stability of the WPT system is effectively improved. In terms of standard research on electrical interfaces for arrow-to-ground equipment, the international standard ‘Space Systems - Electrical Interface Requirements for Launch

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Vehicles and Ground Support Equipment’ led by China Academy of Launch Vehicle Technology and Beijing Aerospace Automatic Control Institute was published on the official website of the International Organization for Standardization on October 11, 2021 [9]. This standard specifies the design principles of electrical interfaces between launch vehicles and ground support facilities, as well as specific requirements for general interfaces, environmental verification, control documents and inspection operations. It can be used to guide the design and verification process of electrical interfaces between launch vehicles and ground support equipment in various countries. The research in this paper mainly designs an arrow-to-ground wireless power transmission system in the form of curved coils according to the power requirements of electrical equipment on the arrow. Considering factors such as coil shape and material, an efficient coupler structure that meets the power requirements is designed. The electromagnetic environment of the arrow-to-ground wireless power transmission system is analyzed, and feasible shielding measures are designed to ensure the normal operation of electromagnetic sensitive components.

2 Analysis of Rocket Structure Model and Power Demand Based on the actual application scenarios of launch vehicles, it can be found that the Long March 8 carrier rocket can meet 59% of the launch missions in medium orbit and 97% in low orbit, making it a key force in executing space launch missions. Therefore, taking the Long March 8 carrier rocket as an example [10, 11], the design and optimization of the arrow-ground wireless power supply system coupling mechanism will be discussed. The schematic diagram of the structural model of the Long March 8 rocket is shown in Fig. 1.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Fig. 1. Rocket structure

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The main body of the rocket in the schematic diagram consists of a core stage and two boosters. The total length from the top to the tail of the rocket is 50.3 m. The central stage is composed of a fairing, a core second stage and a core first stage, connected from top to bottom through inter-stage segments. Two boosters are bundled on both sides of the core first stage. The structural dimensions of the rocket are shown in Table 1. Table 1. Rocket structural parameters. Parameter

Fairing

First-stage engine

Second-stage engine

Booster engine

Value (m)

4.2

3.35

3

2.25

Based on the rocket model schematic diagram and structural dimensions parameters shown in Fig. 1 and Table 1, the following two proposals are presented, and their structural diagrams are shown in Fig. 2.

(a)

(b) Fig. 2. Coupler scheme

In Fig. 2, structure (a) shows a conventional helical coil connected to the rocket system from the bottom of the rocket body. The receiving coil is attached to the inner side of the bottom of the core second stage of the rocket and the transmitting coil is placed on the rocket launch pad with its axis aligned with that of the receiving coil. Structure (b) shows a rectangular curved surface coil, which is connected to the rocket system from the side of the rocket body. The receiving coil is attached to the outside of the rocket body, and the transmitting coil is installed through the rocket launch tower or an independent device. Considering that there are more researches on the bottom access of conventional helical coils, this paper focuses on modeling and exploring the side access of rectangular curved surface coils. Through research and analysis, it can be seen that the electrical load of the launch vehicle before launch requires obtaining 2 kW of electrical energy, and the transmission distance of the coupler needs to be maintained at 0.5 m or more to withstand the offset caused by the rocket body sway due to wind.

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3 Parameter Design of the Curved Surface Coil Taking the core first stage structure parameters of the Long March 8 rocket as an example, a rectangular curved surface coil made of a rectangular coil wrapped with 10 turns of copper wire and bent to fit the outer side of the rocket body bottom has been preliminarily designed. Since there is relatively large space available on the side of the rocket body, the initial design of the coil height is 4 m and the distance between the transmitting and receiving coils is 0.5 m. A part of the core first stage framework is set on the side of the coupling coil and the material is also made of aluminum. Table 2 shows the preliminary structural parameters of the curved surface coil. The structure of the curved surface coil is shown in Fig. 3.

Fig. 3. Structure and Electromagnetic Simulation of Curved Coupler

Table 2. Structural parameters of curved coupler. Coil

Turn

Radius (m)

Height(m)

Transmission distance (m)

Transmitting coil

10

2

4

0.5

Receiving coil

10

2.5

4

The surface coil compensation network adopts an S-S topology structure and the resonant frequency of the coil is set to 50 kHz. The output end stably outputs 2 kW power. The simulated calculated values of the surface coil parameters are shown in Table 3. The data shows that the self-inductance of the transmitting and receiving coils of the curved coupling coil on the primary side is 5272 µH and 5087 µH respectively, and the equivalent resistance of the coil is 2.7  and 2.2 . The mutual inductance between the transmitting and receiving coils is 82.92 µH. The coupling efficiency of the curved coupler is 80.71%. Further research is needed to optimize the electrical parameters of the curved coil and design a better solution.

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Parameters

Value

Parameters

Value

Parameters

Value

L1 (µH) L2 (µH)

5272

R1 ()

2.7

M(µH)

82.92

5087

R2 ()

2.2

PO (W)

2015

4 Impact of Fluctuations in Surface Coil Parameters With the goal of improving the coupling degree of the spiral coil, reducing the current of the transmitting coil and improving the energy transfer efficiency of the spiral coil, the surface coil is studied from three aspects: changes in the working frequency of the flat plane, the number of coil turns and the transmission distance of the coil to improve the performance of the curved coupling coil. 4.1 Transmit-Receive Coil Turn Variation Utilize the effect of coil turns on the coupling degree between the transmitting and receiving coils. Change the number of turns of the transmitting and receiving coils to optimize the mutual inductance of the coupling mechanism, coupling coefficient and transmission efficiency. At the same time, changing the number of turns of the transmitting and receiving coils to 25, 30, 35, 40, 45 and 50 turns, six different numbers of turns, the coupling efficiency improvement can be obtained as shown in Table 4. Table 4. Transmission performance of curved coupling coils with different turns Turn

L1 (µH)

R1 ()

L2 (µH)

R2 ()

M/µH

ï

25

8257.3

3.13

7948.5

2.75

129.57

87.14%

30

12352

3.67

11446

3.30

186.58

89.23%

35

16734

4.18

15579

3.86

253.95

89.91%

40

22437

4.73

20348

4.41

331.69

89.92%

45

27569

5.35

25768

4.96

409.34

89.51%

50

34732

5.81

31794

5.508

518.27

89.05%

It can be seen from the data in the table that the energy transmission efficiency of the coupling coil shows an upward trend from 25 to 40 turns and the transmission efficiency decreases slightly after 40 turns. 4.2 Transmission Distance Variation Based on the above analysis, keeping the number of turns of the coil unchanged at 40 turns, the influence of transmission distance on the transmission performance of

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the curved surface coil is studied. By changing the transmission distance between the coupling coils to 0.7 m, 0.8 m, 0.9 m, 1 m, 1.1 m and 1.2 m, the performance change curve of the curved surface coupler as shown in Fig. 4 can be obtained.

Fig. 4. The Influence of Transmission Distance on the Performance of Curved Couplers

From the figure, it can be seen that as the transmission distance increases, the primary current shows an upward trend, the coil mutual inductance decreases and the coil efficiency decreases. Therefore, the transmission performance of the curved surface coil is optimal when the transmission distance is 0.7 m. Therefore, the parameters of the curved surface coupler designed for the Long March 8 carrier rocket in this paper are: both the transmitting and receiving coils are 40 turns, the height is 4 m, the width is 2 m and the curved part is a semi-circle with a radius of 1 m. The operating frequency is 50 kHz and the transmission distance is 0.7 m.

5 Conclusion In this paper, based on the structure of the carrier rocket and the power demand of the on-board electrical system, two types of coupling coil structures, rectangular curved surface coils, were chosen to be placed on the side of the core first-stage rocket body. The parameter design of the coupling coil was carried out. At the same time, the structure of the curved surface coupler was optimized from three aspects: coil operating frequency, coil turns and transmission distance, which improved the transmission efficiency of the curved surface coupler and obtained the design scheme of the rocket body curved surface coupler. Acknowledgement. This work was funded by the Basic Science (Natural Science) Research Project of Higher Education Institutions in Jiangsu Province (23KJB470013), China Postdoctoral Science Foundation (2023M731640, 2022M711626) and the Natural Science Foundation of Jiangsu Province (BK20221491).

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References 1. Wang, Y., et al.: Ionospheric disturbances triggered by china’s long march 2D rocket. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 16, 1613–1623 (2023) 2. Niederstrasser, C.G.: The small launch vehicle survey a 2021 update (the rockets are flying). J. Space Saf. Eng. 9(3), 341–354 (2022) 3. Zhou, Z., et al.: Visualization analysis of rocket fault detection technology based on Citespace. In: 2021 8th International Conference on Information, Cybernetics, and Computational Social Systems (ICCSS). IEEE (2021) 4. Da Cas, P.L.K.: Launch vehicle overview. In: Cubesat Handbook, pp. 431–444. Academic Press (2021) 5. Zhang, B., et al.: Review of low-loss wireless power transfer methods for autonomous underwater vehicles. IET Power Electron. 15(9), 775–788 (2022) 6. Liu, Y., et al.: A novel wireless energy router for home energy management with omnidirectional power transmission. IEEE Trans. Industr. Electron. 70(9), 8979–8990 (2022) 7. Wang, G., et al.: A Wireless Powered Rocket Energy efficient topology system. CN110932349A (2020) 8. Wen, F., et al.: Curvature angle splitting suppression and optimization on nonplanar coils used in wireless charging system. IEEE Trans. Power Electron. 35(9), 9070–9081 (2020) 9. Space systems - Requirements of launch vehicle (LV) to electrical ground support equipment (EGSE) interfaces (First edition). ISO 22772-2020 (2020) 10. Tao, Z., et al.: Integrated design technology of electrical system for the long march 8 launch vehicle. J. Deep Space Explor. 8(1), 17–26 (2021) 11. Zhao, Y., et al.: Evaluation and Verification of Load Reduction Effect of Long March 8 Launch Vehicle. Aerospace China (2021)

Design of Control System for Electron-Beam Diagnostic Equipment Based on Electrical Magnet Hongjie Xu1 , Yifeng Zeng1 , Tongning Hu1(B) , Xiaofei Li2 , Feng Zhou2 , and Kuanjun Fan1 1 School of Electrical and Electronic Engineering, Huazhong University of Science and

Technology, Wuhan 430074, China [email protected] 2 China Electric Power Research Institute, Wuhan 430074, China

Abstract. An accelerator-based facility, such as an FEL injector, has stringent requirements on the quality of electron beam, and the electron beam is directly determined by beam injector, which is generally a source to provide driven beams with the energy of several MeVs. Since such space-charge dominated relativistic beams are sensitive and easy to be deteriorated during transportation, it is necessary to carry out online monitoring of beam quality under commissioning, so as to achieve accurate measurement of beam parameters such as beam spot size, beam emittance and beam energy spread, and beam current. The whole measuring facility is composed of magnetic components such as analysis magnet and quadrupole magnet. It is necessary to control and monitor the magnet current, and then display the data uniformly to the operating interface and feed back to the user through different control and measuring devices in the system. This paper introduces the basic principle of beam measuring device and the layout design of measuring system. Based on EPICS system and LabVIEW software, a distributed three-layer architecture control and measuring system is developed, which can realize feedback control, remote monitoring and signal acquisition. The whole system is stable and reliable in operation, convenient in use, high in beam parameter accuracy and accurate in calculation, which improves the efficiency of online monitoring. Keywords: Electrical Engineering · Free Electron Laser · Beam Measurement System

1 Introduction In recent years, the rapid development of Free Electron Lasers (FEL) has provided support for various new scientific and industrial applications. Compared to traditional lasers, FELs have the characteristics of high power, high efficiency, continuously tunable wavelength, and high-quality beam [1, 2]. FELs utilize the interaction between spatially periodic magnetic fields and relativistic electron beams to convert the kinetic energy of © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 9–16, 2024. https://doi.org/10.1007/978-981-97-0865-9_2

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the high-energy electron beam into electromagnetic radiation. To obtain high-gain radiation, the electron beam entering the wiggler must meet the performance requirements of the FEL, including low emittance, low energy spread, and high peak current [3, 4]. With the continuous upgrading and optimization of FEL devices, the beam quality can serve as a basis for comparison between different installations. Huazhong University of Science and Technology (HUST) has constructed a compact Free-Electron Laser-Terahertz (FEL-THz) device based on the EC-ITC (Electron Cyclotron Inverse Free Electron Laser) microwave electron gun. The beam transport line of this device consists of quadrupole magnets, correction magnets, and dipole magnets, which guide the electron beam to be captured by the beam target [5]. In the process of beam orbit correction, it is necessary to adjust the excitation current of the correction magnets based on measured beam positions, so that the injector serves as the source of the entire device, responsible for providing high-quality beam. Therefore, to accurately measure the electron beam parameters at different stages and ensure stable, reliable, and closed-loop feedback, an online beam monitoring and adjustment system for beam transport is indispensable. Currently, beam measurement systems are widely used in various facilities. Large facilities such as Swiss-FEL [6], SSRF [7], et al. have complete beam test line. While the designed beam measurement system in this paper may not be as complex as the ones used in large accelerator facilities mentioned above, it is characterized by stable performance and compact structure, fulfilling the precision measurement requirements. Due to the involvement of numerous and large, complex devices in the entire beamline regulation, a centralized control approach is difficult to meet the requirements. Therefore, a distributed control system has become the preferred choice for large-scale measurement systems. EPICS, as the preferred control software for large scientific facility control systems, offers many advantages such as good stability, strong portability, and high scalability [8]. On the other hand, LabVIEW is the preferred control software for small-scale control systems, offering advantages like easy development and good stability [9]. Taking into consideration factors such as a user-friendly interface and the sustainability of laboratory software achievements, this paper is based on the EPICS system and LabVIEW software to develop a distributed three-tier structured measurement and control system capable of implementing feedback control, remote monitoring, and signal acquisition. This passage describes the basic principles of a beam measurement device and the design of the measurement system. Section 2 primarily introduces some fundamental principles of beam measurement, such as energy spread, emittance, beam spot size, and beam intensity measurement. Section 3 discusses the overall control framework and the design of the human-machine interface, including image processing, hardware communication, data analysis, and operational procedures.

2 Basic Theory of Beam Measurement The beam measurement system mainly consists of one Flag target with a YAG crystal screen, one energy analysis magnet, two luminescent ceramic targets, two beam transformers (Toroid), three quadrupole magnets, and three CCD cameras (Fig. 1).

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Fig. 1. Schematic diagram of beam measurement system [10].

2.1 Beam Spot Size Measurement The beam spot size is measured by an optic-based measurement method. The electron beam spot is hit on the luminescent ceramic, and then a CCD camera is used to collect the spot image, and the horizontal or vertical direction is projected according to the grey value of the phase point. The half width and height of the normal distribution image is the beam spot size. 2.2 Energy and Energy Spread Measurement The spread of beam energy is related to the length of the drift section and the analysis magnet. According to the single particle model, the particle states received on the beam target satisfy [11]: ⎞ ⎛ ⎞ ⎡ ⎤⎛ ⎞ ⎛ x0 m11 m12 m13 x0 x1 ⎠ = M2 Mmagnet M1 ⎝ x ⎠ = ⎣ m21 m22 m23 ⎦⎝ x ⎠, (1) ⎝ x 1 0 0 m31 m32 m33 (p/p)1 (p/p)0 (p/p)0 where, M2 is the transmission matrix of the drift section between the analysis magnet and the beam target, M1 is the transmission matrix of the drift section between Flag 1 and the analysis magnet, and Mmagnet is the transmission matrix of the analysis magnet. x0 represents the transverse size of the bundle, x0 represents the transverse spread angle of the bundle, p/p represents the dispersion of the bundle momentum. Subscript 0 represents the reference point, 1 represents the observation point on the beam target. When the momentum is large enough, the momentum dispersion p/p is approximately equal to the energy dispersion E/E. In actual, statistical model is used for calculation, according to Eq. (1), it can be obtained: E/E =

x1  − m11 x0  . m13

(2)

Therefore, the beam dispersion can be obtained by measuring the beam spot size at Flag 1 and the energy spectrum target respectively. 2.3 Beam Emittance Measurement According to beam optics, a beam of charged particles is often studied as a whole, and its motion state can be described in phase space. The emittance is measured by the

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quadrupole magnet scanning method [12], which is used to accelerate the quadrupole magnet at the back end of the tube for particle focusing. By changing the current of the quadrupole magnet, the half-height and width of the beam spot in the x direction on the beam target change accordingly. The Twiss parameter commonly used in beam optics can be rewritten as: σ11 = ε0 (m211 β0 − 2m11 m12 α0 + m212 γ0 ),

(3)

m11 m12 m21 m22



where, α = −σ12 /ε, β = σ11 /ε, γ = σ22 /ε, and βγ − = 1. M = 2 is emittance, σ represents the is the beam transmission matrix. ε = σ11 σ22 − σ12 11 square of the beam cross section radius, σ12 represents the beam size covariance, and σ22 represents the beam spread angle variance. Let the drift section distance between the quadrupole magnet and the beam target be L, and the focusing intensity of the quadrupole magnet be K. Considering the thin lens the phase space transmission matrix M can be described as M =

approximation,  1 + KL L . Then Eq. (3) is rewritten as: K 1

 (4) σ11 = ε0 (1 + KL)2 β0 − 2(1 + KL)Lα0 + L2 γ0 . α2

As shown in Eq. (4), the transverse cross-section size of the beam spot on the beam target can be regarded as a quadratic polynomial with the focusing intensity (K) of the quadrupole magnet as the independent variable: σ11 = a(K −b)2 +c. Then the emittance can be expressed as: √ (5) ε = ac/L2 .

2.4 Beam Intensity Measurement The main component of beam intensity measurement is the beam transformer, the center of which is a high permeability magnetic ring, the beam generated by the injector is called the primary winding of the magnetic ring, and the N-turns coil wrapped around the magnetic ring is called the secondary winding [13]. The relationship between the current in the primary and secondary windings can be expressed by the formula: I1 N1 = I2 N2 ,

(6)

where, I is the winding current and N is the number of winding turns. Subscript 1 represents the primary winding, 1 represents the secondary winding. Since the beam current takes the form of pulse, I1 represents the macro-pulse current intensity. And the beam passes through the beam transformer once, the value of N1 is 1. In order to facilitate measurement, the resistance R is usually connected to the secondary winding, and the macro pulse current intensity is obtained by measuring the resistance R.

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3 Beam Measurement Control System The beam measurement control and processing system has been designed based on the distributed layered architecture scheme, with the server as the host computer and PLC as the bottom controller, and the online control and processing program is developed based on the LabVIEW platform. 3.1 Overall Control Framework Design The beam measurement control and processing system mainly consist of a three-layer structure, as shown in Fig. 2:

Fig. 2. Control system framework.

The bottom layer is the physical layer, which includes all the hardware devices involved in the beam measurement process. These devices are equipped with data exchange ports, and the interaction ports are connected to the data exchange layer through Ethernet, RS-232, or RS-422/485 communication buses. The middle layer is the data exchange layer, which consists of switches and serial port network servers. This layer is primarily used for data acquisition and transmission, as well as receiving and delivering commands. The top layer is the user layer, where the control system client is placed. In order to achieve online processing of big data, the system’s master computer communicates with hardware devices using serial communication, as shown in Fig. 3. The synchronization signal is derived from the accelerator’s timing signal source (indicated by the dashed line) and is used to control data acquisition to ensure that data conflicts do not occur. Due to the different hardware interfaces of each measurement subsystem, switches are selected for integration, and the overall communication control is achieved by the host computer (indicated by the solid line). 3.2 Human-Computer Interaction (HCI) Interface Design Based on the LabVIEW software platform and guided by design principles such as priority, consistency, and maintainability, and taking into account the accumulated humanmachine interaction experience from practical use, various functionalities have been

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45

232

232

232

485

Fig. 3. Data transmission and timing control diagram

developed, including image processing, hardware communication, and database management, as shown in Fig. 4. The beam measurement system’s human-machine interface is divided into three modes: (1) Control mode: This mode is used for system control and includes functions such as remote operation of the flag-driven motor (start, stop, distance setting), remote operation of the power system’s motor, CCD camera display switching and parameter adjustment, setting and real-time mapping of the magnet power supply’s operating status, and beam spot image status analysis (center mean value, center position, full width at half maximum (FWHM), target center position, etc.). (2) Measurement mode: This mode is used for data processing and includes functionalities such as mapping the oscilloscope image and measuring beam parameters (energy spread, emittance, beam energy, etc.). (3) Monitoring mode: This mode is used for monitoring purposes and mainly involves recording the display of vacuum gauges and temperature gauges, among other functions. Based on the above control framework and interactive interface, the entire system’s operating process is shown in Fig. 5. It should be noted that the operators should first confirm that the actual working environment meets the requirements and complete the accelerator beam preparation work. They should also monitor the vacuum, temperature, and humidity in real-time.

Design of Control System for Electron-Beam Diagnostic Equipment

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Fig. 4. Operation interface diagram.

,

1#

1#

2#

2#

Fig. 5. Operation flow chart based on operation interface diagram.

4 Conclusion In order to achieve high-gain radiation for the FEL online monitoring of the beam quality and precise measurement of the beam properties are required during debugging. This paper presents a newly designed beam measurement system based on magnetic elements for the HUST FEL-THz. The system includes four components: beam spot size measurement, beam energy spread measurement, beam emittance measurement, and beam current measurement. Considering the reliability of beam parameter measurement methods and the economic aspects of the physical devices, the beam measurement system mainly consists of one Flag target with a YAG crystal screen, one energy analysis magnet, two luminescent ceramic targets, two beam transformers (Toroid), three quadrupole magnets, and three CCD cameras. Due to the considerable number of devices and their complex nature, this paper develops a distributed three-layered control and measurement system based on the EPICS

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system and LabVIEW software. This system features real-time feedback, remote monitoring, fast response, and a simple and attractive user interface, enhancing operational reliability and efficiency. Moreover, this approach has the potential for extension to other similar accelerator facilities, highlighting its broader relevance and applicability in the field. Acknowledgments. This work is supported by Science and Technology Foundation of State Grid Corporation under Project Numbers 5700-202155197A-0-0-00.

References 1. Huang, N., Deng, H., Liu, B., Wang, D., Zhao, Z.: Features and futures of X-ray free-electron lasers. Innovation 2(2), 100097 (2021) 2. Labat, M., Cabada˘g, J.C., Ghaith, A., et al.: Seeded free-electron laser driven by a compact laser plasma accelerator. Nat. Photonics 17(2), 150–156 (2023) 3. Li, M., Li, P., Wu, D., Zhou, Z., Tang, C.: Development strategy of free electron laser technology in China. Strateg. Study Chin. Acad. Eng. 22(3), 35–41 (2020) 4. Jiang, H., Wang, W.T., Feng, K., Gu, Z.X., Li, R.X.: Research progress of free electron laser based on laser plasma acceleration. High Power Laser Particle Beams 34(10), 104009 (2022) 5. Qin, B., Liu, K.F., Liu, X.L., et al.: Field integral measurement system and optical alignment system for HUST THz FEL. In: 36th International Free Electron Laser Conference, Basel, pp. 80–83. IEEE (2014) 6. Ganter, R.: SwissFEL-Conceptual design report. Paul Scherrer Institute (PSI) (2010) 7. Leng, Y., Zhou, W., Yuan, R., et al.: Beam position monitor system for SSRF storage ring. Nucl. Tech. 33(6), 401–404 (2010) 8. Li, W.M., Li, J.Y., Liu, G.F., et al.: EPICS based HLS control system. In: Proceedings of the 3rd World Congress on Intelligent Control and Automation (Cat. No. 00EX393), Hefei, pp. 3641–3643. IEEE (2000) 9. Thompson, D., Blokland, W.: A shared memory interface between LabVIEW and EPICS. In: 9th International Conference on Accelerators and Large Experimental Physics Control Systems, Gyeongju, pp. 275–277. IEEE (2003) 10. Hu, T.N., Pei, Y.J., Feng, G.Y.: Electron beamline of a Linac-based injector applied to a compact free electron laser-terahertz radiation source. Jpn. J. Appl. Phys. 57(10), 100310 (2018) 11. Wangler, T.P.: RF Linear Accelerators. Wiley, New York (2008) 12. Forck, P.: Lecture notes on beam instrumentation and diagnostics. Joint Universities Accelerator School (2010) 13. Long, J.Y., Yuan, Y.J., Xiao, G.Q.: Toroidal AC transformer for beam intensity measurements in CSR. Nucl. Phys. Rev. 19(1), 73–75 (2002)

Electromagnetic Sensitivity Analysis of Radio Frequency Front-End Module in Wireless Intelligent Sensors Subjected to Nanosecond Electromagnetic Pulse Xin Zhang1 , Linghan Xia2 , Qishen Lv1 , Chengye He2 , Zhijiang Yan2 , Zhanhua Huang1 , Ying Yu1 , Yuting Yan1 , and Guodong Meng2(B) 1 Shenzhen Power Supply Co., Ltd., Shenzhen, Guangdong, China 2 State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong

University, Xi’an, Shaanxi, China [email protected]

Abstract. Wireless intelligent sensors are being widely used in power system, which can perceive the measured information, transform the perceived information into an electrical signal and even conduct analysis and diagnosis. As one of the most important components in wireless intelligent sensors, radio frequency (RF) front-end module becomes more and more sensitive to electromagnetic interference (EMI) with the increasingly severe electromagnetic environment in high voltage and extra high voltage power equipment. Therefore, it is extremely vital to discuss the characteristics of EMI on the typical RF front-end module of wireless intelligent sensors. In the present work, the nanosecond electromagnetic pulse (EMP) wave was produced by high voltage nanosecond pulse generator and radiation antenna. Meanwhile, the electromagnetic model was built by the CST Studio, and the numerical simulation of the coupling and conduction voltages has been carried out. The coupling transient electromagnetic disturbance on the customdesigned RF front-end module was measured. The bent and impedance variation microstrip segments would receive more coupling energy during the radiation. This work should be of great benefit to understand the coupling mechanism under different conditions and explore the method of electromagnetic protection. Keywords: Wireless intelligent sensors · Radio frequency (RF) front-end · Electromagnetic interference (EMI) · Electromagnetic pulse (EMP) · Coupling path

1 Introduction With the rapid development of wireless communication, wireless sensor networks (WSN) bring about a revolution in information perception with its characteristics of low power consumption, low cost and distribution [1]. The wireless power system in the smart power system mainly consists of the following three parts: wireless sensor, sink node and access node [2]. Wireless sensors are © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 17–24, 2024. https://doi.org/10.1007/978-981-97-0865-9_3

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often installed next to the equipment to be monitored and are responsible for collecting and uploading the information of the equipment in time. The sink node communicates with the wireless sensor unit in time through the wireless networking communication protocol and transmits the information to the access node. The access node processes and uploads all sink node data within the communication range [3, 4]. With the gradual large-scale application of wireless intelligent sensors in power system, the electromagnetic environment generated by power equipment is becoming more and more complex. The electromagnetic interference peak intensity of sensor operation is high, the interference signal frequency domain is wide, and the electromagnetic coupling path is complex. Wireless sensors often adopt wireless transmission mode, and the RF front-end module is in a harsher electromagnetic environment and is more sensitive to electromagnetic interference. Therefore, it is of great significance to explore the electromagnetic interference characteristics of RF front-end module to understand the coupling paths under different conditions and explore electromagnetic protection methods [5]. Recently, the research on EMI has attracted a great number of attentions. Ref. [6] established the PCB model of a single microstrip line, and the radiation sensitivity of PCB was analyzed by theoretical calculation, which proposed a good way to analyze the influence of relative orientation on electromagnetic interference by analytical method. Ref. [7] found that when the propagation direction of electromagnetic wave was parallel to the microstrip line, the electromagnetic coupling strength would be greater than that when the propagation direction was perpendicular to the microstrip line. Ref. [8] found that the electromagnetic coupling strength showed the largest intensity when the electric field direction was parallel to the microstrip line, through the combination of experiment and simulation. In addition, the electromagnetic sensitivity of electronic devices or circuits to the frequency of EMP has also been studied [9]. Unfortunately, the research on the electromagnetic sensitivity of PCB mainly includes devices or microstrip antenna, and the research on a whole circuit is rare. In this paper, the EMI evaluation and coupling mechanism of RF front-end module under nanosecond EMP radiated environment were investigated by experimental and simulation methods. The RF front-end module on PCB was designed and prepared, and the coupling transient electromagnetic disturbance on the electronic devices was measured. Meanwhile, the physical model of the transient electromagnetic disturbance was built through three dimensional (3D) electromagnetic analysis software CST Studio Suite, and high-frequency circuit simulations were carried out to derive coupling waveforms and coupling paths based on various conditions.

2 Experiment and Simulation 2.1 Experimental Setup and DUT To investigate the EMI effect on RF front-end module subjected to the nanosecond pulse radiation, the L-band front-end circuit board is designed and prepared as the device under test (DUT), which could function as amplification and filtering of the microwave signal. Figure 1 shows the main feature of the designed L-band front-end circuit prototype used in the experiments. The circuit board comprises of a power supply module (+5 V DC),

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a low noise power amplifier (ADI Model HMC405), a bandpass MEMS filter (CETC Model WLM008013), resistors, inductors, capacitors and several microstrips, which are embedded into a PCB, as shown in Fig. 1(a) and (b). The frequency response curve in the range from 0.2 GHz to 2 GHz is measured and plotted in Fig. 1 (c). During the experiment, a 1.20 GHz microwave signal is feed into the circuit through the RF signal generator (Agilent Model 83732B), and the output signal is measured by the oscilloscope (Agilent Model DSO90604A). Figure 1(d) shows the waveforms of input and output signals without any EMI. It can be seen that, when there is no EMP interference, the voltage amplitude of input signal is about 56 mV, and then magnified to 96 mV in output signal, thus the overall gain is calculated to be 4.68 dB, demonstrating a good agreement with the frequency response curve in Fig. 1(c).

Fig. 1. Feature of RF front-end circuit prototype: (a) Circuit board, (b) Circuit structure, (c) Frequency response curve, (d) Waveforms.

Fig. 2. The schematic diagram of space electromagnetic coupling test system.

Figure 2 shows the schematic diagram of space electromagnetic coupling test system. To provide space electromagnetic radiation, we establish an EMP disturbance platform

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which mainly consists of a nanosecond pulse source, a microwave radiation antenna, a measuring antenna, an oscilloscope, a RF signal generator and shielded room. The incident EMP waves are generated by the radiation antenna driven by the nanosecond pulse source, with the rise time (10%–90%) of 1.2 ns and the repetition rate of 1 kHz. The L-band front-end circuit on PCB is placed at a certain distance away from the radiation source. The signal lines connected to the DUT are wrapped with a shielding layer to ensure that electromagnetic energy could not couple to the signal lines. TEM (Transverse Electric and Magnetic Field) horn antenna (0.1–3 GHz) is adopted to measure the space interference electric field, which is placed near the DUT in order to acquire the electromagnetic waves radiated to the DUT. The operation signal of the DUT is input by the RF signal generator, the induced coupling voltage and the transmission signal are measured by the oscilloscope, and both are placed inside the shielded room. With the aid of the experimental setup, the influence of EMP in the far zone radiation with a vertically polarized electromagnetic field is investigated, and then the incident direction/relative distance dependency of the EMI effect is summarized. 2.2 Simulation Model The electromagnetic interference is simulated by CST 3D EM simulation software, which utilizes the field-circuit coupled method to analyze the distribution of EM far fields, radiation pattern and surface currents distribution. The main simulation process includes model establishment, structure meshing, equivalent circuit parameter calculation and matrix formulation, and it is assumed that the currents in the segments and charges on the areas are constant in the simulation. Table 1. Material Parameters of Each Layer in the PCB Layer Name

Type

Material

Thickness (mm)

TOP_SOLDER

Dielectric

FR4

0.00254

TOP_LAYER

Signal

Copper

0.03556

SUBSTRATE-1

Dielectric

FR4

1.20000

BOTTOM_LAYER

Signal

Copper

0.03556

BOTTOM_SOLDER

Dielectric

FR4

0.00254

Material parameters of each layer in the PCB are shown in Table 1. There are five layers of PCB, the middle is the dielectric substrate the two sides of the substrate are the microstrip and the grounding plane respectively, and the two outermost layers are the solder resist layer. The width of microstrips is 2.4 mm, according to Ref. [2], the characteristic impedance Z c of the microstrips is  √  120 1+ k (1) Zc =  ln 2 √ , εr 1− k

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where k = (D−W )/(D + W ), D is the distance between microstrips, W is the width of microstrips, and εr is the equivalent permittivity of dielectric around microstrips. The expression of εr is εr =

 H  

εr + 1 tanh 0.775 ln W + 1.75 + , kW 2 H [0.04 − 0.7k + 0.01(1 − 0.1εr )(0.25 + k)]

(2)

where εr is the permittivity of the dielectric substrate, H is the thickness of the dielectric substrate. According to the above equations, the characteristic impedance of the microstrip is 49.12 , which meets the requirement of transmission line impedance matching in the radio frequency region. Since the RF front-end module is embed into PCB, the RF front-end module model is built by SPICE (Simulation Program for Integrated Circuits Emphasis) for the circuit simulation, the PCB model is built by Altium Designer and then imported into CST Microwave Studio for electromagnetic field simulation. Given that the size of PCB is much smaller than the radiation space, the space electromagnetic wave is set as a plane wave in the solution domain for simplifying calculation. Figure 3 shows the 3D electromagnetic model (a) and the circuit model (b). During the simulation, the microwave signal is injected into the input port and the external electromagnetic pulse wave is radiated to the RF front-end module on PCB. Some probes are set on specific ports to monitor the real-time voltage and current parameters.

Fig. 3. Simulation: (a) 3D electromagnetic model, (b) circuit model.

3 Results and Discussions In far-field radiation, the form of radiation coupling is electromagnetic field coupling which is the combination of electric field (E) and magnetic field (H) that affects the circuit at the same time [10]. Since the proposed simulation model has been validated to fit well with experiments, the vulnerable coupling paths can be identified and the coupling strength can be evaluated based on the CST numerical calculation. Generally, an electromagnetic field can be particularly effectively in coupling with the antenna, aperture, and wires, which can consequently affect various IC chips on the main PCB. So in this work the electromagnetic susceptible parts on the PCB mainly consist of microstrips printed on the dielectric substrate [9], the energy of EMP is coupled into microstrips, then propagates along the circuit and passes through the amplifier, resistance

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module, filter and other lumped components, and finally outputs [5]. The induced voltage would cause distortion of the transmission signal and functional failure, and even destroy the key components if the induced energy is intense enough. Figure 4(a) shows the distribution of microstrip segments and grounding terminal, of which labels (1) - (6) refer to the various microstrip segments, and label (7) refers to the grounding terminal on the PCB. For a better comparison, various types of microstrip segments have been designed, segment (1) is straight with constant width, segments (4) and (5) are vertically bent with constant width, and segments (2–6) are straight with varying widths. In order to monitor the coupling voltage into microstrips, the input signal is turned off and the following results are obtained in this case. Take the relative distance of 1 m and the EMP incident direction of 1# as an example, Fig. 4(b) shows the simulated waveforms of coupling voltage into segments (1), (6) and grounding terminal (7). The amplitudes of coupling voltages into segments (1) and (6) are 10.83 mV and 33.55 mV. And the amplitude of coupling voltage through the grounding plane is 7.60 mV, demonstrating a less coupling energy.

Fig. 4. (a) distribution of PCB, (b) simulated waveforms, (c) coupling voltages, (d) the coupling electric field intensity distribution on PCB surface.

To evaluate the coupling energy into different types of microstrip segments, we introduce a term of specific voltage which is defined as the coupling voltage divided by the segment length and the unit is mV/mm. Figure 4(c) shows the maximum coupling voltages and the specific voltages into different microstrip segments and ground plane. It can be seen that the overall coupling voltage on segments (5) and (6) are 30.41 mV and 33.55 mV, respectively, which are the greatest among all the microstrips. The overall coupling voltages on segment (2) and ground terminal (7) are the lowest. Therefore, we can tell that the longer the microstrip is, the more coupling energy it will receive. Then we compare the specific voltage on segment (1) with (6), and find that the coupling energy through segment with varying widths is much greater than that through segment with constant width, indicating that the impedance-varying microstrip can induce a significantly greater coupling voltage in L-band [11]. Compare the specific voltage on segment (1) with (4), we can find that the coupling energy through a bent microstrip is greater than that through a straight one. That’s because the bend of the microstrip would increase

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the parasitic capacitance of the conductor and result in charge accumulation and electric field concentration. Additionally, Fig. 4(d) shows the coupling electric field intensity distribution on PCB surface. The localized concentration of surface electric fields can be observed at bent regions and width-varying segments, which are in good agreement with the specific voltage distribution. Besides, the PCB edge is demonstrating a larger electric field intensity as well, which is attributed to the electromagnetic waveform resonance between the power/ground plane at the PCB open edge [12]. As a consequence, we can draw a clear conclusion that, the most significant coupling is generated by the impedance-varying and bent microstrips, as well as the long microstrips, and the coupled voltages and currents will be delivered to the loads through the microstrips and fail the electronic equipment. An external EMP with the electric field intensity of 1500 V/m would induce a 100 mV EMI voltage in the RF front-end module, which could disable the signal transformation and transmission. Therefore, to electromagnetic shield the external EMP similar to the operation frequency is a critical and effective method for guaranteeing the electromagnetic compatibility of the electronic equipment [13].

4 Conclusion Transient electromagnetic field has devastating effects on wireless intelligent sensors due to their intense electric field level. In this work, coupling effect and its influence factors of external electromagnetic pulse waves on a RF front-end module embed into PCB were analyzed in experiment, simulation, and theory. The coupling path analysis indicates that the coupling of an EMP wave on RF front-end module occurs predominantly through the microstrips connecting the lumped components, particularly the bent and impedance-varying microstrip segments. The simulation carried using CST software and the theoretical derivation are both in agreement to practical measurements. These results should be of great significance to the reliability evaluation and electromagnetic protection of wireless intelligent sensors in power grid. Acknowledgements. This work was supported by the key scientific and technological project of China Southern Power Grid Corporation (Grant No. 090000KK52220034).

References 1. Min, S.-H., et al.: Analysis of electromagnetic pulse effects under high-power microwave sources. IEEE Access 9, 136775–136791 (2021) 2. Tan, Z., Li, Y., Song, P.: Relevant research on electromagnetic pulse protection of RF front-end. Trans. Beijing Institute Tech. 40(3), 231–242 (2020). (in Chinese) 3. Huang, L., et al.: Simulation analysis of a composite simulator for the source-region electromagnetic pulse environment. In: 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), Hangzhou, pp. 1–4 (2020) 4. Meng, G., et al.: Breakdown on interconnect system of printed circuit board under square wave pulse. J. Xi’an Jiaotong Univ. 46(4), 58–63 (2012)

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5. Mehri, M., Heidari, S., Masoumi, N.: The analysis of EMI effects on the performance of electronic systems implemented on a PCB. In: 2016 IEEE 20th Workshop on Signal and Power Integrity (SPI), Turin, pp. 1–4 (2016) 6. Leone, M., Singer, H.L.: On the coupling of an external electromagnetic field to a printed circuit board trace. IEEE Trans. Electromagn. Compat. 41(4), 418–424 (1999) 7. Zonouz, F.V., Masoumi, N., Mehri, M.: Effect of IC package on radiated susceptibility of board level interconnection. In: 2015 International Conference on Synthesis, Modeling, Analysis and Simulation Methods and Applications to Circuit Design (SMACD), Istanbul, pp. 1–4 (2015) 8. Peng, Q., et al.: Han. Analysis and experimental verification of the electromagnetic coupling characteristic for the microstrip lines. J. Inf. Eng. Univ. 14(1), 36–41 (2013) 9. Aimonetto, M.B., Fiori, F.: Investigation on the susceptibility of BLE receivers to power switching noise. IEEE Trans. Electromagn. Compat. 60(5), 1529–1538 (2018) 10. Shao, X.: Electromagnetic Compatibility and PCB Design. Tsinghua University Press, Beijing (2009). (in Chinese) 11. Li, C., et al.: Numerical simulation on coupling effects of electromagnetic pulse onto microstrip line. J. Microwav. 29(2), 66–70 (2013) 12. Montrose, M.I., et al.: Analysis on the effectiveness of the 20-H rule for printed-circuit-board layout to reduce edge-radiated coupling. IEEE Trans. Electromagn. Compat. 47(2), 227–233 (2005) 13. Sheng, G., et al.: Key technologies and application prospects for operation and maintenance of power equipment in new type power system. High Voltage Eng. 47(9), 3072–3084 (2021). (in Chinese)

Dielectric Constant Characterization of Artificial Electromagnetic Materials for Ultra-high Field Magnetic Resonance Radio Frequency Field Manipulation Yang Gao1,2(B) , Long Li1 , and Xiaotong Zhang3 1 Hangzhou Institute of Technology, Xidian University, Hangzhou 311200, China

[email protected]

2 School of Electric Engineering, Xidian University, Xi’an 710071, China 3 College of Electrical Engineering, Zhejiang University, Hangzhou 310029, China

Abstract. Magnetic resonance imaging (MRI) technology is the mainstream medical imaging technology today. The use of ultra-high static magnetic field strength (≥7T) can better improve the signal-to-noise ratio of imaging and bring clearer imaging quality. However, the inherent standing wave effect of the classic resonant cavity transmitting coil will cause B1 + field inhomogeneity and high SAR value. Studies have shown that high dielectric constant materials can effectively improve the standing wave effect, but there are problems such as difficulties in manufacturing and long-term stability. This paper proposes a method for measuring the dielectric constant of artificial electromagnetic materials based on the microstrip line resonance method, which improves the traditional method of using scattering parameters to obtain the dielectric constant of artificial electromagnetic materials in the induced near-field region, and can effectively reflect the artificial electromagnetic materials in the near-field region. By loading the artificial electromagnetic material on the 7T birdcage coil and comparing it with the birdcage coil without control material, its B1 + field has been doubled, compared with the artificial electromagnetic material B1 + field designed by the traditional measurement method. The artificial electromagnetic material structure designed by the microstrip line resonance method has a significant field regulation effect in improving the uniformity of the B1 + field in the induced near-field area through experimental verification, and has good clinical applicability. Keywords: MRI · 7T · artificial electromagnetic material · dielectric constant measurement · microstrip line

1 Introduction 1.1 A Subsection Sample The magnetic resonance imaging (MRI) system is a medical imaging diagnostic system widely used in clinical practice. Compared with other electromagnetic imaging technologies such as CT, B-ultrasound, X-ray, etc., MRI has greater advantages in soft tissue © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 25–35, 2024. https://doi.org/10.1007/978-981-97-0865-9_4

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imaging and can clearly Distinguish soft tissues such as muscle and fat [1]. MRI scans are non-invasive, non-radioactive, and harmless to the human body, and have become the mainstream medical imaging examination method in modern medicine. Nowadays, MRI technology has developed towards ultra-high field (≥7T), because as the static magnetic field increases, the radio frequency signal will have better signal-to-noise ratio and resolution, and its imaging quality will be higher [2]. However, at a field strength of 7T, the wavelength of the radio frequency wave decreases with the increase of the field strength. The corresponding wavelength is 1 m, which is about the same size as the human body. The resulting phase delay and standing wave effect caused by reflection cause radio frequency Field B1 + field inhomogeneity [3]. In addition, the natural attenuation of the resistive field to the radiation near-field field and the energy absorption of the load brings about energy attenuation in the propagation direction, which affects the imaging quality and makes quantitative analysis and accurate diagnosis difficult. The Minnesota ultra-high field group [4] used a parallel transmission method to reduce the B1 + non-uniformity of the RF field, but the hardware conditions at the time limited its promotion and use. Alsop et al. [5] placed a water bag near the head under a magnetic field environment of 7T and observed significant changes in the radio frequency field around the head. Haines et al. first used a calcium titanate dielectric plate with a dielectric constant of 120 to 130 [6] to improve the B1 + non-uniformity of the radio frequency field. This high dielectric constant dielectric plate can be made thin and relatively flexible. Achieved better results. The Institute of Materials at Pennsylvania State University [7] designed a new ceramic material dielectric plate with a dielectric constant as high as 1000 and a material conductivity of 0.05 S/m. It is possible to put this high dielectric constant into a dielectric plate. The board’s 20-channel receive array coil has the same signal-to-noise ratio as the case of a separate 64-channel receive array coil. Later, Slobozhanyuk et al. [8] applied artificial electromagnetic materials to improve the signal-to-noise ratio of magnetic resonance imaging for the first time, inserting a metal line array into a water-based stent. Their experimental results showed that this artificial electromagnetic material re-changed the distribution of radio frequency electromagnetic fields, the signal-to-noise ratio has been increased to more than twice the original, and the imaging quality has been further improved. Schmidt et al. [9] designed a two-dimensional metasurface structure composed of a short metal array and a high dielectric constant dielectric plate, and placed it into a 7T 32-channel receiving array to improve the non-uniformity of the radio frequency field. Based on the method proposed by Vorobyev et al. to measure the dielectric constant by setting Floquet boundary excitation to design and simulate an artificial electromagnetic material structure with a high dielectric constant dielectric plate, this paper proposes a measurement method using microstrip line resonance. Dielectric constant of artificial electromagnetic materials in the induced near field region. It improves the accuracy of the characteristics of artificial electromagnetic materials in the induction near-field region, and improves the traditional Floquet boundary excitation method that uses the scattering coefficient parameters obtained in the radiation field to measure the dielectric constant in the induction near-field region. The artificial electromagnetic material structure improved by this method can simulate and have the same performance as a high dielectric constant dielectric plate in improving B1 + field uniformity, and can keep the

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SAR value within a reasonable level. This measurement method has lower cost, higher measurement accuracy, better experimental results, and is widely usable.

2 Artificial Electromagnetic Material Structure Design This high dielectric constant artificial electromagnetic material used in the 7T field strength birdcage coil is composed of multiple artificial electromagnetic material sheets. Each artificial electromagnetic material unit structure is composed of two layers of PCB substrates. Multiple artificial copper sheet structures are attached between PCB substrates, and the thickness between the substrates is equal to the thickness of the copper sheets. The designed artificial electromagnetic material structure is composed of four layers of materials. The second and fourth layers are FR-4 substrates. The first layer is composed of four copper sheets, and the third layer is composed of a single layer of copper plates. Due to its artificial electromagnetic material The unit period is larger than the distance between the upper and lower copper sheets, so it can be equivalent to a capacitor mainly composed of the upper and lower copper sheets to achieve the effect of increasing the high dielectric constant, as shown in Fig. 1. Through simulation, it can be found that its dielectric constant is inversely proportional to the thickness of the substrate and proportional to the unit period of the artificial electromagnetic material. This unit structure can achieve a specific dielectric constant value within a certain range, thereby effectively improving the quality of magnetic resonance imaging.

Fig. 1. Metamaterial structure (a) Geometric dimensions of metamaterial unit (b) Side view of metamaterial unit (c) Floquet port of metamaterial unit (d) Dielectric constant of dielectric pad and corresponding metamaterial measured at 7T 300 MHz The values are 78.4 and 78.8 respectively.

This structure is placed parallel to the polarization direction of the birdcage coil, forming a parasitic capacitance between the upper and lower layers of copper sheets,

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and forms an induced current under the excitation of the radio frequency coil, thereby generating a secondary magnetic field, improving the overall transverse magnetic field, and can Effectively improve the non-uniformity of RF field under 7T ultra-high field strength. The material used for the substrate is FR-4, the dielectric constant is 4.3, the loss tangent is 0.025, the conductivity of the copper sheet is 5.8e + 7 S/m, and f1 is the side length of the second layer of copper sheet, which is 7.7mm. During the simulation process, its electric field lines and magnetic field lines are parallel to the unit structure of the artificial electromagnetic material, and the incident direction of the electromagnetic wave is perpendicular to the unit structure of the artificial electromagnetic material, so that it achieves the same simulation effect as a dielectric plate with a dielectric constant of 78.4.

3 Measurement of Dielectric Constant of Artificial Electromagn-Etic Materials 3.1 Measurements Using Floquet Boundary Conditions The value of the equivalent dielectric constant in this design is one of the most critical factors in the structural characteristics of artificial electromagnetic materials. By selecting the substrate material and changing the size of the unit structure, the dielectric constant is 78.4. In the CST Microwave Studio 2021 commercial simulation software, By setting the artificial electromagnetic material unit structure and Floquet boundary conditions [10], the corresponding scattering coefficient is obtained. Finally, the equivalent dielectric constant value is obtained through the scattering coefficient measurement method proposed by Luukkonen et al. [11]. Its calculation The formula is as follows: 1 i S11 = − (z − )sin(nk0 d )S21 2 z 1 S21 = i cos(nk0 d ) − 2 (z + 1z )sin(nk0 d ) 2 + S2 1 − S11 1 2π m 21 cos−1 n= + k0 d 2S21 k0 d  2 (1 + S11 )2 − S21 Z =± 2 (1 − S11 )2 − S21

(1) (2) (3) (4)

Finally, the relative permittivity and relative permeability values can be calculated through the following relationship between refractive index and wave impedance: n (5) ε= z μ=n·z

(6)

In the formula, n is the refractive index, z is the wave impedance, k_0 is the angular wave number in vacuum, d is the thickness of the sample, ε is the relative dielectric constant, μ is the relative magnetic permeability, and m is an integer, used to identify the inverse cosine function. Branch, if the thickness of the sample is less than one wavelength, its value is set to zero (Table 1).

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Table 1. Structural parameters obtained by Floquet optimization Parameter

Value

Parameter

Value

q1

8.9 mm

m1

4.15 mm

p1

8.9 mm

t1

2.47 mm

g1

0.6 mm

h1

0.035 mm

3.2 Improvement of Dielectric Constant Measurement by Microstrip Resonance Method In order to more accurately reflect the characteristics of artificial electromagnetic materials in the birdcage coil induction near-field region, a microstrip line resonance method was proposed based on Floquet measurements. The measurement method, as shown in Fig. 2, is to use a water model with a dielectric constant of 78.4 as the dielectric substrate of the microstrip line, and load a 50- load resistor at the end to match the characteristic impedance of the microstrip line, and load an adjustment capacitor to adjust the dielectric The resonance point of the plate. In the simulation, the resonance point is adjusted to 297.2 MHz by setting capacitance value to 0.7pF, as shown in Fig. 3(a), and then the artificial electromagnetic material designed through Floquet simulation is used in the same way as the dielectric substrate of the microstrip line for observation. Its resonance point is found to be at 325 MHz, as shown in Fig. 3(b). It can be seen that there is a big difference between the artificial electromagnetic material structure and the dielectric plate designed by Floquet simulation in the induction near field area. f2 is the side length of the second layer of copper sheet, which is 18.8 mm. Afterwards, the structure of the artificial electromagnetic material unit is adjusted, as shown in Fig. 3(c), so that the resonance point of the artificial electromagnetic material can appear at 297.2 under the same measurement method, allowing them to have the same electrical characteristics in the inductive near-field region (Table 2).

Fig. 2. Metamaterial structure (a) Geometric dimensions of metamaterial unit (b) Side view of metamaterial unit (c) Floquet port of metamaterial unit (d) Dielectric constant of dielectric pad and corresponding metamaterial measured at 7T 300 MHz The values are 78.4 and 78.8 respectively.

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Fig. 3. (a) Tuning the dielectric pad resonance point to 297.2 MHz in the inductive near-field region by the microstrip line resonance method (b) Put the metamaterial structure measured by Floquet into the microstrip line, and its resonance point appears at 325 MHz (c) By optimizing the metamaterial structure in the microstrip line, the resonance point of the metamaterial in the induced near-field region is tuned to 297.2 MHz.

Table 2. Structural parameters obtained by microstrip resonance method Parameter

Value

Parameter

Value

q2

20 mm

m2

9.7 mm

p2

20 mm

t2

3.27 mm

g2

0.6 mm

h2

0.035 mm

4 Birdcage Coil Simulation 4.1 Artificial Electromagnetic Materials and Human Body Model Establishment CST commercial simulation software with time domain solver solve the distribution of B1 + under the condition of loading traditional dielectric pad and artificial electromagnetic materials under 7T field strength, which includes a model simulating the human head with a dielectric constant of 68 and conductance rate is 0.5 S/m, the density is 1000 kg/m3 , the radius is 80mm, the length of the cylindrical model is 200 mm, and the birdcage coil is a commonly used transmitting coil working at 7T 300 MHz [12]. The size structure of the dielectric plate is 173 × 128 × 28 mm, the artificial electromagnetic material structure obtained through Floquet boundary conditions is 173 × 128 × 24.7 mm, and the artificial electromagnetic material structure size after microstrip line optimization is 173 × 128 × 29.43 mm. g is 3.27 mm. In order to achieve the corresponding dielectric constant value, the artificial electromagnetic material structure after microstrip line optimization is stacked by nine layers of metamaterial unit structures. Each layer has the same thickness. 4.2 Simulation Results By comparing birdcage coils without regulated materials, artificial electromagnetic materials designed by Floquet and birdcage coils with artificial electromagnetic materials and dielectric pad improved with microstrip lines, the electromagnetic wave can be approximately equivalent at the center of the coil. The propagation direction is along the axial direction, that is, perpendicular to the artificial electromagnetic material model, while

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31

its electric and magnetic field directions are parallel to the artificial electromagnetic material. The magnetic field conditions in the four cases and the impact on the B1 + field were compared respectively. Finally, the SAR value of the average mass of 10g under the condition of 1W receiving power was compared. According to the simulation results, the microstrip line resonance method was improved. The artificial electromagnetic materials have significantly improved the uniformity of the B1 + field. In Fig. 4, the value of the B1 + field in the human body model reaches a maximum of 0.21 uT without regulating materials. The value of B1 + at the same position inside the human body model with a dielectric plate loaded is 0.50 uT. Figure 5 shows that with artificial electromagnetic materials loaded the value of B1 + is 0.38 uT, while the value of B1 + of the artificial electromagnetic material structure improved by the microstrip line resonance method is 0.47uT. Compared with the birdcage coil without regulating material, the value of B1 + is twice as high as that of the traditional Floquet design. The value of artificial electromagnetic materials has also been increased by 20%, which has a great effect on improving the quality of magnetic resonance imaging. In ultra-high field conditions, the size of the SAR value is also one of the crucial factors. If the value is too high, it will cause damage to the safety of the human body. The results show that the highest SAR value of the dielectric plate is 0.239W. /Kg, the SAR value of artificial electromagnetic materials is 0.208 W/Kg. The SAR value of the artificial electromagnetic material structure improved by the microstrip line resonance method in the human body is 0.236 W/Kg, which is lower than the domestic safety maximum value of 1.6 W/Kg, reaching achieve the original goals of the design.

Fig. 4. The B1 + field and SAR value of the birdcage coil without the control material and with the dielectric constant 78.4 dielectric pad. The B1 + field values are 0.21 uT and 0.50 uT. The SAR values are 0.142, 0.239 W/Kg.

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Fig. 5. Obtain the B1 + field and numerical simulation results of SAR through the birdcage coil. (a,b,c) show through commercial simulation software the simulation model of the birdcage coil through the dielectric pad, the metamaterial designed by Floquet and the optimized metamaterial in the microstrip line; (d,e,f) show the zoy plane of the birdcage coil of the B1 + field numerical results of the position of the central axis, the values are 0.50 uT, 0.38 uT, 0.47 uT; (g,h,i) show the numerical results of the SAR value of the position of the central axis of the zoy plane of the birdcage coil, the values are 0.239 W/Kg, 0.208 W/Kg, 0.236 W/Kg.

Fig. 6. (a) The metamaterial designed by the microstrip resonance method (b) The measurement setup of the microstrip resonance method based on VNA (c) The measurement results of the S11 of the dielectric pad and the metamaterial.

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Fig. 7. (a) Side view of dielectric pad, annular RF coil and human body model (b) Front view of dielectric pad, annular RF coil and human body model (c, d, e) are unregulated materials, loaded dielectric pad and optimized artificial The simulation results of electromagnetic materials (f, g, h) are the experimental results of unregulated materials, loaded dielectric pads and optimized artificial electromagnetic materials.

5 Experimental Results Compared with the aqueous solution dielectric plate with a dielectric constant of 78.4, the artificial electromagnetic material structure designed by the microstrip line resonance method has reached the same resonance point as shown in Fig. 6, reflecting the same electrical characteristics in the induced near field. Then, by using an annular radio frequency coil for signal transmission in the Siemens 7T ultra-high field magnetic resonance imaging instrument, as shown in Fig. 7, a comparison was made between the unregulated material. The solution dielectric plate model loaded with a dielectric constant of 78.4, and the microstrip line. The artificial electromagnetic material designed by the resonance method has been subjected to imaging experiments on the three of them. It can be seen that after loading the high dielectric constant dielectric plate and the artificial electromagnetic material, the standing wave effect is obvious on the upper right side of the artificial electromagnetic material. Improvement, and the artificial electromagnetic material has achieved a similar effect to the dielectric plate in improving imaging quality. The experimental results show that the results obtained by using the microstrip line resonance method in 7T 300 MHz are relatively similar to the simulation results. The structure of this artificial electromagnetic material can effectively improve and enhance the field inhomogeneity in the induced near field area.

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6 Conclusion By comparing the simulated design of the artificial electromagnetic material structure with the dielectric plate and the birdcage coil without regulatory materials, the magnetic field and B1 + values have achieved good results. The thickness of each layer in the design of the artificial electromagnetic material is 3.27 mm. It consists of two FR-4 dielectric boards and copper sheets. In order to achieve or better effects than the dielectric board, they are stacked to a thickness similar to the dielectric board. Although the thickness of each layer of PCB is thinner, the overall the thicker thickness results in a larger number of PCB boards, resulting in an increase in the total cost [13]. In the simulation, its magnetic field polarization direction is parallel to the artificial electromagnetic material structure, which is consistent with the direction of the artificial electromagnetic material structure. Therefore, when the artificial electromagnetic material structure is tangential to the polarization direction of electromagnetic waves, it can well improve the field inhomogeneity [14]. The mechanism of action of isotropy and anisotropy on electromagnetic waves can also be considered. On this basis, designing an isotropic artificial electromagnetic material structure that can be used for imaging various parts of the human body such as the abdomen will have better applicability [15]. The proposed microstrip line measurement model can better reflect the electrical characteristics of artificial electromagnetic materials in the induction near field region. In general, the microstrip line measurement method in the induction near field region proposed in this article can be simulated in a 7T 300 MHz birdcage. In human imaging simulation experiments, the contrast medium plate has good effects in improving field uniformity and controlling SAR values, and can be widely used in ultra-high field imaging. Acknowledgements. This work was supported in part by the National Natural Science Foundation of China (52307256), the Fundamental Research Funds for the Central Universities (20103237694), Proof of Concept Foundation of Xidian University Hangzhou Institute of Technology (GNYZ2023YL0404).

References 1. Chi, Z., Yi, Y., Wang, Y., et al.: Adaptive cylindrical wireless metasurfaces in clinical magnetic resonance imaging. Adv. Mater. 33(40), 2102469 (2021) 2. Duan, G., Zhao, X., Anderson, S.W., et al.: Boosting magnetic resonance imaging signal-tonoise ratio using magnetic metamaterials. Commun. Phys. 2(1), 35 (2019) 3. Vorobyev, V., Shchelokova, A., Efimtcev, A., et al.: Improving homogeneity in abdominal imaging at 3 T with light, flexible, and compact metasurface. Magn. Reson. Med. 87(1), 496–508 (2022) 4. Adriany, G., et al.: Transmit and receive transmission line arrays for 7 tesla parallel imaging. Magn. Reson. Med. 53(2), 434–445 (2005) 5. Yang, Q.X., et al.: Manipulation of image intensity distribution at 7.0 T: passive RF shimming and focusing with dielectric materials. J. Magn. Reson. Imaging 24(1), 197–202 (2006) 6. Haines, K., Smith, N.B., Webb, A.G.: Reducing SAR and enhancing cerebral signal-to-noise ratio with high permittivity padding at 3 T. Magn. Reson. Med. 67(3), 890–890 (2012)

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7. Sica, C.T., Rupprecht, S., Hou, R.J., Lanagan, M.T., Lanagan, M.T., Yang, Q.X.: Toward whole-cortex enhancement with a ultrahigh dielectric constant helmet at 3T. Magn. Reson. Med. 83(3), 1123–1134 (2020) 8. Slobozhanyuk, A.P., et al.: Enhancement of magnetic resonance imaging with metasurfaces. Adv. Mater. 28(9), 1832–1838 (2016) 9. Schmidt, R., Slobozhanyuk, A., Belov, P., Webb, A.: Flexible and compact hybrid metasurfaces for enhanced ultra high field in vivo magnetic resonance imaging. Sci. Rep. 7(1), 1678 (2017) 10. Das, P., Gupta, J., Sikdar, D.: Design and modeling of a thin metasurface ‘add-on’ for magnetic field enhancement in 1.5T MRI 11. Luukkonen, O., Maslovski, S.I., Tretyakov, S.A.: A stepwise Nicolson–Ross–Weir-based material parameter extraction method. IEEE Antennas Wirel. Propag. Lett. 10, 1295–1298 (2011) 12. Vorobyev, V., Shchelokova, A., Zivkovic, I., et al.: An artificial dielectric slab for ultra highfield MRI: proof of concept. J. Magn. Reson. 320, 106835 (2020) 13. Webb, A., Shchelokova, A., Slobozhanyuk, A., et al.: Novel materials in magnetic resonance imaging: high permittivity ceramics, metamaterials, metasurfaces and artificial dielectrics. Magn. Reson. Mater. Phys., Biol. Med. 35(6), 875–894 (2022) 14. Del Risco, J.P., Baena, J.D.: Extremely thin fabry-perot resonators based on high permitivity artificial dielectric. In: 2016 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), pp. 40–42. IEEE (2016) 15. Chen, H., Guo, L., Li, M., et al.: Metamaterial-inspired radiofrequency (RF) shield with reduced specific absorption rate (SAR) and improved transmit efficiency for UHF MRI. IEEE Trans. Biomed. Eng. 68(4), 1178–1189 (2020)

A Power-Enhanced Large-Space Wireless Charging System with Relay Energy Conversion Structure Yaju Yuan, Zhuangsheng Xiao, Xingpeng Yu, Yanzhao Fang, and Siqi Li(B) Department of Electrical Power Engineering, Kunming University of Science and Technology, Kunming, China {xiaozhuangsheng,lisiqi}@kust.edu.cn, {yuxingpeng, fangyanzhao}@stu.kust.edu.cn

Abstract. Large-space wireless power transfer (WPT) technology can realize free space wireless power transmission while ensuring electromagnetic safety. However, the power transmission capability of the system is weakened by corresponding non-uniform weak magnetic field. To surmount these limitations, this paper proposes a novel power-enhanced large-space wireless charging system, which can achieve a wide spatial uniform magnetic field that can satisfy the safety requirements, and realize a stable output power of tens of watts across an extensive spatial domain through the relay energy conversion structure. The system design scheme and corresponding solution are introduced. The large-sized coils are compensated in segments to achieve uniform magnetic field. The compact relay energy conversion structure with both receiving and transmitting capabilities is analyzed. The energy of surrounding space is initially captured by the receiving coil in the relay structure and subsequently converted into higher frequency alternating current, seamlessly transferred to the transmitting coil in the relay structure, and ultimately transmitted to the receiving device. In this way, the transmission power can be improved through the two-stage energy conversion structure. The transmission characteristics of the system are derived and analyzed, confirming its effectiveness through simulation and experiment. The results demonstrate that the system can significantly enhance the transmission power capability under the electromagnetic safety standards. The experimental results show that within a space of about 25 m3 , the system can be charged anywhere, and the charging power is about 18 W. Keywords: Wireless power transfer · Large-space · Relay coil · Frequency conversion · Bio-electromagnetic safety

1 Introduction Wireless Power Transfer (WPT) technology has garnered extensive attention from scholars in the realm of electrical engineering both domestically and internationally [1]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 36–44, 2024. https://doi.org/10.1007/978-981-97-0865-9_5

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With the development of WPT technology, the burgeoning demand for flexible and imperceptible charging fuels the trend of surpassing conventional WPT limitations, expanding system space range, and enhancing spatial freedom. The Korean Academy of Science and Technology (KAIST) conducted comprehensive research on large space and long distance omnidirectional WPT coils, featuring crossed dipole Tx and Rx configurations, wide-range Tx coils were designed to generate uniformly distributed DQ magnetic fields, suitable for ubiquitous Wi-Power zone and coreless transmitting coil systems were explored for wide-range ubiquitous IPT applications [2, 3]. Nagoya Institute of Technology proposed a planar omnidirectional WPT system, due to the consideration of human electromagnetic safety, the system is not good enough for fast charging of home appliances [4]. Aalto University in Finland proposes a cylindrical transmitting coil for mobile and portable wireless charging applications and performs SAR evaluation based on human safety limits [5]. Chongqing University devised a reticulated planar transmitter, achieving unrestricted positioning for omnidirectional wireless power transmission [6], reference [7] proposed a three-dimensional omnidirectional WPT system suitable for consumer electronics such as mobile phones and tablet computers. Furthermore, Central South University proposed a structure of transmitting coils placed vertically to form a 3D wireless charging cylinder, enabling simultaneous charging of multiple loads in its vicinity [8]. While the aforementioned references research has made notable strides in high degree of freedom, low power consumption, and multiple load technologies, there remains a dearth of comprehensive analyses concerning large space systems and bio-electromagnetic safety issues. Currently, the prevailing practice for large-space WPT systems entails the utilization of a multi-coil structure featuring relay coils. Reference [9] presented an intermediate range 6.78 MHz WPT system employing segmented coil transmitters, which can provide wireless charging for medical equipment, and conducted SAR finite element analysis. Reference [10] introduced a WPT system with asymmetrical size, low magnetic leakage, and high efficiency for long-range transmission, but under high power transmission, the incident field may exceed the exposure level. In Reference to [11], a mid-range WPT system is presented, capable of charging multiple receivers of various types at 6.78 MHz. Reference [12] proposes an analytical model based on electromagnetic field analysis to evaluate the safety performance of a resonant charging system capable of safe wireless power transfer with watt-level power over meter-level distances. The cited references demonstrate that WPT systems with relay coils offer significant advantages in long-distance and multi-load wireless power transmission. Nonetheless, the increasing transmission distance necessitates a larger number of relay coils, thereby expanding the overall volume of the WPT system. At present, research on large-space wireless power transmission is limited, with a primary focus on long-distance, multi-load, and free-positioning capabilities. Ensuring safe and stable wireless power transmission at tens of watts within large spaces of tens of cubic meters remains a challenging task. To address this issue, this paper proposes a power-enhanced large-space wireless charging system with relay energy conversion structure. The transmission power can be improved through the two-stage energy conversion structure. Through simulations and experiments that adhere to electromagnetic

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safety standards, the system demonstrates its ability to achieve stable tens of watts power transmission in the specified large space range.

2 System Design and Model Building 2.1 System Analysis and Design This paper addresses a critical challenge: achieving stable tens of watts of power transmission with a smaller receiving coil in a large-space while maintaining low electromagnetic field strength. To tackle this problem, the paper presents a sophisticated design scheme and a corresponding technology roadmap, as shown in Fig. 1. 1

1

2

2

3

3

4

4

Fig. 1. System design scheme and corresponding technology roadmap.

In order to maintain stable power transmission, a large-size coaxial three-coil structure is adopted, and distributed capacitance is introduced through segmented compensation to change the current phase to achieve a consistent current direction to generate a nearly uniform spatial magnetic field. Ensuring bioelectromagnetic safety requires balancing electromagnetic safety limits, current, and frequency selection. Key considerations include magnetic and electric field strengths. Coil size affects field distribution, with larger sizes weakening the field near the center. Increasing the current of transmitting coil strengthens the field but raises

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the electric field intensity. Higher frequencies allow greater power transfer and spatial freedom, but safety concerns arise at excessively high frequencies. To maintain safe power transmission at the coil center, we must consider safety limits and coil size to determine an appropriate coil current, minimizing potential electromagnetic radiation effects on humans and the environment. To enhance transmission power, a relay energy conversion structure with dual receiving and transmitting capabilities is utilized. The transmitting coil generates a uniform electromagnetic field with at frequency f1 , and the power in the surrounding space is first captured by the receiving coil in the relay structure, and then converted into an alternating current with frequency f2 (f2 > f1 ), which is seamlessly transmitted to the transmitting coil in the relay structure Coil, finally transmitted to the receiving device. Based on the coil design analysis, the proposed structure of power-enhanced largespace wireless charging system is illustrated in Fig. 2(a). The transmitting coil features a large-size coaxial three-coil structure, while the relay coil employs rectangular and DD coil configurations. The receiving coil adopts a planar spiral coil, with each coil incorporating segmented compensation. This paper establishes a circuit model, depicted in Fig. 2(b). The front inverter employs a full-bridge inverter circuit, while the subsequent high-frequency inverter adopts a class E inverter circuit, the rectifier circuit is a fullbridge rectifier circuit. Within the circuit model, Uab denotes the DC power supply. The pre-stage bilateral LCC compensation network comprises the compensation components (Lf 1 , Cf 1 , C1 )and (Lf 2 , Cf 2 , C2 ). Similarly, the second-stage LCC-S compensation network is formed by Lf 3 , Cf 3 , C3 , and C4 , R0 represents the load.

13

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p 1

2 2

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o

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4 3

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(a)

Fig. 2. System structure. (a) System model and coil structure, (b) Circuit model.

2.2 Equivalent Circuit of the System The values of M13 , M14 , M23 , and M24 are too small to be ignored, the simplified circuit model, as shown in Fig. 3. uAB is the output voltage of the full-bridge inverter, uab is the AC voltage before rectification, and nuab is the output voltage of class E inverter. The compensation network of the system satisfies the relation (1). Lfi =

1 ω2 Cfi

(i = 1, 2, 3), Ci =

1 1 (i = 1, 2, 3), C4 = 2 − Lfi ) ω L4

ω2 (Li

(1)

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1

2

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1

u

3 2

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u

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nu

4

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0

Fig. 3. Simplified circuit model of the system.

Applying Kirchhoff ‘s voltage law (KVL) to the circuit and incorporating the condition of formula (1), we obtain the following circuit equation, as shown in (2). ⎤ ⎡ ⎤ ⎤ ⎡ ⎡ UAB I1 jω1 Lf 1 0 0 0 0 0 0 ⎥ ⎢ I ⎥ ⎢ 0 ⎥ ⎢ 0 0 jω1 Lf 1 0 0 jω1 M12 0 ⎥ ⎥ ⎢ 2 ⎥ ⎢ ⎢ ⎥ ⎢ I ⎥ ⎢ 0 ⎥ ⎢ jω M 0 0 jω1 Lf 2 0 0 0 ⎥ ⎥ ⎢ 3 ⎥ ⎢ ⎢ 1 12 ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ 0 jω1 Lf 2 0 0 0 0 ⎥ · ⎢ I4 ⎥ = ⎢ Uab ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎥ ⎢ I11 ⎥ ⎢ nUab ⎥ ⎢ 0 0 0 0 0 jω2 Lf 3 0 ⎥ ⎢ ⎥ ⎥ ⎢ ⎢ ⎣ 0 0 0 0 0 jω2 M34 jω2 Lf 3 ⎦ ⎣ I22 ⎦ ⎣ 0 ⎦ 0 0 I33 jω2 M34 U0 0 0 0 0 (2) By solving the circuit equation with the condition of formula (2), the voltage and current formulas are derived as shown in (3). I1 =

UAB Uab nUab nUab M34 ; I2 = ; I3 = ; U0 = jω1 Lf 1 jω1 Lf 2 jω2 Lf 3 Lf 3

(3)

In terms of system characteristics, the transmitting coil and relay coil maintain a constant coil current, while the receiving side receives a constant voltage output.

3 Simulation and Analysis 3.1 Simulation of Circuit Model The geometric parameters and main electrical parameters of the coil, as outlined in Table 1,visualize the simulation results in Fig. 4. The simulation results show that the load only receives 0.98 W power without the relay energy conversion structure. However, after the introduction of the relay energy conversion structure, the received power of the load increased rapidly to 20.03 W. This clearly shows that the relay energy conversion structure enables the load to obtain higher power output, thereby improving the performance of the system. 3.2 Assessment of Electromagnetic Safety Following the ICNIRP2020 standard, the electric field intensity limit of the peak reference limit (root mean square value) of 100 kHz–10 MHz electromagnetic field local

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(b)

(a)

Fig. 4. Simulation waveform. (a) The current waveforms flowing through the coils, (b) ZVS of full bridge inverter, and the load receives power. Table 1. The geometric parameters and main electrical parameters of the coil. Parameter

Value

Parameter

Value

Parameter

Value

Transmitting coil R1/m

2

f1 /MHz

1.78

Lf 1 /uH

2

Axis distance d/m

1

f2 /MHz

6.78

Lf 2 /uH

1

Relay coil length L/m

1.2

Load R0 /

5

Lf 3 /uH

0.2

Relay coil width W/m

0.2

L1 /uH

58.14

Lch /uH

47

Receive coil radius R4/mm

75

L2 /uH

3.43

Lp /uH

1.038

turns of receiving coil N

2

L3 /uH

3.27

CP /pF

400

DC power UDC /V

200

L4 /uH

3.08

exposure is 83 V/m, the magnetic field intensity limit is 21 A/m, and the basic limit for local head SAR is 2 W kg−1 . To reduce electromagnetic field intensity, segmented compensation is employed, and is demonstrated in Fig. 5 and Fig. 6. The paper employs 12-segment transmitting coils (Fig. 5) and analyzes the electric field distribution obtained from the simulation of 24 transmitting coils (Fig. 6(a) and Fig. 6(b)). Additionally, local head SAR evaluation is conducted for areas exceeding reference limits (Fig. 6(c)).

(a)

(b)

Fig. 5. At the excitation current of 8A, the distribution of the electric and magnetic field is shown at the moment when values are at the maximum. (a) magnetic field, (b) electric field (12-segment).

In Fig. 5, it is evident that the magnetic field strength within the transmitting coil remains uniform and below the 21 A/m limit. However, due to the power transmission requirements, the magnetic field strength on the coil surpasses 21 A/m. Although the

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(a)

(b)

Fig. 6. Electric field distribution of 24 transmitting coils and local head SAR evaluation. (a) electric field (24-segment), (b) local head SAR.

majority of the electric field strength in most areas adheres to 83 V/m, there are certain hazardous regions surrounding the transmitting coil that necessitate further optimization and evaluation. Employing segmented compensation effectively reduces the electric field intensity, thereby expanding the safe area complying with reference limit for electric field intensity, as depicted in Fig. 6(a), and the safe area extends from 3.3 m diameter to 3.6 m. As shown in Fig. 6(b), the value of local head SAR remains lower than 2 W/kg, further affirming the bio-electromagnetic safety of the system.

4 Experimental Test and Result The experimental platform is built to carry out the design and manufacture of the prototype. The experimental platform and related experimental results are shown in Fig. 7. The experimental results show that the transmitting coil frequency is 1.787 MHz, the frequency upscaling through the relay coil is 6.771 MHz, when the DC voltage is 200 V, the

11

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18.23W

(a)

(b)

Fig. 7. Experimental results. (a) Experimental platform and power, (b) ZVS.

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class E inverter circuit realizes ZVS, and the receiving coil can receive power 18.23 W, which can realize wireless charging at any position.

5 Conclusion This paper proposes a power-enhanced large-space wireless charging system with twostage relay energy conversion structure, which can significantly improve the transmission capability of system and ensure electromagnetic safety to maintain a secure electromagnetic field strength in the charging area. The design scheme and corresponding solution are analyzed. The structure and transmission characteristics of the relay energy conversion structure is introduced and derived. By applying the relay energy conversion structure, along with segmented compensation and frequency increase techniques, the power transmission capability is significantly enhanced, and the watt-level power transmission within a space range of about 25 m3 is realized, the transmission power is about 16 W. Future research aims to optimize system performance, improve power transfer efficiency, and explore applications in diverse scenarios. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant No. 52067011) and Yunnan Fundamental Research Project (Grant No. 202201AT070155).

References 1. Nguyen, H.T., et al.: Review map of comparative designs for wireless high-power transfer systems in EV applications: maximum efficiency, ZPA, and CC/CV modes at fixed resonance frequency independent from coupling coefficient. IEEE Trans. Power Electron. 37, 4857–4876 (2022) 2. Lee, E.S., Sohn, Y.H., Choi, B.G., Han, S.H., Rim, C.T.: A modularized IPT with magnetic shielding for a wide-range ubiquitous wi-power zone. IEEE Trans. Power Electron. 33, 9669– 9690 (2018) 3. Choi, B.G., Sohn, Y., Lee, E.S., Han, S.H., Kim, H.R., Rim, C.T.: Coreless transmitting coils with conductive magnetic shield for wide-range ubiquitous IPT. IEEE Trans. Power Electron. 34, 2539–2552 (2019) 4. Lan, J., Diao, Y., Duan, X., Hirata, A.: Planar omnidirectional wireless power transfer system based on novel metasurface. IEEE Trans. Electromagn. Compat. 64, 551–558 (2022) 5. Ha-Van, N., Liu, Y., Jayathurathnage, P., Simovski, C.R., Tretyakov, S.A.: Cylindrical transmitting coil for two-dimensional omnidirectional wireless power transfer. IEEE Trans. Industr. Electron. 69, 10045–10054 (2022) 6. Feng, T., Zuo, Z., Sun, Y., Dai, X., Wu, X., Zhu, L.: A reticulated planar transmitter using a three-dimensional rotating magnetic field for free-positioning omnidirectional wireless power transfer. IEEE Trans. Power Electron. 37, 9999–10015 (2022) 7. Feng, T., Sun, Y., Feng, Y., Dai, X.: A tripolar plane-type transmitter for three-dimensional omnidirectional wireless power transfer. IEEE Trans. Ind. Appl. 58, 1254–1267 (2022) 8. Han, H., Mao, Z., Zhu, Q., Su, M., Hu, A.P.: A 3D wireless charging cylinder with stable rotating magnetic field for multi-load application. IEEE Access 7, 35981–35997 (2019)

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9. Tang, S.C., Lun, T.L.T., Guo, Z., Kwok, K., McDannold, N.J.: Intermediate range wireless power transfer with segmented coil transmitters for implantable heart pumps. IEEE Trans. Power Electron. 32, 3844–3857 (2017) 10. Wen, F., Chu, X., Li, Q., Li, R., Liu, L., Jing, F.: Optimization on three-coil long-range and dimension-asymmetric wireless power transfer system. IEEE Trans. Electromagn. Compat. 62, 1859–1868 (2020) 11. Oh, H., et al.: Mid-range wireless power transfer system for various types of multiple receivers using power customized resonator. IEEE Access 9, 45230–45241 (2021) 12. Fang, W., et al.: Safety analysis of long-range and high-power wireless power transfer using resonant beam. IEEE Trans. Signal Process. 69, 2833–2843 (2021)

A Practical Method for Calculating Indirect Carbon Emissions of Electricity Users in Large Power Grid Sirui Zhang(B) , Jing Zhang, Fanpeng Bu, Ling Cheng, Zhanbo Wang, and Zihan Gao State Grid China Electric Power Research Institute, Beijing, China [email protected], [email protected]

Abstract. The accurate measurement methods for carbon emissions are critical in both incentivizing consumers towards energy conservation and emission reduction, as well as ensuring fairness in carbon emissions trading. The indirect carbon emissions are generated from user’s electricity consumption. The existing indirect carbon emission calculation method assumes that the carbon emissions per unit of electricity are the same at any nodes and any time in the power grid. Carbon flow calculation method could bridge this gap, however, it still need improvement when applying to large power grid. This paper proposed a practical indirect carbon emission calculation method by parallel computing the divided power grid, thereby significantly reducing the computational pressure. Furthermore, an effective Thévenin equivalent fitting technique is adopted to lessen the computational complexity in the transmission network. By clustering typical scenarios, the annual equivalent carbon emission intensity can be calculated for any node in the power grid. These calculated carbon emission factor can serve as substitutions for the traditional carbon emission factors. The case study proves this method for carbon emission calculation manages to strike a balance between computational complexity and acknowledging the spatio-temporal characteristics in carbon emissions. Keywords: Carbon Emission Calculation · Power Tracing · Equivalent Circuit

1 Introduction The promotion of green, low-carbon, and sustainable economic development has become a global consensus [1]. The carbon trading market operationalizes carbon emission rights as assets for open trading in the market, promoting the carbon reduction target [2]. Accurate carbon accounting is a prerequisite for ensuring market fairness. Corporate users’ carbon emissions can be divided into direct and indirect emissions. Indirect emissions refer to the emissions generated from the electricity purchase. For many companies, purchased electricity is their largest source of carbon emissions and the part with the greatest potential for emission reduction. The measurement of users’ indirect carbon emissions primarily uses the average carbon emission factor method, which calculates the user’s unit electricity carbon emission factor based on the full year’s provincial-level or major grid-level fuel statistics and © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 45–55, 2024. https://doi.org/10.1007/978-981-97-0865-9_6

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electricity generation and the user’s indirect carbon emissions from purchased electricity by multiplying the average emission factor and the amount of electricity used [3]. This method is simple, reliable, and easy to operate, but it cannot reflect the spatial variability of carbon emission factors. With the development of distributed renewable energy, users in different cities, counties, and at different times will have significant differences in the carbon content of their unit electricity use. The average carbon emission factor method will gradually become unfair. To solve this problem, many scholars have referred to the body of research related to loss allocation [4], first obtaining the supply relationship between the generator and the user, which allows the generator side’s carbon emissions to be transmitted to the user and a more precise carbon emission calculation method to be proposed, clarifying the responsibility for carbon emissions [5]. Based on the reverse flow tracking method, Literature [6] obtained a power generation-use relationship matrix, further obtaining the carbon flow in the power lines and the user’s progressive carbon emissions; Literature [7] further discussed the allocation method for carbon emissions due to line losses; Considering the imbalance of real-time carbon flow allocation, each renewable generation unit is treated as a load, and the real-time power network is decomposed into the basic power network and power deviation network. Then, the basic value and correction of carbon flow are calculated respectively, so as to obtain the actual carbon flow distribution with fair apportionment guaranteed. Based on the above methods, Literature [8] proposed a theoretical framework and system for precise real-time carbon measurement from the perspective of full-process carbon calculation in power systems. However, considering that the power grid transmits power stage by stage through 500 kV, 220 kV, 110 kV, 35 kV, 10 kV, and that the basis of power flow tracking is power flow calculation, real-time power flow calculation of large power grids consumes a lot of computing resources. If the user connects to a low voltage level, real-time calculation of the user’s carbon emissions is challenging under the current measurement system. Therefore, this section proposes a more viable solution to the power load carbon emission calculation issue considering multi-stage power transmission. First, the power grid is divided into segments. In the transmission grid, the Thévenin equivalence is used to approximate the power supply relationship between generators and users. In the distribution grid, considering the fast speed and good convergence of the forwardback substitution algorithm, the commonly used reverse power flow tracking method is still applied. At the same time, by extracting typical scenarios, an estimate is made of the user’s annual average carbon emission factor. The method proposed in this paper reduces the calculation load while trying to keep the spatio-temporal characteristics of node carbon emissions as much as possible.

2 Indirect Carbon Emissions Calculation Model 2.1 Handling of Multi-voltage Level Energy Transmission Relationships The main thought of the carbon-flow calculation methods are establishing the power supply relationship between generators and loads, and then calculating how much carbon emissions are transferred from the generation side to the load side along with the power flow. However, it is not feasible to directly model a large-scale grid and analyze the power/carbon flow in terms of data acquisition and computation load. It is therefore

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necessary to first deal with the multi voltage level relationship of the large power grid. Large power grids can be seen as multi-area interconnected systems coupled through shared nodes. The node tearing method is used for layering and partitioning. As shown in Fig. 1, the low-voltage side of the substation can be chosen as the tearing node. The high-voltage side is equivalent to the load, and the low-voltage side is equivalent to the generator. According to the power transmission relationship, the layers are gradually partitioned and a connectivity matrix is formed between the blocks. To ensure the electrical equivalency before and after the partitioning of the interconnected system, the following node voltage consistency constraints and node power balance constraints are added.  1 Vi = Vi2 , δi1 = δi2  (1) h Pi1 , Pi2 = 0, h Qi1 , Qi2 = 0 where Vi , Vi indicate the voltage amplitude of the node i and i respectively; δi , δi indicate the phase angle of the node i and i respectively; Pi , Qi indicate the active and reactive power flowing to the node i; and Pi , Qi indicate the active and to the node i . Let the set of grid    reactive power flowing  blocks be B = bj j = 1, 2, 3, · · · , n , and the nodes inside the blocks are E = {ei |ei ∈ bi , i =1, 2, 3, · · · , m; j = 1, 2, 3, · · · , n}, the connection relationship is R =  bs , bt , eν , eγ s = t, ν = γ , s, t = 1, 2, · · · , n; ν, γ = 1, 2, · · · , m , indicating that grid block bs and bt are electrically connected and the power flows from node eν to node eγ .

Pi1

Qi1

i

i

Pi 2 Qi2

Fig. 1. Grid Partitioning and Connectivity Processing Diagram

2.2 Power Flow Tracing Model The work of performing Thévenin equivalents on power systems is commonly used in voltage stability monitoring and voltage instability prevention. This mainly simplifies complex large-scale power grids. The process to obtain Thévenin equivalent circuit using the method of modifying the node impedance matrix is provided in [9] and [10]. For the load at node k, the equivalent network wanted is as shown in Fig. 2 (a). The equivalent network shows that each generator i supplies node k through an equivalent  . The current flowing through node k can be easily obtained transfer impedance ZTik

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using the superposition theorem. Similarly, the carbon emissions accompanying the flow of current from each generator can be calculated. Considering the impact of load on Thévenin parameters, the load can be converted into load impedance ZLk which is derived from measurement data. ZLk =

VLk |VLk |2 = ILk (PLk + jQLk )∗

(2)

where VLk , ILk , PLk and QLk are the node voltage, load current, active load, and reactive load measured from the load node k, respectively. For nodes where both active and reactive loads are zero, the value of ZLk is positive infinity. Meanwhile, as bus voltage for each generator is different, normalization is employed to prevent loop current in the equivalent network, as shown in Fig. 1 (b). In this way,  . The the original equivalent transfer impedance is updated to the new parameters ZTik    difference of ZTik and ZTik is that ZTik contains the equivalent source internal resistances of the generators. ZT 1k

E1 E2 Em

Eref

ZT 2 k ZTmk

Eref

Z Lk

Eref

ZT 1k

ZT 1k

Z G 2 ZT 2 k

ZT 2 k

Z Gm ZTmk

ZTmk

Z G1

Z Lk

Fig. 2. The equivalent network of large scale power grid

The electromotive forces of all generators are assumed to be the same, which is Eref , thus the equivalent source internal resistance of the generator i is ZGi . ZGi =

∗ (Eref − VGi ) · VGi Eref − VGi = IGi (PGi − jQGi )

(3)

where VGi is the terminal voltage measured for the generator i; IGi , PGi and QGi are the current, active power and reactive power injected into the grid by the generator i respectively. Take one generator for example, the power supply relationship between generator i and load node k can be separate from Fig. 2, as Fig. 3 shows. The equivalent source internal resistances and the equivalent load resistances should added to the original power grid’s impedance matrix to obtain a new one. Define [Y0 ] as the admittance matrix of the original grid, for the load node k, the admittance matrix after adding the equivalent source internal resistances and the equivalent load impedances is [Yk ] = [Y0 ] + [1/ZA\{k} ] + [1/ZG ]

(4)

where A is the set composed of all nodes, ZA/ {k} is the matrix composed of equivalent impedance of other load nodes other than the load node k; ZG is the matrix composed of

A Practical Method for Calculating Indirect Carbon Emissions

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all equivalent source internal impedances. The new impedance matrix is inv([Yk ]), and the diagonal element corresponding to node k is the self-impedance of the load node k, named Zkk ; the matrix element corresponding to the generator i and the load node k is the mutual impedance Zik .

Eref

ZTik

Z Gi

i

ZT 1k

ZT 1k

Eref Z Z G2 T 2k

ZT 2 k

Z Gm ZTmk

ZTmk

Z G1

Z L1

Z G1

k

Z Gm

Z Lk

ZL2

Z Lk

ZTik

Fig. 3. The power supply relationship between generator i and node k

According to the definition of the self-impedance and the mutual impedance, the current provided from generator i to load node k can be calculated as: Ik(i) =

Eref Eref Zik = ZTik (Zkk + ZLk ) ZGi

(5)

 is the transfer impedance between the generator i and load node The impedance ZTik  and Z k, the difference between ZTik Tik is the former one does not include the equivalent  and Z as follows: load impedance ZLk . Express the Ik(i) by the ZTik Lk

Ik(i) =

Eref

  + ZTik

1 ZLk

+

k∈A\{i}

1/ZLk

−1 ·  1 ZTik

1 ZLk

+

k∈A\{i}



(6)

1 ZTik

 satisfy the Comparing the two expressions of Ik(i) , it can be seen that the ZTik following equation: ⎛ ⎛ ⎞−1 ⎞−1

1

1 1 1 Z  ⎠ · Tik − ⎝ ⎠ =⎝ + + (7) ZTik ZLk ZTik ZLk ZLk ZTik k∈A\{i}

k∈A\{i}

 by (7). Therefore, the We can calculate the ZTik by Eq. (5), and then calculate ZTik share of electricity supplied by generator i to the load node k is     Eref − Vk ∗ (8) Pi,k = real Vk  ZTik

It should be noted that for radial networks, the forward/backward sweep method power flow algorithm is simple and has good convergence. And the proportional allocation principle [11] is easy to understand. Although it lacks a theoretical basis, it is still a method worth promoting. In this paper, the commonly used reverse power flow tracing method is used in the medium and low voltage distribution networks.

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2.3 Indirect Carbon Emission of the Target Load Gi,carbon is the carbon emission intensity of the generator i which burning fossil fuels, bt which can be calculated according to [7]. For the electric load PLk whose indirect carbon emission is to be found, which is located at the node k in the grid block bt . The connection matrix of grid blocks shows the upper level block connected with block bt is bs . Then calculate the carbon emission intensity of the generators inside the upper level grid block bs . According to the generator and load correspondence relationship calculated by (8), the carbon emission intensity per kilowatt-hour of the equivalent load node λev is as follows:

(Pi,ev · Gi,carbon )/ Pi,ev (9) λev = i∈bs

i∈bs

where Pi,ev represents the power supply share of generator i to equivalent load node λev .Because the equivalent load node λev in the block bs and the equivalent generator node eγ in the block bt are derived from the same node, we have λeγ = λev . bt is located, the carbon intensity of all generators Similarly, for the block bt where PLk and equivalent generators within the block can be obtained as And then the indirect bt can be calculated as carbon emissions of the load PLk 

Gi,carbon fossil fule generator i in the block bt bt = (Pi,k · λbi t ), λbi t = (10) CLk λeγ equivalent generator i at node eγ i∈bt

Figure 4 is a flow chart of the indirect carbon emission calculation process. Start Read power grid measurement data (grid topology, impedance of lines and transformers, data of current, voltage, power, etc.) calculate the carbon emissions of fossil energy sources

Partition the power grid for parallel processing Is it a large power grid block

Y Form the load matrix, the source matrix and the node admittance matrix Calculate the equivalent load impedance by eq.(2) and the equivalent source internal impedance by eq.(3) Calculate intermediate impedance ZTikby eq.(4)

Calculate transfer impedance ZTik by eq.(7) Calculate the power supply contribution of each generator in each load by eq.(8)

N Calculate the power supply contribution using the reverse power flow tracking method

Power supply composition of each load Calculate the carbon emissions intensity of each power grid block Calculate the carbon emission intensity of the target load by eq. (10) end

Fig. 4. The indirect carbon emission calculation process

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3 Case Studies The grid in Fig. 5 composed of the IEEE14-bus system (Network 1) and the IEEE33-bus system (Network 2), with the total system load being 255.84 MW + j72.61 MVar. The active power load of Network 2 is doubled, while the reactive power load is 2/3 of the original, achieving the injection power at the bus 1 is similar to the load of bus 5 in Network 1.

Fig. 5. The test power grid

A photovoltaic (PV) of 0.78 MW (with a 10% penetration rate in the low-voltage grid) is connected to Network 2.The connection relationship is the power injected from bus 5 of Network 1 to bus 1 of Network 2. Assume that for Grid 1, G1 is a coal generator, G2 is an oil generator; G3-G5 are gas generator. The emission intensity per kilowatt-hour of each type of power unit [11] is shown in Table 1. Table 1. The emission intensity per kilowatt-hour of different type of source

Carbon emission intensity (t/MWh)

coal generator

oil generator

gas generator

1.0201

0.7584

0.5148

Select the PV output and load data for the entire year from a certain region, with an interval of 1 h. After normalizing the load data, the original scenarios of the electrical load are divided into 7 periods according to the method in [12], as shown in Fig. 6 (a). These load data are clustered into typical scenarios in Fig. 6 (b). Then, for each load time segment, the PV clusters are created using the k-means method. Due to space limitations, only the PV scenarios corresponding to Load scenarios 1 and 4 are provided in Fig. 7. In this way, load-PV scenario set is formed. The carbon emission intensity heat map of a total of 28 scenarios (4 different solar scenarios for each of the 7 load scenarios) is plotted in Fig. 8, where S1-1 means “Load Scenario 1 and PV S1 data pair”, quantitatively assessing the impact of the renewable energy integration on the carbon emission intensity of each bus in the lower-voltage

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1

7 2

4 6

3

5

Fig. 6. The clustered load scenarios 0.6

0.6

.

0.5 0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

5

.

0.5

10

15

20

25

0

0

5

10

15

20

25

Fig. 7. The PV output scenarios corresponding to Load Scenario 1 and 4

level grid. It can be observed that the intensity of the buses near the PV connection bus (bus 13–18) is significantly lower, indicating that nearby loads are clearly affected by localized supply of renewable energy. Assuming the PV capacity of 0.78 MW is connected to an unspecified node, a box plot of carbon emission intensity plotted for in which PV is connected from nodes 2 to 33. Figure 9 shows the closer the PV connection bus is to the target load (N25), the lower the carbon emission intensity of the users (N25 < N24 < N23). The box plot of carbon emission intensity for the load at bus 25(N25) when PV integration node is uncertain under different scenarios is shown in Fig. 10. It can be observed that the PV connection bus has a certain impact on the carbon emission in all scenarios. However, there is a significant difference in carbon emission across different scenarios, ranging from a minimum of 0.3 t/MWh to a maximum of 1.045 t/MWh. This indicates that calculating the carbon emissions for users should be done on a scenariospecific basis carbon emission coefficient. If the PV is connected at Bus 25 of network 2 (the same bus of target load), according to the typical scenarios and their probability, the user’s annual average carbon emission factor is shown in Fig. 11. Compared to the average emission factor of the national power grid in 2022, which is 0.5703t CO2/MWh, it can be seen that there is a significant difference.

A Practical Method for Calculating Indirect Carbon Emissions

Fig. 8. The carbon emission intensity heat map under different scenarios

Fig. 9. The carbon emission intensity when PV connected to different bus

53

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Fig. 10. The Carbon emission intensity under different scenario

1.16 1.14 1.12 1.10 1.08 1.06 1.04 1.02 1.00 0.98 0.96

1.200

,1.142

,1.133

,1.111

1.000

,1.099

0.800 ,1.075 1.048

, 1.037 1.024

,1.005

,

,1.030

0.600 0.400 0.200

,0.972 0

2

4

6

8

10

12

3

8

13

18

23

28

33

Fig. 11. The annual carbon emission intensity of the gird

4 Conclusion This paper proposed a practical indirect carbon emission calculation method by parallel computing the divided power grid and proposed an effective calculation method based on Thévenin equivalent fitting. The case study proves this method for carbon emission calculation manages to strike a balance between computational complexity and acknowledging the spatio-temporal characteristics in carbon emissions. The calculated carbon emission factor can serve as substitutions for the traditional carbon emission factors. Acknowledgment. This research is supported by Research on the Mechanism and Optimization Method of Electricity Carbon Collaborative Operation in Electric Energy Substitution Projects (1400-202255304A-2-0-QZ).

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References 1. Huang, W., Wang, Q., Li, H., Fan, H., Qian, Y., Klemeš, J.J.: Review of recent progress of emission trading policy in China. J. Clean. Prod. 349, 131480 (2022) 2. Han, Y., Tan, S., Zhu, C., et al.: Research on the emission reduction effects of carbon trading mechanism on power industry: plant-level evidence from China. Int. J. Climate Change Strategies Manag. (2022) (ahead-of-print) 3. Scarlat, N., Prussi, M., Padella, M.: Quantification of the carbon intensity of electricity produced and used in Europe. Appl. Energy 305, 117901 (2022) 4. Todorovski, M., Rajiˇci´c, D.: Contribution of generator-load pairs in distribution networks power losses. Int. J. Electr. Power Energy Syst. 115, 105433 (2020) 5. Zhou, T., Kang, C., Xu, Q., et al.: Preliminary theoretical investigation on power system carbon emission flow. Autom. Electric Power Syst. 36(7), 38–43 (2012). (in Chinese) 6. Yuan, S., Ma, R.: A research on the allocation model of carbon emission in power system based on carbon emission flow theory. Mod. Electric Power 31(6), 70–75 (2014). (in Chinese) 7. Wang, C., Chen, Y., Wen, F., et al.: Some problems and improvement of carbon emission flow theory in power systems. Power Syst. Technol. 46(5), 1683–1691 (2022). (in Chinese) 8. Zhang, N., Li, Y., Huang, J., et al.: Carbon measurement method and carbon meter system for whole chain of power system. Autom. Electric Power Syst. 47(9), 2–12 (2023). https:// doi.org/10.7500/AEPS20221021001. (in Chinese) 9. Fu, Z., Lu, J., Qiao, L., et al.: Voltage stability analysis based on thevenin equivalent parameters. Electric Power 047(005), 44–47 (2014). https://doi.org/10.3969/j.issn.1004-9649.2014. 05.011. (in Chinese) 10. Wang, C., Wang, Y., Rouholamini, M., Miller, C.: An equivalent circuit-based approach for power and emission tracing in power networks. IEEE Syst. J. 16(2), 2206–2216 (2022). https:// doi.org/10.1109/JSYST.2021.3067296 11. Bi, H., Fan, X., Xiao, H., et al.:A node admittance matrix algorithm to support the carbon emission tracing model of whole power system. In: Proceedings of the CSEE (2022) (aheadof-print). (in Chinese) 12. Li, W., Yan, S., Jiang, Y., et al.: Research on method of self-adaptive determination of DBSCAN algorithm parameters. Comput. Eng. Appl. 55(5), 1–7, 148 (2019). https://doi. org/10.3778/j.issn.1002-8331.1809-0018. (in Chinese)

Design of Wind Turbine Speed Control System Based on Permanent Magnet Synchronous Motor Zhifei He(B) , Xinyao Li, Kai Dong, and Fei Feng Aeronautics Computing Technology Research Institute, Xian 710076, China [email protected]

Abstract. The constant pitch variable speed control system based on permanent magnet synchronous generator is time-varying, nonlinear and strong coupling control system. The wind is strongly disturbed during operation, especially in the high wind speed area, the system is a nonlinear system with local positive feedback and instability. To address these issues, a sliding mode control theory based on interference observation is proposed. On the one hand, a new variable exponential reaching law is adopted to greatly reduce the pulsation of sliding mode variable structure controller; On the other hand, the disturbance observer is used to compensate for the influence of aerodynamic torque, eliminate the instability of the system itself, and achieve stable operation of the unit above the rated wind speed. Finally, the rationality of the design scheme and the robustness of the controller are demonstrated through simulation. Keywords: Wind Power Generation · Sliding Mode · DOB · PID

1 First Section 1.1 A Subsection Sample At present, the development of renewable energy utilization has become the key to solving the serious Energy crisis and environmental pollution. Among various renewable energy sources, wind energy has become the fastest-growing energy due to its wide distribution, environmental friendliness, policy cultivation, and mature technology. Therefore, wind energy technology has become a research hotspot and focus worldwide [1]. Among them, small and medium-sized (1–100 kW) wind turbines are becoming increasingly popular as they can meet the electricity needs of users in remote rural areas. Unlike large horizontal axis wind turbines, small and medium-sized wind turbines typically abandon the complex control system of variable pitch [2]. Scholars are increasingly focusing their research on power regulation based on fixed pitch variable speed control systems throughout the entire operating wind speed range. In this paper, the sliding mode control theory based on disturbance observer is adopted. According to the advantages of sliding mode Variable structure control, such as fast response, insensitivity to parameter disturbances, strong anti-interference and © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 56–63, 2024. https://doi.org/10.1007/978-981-97-0865-9_7

Design of Wind Turbine Speed Control System

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easy implementation [3], a new sliding mode controller is proposed. On the one hand, by designing a sliding mode control law reasonably, the chattering of the system is effectively weakened; On the other hand, the disturbance observer is used to estimate and compensate the aerodynamic torque, so as to eliminate the instability of the system itself, make the system become a stable Linear system, and realize the constant power operation of the wind turbine above the rated wind speed [4]. Then, simulation analysis was conducted using Matlab/Simulink software to prove that the designed controller has good robustness and stability.

2 Modeling and Design of Speed Control System 2.1 Linear Analysis of Speed System The wind turbine is connected to the permanent magnet synchronous generator through direct drive, and the basic dynamic characteristics of the variable speed wind turbine can be reflected through the following mathematical model [5]. Tm − Te = J

dω + Bω dt

(1)

where: Tm is the aerodynamic torque generated by the wind turbine, Te is the electromagnetic torque of the generator, J is the Moment of inertia of the wind wheel and B is the friction coefficient. Due to the fact that the aerodynamic torque of wind turbines is a nonlinear function [6]. Tm = f (v, ω) =

1 ρπ v2 R3 CT (λ) 2

(2)

where: ρ is theDensity of air, R is the radius of the wind turbine, v is the wind speed, CT (λ) is the torque coefficient, λ = ωR/v is the tip speed ratio. Here is a linearized model of Eq. (1) at the static operating point. Linearize Eq. (1) at the static working point and perform Laplace transformation. ω(s)/Te (s) = 1/(Js + B − λ)

(3)

From the above equation, it can be seen that when λ < 0, the wind turbine system is stable; When λ > 0, that is, the wind speed is too high, because the friction coefficient B is very small, the system has a right half plane pole, which makes the system unstable. 2.2 Using Disturbance Observer (DBO) Compensation to Eliminate the Influence of Nonlinear Relationships As mentioned earlier, the nonlinear characteristics of the dynamic model of wind turbines and their instability in high wind speeds are mainly determined by the nonlinear relationship between aerodynamic torque, wind speed, and rotational speed. To solve

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v r

Te

Gc ( s) f

T (s)

1/ ( Js B)

Tˆm Q(s) Q( s ) Gn ( s )

1

H (s)

Fig. 1. Structure diagram of disturbance observer applied to wind power generation system

this problem, an interference observer is used to compensate for the influence of aerodynamic torque. Here is a structural diagram of the improved disturbance observer applied to wind power generation (Fig. 1). [Gn (s)]−1 in DOB is the inverse of the nominal model obtained through system identification, Gc (s) is a sliding mode controller, Q(s) is a low-pass filter, T (s) is the transfer function of the electromagnetic torque link, H (s) is the delay link for speed detection, and T m is the observed compensation value for aerodynamic torque disturbance.  T (s) = 1/(3Ts s + 1) (4) H (s) = 1/(Tω s + 1) 

In the formula, Ts is the switching cycle of the PWM rectifier, and Tω is the delay time for speed detection. According to the design knowledge of disturbance observers, the design of low-pass filters determines the ability of DOB to suppress disturbances. Reasonably design lowpass filter Qs to eliminate measurement noise and improve system robustness [7]. This article adopts a second-order filter: Qs =

1 (τ s) + 2(τ s) + 1 2

(5)

In the formula, τ is the filtering time, τ ∈ [10, 15]T , and T is the sampling period of the discrete system. By equivalent simplification of the speed control system diagram with disturbance compensation, as shown in the figure. Combining Eqs. (4) and (5), the simplified transfer function in Fig. 2 is as follows: ⎧   s 1 ⎨ H1 (s) = γ 1 − =≈ γ T T s+1   T (s)H (s) (6) T s ⎩ H2 (s) = α 1 − 1 =≈ α T (s) T s+1 Based on the above analysis, let G(s) = 1/(JS + B) obtain: G(s) T s + 1

= 2 1 − G(s)H1 (s) T Js + J − T (γ − B) s + B

(7)

Design of Wind Turbine Speed Control System

59

v H 2 ( s)

r

Gc ( s)

Te T

(s)

1/ ( Js B)

f

H1 (s) H s

Fig. 2. Structure diagram of the improved system.

The function of disturbance compensation is to eliminate its own unstable characteristics and nonlinear characteristics. Next, analyze the characteristic equation:

D(s) = T Js2 + J − T (γ − B) + B (8) According to the Routh criterion, the expected characteristic equation does not have a positive real root and needs to meet the following conditions: T = 3Ts + Tω
0, k > 0)

(16)

The traditional exponential approach law has its own drawbacks, as its switching band is banded. Secondly, due to the existence of switching control term −εsign(s), the sliding mode gain of the system always exists when moving towards the origin in the switching band, resulting in it not being able to approach the origin in the end, but rather approaching a oscillation near the origin. This high-frequency oscillation can excite high-frequency components that are not considered in system modeling, increasing the burden on the controller. In order to overcome the shortcomings of the exponential convergence law and improve it, a new convergence law called the variable exponential convergence law is adopted [11]. s˙ = −ε|x2 |α sign(s) − ks In the equation, ε > 0, k > 0, 0 < α 0 λ 1 , Re(λ) = 0 a Dt = ⎩ t (d τ )−λ , Re(λ) < 0 a

(6)

In Eq. (6), a and t are the upper and lower bounds of the fractional order operation, respectively, λ ∈ R is the order of the fractional order operation, and Re(λ) represents the real part of λ. To improve the convergence speed of the system state variables, an improved fractional-order non-singular fast terminal sliding surface function containing fractionalorder linear sliding surfaces and fractional-order non-singular terminal sliding surfaces is constructed. S = 0 Dtλ x1 + c0 Dtλ x2 +

1 g / h 1 m/ n x + x2 μ 1 γ

(7)

In Eq. (7), a Dtλ is the fractional order calculus operator, 0 and t are the initial and final moments of the fractional order calculation process, λ is the order of the fractional order calculus, c, μ, γ ∈ R+ are parameters to be determined, and c, μ, γ are greater than zero, g, h, m, n ∈ N are positive odd numbers to be determined, where n < m < 2n, g/h > m/n > 0.

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3.2 Design of Fractional Order Convergence Laws To ensure fast convergence of the system on the fractional order sliding mode surface, a fractional order double power exponential convergence law is designed. ξ ξ S˙ = −K1 |S|α 0 Dt sgn(S) − K2 |S|β 0 Dt sgn(S) − K3 S

(8)

In Eq. (8), ξ is the order of the fractional-order calculus, K 1 , K 2 , K 3 ∈ R+ are ξ gain coefficients, and K 1 , K 2 , K 3 are greater than zero, and 0 Dt is the fractional-order fundamental operator, where −1 < ξ < 0, 0 < α < 1, 0 < β < 1. In order to weaken the oscillations more effectively, a weighted integral type gain is introduced into the fractional order double power exponential convergence law to suppress the system differences caused by external disturbances. The fractional order convergence law Eq. (8) is rewritten as Eq. (9). ξ ξ S˙ = −K1 |ρ|α 0 Dt sgn(S) − K2 |ρ|β 0 Dt sgn(S) − K3 S t   (9) ρ = 0 Kf ρ + S dt In Eq. (9), K f is the gain coefficient and K f < 0. When ρ > 0, K f ρ < 0; when ρ < 0, K f ρ > 0. Negative weighting values can keep the switching term coefficients in a certain range. 3.3 Design of Fractional-Order Voltage Loop Controller Consider the inverter in an ideal two-phase stationary αβ coordinate system, so that U gq = 0, the power balance equation is Pg =

3 Ugp Igp = Iinv Udc 2

(10)

where, I inv is the current of the inverter input. There is an external disturbance factor in the system, combining with Eq. (10), from Kirchhoff ’s law we get 3Ugp 1 dUdc = IPV − g(t)Igp + d (t), g(t) = dt C2 2C2 Udc

(11)

where, I PV is the output current of the PV cell; d(t) is the DC side voltage interference term. Substituting Eq. (11) into Eq. (5) and deriving, the PVGCI equation of state is obtained as x˙ 1 = x2 = U˙ dc = C12 IPV − g(t)Igp + d (t) (12) x˙ 2 = x¨ 1 = U¨ dc = −g(t)I˙gp Further derivation of Eq. (7) becomes 1 g h 1 S˙ = 0 Dtλ−1 x˙ 1 + c0 Dtλ−1 x˙ 2 + x˙ 1 / + x˙ 2m/ n μ γ

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=

λ−1 + 0 Dt

 

g gh −1 m mn −1 ˙ x2 − D c0 Dtλ−1 + Igp x1 x2 μh γn

(13)

According to Eq. (13), let S˙ = 0, the reference power at the output of the fractionalorder voltage loop controller can be obtained as P ∗ = Udc Igp   

g m −1 −1 U  λ−1 + g x h −1 x + K S|ρ|α Dξ sat(S) + K S|ρ|β Dξ sat(S) + K S 2 c0 Dtλ−1 + γmn x2n = Ddc D dt 0 t 2 1 2 3 0 t 0 t μh 1

(14)

4 System Simulation Analysis To further investigate the PVGCI-MPDPC system and verify the effectiveness of the proposed improved fractional-order non-singular fast terminal sliding mode control algorithm, a PVGCI-MPDPC simulation model is built, as shown in Fig. 1.

inv 1

2

1

b

2

S

*

Sb

u

b

S

u

nd

oop

*

*

oop

Fig. 1. PVGCI-MPDPC structure block diagram

In the control system, the voltage loop maintains the stability of the PVGCI DCside voltage, and the PVGCI is susceptible to factors such as light intensity, so the simulation experiments mainly verify the stability of the PVGCI-MPDPC system under the improved fractional-order non-singular fast terminal sliding mode control when the light intensity varies. In this paper, the DC-side voltage loop controllers are adopted as IOSMC-MPDPC and FONFTSMC-MPDPC for comparative analysis. The system simulation parameters are shown in Table 1. To verify the feasibility of the FONFTSMC-MPDPC method in the PVGCI system, ∗ = 700 V is given, the simulation time is set to 1.5 s. The DC-side reference voltage Udc * and the reactive power is given as Q = 0 var. The PV plant output voltage varies with the local light intensity, and at the same time, the output power also varies. To maintain the stable operation of the system, the controller of PVGCI has to be adjusted in time, so

Improved Fractional-Order Sliding-Mode Voltage Controller

69

Table 1. System simulation parameters Parameter

Value

Unit

C1

4700

µF

C2

500

µF

L1

90

µH

L2

5000

µH

R

0.1



f

50

Hz

e

380

V

Tb

25

°C

the control effect of the FONFTSMC-MPDPC method under different light intensities needs to be verified. The DC-side voltage curves under the IOSMC-MPDPC and FONFTSMC-MPDPC methods are shown in Fig. 2. Under the FONFTSMC-MPDPC method, the amount of overshooting is reduced by 2.71% relative to that of the IOSMC-MPDPC, and the dynamic response is more rapid, and it can track the output voltage reference value better. When the light intensity changes abruptly at 0.5 s and 1 s, both methods can realize the bus voltage tracking the given voltage, and FONFTSMC-MPDPC shortens the response time, reduces the dc-side voltage jitter range, and suppresses the system jitter, so the overall control performance of FONFTSMC-MPDPC is better, and it has a strong anti-disturbance performance. 800

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started from 0 s. When the light intensity changes abruptly at 0.5 s and 1 s, there is a difference between the control effect of the FONFTSMC-MPDPC method and that of the IOSMC-MPDPC method, and the FONFTSMC-MPDPC quickly approximates the reference value after 0.07 s and 0.02 s, respectively, 0.01 s, the tracking speed is improved, and the active power curve of the system can be accurately and quickly tracked to the given power, and the fluctuation range of the active power is kept at ± 504.5 W, which is reduced by ± 64.2 W relative to IOSMC-MPDPC. Therefore, the active power tracking speed of the FONFTSMC-MPDPC is faster, and the power fluctuation is smaller, with a better anti disturbances is stronger. 6

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The A-phase FFT analyses under the IOSMC-MPDPC and FONFTSMC-MPDPC methods are shown in Fig. 4. The A-phase FFT analyses under the FONFTSMC-MPDPC method show that the THD of the three-phase grid-connected currents is 0.86%, and the harmonics of the output current waveforms are small, which is reduced by 0.65% relative to the IOSMC-MPDPC. Both methods are controlled within 5% to meet the gridconnected power quality requirements, but the latter grid-connected current distortion level is significantly improved compared to the first three.

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5 Conclusions In this paper, based on the direct power control strategy for model prediction of PV grid-connected system, an improved fractional-order non-singular fast terminal sliding mode control strategy is proposed, an improved fractional-order sliding mode voltage controller is designed, and the validity of the proposed method is verified by changing the illumination intensity, which provides a new way of thinking for the reliable operation of PV grid-connected system. The results show that the FONFTSMC-MPDPC method has strong anti-interference ability, reduces system jitter, increases the power tracking speed, improves the dynamic and static characteristics of the system, meets the basic requirements of the PV grid-connected inverter, and helps to enhance the utilization rate of photovoltaic energy, which is of great significance in engineering applications. Acknowledgements. This work has been financially supported by the National Natural Science Foundation of China (No. 51867015) and Gansu Province Science and Technology Major Special Project (No. 19ZD2GA003).

References 1. Zhang, L.B., Jin, Y.J., Pan, G.B., Wang, J.F., Ouyang, K., Jin, L.B.: Combined filtering feedforward control strategy for LCL-type grid-connected inverter. Acta Energiae Solaris Sinica 42(12), 388–394 (2021). (in Chinese) 2. Yin, J., Nie, H., Huang, X., Xu, G., Jing, X., Liu, Y.: Nonlinear control method of photovoltaic power generation LVRT based on adaptive maximum power tracking. Frontiers Energy Res. 10, 260–275 (2022). https://doi.org/10.3389/fenrg.2022.900120 3. Liu, X.J., Liu, Y.Y., Kong, X.B., Ma, L.L., Besheer, A.H., Lee, K.Y.: Deep neural network for forecasting of photovoltaic power based on wavelet packet decomposition with similar day analysis. Energy 4(271), 369–386 (2023) 4. Wang, X., et al.: Novel model predictive direct power control strategy for grid-connected threelevel inverters. IET Power Electron. 13(16), 3727–3733 (2020). https://doi.org/10.1049/ietpel.2020.0038 5. Moeti, M., Asadi, M.: Robust model reference adaptive PI controller based sliding mode control for three-phase grid connected photovoltaic inverter. Turk. J. Electr. Eng. Comput. Sci. 29(1), 257–275 (2021) 6. Ullah, N., et al.: Processor in the loop verification of fault tolerant control for a three phase inverter in grid connected PV system. Energy Sourc. Part A-Recov. Utiliz. Environ. Effects 12(23), 286–302 (2021) 7. Li, D.H., Tian, L.Y., Yao, L.L., Dong, N.: Control research of grid-connected inverters under unbalanced grid voltage. Acta Energiae Solaris Sinica 40(9), 2594–2600 (2019). (in Chinese) 8. Hu, J.F., Zhu, J.G., Dorrell, D.G.: Model predictive control of grid-connected inverters for PV systems with flexible power regulation and switching frequency reduction. IEEE Trans. Ind. Appl. 51(1), 587–594 (2015) 9. Cheng, J., Xiao, X.Y., Ma, J.P., Yang, X.Y., You, Y.F., Cao, Z.H.: Finite switching sequence model predictive direct power control of a three-phase energy-stored Quasi-Z-source gridconnected inverter. Power Syst. Technol. 44(5), 1647–1655 (2020). (in Chinese) 10. Mostafa, S., Zekry, A., Youssef, A., Anis, W.R.: Raspberry Pi design and hardware implementation of fuzzy-PI controller for three-phase grid-connected inverter. Energies 15(3), 1–16 (2022)

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11. Tuan, L.A.: Neural observer and adaptive fractional order backstepping fast-terminal slidingmode control of RTG cranes. IEEE Trans. Industr. Electron. 68(1), 434–442 (2021) 12. Zhang, X., et al.: Passive fractional-order sliding mode controller design for PV inverter. Power Syst. Protect. Control 47(24), 145–153 (2019). (in Chinese)

Research on the Key Technologies of Control and Protection for Static Frequency Converter (SFC) Valve Group of Pumped Storage Units Xu Hao1,2 , Zhang Xuejun1,2(B) , Ma Jiayuan1,2 , Tian Anmin1,2 , Liang Shuaiqi1,2 , and Wang Jiayu1,2 1 State Grid Electric Power Research Institute Co. Ltd., Nanjing 211006, China

{xuhao2,zhangxuejun,majiayuan,tiananmin,liangshuaiqi, wangjiayu}@sgepri.sgcc.com.cn 2 NARI Technology Development Co. Ltd., Nanjing 211006, China

Abstract. Pumped storage power station has the functions of peak loading, valley filling, frequency modulation and emergency backup, etc. When the pumped storage power station is running under the working condition of the motor, the static frequency converter (SFC) can realize the smooth start of the synchronous motor, reduce the starting current and weaken the disturbance to the power grid. At present, SFC is the main starting mode of pumped storage unit. SFC can produce frequency variable AC power to start the pumped storage unit, with soft starting function. This paper introduces in detail the control structure of the static frequency converter (SFC) valve group of pumped storage unit and the key technology of control and protection of thyristors. It has solved the technical problems such as wide bandwidth pressure energy extraction and instantaneous protection of thyristor in the valve control unit, and has been applied in many pumped storage units. Keywords: Pumped-storage unit · Static Frequency Converter · Valve group · Valve control device · Thyristor protection

1 Introduction Static Frequency Converter (SFC) is the core equipment for the start-up of peak regulating units such as pumping storage, phase modifier [1]. Pumped storage power station has the functions of peak regulation, valley filling, frequency modulation and emergency backup, which is the main way of large capacity electric energy storage at present [2, 3]. On the one hand, pumped storage power station can provide rapid power support after the failure of large-capacity transmission channel. On the other hand, it can reduce the amount of abandoned wind and abandoned light when the new energy is high. It is an effective means to solve the peak regulation of power system and ensure reliable operation. Under pumping conditions, the pumping unit needs SFC system to drag it to the grid-connected speed in the same period, and the static inverter is the key equipment of © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 73–81, 2024. https://doi.org/10.1007/978-981-97-0865-9_9

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the pumping station [4]. Large phase modifiers, distributed phase modifiers need SFC to drag it from the static state to synchronous or slightly higher than the synchronous speed, and then the simultaneous grid connection operation is carried out by the synchronous device, to avoid the direct closing caused by the impact current [5, 6]. SFC plays an irreplaceable role in the development of new energy system [7]. High voltage and large capacity thyristor valve group is the core component of SFC system, and the reliability of the valve group is the guarantee of normal operation of SFC. This paper introduces the basic principle and key technology of SFC valve group in control and protection in detail, and verifies its feasibility combined with the actual system.

2 Basic Principle of Valve Group in Control and Protection The control architecture of the SFC system valve group includes the SFC master control device and the SFC valve control device in hardware. In order to ensure the safe and reliable operation of the SFC system, the system adopts the integrated design idea of control and protection functions. The protection relies on the control strategy design, and regards the protection operation as a part of emergency control. The main control device adopts high-performance microprocessor as the core of system control, fault detection and function management, and adopts high-speed digital signal processor for control and protection calculation. The valve control device consists of Valve control unit (VCU) and TCU. The valve based electronic device uses high performance FPGA chip as the core of pulse control, condition monitoring and configuration management. The thyristor trigger unit is designed with the simulator, which realizes the energy taking, the thyristor trigger control, the state monitoring and the overvoltage protection in the wide frequency and wide voltage range. VCU is the interface device between the control system and the high voltage valve group. It receives the unlock signal, block signal and trigger pulse commands from the main control device. Then it distributes the trigger signal to each TCU and monitors the operating status of the whole high voltage valve group, and sends the relevant information to the main control device. TCUs receive the trigger signal sent by VCU to trigger thyristors, at the same time protect the thyristor and monitor the operation state of the thyristors, and send it to VCU through the high voltage fiber. TCU mainly has the following functions. Coupling electrical energy from the auxiliary voltage balancing circuit; Convert the trigger light signal sent by the VCU device into an electrical signal; Send trigger pulse of certain amplitude and width to thyristors; Detect the working state of the thyristors, and convert the state signal into an optical signal back to VCU; Once there is an overvoltage at both ends of the thyristor, the trigger pulse is automatically sent to the thyristor to force the thyristor to conduct and achieve the purpose of protecting the thyristor.

3 Key Technologies of Valve Group in Control and Protection 3.1 A Voltage Balance of High Voltage Series Valve Group When SFC is used in high voltage scenarios, the voltage of a single thyristor cannot meet the requirements, the valve group needs multiple high-power thyristor used in series, and need to take voltage balance into consideration.

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The voltage margin factor of the valve bank, sometimes also referred to as the voltage reserve factor, is indicated by symbol δu . It is the sum of the maximum non-repeating voltage peaks of all series thyristors (minus redundancy δn ) compared to the maximum peak rated operating voltage of the valve bank. δu directly reflects the voltage resistance characteristics of the valve group and the ability to resist voltage shock, and its calculation formula is as follows: UDRM × (n − δn ) (1) δu = √ 2 × Ue where n is the total number of thyristor components in series of the valve group; δn is the number of thyristor components redundancy; U e is the maximum rated voltage effective value of the valve group; U DRM is the maximum forward repeatable voltage peak of the thyristor. The voltage margin coefficient of the valve bank is generally designed to be about 2.14. The current margin coefficient of the valve group, sometimes called the current reserve coefficient, is indicated by symbol δi . It is the ratio of the maximum on-state average current value of thyristor to the average half wave of the rated current of the valve groups, expressed by the formula: ITAVM (2) IBP √ 2 IBP = (3) × Ie π where I TAVM is the maximum on-state average current value of thyristor; I BP is the average half-wave value of the rated current of the valve bank; I e is the effective value of the rated current of the valve group. The current margin factor of the valve group is generally designed to be about 2.6. In order to achieve the voltage balance of the valve group, thyristors with the same batch and the same parameters should be selected as far as possible during thyristor selection. In addition, the auxiliary voltage equalization circuit should be designed to ensure the voltage balance between thyristors. The auxiliary voltage balancing circuit is shown in Fig. 1. δi =

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Static voltage equalizing between thyristors can be realized by parallel resistance Rj , that is, voltage equalizing among thyristors in cut-off state. The dynamic voltage balancing between thyristors can be realized by C and Rd in parallel resistance-capacitance circuits, that is, the voltage balancing during the opening and closing of thyristors.

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Select the thyristor produced in the same batch, and test its leakage current, and obtain the maximum leakage current deviation I m . Through the following formula, we can find the maximum voltage of the thyristor operation, and invert the appropriate static voltage balancing resistance Rj value according to the device voltage allowable value. UR =

1 URM + (1 − ) × Rj × Im n n

(4)

where U R is the maximum commutation reverse voltage of the thyristor in the system, U RM is the maximum overshoot voltage of the thyristor. The dynamic voltage equalization is realized through the resistance-capacitance absorption loop. When the thyristor is turned off, the reverse recovery charge is transferred to the absorption capacitor to inhibit the increase of the voltage at both ends of the thyristor. The capacitance value C can be determined by the following formula, and Qrr is the reverse recovery charge of the thyristor, which can be queried in the technical specification of the device product. C=

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(5)

Rd can be estimated according to the maximum voltage under thyristor operation and the ratio of diT /dt corresponding to the maximum reverse recovery current I RM . Rd =

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(6)

3.2 Wide Frequency and Wide Voltage Energy Extraction TCU is an important part of high voltage valve group, and each thyristor needs one TCU for reliable trigger and fault monitoring. TCU has self-energy function, and its energy is taken from the voltage at both ends of the thyristor. In the state of low voltage and low frequency, the current in the RC absorption circuit is small. But at the moment of commutation or the moment of overvoltage protection occurs, the dv/dt at both ends of the thyristor is very large. And there will be an impact current flowing through the RC absorption circuit. During the start-up of SFC system, TCU works under the condition of wide frequency band and wide voltage (such as 0 ~ 52.5Hz/95 ~ 2600V). TCU must ensure reliable energy acquisition within the wide frequency band and wide voltage range [8]. Because the conventional power supply module or power supply chip cannot meet the requirements of wide frequency and wide voltage energy extraction, and considering the power consumption of TCU, a linear voltage regulator circuit is built with analog devices, which not only ensures reliable energy acquisition in low voltage and low frequency state, but also ensures normal operation in high voltage and power frequency state. The energy extraction circuit is shown in Fig. 2.

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Fig. 2. Broadband and wide voltage energy extraction circuit

3.3 Reverse Recovery Protection TCU not only basically triggers the thyristor and monitors its state, but also has the functions of overvoltage protection and reverse recovery protection. During the reverse recovery period, if the positive dv/dt at both ends reaches a certain threshold value, the thyristor may be damaged. It usually occurs within 1ms after the thyristor is triggered and turned on, and the voltage at both ends changes from zero to negative half cycle. Therefore, the reverse recovery protection function is integrated in TCU. During the reverse recovery period, if the positive dv/dt at both ends reaches a certain threshold value, TCU will automatically trigger the thyristor. The judgment time and threshold value can be adjusted according to the actual electrical characteristics of the thyristor. The reverse recovery period protection circuit consists of dv/dt monitoring circuit, negative zero-crossing voltage monitoring loop, reverse recovery time window generating circuit, logic devices and signal amplifying circuit, as shown in Fig. 3.

d

Fig. 3. Schematic diagram of TCU reverse recovery protection

3.4 Thyristor Instantaneous Protection Based on Accurate Adjustment of Voltage Threshold In the high voltage valve group, a thyristor stage may not trigger the corresponding thyristor due to optical device damage and other reasons. The thyristor level will instantly

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Fig. 4. Schematic diagram of TCU overvoltage protection

generate high voltage due to the triggering of other thyristor levels, thereby breaking the thyristor. Generally, BOD (Break Over Diode) components are used to complete the overvoltage protection of thyristors. However, due to the large size of the BOD element itself, and the voltage of the BOD device itself is limited. Therefore, it is often necessary to connect multiple BOD devices in series to achieve over-voltage protection. For example, the overvoltage protection threshold of 4800V requires six 800V BOD devices in series. In addition, with the increase of the number of BOD components in series, the error of the overvoltage protection threshold is also greater. In order to avoid the above defects, this paper proposes a thyristor instantaneous protection technology based on accurate adjustment of voltage threshold. When the voltage at both ends of the thyristor reaches the protection threshold, the TCU will automatically trigger the thyristor to avoid the thyristor being damaged by breakdown. While protecting the trigger thyristor, a return IP optical signal is generated. The signal is fed back to VCU through optical fiber to realize the instantaneous protection of thyristor. The schematic diagram of overvoltage protection is shown in Fig. 4. Firstly, the voltage at both ends of the thyristor is divided by the voltage dividing circuit. Secondly, the twostage sampling circuit is compared with the protection reference value. Then the triode amplifier circuit is used to enhance the control signal. The protection voltage threshold can be accurately adjusted and very stable. The protection action time is less than 30 ns, which improves the rapidity of protection, and the error can be controlled at 10 V or even smaller. In addition, compared with the conventional BOD turning diode protection circuit, this technology does not need to introduce high voltage into the detection circuit, which improves the safety and reliability.

4 Experiments and Waveforms The topological structure of SFC can be divided into 6–6 pulse, 12–6 pulse and 12–12 pulse according to the number of power bridge pulses. At present, the SFC of pumped storage units mostly adopts high-low-high structure [9–11]. In this paper, the SFC with 12–6 pulsating topology and high-low-high structure is taken as an example, and the main parameters are shown in Table 1. According to the system design requirements: commutation inductance L C is 2000 μH, maximum commutation reverse voltage U R of thyristor is 3000 V, and maximum

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Table 1. Main parameters. Item

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3700 A

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KPD 4200–65

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line side: 1; turbine side:3

voltage on line side

4.2 kV 50 Hz

trigger angle range on line side

10° ~ 150°

voltage on turbine side

0 –4.2 kV (0–50 Hz)

trigger angle range on turbine side

Pulse commutation: 180° Natural commutation: 120° –160°

Switching frequency from pulse commutation to natural commutation

3.5 Hz –5 Hz

Turbine side voltage at Switching frequency

0.294 kV

DC voltage at Switching frequency

285 V

Maximum DC voltage on turbine side

6237 V

overshoot voltage U RM is 6237 V, then U RM /U R is less than 2.1. The thyristors KPD 4200-65 produced in the same batch have a maximum leakage current deviation I m of 10 mA. According to the above parameters, diT /dt d iT /dt is 1.5 A/μs, and the corresponding reverse recovery charge Qrr Qrr and the maximum reverse recovery current I RM IRM are 5500 μC and 110 A. Then the static voltage-sharing resistance Rj Rj of the auxiliary voltage-sharing circuit on the machine side is about 138 k, and the dynamic voltagesharing capacitance circuits C and Rd are about 0.9 uF and 57 . The test waveforms of thyristor trigger unit under wide frequency and wide voltage conditions are shown in Fig. 5 and Fig. 6. And Fig. 5 shows the test waveforms of energy acquisition and trigger at low frequency (3.5 Hz) and low voltage (V T = 78 V). Figure 6 shows the test waveform at 50 Hz and VT peak of 2.877 kV. Where VT V T is the voltage at both ends of the thyristor, V Q is the energy-taking voltage of the thyristor trigger unit, and V gt is the thyristor trigger signal. The test waveform of thyristor overvoltage protection is shown in Fig. 7. According to the instantaneous overvoltage threshold value designed by thyristor trigger unit, when V T reaches the protection threshold value of 5.32 kV, TCU will automatically trigger the thyristor.

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Fig. 5. Test waveform of low frequency and low voltage energy acquisition and trigger.

Fig. 6. Energy acquisition test waveforms of 50 Hz.

Fig. 7. Test waveform of TCU instantaneous overvoltage protection

5 Conclusion Aiming at the control and protection of high-power thyristor valve group in SFC valve group of pumped storage unit, this paper introduces the basic principle of valve group control and protection. This paper also expounds the key technologies of high-voltage series valve group, such as dynamic and static equalization, wide frequency and wide voltage energy extraction, reverse recovery protection, thyristor instantaneous protection based on accurate adjustment of voltage threshold, and verifies the above technologies in actual system test platform and engineering application. Acknowledgments. This research is supported by the State Grid Corporation of China Science and Technology Project under Grant 5100-202240496A-3-0-ZZ.

References 1. Zheng, K., Chen, J., Wang, X., et al.: Study on hybrid reactive power compensation system based on SVG+LC. Power Capacit. React. Power Compens. 42(3), 23–28 (2021). (in Chinese)

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2. Xu, X., Hu, W., Cao, D., Qi, H., Chen, C., Chen, Z.: Optimized sizing of a standalone PVwind-hydropower station with pumped-storage installation hybrid energy system. Renew. Energy 147, 1418–1431 (2020). https://doi.org/10.1016/j.renene.2019.09.099 3. Wang, F., Liu, K., Qin, L., Chen, M., Zhu, S., Du, Y.: Impedance modeling and stability analysis of power system with variable-speed pumped storage and direct-drive wind turbines. Autom. Elect. Power Syst. 45(17), 61–69 (2021). (in Chinese) 4. Chazarra, M., Perez-Diaz, J.I., Garcia-Gonzalez, J.: Optimal joint energy and secondary regulation reserve hourly scheduling of variable speed pumped storage hydropower plants. IEEE Trans. Power Syst. 33(1), 103–115 (2018). https://doi.org/10.1109/TPWRS.2017.269 9920 5. Hu, J., Jian, Y., Yang, H., Wu, W.: The sequential control logic strategy of the SFC system for large synchronous compensator. Elect. Eng. 19(9), 86–90 (2018). (in Chinese) 6. Kazem, B., Wang, X., Blaabjerg, F., et al.: Couplings in phase domain impedance modeling of grid-connected converters. IEEE Trans. Power Electron. 31(10), 6792–6796 (2016) 7. Luo, S., Hu, W., Huang, Q., Han, X., Chen, Z.: Optimization of photovoltaic/small hydropower/pumped storage power station system sizing under the market mechanism. Trans. China Electrotechn. Soc. 35(13), 2792–2804 (2020). (in Chinese) 8. Dong, Y., Zhu, R., Hou, K., Pan, R., Hu, J.: Fault analysis and frequency conversion differential protection of machine bridge of synchronous compensator SFC system. Elect. Eng. 21(11), 114–118, 124 (2020). (in Chinese) 9. Wang, X., Man, Z., Liu, Y., et al.: Optimal power control method for SFC pulse commutation phase. Power Electron. 54(3), 68–70 (2020). (in Chinese) 10. Zhang, Y.: Study of starting process of pumped storage machines by static frequency converter. In: 2010 2nd International Conference on Signal Processing Systems, pp V1–228-V1–231. IEEE, Dalian (2010) 11. Wang, D., Zhang, L., Yang, B., et al.: Developing and simulation research of the control model and control strategy of static frequency converter. In: 2012 Second International Conference on Intelligent System Design and Engineering Application, pp 1032–1035. IEEE, Sanya (2012)

A Carbon Emission Prediction Model Based on PSO and Stacking Ensemble Learning for the Steel Industry Yingqiu Wang1 , Chenguan Xu2,3(B) , Chenyang Zhao1 , Meng Zhao1 , and Runze Tian1 1 State Grid Tianjin Electric Power Company, Tianjin, China

{yingqiu.wang,chenyang.zhao,meng.zhao,runze.tian}@tj.sgcc.com.cn 2 State Grid Electric Power Research Institute Wuhan Efficiency Evaluation Company Limited, Wuhan, China [email protected] 3 State Grid Electric Power Research Institute, Nanjing, China

Abstract. As global concern for environmental issues continues to grow, reducing carbon emissions has become one of the key tasks across various industries. The steel industry, as one of the major contributors to carbon emissions, holds significant importance in accurately predicting carbon emissions. This paper proposes a carbon emission predicting model based on Stacking framework with Particle Swarm Optimization. To address the issues of missing data and dimensionality in the carbon emission prediction process, the data is preprocessed, and within the Stacking ensemble learning framework, foundational models such as XGBoost, SVR, and KNN are selected as base learners, while Ridge regression is chosen as the meta-learner. The fitness function is defined using the error metric of model outputs, and PSO is utilized to optimize the hyperparameters of the base learners. Finally, the optimized hyperparameters obtained are incorporated into the model to validate the effectiveness of the proposed model through practical examples. The experimental results demonstrate that the optimized Stacking model can further improve prediction accuracy compared to the non-optimized Stacking model. Keywords: Carbon Emission Prediction · PSO · Stacking Ensemble Learning

1 Introduction With the rapid global industrialization and urbanization, carbon emissions have become a significant environmental challenge. The steel industry, in particular, stands out as an energy-intensive sector with substantial carbon emissions, making its impact on the environment particularly significant. Therefore, carbon emission prediction and reduction in the steel industry have become crucial topics for environmental protection and sustainable development. Steel production involves multiple processes [1], as shown in Fig. 1, including sintering, coking, ironmaking, and steelmaking, with each process contributing differently to carbon emissions. Therefore, carbon emission prediction is influenced by various factors © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 82–91, 2024. https://doi.org/10.1007/978-981-97-0865-9_10

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[2], including the production processes, combustion of fossil fuels, purchased electricity and heat, transportation, and raw material extraction. These factors make carbon emission prediction complex and challenging.

Fig. 1. Production process diagram of steel enterprises

The research on energy-saving and emission reduction in high-energy-consuming industries has been a topic of widespread interest among scholars. Existing carbon emission calculation methods use carbon accounting for calculation. [3] applies the principle of carbon balance to analyze the carbon inputs and outputs of steel enterprises, as well as the associated factors, in order to develop a carbon emissions calculation model for these enterprises. However, traditional methods of calculating carbon emissions often lack real-time capabilities and cannot provide timely emission reduction recommendations. They are no longer suitable for carbon emission calculations in the modern steel industry. Considering the randomness and nonlinearity of carbon emission data, researchers have used gray prediction models [4], LSTM [5], and SVR [6] to predict carbon emissions separately, leveraging the advantages of each model and achieving certain improvements in accuracy. However, traditional statistical models and machine learning methods still have limitations in predicting nonlinear data. With the continuous research and development of ensemble learning methods, [7] introduces a Stacking ensemble learning model to predict carbon emissions based on electricity consumption. Additionally, [8] predicts fossil fuel consumption and transforms it into carbon emissions using the Stacking ensemble learning method. Compared to single models, the Stacking model effectively improves prediction accuracy, but there is still room for further improvement. Currently, many researchers have proposed various methods for hyperparameter optimization. [9] introduces a sparrow search algorithm for optimizing the XGBoost model, addressing the challenge of selecting appropriate parameters for the XGBoost model and improving its regression performance. [10] combines particle swarm optimization and LSTM neural networks in the power load forecasting method, optimizing the learning rate and the number of neurons using particle swarm optimization, resulting in higher prediction accuracy and stability.

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Based on the limited existing research on carbon emission prediction in the steel industry, this study proposes a PSO-enhanced Stacking ensemble learning method for carbon emission prediction. The main work and contributions include the following aspects: First, preprocessing was performed on the carbon emission dataset of the steel industry, and feature engineering was conducted using Pearson correlation coefficient and PCA methods. Then, within the Stacking ensemble learning framework, a carbon emission prediction model for the steel industry based on PSO optimization and multi-model fusion was established. The output error metric of the Stacking ensemble learning was used as the fitness function to optimize the hyperparameters of the first-level base learners. Finally, the effectiveness of the algorithm was validated using carbon emission data from a steel company in a specific province. The results demonstrate that the PSO-based improved Stacking ensemble learning method exhibits good predictive performance and stability in carbon emission forecasting for the steel industry.

2 Data Preprocessing 2.1 Feature Engineering The purpose of feature engineering is not only to reduce dimensionality but also to eliminate redundant and irrelevant features. The Pearson coefficient can measure the relationship between features, and its formula is as follows: ρX ,Y =

cov(X , Y ) E(XY ) − E(X )E(Y )  = 2 σX σY E(X ) − (E(X ))2 E(Y 2 ) − (E(Y ))2

(1)

where: X and Y represent the feature variables of electricity consumption and coal consumption, respectively, in the sample data of the steel industry. E(·) denotes the mathematical expectation function, cov(X , Y ) represents the covariance between the feature variables According to the results of Pearson correlation coefficient, PCA was used to construct the feature variables. 2.2 Data Standardization In a dataset, the features often have different units and scales due to their inherent nature. This disparity can lead to slow convergence or complete failure of algorithms when processing the data. To address these issues, it is necessary to employ a standardization method to eliminate the differences between features. The purpose is to ensure that all features have a similar scale, enabling algorithms to handle the data more effectively. The formula for standardization is shown as Eq. (2): x =

x−μ σ

(2)

where: μ and σ represent the mean and standard deviation of the sample data, respectively.

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3 Theoretical Part 3.1 Stacking Ensemble Learning Stacking is a machine learning technique based on the principles of statistical learning theory, which combines multiple algorithms to create an integrated model.

Fig. 2. Stacking Ensemble Technology

Figure 2 illustrates the algorithm framework of Stacking ensemble learning. It starts by partitioning the original dataset into several subsets according to certain rules. These subsets are then fed into the first-layer predictive models, where each base learner is trained. The outputs of the base learners serve as the predictions of the first layer. These predictions are then used as inputs to the second-layer model, which is trained using a meta-learner. The final predictions are obtained from this second layer. When training a Stacking model, there are typically three main steps involved: • Data Set Partitioning and Base Learner Determination: The original data set is divided into training set and test set, and the base learner and meta-learner are determined • K-fold Cross-Validation: The training set is divided into k subsets, k − 1 subsets are used as training, and the rest are used as validation data • Meta-learner training: Using the data generated in the first layer to train the metalearner, evaluate the performance of the meta-learner, and get the best trained model. 3.2 Particle Swarm Optimization Algorithm The Particle Swarm Optimization (PSO) algorithm was proposed in 1995, simulating the complex collective behavior observed in bird flocks and other social phenomena. The flowchart of the PSO algorithm is shown in Fig. 3. The formulas for updating the velocity and position of a particle are as follows:   (3) vmd  = wvmd + c1 a1 (pmd − xmd ) + c2 a2 pgd − xmd xmd  = xmd + νmd

(4)

where: w is the inertia weight that influences the inertia term in the velocity up-date formula and affects the global and local search abilities of the algorithm; c1 and c2 are

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Fig. 3. PSO Technology

the learning factors that respectively reflect the impact of the personal best and global best on the particle’s velocity, both of which are non-negative constants; a1 and a2 are random numbers within the range of [0,1]. In practical optimization problems, a constant inertia weight cannot effectively balance the search preferences of the particle swarm and often leads to the swarm getting trapped in local optima. To improve the optimization capability of the particle swarm throughout different search stages, a dynamic inertia weight is commonly used to update the velocity formula. The new inertia weight coefficient is given by the following formula: w = wmax − (wmax − wmin )

t tmax

(5)

where: wmax and wmin represent the maximum and minimum values of the inertia weight, respectively; t and tmax represent the current generation and the maximum number of generations, respectively.

4 A PSO-Based Hyperparameter Optimization Ensemble Learning Model for Carbon Emission in the Steel Industry 4.1 Carbon Emission Prediction Process To further improve the prediction accuracy of the model, this study introduces the Particle Swarm Optimization (PSO) algorithm to optimize the Stacking model. The flowchart of the PSO algorithm on top of the Stacking model is shown in Fig. 4. The establishment of the PSO-based optimization involves the following steps: • Data preprocessing. Firstly, missing values in the sample data are filled with the mean value of the attribute. The Pearson correlation coefficient is used to deter-mine the correlation between feature variables, which is then used to determine the parameters for PCA dimensionality reduction. To eliminate the influence of dimensional differences between the original data in the experiment, the original data is standardized.

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• Splitting into training and testing sets. In this experiment, there are a total of 150 samples. The data will be randomly divided into training and testing sets in an 8:2 ratio. • Model training and hyperparameter optimization. K-fold cross-validation was used for the training set, and eMAPE was taken as the fitness function. After iteration, the trained model and hyperparameters were obtained.

Fig. 4. PSO-Stacking Flowchart

4.2 Model Evaluation Indicators In order to evaluate the predictive performance of the model, this study uses two evaluation metrics: Mean Absolute Percentage Error and Root Mean Square Error. 100%  |yi − yi | eMAPE = n yi i=1   n 1  (yi − yˆ i )2 eRMSE = n n



(6)

(7)

i=1

where: yi represents actual carbon emissions data; yˆ i represents predicted carbon emissions data; n represents the number of carbon emissions data points.

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5 Example Analysis 5.1 Experimental Data and Platform The carbon emissions data in the experimental dataset is derived from historical operational data of several steel enterprises in a province in China. It includes multiple feature variables such as diesel fuel consumption and electricity consumption. The dataset consists of 150 samples. The hardware platform used in this study is an Intel(R) Core (TM) i7-8750H CPU. The code is compiled in the Python3.7 environment. 5.2 Analysis of Single Model Prediction Results Firstly, the experiment is designed to compare and analyze the individual predictions of each base learner on the original dataset. Cross-validation is applied to each base learner model by further dividing the data into training and validation sets. The performance of the models on the validation set is observed using different sets of hyperparameters to determine the optimal parameter set for each model. The performance of each individual model’s prediction is shown in Table 1. Table 1. Prediction error of single model Model

Error indicator eMAPE

eRMSE

KNN

4.567

351.711

XGBoost

3.268

239.844

SVR

3.739

256.095

LightGBM

3.577

237.213

GBDT

3.406

257.511

From the results, it can be observed that when performing individual predictions, XGBoost has the smallest prediction error compared to KNN and SVR. The eMAPE of XGBoost is reduced by 28.44% and 12.59% compared to KNN and SVR, respectively. The eRMSE of XGBoost is reduced by 31.81% and 6.34% compared to KNN and SVR, respectively. XGBoost utilizes second-order Taylor expansion to optimize the loss function and utilizes first and second derivative information for parameter updates, enabling it to capture complex relationships and interactions among features more effectively, thus improving its pre-diction accuracy. In contrast, KNN and SVR are relatively simple models, leading to larger biases in their predictions. Due to the complexity of the data, their fitting ability is relatively weak, and they cannot capture non-linear and complex relationships in the data well. Due to XGBoost, LightGBM, and GBDT all being ensemble learning algorithms based on decision trees, their error metrics are very close. Finally, XGBoost, KNN, and SVR were selected as base learners.

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5.3 Analysis of Ensemble Learning Prediction Results To further improve the prediction accuracy of the model, Particle Swarm Optimization (PSO) is used to optimize the hyperparameters of the base learners in the Stacking framework. The parameter ranges for PSO and grid search for each base learner model are presented in Table 2.

Fig. 5. Model hyperparameter convergence Table 2. Base Learner Hyperparameter Range Model

Hyper-parameters

PSO

Grid search

KNN

n_neighbors

[1, 10]

[1, 10]

XGBoost

max_depth n_estimators

[3, 10] [20,200]

[3, 10] [20,200,4]

C

[10–2 ,102 ]

[0,100,4]

SVR

The fitness function of the PSO optimization during its iterative process is shown in Fig. 5. After approximately 70 iterations, the error converges to a stable value. Compared to traditional grid search methods, PSO optimization can effectively address the issue of a large search space when there are a large number of parameters or a wide range of candidate values. It can discover the global optimal solution through cooperation and competition among particles and is suitable for optimizing continuous parameters. It only requires setting parameter ranges without explicitly specifying candidate values. The optimized parameters are applied to the base learners in the first layer of the Stacking model, resulting in the final model. The prediction results are shown in Fig. 6. The results indicate that the optimized Stacking model exhibits higher robustness and accuracy. According to Table 3, the PSO-Stacking ensemble learning method achieves excellent performance in predicting carbon emissions in the steel industry, with significant improvements in evaluation metrics eMAPE and eRMSE . Compared to the Stacking

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Fig. 6. Comparison of Ensemble learning prediction results

ensemble learning model with hyperparameter optimization using grid search, the PSOoptimized Stacking model can effectively improve prediction accuracy. Metrics eMAPE and eRMSE are reduced by 19.25% and 16.89% respectively, indicating that the predicted values are closer to the true values. Table 3. Prediction error of Ensemble learning Model

Error indicator eMAPE

eRMSE

Stacking

2.676

161.202

PSO-Stacking

2.161

133.980

6 Conclusions To fully utilize the energy consumption and electricity consumption data features of the steel industry, this paper proposes a PSO-optimized Stacking ensemble learning model. The MAPE error of the Stacking model’s predicted values is used as the fitness function, and the PSO algorithm is employed to optimize the hyperparameters of the first-layer base learners in the Stacking model. This approach addresses the limitations of exhaustive parameter optimization through grid search and improves computational efficiency. It effectively enhances the prediction accuracy and stability of the model. Acknowledgements. This research was supported by State Grid Tianjin Electric Power Company. The grant number is 5400-202112582A-0-5-SF. It was entitled with “Research and Demonstration Application of User Side Smart Energy Service Technology Based on the Integration of Green State Grid and Provincial Smart Energy Service Platform”.

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References 1. Wang, Y., Hu, Q.: Research and application of optimization method for iron and steel sintering ingredients. In :2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference (IAEAC) IEEE, pp. 1819–1823. IEEE (2018) 2. Hao, Y., Zhu, Z., Li, S., Cang, D.: A case study of LCA for environmental protection in steel company. In :2012 Third International Conference on Digital Manufacturing & Automation, pp. 13–16 (2012) 3. Li, H., Cang, D., Guo, Y., Bai, H., Jin, B.: The analysis of energy structure of coal using and co2 emission of a typical steel industry. In: 2011 International Conference on Materials for Renewable Energy & Environment, pp. 982–986 (2011) 4. Gao, R., Li, X., Yu, H.: Prediction method of green transportation carbon emission in smart city based on gray joint algorithm. In :2021 6th International Conference on Smart Grid and Electrical Automation (ICSGEA), pp. 30–34 (2021) 5. Zhang, Q., Li, F., Long, F., Ling, Q.: Vehicle emission forecasting based on wavelet transform and long short-term memory network. IEEE Access 6, 56984–56994 (2018) 6. Li, J., Zhou, S., Ni, J.: Research on carbon emission prediction trend of electric power system based on CS-SVR. In: ECITech 2022; The 2022 International Conference on Electrical, Control and Information Technology, pp. 1–6 (2022) 7. Shen, Y., Zeng, Z., Lin, W., Que, D., Huang, Z.: Electric power carbon emission prediction based on stacking ensemble model with k-fold cross validation. In :2022 China Automation Congress (CAC), pp. 6600–6605 (2022) 8. Zhang, Q., et al.: Carbon emissions forecasting based on stacking ensemble learning. In :2022 IEEE 5th International Electrical and Energy Conference (CIEEC), pp. 2725–2730 (2022) 9. Song, J., Jin, L., Xie, Y., Wei, C.: Optimized xgboost based sparrow search algorithm for short-term load forecasting. In :2021 IEEE International Conference on Computer Science, Artificial Intelligence and Electronic Engineering (CSAIEE), pp. 213–217 (2021) 10. Zhang, Z., Xu, W., Gong, Q.: Short-term power load forecasting based on particle swarm optimization long short-term memory neural network. In :2023 IEEE 2nd International Conference on Electrical Engineering, Big Data and Algorithms (EEBDA), pp. 412–416 (2023)

Approximate Analytical Calculation of Magnetic Shielding of Double-Layer Conducting Plates with Periodic Apertures Jiancheng Huang1 , Xingxin Guo2 , Yang Wang3 , and Chongqing Jiao1(B) 1 School of Electrical and Electronic Engineering, North China Electric Power University,

Beijing 102206, China [email protected], [email protected] 2 Electric Power Research Institute of State Grid Jiangsu Electric Power Co., Ltd., Nanjing 211103, China 3 State Grid Jibei Electric Power Co., Ltd., Langfang Power Supply Company, Langfang 065000, China

Abstract. This article focuses on the theoretical calculation method of lowfrequency magnetic shielding of double-layer conducting plates with periodic apertures. The shielding effectiveness is measured when the double-layer CPPA is placed be-tween a pair of conductor rings, one ring for emissing and another ring for receiving. A surface-impedance-based theoretical model is developed to predict the shielding effectives, and the model is simplified under the quasi-static condition. The integral formula works well when the plate-to-plate distance is larger than the aperture diameter. In addition, a physical model was built in the laboratory for measurement, and the theoretical calculation results were compared with the actual measurement results. Finally, an approximate formula is obtained by simplifying the formula under some assumptions and the conclusions of some literatures. Keywords: Low frequency · magnetic shielding · double-layer plates · periodic apertures

1 Introduction In engineering applications, many devices will be covered with shells [1–5], wire meshs [6–9] and other structures to prevent electromagnetic interference. The engineering principle is low-frequency magnetic shielding. The perforated board has a relatively balanced performance in terms of weight and shielding effectiveness, so it has become one of the choices [10–12]. A recent study [5] showed that for a single-layer conductor plate with periodic apertures, the variation of its shielding effectiveness in the face of electromagnetic field sources of different frequencies is mainly related to the behavior of magnetic diffusion and aperture leakage at different frequencies. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 92–101, 2024. https://doi.org/10.1007/978-981-97-0865-9_11

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Replacing single-layer shield with a multilayer shield can improve SE further. In [8], the SE of multiple cylindrical shells in a homogeneous electromagnetic field was investigated, and it was shown that the shielding performance was significantly improved by the use of multiple layers compared with a single layer of equivalent thickness. Similar behavior has also been observed for both solid plate and wire mesh shields [13]. This article extends the earlier research on monolayer CPPA [5] to the theoretical research and experimental verification of double-layer CPPA. In particular, it was observed during analysis and validation that SE was clearly dependent on board to board spacing. The influence on the SE of the lateral deviation between the two layers is also investigated experimentally. This paper consists of four parts, the rest of the article is arranged as follows. Section 2 explain the electromagnetic problem and details of the layout of the validation tests. In Sect. 3, formulas for the calculation of the SE are derived based on the surface-impedance model, including an integral formula solution and its simplified form, and the verification experiment is carried out in the laboratory. Finally, the article is summarized in Sect. 4.

2 Problem Description and Test Bench Setup As shown in Fig. 1, The magnetic field emission coil is located in the z = 0 plane and has a time-harmonic current i with frequency f. The thickness of each CPPA shield layer is t, the first layer is located in z1 < z < z1 + t, and the second layer is located in z2 < z < z2 + t. The conductivity of the shielding material is σ, the permeability is μ, and the permittivity is ε. P d

z

Plates

2r

z = z2

z = z1

t

z y

i x

Fig. 1. Layer model.

The plate is distributed with periodic circular holes of radius r. Our aim is to evaluate the shielding effectiveness (SE) of the double-layer CPPA against the magnetic field produced by the emitting loop. Here, the SE is defined in the usual manner as the ratio of the magnetic field magnitude in the absence of the double-layer CPPA to that with the CPPA present. Figure 2 shows a brief layout of the validation experiment [3]. The signal source of the transmit loop (ZN30303, 12 cm diameter) is a low-frequency power signal gen-erator

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(ZN1042A). The generator can emit sine waves with frequencies between 1 and 500 kHz. The launch ring is made of 20 turns of enameled wire and fixed on the insulating metal shell. The height of the insulating metal shell is 6 cm, and the fixed position of the launch ring is 5 cm from the bottom of the shell. The signal receiving ring (AARONIAAG, PBSH4, 5 cm diameter, 5 mm wire shell radius) is located on the other side of the double-layer conductor plate, and the received sig-nal is transmitted to the spectrum analyzer. The magnetic SE is the ratio of the measured voltage of the receiving loop with the conductor plate removed to the measured voltage of the receiving loop with the conductor plate attached. The ex-periment uses a square aluminum plate with a side length of 1m and a thickness of 1mm. The electrical conductivity of the plate is 3.77 × 107S/m and the relative magnetic permeability is 1. Each aluminum plate has 2,500 circular holes at equal intervals, with a radius of 5 mm and a center distance of 20 mm. 5 mm

5 cm

Receiving loop EMI test receiver

d The plates z Low-frequency power signal generator

x i

t

12 cm

y Emitting loop

6 cm

Fig. 2. Magnetic shielding effectiveness measurement layout.

3 Theoretical Model and Comparison with Experimental Results 3.1 Unshielded Field “Unshielded” here means that the double-layer CPPA in Fig. 1 is absent. Thus, the unshielded field is the free-space field produced by the emitting loop alone. As early as 1967, Moser [15] solved the problem of magnetic shielding of an infinitely extending planar solid plate in the presence of a toroidal field source. He used the separation of variables method to solve the magnetic potential vector wave equation in the cylindrical coordinate system and obtained an exact solution in the form of an infinite integral. According to Moser’s formulation, the expression of the electromagnetic field without shielding is μ0 ai eρ B0 = 2

∞

λJ1 (λa)J1 (λρ)e−τ0 |z| dλ

0

+

μ0 ai ez 2

∞ 0

λ2 τ0

(1) J1 (λa)J0 (λρ)e−τ0 |z| dλ

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and jωμ0 ai E0 = − eφ 2

∞ 0

λ J1 (λa)J1 (λρ)e−τ0 |z| dλ τ0

(2)

in the formula, ω is the angular frequency of the signal, μ0 is the free space magnetic permeability, J0 is the 0th-order Bessel function of the first kind, J1 is the 1st-order Bessel function of the first kind, and  (3) τ0 = λ2 − ω2 μ0 ε0 with E0 the permittivity of free space. Particularly, for a field point whose coordinates are on the z-axis, E0 = 0 and √

μ0 aI e−jk0 a +z B0 = ez 2 a2 + z 2 2

2

  a jk0 a + √ a2 + z 2

(4)

where k0 = ω(μ0E0)1/2 is the free-space wavenumber. 3.2 Shielded Field in Integral Form Our procedure is similar to that in [5], where a solution was obtained for a single-layer CPPA configuration. The key to this approach is the use of the surface imped-ance method, in which the CPPA layer should be modelled with the following bound-ary conditions: 1) The tangential electric field on both sides of the conductor plate is continuous 2) The value of the tangential electric field is the product of the surface impedance Zs and the equivalent surface current K. The whole space is divided into three parts: region 1 (z < z1), region 2 (z1 < z < z2), and region 3 (z > z2) (Fig. 3). Impedance boundary

Unit cell z = z2 d z = z1

Impedance boundary

Region 3 2r Region 2 Region 1

w

z i

a x

y Emitting loop

Fig. 3. Geometry of the theoretical model of the magnetic shielding configuration.

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Within region 1, the fields are superpositions of the unshielded fields and the backward wave produced by the eddy current in the CPPA shield: B1 =

μ0 ai eρ 2

∞

  λJ1 (λa)J1 (λρ) e−τ0 z − C1 eτ0 z dλ

0

μ0 ai ez + 2

∞ 0

(5)

  λ2 J1 (λa)J0 (λρ) e−τ0 z + C1 eτ0 z dλ τ0

and jωμ0 ai eφ E1 = − 2

∞ 0

 λ J1 (λa)J1 (λρ) e−τ0 |z| + C1 eτ0 z dλ τ0

(6)

where the coefficient C1 represents the backward-wave amplitude. Within region 2, the fields are superpositions of the unshielded fields and the backward wave: μ0 ai eρ B2 = 2

∞

  λJ1 (λa)J1 (λρ) C2 e−τ0 z − C3 eτ0 z dλ

0

+

μ0 ai ez 2

∞ 0

(7)

λ2 τ0

  J1 (λa)J0 (λρ) C2 e−τ0 z + C3 eτ0 z dλ

and jωμ0 ai E2 = − eφ 2

∞ 0

  λ J1 (λa)J1 (λρ) C2 e−τ0 z + C3 eτ0 z dλ τ0

(8)

Within region 3, the fields are only those of the forward wave: μ0 ai eρ B3 = 2

∞

C4 λJ1 (λa)J1 (λρ)e−τ0 z dλ

0

μ0 ai ez + 2

∞ 0

(9)

λ2 C4 J1 (λa)J0 (λρ)e−τ0 z dλ τ0

and jωμ0 ai eφ E3 = − 2

∞ C4 0

λ J1 (λa)J1 (λρ)e−τ0 z dλ τ0

(10)

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The surface impedance boundary conditions corresponding to the first and second layers of the CPPA are respectively

 (11) E1φ =E2φ = Zs H2ρ − H1ρ with z=z1 and

 E2φ =E3φ = Zs H3ρ − H2ρ with z=z2

(12)

Under the assumption that the plate is a perfect electrical conductor, the surface impedance can be expressed as [5, 16] Zs =

jπ 8r 3 Z0 3Sλ0

(13)

where Z0 = (μ0/E0)1/2 is the free-space wave impedance, λ0 is the free space wavelength, and S = d1d2 is the area of a unit cell. Combining (5)–(12), we get C4 = 



jωμ0 jωμ0 Zs τ0 + 2Zs τ0

2

1 

jωμ0 2 2τ0 (z1 −z2 ) + 1 − 2Z e s τ0

(14)

Equations (9) and (14) indicate that the shielded field depends on the distance between the two plates rather than their specific locations. At a given field point P(ρ, φ, z), the SE is calculated as the ratio of the z components of the magnetic field:    B0z (ρ, z)   (dB)  (15) SE = 20 log10  B3z (ρ, z)  In the magnetic field expression formula in (5)–(10), due to the existence of the exponential decay factor e−τ0 z , when the value of λ is relatively large, the integral value of the function will become very small. If the value of λ is restricted to a limited range between 0 ~ λm, the integrated value does not change significantly. According to [17], λm = 10/z is a suitable value, where z is the height from the magnetic field observation point to the plane where the loop is located as the reference plane. 3.3 The Shielded Field in the Form of Simplified Formula Usually, at low frequencies, Zs < < ωμ0/τ0 [5, 18], and (14) can then be approximated as  

−1 jωμ0 −2 1 − e2τ0 (z1 −z2 ) (16) C4 ≈ 2Zs τ0 substituting of which into (9) gives B3z

 ∞  λ2 τ0 μ0 ai 2Zs 2 ≈ 2 jωμ0 1 − e2τ0 (z1 −z2 ) 0

×J1 (λa)J0 (λρ)e−τ0 z dλ

(17)

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Using the series expansion 1 1 − e2τ0 (z1 −z2 )

=

∞ 

e2nτ0 (z1 −z2 )

(18)

n=0

we have B3z

 ∞ ∞  μ0 ai 2Zs 2  = λ2 τ0 2 jωμ0

×J1 (λa)J0 (λρ)e

n=0 0 −τ0 [2n(z2 −z1 )+z]

(19)

dλ

Combining (1) and (19), we get  B3z =

2Zs jωμ0

2  ∞ n=0

∂ 2 B0z (ρ, 2n(z2 − z1 ) + z) ∂z 2

(20)

Particularly, for a field point on the z axis and under quasistatic conditions, (4) can be approximated as μ0 ia2 B0z ≈

3 2 2 a2 + z 2 /

(21)

The assumption of quasistatic conditions is valid if only the distance from the field points to the emitting loop is much smaller than the free-space wavelength. For a typical size of 1 m, the applicable frequencies are up to 30 MHz. The expression (20) can then be simplified to B3z

 ∞  −5/ 2 3μ0 ia2 2Zs 2   2 a + [2n(z2 − z1 ) + z]2 ≈− 2 jωμ0 n=0   5[2n(z2 − z1 ) + z]2 1− a2 + [2n(z2 − z1 ) + z]2

(22)

3.4 Comparison of Theoretical and Experimental Results The theoretical model developed in Section III has two limitations: it treats the plates as perfect electrical conductors and it neglects the coupling between them. The first of these approximations means that the model is suitable only for frequencies at which the aperture leakage effect is dominant. The second approximation makes the model suitable only for larger plate-to-plate spacings. These two limitations are illustrated clearly in Fig. 4, in which both the measured and calculated SEs of the double-layer shield with d = 0 mm are displayed together. Over the whole frequency range containing both diffusion and aperture leakage effects, there are obvious disagreements between the two curves. In particular, the calculated SE is frequency-independent over the whole frequency range.

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50

SE (dB)

40

30

d = 0 mm Measurement Integral formula (9)

20 0

100

200

300

400

500

Frequency (kHz)

Fig. 4. Measured SE versus frequency for a loop-to-loop distance of 92 mm and a plate-to-plate spacing of 0 mm.

For a loop-to-loop distance of 92 mm, further comparisons are carried out for d = 3 mm, 6 mm, 9 mm, 12 mm, 15 mm and 30 mm in Figs. 5(a)–(f), respectively. For each value of d, four curves are plotted: the measured results, the calculated results from the integral formula (9), the calculated results from the simplified formula (22), and the calculated results for the corresponding double-layer solid plates. A comparison between the integral formula (9) and the simplified formula (22) shows that the two are in good agreement, with the difference being within 3 dB for d = 3 mm and less than 1 dB for d ≥ 9 mm. The larger the plate-to-plate spacing, the more consistent are 70

70

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d = 6 mm

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d = 3 mm

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Measurement Integral formula (9) Simplified formula (22) Solid aluminum plates

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Measurement Integral formula (9) Simplified formula (22) Solid aluminum plates

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Measurement Integral formula (9) Simplified formula(22) Solid aluminum plates 0

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(d)

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d = 15 mm

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d = 12 mm

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100 200 300 400 500

(b)

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Measurement Integral formula (9) Simplified formula (22) Solid aluminum plates

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Frequency (kHz)

(a)

50

d = 9 mm

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d = 30 mm

50

Measurement Integral formula (9) Simplified formula (22) Solid aluminum plates

40 30 20 0

100

200

300

400

500

Frequency (kHz)

(f)

Fig. 5. Comparison of the measured results, the calculated results from the integral formula (9), the calculated results from the simplified formula (22), and the calculated results for the corresponding double-layer solid plates with different plate-to-plate spacings.

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the two solutions. For frequencies at which the aperture leakage effect is dominant, the difference between the integral formula and the measurements is about 4 dB for d = 3 mm and within 1–3 dB for d ≥ 6 mm. However, for frequencies near the low-frequency resonance, this difference can be as large as 15 dB (Fig. 5).

4 Conclusion A theoretical model based on surface impedance is proposed to predict the shielding efficiency of double-layer conductive plates with periodic holes. After deriving the integral calculation formula, the formula is simplified under the assumption of quasi-static conditions. Finally, a model was built in the laboratory to verify the theoretical formula. The results show that the integral formula is in good agreement with the measured value in the frequency where the aperture leakage effect is dominant. At the same time, the larger the plate spacing, the more consistent the solutions of the integral formula and the simplified formula. The theoretical model is verified in the laboratory.

References 1. Lovat, G., Burghignoli, P., Araneo, R., Stracqualursi, E., Celozzi, S.: Closed-form LF magnetic shielding effectiveness of thin planar screens in coplanar loops configuration. IEEE Trans. Electromagn. Compat. 63(2), 631–635 (2021). https://doi.org/10.1109/TEMC.2020.3007864 2. Jiao, C., et al.: Low-frequency magnetic shielding of planar shields: a unified wave impedance formula for the transmission line analogy. IEEE Trans. Electromagn. Compat. 63(4), 1046– 1057 (2021). https://doi.org/10.1109/TEMC.2021.3052779 3. Zhang, Z., Yang, X., Jiao, C., Yang, Y., Wang, J.: Analytical model for low-frequency magnetic field penetration through a circular aperture on a perfect electric conductor plate. IEEE Trans. Electromagn. Compat. 63(5), 1599–1604 (2021). https://doi.org/10.1109/TEMC.2021.306 5064 4. Park, H.H.: Analytic magnetic shielding effectiveness of multiple long slots on a metal plate using rectangular loops. IEEE Trans. Electromagn. Compat. 62(5), 1971–1979 (2020). https:// doi.org/10.1109/TEMC.2019.2954671 5. Bai, W., Ning, F., Yang, X., Jiao, C., Chen, L.: Low frequency magnetic shielding effectiveness of a conducting plate with periodic apertures. IEEE Trans. Electromagn. Compat. 63(1), 30–37 (2021) 6. Hyun, S., Jung, I., Hong, I., Jung, C., Kim, E., Yook, J.: Modified sheet inductance of wire mesh using effective wire spacing. IEEE Trans. Electromagn. Compat. 58(3), 911–914 (2016) 7. Naranjo-Villamil, S., Guiffaut, C., Gazave, J., Reineix, A.: Lightning-induced magnetic fields inside grid-like shields: an improved formula complemented by a polynomial chaos expansion. IEEE Trans. Electromagn. Compat. 63(2), 558–570 (2021). https://doi.org/10.1109/ TEMC.2021.3056320 8. van Helvoort, M.J.A.M., Harberts, D.W.: Low-frequency electromagnetic shielding and scattering of multiple cylindrical shells. IEEE Trans. Electromagn. Compat. 63(1), 46–56 (2021). https://doi.org/10.1109/TEMC.2020.3011757 9. Kunkel, G.M.: Shielding theory and practice. In: Proceedings 1992 Regional Symposium on Electromagnetic Compatibility, pp. 4.2.1/1–4.2.1/5 (1992). https://doi.org/10.1109/ISEMC. 1992.257557

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10. Criel, S., Martens, L., De Zutter, D.: Theoretical and experimental near-field characterization of perforated shields. IEEE Trans. Electromagn. Compat. 36(3), 161–168 (1994). https://doi. org/10.1109/15.305460 11. Araneo, R., Lovat, G., Celozzi, S.: Shielding effectiveness of periodic screens against finite high-impedance near-field sources. IEEE Trans. Electromagn. Compat. 53(3), 706–716 (2011). https://doi.org/10.1109/TEMC.2010.2081367 12. Sarto, M.S., Greco, S., Tamburrano, A.: Shielding effectiveness of protective metallic wire meshes: EM modeling and validation. IEEE Trans. Electromagn. Compat. 56(3), 615–621 (2014). https://doi.org/10.1109/TEMC.2013.2292715 13. Metwally, I.A., Heidler, F.H.: Reduction of lightning-induced magnetic fields and voltages inside struck double-layer grid-like shields. IEEE Trans. Electromagn. Compat. 50(4), 905– 912 (2008). https://doi.org/10.1109/TEMC.2008.2002575 14. Zhou. F., Wu, Y.: Approximate analytical calculation of magnetic shielding of double-layer conducting plates with periodic apertures 15. Ronald Moser, J.: Low-frequency shielding of a circular loop electromagnetic field source. IEEE Trans. Electromagn. Compat. 9(1), 6–18 (1967). https://doi.org/10.1109/TEMC.1967. 4307447 16. Otoshi, T.Y.: A study of microwave leakage through perforated flat plates (short papers). IEEE Trans. Microwave Theory Techn. 20(3), 235–236 (1972). https://doi.org/10.1109/TMTT. 1972.1127723 17. Ryan, C.M.: Computer expression for predicting shielding effectiveness for the low-frequency plane shield case. IEEE Trans. Electromagn. Compat. 9(2), 83–94 (1967). https://doi.org/10. 1109/TEMC.1967.4307468 18. Mohammadi, E., Dehkhoda, P., Tavakoli, A., Honarbakhsh, B.: Shielding effectiveness of a metallic perforated enclosure by mesh-free method. IEEE Trans. Electromagn. Compat. 58(3), 758–765 (2016). https://doi.org/10.1109/TEMC.2016.2526662

A Novel Method for Electric Energy Substitution Technology Evaluation Based on the Cloud-TOPSIS Method Hang Xu1(B) , Xingong Cheng1 , Shengnan Zhao1 , Minjiang Xiang2 , Xu Zhang2 , and Biao Fu2 1 Jinan University, Jinan 250022, China

{cse_xuh,cse_cxg,cse_zhaosn}@ujn.edu.cn 2 State Grid Jinan Power Supply Company, Jinan 250001, China

Abstract. In order to enable effective assessment of the development factors and benefits of various electric energy substitution technologies, and provide clear goals and reasonable development directions for the development of electric energy substitution technologies at the county level, it is necessary to establish a comprehensive, universally applicable, and rational indicator system and method for selecting electric energy substitution technologies. In this paper, a method for electric energy substitution technologies selection based on the cloud theory and the improved technique for order preference by similarity to ideal solution (TOPSIS) method is proposed. Firstly, based on the investigation of the county’s energy consumption market, the selection indicators for electric energy substitution technologies are constructed. Secondly, considering the fuzziness of different indicator weights in the process of selecting electric energy substitution technologies, the reverse cloud combination weight method is proposed to achieve the fuzzy dynamic description of indicator weights. Finally, based on the TOPSIS model and cloud model calculations, a comprehensive cloud model of weighting for electric energy substitution technologies is obtained, and the cloud distance is used to replace the traditional Euclidean distance, thereby achieving the comparison and selection of electric energy substitution technologies. The results of the case study verify the effectiveness of the proposed method. Keywords: Electric Energy Substitution · Combined Weight · Cloud-TOPSIS Method

1 Introduction China adheres to the deep implementation of the concept of green development and accelerates the transformation and upgrading of electric energy substitution work, continuously enhancing the development efforts in electric energy substitution [1–4]. Currently, it has entered a stage of vigorous development in the field of electric energy substitution. However, there are several issues in the promotion of electric energy substitution at the county level [5, 6]. The scope of electric energy substitution is extensive, covering © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 102–110, 2024. https://doi.org/10.1007/978-981-97-0865-9_12

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five major fields, 21 categories, and 56 specific technologies. The responsible personnel for promoting electric energy substitution at the county level find it is difficult to have a deep understanding of these specific technologies, resulting in a lack of knowledge regarding their working principles, technical advantages, and applicability. Furthermore, there is inadequate understanding of product types, suppliers, and typical cases when dealing with specific implementation scenarios [7, 8]. This lack of knowledge makes it challenging to develop advantageous and tailored electric energy substitution plans and technical solutions specific to the local energy consumption patterns, thus hindering the implementation of electric energy substitution work. Therefore, there is a need to establish a comprehensive, universally applicable, and rational system of selection indicators and methods for electric energy substitution technologies. The TOPSIS method is widely favored in the field of technical type selection due to its simplicity, convenience in calculation, strong reliability in evaluation results, and greater rationality [10]. It has been widely applied and is well-regarded for its easy-to-understand principles and high flexibility. However, it also has certain drawbacks and limitations that need to be addressed: (1) The TOPSIS method involves determining weights, and existing weighting methods have their own advantages and disadvantages. Regardless of the method used, there can be significant differences between the resulting weight values, leading to a high degree of uncertainty in their magnitude. Existing combination weighting methods cannot clearly indicate whether the advantages of various weighting methods are simultaneously considered, making it difficult to assign comprehensive and objective values to the weights [11]. (2) The TOPSIS method typically calculates the Euclidean distance between the target value and the ideal value when determining the proximity of alternatives. However, there may be instances where the Euclidean distance between the selected solution and the negative ideal point is also small, resulting in poor accuracy of the evaluation results and an incomplete reflection of the quality of each evaluated object [12]. In order to better evaluate and select electric energy substitution technologies, this paper proposes a method for electric energy substitution technology selection based on optimized combination weights and cloud-TOPSIS. It effectively solves the problems of uncertain weight assignment and inaccurate evaluation results in the technology assessment process, significantly improving the accuracy and reliability of electric energy substitution technology selection.

2 A Novel Method for Electric Energy Substitution Technology Evaluation 2.1 Evaluation Indicator System for Energy Substitution Technologies Following the standards of comprehensiveness, reasonableness, objectivity, and representativeness, a thorough analysis of various factors influencing the development process of energy substitution is conducted. The main and secondary factors are distinguished, and a comprehensive and reliable evaluation indicator system for energy substitution technologies is established. This evaluation system includes four primary indicators:

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technological characteristic indicators, economic characteristic indicators, environmental characteristic indicators, and promotion difficulty indicators, along with several secondary indicators. It aims to comprehensively, reasonably, and objectively describe the evaluation indicator system for the adaptability of energy substitution technologies. 2.2 Combined Weight Method The weight matrix for each indicator obtained through the c common weighting methods for evaluation criteria is as follows: ⎤ ⎡ w11 w12 · · · w1n ⎢ ··· ··· ··· ··· ⎥ ⎥ ⎢ ⎢ 1 2 n ⎥ (1) W = ⎢ wc1 wc1 · · · wc1 ⎥ ⎥ ⎢ ⎣ ··· ··· ··· ··· ⎦ wc1 wc2 · · · wcn j

where, W represents the weight matrix, wi represents the weight value obtained by applying the i-th weighting method to the j-th indicator. The uncertain combined weight clouds N(E x , E n , H e ) for each indicator can be obtained based on the reverse cloud generator, which determines the expected value, fuzziness, and dispersion of the cloud droplet distribution. The numerical values are as follows: 

c c c 1 1 1 2 1 n Ex = wi , × wi , · · · , × wi (2) × c c c i=1

En =

i=1

i=1

c

  n 1 π w − Ex × × i n 2 i=1   He = S 2 − En2 

(3) (4)

In the equation, S 2 represents the variance value of each weight, and its magnitude is calculated as follows: 

2 c c 1 1 × S2 = win (5) win − c−1 c i=1

i=1

T

For every indicator U j , a corresponding set of weights W j = wj1 , wj2, · · · , wjm can be obtained for the reverse cloud combined weights Nwj Exj , Enj , Hej . This combined weight can ensure the completeness of the weight information and the fuzziness of the weights, providing an important reference for the evaluation of energy substitution technologies.

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2.3 Generation of Weighted Cloud Assuming there are n technologies to be evaluated and m evaluation indicators, the original value of the j-th indicator for the i-th technology is denoted as U ij . The matrix representing the standardized scores for each indicator is denoted as V = (Vij )n×m . The calculation method for the standardized scores matrix is as follows: Vij = 

Uij n 

i=1

(6)

Uij2

For the matrix of indicator scores,

 standardized the weighted cloud NFij ExFij , EnFij , HeFij for the j-th indicator of the i-th alternative is shown as follows:   

(7) NFij = Vij Nwj = mVij Exj , Vij Eni , Vij Hej The positive ideal point S + and the negative ideal point S − can be obtained based on the standardized scores matrix (Vij )n×m :         (8) S + = sj+ j = 1, 2, . . . , n , S − = sj− j = 1, 2, . . . , n   When V j is a positive indicator, we have Sj+ = max1≤i≤m Vij as the positive ideal   point and Sj− = min1≤i≤m Vij as the negative ideal point. When V j is a negative indica    tor, we have Sj+ = min1≤i≤m Vij as the positive ideal point and Sj− = max1≤i≤m Vij as the negative ideal point. For the positive ideal point and the negative ideal point, the weighted cloud can be obtained by the same method shown in Eq. (7). 2.4 Generation of Integrated Cloud For the comparative evaluation of alternatives, it is usually done by comprehensively comparing multiple indicators. Each candidate alternative can be defined as a set of vectors, represented by the i-th alternative: 

  Ci = Exi1 , Eni1 , Hei1 , · · · , Exim , Enim , Heim (9) According to the synthesis theory of cloud models, the size relationship for the integrated cloud ZCi (Exi , Eni , Hei ) of the candidate alternatives is satisfied as follows: ⎧ Ex = Ex + Ex2 + · · · + Ex2 ⎪ ⎪ ⎨ i 1  1 2 2 ZCi = Eni = m En1 + En2 + · · · + En2m (10) ⎪ ⎪ ⎩ He = 1 He2 + He2 + · · · + He2  i

m

1

2

m

By using the method described above, we can generate the integrated cloud + LCl+ (Exl+ , En+ l , Hel ) for the positive ideal alternative and the integrated cloud − − − LCl (Exl , Enl , Hel− ) for the negative ideal alternative.

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2.5 Evaluation of the Integrated Cloud The distance between the integrated cloud of the candidate alternatives and the integrated cloud of the positive ideal alternative is:   2  2   1/2  + Hei − He+ 2 Di+ = (1/2) Exi − Exl+  + Eni − En+ l l

(11)

The distance between the integrated cloud of the candidate alternatives and the integrated cloud of the negative ideal alternative is:   2  2   1/2  + Hei − He− 2 Di− = (1/2) Exi − Exl−  + Eni − En− l l

(12)

The non-normalized score for the i-th (i = 1, 2, …, n) alternative is calculated as follows: Si =

Di−

Di+ + Di−

(13)

It is obvious that 0 ≤ S i ≤ 1, and the larger S i indicates that the research solution is farther away from the worst-case scenario.

3 Case Study 3.1 Original Values of Indicators Regarding the technology selection issue in the field of building electric heating, a selection is made for three technologies: air source heat pumps, electric boilers, and ground source heat pumps. The original values of indicator are shown in Table 2. 3.2 Decision-Making Process and Evaluation Results The raw matrix U ij is normalized to obtain the standardized indicator matrix V ij . The results is shown in Table 3. The positive ideal point S + and negative ideal point S − and the results are shown below. S + = [0.594, 0.591, 0.6, 0.204, 0.524, 0.686, 0.823, 0.683, 0.628, 0.628] S − = [0.561, 0.564, 0.552, 0.728, 0.647, 0.514, 0.347, 0.486, 0.528, 0.528] The common weighting methods including Analytic Hierarchy Process (AHP), Entropy weight Method, Coefficient of Variation Method are utilized to determine the weights of evaluation indicators for the electric heating configuration scheme. Then the weights information are combined based on Eqs. (2)–(5) to obtain the corresponding weight cloud model of evaluation indicators. The weight cloud results are shown below.

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Table 1. Evaluation indicator system for energy substitution technologies. Evaluation object

Primary indicator

Secondary indicator

Indicator attribute

Evaluation of applicability of electric energy substitution technologies

Technical features

Reliability U1

Qualitative

Work efficiency U2

Quantitative

Maturity U3

Qualitative

Initial investment and construction cost U4

Quantitative

Operating cost U5

Quantitative

Economic features

Environmental features

Difficulty of adoption

Service life U6

Quantitative

Carbon emission reduction U7

Quantitative

Reduction of harmful gas emissions U8

Quantitative

Government support U9

Quantitative

Promotional effort U10

Qualitative

Table 2. Original values of indicators for electric heating technology selection. Indicator types

U1

U2

U3

U4

U5

U6

U7

U8

U9

U10

Air source heat pump

82.5

85.3

82.3

17.5

1.7

20

23.2

275.3

79.1

69.2

Electric boiler

80.3

81.5

85.4

62.3

2.1

15

9.8

195.8

86.7

77.6

Ground source heat

85.1

83.3

78.5

56

1.8

15

12.7

220.1

72.9

71.3

The standardized indicator matrix, positive and negative ideal points, and weighted cloud of different indicators are combined to generate the integrated cloud of the candidate alternatives and the integrated cloud of the ideal alternative respectively. The calculation results are shown in Tables 5 and 6. The distance between the integrated cloud of the candidate alternatives and the integrated cloud of the ideal alternative are shown in Table 7, as well as the scores of the candidate solutions. According to the calculation results in Table 7, the air-source heat pump has the highest comprehensive evaluation value followed by the electric boiler and groundsource heat pump. It is concluded that the air-source heat pump has better suitability for electricity substitution application compared to the electric boiler and ground-source

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Indicator types

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

Air source heat pump

0.576

0.591

0.579

0.204

0.524

0.686

0.823

0.683

0.573

0.573

Electric boiler

0.561

0.564

0.600

0.728

0.647

0.514

0.347

0.486

0.628

0.628

Ground 0.594 source heat

0.577

0.552

0.654

0.554

0.514

0.450

0.546

0.528

0.528

Table 4. Weight cloud of different indicators. Indicators

Weight cloud

U1

(0.1153,0.0212,0.0028)

U2

(0.0878,0.0198,0.0048)

U3

(0.0953,0.0256,0.0032)

U4

(0.0819,0.0329,0.0046)

U5

(0.0968,0.0206,0.0029)

U6

(0.1107,0.0196,0.0034)

U7

(0.0978,0.0203,0.0048)

U8

(0.084,0.0394,0.0053)

U9

(0.1367,0.0378,0.0062)

U 10

(0.0943,0.0423,0.0059)

Table 5. The integrated cloud of the candidate alternatives. Solution

Weight cloud

U1

(5.8646,0.036,0.0035)

U2

(5.7007,0.0334,0.0033)

U3

(5.4744,0.0329,0.0032)

heat pump. The proposed method can provide some reference for the electric heating technology evaluation in electricity substitution application. To further validate the effectiveness of the proposed method, several commonly used methods were selected for comparison (Method 1: AHP-TOPSIS; Method 2: Entropy weight-TOPSIS; Method 3: the method proposed in this study). The ranking results are shown in Table 7.

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Table 6. The integrated cloud of the ideal alternatives. Indicators

Weight cloud

Positive ideal solution

(6.0333,0.0362,0.0033)

Negative ideal solution

(5.4238,0.0329,0.0032)

Table 7. Evaluation results of the candidate solutions. Solution

D+

D−

S

Solution 1

0.121957904

0.311735228

0.718792171

Solution 2

0.235579268

0.195845322

0.453950301

Solution 3

0.395025656

0.035832968

0.083166417

Table 8. Comparison results for the same case. Method 1

Method 2

Method 3

Solution 1

2

1

1

Solution 2

1

3

2

Solution 3

3

2

3

According to the ranking results in Table 8, there are notable differences in the results among the three methods. Except for Method 1, all the other algorithms rank Solution 1 as the optimal choice. The reason behind these differences can be attributed to the weighting method AHP used in Method 1, which introduces subjectivity for the evaluation. As for Method 2, the differences mainly arise in the rankings of Solutions 2 and 3. This is because the entropy weight method primarily considers the numerical values of the criteria while disregarding the inherent importance of each criterion. Consequently, it results in a “shortcoming effect” in the weighting results, which distorts the ranking outcomes. Overall, these variations highlight the limitations of certain weighting methods and emphasize the importance of a comprehensive and objective evaluation approach. The proposed method takes into account both the data relationships and the relative importance of the criteria, providing a more accurate and reliable ranking of the candidate solutions.

4 Conclusion This study examines the evaluation of electrical energy substitution technology. A set of indicators is selected from four aspects to form the indicator system for evaluating the electrical energy substitution technology. The improved TOPSIS method with the cloud theory is applied to conduct a comprehensive evaluation of the electrical energy substitution technology. The following conclusions can be drawn:

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(1) The evaluation indicator system and the improved TOPSIS method established in this study can simultaneously assess and rank multiple technology, which effectively improves the feasibility of the traditional TOPSIS model. (2) The adaptability of three electric heating technologies is evaluated and analyzed based on actual project measurement data and qualitative assessment data. The evaluation results indicate that air source heat pumps exhibit outstanding adaptability. Acknowledgments. This research was funded by the Science and Technology Project of State Grid Corporation of China under grant 5108-202218280A-2-392-XG (Research and Application of Key Technologies for Coordinated Planning of Multiple Electric Energy Substitution in County Areas under Carbon Peaking and Carbon Neutrality Goals).

References 1. Xiaoli, L., Wenbing, L., Haiming, Z.: Alternative energy in the energy network. Smart Grid. 3(12), 1192–1196 (2015). (in Chinese) 2. IEA. China energy system carbon neutrality roadmap. IEA, France (2021) 3. Niu, D., Song, Z., Xiao, X.: Electric power substitution for coal in China: Status quo and SWOT analysis. Renew. Sustain. Energy Rev. 70, 610–622 (2017). https://doi.org/10.1016/j. rser.2016.12.092 4. Dennis, K.: Environmentally beneficial electrification: electricity as the end-use option. Elect. J. 28(9), 100–112 (2015) 5. Javadi, F.S., Rismanchi, B., Sarraf, M., et al.: Global policy of rural electrification. Renew. Sustain. Energy Rev. 19(1), 402–416 (2013) 6. Xu, Z., Nthontho, M., Chowdhury, S.: Rural electrification implementation strategies through microgrid approach in South African context. Int. J. Electr. Power Energy Syst. 82, 452–465 (2016) 7. Yu, S., Qianggang, W., Chao, L., et al.: A planning method of on-load capacity regulating distribution transformers in urban distribution network after electric energy substitution. Trans. China Electrotechn. Soc. 37(6), 1572–1582 (2022). (in Chinese) 8. Xin, S., Yuyun, Z., Jingdong, X., et al.: Design of holistic clearing modes in power-heat spot market based on ‘Space Quotes’. Power Syst. Technol. 46(2), 4741–4750 (2022). (in Chinese) 9. Yi, S., Mo, S., Baoguo, S., et al.: Electric energy substitution potential analysis method based on particle swarm optimization support vector machine. Power Syst. Technol. 41(6), 1767–1771 (2017). (in Chinese) 10. Yanmei, L., Zeng, C.: Study on regional electric energy substitution potential evaluation based on TOPSIS method of optimized connection degree. Power Syst. Technol. 43(2), 687–693 (2019). (in Chinese) 11. Guanqiang, L., Tianwen, M.: Critical node identification of power networks based on TOPSIS and CRITIC methods. High Voltage Eng. 44(10), 3383–3390 (2018). (in Chinese) 12. Yanan, J., Yongjin, Y., Changyun, L.: Evaluation method of insulation paper deterioration status with mechanical-thermal synergy based on improved TOPSIS model. Trans. China Electrotechn. Soc. 37(6), 1572–1582 (2022). (in Chinese)

Reluctance Torque Optimization of Dual Rotor Permanent Magnet Reluctance Motor Reluctance Torque Xiaoguang Kong(B) , Yaowen Zhang, and Zhuo Yang Shenyang University of Chemical Technology, Shenyang, China [email protected]

Abstract. The permanent magnet-assisted synchronous reluctance motor combines the advantages of the permanent magnet-synchronous application prospects of motors. This article designs a double-rotor permanent magnet reluctance motor, and the two-dimensional finite element model of the motor is established by using the RMxprt module. Conduct sensitivity analysis on the key parameters affecting the torque of synchronous reluctance motors, determine the optimization variables, stratify the variables, establish the kriging response surface model of the average torque and torque ripple, and use the genetic evolution optimization algorithm to obtain the optimal solution set. Finally, the feasibility of the optimization method is verified by simulation, and the results show that the performance of the optimized motor has been improved and the optimization goal has been achieved. Keywords: dual-rotor motor · sensitivity analysis · response surface model · genetic algorithm

1 Introduction With the rapid development of integrated circuit technology, electronic components, and microcomputer technology, the permanent magnet motor has ushered in its era by virtue of its advantages of high power, high efficiency, small size, and low energy consumption [1–3]. As early as the 1990s, Toyota Motor Corporation had designed and manufactured plug-in permanent magnet synchronous motors and used them successfully in automobiles. However, due to the low-speed performance and high manufacturing costs of permanent magnet synchronous motors, their large-scale application and promotion are still big problems [4]. The synchronous reluctance motor has a simple structure, and the synchronous torque is generated by using the unequal air gap reluctance of the direct axis and the quadrature axis on the rotor. Compared with the permanent magnet synchronous motor, it does not have to consider the field weakening effect, no permanent magnet is required, and the manufacturing cost is low [5], which is a strong competitor to the permanent magnet synchronous motor. However, synchronous reluctance motors have disadvantages such as low torque density and low power factor, which also limit the application range of synchronous reluctance motors [6]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 111–118, 2024. https://doi.org/10.1007/978-981-97-0865-9_13

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This paper proposes a dual-rotor permanent magnet reluctance motor (PM-SynRM). The motor rotor consists of a surface-mounted permanent magnet outer rotor and a synchronous reluctance inner rotor. The motor makes full use of the internal space to combine the reluctance torque and permanent magnet resistance. The magnetic torque is organically combined to achieve the purpose of increasing the output torque. This paper takes improving the average torque and reducing torque ripple as the optimization goals and conducts parameter sensitivity analysis on the initial electromagnetic parameters based on the Spearman correlation coefficient. Based on the sensitivity analysis results, the parameters are appropriately selected, and a response surface model is constructed. Using Gram The Liggin response surface model establishes the relationship between key parameters and optimization objectives and corrects the model’s accuracy. Finally, the optimal solution to the structural size of the synchronous reluctance rotor was obtained through a genetic algorithm, and the effectiveness of this optimization scheme was verified in the finite element software.

2 Preliminary Design of The Motor 2.1 Topology Figure 1 is a two-dimensional model of a dual-rotor permanent magnet reluctance motor, and the main structural parameters are shown in Table 1. A dual-rotor motor combines a synchronous reluctance rotor and a permanent magnet rotor into a single entity. The interior is a multi-flux barrier synchronous reluctance rotor, and the exterior is a permanent magnet rotor with surface-mounted permanent magnets. Permanent magnets made of samarium cobalt are used in the rotor to avoid excitation loss. An important feature of this dual-rotor motor is to separate the design of the synchronous reluctance rotor and the permanent magnet rotor so that the reluctance torque and permanent magnet torque components can be controlled more flexibly. Depending on the relative orientation of the dual rotors, the stator windings can be designed with ring or distributed winding structures [7]. In addition, in order to make the two stators magnetically insulated, an aluminum magnetic insulator is installed in the middle of the stator yoke, which plays the role of magnetic isolation.

3 Optimization of Motor Structure Parameter 3.1 Optimization Goals and Processes The reluctance torque of the synchronous reluctance motor depends on the difference between the d-axis inductance and the q-axis inductance. In the design of the synchronous reluctance motor, ensuring the maximum dq-axis inductance difference is the primary task of the design. In order to maximize the d-axis inductance, the magnetic barrier should increase in width, but this will lead to an increase in the q-axis inductance, which cannot be avoided. The geometric parameters of the magnetic barrier have the greatest influence on the performance of the synchronous reluctance motor, so it is particularly important to determine the relevant geometric parameters of the magnetic barrier in the finite element analysis. For the synchronous reluctance motor, the optimization goal is the maximum output torque and the minimum torque fluctuation.

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Table 1. Main parameters of the motor Parameter

Value SynRM unit

PMSM unit

Rotor poles

6

6

Number of stator slots

36

36

Stator radius/mm

48.65

63.95

Rotor outer radius/mm

36

74.65

Rotor inner radius/mm

12

66.65

Air gap length/mm

0.35

0.5

Core length/mm

70

70

Fig. 1. 2D model of the motor

3.2 Sensitivity Analysis of Optimized Parameters Sensitivity analysis is an analytical method to test the correlation between variables. Parameter sensitivity analysis can intuitively express the degree of influence of different parameters on the output objective function. According to the sensitivity analysis results, an appropriate choice of parameters can reduce the amount of calculation and simplify the complexity of the objective function degree. As shown in Fig. 3, this paper selects five key structural size parameters of the internal magnetic barrier rotor of the motor as the initial optimization parameters, and the initial values and optimization ranges of the parameters are given in Table 2. Figure 2 shows the optimized parameters of the reluctance motor, and Fig. 3 shows the sensitivity analysis results of each parameter to the reluctance torque and torque ripple. It can be seen that the height of the magnetic bridge H0 , the thickness of the bottom magnetic barrier B0 and the thickness of the bottom magnetic layer Y0 have a great influence on the output torque. The radius Rb of the bottom of the magnetic barrier, the thickness of the bottom magnetic barrier B0 and the thickness of the bottom magnetic layer Y0 have a significant impact on the torque ripple. Therefore, considering the above,

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Structural parameters

Initial value

Bridge height H0 /mm Magnetic barrier bottom radius Rb /mm

Variation range

0.42

0.35–0.5

14.26

12.5–16.5

Bottom magnetic barrier thickness B0 /mm

3.1

3–4.2

Bottom magnetic layer thickness Y0 /mm

3.21

2–3.5

Magnetic barrier chamfer radius R1 /mm

0.9

0–1

Fig. 2. Parametric model of the inner rotor

the other four parameters, except the magnetic barrier chamfer radius R1 are selected as optimization parameters to construct the response surface model. 3.3 Building a Response Surface Model The response surface model has been widely used in the field of motor optimization design due to its potential to improve the optimization environment and improve design efficiency [8]. Among them, the Kriging model is an easy-to-construct adaptive optimization strategy that can guide the optimization process to converge quickly. Figure 4 shows the response surface model composed of each parameter and output torque. According to the response surface model of different parameters, the effect of different parameters on the output torque and torque ripple can be obtained. According to Table 3, it can be concluded that in order to obtain a larger output torque and a smaller torque ripple, a higher output torque should be selected. Small ones, as well as larger ones. As can be seen from Fig. 5, the values of each parameter are: the height of the magnetic bridge H0 is 0.35 mm, the thickness of the bottom magnetic barrier B0 is 3.99 mm, the radius of the bottom of the magnetic barrier Rb is 13.2 mm, and the

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Fig. 3. Sensitivity analysis results for optimized parameters

thickness of the bottom magnetic layer Y0 is 2.02 mm. There is not much difference compared with the response surface model result analysis Table 3. 3.4 Intelligent Algorithm Optimization Verification After the optimization is completed, the finite element software is used to analyze the results before and after optimization. Figure 6 shows the waveform comparison results before and after optimization. The comparison before and after shows that the average output torque of the motor after optimization increases from 4.15 N.m to 4.35 N.m, average torque increased by 5%; the torque ripple drops from 7.3% to 4.5%, a decrease of about 38.3%, and the waveform of the output torque is optimized, the final effect is better, and the effectiveness of the optimized design is verified by finite element simulation, and the quality of the motor output torque is improved.

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Fig. 4. Response of output torque with different parameters

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Table 3. Correlation of different parameters with torque and torque ripple

Fig. 5. 2D Pareto Chart

Output Torque/(N.m)

Optimized output torque/(N.m) 5

Output torque before optimization/(N.m)

4.5 4 3.5 0

2

4

Time/(ms)

6

8

10

Fig. 6. Optimize before and after waveform contrast

4 Conclusion This paper performs an optimization analysis on a new permanent magnet reluctance motor with a complex dual-rotor structure. For the inner rotor synchronous reluctance motor, a new multi-objective optimization idea is introduced. The response surface model

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is constructed by screening parameter sensitivity analysis, and finally, the optimal solution set is obtained based on the response surface model. This method is more direct. The calculation time and calculation cost of the solution are greatly reduced, and the solution efficiency is greatly improved. It is especially suitable for the design of multi-parameter and multi-objective optimization solution schemes and has reference significance for the optimization design of such schemes. Finally, the electromagnetic performance after the optimized design is evaluated and compared with the initial design. The output torque after the optimized design is significantly improved, and the torque ripple is also significantly reduced, which verifies the feasibility of the above-mentioned method. Acknowledgments. This research is supported by National Natural Science Foundation of China (51877139) and Basic Research Project of Liaoning Provincial Department of Education (LJKMZ20220778).

References 1. Nguyen, T., Lee, J.-Y., Lee, J.-H.: High power density axial-flux permanent magnet motor for electric bike application. IEEE Access 11, 61621–61629 (2023). https://doi.org/10.1109/ACC ESS.2023.3281744 2. Soomro, A.H.: Design and analysis of interior permanent magnet motor for hybrid electric vehicles. Int. J. Electric. Eng. Emerg. Technol. 6(1), 44–52 (2023) 3. Quan, L., Yu, X., Fan, D., et al.: High-efficiency region analysis and broadening design of permanent magnet motor based on variable magnetic field effect. (in Chinese) 4. Petrelli, G., Nuzzo, S., Zou, T., et al.: Review and future developments of wound field synchronous motors in automotive. In: 2023 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), pp. 1–6. IEEE (2023) 5. Mahamat, A.L., Gözüaçık, E., Akar, M.: Sensitivity-based design and optimization of line start synchronous reluctance motor. Electric Power Comp. Syst. 51(20), 2499–2511 (2023). https:// doi.org/10.1080/15325008.2023.2215773 6. Jamali-Fard, A., Mirsalim, M.: Design and prototyping of a novel line-start permanent magnet assisted synchronous reluctance motor for fan application. IEEE Trans. Energy Conv. 1–9 (2024). https://doi.org/10.1109/TEC.2023.3308508 7. Wang, Y., Zhu, T., Geng, W., et al.: Cooling system analysis of an enclosed yokeless stator for high-power axial flux PM motor with distributed winding. IEEE Trans. Industr. Electron. 99, 1–10 (2023) 8. Shigematsu, H., Wakao, S., Murata, N., et al.: Multi-objective topology optimization of synchronous reluctance motor using response surface approximation derived by deep learning. IEEJ Trans. Electr. Electron. Eng. 18(1), 120–128 (2023)

Research on Temperature Characteristics Based on Optical Magnetic Field Sensors Yiming Xie1 , Qifan Li2(B) , Yi Zhao2 , Tao Wen2 , Xingwang Wu1 , Haitao Yang1 , Jie Wu1 , and Xiaoyu Hu1 1 State Grid Anhui Electric Power Co, Ltd. Electric Power Research Institute, Hefei 230022,

China 2 School of Electrical Engineering and Automation, Hefei University of Technology,

Hefei 230009, China [email protected]

Abstract. Optical magnetic field sensors have the advantages of small size, light weight, good insulation properties, and high stability. They have a wide range of applications in the field of magnetic field detection, especially in the internal magnetic field detection of transformers. During long-term operation, the temperature inside the transformer will rise, causing drift in the static operating point, which affects the measurement accuracy. In order to study the interference of temperature changes on magnetic field measurement, this paper analyzes the mechanism of temperature affecting the static operating point and the optical rotation coefficient based on the model of light reflection and refraction in crystals established by the team. Finally, a method using a broad-spectrum light source to suppress interference caused by temperature fluctuations is proposed. Keywords: The Faraday effect · magnetic field sensor · temperature · White light interference

1 Introduction As the most important equipment in the power system, transformers play a crucial role in transmission and distribution, and their operational status is closely related to the stability of the entire power system. When the transformer is short-circuited, the short-circuit current amplitude of the winding increases sharply, and the generated electromagnetic force may cause the axial or radial distortion of the winding structure, which will further aggravate the internal fault of the transformer, make the transformer turn-to-turn discharge, insulation failure, etc., and then endanger the safety of the entire power system [1–3]. The optical magnetic field sensor based on the Faraday effect utilizes the deflection of polarized light in a magneto-optical crystal under the influence of a magnetic field to measure the magnetic field. Compared to traditional magnetic field sensors, optical magnetic field sensors have excellent insulation performance, a wider frequency response © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 119–126, 2024. https://doi.org/10.1007/978-981-97-0865-9_14

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range, and a small size that is easy to install. These characteristics give optical sensors a unique advantage in measuring the internal magnetic field of transformers. Because the application scenarios have high requirements for the accuracy of magnetic field measurement, reducing the error of optical magnetic field sensors has become an important research direction. During the long-term operation of the transformer, the high temperature may affect the accuracy of the measurement. In recent years, many scholars have conducted research on the influence of temperature on optical magnetic field sensors, mainly focusing on the effect and compensation of temperature on the Verdet constant of paramagnetic materials. Reference [4] pointed out that the natural drift of the Verdet constant and the phenomenon of birefringence in the medium are inherent temperature dependencies of crystals. Reference [5] indicated that the Verdet constant of different materials varies with temperature in different patterns. Terbium glass is a typical paramagnetic material, and its Verdet constant decreases with increasing temperature, while quartz glass, as a diamagnetic material, has an increasing Verdet constant with temperature. Reference [6] proposed a method of using a permanent magnet as a reference and adaptive compensation for temperature drift of the sensing material, simultaneously compensating for the influence of both the Verdet constant and linear birefringence due to temperature. However, the Verdet constant and linear birefringence are only two factors affected by temperature, and the variation of the static operating point with temperature is also an important factor affecting the response characteristics of the sensor [7]. Based on the temperature dependency model of the optical magnetic field sensor proposed by our team, this paper analyzes the mechanism of temperature influence on the refraction and reflection process of light, elucidates the impact of light interference on the static operating point, and proposes a solution that uses a broad-spectrum light source as the input for the light source. The role of a broad-spectrum light source in improving the temperature performance of the sensor is analyzed.

2 Theoretical Analysis The Faraday effect refers to the phenomenon that the polarization angle of light is rotated when it passes through a magneto-optical crystal in a magnetic field, and the rotation angle is linearly related to the magnetic field component along the direction of light propagation. The principle of an optical magnetic field sensor is shown in Fig. 1. Under ideal conditions, the Faraday rotation angle can be expressed as: θ = BLV

(1)

In the equation, B represents the magnetic induction intensity in the crystal, L represents the path of light in the crystal, and V represents the Verdet constant of the crystal. After passing through the polarizer and becoming linearly polarized light, the light enters the crystal from one side, undergoes rotation inside the crystal, and then exits from the other side. It passes through the analyzer and is finally converted into an electrical signal by the detector. In this process, due to the smooth surfaces of the crystal, there may be partial light reflection on the inner walls of the incident and exit surfaces. Each

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Fig. 1. Schematic diagram of an optical magnetic field sensor.

time the light passes through the crystal, the phase of the light changes, and the phase difference between the two beams of light may lead to an increase or decrease in the intensity of the interfered light. As shown in Fig. 2, when the phase difference is π/3, the intensity of the interfered light is greater than the intensity of the light without reflection, while when the phase difference is 2π/3, the intensity of the interfered light is smaller than the intensity of the light without reflection.

Fig. 2. Light with different phases interferes

Due to the non-reciprocal nature of the Faraday effect, the polarized light undergoes a rotation of angle θ after passing through the crystal, and after the second reflection, the polarized light undergoes a rotation of angle 3θ. Taking into account these two factors, the intensity and rotation angle of the interfered light can actually fluctuate with the change in phase difference. However, the Verdet constant can only represent the inherent optical rotation ability of the material [7] and cannot fully express the influence of temperature. The rotation coefficient R = θ/BL is defined as the optical rotation ability per unit length of the magneto-optical crystal in the sensor. When the temperature changes, the temperature characteristics of the Verdet constant and the variation of the static operating point can all be characterized by the rotation coefficient R [8].

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The literature [8] shows that the outgoing light intensity after interference can be expressed as: I =

4n1 n2 (n1 + n2 )

2

· [1 −



1 n1 −n2 n1 +n2

2

ei2ϕ ]

2

· I1

(2)

The Faraday rotation angle can be expressed as:

θ =

1+ 1−

 

n1 −n2 n1 +n2 n1 −n2 n1 +n2

2 2

ei2ϕ

·θ

(3)

ei2ϕ

where n1 is the refractive index of the crystal, n2 is the refractive index of air, I1 is the intensity of the incident light, and ϕ is the phase difference generated by passing through a crystal. As can be seen in Eqs. (2) and (3), the phase difference and refractive index are direct factors affecting the light intensity and rotation angle. According to Eqs. (1) and (3) and the definition of the optical rotation coefficient [8], the optical rotation coefficient can be found as:    2   i2ϕ 2   1 + nn1 −n e 1 +n2   (4) R= ·V 2    n1 −n2  1 − n1 +n2 ei2ϕ  A static operating point can be represented as: 1 A=  2 · A0  2   1 − n1 −n2 ei2ϕ    n1 +n2

(5)

From Eqs. (4) and (5), it can be seen that both the static operating point and the rotation coefficient are related to the phase difference. When the temperature changes, the variation in optical path length can be expressed as: δ = Ln + nL

(6)

From Eq. (6), it is evident that the phase variation is influenced by two factors. The Ln term represents the phase variation caused by the refractive index change due to the thermal-optic effect, while the nL term represents the phase variation caused by the volume change of the crystal due to thermal expansion [9]. The phase difference and the change in refractive index result in interference of the reflected light, leading to the phenomenon of output fluctuation with temperature. As shown in Fig. 3, temperature variation has different effects on crystals of different lengths. This is mainly because, as the length of the crystal increases, the thermal expansion also increases, resulting in a shorter temperature period for the fluctuations.

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Fig. 3. The static operating point of crystals of different lengths changes under the influence of temperature

3 Broad-Spectrum Light Sources Suppress Fluctuations In order to suppress the output fluctuation caused by temperature, magneto-optical materials with smaller thermo-optical coefficient and thermal expansion coefficient can be selected to improve the temperature characteristics of the sensor. In addition, a light source with a wide spectrum can be used as an input to reduce the influence of light interference, thereby suppressing the influence of temperature. The interference result of monochromatic light is only related to its optical path, and the resolution of a broad-spectrum light source also depends on the bandwidth of the light source. In the system of broad-spectrum light interference, on the one hand, the various wavelengths of light of the broad-spectrum light source themselves will interfere with each other to form different interference fringes; On the other hand, interference light of different wavelengths is superimposed, which ultimately affects the interference light intensity [10, 11]. The same interference simulation was performed with monochromatic light with a wavelength of 550 nm and white light with a wavelength range of 400 nm to 700 nm (uniform distribution of light at different wavelengths), and the results of Fig. 4 were obtained.

Fig. 4. Displacement response under excitation at fixed intervals.

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As shown in Fig. 4, when the phase difference is zero, the stripes of each wavelength coincide completely, and this time strength is the greatest; As the phase difference increases, the interference fringes of different wavelengths are gradually staggered, which will reduce the overall visibility of the interference fringes [12]. Interference fringes can be observed only when the optical path difference between the two light waves produced by a broad-spectrum light source is extremely small, and once this range of optical path difference is exceeded, the interference light intensity will decrease sharply. Suppose a broad-spectrum light source has a wavelength range of 1000 nm to 1130 nm, a central wavelength of 1064 nm, and the light intensity of different wavelengths obeys the Gaussian distribution [13], and 12 different wavelengths of light are selected for interference.

Fig. 5. Broad-spectrum light source interference result plot

As shown in Fig. 5, 12 beams of light of different wavelengths were selected from 1000 nm to 1130 nm wavelengths to interfere. When the optical path difference is 0, the light intensity reaches the maximum value; When the optical path difference gradually increases, the peak value of the relative light intensity decreases. When the optical path difference reaches 16 μm, the relative light intensity has been attenuated to less than 1 and continues to decrease. Therefore, it can be concluded that interference intensity can only be observed near the points of equal optical path length when using a continuous spectrum source [12]. Inside the magneto-optical crystal, when the reflected light and the unreflected emergent light interfere, the optical path difference reaches at least twice the crystal length (millimeter level). At this time, the optical path difference of the two beams is much larger than the optical path difference range of the observed interference light. Therefore, it can be considered that when the continuous spectrum is used as the light source, the interference light intensity is very small, and the influence on the static working point and the optical rotation coefficient of the sensor can be neglected. In conclusion, a wide-spectrum SLD (Superluminescent Diode) light source can be chosen as the input. When the light is reflected by the crystal and interferes with the original light, the interference phenomenon is almost eliminated, thus eliminating the fluctuations caused by the phase difference changes due to temperature.

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4 Conclusions In this paper, through theoretical analysis and calculation, the influence of temperature on magneto-optical sensing process is explored, and a method to suppress temperature fluctuation is proposed. The main conclusions are as follows: (1) Temperature will affect the measurement results from many angles, in addition to changing the Verdet constant and linear birefringence, it will also affect the crystal length and refractive index to change the phase difference of the reflected light, causing fluctuations in the output light intensity. (2) The interference of broad-spectrum light sources is more complex than singlewavelength light, not only the optical path difference will affect the interference results, but also the interaction between different wavelengths of light will also change the state of light intensity. With the increase of optical path difference, the interference light intensity of broad-spectrum light sources decreases rapidly. In the application scenario of the sensor, the optical path difference is much larger than the range of interference light that can be observed by interference light, and the output light intensity can completely ignore the influence of interference light, thereby suppressing the fluctuation of light intensity and rotation angle and improving the temperature characteristics of the sensor. Acknowledgments. This work was funded by the Science and Technology Projects of State Grid Corporation of China (SGAHDK00SPJS2310258).

References 1. Wang, D., Zhan, Z.Y., Wang, W., et al.: Review on vibration and noise of converter transformer. Adv. Technol. Electric. Eng. Energy 41(11), 28–42 (2022). (in Chinese) 2. Li, T.R., Gao, S.G., Sun, L., et al.: Analysis on the simulation calculation of multiple short circuits of transformers considering cumulative effect. Hebei Electric Power 41(03), 73– 77+87 (2022). (in Chinese) 3. Jin, M.K., Guo, P.H., Chen, W.J., et al.: Two-way magnetic-structural coupling effect on vibration process of power transformer windings. High Voltage Eng. 1–9 (2023). (in Chinese) 4. Willsch, M., Richter, M., Kaiser, J., et al.: Compensation methods of the temperature dependence of glass ring type optical current sensors. European Workshop on Optical Fibre Sensors (2019) 5. Di, N., Zhao, J.L., Wei, D.L., et al.: Temperature characteristics and compensation studies of Feld’s constant for terbium glass and quartz glass. In: Proceedings of the 2006 Academic Conference of the Optical Society of China (2006). (in Chinese) 6. Chen, J., Li, H., Zhang, M., et al.: New compensation scheme of magneto-optical current sensor for temperature stability improvement. Metrol. Measur. Syst. XIX(3) (2012) 7. Madden, W., Michie, C.W., Cruden, A., et al.: Temperature compensation for optical current sensors. Opt. Eng. 38(10) (1999) 8. Li, J.X., Wen, T., Xing, F., et al.: Research on the influence of temperature on the sensing function of Faraday effect optical magnetic field sensor. Meas. Sci. Technol. 33(9), 169–178 (2022)

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9. Chen, S.S., Hu, J.X., Li, Z., et al.: Temperature response characteristics analysis and experimental study of optical voltage sensor. J. Electron. Measure. Instrument. 37(03) (2023). (in Chinese) 10. Yuan, L.B., Yang, J.: Principle and Application of Optical Fiber White Light Interference, pp. 23–38. Science Press, Beijing (2016). (in Chinese) 11. Ou, P.: Advanced Optical Simulation, pp. 40–46. Beihang University Press, Beijing, (2019). (in Chinese) 12. Chen, Y.P.: Discussion on the light source performance of OCT in white spectrum domain. China-Arab States Sci. Technol. Forum 27(05), 108–111 (2021). (in Chinese) 13. Chen, Y., Zhang, Y.Q., Chen, Q.: Coherence characteristic analysis of broad-spectrum light source for fiber optic gyroscope. Semiconduct. Optoelectron. 33(02), 175–178 (2012). (in Chinese)

Active Distribution Network Optimal Dispatch Model Considering Day-Ahead-Intraday Scale Demand Side Response Changbin Hu1 , Zhicheng Yang1(B) , Shanna Luo1 , and Yu He2 1 North China University of Technology, Beijing, China

[email protected], [email protected]

2 China National Building Material Group Co., Ltd., Beijing, China

[email protected]

Abstract. For the power quality problems caused by the large-scale access of distributed renewable energy to the distribution network, considering the fluctuation and uncertainty of distributed generator (DG) output and the characteristics of different response time scales of different load types, a method using optimal dispatch model for active distribution network (ADN) with demand-side response on day-ahead-intraday scale. Firstly, the loads are classified and the curtailable and shifting loads are modeled and analyzed from the perspective of user side and distribution network side simultaneously. Secondly, a day-ahead-intraday optimal dispatch framework based on MPC (Model Prediction Control) is proposed, and the role and relevance of the day-ahead and intraday parts are explained respectively. Then it analyzes the day-ahead and intraday goals and constraints respectively and elaborates its control process. Finally, the improved IEEE-33 node model is used to verify and analyze the model, and it is verified that the proposed model can precisely analyze and effectively optimize the power quality of the distribution network and improve the economy of the grid side. Keywords: Demand Response · Optimal Dispatch · Day-ahead-intraday Scale

1 Introduction With the popularization of ADN, DG such as wind turbines (WT) and photovoltaics (PV) continue to replace traditional coal-fired methods and become the main energy source in the power system [1, 2]. The optimal dispatching of ADN under the traditional mode is mostly considered from the source side and the optimization potential of the load has not been tapped. With the continuous development and improvement of flexible loads and demand side management technology, the user’s demand side has gradually become an adjustable and controllable resource form [3]. The power grid considers adding demand response (Demand Response, DR) [4]. At present, many scholars have conducted research on demand side response. Ref. [5] considered the uncertainty and volatility of WT output, proposed a price-based demand response and dealt with the uncertainty of the model through fuzzy theory. Ref. [6] further © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 127–136, 2024. https://doi.org/10.1007/978-981-97-0865-9_15

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analyzed user behavior and proposed incentive demand response. The paper introduced its characteristics and dispatched randomly. Ref. [7] considered two measures to participate in DR and verified the effect of DR on power system reliability improvement. Ref. [8] considered the characteristics of integrated energy and proposed the demand response of integrated energy. Ref. [9] mentioned the cuttable and transferable types of demand-side loads within the integrated energy system. On the basis of the above research, this paper takes advantage of the characteristics of large differences in the response time scales of different loads on the demand side, uses the control mode of day-ahead-intraday optimization, and analyzes from the side of users and distribution network simultaneously. First, according to the 1-h-scale day-ahead forecast output, use the long-term-response scale flexible load aiming at the optimal economy of the power grid side, and plan the output of the DR. Secondly, according to the 15-min-intraday scale forecast output, use the short-time-response scale flexible load to correct their output, minimizing the fluctuation and making day-ahead results more precisely. Finally, through the analysis of the calculation example in this paper, the power quality and its changes before and after are quantitatively analyzed and the validity of the model and scheme is verified.

2 Load Demand Response Model The loads under the ADN are generally divided into three categories: important loads, curtailable loads and transferable loads. The important loads are major guarantee for normal daily life. Once they are interrupted, they may cause major economic losses so that they should not be adjusted. Incentive-based DR usually signs incentive-response contracts with users according to their characteristics. For curtailable load and transferable load, there are load curtailment (LC) and load shifting (LS) contract respectively. 2.1 Curtailable Loads and LC Contracts The curtailable loads are mainly with short-term power outage tolerance and certain cold/heat storage capacity. These loads can cut their output within a certain period of time and reduce the peak load of the system to ensure the stability of the system. The LC contract includes the load reduction duration range, unit compensation price, start-up price and time limit of reduction. During the time period stipulated in the LC contract, the user reduces the usage. For any i-th LC load, the compensation at time t is shown as follows: LC LC LC LC0 LC = (ca,t Pi,t + Ci,t )xi,t Ci,t

LC xi,t

(1)

LC is total LC compensation; cLC is the compensation unit price; In the formula: Ci,t a,t LC is the reduced power and C LC0 is the fixed compensation. is the response status; Pi,t i,t For any i-th LC load, the constraints are shown as follows:  LC LC LC LC − ti,1 < Di,max Di,min < ti,2 (2) LC LC LC LC xiLC Pi,x ≤ Pi,max ,ti,1 < xiLC < ti,2

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LC , DLC In the formula: Di,min i,max are the minimum and maximum duration of LC LC response; tLC i,1, tLC i,2 are the start and stop time of LC response; Pi,max is the maximum LC power.

2.2 Transferable Loads and LS Contracts Transferable loads are mainly some equipment with flexible power consumption periods. By adjusting their output periods, it can play the role of peak shaving and valley filling to ensure the stability of the system. The LS contract includes the load transfer duration range, unit compensation price, start-up price and transfer time constraints. During the time period stipulated in the LS user, the user changes the usage habits and transfers the usage time. For any i-th LS load, the compensation at time t is shown as follows: LS LS LS LS0 LS1 = (ca,t Pi,t + Ci,t )xi,t Ci,t

(3)

LS is total LS compensation; cLS is the compensation unit price; In the formula: Ci,t a,t LS1 is the transfer response status and C LS0 is the fixed compensation. xi,t i,t For any i-th LS load, the constraints are shown as follows: ⎧ LS LS1 LS1 LS Di,min < ti,2 − ti,1 < Di,max ⎪ ⎪ ⎪ ⎪ ⎨ t LS2 − t LS2 = t LS1 − t LS1 i,2 i,1 i,2 i,1 (4) LS2 LS2 LS1 LS1 ⎪ (t − t )(t − t ) > 0 ⎪ i,2 i,1 i,2 i,1 ⎪ ⎪ ⎩ LS LS LS LS2 LS2 xi Pi,x < Pi,max ,ti,1 < xiLS < ti,2 LS , DLS LS1 In the formula: Di,min i,max are the minimum and maximum LS duration; ti,1 , LS1 LS2 are the start and end LS transferred-out states and ti,1 , ti,2 are the corresponding LS transfer-in states; Pi,max is the maximum LS power.

LS1 ti,2

3 MPC-Based Day-Ahead-Intraday Optimal Dispatch Model The optimal dispatch process is shown in Fig. 1:

Fig. 1. Schematic diagram of day-ahead-intraday complementary optimization

The optimal dispatch model adopts the MPC control method. Due to the uncertainty of DG output and load, there are errors between the forecast and actual results. The time scale is gradually shortened by means of day-ahead-intraday complementarity.

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3.1 Day-Ahead Optimal Dispatch Phase The day-ahead optimal dispatch needs to predict the 24 h data output of DGs and load in advance, and its data scale is 1 h. Many loads take a long time to control due to their complicated operation process. This type of load can only be scheduled in his phase so it has a higher priority. In this phase, through optimal dispatch of DR and energy storage systems (ESS), the stability and economy of the ADN is guaranteed and optimized. 3.2 Intraday Optimal Dispatch Phase Due to the large time scale (1 h) of day-ahead forecasting, its accuracy is not enough to meet the actual situation. Intraday optimal dispatch predicts 15-min-scale output of the DGs and loads in the next 3 h. Many loads require a short control time due to their simple operation process. This type of load is the main control part of the intraday optimal dispatch phase. In this phase, by adjusting the dispatch output, the fluctuation in the next 3 h is minimized, making the day-ahead optimal dispatch more precisely.

4 Day-Ahead-Intraday Complementary Optimal Dispatch Model 4.1 Day-Ahead Optimal Dispatch Model The day-ahead optimal dispatch phase is carried out with the LC and LS loads and ESSs through 1-h-scale 24 h-output of the DGs and loads in day-ahead. Objective Function. The goal is to maximize the profit of the ADN in the day-ahead optimal dispatch period, and its expression is shown as follows: max C = −CD + CG − CF

(5)

In the formula: C is the revenue of the ADN; C D is the DR response cost; C G is the electricity sale income of the power grid; C F is the power quality cost. USER Response Cost. The cost is shown as follows: ⎧ LC LS ⎪ ⎪ CD = CD + CD ⎪ ⎪ ⎪ ILC 24  ⎪  ⎪ ⎪ LC LC LC0 LC ⎨ CDLC = (ca,t Pi,t + Ci,t )xi,t t=1 i=1 ⎪ ⎪ ⎪ ILS 24  ⎪  ⎪ ⎪ LS LS LS LS0 LS1 LS1 ⎪ (ca,t Pi,t + Ci,t + Ci,t )xi,t ⎪ ⎩ CD =

(6)

t=1 i=1

In the formula: CDLC and CDLS are the response costs of LC and LS user; I LC and I LS LS1 is the price difference compensation for the LS are the sum of LC and LS users; Ci,t user. Comparing formula (6) with formulas (1) and (3), it can be found that they are LS1 to formula (3). This is basically the same, the difference is that formula (6) adds Ci,t

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because when the LS users transfer the corresponding load, the electricity price may LS1 is shown as follows: change according to the transfer time. The expression of Ci,t  LS1 Ci,t

=

LS LS1 (cg,τ − cg,t )Pi,t , (cg,τ − cg,t )xi,t >0

0

,other

(7)

In the formula: cg,τ is the electricity price at time τ, where τ, is the transfer-out time corresponding to the i-th LS user at time t. Formula (7) shows that if the transfer-in electricity price cg,τ is not greater than the transfer-out price cg,t , the user will not cost more and the ADN does not need to compensate the price difference; otherwise the user LS1 is needed. will cost more and additional compensation Ci,t Electricity Sales Income of the Grid. At time t, the income is shown as follows: ⎧ LC LS1 LS2 P = P0,t − PD,t − PD,t + PD,t ⎪ ⎪ ⎨ g,t 24  ⎪ C = cg,t Pg,t ⎪ ⎩ G

(8)

t=1

In the formula: Pg,t is the power actually sold by the grid; P0,t is the power ready to LC is the power of the LC users; P LS1 , P LS2 are the power of the sell before dispatch; PD,t D,t D,t transferred-out and in power of LS users, respectively. The Cost of Power Quality. For the normal operation of the ADN, the power quality must be guaranteed. Perform power flow calculation and compare if all voltage offsets meet the requirements. CF is 0 if all nodes meet, else a penalty item will be set up. Taking the case of overvoltage as example, the penalty function is shown as follows: ⎧ ⎧ 0 , V ≤ Vmax ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ a1 (V − Vmax ) + b1 , Vmax < V ≤ Vmax 1 ⎪ ⎪ ⎪ ⎪ a2 (V − Vmax 1 ) + b2 , Vmax 1 < V ≤ Vmax 2 C = ⎪ F,i,t ⎪ ⎪ ⎨ ⎪ ⎪ a3 (V − Vmax 2 ) + b3 , Vmax 2 < V ≤ Vmax 3 ⎪ (9) ⎪ ⎪ ⎩ ⎪ ⎪ a (V − V ) + b , V > V ⎪ 4 max 3 4 max 3 ⎪ ⎪ ⎪ ⎪ 24  I ⎪  ⎪ ⎪ ⎪ C = CF,i,t ⎪ ⎩ F t=1 i=1

In the formula: C F,i,t is the power quality cost of the i-th node at time t; I is the total number of nodes; a1 –a4 , b1 –b4 represent penalty factors, which change with the increase of the violation degree. The undervoltage situation is the same as (9). Through optimal dispatch, the ultimate goal is to eliminate all offset so that C F is 0. Constraints User Response Constraints. The response constraints of LC and LS users have been mentioned in formulas (2) and (4), and will not be repeated here.

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The Constraints of ESS. At time t, for any i-th ESS, the constraints are as follows: ⎧ ESS ESS ESS Pi,min ≤ Pi,t ≤ Pi,min ⎪ ⎪ ⎪ ⎪ ESS ESS ESS ⎨ Ri,min ≤ Pi,t − Pi,t−1 ≤ RESS i,max (10) SOC SOC SOC ⎪ s ≤ s ≤ s ⎪ i,min i,t i,max ⎪ ⎪ ⎩ SOC SOC SOC λ1 si,t0 ≤ si,t0+T ≤ λ2 si,t0 max 1 ESS is the ESS output; P ESS and P ESS are the minimum and In the formula: Pi,t i,min i,max ESS are corresponding climbing output; sSOC is the maximum output and RESS and R i,min i,max i,t SOC , sSOC are the minimum and maximum SOC; t and T state of charge (SOC); si,min 0 max1 i,max indicate the first dispatch moment and the entire day-ahead dispatch cycle; λ1 and λ2 are factors slightly less and greater than 1, respectively.

4.2 Intraday Optimal Dispatch Model Intraday optimal dispatch phase predicts output of the DGs and loads at a 15-min scale in next 3h to modify the output of loads and continue rolling optimization. Predicting Model. Considering that the optimal dispatch is a non-linear and uncertain multi-input-and-output problem, the state space expression is used as a prediction model. For any u-th controllable unit, the expression is as follows: Pu (k + i|k) = Pu (k) +

i 

Pu (k + j|k)

(11)

j=1

In the formula: Pu (k + i|k) is the predicted time k + i output at time k; Pu (k) is the output at time k; Pu (k + j|k) is the predicted output increment in [k + j – 1,k + j] period at time k. Objective Function. The goal is to minimize the output fluctuation of the DR loads, and its expression is shown as follows: min F =

t+T +ILS  max 2 −1 ILC 

  D D Pj (k + i|k) − Pj,i )

(

i=t

(12)

j=1

In the formula: F is the total fluctuation; T max2 is the duration of the intraday dispatch D is the day-ahead forecast output at i-th moment. cycle; Pj,i Constraints. For each controllable unit, its output needs to satisfy the constraints of formula (2) and formula (4). In addition, the constraints need to be satisfied as follows: Rumin ≤ Pu (k + j|k) ≤ Rumax In the formula:

Rumin

and

Rumax

(13)

are the climbing output lower and upper limit.

Feedback Correction. Because there is a deviation in the output control sequence obtained by the actual and predictive control, the feedback correction link is introduced to correct the model output of the system with the actual measured value.

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5 Case Analysis 5.1 Case Introduction Take the improved IEEE-33 node ADN model as example. The topology of adding WT and PV, LC and LS loads including Commercial Load (CL), Industrial Load (IL) and Residential Load (RL) and ESS is shown in Fig. 2(a) and daily curves in Fig. 2(b).

(a)

23

1

24

(b)

25

2

3

4

5

19

20

21

22

26

27

28

29

30

31

32

33

6

7

8

9

10

11

12

13

14

15

16

17

18

Fig. 2. (a) Schematic diagram of improved IEEE-33 node topology (b) Daily curves

The load parameters are shown in Table 1. The ESS output ranges from –80 kW to 80 kW and the capacity is 800 kVA. The SOC should range from 20% to 80% and its initial SOC is 50%. The final SOC should range from 0.95 to 1.05 times of the initial SOC. Penalty factors a1 –a4 are 40000, 80000, 120000, 160000 and b1 –b4 are 1500, 3000, 4500, 6000 respectively. Response duration of all LC and LS loads is 1-3h and 2-5h. Table 1. Adjustable load specific parameters Node No.

7

8

11

13

14

16

24

25

32

Contract Type

LC LC LS

LS

LC LS LS

LS

LS

LS

Day-Ahead Maximum Output (kW)

56

52

9.9

14.4 34

Intraday Maximum Output (kW) 16

16

2.25 4.2

9

15 12

12

170 115.2 48.3

3

4.2 35

28.8

18.9

5.2 Day-Ahead Optimal Dispatch According to the data above, the day-ahead optimal dispatch is carried out without and with utilizing the resources on the demand side in Figs. 3 and 4, respectively. In Fig. 3(a, b), it can be seen that in the interval of 18–20 h of the peak power consumption, the ESS output reaches the peak value but the voltage of nodes 17–18 still exceeds the limit. In Fig. 4(a, b), it can be seen that after dispatching the demand side, its voltage has been significantly increased. The output of DR loads is shown in Fig. 5: Various economic indicators can be obtained as shown in Table 2. It can be seen that before and after the demand-side response, the cost is reduced by increasing the response cost to meet the stability constraints.

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(a)

(b)

t/h

t/h

Fig. 3. Schematic diagram before DR optimal dispatch (a) Voltage situation, (b) ESS output

(a )

(b)

t/h

t/h

Fig. 4. Schematic diagram after DR optimal dispatch (a) Voltage situation, (b) ESS output

1 2 3 4 5 6 7 8 9 10

t/h

Fig. 5. Day-ahead response output of demand response loads

Table 2. Comparison of economic indicators before and after dispatch of day-ahead DR Economic Type

DR Cost

Electricity Sales Income

Power Quality Cost

Total Income

Before DR

0

34689

11197

23492

After DR

7866

34562

0

26696

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5.3 Intraday Optimal Dispatch Considering there are differences in accuracy between the day-ahead and actual curve, the difference may cause the day-ahead dispatch result deviating from the ideal value. Therefore, it is necessary to adjust DR loads to make fluctuation smaller. It should be noted that since the usage has been changed according to day-ahead dispatch, it is not appropriate to interrupt the user not scheduled currently in day-ahead phase. The output of the current moment in the next 3 h is predicted with a time scale of 15 min. The minimum fluctuation within 3 h is the goal, and only the first output component is adjusted. Select typical CL and IL curves as a schematic diagram, as shown in Fig. 6, and the 24h total fluctuation is reduced from 10574 kW to 9754 kW:

(a)

(b)

t

t

Fig. 6. Comparison of fluctuations before and after intraday optimal dispatch (a) CL (b) IL

It can be seen the output fluctuation after intraday phase is significantly smaller than that before optimization, which is closer to the day-ahead optimal dispatch situation.

6 Conclusion This paper proposes an ADN optimization model that utilizes demand-side resources, formulates output plans and adjusts output through the day-ahead-intraday dual scale. Through the example analysis, the following conclusions can be drawn: Dispatch using demand-side resources can effectively promote peak shaving and valley filling so that voltage stability can be guaranteed. Meanwhile, the multi-time response scale characteristics of demand-side resources are fully utilized. Due to the adoption of the MPC, the optimization process includes rolling optimization and feedback correction. There is a link between actual and predicted output and the MPC can improve the control accuracy and form a closed-loop control. The model converts power quality problems into economic indicators and can quantitatively analyze the severity of voltage violations. For areas with severe violations, it can be used to evaluate the optimization effect and guide subsequent optimization. The day-ahead-intraday optimal dispatch model of ADN considering the DR proposed in this paper has achieved certain results. However, more in-depth research is needed for DR: for example, how to realize in-depth analysis of users’ behavior and perform more detailed classification [10]. Meanwhile, the rapid popularization of electric vehicles also brings new challenges to demand side response [11].

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Acknowledgements. This work is supported by National Key R&D Program of China (2021YFE0103800) and R&D Program of Beijing Municipal Education Commission (KM201710009002).

References 1. Lü, Z.L., Liao, P.S., Yang, X.: Bi-level optimization of photovoltaic microgrid group and active distribution network considering demand side response. J. Power Syst. Autom. 33(8), 70–78 (2021). (in Chinese) 2. Pan, B.R., Wang, H.C., Zhang, Y., et al.: Study on an active distribution network reconstruction strategy with distributed power supply. Power Syst. Protect. Control 48(15), 102–107 (2020). (in Chinese) 3. Zhu, Z., Xu, Y., Cen, H.F., et al.: Optimal configuration of park-level integrated energy system considering demand response. Smart Power 50(1), 37–44 (2022). (in Chinese) 4. Zhou, B.X., Zhang, G.J., Xu, J.H., et al.: Schedulable potential analysis as well as supply and demand coordination strategy for demand side load. Shandong Electric Power 48(1), 1–5 (2021). (in Chinese) 5. Luo, C.J., Li, Y.W., Xu, H.P., et al.: Influence of demand response uncertainty on day-ahead optimization dispatching. Autom. Electric Power Syst. 41(5), 22–29 (2017). (in Chinese) 6. Zhang, M.L., Hu, Z.J., Wang, X.F., et al.: Two-stage stochastic programming scheduling model based on dynamic scenario sets and demand response. Autom. Electric Power Syst. 41(11), 68–76 (2017). (in Chinese) 7. Lei, M., Wei, W.Q., Zeng, J.H., et al.: Effect of load control on power supply reliability considering demand response. Autom. Electric Power Syst. 42(10), 53–59 (2018). (in Chinese) 8. Muthirayan, D., Kalathil, D., Poolla, K., et al.: Mechanism design for demand response programs. IEEE Trans. Smart Grid 11(1), 61–73 (2019) 9. Anwar, M.B., O’Malley, M.: Strategic participation of residential thermal demand response in energy and capacity markets. IEEE Trans. Smart Grid 12(4), 3070–3085 (2021) 10. Liang, W., Zhang, D.F., Lei, X., et al.: Circuit copyright blockchain: blockchain-based homomorphic encryption for IP circuit protection. IEEE Trans. Emerg. Top. Comput. 9(3), 1410–1420 (2021) 11. Trujillo, D., Torres, E.M.G.: Demand response due to the penetration of electric vehicles in a microgrid through stochastic optimization. IEEE Latin America Trans. 20(4), 651–658 (2022). https://doi.org/10.1109/TLA.2022.9675471

Design of a Vibration Energy Harvester for Power Transformers Monitoring Li Zheng(B) , Wenbin Zheng, Jiekai Pan, and Qianyi Chai State Grid Wenzhou Power Supply Company, Wenzhou 325028, China [email protected]

Abstract. The fault monitoring of transformers is critical for the operation of power systems. However, the traditional wireless sensor networks (WSNs) node has a short battery life, making it difficult to maintain the power supply in harsh environments such as strong electromagnetic fields and vibration noise in transformers. A MEMS AlN piezoelectric beam was designed to harvest the vibration energy at the transformer vibration frequency of 50 Hz. The resonance frequency of vibration harvester system is usually higher than 50 Hz. To reduce the resonance frequency of the MEMS harvester, a folded beam was designed and optimized using the finite element method and theoretical calculation. The results of the two methods are basically consistent. The resonance frequency, output voltage and power were analyzed, and the results show that the structure can effectively reduce the resonance frequency to 50 Hz. Keywords: Vibration energy harvesting · MEMS devices · AlN film · Piezoelectric · folded beam

1 Introduction Recently, great effort has been devoted to the development of wireless sensor networks (WSNs) which are widely used for structural health monitoring. A critical problem is the limited battery lifetime, which results in frequent battery replacement or recharging. Battery-free micropower harvesting energy from the environment presents a promising solution for the problem. Vibration energy is ubiquitous such as human body, vehicle and power transformers. The vibration harvester generates electrical power using the principle of piezoelectric [1, 2], electromagnetic [3], electrostatic [4], triboelectric [5], flexoelectric [6], magnetostrictive [7], and reverse electrowetting [8] effects. Piezoelectric harvesters have drawn much attention due to the high conversion efficiency and simple structure. A piezoelectric vibration energy harvester (PVEH) can be seen as a mass-springdamper system, and generates maximum electric power when resonance occurs. The frequency bandwidth of the PVEH is very small, usually several Hz. While the frequency of vibration source is not a fixed value, and even is variant in a wide range. For this reason, a key problem is raised that the resonant frequency is not match with the vibration source. Several methods have been reported, such as extending the bandwidth by array © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 137–144, 2024. https://doi.org/10.1007/978-981-97-0865-9_16

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structure [9] and nonlinear technology [10], adjusting resonance frequency to match the source frequency [11]. However, for some specific applications, the vibration source has one or several relatively stable frequencies, at which the vibration energy density is relatively high. So, the resonance frequency of the PVEH can been designed to be near to the vibration source frequency. The 50 Hz power frequency is ubiquitous in industrial and civil affairs. Experimental results demonstrate that the main vibration frequency components of the transformer focus on 50 Hz [12]. Therefore, a simple linear vibration system with a resonance frequency of 50 Hz can be used to harvest the vibration energy, without special consideration of the frequency band. This paper presents a PVEH with 50 Hz resonance frequency for transformer monitoring. PVEH can be easily fabricated MEMS process based on silicon wafers. But the Young’s modulus of silicon (170 GPa) is so lager that the resonance frequency of PVEH is high to several hundred Hz. Decreasing the thickness of the cantilever beam or increasing the mass can reduce the resonance frequency, but the cantilever beam tends to break up. Increasing the length of the cantilever beam is an alternative method, but the size of the MEMS device is limited. This paper proposes a PVEH with a folded aluminum nitride (AlN) piezoelectric beam that can increase the effective beam length and decease the resonance frequency.

2 Device 2.1 Structure Figure 1 shows the PVEH structure. Structure A is a regular PVEH, and structure B is a PVEH with a folded AlN piezoelectric beam. The piezoelectric cantilever beam with a Si proof mass is fixed at one end. The PVEH device in this paper is designed on a small silicon slice (size: 10 mm × 10 mm). For regular structure A, the thickness of the Si beam should be less than 16 µm for 50 Hz resonant frequency. However, the vibration acceleration at which the PVEH can work properly is not larger than 0.3 g (1g = 9.8 m/s2 ). For structure B, the length of the folded piezoelectric beam can reach to 30 mm, and the resonant frequency can be effectively reduced to 50 Hz.

(a) Structure A

(b) Structure B

Fig. 1. The structure of PVEH: (a) named as structure A is a regular PVEH, a piezoelectric cantilever beam with a proof mass at the free tip. (b) named as structure B is a PVEH with a folded piezoelectric beam.

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2.2 Principle The PVEH can be equivalent to a second-order spring-damper-mass vibration system. Total system damping includes mechanical damping and equivalent electrical damping. The mechanical damping results from the materials inherent mechanical kinetic energy dissipation, while the electrical damping arises from the vibration reaction force caused by piezoelectric effect of the PVEH. For a second-order vibration system, the resonance frequency f n of the cantilever beam-mass system is expressed as [13]:  λ2n EI . (1) fn = 2π ρl Where, EI is the bending stiffness of the cantilever beam, ρ l is the linear density in the length direction of the cantilever beam, and λn is the mode-dependent coefficient, which is obtained from the boundary conditions of the cantilever beam. Equation (1) is the mechanical resonance frequency, which will be reduced by the electrical damping caused by the piezoelectric effect. In fact, the maximum output power at resonance is a function of frequency and load resistance [14]. The analysis results show that the load causes a resonance frequency shift (Fig. 2). There are two maximum points A and C, and the power values of the two points are basically the same. The resonance frequency increases with the load, as shown in Fig. 2. Near the resonance point A, the PVEH resonance is greatly affected by the load, and the output power decreases greatly when it deviates from point A. However, near point C, the resonance frequency is almost unaffected by the load. The change of external load hardly reduces the output power, which means that the PVEH can drive a wide range resistance near point C. This conclusion has very important practical significance for PVEH. The current at resonance point A is large and the voltage is small, which is known as the short-circuit resonance of the piezoelectric beam [15]. On the contrary, point C corresponds to an open-circuit resonance. There is also a saddle point B between A and C on the dashed line. Although resonance occurs at point B, the output power is reduced by 26%.

Fig. 2. The output power of a PVEH as a function of load and vibration frequency

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2.3 Design Theory [13] and finite element method (FEM) software were used to design and optimize the PVEH. The piezoelectric thin film lead zirconate titanate (PZT) and AlN is widely used in MEMS devices. The AlN film as the functional material because the AlN thin film is lead-free and can be easily prepared using magnetron sputtering method. The study utilized modal simulation to calculate the resonant frequency and mode shape of the folded piezoelectric beam. Additionally, harmonic response analysis was used to analyze the relationship between the output voltage and power with load resistance and excitation frequency. The material properties of AlN piezoelectric film and Si material were set as shown in Table 1. The device overall size is limited in 10 mm × 10 mm × 0.5 mm. The gap b = 50 µm, and the thickness of the AlN film and the Si mass are 1 µm and 0.5 mm, respectively. Three cases of PVEH were analyzed with Si beam thickness t b 30 µm, 40 µm, 50 µm, respectively. The width a of the folded beam was optimized. Table 1. Material parameters of AlN and Si Materials

Parameters

Value

Si

Density (kg/m3 )

2330

Young’s modulus (GPa)

170

Poisson’s ratio

0.28

Density (kg/m3 )

3300

AlN

compliance ratio s11 (10–12 /Pa)

2.86

Piezo. Coeff. d 31 (pC/N)

−1.73

permittivity εr

9.2

3 Results 3.1 Resonance Frequency The resonance frequency increases with the width of folded beam as shown in Fig. 3. The theoretical results are consistent with the FEM results, and the resonance frequency increases with increasing folding beam width a. The optimized size a are 2.63 mm, 2.12 mm, 1.65 mm for the case t b = 30 µm, 40 µm, 50 µm, respectively. Actually, the optimized resonance frequency is slightly larger than 50 Hz. On the one hand, there are errors in the FEM software simulation results and fabrication process of the FEM software. On the other hand, lowering resonance frequency of the PVEH is easier by attaching little mass on the integrated Si mass. The vibration modals of the PVEH are shown in Fig. 4. The device usually operates in the first modal (Fig. 4a). The simulation results show that the frequency of the second modal (Fig. 4b) is about 1.9 times as that of the first modal. By optimization design on the size, the second modal frequency of the PVEH can reach to 100 Hz, which is the second harmonic frequency of the source as

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coincidental. The advantage is that the PVEH can harvest more power from the vibration source, but a modal superposition problem will arise.

Fig. 3. The resonance frequency of the PVEH vs. the folded piezoelectric beam width

(a)1st

(b)2nd

Fig. 4. The first three vibration modals of the PVEH

3.2 Output Voltage The open circuit voltage amplitude was analyzed as shown in Fig. 5. Referring the experimental results [16], the damping ratio was set to be 0.01 in the FEM software. The acceleration of excitation vibration is 1 g. The max FEM voltage are 1.74 V, 2.05 V, 2.19 V, for the case t b = 30 µm, 40 µm, 50 µm, respectively. The theoretical results are slightly larger, which are 1.936 V, 2.228 V, and 2.678 V respectively. The same trend indicates that the thicker the cantilever beam, the higher the output voltage. When t b = 50 µm, the output voltage is the highest. While the displacement of the mass and the stress at fix end are largest as well. 3.3 Output Power To evaluate the output power of the PVEH, a resistor load was connected to the electrode of the piezoelectric element. The voltage across the resistor and power is shown in Figs. 6 and 7. FEM simulation results show that the output power is within the range of 3.2 µW–3.6 µW, and the theoretical output power range is 2.50 µW–3.03 µW. The FEM optimized resistor of the three cases reduces from 700 k to 500 k with the

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(a)FEM

(b)Theoretical

Fig. 5. The open circuit voltage amplitude vs. vibration frequency

increasing of t b . And theoretical optimized resistor reduces from 1040 k to 713 k. The regular PVEH with the same size (length along the x-axial, width, and thickness of beam and proof mass) for the three cases, by contrast, is simulated. The resonance frequency of the regular PVEH can reaches up to 150–252 Hz, and the output power reaches up to 7.1–9.1 µW. The results show that the PVEH with folded beam can reduce the resonance frequency to 50 Hz in the limited size.

Fig. 6. The FEM simulated voltage (a) and power (b) vs. resistor load

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(a)

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(b)

Fig. 7. Theoretical voltage (a) and power (b) vs. resistor load

4 Conclusion A MEMS piezoelectric vibration energy harvester was designed using FEM method and theoretical calculations. The results of the two methods were basically consistent. To reduce the resonance frequency to 50 Hz in limited size, a folded AlN piezoelectric beam was designed. The beam size was optimized, and output voltage and power were analyzed. The results show that the folded beam can reduce the resonance frequency from 252 Hz to 50 Hz, and max power is 3.6 µW. Two problems were not mentioned in this paper. First is the charge distribution of the piezoelectric element along. Not all the charge on the up or bottom electrode are the negative or positive. Second is that the second modal twisting motion of the mass will be more powerful, and the rotation axis of the proof mass should be further studied. Acknowledgement. This work supported by the science and technology project of State Grid Zhejiang Electric Power Co., Ltd (5211WZ2000X2). The authors sincerely thank the anonymous reviewers for their valuable comments and suggestions on the paper.

References 1. Zhang, H., et al.: A flexible and implantable piezoelectric generator harvesting energy from the pulsation of ascending aorta: in vitro and in vivo studies. Nano Energy 12, 296–304 (2015) 2. Abdelkefi, A., Hajj, M.R., Nayfeh, A.H.: Piezoelectric energy harvesting from transverse galloping of bluff bodies. Smart Mater. Struct. 22(1), 015014 (2012) 3. Dai, H., Abdelkefi, A., Javed, U., Wang, L.: Modeling and performance of electromagnetic energy harvesting from galloping oscillations. Smart Mater. Struct. 24(4), 045012 (2015) 4. Tao, K.S., Lye, W., Miao, J., Hu, X.: Design and implementation of an out-of-plane electrostatic vibration energy harvester with dual-charged electret plates. Microelectron. Eng. 135, 32–37 (2015) 5. Lee, S.H., Ko, Y.H., Yu, J.S.: Facile fabrication and characterization of arch-shaped triboelectric nanogenerator with a graphite top electrode. Phys. Status Solidi 212(2), 401–405 (2015)

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6. Deng, Q., Kammoun, M., Erturk, A., Sharma, P.: Nanoscale flexoelectric energy harvesting. J. Intel. Mat. Syst. Str. 51(18), 3218–3225 (2014) 7. Li, M., Wen, Y., Li, P., Yang, J., Dai, X.: A rotation energy harvester employing cantilever beam and magnetostrictive/piezoelectric laminate transducer. Sensor. Actuat. A-Phys. 166(1), 102–110 (2011) 8. Krupenkin, T., Taylor, J.A.: Reverse electrowetting as a new approach to high-power energy harvesting. Nat. Commun. 2(448), 1–8 (2011) 9. Lien, C., Shu, Y.C.: Array of piezoelectric energy harvesting by the equivalent impedance approach. Smart Mater. Struct. 21(8), 82001 (2012) 10. Stanton, S.C., Erturk, A., Mann, P.B., Dowell, H.E., Inman, D.J.: Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects. J. Intel. Mat. Syst. Str. 23(2), 183–199 (2012) 11. Wang, Y.J., Chen, C.D., Sung, C.K.: Design of a frequency-adjusting device for harvesting energy from a rotating wheel. Sensor. Actuat. A-Phys. 159(2), 196–203 (2010) 12. Romaric, K.N., Liu, D., Du, B.: Investigation on vibration characteristics of amorphous metal alloy core dry-type distribution transformer. CES Trans. Electric. Mach. Syst. 6(3), 324–331 (2022) 13. Zhang, Z., Xiang, H., Shi, Z.: Experimental investigation on piezoelectric energy harvesting from vehicle-bridge coupling vibration. Energ. Convers. Manage. 163, 169–179 (2018) 14. Abdelkefi, A., Barsallo, N., Tang, L.H., Yang, Y.W., Hajj, M.: Modeling, validation, and performance of low-frequency piezoelectric energy harvesters. J. Intel. Mat. Syst. Str. 25(12), 1429–1444 (2014) 15. Song, H.C., Kim, S.W., Kim, H.S.: Piezoelectric energy harvesting design principles for materials and structures: material figure-of-merit and self-resonance tuning. Adv. Mater. 32(51), 2002208 (2020) 16. Wen, Z., Deng, L., Zhao, X., Shang, Z., Yuan, G., She, Y.: Improving voltage output with PZT beam array for MEMS-based vibration energy harvester: theory and experiment. Microsyst. Technol. 21, 331–339 (2015)

Substation WSN Coverage Optimization Technology Based on Improved Dragonfly Algorithm Donglei Zhang1(B) , Jianding Fu1 , Hongjian Gao1 , Longwei Wang2 , and Fei Du2 1 State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China

[email protected], [email protected]

2 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources,

North China Electric Power University, Beijing 102206, China {wanglongwei,dufei}@ncepu.edu.cn

Abstract. The reliability of substation equipment is the foundation for the safe operation of the power grid. Wireless sensor networks play a crucial role in the perception, transmission, and processing of operational data, providing important support for the maintenance and operation control of power grid equipment. To figure out the coverage problem of wireless sensor networks in substation scenarios, an improved dragonfly algorithm based on chaotic mapping and Cauchy mutation (CCDA) is proposed in this article. The initial velocity of the population is generated by the algorithm using two-dimensional logical chaotic mapping to guarantee population diversity. With a probability decreasing as the number of iterations increases, Cauchy mutation is applied to the current iteration’s best individual to escape local optima, enhance the ability to explore the overall situation and improve solution accuracy. The simulation results show that, compared with dragonfly algorithm, sparrow search algorithm and random deployment algorithm, the proposed algorithm can effectively improve the network coverage performance under the premise of high convergence speed and strong global search ability. Keywords: Wireless Sensor Networks · Chaotic Mapping · Cauchy Mutation · CCDA

1 Introduction With the advancement of communication technology, the Internet of Things (IoT) applications have made rapid development. Wireless sensor networks (WSN), as a type of distributed multi-hop self-organizing network based on wireless communication technology, consist of a series of sensing nodes with communication and storage capabilities that are widely distributed within the monitoring area [1, 2]. Compared with the optical cable communication mode, WSN has the characteristics of economy. The application of this technology in the communication system of distribution network can significantly reduce the system construction cost and provide comprehensive signal coverage for the © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 145–154, 2024. https://doi.org/10.1007/978-981-97-0865-9_17

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distribution network system. Therefore, it is widely used in smart grid power information monitoring, collection and other scenarios [3]. For wireless communication nodes with information aggregation and forwarding functions, the deployment mode is one of the important links affecting the performance of WSN and a necessary condition for the reliable operation of the whole network. In other words, how to deploy communication nodes can maximize the coverage and reduce the existence of blind areas as much as possible [4]. The common solutions include expert experience, operation planning and heuristic search algorithm, among which the heuristic search algorithm has a fast solving speed and accuracy, and has a wide range of applications in wireless sensor network nodes deployment. In the existing researches, swarm optimization algorithms such as particle swarm optimization (PSO) are broadly utilized to solve the sensor deployment problem in WSN [5]. Reference [6] took the coverage rate of wireless sensor network as the optimization target, the firefly algorithm was applied to nodes deployment location optimization. Compared with genetic algorithm and particle swarm algorithm, although firefly algorithm had faster search speed and better performance, its optimization results came from the characteristics of the algorithm itself, and the algorithm has not been improved. In reference [7], the effective connectivity rate of nodes and network coverage rate were taken as objective functions, the multi-objective particle swarm optimization algorithm was improved by adaptive adjustment of inertia weight and particle velocity update, and the optimal scheme set was dynamically maintained by Pareto multi-objective optimization strategy. Although it did not achieve the accuracy mentioned in the literature, the advantages of short optimization time, low cost and high optimization efficiency of the algorithm were worthy of attention. Motivated by improving network coverage size and reducing the overall energy consumption of sensor nodes, the moth flame search algorithm has been improved in reference [8], using a variable spiral position update strategy to achieve coverage optimization by guiding individuals to uncovered gaps, but without considering the presence of obstacles in the monitoring area. By introducing nonlinear convergence factors to balance global exploration and local optimization, literature [9] overcame the shortcomings of Gray Wolf algorithm with slow convergence speed and low convergence accuracy. The algorithm was applied to the wireless network deployment problem with existing obstacles, but the implementation complexity of the algorithm was too high. The coverage optimization capability of the proposed algorithm in the monitoring area with obstacles was not analyzed. Based on the above research, an improved dragonfly algorithm based on chaotic mapping and Cauchy mutation (CCDA) is proposed in this paper and applied to WSN nodes coverage optimization in substation scenarios. In this paper, the coverage perception model is first established, and then the proposed coverage optimization algorithm is simulated in the substation scene with obstacles. At the same time, three algorithms in the existing literature are selected to make a comparison in the same environment. The results exhibit that, the proposed algorithm has faster convergence speed and achieves higher network coverage increment.

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2 Wireless Network Coverage Model For the two-dimensional point coverage problem in the substation, assume that n wireless communication nodes are pre-deployed in the two-dimensional deployment area of area M × L, the node set is S = {s1 , s2 , · · · , si , · · · , sn }, the communication radius of each point is Rc , and the coordinate of the i-th WSN communication node is si = (xis , yis ). To simplify the coverage problem, the monitored area is discretized into m × l unit square areas, and the central coordinate target of the deployment   of each subarea is the coverage node, the target set is C = c1 , c2 , · · · , cj , · · · , cm×l , and the coordinate of the j-th sensing target node is cj = (xjc , yjc ). cj is covered if the distance between the center point cj and any communication node is less than or equal to the sensing radius Rc . Euclidean distance is used to represent the distance between node si and center point cj . d (si , cj ) = ((xis − xjc )2 + (yis − yjc )2 )1/2

(1)

The probability that the center point cj is sensed by the node si can be defined as follows.  0, Rc ≤ d (si , cj ) p(si , cj ) = (2) 1, Rc > d (si , cj ) Assuming that the event of the center point cj being sensed by each communication node is mutually independent, the probability of the center point cj being jointly sensed by all communication nodes can be defined as follows. n

P(s, cj ) = 1 −  [1 − p(si , cj )]

(3)

i=1

We can obtain the probability that the set of monitoring points C in the substation deployment area is sensed by the set of communication nodes S, which represents the wireless sensor network coverage rate. m×l 

RCov =

P(s, cj )

j=1

ml

(4)

When the deployment of communication nodes can achieve full coverage of the area, there must be repeated areas between adjacent nodes, as shown in Fig. 1. In Fig. 1,s1 , s2 , and s3 represent three wireless network communication nodes, the distance between s3 and L is Rc , which is the communication radius of the nodes. Based on the geometric properties of circles and mathematical derivation, in a two-dimensional scenario with an area of M × L, the theoretically required number of nodes is given by the equation.    L M count = √ +1 +1 (5) √ ( 3/2)Rc + Rc ( 3/2)Rc + Rc

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y

s1

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Fig. 1. Wireless communication node coverage diagram.

3 Improved Dragonfly Algorithm-CCDA In this paper, the objective function of the optimization model is to maximize the total coverage of the substation area. The dragonfly algorithm (DA) is adopted to simulate the behavior of dragonflies seeking prey and avoiding natural enemies in nature, which are called static swarm and dynamic swarm respectively [10]. Local motion and flight path mutation are the main characteristics of static groups, which makes the algorithm have strong global search ability. In dynamic group, a large number of dragonflies make groups in one direction for long-distance migration which makes the algorithm have strong local development ability. However, due to factors such as the inability to retain the optimal position in the iterative process and the unknown location of the food source, the algorithm is prone to fall into the local solution with slow convergence speed [11]. Therefore, the CCDA based on dragonfly algorithm is proposed in this paper, initializing dragonfly population speed through chaotic mapping and introducing Cauchy mutation to get rid of local optimal solutions. The implementation process of the proposed algorithm consists of the following stages. 3.1 Dragonfly Algorithm The whole dragonfly algorithm optimization process has the advantages of simple principle and few parameters, which can be summarized into five behaviors: separation, alignment, alliance, hunting and avoiding enemies. The algorithm updates the velocity vector, which calls X , of each iteration dragonfly by combining five behavior patterns. Xt+1 = (sSi + aAi + cCi + fFi + eEi ) + wXt

(6)

where S,A, C, F and E represent the above five behavioral parameters. s, a, c, f and e represent the weights for separation, alignment, cohesion, hunting, and predator avoidance, respectively. t indicates the current iteration, and w is the inertia weight.

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When a dragonfly has adjacent individuals, the position vector for the next iteration of the dragonfly is: Xt+1 = Xt + Xt+1

(7)

In the absence of neighboring solutions, in order to enhance the global exploration capability of the artificial dragonflies, a random walk is employed to navigate through the search space. Xt+1 = Xt + Levy(d ) × Xt

(8)

Levy(d ) is Levy’s flight function, where d is the dimension of the position vector, Xt is current location of individual dragonfly. 3.2 Improved Dragonfly Algorithm 1) Chaotic initialization population velocity Suppose that there are K dragonfly individuals in the population, and the initial velocity of each dragonfly individual plays a key role in the position update of the later iteration. Corresponding to the spatial dimension of dragonfly, the speed set of dragonfly population can be represented as X = [X1 , X2 , · · · XK ], and the speed vector of the k-th individual in the population can be denoted as Xk = [Xk,1 , Xk,2 , · · · , Xk,2I ], where the former I-dimensional variable represents the transverse movement speed of nodes, and the latter I-dimensional variable represents the longitudinal movement speed of nodes. In this section, the chaotic value is introduced into the search space by using the initialization method based on two-dimensional logical mapping. A two-dimensional logical map is a chaotic map with nonlinear feedback, which is mainly constructed by sine and cosine functions and can be expressed as follows:  hn+1 = sin(π(4ahn (1 − hn )) + (1 − a) sin(π yn )) (9) yn+1 = sin(π(4ayn (1 − yn )) + (1 − a) sin(π h2n+1 ))) where hn and yn represents the chaotic value corresponding to the initialization of the n-th dragonfly individual, and a represents the scaling factor, typically chosen from the interval [0.78, 0.86]. In this study, we set a = 0.84, the bifurcation diagram is as follows (Fig. 2). 2) Cauchy mutation In the CCDA algorithm, Cauchy mutation is introduced to perturb the best dragonfly individual after each iteration. The mutation strategy enhances the diversity of the population and improves the algorithm’s ability to escape local optima. In the early iterations, a larger dynamic mutation probability is used to promote global exploration. In the later iterations, the mutation probability is reduced to to speed up convergence. The position update strategy is as follows. Xnewbest = Xbest + Xbest × Cauchy(0, 1)

(10)

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(a) h chaotic mapping bifurcation diagram

(b) y chaotic mapping bifurcation diagram

Fig. 2. Two dimensional logical chaotic mapping bifurcation diagram.

The standard Cauchy distribution is given by: Cauchy(x; 0, 1) =

1 π(1 + x2 )

(11)

After the mutation is completed, the new individual will be compared with the original individual, and the individual with higher fitness will be selected.  Xnewbest , fitness(Xnewbest ) > fitness(Xbest ) (12) Xbest = Xbest , else where fitness(X ) represents the fitness function value of the X individual.

4 Nodes Deployment Based on Improved Algorithm This paper optimizes the deployment of WSN nodes in a substation scenario based on the proposed algorithm. The goal in this paper is to maximize the coverage rate of the target area by optimizing the positions of the nodes. 4.1 Node Deployment Process Through the process of finding the optimal solution for abstract damselflies process of prey and predators, node deployment optimization steps based on CCDA are as follows: 1. Initialize the task information of count nodes to be deployed, communication radius Rc , population number K, maximum number of iterations Tmax , deployment area of nodes and other related parameters; 2. The chaotic initialization of dragonfly population was carried out by using twodimensional logical chaotic mapping method, in which each dragonfly individual contained I locations of WSN nodes, representing a velocity distribution scheme of WSN nodes;

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3. The individual fitness values of each dragonfly were calculated according to Eq. (4), and the individual with the largest fitness value was set as the natural enemy, and the individual with the smallest fitness value was set as the food. If the mutation conditions are met, Cauchy mutation operation is performed on the current food individual according to Eq. (10). If it is better than before the disturbance, the food position is updated to the position after the mutation; otherwise, the original position remains unchanged; 4. Calculate the five behavioral parameters of dragonflies and update the corresponding weight parameters; 5. The dragonfly individual is used to search whether there are adjacent individuals within the radius. If there are adjacent individuals, the location information of each individual dragonfly is updated according to formula (7); If it does not exist, perform Levy flight according to formula (8) to update the location information of individual dragonflies; 6. Record the current population information and optimal individual information, and judge whether the number of iterations of the algorithm reaches the maximum number of iterations. If so, the optimal dragonfly individual will be used as the optimal node deployment scheme and output the optimal coverage; otherwise, return to Step 3 to continue the loop.

Table 1. Parameters setting. Parameter

Value

System frequency/GHz

2.4

Total system bandwidth/ MHz

20

Population size

60

Maximum iterations

200

Number of nodes

21

WSN node transmit power /dBm

8

Minimum accepted power of the sensor node /dBm

−85

4.2 Parameter Configuration This paper takes substation scene as an example, modeling the area to be monitored as a rectangular plane of 600 m × 500 m, and building a network simulation environment. There are seven obstacle areas, the green, purple, yellow, and blue rectangles represent the AC filter bank, the high-end valve hall, the gas insulated combined electrical equipment, and the low-end valve hall, respectively. The communication radius of WSN nodes is calculated by establishing the road loss model based on the measured data, Rc = 75 m. In addition, according to formula (5), twenty-one communication nodes need be deployed in the monitoring area. Other parameters set in the experiment are shown in Table 1.

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4.3 Simulation Result Analysis In the context of a substation scenario that incorporates a large number of electrical devices, WSN enables remote monitoring of various physical environmental data, such as electromagnetic interference, humidity, temperature, and mechanical vibration, within the substation. The collected information is promptly transmitted to the control platform. Figure 3 illustrates the coverage optimization of the proposed CCDA algorithm in a substation environment. Figure 3(a) shows the initial node distribution at t = 0, where WSN nodes are randomly deployed in the target area, resulting in a coverage rate of 72.98% with coverage holes and redundancies. Figure 3(b) presents the final deployment of wireless communication nodes after optimization by the CCDA algorithm. Compared to the initial random deployment, the node positions are more evenly distributed, leading to a significant improvement in the coverage rate. By making a comparison between Fig. 3(a) and Fig. 3(b), it can be observed that the network’s final deployment achieves a coverage rate of 94.07% using the CCDA algorithm, resulting in a coverage rate increment of 21.09%. 500

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600

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Fig. 3. Coverage comparison of using CCDA algorithm in transformer substation environment.

Figure 4 shows the convergence of the CCDA algorithm, dragonfly algorithm (DA), sparrow search algorithm (SSA), and randomized algorithm (RA) when the sensor node count is 21 and the initial population has the same optimal coverage rate. From the graph, it can be observed that all three population-based intelligent optimization algorithms significantly improve the coverage rate compared to random deployment. Among them, the proposed CCDA algorithm exhibits good convergence behavior, entering the convergence phase at around 140 iterations. From Fig. 4, it can be observed that the CCDA algorithm has a fast convergence speed during the iteration process and can escape from local optima multiple times. On one hand, the introduction of the Cauchy mutation strategy significantly improves the ability of the CCDA algorithm to search for global optimal solutions. The wireless communication nodes can dynamically adjust their deployment strategies in complex environments, allowing the population search to more effectively approach the optimum

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and avoid local optima, thereby improving the optimization accuracy of the algorithm. On the other hand, thanks to the two-dimensional logical chaos initialization, the initial velocities of individual dragonflies in the population do not gather in the same region, ensuring the diversity of the population and accelerating the convergence of the algorithm. The SSA algorithm can not balance the ability of global development and local search well, and it has difficulties in maintaining population diversity and preserving optimal solutions. Therefore, it has a slower convergence speed and is prone to local optima. In summary, the proposed CCDA algorithm can effectively address the wireless communication node deployment optimization problem in a substation scenario with a fast convergence speed and high convergence accuracy. 0.95

Convergence curve

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0.8 CCDA DA SSA RA

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Fig. 4. Relationship between network coverage and iteration times obtained by four algorithms in substation environment.

5 Conclusion To enhance the coverage of WSN in a substation environment, this study proposes the CCDA algorithm, which combines the DA algorithm with two-dimensional logical chaos mapping and Cauchy mutation. The algorithm is designed to address the coverage optimization problem of WSN nodes in a substation scenario. Simulation results demonstrate that the CCDA outperforms the SSA and RA in improving network coverage performance and ensuring communication quality for power system operations in substation environments. Future work will focus on the integration of node energy management and mobility, as well as the application of multi-objective optimization strategies in substation scenarios. Acknowledgments. This work has been supported by State Grid Corporation of China science and technology project “Research and application of reliability improvement technology of substation sensors and sensor network considering the influence of multi-physics coupling” (5700-202232441A-2-0-ZN).

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References 1. Wang, M., Zeng, J.: Hierarchical clustering nodes collaborative scheduling in wireless sensor network. IEEE Sens. J. 22(2), 1786–1798 (2022) 2. Morarji, C., Kumar, N.: Smart-grid monitoring using IoT with modified lagranges key based data transmission. Tech Sci. Press 35(3), 2875–2892 (2023) 3. Chandel, S., Sharma, S.: Optimization based sink deployment technique in WSN to improve network performance. Int. J. Sens. Wireless Commun. Control 10(2), 217–230 (2020) 4. Wang, W.: Deployment and optimization of wireless network node deployment and optimization in smart cities. Comput. Commun. 155, 117–124 (2020) 5. Singh, S., Poonkuzhali, R., Nithya, G., et al.: Enhanced particle swarm optimization based node localization scheme in wireless sensor networks. In: 2022 International Conference on Augmented Intelligence and Sustainable Systems (ICAISS), pp. 1019–1024. Trichy, India (2022) 6. Liu, W., Li, P., Ye, Z., et al.: A node deployment optimization method of wireless sensor network based on firefly algorithm. In: 4th International Conference on Advanced Information and Communication Technologies, pp. 167–170. IEEE, Lviv, Ukraine (2021) 7. Wang, W.: Optimization of wireless network node deployment in smart city based on adaptive particle swarm optimization. J. Intell. Fuzzy Syst. Appl. Eng. Technol. 39(4), 1–11 (2020) 8. Yao, Y., Hu, S., Li, Y., et al.: A node deployment optimization algorithm of WSNs based on improved moth flame search. IEEE Sens. J. 22(10), 10018–10030 (2022) 9. Wang, Z., Xie, H., Hu, Z., et al.: Node coverage optimization algorithm for wireless sensor networks based on improved grey wolf optimizer. J. Algorith. Comput. Technol. 1, 1–15 (2019) 10. Mirjalili, S.: Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput. Appl. 27(4), 1053– 1073 (2015). https://doi.org/10.1007/s00521-015-1920-1 11. Liu, Z., Wang, A., Sun, G., et al.: Evolutionary feature selection method via a chaotic binary dragonfly algorithm. In: International Conference on Systems, Man, and Cybernetics (SMC), pp. 2471–2478. IEEE, Prague, Czech Republic (2022)

Application of Flexible Control Devices in Typical Scenarios of the Hebei South Network Peng Yang1 , Jiahui Tian2 , Xudong Li3 , Yubin Li4 , and Yanhui Xu4(B) 1 State Grid Hebei Electric Power Company, Shijiazhuang 050022, China 2 State Grid Hebei Power Company Economic Research Institute, Shijiazhuang 050000, China

[email protected]

3 State Grid Smart Grid Research Institute Company, Beijing 102211, China 4 School of Electrical and Electronic Engineering, North China Electric Power University,

Beijing 102206, China [email protected]

Abstract. With the integration of large-scale new energy into the grid, flexible control equipment is crucial to the quality, safety and stability of grid power supply. This paper firstly introduces the mathematical models of flexible power transformer and United power flow controller (UPFC), and based on the unique background and existing problems of Hebei South Grid, we study the impact of two flexible control devices on the current distribution of Hebei South Grid based on PSD-BPA simulation. The simulation results show that selecting the transformer tap voltage based on the current delivery capacity can effectively solve the problem of heavy and overloaded main transformer of 1000 kV Xiong’an station. At the same time, installing UPFC equipment on the most serious overload lines can improve the heavy and overload situation of 500 kV Langfang area lines. It is concluded that the flexible control equipment can solve the problem of uneven current distribution, exceeding the limit and not meeting the N−1 calibration, and support the safe and stable operation of the power system. Keywords: Flexible control equipment · Flexible power transformer · UPFC

1 Introduction At present, countries around the world are continuously promoting the transformation of the energy structure, the study of wind power, photovoltaic and other new energy generation more and more attention. China in September 2020 clearly put forward the “double carbon” target, continue to promote the adjustment of energy structure, put forward the construction of new power system with new energy power generation as the main body, and in 2022 introduced the “14th Five-Year Plan” renewable energy development plan, clearly pointed out that by 2025, the annual power generation of renewable energy will reach 3.3 trillion kilowatt-hours, and achieve the wind power generation of wind power, photovoltaic and other new energy. It is clearly pointed out that by 2025, the annual power generation of renewable energy will reach about 3.3 © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 155–168, 2024. https://doi.org/10.1007/978-981-97-0865-9_18

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trillion kWh, doubling the power generation capacity of wind power and solar energy; in 2030, the total installed capacity of wind power and solar power will reach 1.2 billion kW. However, with the future of large-scale new energy grid, in addition to bringing reactive power regulation, voltage stability and other issues, but also affect the transient stability of the power system, reducing the power supply quality, security and economy of the power system, seriously affecting the normal operation of the power system. With the vigorous development of power electronics technology, flexible control devices can be used to solve the above problems. There are Flexible AC Transmission Systems (FACTS) devices such as Static Synchronous Compensator (STATCOM), State Synchronous Series Compensation (SSSC) and UPFC in the flexible AC transmission system, which can make the new energy grid-connected access with higher flexibility and improve the stability of the power system. UPFC is a bi-directional converter combined in series and parallel, with strong reactive power compensation, node voltage maintenance capability and strong line voltage compensation, line current control capability, which can realise multi-functional integrated control of the line. At present, there are 6 UPFC projects in operation at home and abroad. There are 138 kV UPFC project of INEZ substation in Kentucky, U.S.A., which was put into operation in 1998 [1], 154 kV UPFC project of Kangjin substation in South Korea, which was put into operation in 2003 [2], and 345 kV CSC project of Marcy substation in New York, U.S.A., which was put into operation in 2004 [3]. The first UPFC project in China, i.e., the world’s first MMC-based UPFC project, was the 220 kV UPFC project of Nanjing West Ring Network, which was commissioned in December 2015 [4, 5]. China then commissioned the 220 kV UPFC project at Shanghai Yunzaobang station in November 2017 [6]; and the 500 kV UPFC project in southern Suzhou in December 2017 [7], which is currently the highest voltage level UPFC project in the world. These UPFC projects have solved the problems of uneven current distribution, voltage overrun and insufficient reactive power support that exist in the actual operation of power grids, and have good application effects. As new power systems need to have fast and continuous voltage regulation capability, traditional power transformers cannot meet the demand. In recent years, flexible power transformers [8] has appeared, taking the fully-controlled power electronic device as the core, combining the Voltage Source Converter (VSC) with the traditional power transformer, which can achieve the control of the transformer output voltage and current without changing the transformer turns ratio, and it has the advantages of arc-free switching, fast response speed, and high reliability, Low cost and other advantages. This paper firstly introduces the basic structure, working principle and mathematical model of flexible power transformer and UPFC respectively. Then it introduces the overview of China’s Hebei South Network, based on PSD-BPA simulation software, puts forward the problems existing in the power grid according to the planning data of Hebei South Network in 2025, and researches the influence of the above flexible control equipment on the current distribution of Hebei South Network. The simulation results show that the flexible control equipment can solve the problems of uneven trend distribution, trend overrun and failure to satisfy the N-1 check, and improve the stability of the system.

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2 Mathematical Modelling of Two Flexible Control Devices This section introduces the basic structure, working principle and mathematical model of flexible power transformer and UPFC. 2.1 Flexible Power Transformers Flexible power transformer consists of the main transformer [8], converter and bypass device, the basic structure shown in Fig. 1. Among them, the main transformer is a threewinding transformer; the converter is connected in series between the end of the primary winding and the end of the three windings; the secondary winding provides the power required by the line or the load; the three windings are connected to the input side of the converter to provide active power support for the converter to realise the flexible control of the voltage and the current, the flexible expansion of ports and the improvement of the quality of the power, etc. The bypass device is connected in parallel to both ends of the inverter side of the converter, which consists of anti-shunt thyristors and mechanical bypass devices. The bypass device is connected in parallel at both ends of the inverter side of the converter, which consists of anti-parallel thyristors and mechanical switches; when the converter fails, the bypass device shorts out the converter, and at this time, the flexible power transformer is operated as a conventional power transformer to ensure the reliability of the equipment. IS

U2

W2

XS U1 US

W1

U3

W3

Fig. 1. Basic structure diagram of flexible power transformer.

The simplified structure of the flexible power transformer shown in Fig. 2, equivalent to the transformer directly in the net side winding end and ground series between the amplitude and phase can be flexibly adjusted voltage source, change the net-side winding voltage, can be realised on the load side winding voltage regulation.

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U2

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XS U1'

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US

U4

Fig. 2. Simplified structural diagram of a flexible power transformer.

The equivalent circuit of the simplified flexible power transformer normalised to the primary side is shown in Fig. 3, ignoring the transformer branch to ground. Let the equivalent voltage of the AC system at the sending end be U˙S , the equivalent reactance is X S ; the number of turns of the primary winding of the transformer is W 1 , and the number of turns of the secondary winding is W 2 ; the amplitude of the voltage at the receiving end of the AC system side is U 2 , and the phase is γ2 , i.e., the voltage of the transformer’s secondary winding is U˙2 ; the voltage of the tertiary winding voltage is U˙3 , the number of turns is W 3 ; ignore the resistance of the main transformer, the transformer reactance converted to the primary winding equivalent to the reactance X T1 ; controlled voltage source output voltage amplitude is U 4 , phase is γ4 ; flow through the primary winding current is I˙S . Let the voltage amplitude on the sending side be U 1 and the phase be 0° before the controllable voltage source is strung in; after the controllable voltage source is strung in, the voltage on the sending side is U˙1 . US

IS XS

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X T1

P

jQ

Fig. 3. Equivalent circuits for current regulation by flexible power transformers.

From Fig. 3, the voltage relationship of the flexible power transformer is ⎧ ˙ ⎨ U 1 = U˙ 1 + U˙ 4 W ⎩ U2 = U1 × 2 W1

(1)

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From Eq. (1), without changing the number of turns of the transformer windings, only change the voltage of the controllable voltage source U˙4 , you can regulate the voltage at both ends of the primary winding U˙1 , and the voltage induced to the secondary winding U˙2 is also changes accordingly. With the controlled voltage source in series, the active power P and reactive power Q delivered by the line are ⎧ U1 U2 ⎪ ⎪ ⎪ P = sin(ϕ − δ2 ) ⎪ ⎪ XT1 ⎪ ⎪ ⎪ ⎪  U  ⎪ ⎪ ⎨ Q = 1 U1 − U2 cos(ϕ − δ2 ) XT1 (2)  ⎪ ⎪  2 2 ⎪ U1 = U1 + U4 ⎪ ⎪ ⎪ ⎪

⎪ ⎪ U4 sin δ4 ⎪ ⎪ ⎩ ϕ = arctan U1 + U4 cos δ4 From the Eq. (2) can be obtained, in the case of not changing the number of turns of the transformer windings, only change the voltage of the controllable voltage source, you can adjust the flexible power transformer connected to the line current. Therefore, by adjusting the amplitude and phase of the output voltage of the converter, the voltage of each winding of the main transformer can be adjusted quickly, without arc and smoothly without changing the turns ratio of the transformer, and at the same time, the current of the branch where the flexible power transformer is located can be changed, which can play the role of trend regulation. 2.2 UPFC The following section describes the MMC-based UPFC device, which is currently the most widely used in practical engineering and has the advantages of high modularity and low harmonic content [9–11]. The basic structure of MMC-UPFC is shown in Fig. 4, in which the shunt converter is connected in parallel with the transmission line through the link transformer, similar to the function of STATCOM, and the series converter is connected in series with the transmission line through the link transformer, similar to the function of SSSC. In order to inhibit the zero-sequence currents, the secondary windings of the link transformer are usually angularly wired. The two MMCs are connected back-to-back via two common DC buses. This topology enables the active power to flow in both directions between the AC terminals of the two converters, while each converter can generate or absorb reactive power at its AC output. In addition, each bridge arm in the MMC is equipped with a reactor to reduce the harmonic content of the output voltage and to suppress the inter-phase circulating currents of the converters. The main function of UPFC is realised by series and shunt converters. The series converter injects a voltage with adjustable amplitude and phase into the grid through the transformer connected in series in the transmission line, which is equivalent to a fundamental frequency AC synchronous voltage source, thus realising the accurate regulation of active and reactive power on the line and improving the line delivery capacity, and is the main part of UPFC to realise the control function. The main function

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Fig. 4. Basic structure diagram of MMC-UPFC.

of the shunt converter has two points: one is active regulation, to maintain a constant capacitor voltage on the DC side, to provide the active power required for the series converter and the system to generate power exchanges, so that the input active power and the output active power are equal when the UPFC is running; the second is reactive power regulation, capable of issuing or absorbing the controllable reactive power, to provide the line with an independent shunt reactive power compensation. The equivalent circuit of UPFC is shown in Fig. 5. Neglecting the system resistance, U˙S , I˙S and X S are the equivalent voltages, currents, and reactances, respectively, of the sending system of the transmission line A-B to which the UPFC device has been added; U˙R and X R are the equivalent voltage and reactance of the receiving system, respectively; U˙1 , U˙r and X L are the voltage and equivalent reactance at the ends of the transmission line A-B, respectively; U˙sh is the shunt equivalent voltage source, U˙se is the series equivalent ˙ is the series-side current; Z sh and ˙ is the shunt-side current and Ise voltage generator; Ish Z se are the impedances of the shunt and series transformers, respectively; and the active power Psh +Pse = 0. If the UPFC impedance is neglected, the voltage relationship of the UPFC is •

•

•

U 2 = U 1 + U se

(3)

The expression for the power flowing from the sending end system to the transmission line A-B via UPFC is given by ⎧ U2 Ur ⎪ ⎪ sin(θ2 − θr ) ⎨ PL = XL (4) U ⎪ ⎪ ⎩ QL = 2 [U2 − Ur cos(θ2 − θr )] XL

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Fig. 5. Equivalent circuit diagram for UPFC.

By controlling the amplitude and phase of U˙se , the four functions of voltage regulation, series compensation, phase regulation and multifunctional trend control of the line can be realised.

3 Overview and Problems of Hebei South Network 3.1 Overview of Hebei South Network China’s Hebei South Power Grid is an important channel for the North China Power Grid to send electricity from the west to the east and supply electricity from the north to the south, and the Beijing-Tianjin-Tangshan and Shandong Power Grids all transfer a large amount of electricity through the Hebei South Power Grid. By the end of 2021, Hebei South Grid had 2 1000 kV substations and 24 500 kV substations. The installed power supply is 54.42 million kW, including 30.7 million kW of thermal power, 1.27 million kW of hydropower and 22.45 million kW of new energy. During the “14th Five-Year Plan” period, the overall electricity load of the whole society has been growing steadily, and in 2021 and 2022, the maximum daily load of Hebei South Network reached 42 million kilowatts and 44.4 million kilowatts. In the future, with the development of social economy as well as power grid, it is expected that the annual maximum load will reach 60 million kilowatts in 2025 and 72 million kilowatts in 2030; it is expected that the new energy installed capacity will reach 51.39 million kilowatts in 2025, including wind power of 4.35 million kilowatts and photovoltaic power generation of 4.704 million kilowatts. 3.2 Problems with the Hebei South Network Based on the 2025 planning data, the Hebei South Network will have the following main problems in transmission and distribution: (1) Heavy and overload problem of 1000 kV main transformer. In 2025, the main transformer of Xiong’an and Xingtai UHV AC stations will be expanded in Hebei South Network, and there will be four 1000 kV main transformers in Xiong’an and Xingtai

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stations respectively after the expansion. Due to the adjustment of power delivery policy in relevant areas, it will lead to heavy and overload problems of 1000 kV Xiong’an station main transformer during N-1 calibration, which will affect the acceptance of green power such as wind power and photovoltaic power from Zhangbei - Xiong’an UHV. The basic structure of 1000 kV network frame of Hebei South Network is shown in Fig. 6.

Fig. 6. Basic structure diagram of 1000 kV grid of Hebei South Network.

The main transformer trend of Xiong’an station in normal operation mode and N-1 calibration is shown in Table 1, and the main transformer’s JJXEH-JJX51 line will have the problem of heavy loading, up to 91.91%; JJXEH-JJX52 line will have the problem of overloading, up to 112.23%. Table 1. Xiong’an main transformer current under normal operation mode and N-1 calibration. operation mode

Main transformer line

active power/MW

Load rate

Normal operation heading

JJXEH-JJX51

1857.8

62.90%

JJXEH-JJX52

2320.2

78.42%

Xiong’an main transformer 1/3 disconnected

JJXEH-JJX51

2720.5

91.91%

JJXEH-JJX52

2424.0

81.91%

Xiong’an main transformer 2/4 disconnected

JJXEH-JJX51

1982.1

67.06%

JJXEH-JJX52

3320.7

112.23%

(2) Uneven distribution of 500 kV line currents and heavy and overload problems. According to the plan, in 2025, the existing 500kV Xiongdong-Bazhou double circuit

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line will be disconnected with the implementation of the project, which will lead to the lack of power support in Langfang area in the eastern part of Hebei South Network, the basic structure of the eastern 500 kV network frame is shown in Fig. 7, in which Gu’an, Luotu, Bazhou, Dacheng belongs to Langfang, and Langfang area is connected to the 500 kV line for the west of Beijing -Gu’an, Anding -Gu’an, Dacheng -Wuzhuang, Tobayuan -Bazhou.

Fig. 7. Basic structure of the 500 kV grid in the eastern part of the Hebei South Network.

The Langfang line currents in normal operation mode and during N-1 calibration are shown in Table 2, and the lines all have more serious uneven current distribution, with the Dacheng-Wuzhuang and Anding-Gu’an lines having too light currents, and the Torbayuan-Bazhou line having heavy currents. When the Beijing West-Gu’an line is disconnected, the current load ratio of the other line reaches 79.5%, which is close to heavy load. When the Toba-Yuan-Bazhou line is disconnected from one circuit, the current load ratio of the other circuit reaches 98.5 per cent, which will be overloaded if, with the planned development, a large number of new energy generators are connected to the line.

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4 Simulation Analysis of Flexible Control Equipment Access to Hebei Power Grid In order to solve the problems of Hebei South Network, this section is based on PSDBPA simulation software to study the impact of flexible power transformer and UPFC connected to 1000 kV and 500 kV of Hebei South Network on the current distribution, respectively. 4.1 Impact of 1000 kV Flexible Power Transformers on the Grid The main transformer of 1000 kV Xiong’an station is replaced by flexible power transformer, because there is no corresponding model of flexible power transformer in PSDBPA software, and the principle of controlling the trend of flexible power transformer is to control the voltage of the equivalent voltage source, thus controlling the voltage of the primary winding of the transformer, therefore, the effect of flexible power transformer is realised by changing the voltage of fixed tap on the primary side of the main transformer here instead. Under normal operation mode, the primary side fixed tap voltage of main transformer is 1050 kV, and in the most serious case of main transformer line current, considering the regulation ability of flexible power transformer on main transformer line current and economy, the fixed tap voltage selected in this paper is 1090 kV. Replace the main transformer of 1000 kV Xiong’an station with flexible power transformer, change the fixed tap voltage of the main transformer from 1050 kV to 1090 kV, and the trend of Xiong’an main transformer after adding flexible power transformer is shown in Table 3. Comparison of Tables 1 and 3 can be obtained, although in N-1 JJXEH-JJX52 line is still overloaded, but normal operation and N-1 when the line load factor have been reduced to a certain extent, and the active power are reduced, so the use of flexible power transformer can improve the system trend, while other measures can be taken to reduce

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Table 3. Xiong’an main transformer current after retrofitting flexible power transformer. operation mode

Main transformer line

active power/MW

Load rate

Normal operation heading

JJXEH-JJX51

1837.6

61.83%

JJXEH-JJX52

2289.6

76.63%

Xiong’an main transformer 1/3 disconnected

JJXEH-JJX51

2674.1

89.25%

JJXEH-JJX52

2392.5

80.00%

Xiong’an main transformer 2/4 disconnected

JJXEH-JJX51

1960.5

65.83%

JJXEH-JJX52

3256.2

108.55%

the active power of the line or increase the rated capacity of the main transformer and so on to further reduce the load factor. 4.2 Impact of 500 kV UPFC on the Grid Referring to the 220 kV UPFC project in Nanjing West Ring Network [4, 12–14] and the 500 kV UPFC project in Suzhou South [6, 15], two series converters and one shunt converter, two series transformers and one shunt transformer are also adopted for the UPFC retrofitted in Hebei South Network, with the converter capacity of the series side of the converter being 195 MVA, the shunt side of the converter being 300 MVA, and all three link transformers having a capacity of 300 MVA. The series side is connected to Tobayuan-Bazhou double circuit, and the shunt side is connected to 500 kV Bazhou bus, and the node voltage of the shunt side is maintained at the normal operation mode without UPFC [16, 17], i.e., the standardised value of 0.991, which can provide reactive power voltage support capacity in Langfang area. After the UPFC is installed, the line loading ratio under normal operation mode and N-1 calibration is shown in Table 4. Comparison of Tables 2 and 4 shows that the addition of UPFC to the TobayuanBazhou line is able to reduce the load factor of this line during normal operation and N−1. Especially, it can reduce the active power of 2214.5 MW to 1796.8 MW and the load ratio from 98.5% to 79.3% in the most serious case of tidal current, i.e., when Tobayuan-Bazhou disconnects one loop of the line, which greatly increases the transmission capacity of the section. Besides, it can be seen that after adding UPFC, the load ratio of three lines, Beijing West-Gu’an, Anding-Gu’an and Dacheng-Wuzhuang, is increased in normal operation and N−1, and UPFC transfers the tidal currents on Tobayuan-Bazhou to the other lines, which reduces the unevenness of tidal currents distribution to a certain extent. Comparing the node voltage before and after adding UPFC in the most serious case of line current, i.e., when Tobayuan-Bazhou disconnects a circuit, as shown in Fig. 8, the Bazhou node connected to the parallel side of the UPFC is able to maintain the set value of 0.991 pu, i.e., 520.3 kV; the voltages of the other plants and stations in Langfang area are all improved; the voltage of Tobayuan node is lowered from 527.5 to 519.9 kV, but within the range stipulated by the national voltage standard; the voltages of other plants and stations except Langfang area remain almost unchanged. Therefore, the addition of

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P. Yang et al. Table 4. Line load factor after adding UPFC.

UPFC can shift the line current and at the same time, it can also moderately increase the voltage of the area where UPFC is installed while keeping the voltage of other areas almost unchanged.

(a) Before adding UPFC.

(b) After adding UPFC.

Fig. 8. Node voltage before and after adding UPFC.

5 Conclusions This paper firstly introduces the basic structure, working principle and mathematical model of flexible power transformer and UPFC, then based on PSD-BPA simulation software and 2025 planning data, introduces the overview of Hebei South Network and its problems, and studies the impact of the above two devices on the tidal current distribution of Hebei South Network.

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(1) Aiming at the problem of heavy and overloaded main transformer of 1000 kV Xiong’an station, the fixed tap voltage is selected according to the tidal conveyance enhancement capacity, and the change of load ratio is compared before and after the retrofitting of flexible power transformer. The simulation results show that although the main transformer is still overloaded at N−1, the load ratio of all main transformer lines in Xiong’an station is reduced to a certain extent in normal operation and N−1, indicating that the flexible power transformer can control the current. (2) For the 500 kV Langfang area line tidal current heavy, overload problem, consider the most serious situation line installation UPFC, consider capacity utilisation and economic selection of capacity, compare the line tidal current changes before and after the addition of UPFC. Simulation results show that UPFC can reduce the line load ratio, increase the section transmission capacity, but also reduce the uneven distribution of the current, can be maintained in other areas of the voltage is almost unchanged, moderately increase the voltage in the area of the UPFC installed. The simulation results show that the flexible control equipment can solve the problems of uneven current distribution, overstepping the limit of the current and failing to meet the N-1 check, and improve the stability of the system. Acknowledgments. This work was funded by the State Grid of China, Hebei Electric Power Company Limited (SGHEJY00GHJS2100067).

References 1. Rahman, M., Ahmed, M.: UPFC application on the AEP system: planning considerations. IEEE Trans. Power Syst. Publ. Power Eng. Soc. 12(4), 1695–1701 (1997) 2. Choo, J.B., Chang, B.H., Lee, H.S., et al.: Development of FACTS operation technology to the KEPCO power network-installation and operation. In: Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference and Exhibition, 2008–2013. IEEE, ASIA PACIFIC (2002) 3. Uzunovic, E., Fardanesh, B., Hopkins, L., et al.: NYPA convertible static compensator (CSC) application phase I: STATCOM. In: Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference and Exposition, pp. 1139–1143. IEEE, Atlanta, GA, USA (2001) 4. Cai, H., Qi, W., Huang, J., et al.: Application of UPFC in Nanjing Western power system. Electric Power Construct. 36(08), 73–78 (2015). (in Chinese) 5. State Grid Corporation of Jiangsu Province: Unified Flow Controller Engineering Practice-Nanjing West Ring Network Unified Flow Controller Demonstration Project. China Electric Power Press, Beijing (2015). (in Chinese) 6. Xie, W., Cai, Y., Feng, Y., et al.: Analysis of application effect of 220 kV UPFC demonstration project in Shanghai Grid. Power Syst. Protect. Control 46(06), 136–142 (2018). (in Chinese) 7. Liu, G., Cai, H., Qi, W., et al.: Study on application of 500 kV unified power flow controller at southern power system of Suzhou. Power Cap. React. Power Comp. 46(06), 136–142 (2018). (in Chinese) 8. Zhao, G., Qiao, G., Li, W., et al.: A flexible power transformer. CN114884071A, Beijing (2022). (in Chinese) 9. Zheng, B.: Research on modular multilevel UPFC device-level control strategy. China Electric Power Research Institute, Beijing (2013). (in Chinese)

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10. Zheng, T., Wang, K., Zheng, Z., et al.: A review of research on power electronic transformers based on MMC topology. Proc. CSEE 42(15), 5630–5649 (2022). (in Chinese) 11. Tian, Z., Bai, S., Han, L., et al.: A novel double-loop voltage stabilization control strategy based on MMC-UPFC. Power Cap. React. Power Compen. 42(03), 105–111 (2021). (in Chinese) 12. Dou, F.: Study on the Application of Unified Trend Controller in 220kV Western Ring Network of Nanjing. North China Electric Power University, Baoding (2015). (in Chinese) 13. Zhen, H.: Study on the Application of Unified Trend Controller in Nanjing Power Grid. North China Electric Power University, Baoding (2017). 14. Wang, Y., Zhen, H., Chang, B., et al.: Research on the application of UPFC in Nanjing Western Grid. Jiangsu Electric. Eng. 35(01), 53–56 (2016). (in Chinese) 15. Yang, L., Cai, H., Wang, W., et al.: Application of 500 kV UPFC in Suzhou Southern Power Grid. Electric Power 51(02), 47–53 (2018). (in Chinese) 16. Liu, B., Zhang, X., Yu, X., et al.: Siting and capacity sizing methods for UPFC application in provincial grids. J. Power Syst. Autom. 33(01), 123–129 (2021). (in Chinese) 17. Shahgholian, G., Mahdavian, M., Janghorbani, M., et al.: Analysis and simulation of UPFC in electrical power system for power flow control. In: International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, pp. 62–65. IEEE, Phuket, Thailand (2017)

Short-Circuit Fault Section Location Method of Flexible Interconnected Distribution Network Based on Transient Component Similarity Hongxu Yin1 , Liang Song1(B) , Zhitong Xing1 , Wencong Chen2 , Ning Chu1 , and Chenxu Mao1 1 State Grid Dezhou Power Supply Company, Dezhou 253011, China

[email protected] 2 College of New Energy, China University of Petroleum (East China), Qingdao 266580, China

Abstract. The existence of soft normal open points (SNOP) in flexible interconnected distribution networks makes traditional fault location methods difficult to apply. This article proposes a method for locating fault sections in flexible interconnected distribution networks using waveform similarity of positive sequence current transient components. Firstly, considering the typical topology and control strategy of the system, analyze the fault characteristics of the flexible interconnected distribution network during short circuit faults. On this basis, the transient components of positive sequence current at different positions are extracted, and the waveform similarity is described by calculating cosine similarity. Finally, the Teager energy operator is used to accurately calibrate the fault time, and the intelligent distribution terminal is used to transmit information. By comparing the waveform similarity at different positions, a flexible interconnected distribution network short-circuit fault location criterion is constructed. The feasibility of the proposed method was verified through modeling and simulation, and the effects of fault location, fault type, transition resistance, and sampling frequency on the positioning results were analyzed. Keywords: Flexible interconnected distribution network · Flexible multi-state switch · Fault feature analysis · Transient components · Waveform similarity · Fault location method

1 Introduction The flexible interconnected distribution network utilizes soft normal open points (SNOP) to flexibly regulate the power flow between AC feeders, which can improve the flexibility, economy, and reliability of the system [1]. The different operating states of the system correspond to different control strategies of SNOP. When a fault occurs, the control strategy will have an undeniable impact on the fault characteristics, making traditional fault location methods for distribution networks not fully applicable [2]. The potential faults that may occur in the inverter itself further increase the complexity of system faults [3, 4], and considering the ability of power electronic devices to withstand © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 169–180, 2024. https://doi.org/10.1007/978-981-97-0865-9_19

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impulse currents, Research is needed to quickly and accurately locate faults in flexible interconnected distribution networks. At present, the fault handling of flexible interconnected distribution networks is mainly focused on the control strategy of SNOP [5, 6], and there is no relevant literature proposing a systematic fault location method. It can be combined with fault location and protection methods of similar structures such as circular distribution networks, flexible DC distribution networks, AC DC hybrid distribution networks, and AC power networks with inverter power sources connected. [7] transmit fault information through smart terminal units (STU) to achieve rapid fault localization and isolation in the circular distribution network. [8, 9] analyze and model the fault characteristics of inverters under dual loop control, and propose corresponding protection methods. [10] proposes a short-circuit current calculation method for flexible interconnected power grids based on the transient equivalent model of the current inner loop of voltage source inverters. [11] proposed a longitudinal protection method based on voltage waveform similarity comparison based on the output current and voltage characteristics after faults in AC/DC hybrid power grids. [12] proposed a protection method for AC/DC lines based on the comparison of traveling wave waveforms, based on the difference in waveform similarity between the traveling waves on both sides of the DC line during internal and external faults. The above methods utilize the positive or negative correlation characteristics of the voltage or current waveforms on both sides of the line to determine faults inside and outside the area. However, the voltage and current on both sides of the fault point in a flexible interconnected distribution network are not purely negative correlation characteristics, and effective methods are needed to identify and locate faults at different locations in the distribution network. This article analyzes the short-circuit fault characteristics of flexible interconnected distribution networks under the typical control strategy of SNOP. By calculating the cosine similarity of transient components in positive sequence current fault components at different positions, the similarity of waveforms is reflected. The Teager Energy Operation (TEO) is used to initiate fault localization and calibrate fault timing. By utilizing STU to transmit and analyze fault information, and comparing waveform similarity at different positions, a criterion for short circuit fault location in flexible interconnected distribution networks is constructed. Finally, the feasibility of the method and its ability to resist interference from multiple influencing factors were verified through modeling and simulation.

2 Fault Transient Characteristics Analysis of Flexible Interconnected Distribution Network 2.1 Flexible Interconnected Distribution Network Structure and Typical Control Strategy of SNOP In the flexible interconnected distribution network, SNOP interconnects the ends of two feeder lines and installs STUs in each Ring Main Unit (RMU). SNOP adopts a back to back voltage source converter (B2B VSC) structure composed of two-level voltage source converters [1, 13]. The structure of the flexible interconnected distribution network is shown in Fig. 1.

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Fig. 1. Typical structure of flexible interconnected distribution network

B2B VSC adopts internal and external dual closed-loop control. The outer loop inputs the control target and outputs the dq axis component target values idref and iqref of the VSC port current. The inner loop tracks and controls idref and iqref as the control targets, and the VSC outputs the modulated voltage fundamental component to achieve the control target. The typical control strategy of SNOP is: during normal operation, SNOP adopts DC voltage power control (Udc Q-PQ). After a fault occurs, the non-fault side controls the DC voltage, and at the same time, the fault side locks the outer loop directly using the current inner loop for control [14]. The structural diagram of the control system is shown in Fig. 2.

a b

Fig. 2. B2B VSC double closed loop control system

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2.2 Transient Characteristics Analysis of Short Circuit Fault in Flexible Interconnected Distribution Network When a fault occurs, in order to maintain the constant port voltage, the dq-axis current setting value of the VSC1 control system on the fault side suddenly changes [15]. It is known from [16] that there is a DC attenuation component in the d-axis current after the fault. Further considering the sudden change in the q-axis current, the dq-axis output current of VSC1 during three-phase short circuit can be obtained as follows:  id 1 (t) = I1 er1 (t−t0 ) + I2 er2 (t−t0 ) + I3 , t ≥ t0 (1) iq1 (t) = I4 er1 (t−t0 ) + I5 er2 (t−t0 ) + I6 In the formula, I 1 , I 2 , I 4 and I 5 are the initial values of the current transient component, I 3 and I 6 are the d-axis and q-axis current command values after the fault, r 1 and r 2 are the attenuation constants, and t 0 is the time of the fault occurrence. According to formula (1), after VSC1 three-phase short circuit, the DC attenuation component of current in dq coordinate system is represented as the power frequency sine attenuation component of three-phase current in abc coordinate system. The set value of q-axis current of VSC2 on the non-fault side does not change abruptly, and there is no fluctuation after the fault. According to [16], d-axis current has transient DC attenuation component, which is represented as power frequency sinusoidal attenuation component of three-phase current in abc coordinate system. According to [17], it can be seen that the power grid is regarded as an infinite high-power power source, and there is a DC attenuation component in the three-phase short-circuit current. Meanwhile, due to the control strategy being a single dq rotating coordinate system before and after the fault, only the positive sequence component is controlled. Therefore, the characteristics of the positive sequence current fault component during a two-phase short circuit are consistent with those of a three-phase short circuit. Extract the waveform similarity of the transient component of the positive sequence current fault component as a criterion for short-circuit fault location.

3 Short-Circuit Fault Section Location Method of Flexible Interconnected Distribution Network Based on Transient Component Similarity 3.1 Method for Calculating Waveform Similarity Cosine similarity is a common similarity judgment method in power systems, and its expression is shown in Eq. (2). n 

cos(x, y) = 

(xi · yi )  n n   xi2 yi2 i=1

i=1

i=1

(2)

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In the formula, vectors x = {x1 , x2 ,…, xn }, y = {y1 , y2 ,…, yn } represent two sets of waveform data respectively, n is the number of sampling points, i is the i-th sampling point, cos (x, y) is the cosine value of the angle between two vectors, and C represents cosine similarity in the following text. The range of cosine similarity values is [−1, 1]. When approaching 1, it indicates a positive correlation, indicating the same pattern. When approaching −1, it indicates a negative correlation, indicating the opposite pattern. When approaching 0, it indicates that the two are not related. The cosine similarity only reflects the correlation of the waveform change trend, which meets the requirements of this article for comparing the waveform similarity of positive sequence current transient components [11]. 3.2 Fault Location Initiation and Information Exchange This method uses the sudden change of any phase current at any position as the starting criterion, and simultaneously calibrates the fault time of the sudden change of three-phase current. TEO enhances the sudden change of fault current through differential operation, and more accurately identifies the fault time. The activation criterion expression is shown in Eq. (3). ψ[ik (t)] = [ik (t)]2 − [ik (t − 1)] · [ik (t + 1)] > ψset

(3)

In the formula, ik (t − 1), ik (t) and ik (t + 1) are the transient components of the kphase positive sequence current at three adjacent sampling points, and ψ set is the starting threshold value. When a short circuit fault occurs at time t, the TEO of the k-phase current is greater than the set value, and the fault location is quickly initiated and the time t at which the fault occurred is accurately calibrated. After the fault location is initiated, select the positive sequence current transient component data from a certain time window after time t, exchange fault information between adjacent STUs, and perform similarity calculation and analysis. The stations with different feeder lines adopt independent terminals to avoid misjudgment of fault positioning devices on both sides of SNOP. The measurement device data located in the same ring network cabinet is processed internally. The STU and its communication network are shown in Fig. 1. 3.3 Criteria for Identifying Internal and External Faults Feeder Fault. When a fault occurs on a feeder, the positive sequence current transient components with different characteristics are provided by the power grid and SNOP on both sides of the fault point. Therefore, the similarity of the positive sequence current transient components on both sides of the line can be calculated to determine whether it is a fault within the feeder area. The specific fault Discriminant is as follows:  [−1, cosset ), internal fault (4) cosL = cos(iL1 , iL2 ) ∈ [cosset , 1], external fault In the formula, cosL is the cosine similarity of the transient components of the positive sequence current at both ends of the feeder, iL1 and iL2 respectively represent

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the transient components of the positive sequence current at both ends of the AC feeder, cosset is the action setting value, when cosL is less than cosset , it is an internal fault, and when cosL is greater than cosset , it is an external fault. Bus or Branch Fault. When a fault occurs on the bus or its connected branch, the network side and SNOP side respectively provide different characteristics of positive sequence current transient components to the bus. Therefore, the similarity of the positive sequence current transient components of the feeder lines on both sides of the bus can be calculated to determine whether the fault is located on the bus or branch. The specific fault Discriminant is as follows:  1, cos(iBL1 , iBL2 ) ∈ [−1, cosset ) (5) cosBL = 0, cos(iBL1 , iBL2 ) ∈ [cosset , 1] In the formula, iBL1 and iBL2 respectively represent the positive sequence current transient components of the feeder lines on the grid side and SNOP side connected to the bus. When cosBL = 1, it is necessary to further determine that the fault is located on the bus or a certain branch; When cosBL = 0, it indicates that the fault is not on the bus or connected branch. Branch Fault. When a fault occurs on a branch, both the fault current on the power grid and SNOP side flows to the fault branch, and no current flows through the non-fault branch. Therefore, the transient characteristics of the positive sequence current on both sides of the feeder lines connected to the fault branch and bus are the same, while the transient characteristics of the positive sequence current on both sides of the feeder lines connected to the non-fault branch and bus are different. The specific fault Discriminant is as follow:  1, cos(iBL , iBSm ) ∈ [−1, cosset ) , m = 1, · · · , k (6) cosLSm = 0, cos(iBL , iBSm ) ∈ [cosset , 1]  (1, 0), internal fault (7) cosSm = (cosBL , cosLSm ) = (1, 1), external fault In the formula, iBL represents the sum of iBL1 and iBL2 , iBSm represents the positive sequence current fault component of the branch m connected to the bus, and k represents the total number of branches connected to the bus. CosSm = (1,0) indicates that the similarity between the positive sequence current transient components of the feeders on both sides of the bus is lower than the set value, while the similarity between the positive sequence current transient components of branch m and the positive sequence current transient components of the feeders on both sides of the bus is higher than the set value, indicating that the fault is located on branch m, and in other cases, it is an out of area fault. Bus Fault. When a fault occurs on the bus, no current flows through each branch, so the sum of the positive sequence current transient components of each branch and the positive sequence current transient components of the feeder connected to the bus is not

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consistent. The specific fault Discriminant given by combining Formula (5) and Formula (6) is as follows:  1, internal fault (8) cosB = cosBL ∩ cosLS1 ∩ · · · ∩ cosLSk = 0, external fault In the case of high similarity between the fault components of the positive sequence current mentioned above, the cosine similarity approaches 1 while leaving a certain margin, and the final setting is cosset = 0.98.

3.4 Fault Location Process This article designs a method for locating short circuit fault sections in flexible interconnected distribution networks based on transient component similarity, and the specific process is shown in Fig. 3.

ik (t )

2

ik (t )

ik (t )

cos(iL1 , iL2 ) [ 1, cosset )?

ik (t 1) ik (t 1)

set

cos(iBL1 , iBL2 ) [ 1, cosset )?

cos(iBL , iBSm ) [ 1, cosset )?

Fig. 3. Fault section location flowchart

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4 Simulation Analysis This article uses PSCAD/EMTDC simulation software to build a flexible interconnected distribution network model as shown in Fig. 1. 4.1 Parameter Settings The distribution line parameters are shown in Table 1. Table 1. Distribution line parameters Sequence component

Resistance/ (/km)

Inductance/ (mH/km)

Capacitance/ (µF/km)

Positive and negative sequence

0.17

1.21

0.0097

Zero sequence

0.23

5.48

0.0060

The parameters of the SNOP system are shown in Table 2. Table 2. SNOP parameters Parameters

Numerical value

Converter filter inductance/mH

0.5

Converter equivalent resistance/

0.05

DC capacitor/mF

10

DC capacitance voltage /kV

20

4.2 Analysis of Simulation Results When a fault occurs during the simulation setting of 0.2 s, the positive sequence current fault component of 0.22–0.26 s is processed, and the transient component characteristics of 0.24–0.26 s are analyzed and calculated. Fault Starting Current. When a short circuit fault occurs, there is a sudden change in current, and the sudden change in short-circuit current on the grid side is large. Usually, the sudden change in phase current on the grid side causes the fault location to start. The sudden change in phase A current is shown in Fig. 4. From Fig. 4, it can be seen that at the time of the fault, the TEO value of the grid side phase current suddenly changes, which can determine the occurrence of a short circuit fault and then initiate the fault localization.

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5

Fig. 4. TEO waveform of A-phase current at the network side during three-phase short circuit

Fig. 5. Waveforms of positive sequence current transient components on both sides of the fault section

Fault Side Feeder. The waveforms of the transient components of the positive sequence current on both sides of the fault section are shown in Fig. 5. From Fig. 5, it can be seen that the waveform characteristics of the positive sequence current transient components on both sides of the fault section are consistent with the analysis in Sect. 2.2, and have different variation patterns. The cosine similarity of the transient components of the two positive sequence currents calculated is −0.1768, which is lower than the set value and meets the fault criterion in the feeder area. The waveforms of the transient components of the positive sequence current on both sides of the non-fault section are shown in Fig. 5.

Fig. 6. Waveforms of positive sequence current transient components on both sides of the nonfault section

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From Fig. 6(a) and (b), it can be seen that the waveform of the positive sequence current transient component on both sides of the non-fault section has the same variation characteristics. The calculated cosine similarity is 1.0000, which is higher than the set value and meets the fault criteria outside the feeder area. Non-fault Side Feeder. The waveforms of positive sequence current transient component on both sides of a feeder line in a certain section on the non-fault side are shown in Fig. 7.

Fig. 7. Positive sequence current transient component waveforms on both sides of the non-fault feeder

From Fig. 7, it can be seen that the waveform characteristics of the positive sequence current transient components on both sides of each section the non-fault side are consistent. The calculated cosine similarity is 1.0000, which is higher than the set value, and there is no misjudgment on the non-fault side.

4.3 Analysis of Influencing Factors The accuracy of fault location needs to consider multiple factors. This method uses TEO to obtain accurate fault time and uses STU to achieve unified control through the terminal, which can avoid the impact of timing errors; Meanwhile, this method includes the judgment of short-circuit faults occurring at different locations. Therefore, only the effects of transition resistance and sampling frequency on the accuracy of fault location were verified, as shown in Table 3. When the bus fault and branch1 fault in the above table occur, the three cosine similarities corresponding to a fault scenario represent the positive sequence current transient components between the feeders connected to the bus, the sum of the faulty branch1 and the feeders on both sides of the bus, and the sum of the non faulty branch2 and the feeders on both sides of the bus. From the above table, it can be seen that different types of short circuit faults occur at different fault locations. By changing the values of transition resistance and sampling frequency, and calculating the cosine similarity between different locations, all of them meet the fault location criteria within the proposed fault location method. Therefore, this method has good resistance to the influence of transition resistance and sampling frequency.

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Table 3. Simulation results under different fault conditions Fault location

Type of short circuit

Feeder

Three phase Two phase Three phase

0

100

10

10

0

100

Bus

Two phase Branch1

Three phase Two phase

Transition resistance/ 

Sample frequency/ kHz

Cosine similarity

Fault interval

0

100

−0.1768

Internal

10

10

−0.0153

Internal

0

100

−0.5001

Internal

10

10

0.1708

Internal

−0.2539/0.3012/0.3081

Internal

0.0703/−0.2029/−0.2833

Internal

−0.4883/−0.1595/−0.1314

Internal

10

10

0.0217/0.2914/0.1121

Internal

0

100

0.3828/0.9934/−0.0658

Internal

10

10

0.0694/0.9505/−0.2819

Internal

0

100

−0.4834/1.0000/−0.1123

Internal

10

10

0.0248/0.9931/0.1102

Internal

5 Conclusion Based on the analysis of fault characteristics in flexible interconnected distribution networks, this article proposes a method for locating short circuit fault sections in flexible interconnected distribution networks based on transient component similarity. This method extracts the transient component of positive sequence current as fault information, and establishes a criterion for locating short circuit fault sections by calculating the cosine similarity between fault information at different locations. The effectiveness of this method and its ability to resist interference from multiple influencing factors were verified through simulation. This method only targets typical flexible interconnected distribution network topologies and SNOP control strategies, and further improvements are needed for more complex structures and scenarios. Acknowledgments. This research is supported by the Science and Technology Project of State Grid Shandong Electric Power Company (Research on Distribution Network Structure Optimization and Regulation Strategies Based on Flexible Interconnection, 520608220001).

References 1. Yang, H., Cai, Y.Y., Qu, Z.S., Deng, Y., Lu, Y., Zhao, R.X.: Key techniques and development trend of soft open point for distribution network. Autom. Electric Power Syst. 42(07), 153–165 (2018). (in Chinese)

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2. Zhu, M.L., Hang, L.J., Li, G.J., Jiang, X.C.: Protected control method for power conversion interface under unbalanced operating conditions in AC/DC hybrid distributed grid. IEEE Trans. Energy Convers. 31(1), 1–12 (2016) 3. Dong, C.Y., Koh, L.H., Jia, H.J., Ong, H.C., Zhang, Z., Wang, J.J.: Arc analysis for the interlinking AC/DC buses in hybrid AC/DC building microgrids. In: 2018 IEEE International Conference on Industrial Electronics for Sustainable Energy Systems (IESES), pp. 333–338 (2018) 4. Ge, B.C., Wu, X., Huang, L.C., Li, S.W.: Characteristic research of commutation failure for hybrid AC/DC system. In: 2nd International Conference on Power and Renewable Energy (ICPRE), pp. 56–60 (2017) 5. Zhang, G.R., Shen, C., Peng, B., Zhu, Y.M., Wang, C.L., Zheng, M.: Smooth switching strategy of flexible multi-state switch in the case of feeder fault. High Voltage Eng. 45(10), 3050–3058 (2019). (in Chinese) 6. Xu, F., Huang, X.M., Lu, Y., Zhang, Z.R.: AC fault ride-through strategy of a transformerless soft normally open point. Appl. Sci.-Basel. 12(13), 6773 (2022) 7. Sun, D., Zhang, Z.H., Zhao, Q.P., Long, M.M., Ren, J.Z.: Distribution automation based short-circuit fault location and isolation method for closed-loop distribution network with underground cable. Proc. CSU-EPSA. 30(10), 21–27 (2018). (in Chinese) 8. Xu, K.H., Zhang, Z., Liu, H.Y., Liu, W., Ao, J.Y.: Study on fault characteristics and its related impact factors of photovoltaic generator. Trans. China Electrotechn. Soc. 35(02), 359–371 (2020). (in Chinese) 9. Kuang, X.Y., Fang, Y., Guan, H.B., Li, J., Jia, K., Bi, T.S.: Full-time domain short circuit current calculation method suitable for power network with inverter-interfaced renewable energy source. Electric Power Autom. Equip. 40(05), 113–122 (2020). (in Chinese) 10. Su, Y.F., Cui, J.Y., Lin, K.F., Zhang, B., Peng, M.X., Sun, J.Y.: Analysis of equivalent model for short-circuit current calculation of flexible interconnected power grid. Eng. J. Wuhan Univ. 55(11), 1159–1166 (2022). (in Chinese) 11. Zhang, H.Z.: Longitudinal protection method of AC/DC hybrid system based on voltage wave similarity comparison. Shandong University (2022). (in Chinese) 12. Kong, H.: AC/DC line protection method based on waveform comparison of traveling wave. Shandong University (2022). (in Chinese) 13. Sun, Y., Zhang, J.W., Zhou, J.Q., Shi, G., Yang, X.W., Cai, X.: A novel multiport flexible interconnection switch for AC/DC hybrid distribution network. Proc. CSEE 1–13 (2022). (in Chinese) 14. Kong, X.P., Zhang, Z., Yin, X.G., Wang, F., He, M.H.: Study on fault current characteristics and fault analysis method of power grid with inverter interfaced distributed generation. Proc. CSEE 33(34), 65–74+13 (2013). (in Chinese) 15. Fang, Y.: Analysis and calculation of fault characteristics of power system with inverterinterfaced renewable power sources. North China Electric Power University (2020). (in Chinese) 16. Jja, K., Yang, B., Bi, T.S., Wu, W.Q., Zheng, L.M., Hou, Y.L.: Two port equivalent modeling method for back to back VSC fault transient calculation: CN112994072B (2022). (in Chinese) 17. He, Y.Z., Wen, Z.Y.: Power system analysis, vol. 1. Huazhong University of Science and Technology Press, Wuhan, China (2002). (in Chinese)

Thermal Layout Optimization of Power Devices on PCB Dan Luo, Yao Zhao, Zhiqiang Wang(B) , and Guofeng Li Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China [email protected]

Abstract. The layout of PCB power devices is a key factor affecting the temperature distribution of power electronics. However, the current targeted optimization methods suffer from large temperature calculation errors and optimization limitations. Therefore, this paper carries out a thermal layout optimization study of PCB power devices based on finite element and genetic algorithm, and verifies it. Firstly, this paper writes a MATLAB finite element program (hereinafter referred to as MFEP) for the initial layout temperature calculation of PCB power devices, and the error is found to be around 0.3% by comparing with the simulation results of ANSYS and the simulation time is reduced by about 71% compared with that of ANSYS. Then the optimization model is established. Finally, This paper uses MFEP and genetic algorithm for PCB power device thermal layout optimization, and ANSYS is used to verify the optimization results, and the maximum junction temperature of the MOSFETs on the PCB after optimization is reduced by about 19 °C compared with the initial layout, down to 83.3% of the initial layout. Keywords: Thermal layout optimization · PCB · finite element · temperature calculation

1 Introduction As an important part of power electronic equipment, PCB not only provides electrical connections between components, but also provides heat dissipation paths for components, and its layout rationality and reliability directly affect the performance of the equipment [1]. With the continuous advancement of power electronics technology, equipment is constantly developing in the direction of high frequency, small size, and high power density [2]. The increase in frequency leads to an increase in the loss of the device and the need for high power density leads to compression of space size, more compact power devices on PCBs, and more thermal coupling between devices. The temperature of the power devices on the PCB, especially the power devices in the middle area, increases significantly, greatly reducing their thermal performance, which in turn affects the reliability of the entire circuit board. Studies have shown that the reasonable layout of power devices on PCB can effectively reduce the temperature of power devices, thereby improving the reliability of equipment, so the optimization of thermal layout of PCB power devices is very important. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 181–188, 2024. https://doi.org/10.1007/978-981-97-0865-9_20

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Aiming at the optimization problem of thermal layout of PCB power devices, Huang Y et al. proposed a fuzzy model force-oriented algorithm, which equates the coupling effect of temperature between chips as the influence of repulsive force, believing that the repulsion is proportional to the power consumption of the chip and inversely proportional to the square of the distance between chips [3]. On this basis, Lee J proposed a thermal force-directed placement algorithm(TFPA), which mirrors the heat source in the PCB to transform the bounded thermal problem into a boundless thermal problem [4]. In summary, although the force-oriented algorithm is easy to implement, it does not take temperature as a direct evaluation index. Mingxiang Zang et al. proposed a simulated annealing and particle swarm mixing algorithm (SA-PSO) for thermal layout optimization. In this paper, the fitness function is obtained based on the thermal superposition model and the heat conduction equation. Then select the core temperature of the chip as the evaluation index, and get the corresponding optimization scheme. Finally, the validity of the optimization is verified by using finite element analysis (FEA) software [5]. SunWei et al. optimize the position of PCB components in an electric vehicle controller by using Tagushi, a local optimization method based on orthogonal experiments and SNR (Signal-to-Noise Ratio) design, and verify the validity of the optimization by simulation [6]. Li Tianming et al. optimized the layout of the thin-layer resistors in the embedded substrate by fuzzy genetic algorithm, and proved that the temperature distribution after optimization was more uniform through ANSYS simulation, which verified the feasibility of the algorithm [7]. Lianlian Wang et al. proposed a local grid model method, and used ant colony algorithm for device layout optimization [8]. The above literature has greatly promoted the research of PCB thermal layout optimization, but there are still some shortcomings, mainly in the following two aspects, (1) large errors in temperature calculation (2) in terms of layout optimization, the existing method uses the method of exchanging the position of components to obtain a better layout, and does not consider the influence of factors such as the spacing between devices and the distance between devices and the edge of the PCB on the optimization results. In view of the above shortcomings, this paper carries out a research on the thermal layout optimization of PCB power devices based on MFEP and genetic algorithm. In this paper, the temperature simulation of the initial PCB layout is performed using ANSYS and MFEP respectively to verify the accuracy of the MFEP temperature simulation. Then, this paper uses MFEP and genetic algorithm to optimize the horizontal and vertical coordinates of the power devices on the PCB to obtain the optimal layout.

2 Temperature Calculation of PCB Power Devices with Initial Layout 2.1 Establishment of Simulation Model The device model used in this paper is IPD320N20N3, and the open-capped result is shown in Fig. 1(a). The model of this MOSFET is created in SpaceClaim as shown in Fig. 1(b). In order to facilitate the simulation optimization, the model is simplified with removing the pins, bonding wires, and MOS shells and other irregular parts that have a

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small impact on the MOS junction temperature, and the simplified results are shown in Fig. 1(c).

(a) Open-capped result

(b) Device model in exploded view

(c) Simplified model

Fig. 1. Model of MOSFET.

The PCB used in this paper is a 2-layer board with the length of 100 mm, width of 50 mm and thickness of 1.6 mm. The thickness of the top copper layer and the bottom copper layer are 1oz. The PCB is placed with 6 MOSFETs, which are arranged uniformly at equal spacing. Table 1. Initial coordinates of MOSFETs. x(mm)

y(mm)

chip 1

30.85

13.4

chip 2

46.95

13.4

chip 3

63.05

13.4

chip 4

30.85

30

chip 5

46.95

30

chip 6

63.05

30

In the view of Fig. 1(a), the upper right corner of the MOSFET device housing is selected as the coordinate reference point, and the initial coordinates are shown in Table 1.The thermal conductivity of materials used in this paper is shown in Table 2 [9–11]. Table 2. Thermal conductivity of materials. Material

Thermal Conductivity W/(m·K)

copper

393

FR4

0.29

silicon

112

solder

57

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2.2 Temperature Calculation Temperature calculations are performed using the governing equations for the heat transfer problem based on Fourier’s law of heat transfer and the law of conservation of energy,       ∂ ∂ ∂ ∂T ∂T ∂T ∂T kx + ky + kz + Q = ρc (1) ∂x ∂x ∂y ∂y ∂z ∂z ∂t where T is the transient temperature of the object, ρ is the density of the material in kg/m3 , c is the specific heat capacity of the material in J/(kg·K), k x , k y , and k z are the coefficients of thermal conductivity of the material along the x, y, and z directions respectively in W/(m·K), Q is the intensity of the heat source of the power device in W/m3 . Since the steady state temperature is calculated in this paper, ∂T =0 ∂t

(2)

The time-dependent transient heat transfer equation degenerates into the steady state heat transfer equation, which can be obtained as       ∂ ∂ ∂ ∂T ∂T ∂T kx + ky + kz +Q =0 (3) ∂x ∂x ∂y ∂y ∂z ∂z Heat transfer problems generally have three types of boundary conditions, respectively, the temperature boundary, heat flow density boundary and convective heat transfer boundary, this paper focuses on the consideration of convective heat transfer of the power device, at this time the control equation of the external boundary of the power device is kx

∂T ∂T ∂T nx + ky ny + kz nz = hc (Tamb − T ) ∂x ∂y ∂z

on S

(4)

Where nx , ny , and nz is the cosine of the normal direction outside the boundary, hc is the convective heat transfer coefficient between the power device and the external gas in W/(m2 ·K), T amb is the ambient temperature, S is the convective heat transfer surface of the power device. The temperature calculation in this paper is mainly divided into two parts, the first part is based on ANSYS simulation software, and the second part is based on MFEP. (1) The model is imported into ANSYS for temperature simulation, the convection coefficient is set to 24 W/(m2 ·°C), the power consumption of the chip is set to 2 W, and the initial temperature is 22 °C. The temperature distribution cloud diagram of the initial layout is obtained as shown in Fig. 2. The simulation takes about 2 min (the computer is with Intel Core i7-8550U @ 1.80 GHz quad-core), and the optimization requires thousands of temperature calculations, which has a high time cost. (2) Use MFEP to carry out the temperature calculation for the initial layout of PCB power devices, the main steps are as follows.

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Fig. 2. Temperature Distribution Cloud Map of ANSYS simulation

a. According to the model, six cuboids with the same thickness as the actual and the same length and width as the PCB are built in sequence. From bottom to top, they represent the bottom copper layer of the PCB, FR4, the top copper layer of the PCB, the copper substrate of the chip, the solder layer of the chip and the chip layer respectively. b. Grid division. c. Set the heat dissipation coefficient of the external surface of the model to be 24W/(m2 ·°C), the same as that of ANSYS simulation. d. According to the device coordinates and the size information of the chip copper substrate, chip and solder, the segmented mesh is divided into regions, and the corresponding material properties are assigned. For the mesh that is not in the region, the material is set as air. e. Apply power to the grid in the chip area. f. Calculate the temperature. According to the calculation of MFEP, the maximum junction temperature of MOSFETs on PCB is 117.6623 °C. Compared with the simulation result of ANSYS 118.02 °C, the error is about 0.3%. The calculation time is approximately 35 s (computer model remains the same as above), and the simulation speed is approximately 71% faster than ANSYS, which will greatly reduce the time required for optimization.

3 Thermal Layout Optimization of PCB Power Devices Based on MFEP 3.1 Establishment of Optimization Model In this paper, a total of 12 variables of the horizontal and vertical coordinates of 6 MOSFETs device reference points are taken as the optimization independent variables, and the maximum junction temperature of 6 MOSFETs is minimized as the optimization goal, and the optimal layout is obtained by genetic algorithm. The optimization diagram is shown in Fig. 3. The optimization objectives and constraints are shown in Eq. (5).  Min max(Temp1, · · · , Temp6) (5) s.t. min ≤ xi ≤ max, min ≤ yi ≤ max, i = 1 · · · 6 The optimization variables and their optimization range are shown in Table 3.

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2

3

1

6

5

4

Fig. 3. Schematic diagram of thermal optimization of layout Table 3. Optimization variables and their ranges x i min(mm) x i max(mm) yi min(mm) yi max(mm) 1 3

91

3

40.5

2 3

91

3

40.5

3 3

91

3

40.5

4 3

91

3

40.5

5 3

91

3

40.5

6 3

91

3

40.5

3.2 Optimization Results In this paper, genetic algorithm is used for optimization, setting the number of genetic algorithm populations as 100 and the number of population generations as 150, obtaining the optimization iteration curve as shown in Fig. 4. 103 102 101

Temperature

100 99 98 97 96 95

0

20

40

60

80

100

120

140

Generation

Fig. 4. Iteration curves of optimization

As can be seen from Fig. 4, the maximum junction temperature of the MOSFETs decreases very rapidly in the first 22 generations; in the 22nd–46th generations, the maximum junction temperature is basically unchanged, and then starts to decrease slowly in the 46th–90th generations until it stabilizes, and the final temperature is 95.678 °C. The coordinates of the optimized MOSFETs are shown in Table 4.

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Table 4. Optimal coordinates x(mm)

y(mm)

chip 1

5.4065

27.0562

chip 2

77.2750

8.6535

chip 3

39.1766

34.9755

chip 4

85.5738

30.6299

chip 5

51.1059

15.0550

chip 6

25.2501

6.9637

According to the coordinates shown in Table 4, the model is built in SpaceClaim and substituted into ANSYS for temperature simulation, the parameter settings are kept consistent with those in 2.2, and the temperature cloud is obtained as shown in Fig. 5.

Fig. 5. Temperature Distribution Cloud Map of ANSYS simulation after layout optimization

As can be seen in Fig. 5, the maximum junction temperature of the MOSFETs after layout optimization is 98.335 °C. The error is 2.7% compared to the temperature of 95.678 °C calculated by MFEP in the previous section. The ANSYS simulation temperature is taken as a standard for comparison and the temperature comparison before and after optimization is shown in Table 5. Table 5. Temperature comparison before and after layout optimization

Temperature(°C)

Before optimization

After optimization

Temperature decrease

118.02

98.335

19.685

As can be seen from Table 5, the maximum junction temperature of the MOSFETs on the PCB is reduced from 118.02 °C before optimization to 98.335 °C after optimization, which is a reduction of 19.685 °C, down to 83.3% of the original.

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4 Conclusions The main results of this paper are as follows, (1) Compared with ANSYS, MFEP takes less time while maintaining calculation accuracy. (2) In this paper, the thermal layout optimization method of PCB power devices based on MFEP and genetic algorithm is verified by ANSYS simulation, which can reduce the maximum junction temperature of MOSFETs on PCB by about 19 °C, to 83.3% of the original, which effectively proves the importance of thermal layout optimization of power devices on PCB and the effectiveness of the adopted method. The disadvantage of this paper is that it only considers the influence of PCB power device heat generation in the optimization process, and does not consider the influence of electromagnetic compatibility, which needs to be improved in practical application.

References 1. Chen, Y: Analysis and research on thermal-force coupling performance of a vehicle controller PCB board. In: 3rd International Conference on Electron Device and Mechanical Engineering (ICEDME), pp. 373–376 (2020) 2. Jieyang, N., Ye, H., Shen, D.D.,et al.: A novel optimization algorithm for thermal design of MCMs. In: Chinese Control And Decision Conference (CCDC), pp. 1567–1570 (2020) 3. Huang, Y.J., Fu, S.L.: Thermal placement design for MCM applications. J. Electron. Packag. 122(2), 115–120 (2000) 4. Lee, J.: Thermal placement algorithm based on heat conduction analogy. IEEE Trans. Compon. Packag. Technol. 26(2), 473–482 (2003) 5. Zang, M., Wang, M., Lai, X., et al.: Thermal layout optimization of stacked chips based on hybrid algorithm of simulated annealing and particle swarm. In: Proceedings of 2012 2nd International Conference on Computer Science and Network Technology, pp. 1456–1460. IEEE (2012) 6. Wei, S., Ye, L., Shaokun, Z., et al.: Optimal design of pcb layout based on thermal analysis using taguchi method. In: 3rd Asia Energy and Electrical Engineering Symposium (AEEES), pp. 198–202. IEEE (2021) 7. Li, T., Zhang, R., Huang, C.: Thermal placement optimization for embedded resistances based on orthogonal design and fuzzy genetic algorithm. In: 16th International Conference on Electronic Packaging Technology (ICEPT) (2015) 8. Wang, L., Lu, G., Yang, K.: Thermal optimization of electronic devices on PCB based on the ant colony algorithm. In: International Conference on Electronics Technology (ICET), pp. 55–59. Chengdu, China (2018) 9. Ma, M., Guo, W., Yan, X., et al.: A three-dimensional boundary-dependent compact thermal network model for IGBT modules in new energy vehicles. IEEE Trans. Industr. Electron. 68(6), 5248–5258 (2020) 10. Heat Capacity of Epoxy Molding Compound [EB/OL]. https://www.caplinq.com/blog/heatcapacity-of-epoxy-molding-compound_102/. Accessed 24 July 2023 11. Shen, Y., Wang, H., Frede, B., et al: Thermal modeling and design optimization of PCB Vias and pads. IEEE Trans. Power Electron. 35882–35900 (2020)

Calculation of Dead Time in Full-Bridge Converters Considering MOSFET Parasitic Capacitance Lei Xu, Fuchao Lu, and Zhenquan Zhang(B) School of Physical Science and Technology Southwest, Jiaotong University, Chengdu 610031, China [email protected]

Abstract. Currently, the calculation of dead time in a full-bridge Class-D zerovoltage switching (ZVS) converter is mainly based on the snubber capacitance structure connected in parallel with the fixed capacitance switching devices. There are few analyzes for calculating the dead time for Class-D full-bridge converters using the parasitic capacitance of the switching devices as the snubber capacitance. Under high-frequency operating conditions, too short or too long a dead time can cause the Class-D full-bridge converter to lose ZVS, resulting in significant power loss or even damage to the device. Therefore, this paper analyzes the operation of a Class-D full-bridge converter using the parasitic capacitance of the switching devices as the snubber capacitance, and calculates a suitable dead time. Then, a prototype 4 MHz Class-D full-bridge converter based on silicon carbide devices is developed, and the experimental results show that setting the dead time according to the calculation method proposed in this paper ensures the operation of the prototype under ZVS conditions. Keywords: Class-D · full-bridge converters · zero voltage switching · dead time calculation · MHz

1 Introduction With the application and advancement of third-generation semiconductor devices, the switching frequency of converters has also increased, and miniaturization, high power density, and high efficiency have become inevitable trends [1, 2]. However, at high frequencies, converters are more sensitive to the parasitic parameters of switching devices. For this reason, researchers have applied resonant soft-switching technology to converters, which controls the switches to achieve zero voltage switching (ZVS) so that converters operating at MHz frequencies function properly and achieve high conversion efficiency. Without ZVS, the energy stored in the parasitic capacitance is directly released, resulting in significant efficiency losses, serious electromagnetic interference problems, and rapid device degradation due to heat generation at the switching devices. References [3, 4] propose Class-D half-bridge and full-bridge converters for driving inductively coupled plasma (ICP) that achieve ZVS at 3 MHz and drive ICP efficiently, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 189–196, 2024. https://doi.org/10.1007/978-981-97-0865-9_21

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analyzing the ZVS region of the converters. In references [3, 4], the influence of device intrinsic parasitic capacitance is approximately ignored by connecting a larger fixed value snubber capacitance in parallel at both ends of the switching devices. However, the parallel capacitor approach reduces the ZVS operating range of the converter and makes ZVS implementation more difficult because more energy is required to charge and discharge the parallel capacitor. Using the inherent parasitic capacitance of the switching devices to achieve ZVS reduces the volume, simplifies the circuit structure, and increases the power density. In this paper, the ZVS dead time of a full-bridge Class-D converter using the inherent parasitic capacitance of silicon carbide devices as a snubber capacitance is calculated and verified by experiments.

2 Topology and Operating Principle of Class-D Full-Bridge Converter Based on Silicon Carbide Devices The topology structure of the Class-D full-bridge converter based on silicon carbide devices is shown in Fig. 1. The main component consists of a full bridge structure with four silicon carbide devices. Coss1 ~Coss4 represent the parasitic capacitance of the silicon carbide switching devices. Vdc is the DC voltage source of the Class-D fullbridge converter, and the load is formed by the series connection of the capacitor Cr , the inductor L and the resistor R.

Fig. 1. The topology structure of a Class-D full-bridge converter based on silicon carbide devices

The operation of the Class-D full-bridge converter can be divided into four modes. Mode 1: Before time t1 , the silicon carbide devices S1 and S4 are conducting. At this time, the voltages at switches S1 and S4 (Vs1 and Vs4 ) are zero, while the voltages at switches Vs2 and Vs3 are Vdc . The output voltage Vac is positive; Mode 2: From time t1 to t2 , the converter enters a dead time in which switches S1 to S4 are off. Due to the presence of resonant inductance L, the current direction remains positive. The resonant circuit current iAC charges Coss1 and Coss4 and discharges Coss2 and Coss3 . The voltages Vs1 and Vs4 gradually increase to Vdc , while the voltages Vs2 and Vs3 gradually decrease to zero. At this point, switches S2 and S3 can be turned on to achieve zero voltage switching (ZVS); Mode 3: The silicon carbide devices S2 and S3 are conductive, and the current iAC changes from positive to negative, similar to mode 1; Mode 4: When entering dead time again, switches S1 to S4 are turned off, similar to mode 2.

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3 Conditions for ZVS in Class-D Full-Bridge Converters 3.1 The Relationship Between ZVS and Resonant Load From the typical voltage and current waveforms of the Class-D full-bridge converter shown in Fig. 2, it can be seen that to achieve ZVS, the resonant current is required to charge and discharge the parasitic capacitance of the devices. At time t1 , switches S1 and S4 are turned off, and in order to charge the parasitic capacitance Coss1 and Coss4 and discharge Coss2 and Coss3 , the direction of the resonant current must be positive. Therefore, it must be ensured that the resonant circuit voltage precedes the current, which means that the resonant load must be inductive.

0

Fig. 2. Schematic diagram of voltage and current waveforms in a full-bridge converter

If fload < fs , the resonant load is inductive and satisfies the ZVS condition. However, when fload >fs , the resonant load becomes capacitive and the current is ahead of the voltage. The resonant current cannot fully charge and discharge the parasitic capacitance of the device within the dead time, so that ZVS cannot be achieved. 3.2 The Relationship Between ZVS and Dead Time A too short dead time duration leads to the waveform shown in Fig. 3(a). In this scenario, the resonant current cannot fully charge and discharge the parasitic capacitance of the switching devices within the dead time duration. The voltage across the switching devices has not yet dropped to zero before the switch drive voltage arrives, resulting in direct conduction through the devices and preventing ZVS. The ideal waveform for the dead time duration is shown in Fig. 3(b), where the resonant current fully charges and discharges the parasitic capacitance of the switching devices within the dead time duration and the voltage across the switching devices drops precisely to zero, resulting in ZVS.

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Fig. 3. Different dead time voltage and current waveform diagrams

With a slightly longer dead time duration is shown in Fig. 3(c), the resonant current continues to fully charge and discharge the parasitic capacitance of the switching devices. Since the direction of the resonant current remains unchanged, the body diode of the switching devices conducts during this time and limits the voltage across the switching devices to the forward voltage drop of the diode, which is negligible. In this case, ZVS is also achieved. An excessively long dead time duration is shown in Fig. 3(d), causes the resonant current to cross zero due to the extended duration within the dead time period. This change in current direction affects the charging and discharging of the parasitic capacitance of the switching devices, resulting in alternate discharging and charging cycles and thus voltage dips. Therefore, too long a dead time duration also prevents ZVS. 3.3 Fitting of Parasitic Output Capacitance of Devices According to references [5–7], the value of parasitic output capacitance can be fitted by Eq. (1). C0 Coss =  λ 1 + kv

(1)

Within the equation, the coefficients k and λ serve as adjustable parameters that can be fitted to the specific parasitic capacity curve. The variable v represents the drainsource voltage, while C0 denotes the capacitance at zero voltage. The fitting results for the parasitic capacitance curve are as follows. ⎧ 1550 ⎪ ⎨ , 0 < Vds ≤ 400V Vds 0.6 ) Coss = (1 + 3.6 (2) ⎪ ⎩ 75, 400 < Vds ≤ 900V In the process of operation, because the voltage across the device changes from the input voltage to zero, and the parasitic capacitance of the device also changes with the voltage Vds , the parasitic capacitance of the device cannot be regarded as a constant value at a certain voltage. Therefore, equivalent output capacitor Ceq should be used to calculate the ZVS dead time [8, 9].  Vds Coss (Vds )dVds Ceq = 0 (3) Vds

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4 Class-D Full-Bridge Converter ZVS Dead Time Calculation 4.1 Calculation of Minimum ZVS Dead Time As shown in Fig. 2, the direction of current in the loop at time t1 is indicated by the red arrow in the figure. Before time t1 , S1 and S4 are on, and S2 and S3 are off. At this time, VCoss1 = VCoss4 = 0, VCoss2 = VCoss3 = Vdc ; S2 and S4 are off at time t1 and enter dead time. The inductance in the loop continues to flow, and the current direction in the resonant cavity continues to flow as shown in the figure. At this time, the current discharges Coss3 and charges Coss1 (Fig. 4). An analysis of switch S1 and S3 , resulting in VCoss1 du = Coss1 dt t

(4)

VCoss3 du = −Coss3 dt t

(5)

i1 = C i2 = C

Apply KCL to node a, resulting in iAC = Coss1

dVCoss1 dVCoss3 − Coss3 dt dt

(6)

According to the fitting result of the previous parasitic capacitance, it can be considered that Coss1 = Coss3 = Ceq , and integrating the current between time t1 ~t2 can obtain the resonant current charge Q in the dead time t1 Q= iAC dt = 2Vdc Ceq (7) t2

Fig. 4. Modal analysis diagram in dead time

Under the approximation of a high enough quality factor [10], the effective current IAC can be expressed in terms of the amplitude of first harmonic of the voltage. The first (1) Fourier coefficient of a voltage waveform VAC can be calculated resulting in: √ 2 2 (1) sin c(fs τ ) VAC = Vdc (8) π

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IAC =

√ (1) VAC Vdc 2 2 sin c(fs τ ) = |ZAC | |ZAC | π

The resonant tank current iAC(t) can be expressed as: √ iAC(t) = 2IAC sin(ωt − ϕ) Substituting Eqs. (9) and (10) into Eq. (7) and simplifying, resulting in: √  2IAC

2 sin(π fs τ ) sin(ϕ) = 2Vdc Ceq Q= ω |ZAC |2 Ceq fs π = 2(fs τ ) sin c2 (fs τ ) XAC

(9)

(10)

(11) (12)

By solving Eq. (12), we determine the minimum dead time τmin . 4.2 Calculation of Maximum ZVS Dead Time From the analysis in Sect. 3.1 it is known that the switching device must be turned on before the resonance current commutates, before the corresponding time t3 in Fig. 2. The maximum value of the dead time τmax = t3 − t1 . tϕ in Fig. 2 represents the time corresponding to the phase difference angle between voltage and current: tϕ =

ϕ 1 360 fs

τmax = t3 − t1 = tϕ +

(13) τmin 2

(14)

5 Experimental Results In order to verify the feasibility of the ZVS dead time range, a full-bridge Class-D converter prototype was produced. The resonant circuit was composed of a vacuum capacitor Cr = 300 pF, an inductor L= 6.98 uH and R= 10  connected in series. The four silicon carbide devices are controlled by two complementary PWM waves generated by the FPGA control platform. Switching frequency fs = 4 MHz, DC input voltage Vdc = 30 V, the measured waveform is shown in Fig. 5 below. Solving Eqs. (12) and (14), the minimum value of the dead time is τmin = 52 ns, the maximum value of the dead time is τmax = 79 ns, and the range of the dead time is 52 ns < Td Eg) is absorbed by the perovskite material, and then the electrons are excited from the top of the valence band to the bottom of the conduction band, forming an electron-hole pair with Coulomb barrier. The second stage is the diffusion of carriers, driven by the built-in electric field, electrons and holes diffuse towards the negative and positive electrodes inside the perovskite, respectively. The third stage is carrier transport, in which the electrons specifically migrate through the interface between the perovskite layer and the electron transport layer, the holes traverse the interface between the perovskite layer and the hole transport layer, the electrons and holes are extracted and subsequently transported by their corresponding functional layers. In the fourth stage, carriers are collected by electrodes. In this way, a stable loop current is formed inside the battery.

Fig. 2. (a) Schematic diagram of photovoltaic effect process of solar cell, (b) J-V curve of solar cells [5].

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The above process is based on the ideal state, but during the operation of the device, carrier recombination, ion migration and material decomposition will also be encountered, which will have a great impact on the stability of the perovskite device. Therefore, in addition to improving the perovskite conversion efficiency, the key to realizing the commercial application of perovskite cells is to improve the stability of perovskite devices. Perovskite solar cells evolved on the basis of the mesoscopic structure of DSSC, in which dye sensitizers are replaced by halide perovskites. After that, planar device structures were developed, in which the perovskite absorber layer was between the electron transport layer and the hole transport layer (Fig. 3). Depending on the stacking order, it can be divided into two structures: n-i-p is called the planar formal structure, and the p-i-n structure is called the planar inverted structure.

Fig. 3. Typical device structures of perovskite solar cells: (a) Regular, (b) Mesoporous and (c) Inverted structure [6].

The n-i-p structure is mainly composed of a conductive substrate FTO, an n-type electron transport layer (TiO2 or SnO2 ), a perovskite photo absorbing layer, a p-type hole transport layer (Spiro-OMeTAD or P3HT), and metal electrodes. In the mesoporous structure of the n-i-p configuration, nanoparticles (NPs) are sintered on the TiO2 layer to form a porous structure, and then the perovskite layer is filled in the voids of the mesoporous TiO2 layer. Planar structures offer many advantages over mesoporous structures, such as ease of handling and low-temperature preparation, no vacuum deposition required, and compatibility with roll-to-roll device manufacturing. 2.3 Preparation Process The quality of perovskite films is the most critical factor in determining the performance of perovskite solar cells (PSCs). The morphology, uniformity, crystallinity, and phase purity of the film are closely related to the preparation process, so the preparation process will directly affect the performance of PSCs. Figure 4 shows the principle diagram of the deposition methods of perovskite thin film. One-Step Solution Deposition Method. In laboratory settings, the one-step solution deposition technique is widely employed to fabricate perovskite films. This method involves mixing and dissolving the precursor components in an aprotic polar organic solvent, such as N, N-dimethylformamide (DMF), to form the precursor solution. The solution is then applied onto the substrate using the spin-coating method. Subsequently, the coated film undergoes thermal annealing treatment to yield the desired perovskite films. What’s more, anti-solvents such as toluene, chlorobenzene, or ether are often used

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to induce homogeneous nucleation in this process. One-step solution deposition method is simple to perform in the laboratory, while anti-solvent can also be used as an additive carrier for defect passivation strategies. Two-Step Solution Deposition Method. The perovskite film prepared by one-step solution deposition method has poor surface coverage and inevitably exhibits filmforming inhomogeneity. To avoid this, a two-step solution deposition method was used to prepare perovskite films, which has better reproducibility. The DMF solution of PbI2 is first coated on the substrate at 70 °C through the spin-coating method, and then allow it to react with the MAI isopropanol solution (MAI isopropanol solutions usually react with PbI2 by spin-coating or immersion method), finally, a perovskite film is formed by thermal annealing. Compared with the one-step solution deposition method, the twostep sequential solution deposition method can eliminate the influence of the surrounding environment, thereby controlling the morphology of perovskite film better. Vacuum Thermal Evaporation Deposition Method. Vacuum thermal evaporative deposition method usually rapidly heats and sublimates PbI2 and MAI compounds and then deposits them on the substrate by dual-source co-evaporation method. Compared to solution treatment methods, this technology can easily control the composition and thickness of the film and has high reproducibility. The perovskite films prepared by Vacuum thermal evaporative deposition method have uniform texture, high crystallization quality with no pinholes, and nanoscale crystal structures. The dual-source co-distillation vacuum deposition method is difficult to control the deposition rate of MAI. In order to solve this problem, the sequential deposition method is used. In this method, PbI2 solid films are prepared by vacuum thermal evaporation firstly, and then perovskite films are obtained by reacting PbI2 solid films by vacuum deposition with MAI gas phase. Nevertheless, this fabrication method relies on the utilization of costly equipment. However, it retains the advantage of producing large-area films without the need for toxic solvents, making it a promising approach for the manufacturing of perovskite components.

Fig. 4. Principle diagram of the deposition methods of perovskite thin film: (a) One-step spincoating method; (b) Two-step spin-coating method; (c) Dual-source vapour deposition [7].

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Knif-Coating Technique. Knif-coating technique is at low-cost, simple, highly productive, compatible with roll-to-roll manufacturing and suitable for PSCs large-scale production. Knif-coating is a technology in which a certain amount of perovskite precursor solution is applied to the substrate and spread out through a high-speed linear sliding scraper to achieve the preparation of perovskite films. This technology does not require the aid of any specific instrumentation. In the knif-coating process, the substrate can be heated or purged with nitrogen in order to obtain a uniform, dense, crystalline and porous film. The heated substrate and flowing air flow increase the solvent evaporation rate, promoting nucleation and growth of crystals. This method controls the crystallization and thickness of the film by adjusting the gap between the scraper and the substrate, the concentration and solvent class of the precursor solution, the movement speed of the scraper, and the purge angle and speed of nitrogen. In particular, this method requires relatively few precursor solutions compared to traditional solution spin coating techniques. Slit Coating Technology. Slit coating technology is similar to the previously described scraping technique, except that slit coating technology provides the scraper with a precursor injection slit, allowing a more uniform diffusion of the precursor solution to the substrate. Compared with the scraping technique, this technique requires a larger amount of precursor solution, but results in a better film quality.

Fig. 5. The blade coating of a perovskite film and the evaporative and Landau–Levich regimes [8].

The blade coating process for forming a perovskite film is illustrated in Fig. 5. This process occurs under the Landau-Levich regime, where the solvent evaporates, and the film thickness, denoted as h, is controlled. In Fig. 6, the right part provides a more detailed depiction of the evaporative and Landau-Levich regimes. Several parameters are defined: v represents the speed of the blade or substrate. Qevap represents the flow rate of solvent leaving the box through evaporation; Qsolvent represents the flow rate of solvent entering the box; Jfilm represents the outward mass flux within the film; Jsolute represents the inward mass flux in the solution; d represents the height of the meniscus; z represents the vertical direction; θa , θb and I are geometric parameters used in the calculation of the dynamic meniscus.

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3 Photoelectric Conversion Efficiency and Stability 3.1 Further Improvement of Photoelectric Conversion Efficiency Photoelectric conversion efficiency is the most important index to measure the performance of perovskite solar cells. To enhance the performance of devices, researchers have conducted extensive research in solvent engineering, interface engineering, and additive engineering, tandem cell devices and other aspects. Solvent Engineering: Achieving high-quality perovskite films is crucial for the efficiency of perovskite solar cells. Solution processing and preparation techniques are widely employed in perovskite solar cell research due to their low cost and ability to produce dense, uniform perovskite films with high crystallinity. During the dissolution process of perovskite precursors, solvents not only dissolve solutes but also participate in the perovskite crystallization process. Solvents play multiple roles in controlling reaction rate, nucleation growth, and grain coarsening. Additionally, solvent properties such as boiling point, vapor pressure, Lewis basicity, molecular size, and miscibility significantly impact the formation process of perovskite films. Therefore, solvent engineering is an effective method for laboratories to enhance the properties of perovskite films [9]. Interface Engineering: Typical perovskite solar cells consist of two charge transport layers (electron transport layer and hole transport layer) above and below the perovskite layer. However, non-radiative recombination centers can form at the interfaces, leading to increased carrier recombination, open-circuit voltage loss, and reduced device photoelectric conversion efficiency and stability. Hence, interface engineering is an effective approach to further improve the photoelectric conversion efficiency [10]. Additive Engineering: Additives, such as salts and polymers, are widely employed in the preparation of efficient, stable, and non-hysteresis perovskite solar cells. Additive engineering is an effective means to optimize perovskite solar cells. Different additives exhibit diverse coordination abilities with Pb2+ and I−, allowing for a wide range of additive types [11]. Tandem Cells: To surpass the Shockley-Queisser limit of single-junction solar cells, researchers have focused on perovskite-based tandem cells, including perovskite/perovskite (all-perovskite) solar cells and perovskite/silicon solar cells (as shown in Fig. 6). The theoretical photoelectric conversion efficiency of crystalline silicon technology is 29.3%, while single-junction perovskites have a theoretical efficiency of 33%. Multi-junction perovskite solar cells can achieve even higher efficiencies, reaching up to 47%. Improving the band structure of the device is key to enhancing the photoelectric conversion efficiency of photovoltaic devices. The band gap can be adjusted by controlling the perovskite components, and the fabrication of multi-junction stacked solar cells with different band gaps is an important direction for improving photoelectric conversion efficiency [12]. 3.2 The Improvement of Battery Stability Improve the Stability of Perovskite Materials. In 2009, MAPbI3 was first used in liquid form in solar cells, and its efficiency and stability were very low. With the continuous development of doping and modification technology of perovskite materials, there

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Fig. 6. Device structure, the external quantum efficiency (EQE) and J–V curves of perovskite/silicon tandem solar cell [13].

are more and more types of perovskite materials used in solar cells, and their stability is gradually improving. For instance, mixed cationic and halide anionic perovskite materials, organic polymers or inorganic doped perovskite composites, two-dimensional perovskite composites (2D/3D perovskite composites) and so on. In addition, finding existing or synthesizing more stable perovskite materials will also be a new way to improve the stability of perovskite materials [14]. Optimize the Stability of the Transport Layer and Electrode Materials. At present, the electron transport materials in forward structure perovskite devices are mostly TiO2 , SnO2 , ZnO and some other doped oxides. Traditional TiO2 materials and oxygen in the presence of organic matter after being excited by ultraviolet light will induce defect energy levels inside the battery to form a composite center, so reducing oxygen content (such as nitrogen protection) during device preparation can effectively reduce the generation of defect energy levels. In perovskite solar cells, hole transport materials not only play the role of transmitting holes and blocking electrons, but also form a barrier layer above the perovskite layer, which can reduce the corrosion of the perovskite layer by external factors such as water, oxygen and heat [15]. Add the Buffer Layer to Improve the Stability of the Device. Perovskite solar cells, whether they are formal or inverted structures, are all sandwich-like structures, and the perovskite material sandwiched in the middle is easily affected by adjacent charge transport layers, and hole transport layers, moreover, electron transport layers are also affected by anodes and cathodes, respectively. By adding a buffer layer to the perovskite cell, the influence between adjacent layers can be effectively reduced and the stability of the device can be improved [16].

4 Industrialization Trend At present, the area of perovskite solar cells with high efficiency generally does not exceed 1 cm2 , which belongs to the laboratory scale. Under the current technical conditions, the efficiency and stability of perovskite solar modules are relatively low, so how to maintain the efficiency and stability of perovskite photovoltaic modules when using scalable methods to prepare perovskite photovoltaic modules is the main scientific problem need to be solved in the commercialization process (Fig. 7). Among them, the

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deposition preparation technology of large-area high-quality perovskite films is the key point. In addition, in the case of the industrial production of gigawatt-level perovskite photovoltaic devices in the future, the modules deposited every year will reach millions of square meters definitely. This not only requires the development of deposition techniques for the preparation of homogeneous and high-quality films (>100 cm2 modules), but also the speed of the process is a key factor to consider. Increasing process speed is critical to reducing costs [17].

Fig. 7. Critical challenges for perovskite solar cells [17].

The performance and stability of perovskite photovoltaic devices are closely related to the quality of perovskite films, and the thickness, surface morphology and crystallinity of perovskite films directly affect the light absorption, carrier generation and transmission performance of photovoltaic devices. However, the deposition of large-area perovskite films is difficult to control, and according to the LaMer and Ostwald maturation models, rapid nucleation and slow crystallization are the keys to improving the quality of perovskite films [18]. Although there are no large-scale commercial components available, the industry has paid great attention to them, and the commercial application of perovskite cells is gaining steam. In the future, perovskite solar cells can be developed from the following aspects: (1) Optimize device performance, achieve technological breakthroughs from efficiency, area and stability, develop large-scale perovskite battery production equipment, and low-cost production of perovskite solar modules. (2) As an important supplement to the photovoltaic market, perovskite cells are not only competitive to crystalline silicon cells, but also complementary, therefore, perovskite crystalline silicon tandem cells can combine the advantages of both two to achieve full use of solar resources. In addition, due to the deep accumulation and the far exceeded industrial scale over other technical routes of crystalline silicon technology, perovskite batteries cannot compete with it in large-scale photovoltaic power plants in the short term. So, it is recommended to use the unique advantages of perovskite cell technology in the market segment to find application breakthroughs, such as BIPV, BAPV, or developing self-powered devices for Internet of Things key components based on wireless sensors for the Internet of Things.

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5 Conclusion and Prospect In the process of practical application of perovskite solar cells, the problems of largescale module preparation and stability have not been solved. In this paper, the working principle and device structure of perovskite solar cells are briefly described, the research progress of perovskite solar cells in improving photoelectric conversion efficiency and stability, as well as the bottleneck of industrialization are summarized. In the face of the mature technology and huge market share of traditional silicon cells, the application direction of perovskite solar cells is also worth thinking about. In the future, perovskite solar cells can be used in constructing a “photovoltaic, energy storage, direct current, flexibility” building which can integrate building-integrated photovoltaics, flexible interconnection of platform area, distributed energy storage and DC power supply. Perovskite solar cell is an advanced photovoltaic technology, of which photovoltaic power generation is the core body, energy storage and flexible load is the main means, direct current is the way to improve the efficiency of electricity consumption. The goal of the technology is to make good use of the electric energy emitted by photovoltaics, reduce the steps of secondary regulation of the large power grid. In addition, high-efficiency perovskite solar cells can solve the huge pressure brought to the power grid by the large charging demand of new energy vehicles. Through the coordinated control and unified management of AC power network with DC loads photovoltaic system, charging pile and energy storage, the energy interconnection and microcirculation architecture of low-voltage power grid is constructed, so as to realize the flexibility in power of platform area and alleviate the impact of large-scale use of charging piles on the residential power grid. Perovskite photovoltaics covers all scientific problems from basic to industrialization, including basic scientific problems in materials and laboratory equipment research, as well as industrial-scale manufacture and application problems. Acknowledgments. This work is supported by State Grid Zhejiang Electric Power Co., Ltd. Technology Project (5211WZ230006), Research on key technologies for energy efficiency improvement of full DC public buildings based on low-carbon building photovoltaic integrated materials.

References 1. 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) 2. Sun, H., Zhai, H.B., 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) 3. Zhang, Y.M., Liu, X.Z., Yan, Z., Zhang, P.C.: Decomposition-coordination based optimization for PV-BESS-CHP integrated energy systems. Trans. China Electrotech. Soc. 35(11), 2372– 2386 (2020) 4. Cole, J.M., Pepe, G., Al Bahri, O.K., et al.: Cosensitization in dye-sensitized solar cells. Chem. Rev. 119(12), 7279–7327 (2019)

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5. Bosio, A., Pasini, S., Romeo, N.: The history of photovoltaics with emphasis on CdTe solar cells and modules. Coatings 10(4), 344 (2020) 6. Song, Z., Watthage, S.C., Phillips, A.B., et al.: Pathways toward high-performance perovskite solar cells: review of recent advances in organo-metal halide perovskites for photovoltaic applications. J. Photonics Energy 6(2), 022001 (2016) 7. Wang, X., Rakstys, K., Jack, K., et al.: Engineering fluorinated-cation containing inverted perovskite solar cells with an efficiency of >21% and improved stability towards humidity. Nat. Commun. 12(1), 1–10 (2020) 8. Deng, Y., et al.: Surfactant-controlled ink drying enables high-speed deposition of perovskite films for efficient photovoltaic modules. Nat. Energy, 560–566 (2018) 9. Zha, W., Zhang, L., Wen, L., et al.: Controllable formation of PbI2 and PbI2 (DMSO) nano domains in perovskite films through precursor solvent engineering. Acta Phys.-Chim. Sin. 36(X), 2003022 (2020) 10. Hou, M., Zhang, H., Wang, Z., et al.: Enhancing efficiency and stability of perovskite solar cells via a self-assembled dopamine interfacial layer. ACS Appl. Mater. Interfaces 10(36), 30607–30613 (2018) 11. Ke, W., Xiao, C., Wang, C., et al.: Employing lead thiocyanate additive to reduce the hysteresis and boost the fill factor of planar perovskite solar cells. Adv. Mater. 28(26), 5214–5221 (2016) 12. Xiao, K., Lin, R., Han, Q., et al.: All-perovskite tandem solar cells with 24.2% certified efficiency and area over 1 cm2 using surface-anchoring zwitterionic antioxidant. Nat. Energy 5(11), 870–880 (2020) 13. Al-Ashouri, A., Köhnen, E., Li, B., et al.: Monolithic perovskite/silicon tandem solar cell with >29% efficiency by enhanced hole extraction. Science 370(6522), 1300–1309 (2020) 14. Zhang, Z., Qiao, L., Meng, K., et al.: Rationalization of passivation strategies toward highperformance perovskite solar cells. Chem. Soc. Rev. (2023) 15. Azmi, R., Zhumagali, S., Bristow, H., et al.: Moisture-resilient perovskite solar cells for enhanced stability. Adv. Mater., 2211317 (2023) 16. Zhao, X., Liu, T., Loo, Y.L.: Advancing 2D perovskites for efficient and stable solar cells: challenges and opportunities. Adv. Mater. 34(3), 2105849 (2022) 17. Liu, Y., Yuan, S., Zheng, H., et al.: Structurally dimensional engineering in perovskite photovoltaics. Adv. Energy Mater., 2300188 (2023) 18. Wang, A., Wang, S., Lin, H., et al.: Research progress and key challenges of perovskite solar cells. J. Silic. 49(7), 1306–1322 (2021). (in Chinese)

Modeling and Fault Characteristics Analysis of Ultra High Voltage Direct Current Transmission System Yaoqi Xu, Cui Tang(B) , Qi Xu, and Jian Liu College of Electrical and Electronic Engineering, Wuhan Institute of Technology, Wuhan 430205, Hubei, China [email protected]

Abstract. With the increasing demand for energy, the ultra high voltage direct current (UHVDC) transmission system has received extensive attention. Line commutated converter (LCC) is the most commonly used converter technology in HVDC system. The analysis of its fault characteristics is very significant for the system. In this article, the system structure and basic principle of LCC UHVDC transmission are described, and the situations of normal operation and fault are analyzed theoretically. Based on the actual engineering parameters of the project, the simulation model of ±800 kV UHVDC transmission system is built by using electromagnetic transient simulation software PSCAD/EMTDC. And the fault characteristics are simulated to validate the accuracy of the theoretical analysis. Keywords: UHVDC · Fault · Characteristic Analysis · PSCAD/EMTDC

1 Introduction The abundant primary energy resources in China are mainly concentrated in its western regions. However, there are significant power supply-demand tensions and large electricity deficits in three major areas: the Beijing-Tianjin-Hebei-Shandong, the JiangsuZhejiang-Shanghai, and the Central China-Eastern Four Provinces regions. As a result, “West-East Electricity Transmission” has become a crucial method for ensuring an equilibrium between power need and supply [1]. The use of HVDC transmission allows for the maximization of transmission capacity and power transfer on existing lines, making HVDC transmission technology one of the crucial methods in power systems. Its advantages include long-distance transmission, low line losses, and improved system stability. In comparison to conventional alternating current (AC) transmission systems, conventional direct current (DC) transmission offers several advantages. The DC system’s capacity for transmission is solely restricted by the thermal stability of the conductors, enabling the maximum utilization of transmission capabilities [2, 3]. As a commonly used converter technology in HVDC systems, Line Commutated Converters (LCC) analysis of its control and fault characteristics is crucial for the reliable operation of the system. The fast control and network segmentation capabilities of DC © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 644–652, 2024. https://doi.org/10.1007/978-981-97-0865-9_69

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transmission technology can effectively alleviate certain issues in AC systems, including excessive short-circuit currents, intensified low-frequency oscillations, and widespread propagation of faults [4, 5]. Therefore, conducting in depth analysis of the control and fault characteristics of high voltage direct current transmission systems holds significant theoretical and practical significance. This study provides a detailed analysis of the basic structure and mathematical model of UHVDC transmission systems. Furthermore, it delves into its correlation properties, encompassing various aspects such as the rectifier side (RS), inverter side (IS), and DC side (DS). The software for electromagnetic transient simulation, known as PSCAD, which was employed in this research to accurately model the ±800 kV UHVDC transmission system using the LCC bipolar double 12-pulse connection mode based on the real engineering parameters. Additionally, various faults were introduced into the simulation model. These simulations validated the reliability of the model and analyzed the control characteristics under AC and DC fault conditions.

2 System Architecture and Mathematical Model 2.1 System Architecture The UHVDC transmission system’s structure diagram is shown in Fig. 1. This is an LCC bipolar dual-end UHVDC transmission system. 

 

 



















 

Fig. 1. Structural Diagram of UHVDC Transmission System

2.2 Mathematical Model Figure 2 depicts the equivalent circuit for the UHVDC system. Through Fig. 2, the following equation can be established: 3 XtR Id π 3 UdI = UdioI cos γ − XtI Id π

UdR = UdioR cos α −

UdR − UdI = Rd · Id Id =

UdR − UdI Udi0R cos α − Udi0I cos γ = 3 3 Rd π XtR + Rd + π XtI

(1) (2) (3) (4)

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Rd

−

3 X tI π

 

 Id Udi0I cosγ

Udi0Rcosα

U dR

U dI







Fig. 2. Equivalent circuit of UHVDC transmission system

3 Analysis of Control Characteristics of UHVDC Transmission 3.1 The Inherent Control Characteristics of LCC of RS in the Steady-State The principle of the LCC control algorithm on the RS is shown in Fig. 3, where idref is DC current reference value, αmin is the minimum firing angle. The actual steady-state control characteristic curve of the RS is shown in Fig. 4. The AB segment represents a fixed minimum triggering angle α control, the BC segment represents constant DC current control, the CD segment represents the constant current control, the DE segment represents minimum constant current control. id ud

G 1 + sT

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idref voltage dependent current order limiter



+

A

α

B

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Fig. 3. Principle of LCC control system on the RS

Ud2

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D E Idref_min

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Fig. 4. The actual steady-state control characteristic curve of the RS

3.2 The Inherent Control Characteristics of LCC of IS in the Steady-State The principle of the LCC control algorithm on the IS is shown in Fig. 5, and the actual steady-state control characteristic curve is shown in Fig. 6. The FG section has a fixed shut-off angle γ control, the FG section has a fixed shut-off angle γ control, the KL section is controlled by minimum constant current. 3.3 Analysis of Control Characteristics Under AC/DC Fault Conditions Figure 7 displays the control characteristic curve when a fault occurs on the RS. When a short-circuit fault arises within the AC system on the RS, Udi0R decreases. According to the formula (1), in order to control Id to the target value, the rectifier side LCC will reduce the trigger angle until the trigger angle reaches the minimum value. During this period, the DC current cannot be controlled by changing the α. The final DC system voltage can generally be stabilized at 0, and the current can generally be stabilized at 0.45 p.u.

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ud

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+

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γ

G

UN

α MIN

∆ I dH

K

α2

L IdIref_min

0

γN

F

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0.9IN

Fig. 6. The actual steady-state control characteristic curve of the IS

Fig. 5. Principle of LCC control system on the IS

Figure 8 displays the control characteristic curve when a fault occurs on the IS. According to the formula (2), in order to control the Id to the target value, the LCC on the IS will decrease the γ until it reaches its minimum value. The final DC system voltage can generally be stabilized at 0, and the current can generally be stabilized at 0.55 p.u. Figure 9 displays the control characteristic curve when a fault occurs on the DS. After the DC line fails, the DC voltage almost drops to 0. During the steady-state of DC fault, both the RS and IS LCCs will operate in their respective minimum constant current control procedure. Finally, during steady-state period of the RS fault, the DC current is 0.55 p.u., the DC current of the IS is 0.45 p.u., and the fault branch current is 0.1 p.u. Ud A

Ud A

B G S I J

I J

F C

L E

Idc

Fig. 7. Control characteristic curve under rectifier side fault condition

0

L E

B G S I J

F C

K D

K D 0

Ud A

B G S

F C

K D

Idc

Fig. 8. Control characteristic curve under inverter side fault

0

LE

IN

Idc

Fig. 9. Control characteristic curve under DC line fault condition

4 Model of UHVDC Transmission System 4.1 Model Parameter Combined with the actual engineering parameters, the model is built by PSCAD. The UHVDC transmission system is ±800 kV. The converter transformers for RS and IS are connected in Y0/Y and Y0/ configurations, respectively, and commutation impedance is 0.18. Other engineering parameter settings are shown in Table 1.

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DC rated current

3.125 kA

DC rated power

5000 MW

Rated voltage of AC system on RS and IS

525 kV

Short-circuit ratio

2.5/84°

Single-phase capacity of rectifier side and inverter side converter transformer 760 MVA Rated voltage on both sides of the RS and IS converter transformer

525 kV, 170 kV

Length of DC transmission line

1400 km

Average value of earth resistivity along the line

1000 ·m

4.2 Simulation Model in PSCAD The simulation model is shown in Fig. 10.

Fig. 10. ±800 kV UHVDC transmission system simulation model

5 Simulation of UHVDC System 5.1 AC Short-Circuit Situation Simulation on RS Figure 11(a) and (b) display the voltage and current waveforms for RS obtained through simulation, while Fig. 11(c) and (d) present the corresponding voltage and current waveforms for IS. In these figures, we use labels ‘1’ and ‘2’ to distinguish between positive and negative curves. Following a 1 s fault in this system, the DC voltage of the IS gradually decreases and eventually reaches approximately 0 V, meanwhile positive and negative DC currents are stabilized at +1.412 kA and −1.409 kA, respectively. The DC voltage of the IS eventually approach near 0 V, and those DC currents of the IS are stable at +1.414 kA and −1.421 kA, respectively.

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(a) DC voltage on the RS

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(b) DC current on the RS

(c) DC voltage on the IS

(d)DC current on the IS

Fig. 11. AC fault waveforms on the RS

Based on the simulation results, it is evident that following the AC line failure that the voltage drops to 0 V after the RS fault, and the current can be stabilized near 0.45 p.u., which aligns with the outcomes of the theoretical analysis. 5.2 AC Short-Circuit Situation Simulation on IS The DC voltage and current variations during 3 phase short-circuit situation on the AC side of the IS are investigated. At 1.0 s, 3 phase fault takes place. Refer to Fig. 12 (a) and (b) for the voltage and current waveforms on the RS, respectively. Those waveforms on the IS can be observed in Fig. 12 (c) and (d), respectively.

(a) DC voltage on the RS

(b) DC current on the RS

(c) DC voltage on the IS

(d) DC current on the IS

Fig. 12. AC fault waveform on the IS

The positive curves and negative curves are represented by 1 and 2, respectively. After the 1.0 s fault of this system, the DC voltage of the RS finally falls near 0 V,

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and the positive and negative DC currents are stabilized at +1.711 kA and −1.717 kA, respectively. The DC voltage of the IS finally reaches near 0 V, and those DC currents of the IS are stable at +1.715 kA and −1.714 kA, respectively. Based on the simulation results, it is evident that following the AC line failure that the voltage approach 0 V after the IS fault, meanwhile its current can be stabilized near 0.45 p.u., which aligns with the outcomes of the theoretical analysis. 5.3 Simulating a Bipolar Ground Short-Circuit Situation in a DC Transmission Line An analysis is conducted to examine the variations in DC voltage and current when a short-circuit situation occurs in a DC transmission line. Three-phase fault occurs at 1.0 s. The DC current waveforms of RS, IS and fault branch can be observed in Fig. 13(a), (b) and (c), respectively. The DC voltage waveforms of RS, IS and fault branch are displayed in Fig. 14(a), (b) and (c), respectively.

(a) RS current

(b) IS current

(c) fault branch current

Fig. 13. Current waveforms of RS, IS and fault branch of DC-side bipolarground fault

(a) RS voltage

(b) IS voltage

(c) fault branch voltage

Fig. 14. DC side bipolar ground fault RS, IS, fault branch voltage waveform

The positive and negative curves are represented by 1 and 2 respectively. After the 1.0 s, the positive electric current and negative electric current of the RS is finally stabilized at +1.731 kA and −1.724 kA, respectively. Moreover the DC voltage finally reach near 0 V; Meanwhile those currents of the IS are finally stabilized at +1.425 kA and −1.427 kA, respectively, and the DC voltage finally decrease to around 0V. Meanwhile, those currents of the fault branch are finally stabilized at +0.319 kA and −0.321 kA, respectively, as well as its voltage finally falls to around 0 V. Based on the simulation results, it is evident that following the DC line failure that the DC voltage reach near 0 V, the DC current on the RS can be stabilized at 0.55 p.u.,

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while on the inverter side, it remains steady at 0.45 p.u. Additionally, the fault branch current can be stabilized at 0.1 p.u., which aligns with the outcomes of the theoretical analysis.

6 Conclusion Within this research, the fundamental framework and mathematical model of UHVDC system are analyzed, and its corresponding characteristics in RS, IS and DS are discussed. PSCAD is employed to build an accurate simulation model of ±800 kV UHV DC transmission system under LCC bipolar double 12-pulse connection mode. In addition, simulation includes AC three-phase short-circuit faults on both the RS and IS, as well as a bipolar fault on the DS is carried out. Through the analysis and discussion of this study, we can more accurately simulate and analyze the function of that system under LCC bipolar double 12-pulse connection mode. At the same time, we can also verify the control characteristics of the system under different fault conditions, and provide support and assistance for ensuring the secure function and fault handling of the UHVDC transmission system. Acknowledgments. This research is funded by the Scientific Research Foundation at Wuhan Institute of Technology 2019: (K201906).

References 1. Ma, F.: Discuss the current situation of UHVDC transmission technology and its application prospect in China. In: Electric Power Equipment Management, no. 1, pp. 43–44 + 65 (2021). (in Chinese) 2. Zhao, W.: High Voltage Direct Current Transmission Engineering Technology. China Electric Power Press, Beijing (2010). (in Chinese) 3. Han, M., Wen, J., Xu, Y.: Principle and Operation of HVDC Transmission. China Electric Power Press, Beijing (2012). (in Chinese) 4. Hiremath, R., Moger, T.: Transient analysis of LCC based HVDC offshore wind farms using DIgSILENT PowerFactory. In: 7th Iran Wind Energy Conference, pp. 1–5 (2021) 5. Xiao, H., Sun, K., Pan, J., Li, Y., Liu, Y.: Review of hybrid HVDC systems combining line communicated converter and voltage source converter. Int. J. Electric. Power Energy Syst. 129, 1–5 (2021) 6. Zhu, Y., Guo, Q., Li, C., Chang, D., Chen, D., Zhu, Y.: Research on power modulation strategy for MMC-HVDC and LCC-HVDC in parallel HVDC system. In: 2019 IEEE 3rd Conference on Energy Internet and Energy System Integration, pp. 1456–1461 (2019) 7. Farghly, A., El Habrouk, M., Ahmed, K.H., Abdel-Khalik, A.S., Hamdy, R.A.R.: Active power filter for12-pulse LCC converter employed in LCC-MMC hybrid HVDC system. In: 2022 23rd International Middle East Power Systems Conference, pp. 1–7 (2022) 8. Chai, X., Han, P.: Analysis of fault characteristics of HVDC transmission lines. In: Electrical Switches, vol. 58, no. 5, pp. 5–8 (2020). (in Chinese) 9. Kumar, A., Jhampati, S., Suri, R.: HVDC converter stations design for LCC based HVDC transmission system-key consideration. In: 2017 14th IEEE India Council International Conference, pp. 1–6 (2017)

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10. Dhaliwal, N., Crowe, L., Kolt, R., Rashwasn, M.: Replacement of control and protection in line commutated converter (LCC) HVDC systems. In: 2021 AEIT HVDC International Conference, pp. 1–4 (2021) 11. Gao, S., Zhu, H., Zhang, B., Song, G.: Modeling and simulation analysis of hybrid bipolar HVDC system based on LCC-HVDC and VSC-HVDC. In: 2018 IEEE 3rd Advanced Information Technology, Electronic and Automation Control Conference, pp. 1448–1452 (2018) 12. Han, M., Zuo, W., Xiao, Y., Zhang, G., Zhou, M., Wen, J.: Topology and control strategy of push-pull DC autotransformer suitable for interconnecting LCC-HVDC and VSC-HVDC. In: 2021 IEEE 4th International Electrical and Energy Conference (CIEEC), pp. 1–6 (2021)

How Does Current Establish in Transient Electromagnetic Field Shuqi Liu and Dezhi Chen(B) State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China [email protected]

Abstract. Eddy current fields are usually used to describe the electromagnetic phenomena in fast-response devices, but this numerical simplification has errors in explaining the current establishment mechanism of conductors. This paper uses the full-wave Maxwell equations and takes an axisymmetric power sourcecoaxial line-axisymmetric load loop as a typical example to clarify the current establishment mechanism in the conductor under sudden voltage excitation. The field in the air is not established instantaneously, but is sent from the power source to the load in the form of electromagnetic waves along the waveguide. If the characteristic impedance of the waveguide does not match the load resistance, the wave will refract and reflect repeatedly, progressively delivering energy into the load. And the load voltage and current rise in steps, and the rise time is related to the matching degree of the waveguide and the load. Then the solution of the full-wave equation is compared with transmission line theory. The transmission line theory is a circuit simplification from the full-wave equations, but cannot take into account the dynamic circuit parameters of the waveguide and load, which can cause distortion of the solution. Keywords: Current establishment · Maxwell equations · Reflect · Transient electromagnetic fields

1 Introduction Some times ago, there was a lot of discussion about a very interesting video on the Internet called ‘the big misconception about electricity’ [1]. In the circuit diagram shown in Fig. 1, an ideal power supply is connected to a light placed 1 m away by a 300,000 km long conductor with zero resistance. Since it is not set whether the light is sensor-based or not, there are several reasonable explanations for how long the bulb will stay on. Also, this inspires the question of how the current is established in a fast response device such as high-speed electromagnetic railguns [2, 3], power electronic structures [4] and winding equipments [5].

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 653–659, 2024. https://doi.org/10.1007/978-981-97-0865-9_70

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Fig. 1. A circuit diagram in the video called ‘the big misconception about electricity’.

Eddy current models are often used as a tool for calculating electromagnetic fields in fast response devices containing conductors, which ignore the displacement current on the basis of full-wave Maxwell equations [6]. However, ignoring the displacement current is a simplification after weighing the numerical value, which cannot describe the real physical process of current establishment. The transmission line theory is a circuit simplification from the full-wave Maxwell equations [7]. Although displacement currents are considered, they cannot take into account the dynamic circuit parameters of the waveguide and load, which causes distortion of the solution. In this paper, using the full-wave Maxwell equations and taking an axisymmetric conductor loop as a typical example, the current establishment mechanism of the conductor under sudden voltage excitation is clarified. It is also compared with transmission line theory to evaluate the negative effects in transient electromagnetic fields.

2 Model and Space-Time Discretization As shown in Fig. 2, we use an axisymmetric power source-coaxial line-axisymmetric load loop model, which is convenient for calculations and is also suitable for the current establishment mechanism of complex loop models. The size and conductivity parameters are la = 0.005 m, lb = 0.035 m, lc = 0.00015 m, γc = 106 S/m, γL = 103 S/m. According to the axisymmetric property, the calculation variable is field Eρ , Ez , and Hφ . The calculation area is coaxial line, air and load (0 < z < l + lc, 0 < ρ < lb). And the governing equations are full-wave Maxwell equations ⎧   ∂Hφ ∂Ez 1 ∂Eρ ⎪ ⎪ ⎨ ∂t = − μ0 ∂z − ∂ρ 1 ∂ z . (1) ε0 ∂E ∂t +γ Ez = ρ ∂ρ (ρHφ ) ⎪ ⎪ ⎩ ε ∂Eρ +γ E = − ∂Hφ 0 ∂t

ρ

∂z

The boundary conditions are ⎧ ⎪ Eρ = 0(0 < ρ < la, z = 0) ⎪ ⎪ ⎪E = U ⎪ ⎨ ρ ρ ln(lb/la) (la < ρ < lb, z = 0) . Eρ = 0(ρ = 0) ⎪ ⎪ ⎪ = 0(ρ = lb) E ⎪ z ⎪ ⎩ Ez = 0(z = l + lc)

(2)

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Fig. 2. An axisymmetric power source-coaxial line-axisymmetric load loop model.

And the initial conditions are ⎧ ⎨ Eρ |t=0 = 0 =0 . E| ⎩ z t=0 Hφ |t=0 = 0

(3)

We use the finite difference time domain method to discrete Maxwell equations [8, 9]. In this method, the space is discretized into a Yee grid. The electromagnetic field components are set at the center of each side and each face of the Yee grid. The iterative formula calculates the electromagnetic field components at each discrete point position at each time step, simulating the algorithm of time progression.

3 Results and Physical Meanings 3.1 Reflection of Electromagnetic Waves in Air A voltage source close to a step is chosen as the excitation. And the step current source is not considered because its energy is infinite, which is unrealistic. Field Eρ and Hφ of line l located in air at different typical moments is drawn in Fig. 3. The field in the air is not established instantaneously, but is sent from the power source to the load in the form of electromagnetic waves along the waveguide. If the characteristic impedance of the waveguide does not match the load resistance, the wave is refracted repeatedly, gradually providing energy into the load. As shown in Fig. 3, the time for the electromagnetic wave to travel along the coaxial line from the power source to the load T0 =

0.3 m length of line l = = 10−9 s v 3 × 108 m/s

(4)

is a characteristic time. Eρ , Hφ propagate to the load in the form of a wave at 0 < t < T0 and are reflected from the load at T0 < t < 2T0 . And they are reflected from the source and propagates towards the load at 2T0 < t < 3T0 .

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t=2.7ns t=2.5ns t=2.3ns 16.8 t=1.7ns t=1.5ns 11.2 t=1.3ns t=0.7ns 5.6 t=0.5ns t=0.3ns 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 z (mm)

Er(V/m)

22.4

(a) Field E ρ

t=2.7ns t=2.5ns t=2.3ns 0.129 t=1.7ns t=1.5ns 0.086 t=1.3ns t=0.7ns 0.043 t=0.5ns t=0.3ns 0.000 0.00 0.05 0.10 0.15 0.20 0.25 0.30 z (mm)

Ht(T)

0.172

(b) Field Hφ

Fig. 3. Field Eρ , Hφ of line l located in air at different typical moments.

3.2 Load Voltage and Current Assuming that the waveguide circuit parameters are constants that do not vary with frequency and the load resistance is constant, the transmission line theory has analytical formulas [7] for the load voltage and current  0 (0 < t < T0 ) , (5) Uload = 1 + (−1)i−1  i ((2i − 1)T0 < t < (2i + 1)T0 , i ∈ N+)

How Does Current Establish in Transient Electromagnetic Field

Iload =

⎧ ⎪ ⎨0 ⎪ ⎩

1+2[

i

657

(0 < t < T0 ) (−1)k−1  k−1 ]+(−1)i  i

k=2

Zc

,

(6)

((2i − 1)T0 < t < (2i + 1)T0 )

where reflection coefficient  √= (−Zc + Zload )/(Zc + Zload ), and the waveguide characteristic impedance Zc ≈ Lc /Cc . As shown in Fig. 4, the load voltage and current are plotted using transmission line theory and full-wave model. According to the full-wave model solution, the load voltage is not equal to the power source voltage. During the reflection progress, the load voltage rises in steps, and the rise time is related to the matching degree of the waveguide full_wave model transmission line theory

1.0

full_wave model transmission line theory

0.15

0.5

UL (V)

UL (V)

0.20

0.10 0.05 0.00 0

0.0 0

2

4

6 8 t (ns)

100 t (ns)

10 12

200

(a) Load voltage

0.6

full_wave model transmission line theory

IL (A)

0.4

full_wave model transmission line theory

IL (A)

0.10

0.2

0.05

0.00 0 2

0.0 0

4 6

100 t (ns)

8 10 12 14 16 t (ns)

200

(b) Load current

Fig. 4. Load voltage and current using transmission line theory and full-wave simulation.

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characteristic impedance and the load impedance. Similarly, the load current rises in steps. There is a low difference between transmission line theory and full-wave model. In transmission line theory, DC circuit parameters are used instead of frequency dependent circuit parameters, which can cause errors in voltages and currents affected by impedance matching. And the step voltage source has rich frequency information, so the actual waveguide and load cannot be equated to a single frequency circuit parameter. 3.3 Uniformity of Load Current Density We define a variable M = Uload /Iload to represent the uniformity of load current density, and it is calculated in Fig. 5 under conditions that the magnetic penetration time is less than T0 and greater than T0 . The magnetic penetration time represents the rate at which the electric field penetrates from the surface to the interior of the conductor, which is related to the conductivity and the thickness of the conductor [10].

4.0

full-wave model

M (V/A)

3.5 3.0 2.5 2.0 0

4

8

12 16 t (ns)

20

24

(a) Variable M when the magnetic penetration time is less than T0

M (V/A)

full-wave model

1

0.1 0

50 t (ns)

100

(b) Variable M when the magnetic penetration time is greater than T0

Fig. 5. Variable M when the magnetic penetration time is less than T0 and greater than T0 .

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And the size and conductivity parameters of the case less than T0 is equal to part 2. The parameter of the case greater than T0 is adjusted to lc = 0.005 m, where the load becomes thicker and this increases the magnetic penetration time. In the full-wave model, the variable M increases rapidly at t = (2i + 1)T0 , i ∈ N and then decreases slowly. Since the load current rises in steps, the surface field of the conductor changes instantaneously at the moment t = (2i + 1)T0 , i ∈ N, leading to a sharp increase of the variable M. After this moment, the conductor starts to magnetic penetrate again and M decreases slowly.

References 1. Maclsaac, D.: The big misconception about electricity (or how do circuits transport energy?). Phys. Teach. 60(1), 80 (2022). https://doi.org/10.1119/10.0009123 2. Tan, S., Lu, J., Li, B., Zhang, Y., Jiang, Y.: A new finite-element method to deal with motion problem of electromagnetic rail launcher. IEEE Trans. Plasma Sci. 45(7), 1374–1379 (2017). https://doi.org/10.1109/TPS.2017.2705238 3. Li, C., et al.: Influence of armature movement velocity on the magnetic field distribution and current density distribution in railgun. IEEE Trans. Plasma Sci. 48(6), 2308–2315 (2020). https://doi.org/10.1109/TPS.2020.2990926 4. Wang, L., Ma, H., Yuan, K., Liu, Z., Qiu, H.: Modeling and influencing factor analysis of SiC MOSFET half-bridge circuit switching transient overcurrent and overvoltage. Trans. China Electrotech. Soc. 35(17), 3652–3665 (2020). https://doi.org/10.19595/j.cnki.1000-6753.tces. 191105. (in Chinese) 5. Li, H., Han, L., Ye, G., Chen, Q., Jiao, Y.: A suppressing method for very fast transient overvoltage based on a frequency-sensitive busbar with a laminated-material structure. Trans. China Electrotech. Soc. 37(19), 1042–1051 (2022). https://doi.org/10.13336/j.1003-6520. hve.20211779. (in Chinese) 6. Biro, O., Preis, K.: On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents. IEEE Trans. Magn. 25(4), 3145–3159 (1989). https://doi. org/10.1109/20.34388 7. David, M.P.: Microwave Engineering, 4th edn. Wiley, United States (2011) 8. Yee, K.S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propagat. 14(3), 302–307 (1966). https://doi. org/10.1109/TAP.1966.1138693 9. Kunz, K.S., Luebbers, R.J.: The Finite Difference Time Domain Method for Electromagnetics. CRC Press, New York (1993) 10. Barber, J.P.: The acceleration of macroparticles and a hypervelocity electromagnetic accelerator. Ph.D. dissertation, The Australian National University, Australia (1972)

Thermal Resistance Measurement Methods for Double-Sided Heat Dissipation IGBTs Yuqing Zhang(B) and Zhibin Zhao College of Electronic and Electrical Engineering, North China Electric Power University, Beijing 100096, China [email protected], [email protected] Abstract. With the continuous development of electronic devices and increasing performance requirements, thermal resistance, as one of the important parameters for evaluating the performance and thermal management effectiveness of heat dissipation devices, is crucial for device performance and reliability. For the thermal resistance measurement of single-sided heat dissipation devices, there are mature calculation and measurement methods available. However, for doublesided heat dissipation devices, the existing measurement methods suffer from significant measurement errors and limitations due to structural asymmetry and dual-sided heat flow paths. In this paper, focusing on rigid press-pack IGBTs, the applicability, error sources, and limitations of commonly used theoretical calculation methods, finite element simulation methods, and experimental measurement methods in double-sided thermal resistance measurement are discussed. By comparing the advantages, disadvantages, and applicable ranges of different methods, this study provides references and guidance for double-sided thermal resistance measurement. Keywords: Double-sided heat dissipation devices · press pack IGBTs · thermal resistance

1 Introduction IGBT modules exhibit characteristics such as low power loss and fast switching speed. Consequently, they are considered one of the key technologies for addressing energy scarcity and reducing carbon emissions. These modules offer broad prospects for applications in areas like smart grids, renewable energy generation, and electric vehicles. However, during operation, IGBT modules generate power loss, resulting in increased temperatures of the chips and associated components. This temperature rise significantly impacts the performance and reliability of the devices, and in severe cases, can lead to device failures. Research indicates that within the normal operating range of IGBT modules, a 10 °C increase in operating temperature doubles the module failure rate [1]. Hence, effective heat dissipation management is essential for controlling the operating temperature of these components. Thermal resistance, which reflects the resistance to heat transfer within the device, stands as the most crucial factor influencing its heat dissipation effectiveness. Therefore, precise measurement of thermal resistance parameters holds significant importance in ensuring device performance and reliability. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 660–668, 2024. https://doi.org/10.1007/978-981-97-0865-9_71

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Steady-state junction-to-case thermal resistance is calculated by Eq. 1. Rth =

TJ − TC P

(1)

where: T J is the chip surface temperature, known as junction temperature; T C represents the device’s casing temperature, known as case temperature; P is the power dissipation of the IGBT device during operation. Traditional IGBT packages predominantly feature single-sided heat dissipation devices, as illustrated in the left of Fig. 1. Obtaining the thermal resistance parameters of these devices can be accomplished through three primary methods: thermal network modeling [2], finite element simulation [3], and experimental measurement. The theoretical calculation method for determining device thermal resistance considers only the influence of thermal conduction, allowing for online and rapid calculation of junction temperatures, thereby demonstrating high applicability but lower accuracy. Finite element simulation, while capable of simulating actual measurement conditions and visualizing changes in relevant physical quantities, is limited by computational speed due to modeling precision and is often employed as an auxiliary research tool. Experimental measurement methods exhibit higher accuracy and are suitable for offline measurements, providing valuable guidance for the design of the device’s external circuitry. Three internationally adopted standards for measuring the thermal resistance of singlesided heat dissipation devices include MIL-STD 750E and IEC 60747-9, which employ thermocouple measurement of case temperature and are referred to as thermocouple measurement methods. However, due to systematic errors associated with thermocouple measurement and non-uniform temperature distribution between the chip and the case during practical measurements, obtaining satisfactory repeatability results proves challenging. JESD51-14 utilizes the transient dual interface method, which avoids measuring the case temperature and offers good repeatability, but it is not universally applicable to all packaging types. Consequently, both aforementioned methods find wide application in the field.

Fig. 1. IGBT structure diagram.

In recent years, with the continuous increase in device power levels, single-sided heat dissipation devices have been limited in achieving double-sided heat dissipation due to their surface bonding structure. The heat dissipation management of such devices has reached its limits, making it difficult to meet market demands [4]. Consequently, a dual-sided heat dissipation device has emerged, which possesses high power density and reliability, as illustrated in the right of Fig. 1. However, due to the asymmetric nature of the heat dissipation paths and structure in this type of package, the current focus of

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research by domestic and international experts and scholars is centered on improving the thermal resistance measurement methods for existing single-sided heat dissipation devices. In this paper, a press-pack IGBT device with dual-sided heat dissipation paths is selected as the research subject. Following the classification method for obtaining single-sided device thermal resistance values, we review the research achievements in the measurement methods of thermal resistance for dual-sided heat dissipation devices and discuss the applicability of testing methods. Additionally, we summarize the challenges faced in measuring the thermal resistance of dual-sided heat dissipation devices and provide an outlook on future research directions.

2 Methods for Obtaining Thermal Resistance of Double-Sided Heat Dissipation Devices The press pack IGBT achieves electrical connection by applying external mechanical pressure (typically 1–2 kN/cm2 ). It is mainly used in high-voltage and high-power applications, hence adopting a packaging form with multiple chips in parallel. This packaging structure allows each chip to be assembled into sub-modules, which are then tested individually. After testing, the sub-modules are screened, and suitable ones are selected for combination before the final assembly. This approach simplifies the research on thermal resistance measurement [5]. 2.1 Methods for Obtaining Thermal Contact Resistance Due to the pressure contact packaging of double-sided heat dissipation devices, electrical connections are achieved through applied pressure. Unlike soldering packaging, where the macroscopic behavior of each material layer is complete contact under rated pressure, at the microscopic level, actual contact occurs only at discrete contact points due to the roughness of solid surfaces. The majority of the contact interface remains uncontacted and is filled with air or other media, as shown in Fig. 2. When heat passes through the contact interface, the presence of gaps impedes heat propagation, causing thermal resistance. Since the speed of heat conduction between different contact materials is relatively consistent, the primary difference lies in temperature, and the thermal capacitance of the contact interface can be neglected [6]. Even under rated pressure, the actual contact area accounts for only about 1% of the total contact area [7]. However, the contact resistance in IGBT modules contributes to approximately 50% of the total thermal resistance. Therefore, accurate calculation of contact resistance is crucial in pressure contact IGBTs. The total contact thermal resistance of the contact interface is given by Eq. 2. Rctotal =

1 1 = Sm · hc Sm · (hs + hf + hr )

(2)

where hc represents the contact thermal conductivity between the contact interfaces; hs represents the solid thermal conductivity coefficient; hf represents the gap thermal conductivity coefficient; hr represents the radiation conductivity coefficient.

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Fig. 2. Microscopic schematic diagram of solid surface contact

In the study of contact thermal resistance, the influence of thermal radiation and the thermal conductivity of the gap is usually ignored. Currently, a widely used semi-empirical formula is employed to calculate the contact thermal conductivity. hs = 1.25

ks m P 0.95 ( ) σ Hmic

(3)

where k s is the average thermal conductivity between the two contact surfaces; m is the average roughness slope of the two contact surfaces; σ is the root mean square roughness of the surfaces; P is the apparent contact pressure applied to the contact surfaces; and H mic is the micro-hardness of the softer material on the contact surfaces. By using the above equations, it can be observed that the contact thermal resistance is influenced by factors such as contact pressure, microhardness, surface roughness, and surface roughness slope. Therefore, the accuracy of material parameters directly determines the calculation accuracy of contact thermal resistance. Calculating the contact thermal resistance between the layers of a device in steady-state directly using the equations can be challenging, so finite element modeling is often employed. In the case of a single chip module, contact pairs are typically set up in finite element modeling to represent the contact thermal resistance. However, to simplify the complexity of the finite element calculations, it is assumed that the contact heat transfer coefficient remains constant for each contact surface [8]. The pressure between the materials in steady-state is obtained through finite element simulation and used as a known parameter for subsequent thermal resistance simulation. However, this method does not consider the transient changes in contact pressure during the operation of the pressure-contacted IGBT and their impact on the contact thermal resistance between the material layers, which affects the accuracy of thermal resistance simulation. Reference [9] establishes a functional relationship between the contact thermal resistance on the collector side, the contact thermal resistance on the emitter side, and the pressure through experimental measurements. Reference [10] applies this relationship in a finite element model of a pressure-contacted IGBT module, but it only considers the contact thermal resistance between the chip and the emitter tungsten plate as the overall contact thermal resistance on one side. Reference [11] takes into account the contact between all layers of materials to establish a more realistic physical model. The aforementioned theoretical calculation method and finite element simulation method both require obtaining detailed material parameters. Lutz’s team [12] proposes a combination of genetic algorithms and finite element methods to identify the contact thermal resistance using experimental data obtained through the indirect thermocouple

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method. Due to limited measurement data, the assumption is made that temperature does not affect the thermal resistance. This method simplifies the equivalent contact thermal resistance between layers to two contact thermal resistances, thus only providing the overall contact thermal resistance. However, Deng [13] and others have found that different junction temperatures have a significant impact on thermal resistance, mainly because the hardness of materials changes with temperature in practical experiments. Based on this, the scholar [14] applies the transient dual-interface method to the pressurecontacted IGBT by analogizing the welding thermal resistance measurement method and uses the structure function method to determine the thermal resistance of different parts of the pressure-contacted IGBT module. However, due to the small thermal capacity of the contact thermal resistance, when using the structure function method, the contact thermal resistance can be overshadowed by the thermal resistance of the previous layer, limiting the accuracy of this method and requiring further improvement. In conclusion, the current methods for obtaining the contact thermal resistance of pressure-contacted IGBT devices are mainly based on theoretical modeling, combined with finite element simulation, intelligent algorithms, and experimental measurement data, taking into account the effects of temperature and pressure on contact thermal resistance to simulate the actual operation of the devices. Currently, there is no effective measurement method through experimental measurement that can directly obtain the contact thermal resistance between the layers. For a press-pack IGBT module, the contact thermal resistance caused by its unique electrical connection method can be equivalently represented as a variable thermal resistance in the thermal network model, based on the analysis in Sect. 2.1. The remaining components can be analogized to a first-order heat transfer network. Reference [15] provides a detailed description of the thermal network model for single-sided heat dissipation devices. 2.2 Experimental Measurement Methods for the Thermal Resistance of Double-Sided Heat Dissipation Devices Based on the definition of thermal resistance Eq. 1, different methods can be used in experimental measurements to determine the junction temperature of single-sided heat sink devices, including optical methods, thermocouple measurements, and electrical methods. Optical methods are non-contact measurement techniques but require exposing the chip surface, making them unsuitable for measuring the junction temperature of presspack IGBTs. Thermocouple measurements involve direct contact. However, in press-pack IGBT chips, both sides are surrounded by molybdenum plates and subjected to external clamping force to ensure reliable contact. The top and bottom surfaces are constrained by clamping force, making it impossible to measure the junction temperature. In literature [17], thermocouples were placed on the side of the chip to measure the junction temperature. However, the measurement standards specify that the junction temperature is the surface temperature of the chip, rendering the aforementioned measurement inaccurate.

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For widely used electrical methods, literature [18] indicates that compared to singlesided heat sink devices, double-sided heat sink devices with their dual heat flow paths improve the uneven surface temperature distribution. Consequently, the electrical method yields smaller errors in measuring the junction temperature of double-sided heat sink devices. Among the aforementioned methods, except for the optical method, the remaining two can be applied to single-module studies. According to thermal resistance definition Eq. 1, the casing temperature can be measured using the thermocouple method and transient dual-interface method [19]. Due to the presence of double-sided heat flow paths in double-sided heat dissipation devices, currently, three main measurement approaches are employed. The first approach involves placing a thermal insulation plate on one side and separately measuring the collector-emitter thermal resistance and emitter-collector thermal resistance. According to the thermal network model, under good heat dissipation conditions where the upper and lower surface temperatures of the casing are as equal as possible, these two heat dissipation paths are considered to be in parallel, allowing for the parallel determination of the thermal resistance of the double-sided heat dissipation device. The advantage of this method is the ability to obtain thermal resistances on both sides as well as the total junction-casing thermal resistance, guiding subsequent device usage. However, this method inevitably introduces errors. Firstly, the placement of the thermal insulation plate affects the change in internal pressure distribution, thereby altering the contact thermal resistance and affecting measurement accuracy. Secondly, the thermal insulation plate does not completely insulate, resulting in insufficient precision. The second approach is to measure directly the junction-casing thermal resistance of the double-sided heat dissipation device while maintaining ideal heat dissipation conditions under double-sided heat dissipation. This method offers the advantage of simplicity in operation. However, due to the structural asymmetry of the double-sided heat dissipation device, it is challenging to maintain consistent casing temperatures on both sides during the measurement process. The third approach involves simultaneous measurement of the collector-emitter and emitter-collector thermal resistances and parallelizing them. While this approach can avoid the issues associated with the previous two methods, it is only applicable to the thermocouple measurement method, which will be discussed in Sect. 2.3. The challenge of employing this method for measurement lies in determining the thermal dissipation on both sides. In 2019, Chang Yao [6] proposed a liquid colorimetric method for calculating the total heat absorbed by the heat sink using the same water-cooled heat sink and controlling the water flow rate to be the same. The calculation is expressed in Eq. 4: H = Q · C · ρ · T

(4)

where H represents the heat absorbed by the heat sink, Q represents the flow rate of the cooling liquid, C and ρ represent the specific heat capacity and density of the liquid, and ΔT represents the temperature difference between the inlet and outlet of the heat sink. The systematic errors caused by the measurement instrument accumulate and have an error of approximately 5% compared to the simulation values. In 2022, Chen J [20] proposed a simplified measurement method. By ensuring complete symmetry of the

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heat dissipation on the upper and lower surfaces of the device and measuring only the water temperature, the heat dissipation ratio between the upper and lower surfaces of the device can be obtained, as shown in Eq. 5. Tc1 − Tw1 PE = PC Tc2 − Tw2

(5)

where PE and Pc represent the power losses on the two sides. T c1 and T c2 are the casing temperatures on the two sides. T w1 and T w2 represent the water temperatures of the heat dissipators on the two sides. 2.3 Discussion The thermocouple measurement method applies to the aforementioned three types of double-sided thermal resistance measurement schemes. However, due to the requirement of applying external clamping force for electrical connection in the case of pressurecontacted IGBT, the thermocouple measurement method is unable to measure the surface temperature of the casing. Furthermore, since the thermocouple is a direct measurement method, it to some extent affects the heat flow distribution, resulting in lower measurement accuracy of junction temperature and casing temperature, consequently affecting the measurement accuracy of thermal resistance. The transient dual-interface method measures the transient thermal resistance value. Under the condition of single-sided heat dissipation, through one-dimensional heat transfer finite element simulation, it has been found that for specific packaging, the difference between transient thermal resistance and steady-state thermal resistance is not significant. However, due to the asymmetry in the structure of double-sided heat dissipation devices, the heat flow distribution under transient conditions has not been accurately studied and explained. Therefore, whether the transient thermal resistance obtained from the transient dual-interface method is approximate to the steady-state thermal resistance still requires further research. Additionally, this approach requires the use of the structurefunction method for thermal resistance identification, and its accuracy also needs to be further investigated. Hence, this method can only be applied to the first and second schemes.

3 Conclusion In summary, the inconsistent double-sided heat flow and the structural asymmetry of double-sided heat dissipation devices result in inconsistent shell temperature. Therefore, many researchers have conducted studies under the premise of maintaining an isothermal surface of the heat sink, assuming ideal water cooling conditions. The consistency of the isothermal surface is essential for the parallel connection of single-side thermal resistances in double-sided thermal resistance testing [17]. The thermal flow distribution in the transient dual-interface method is not yet clear and requires further investigation. Consequently, the measurement of shell temperature using thermocouples is commonly employed; however, it inevitably introduces errors and leads to poor repeatability of the obtained thermal resistance values. The future research focus lies

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in how to effectively utilize existing thermal resistance testing methods to conveniently and accurately determine the junction-to-case thermal resistance under various practical scenarios. This remains a significant research area in the field of electronic device reliability. Due to the presence of contact thermal resistance in press-pack IGBTs, the thermal resistances of different layers of materials can only be analyzed and studied based on theoretical models. In experimental measurements, only the overall thermal resistance of the device can be obtained. Existing research focuses on studying the impact of various factors, such as temperature variations, pressure changes, and modeling of material surface morphology, on the contact thermal resistance in operational press-pack IGBT devices. However, few researchers have been able to consider all these. Acknowledgments. This thesis is the project supported by the Science and Technology Project of State Grid Cor-po-ration of China (5500-202158439A-0-0-00).

References 1. Fabis, P.M., Shum, D., Windischmann. H.: Thermal modeling of diamond-based power electronics packaging. In: Fifteenth Annual IEEE Semiconductor Thermal Measurement and Management Symposium (Cat. No. 99CH36306), pp 98–104 (1999) 2. Liu, B., Luo, Y., Xiao, F.: IGBT thermal model for thermal simulation of device to system. Trans. China Electrotech. Soc. 32(13(07)), 1–13 (2017). https://doi.org/10.19595/j.cnki.10006753.tces.160954. (in Chinese) 3. Chen, M., Hu, A., Tang, Y., Wang, B.: Modeling analysis of IGBT thermal model. High Voltage Eng. 37(2(2)), 453–459 (2011). https://doi.org/10.13336/j.1003-6520.hve.2011.02.033 (in Chinese) 4. Liu, M., Coppola, A., Alvi, M.: Comprehensive review and state of development of doublesided cooled package technology for automotive power modules. IEEE Open J. Power Electron. 3, 271–289 (2022). https://doi.org/10.1109/OJPEL.2022.3166684 5. Tang, X., Zhang, P., Chen, Z.: Review of high voltage high power press pack IGBT package technology. Proc. CSEE 39(12(6)), 3622–3638 (2019). https://doi.org/10.13334/j.0258-8013. pcsee.181752. (in Chinese) 6. Chang, Y.: Mechanical-Thermal Coupling Mechanism and Stress Optimization Design for Press-Pack Power Semiconductor Module. Hangzhou (2021). (in Chinese) 7. Bejan, A., Kraus, A.D.: Heat transfer Handbook. J. Wiley, New York (2003) 8. Long, H.: Electro-Thermal-Mechanical Stress Multiphysics Modeling and Failure Analysis of Nanosilver Sintered Package Press Pack IGBT. Chongqing (2020). (in Chinese) 9. Deng, E., Chen, W., Heimler, P.: Temperature influence on the accuracy of the transient dual interface method for the junction-to-case thermal resistance measurement. IEEE Trans. Power Electron. 36, No.7(7), 7451–7460 (2021). https://doi.org/10.1109/TPEL.2020.3042495 10. Ren, B., Huang, Y.: Simulation on reliability lifetime of single IGBT chip module of presspack IGBTs. J. North China Electric Power Univ. 47, No.3(7), 49–57 (2020). DOI:https:// doi.org/10.3969/j.ISSN.1007-2691.2020.03.07. (in Chinese) 11. Guo, J., Zhang, Y., Deng, E.: Prediction of power cycle life of press-pack IGBTs considering full contact of contact interface. J. North China Electric Power Univ. 50, No.2(3), 63–72 (2023). Doi:10. 3969/j.ISSN.1007–2691.2023.02.07. (in Chinese)

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12. Poller, T., Lutz, J., D’Arco: Determination of the thermal and electrical contact resistance in press-pack IGBTs. In: 2013 15th European Conference on Power Electronics and Applications (EPE), pp: 1–9 (2013). DOI: https://doi.org/10.1109/EPE.2013.6634440 13. Deng, E., Zhao, Z., Zhang, P.: Study on the methods to measure the junction-to-case thermal resistance of IGBT modules and press pack IGBTs. Microelectron. Reliab.Reliab. 79, 248–256 (2017). https://doi.org/10.1016/j.microrel.2017.05.032 14. Deng E. Modeling the Electro-Thermo-Mechancial Multi-physics Coupling Model for Press Pack IGBTs. Beijing (2018). (in Chinese) 15. Wu, Y., Huang, Y., Deng, E.: Survey of thermal network modeling for power devices. Trans. China Electrotech. Soc. 17, 12–22 (2022). https://doi.org/10.19768/j.cnki.dgjs.2022.17.004 (inChinese) 16. Han, L., Liang, L., Kang, Y.: Thermal resistance distribution experiment of paral-lel submodule in press-pack IGBT device. Electric Power 53, No.12(12), 37–44 (2020). https://doi. org/10.11930/j.issn.1004-9649.202007196. (in Chinese) 17. Han, L., Liang, L., Zhang, Z., Kang, Y.: Understanding inherent implication of thermal resistance in double-side cooling module. IEEE Trans. Power Electron. 38, No. 2(3), 2435–2445 (2022). https://doi.org/10.1109/TPEL.2022.3205598 18. Deng, E., Chen, J., Zhao, Y., Zhao, Z.: Influence of IGBT Package Types on the Accuracy of Junction Temperature Measurement. Semiconductor Testing and Equipment vol.43, No.12(12): 956–963 (2018). DOI:https://doi.org/10.13290/j.cnki.bdtjs.2018.12.013. (in Chinese) 19. Deng, E., Zhao, Y., Zhao: Comparative Study on the Method of Thermal Resistance Measurement for Press Pack IGBT and IGBT Modul. Smart Grid 7, No.7(6) 631–638 (2016). https:// doi.org/10.14171/j.2095-5944.sg.2016.07.001. (in Chinese) 20. Chen, J., Deng, E., Zhang, Y., Huang, Y.: Junction-to-case thermal resistance measurement and analysis of press-pack IGBTs under double-side cooling condition. IEEE Trans. Power Electron. 37, No.7,(7), 8543–8553 (2022). https://doi.org/10.1109/TPEL.2022.3151411

Analysis of EIT Effect Under Different Fine Level Selections of Cesium D2-Line Chao Ding1 , Baoshuai Wang2,3(B) , Zengxing Pu1 , Dongping Xiao4 , Hongtian Song2,3 , Shanshan Hu2,3 , Huang Yu1 , and Xutao Wei4 1 Electric Power Research Institute of Guizhou Power Grid Co., Ltd., Guiyang 550002, China 2 CSG Electric Power Research Institute, Guangzhou 510700, China

[email protected]

3 Guangdong Provincial Key Laboratory of Intelligent Measurement and Advanced Metering of

Power Grid, Guangzhou 510700, China 4 National Key Laboratory of Power Transmission Equipment Technology, School of Electrical

Engineering, Chongqing University, Chongqing 400044, China

Abstract. In recent years, Rydberg atoms have been widely employed for electric field quantum measurements. The fundamental principle behind these measurements is the utilization of the double-photon three-level structure to achieve Electromagnetically Induced Transparency (EIT). When cesium atoms are employed as the sensor, the detection light needs to be locked at 852 nm to excite the cesium atoms from the ground state 6S1/2 to the intermediate state 6P3/2. Frequency locking is achieved through the saturated absorption spectroscopy method. Due to the fine energy level structure of the cesium atom’s D2 line, the saturated absorption spectrum exhibits six spectral peaks, providing the flexibility to select any one of them as a reference for frequency locking. In this paper, we present an experimental setup where we compare the EIT effects resulting from frequency locking to five different spectral peaks and discuss the influencing factors and optimal selection. Keywords: Electromagnetically induced transparency · Probe light · Saturation absorption spectroscopy · Cesium D2-line

1 Introduction Traditional methods for electric field measurements have undergone more than a century of development and can be broadly classified into electrical-based and optical-based approaches. Electrical-based methods include the use of sphere sensors, potential shift techniques, capacitance charging methods, and charge-induced electric field sensors [1– 6]. However, instruments based on electrical principles often suffer from electric field distortion and poor measurement accuracy in field conditions, making precise electric field measurements challenging. Additionally, these sensors are often bulky and heavy, limiting their portability. On the other hand, optical-based measurement methods can be categorized into functional and non-functional fiber optic electric field measurement techniques, with the mainstream approach relying on the Pockels effect or Kerr © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 669–676, 2024. https://doi.org/10.1007/978-981-97-0865-9_72

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effect to measure electric fields [7–9]. Both of these methods fall under the category of electro-optic effects. However, electro-optic effects are known to have temperaturerelated issues, resulting in temperature drift in electric field sensors [10, 11], particularly in outdoor environments prevalent in the power industry. Furthermore, when the power frequency electric field acts on an electro-optic crystal, the internal charges in the crystal undergo displacement, altering the distribution of the electric field and causing instability in the output electric field sensing signal. Moreover, mobile free charges accumulate on the surface of the sensing crystal, affecting the internal electric field distribution [12]. In recent years, quantum precision measurement techniques based on Rydberg atoms have gained significant attention. The large electric dipole moment, high polarizability, and long coherence time of Rydberg atoms make them highly sensitive to external electric fields and easily manipulable by external fields, enabling the measurement of related effects. Rydberg atom-based quantum measurement provides a more precise method for electric field measurements. Its all-optical, high sensitivity, and calibrationfree characteristics have made it a research hotspot [13–15].

Fig. 1. Schematic diagram of two-photon three-level formation EIT.

Quantum measurement of electric fields based on Rydberg atoms involves the formation of Electromagnetically Induced Transparency (EIT) as a key step. Specifically, a low-power probe light is applied to the atomic system. When the frequency/wavelength of the probe light resonates with a pair of transition energy levels, the probe light is completely absorbed by the atoms. Introducing a strong coupling light induces resonant transitions in the atomic levels again, reducing or even eliminating the absorption of the probe light. This creates a “window” in the spectrum of the probe light, resulting in a transparent peak known as the EIT peak, as shown in Fig. 1. In this process, it is necessary to calculate the resonance frequency/wavelength of the probe light based on the transition levels and lock it accordingly. This article uses cesium atoms to form a sensor, with a ground state of 6S1/2 (F = 4) and an intermedi ate state of 6P3/2 F  = 3, 4, 5 , resulting in a detection wavelength of approximately 852.3nm. Frequency locking of the probe light is performed using saturated absorption spectroscopy. Due to the fine structure level structure in the cesium atom’s D2-line, the saturated absorption spectrum exhibits six distinct peaks. The main focus of this study is to investigate the influence of locking the probe light to different fine structure level peaks on the subsequent EIT spectrum.

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The structure of this paper is as follows: Sect. 1 introduces the principles and methods of locking the probe light based on saturated absorption spectroscopy in the fine structure levels of the cesium atom’s D2-line. Section 2 describes the experimental setup. Section 3 presents the experimental results and analysis.

2 Frequency Locking Method of Saturated Absorption Spectroscopy for Fine Level of Cesium Atom D2 Line 2.1 Saturation Absorption Spectroscopy As shown in Fig. 2(a), when two laser beams with the same frequency, opposite directions, overlapping optical paths, and different powers are injected into the atomic vapor pool, the stronger beam serves as the pump light to pump the atom into the excited state, while the lower beam serves as the detection light after passing through the gas chamber and entering the photodetector to obtain a saturated absorption spectrum. For a three-level system, the saturated absorption spectrum obtained is shown in Fig. 2(b). It can be seen that there are two transition levels but three absorption peaks. We call the peaks generated by atomic level transitions on both sides the intrinsic peaks, and the peaks generated by Doppler effect in the middle the cross peaks. It is known that every two transition energy levels will generate three absorption peaks.

Fig. 2. Schematic diagram of saturated absorption spectrum optical path and three-level system.

2.2 Saturation Absorption Spectroscopy Figure 3 shows the hyperfine level structure of the D2 line of cesium atoms. If the fine energy level of the ground state is in the F = 4 state, according to the energy level transition rules, there may be three types of transitions when transitioning to the intermediate state: F = 4 → F  = 3, F = 4 → F  = 4, F = 4 → F  = 5. The specific state to which the transition occurs depends on the more precise resonance frequency corresponding to the detected light frequency. In this systems, the probe beam is initially frequency-scanned around 852 nm while achieving F = 4 → F  = 3, 4, 5 transitions. This configuration allows for obtaining a saturated absorption spectrum, as depicted in Fig. 4. Since the cesium atomic vapor cell operates at room temperature, the saturated absorption spectrum exhibits multiple absorption peaks due to the presence of a Doppler background. The energy level transitions corresponding to each peak have been delineated in the transition diagram.

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Fig. 3. Schematic diagram of D2 line energy level structure and sweep spectrum of cesium atom.

Fig. 4. Saturated absorption spectroscopy of cesium atom.

3 Experimental System Figure 5 is the schematic diagram of the power frequency electric field measurement system based on Rydberg atom. The 852 nm laser beam is divided into two beams after passing through PBS. One beam enters the Cs atom Saturated absorption spectroscopy to detect the optical frequency stabilization, and the other enters the cesium bubble to interact with the 509 nm laser beam to produce the EIT spectrum of Rydberg atom. The 852nm external cavity semiconductor laser outputs the laser and eliminates optical feedback through an optical isolator. Then, the polarization angle is modulated by a half wave plate and two laser beams are separated through a polarization beam splitter. The first laser beam enters the Cs atomic saturation absorption spectrum frequency stabilization system, and then the polarization angle of the laser beam is adjusted again through a half wave plate. After the laser beam passes through the polarization splitting prism and is reflected into the cesium atomic gas chamber, it serves as a pump light to pump the cesium atom in the ground state to the excited state. The pump light leaves the cesium atomic gas chamber and passes through an attenuator to reach the full reflection mirror. After being reflected by the full reflection mirror, the laser beam returns to the original path and enters the cesium atomic gas chamber, As the detection light passes through the cesium atomic gas chamber and finally enters the photodetector, a saturated absorption spectrum of 852 nm laser is obtained. The second beam of laser is the EIT

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probe light, which is divided by a beam splitter and then adjusted by an acoustooptic modulator (AOM) (power stabilization) to enter the second beam splitter through a half wave plate. It is then refracted by a fully reflective mirror through a dichroic plate and enters the cesium atomic gas chamber, where it interacts with a 509nm laser and enters the photodetector to generate an EIT spectrogram. The 509nm laser is also an external cavity semiconductor laser which enters the cesium atomic gas chamber through the reflection of a dichroic plate through an optical isolator and an all reflection mirror as the coupling light generated by EIT.

Fig. 5. Schematic diagram of experimental device for power frequency electric field measurement system based on Rydberg atom.

4 Experimental Results and Analysis For the obtained Saturated absorption spectroscopy of cesium atom, we lock the frequency for each numbered peak, that is, select the first transition energy level of EIT. In this experimental setup, due to the small frequency difference between the two absorption peaks ➂ and ➃, the absorption peak positions in the spectrum are close to overlapping, making it difficult to separate the two peaks for separate frequency locking during the locking process. Therefore, they were set as one experimental group in the experiment. The intrinsic absorption peak ➀ generated by F = 4 → F  = 3 is difficult to successfully lock in the spectrum due to its small amplitude value, and the EIT phenomenon cannot be observed when selecting it as the lock in peak. Therefore, it will not be discussed in this article. The peak value selected for frequency locking includes 5 components, namely ➁➂➃➄➅. ➂ and ➃ were used as one experimental group for the experiment. Finally, the EIT effect in the Measurement in quantum mechanics system after frequency stabilization of the 852nm laser is shown in Fig. 6. From Fig. 6, it can be observed that when locking to peak, the optical intensity fluctuates within the range of 0.0032 to −0.0048. The EIT peak is well-defined, and the atomic transition probability is maximized, resulting in the highest peak intensity. However, when peak ➄ is chosen for locking, the optical intensity fluctuates within a

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Fig. 6. Comparison of EIT effects under different frequency locked peaks.

wider range of 0.0144 to −0.0184. This leads to a decrease in the EIT peak intensity and a reduction in atomic transition probability. In the case where the composite component of peak number ➂➃ is selected for locking, the detected optical intensity exhibits significant oscillations, with a substantial fluctuation range of 0.028 to −0.04. This results in the observed EIT peak being less pronounced and relatively smaller in peak intensity compared to other experimental configurations. Finally, when peak number ➁ is used for locking, it can be observed from Fig. 6 that only a very indistinct EIT peak is visible, with the lowest EIT peak intensity and an optical intensity fluctuation range between 0.016 and −0.0096. From the above we can see that with the change of transition energy level selection in Saturated absorption spectroscopy (➅→➄→➂➃→➁), the EIT peak gradually decreases, the atomic transition probability gradually decreases, the position of the wave peak shifts from left to right, and the fluctuation of the detection light intensity gradually increases, but it is worth noting that when the frequency locking peak is selected as the composite component of ➂➃, the fluctuation amplitude of the detection light intensity is larger than that of ➁, This is because although ➂➃ is shown as approximately one peak in the Saturated absorption spectroscopy, there are still two peaks in essence, which will bounce back and forth between the two peaks when the frequency locking device locks the frequency, resulting in the worst frequency stabilization effect when ➂➃ is selected as the frequency locking peak. Due to the selection of other peaks to add an external electric field experiment, the EIT disappeared and the measurement effect could not be obtained. Therefore, we chose to apply a 5V external electric field to the peaks of ➄ and ➅ for the experiment, and obtained the effect diagrams in Fig. 7. From Fig. 7, it can be seen that when peak ➄ is selected as the lock in peak, the peak decreases after applying an electric field, and the observed effect is more obvious. However, in Fig. 7, the EIT peak amplitude decreased from 0.08 to 0.0504 after applying an electric field, and the peak value decreased by 0.296. When peak ➅ is selected as the frequency locked peak, the EIT peak also decreases after applying an electric field, from 0.992 to 0.536, with a variation of 0.456.

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Fig. 7. Effect diagram of EIT before and after applying electric field when selecting peak ➄ frequency locking.

Hence, it can be inferred that when selecting peak ➄ for locking, the change in EIT relative to peak ➅ under the same electric field conditions is relatively small. This enables a broader range of electric field measurements.

5 Conclusion This study, by altering the selection of detection-level transitions, compared the EIT effect obtained under the same conditions with a quantum frequency measurement system based on Rydberg atoms to analyze the influence of different fine-level transitions used for locking in the cesium atomic D2 line. It was determined that the EIT effects obtained when locking to absorption atoms  peaks ➄ and ➅, associated   with cesium 6S1/2 (F = 4) → 6P3/2 F  = 4, 5 and 6S1/2 (F = 4) → 6P3/2 F  = 5 , were superior, while the EIT effects for other absorption peaks in the experimental groups were less favorable. Locking to peak ➅ yielded better EIT effects, while locking to peak ➄ allowed for measurement over a relatively larger electric field range. Acknowledgments. This work is supported by the funding program from China Soutern Power Grid Guizhou Power Grid Co., Ltd. (GZKJXM20222158, GZKJXM20222147, GZKJXM20222200).

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Frequency Calibration Method Based on Cesium Atom nDJ Rydberg State Laser Spectroscopy Baoshuai Wang1,2 , Chao Ding3(B) , Hongtian Song1,2 , Zengxin Pu3 , Shanshan Hu1,2 , Huaiqing Zhang4 , Yu Huang3 , and Wenyu Lin4 1 CSG Electric Power Research Institute, Guangzhou 510700, China 2 Guangdong Provincial Key Laboratory of Intelligent Measurement and Advanced Metering of

Power Grid, Guangzhou 510700, China 3 Electric Power Research Institute of Guizhou Power Grid Co., Ltd., Guiyang 550002, China

[email protected] 4 National Key Laboratory of Power Transmission Equipment Technology, School of Electrical

Engineering, Chongqing University, Chongqing 400044, China

Abstract. This paper presents a measurement technique for low-frequency electric fields based on the Rydberg atoms. It utilizes the principle of the Stark effect, where non-resonant external electric fields cause the splitting of atomic energy levels, leading to spectral peak frequency shifts. In the measurement system, the photoelectrically converted signal is typically directly connected to an oscilloscope to display the corresponding spectrogram. Therefore, calibration of the laser spectral frequency variations is necessary to convert the time axis of the oscilloscope into a frequency axis. This paper proposes a calibration method that utilizes the existence of two optical peaks, corresponding to the nD3/2 and nD5/2 states of cesium (Cs) atoms, in the absence of an electric field. The theoretical calculation of the frequency difference between these two peaks provides an internal frequency scale without the need for external devices. By applying this calibration method, the time shift of the two peaks measured on the oscilloscope is converted into a frequency shift, allowing the determination of the applied field strength based on the mathematical relationship between the frequency shift and the applied electric field. The principles of the technique are described, and experimental validation is performed. Keywords: Rydberg atom · electric field measurement · laser spectroscopy · frequency calibration · stark effect

1 Introduction Rydberg atoms are a class of atoms in which the outer electrons are excited to high quantum states (orbitals with larger principal quantum number, n). The excited valence electrons are far from the atomic nucleus, and the energy level structure can be analogous to that of a hydrogen atom. A hydrogen atom in a highly excited state is the simplest example of a Rydberg atom. Rydberg atoms possess characteristics such as long lifetimes, strong electric dipole moments, sensitivity to external electric fields, and © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 677–684, 2024. https://doi.org/10.1007/978-981-97-0865-9_73

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the ability of external electric fields to induce energy level shifts. These characteristics make them suitable for non-contact measurement of electric fields [1]. In the context of Rydberg electric field measurement techniques, the first step is to select a suitable Rydberg atom, such as cesium or rubidium, for the measurement. The choice of the Rydberg atom’s ground and excited states depends on the frequency of the electric field to be measured. Under the perturbation of an external electric field, based on the Stark effect [2, 3] between the Rydberg atom and the electric field, the originally degenerate energy levels of the atom split, resulting in changes in their energies. Moreover, the interactions between different states and the external electric field differ from each other. The energy level splitting leads to various electron transitions, which can be observed as spectral line splitting and multiple peaks in laser spectroscopy. Therefore, quantum measurement techniques based on the high sensitivity properties of Rydberg atoms, such as Electromagnetically Induced Transparency (EIT) spectroscopy [4], offer significant advantages in terms of measurement accuracy and reliability compared to traditional electric field measurement techniques. Furthermore, they provide a new non-contact measurement approach for electric field measurement. The Schrödinger equation describing the interaction with the atomic system through an electric field is given by the following equation:   H0 + H ψ = Wψ   (1) 1 − ∇ 2 + V (r) + er · E ψ = W ψ 2 H is the Hamiltonian operator; W represents the eigenenergy; ψ is the wave function; V(r) is the Coulomb potential due to the atomic nucleus and valence electrons. From this, we can obtain the relationship between eigenenergy variation and field strength, as shown in Fig. 1.

Fig. 1. Relationship between Eigenenergy Variation and Field Strength.

Before avoiding crossing points, there is a linear relationship between eigenenergy W and frequency shift f , as given by the following equation: W = hf

(2)

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h is Planck’s constant. This leads to the expression for the relationship between frequency shift and electric field intensity. Quantifying the frequency shift in measuring the electric field is crucial, thus requiring frequency calibration, as shown in Fig. 2.

Fig. 2. Spectral Stark Shift under a Certain Field Strength.

At present, the method of measuring electric field by using the Stark effect of Rydberg atoms in Rydberg electric field measurement technology is mainly based on the spectral characteristics of nS1/2 state (n is the main quantum number, S is the Rydberg state with angular quantum number l = 0), and the two-photon resonance transition of threelevel system is realized by probing light and coupling light [5–7]. Theoretically, when the laser is accurate enough and the fluctuation is small (the frequency locking effect of the laser [8, 9] is good enough), the atomic energy can be accurately guaranteed to transition from the nS1/2 state to the intermediate state and excited to the Rydberg state. However, the measurement accuracy of this method is low, because the energy level spacing is small, it is easily affected by environmental factors, and there is only one optical peak of nS1/2 state. At the same time, the movement of atomic energy level under the action of external field is represented as the change of laser spectral frequency on the oscilloscope (the movement interval of light peak), so it is necessary to calibrate the change of laser spectral frequency by additional optical path and equipment (introducing a series of devices with equal frequency interval) to convert the Timeline of oscilloscope into frequency axis optical frequency comb [10, 11], which is difficult to be used in actual electric field measurement.

2 Principle of Spectral Frequency Calibration A schematic of the cesium level using Rydberg atom Stark effect spectral features to measure the electric field based on the nDJ state is shown in Fig. 3, the electron spin-orbit coupling produces the fine structure of the cesium atom (6S1/2 , 6P3/2 and nDJ states), which is related to the total angular momentum of the electron. The Hyperfine structure of an atom, such as 6P3/2 (F’ = 2, 3, 4, 5) is produced by the spin-coupling of the electron with the nucleus, and the difference in energy levels between the Hyperfine structure is small. In a three-level quantum measurement system, a laser with a wavelength of about

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852 nm is used for saturation frequency-stabilized locking as a weak detection light for excitation of the ground state 6S1/2 to the intermediate state 6P2/3 of the cesium atom, the laser with a wavelength of about 509 nm is used to scan the strong-coupling light from the first excited state 6P2/3 to the Rydberg state of cesium atom near the wavelength of 509 nm. 852 nm detection light is converted into electrical signal by photoelectric detector, and then converted into visual waveform by oscilloscope. In the two-photon resonant transition of a three-level system, we can establish a frequency scale based on the fine structure of 6P3/2 (F’ = 3, 4, 5), with a frequency difference of 251.1 MHz for EIT spectral peaks (F’ = 4, 5) or 201.3 MHz for EIT spectral peaks (F’ = 3, 4) [12]. However, the frequency difference between the spectral peaks does not appear as 251.1 MHz or 201.3 MHz on the oscilloscope. Taking into account the Doppler effect, the original value needs to be multiplied by a corresponding coefficient in order to convert the oscilloscope’s time scale into a frequency scale for calibrating the frequency shift of spectral peaks under the influence of an external electric field. In comparison, the calibration of the frequency difference between the spectral peaks based on the nDJ states’ spectral features, 6S1/2 → 6P3/2 (F’ = 4) → nD5/2 and 6S1/2 → 6P3/2 (F’ = 4) → nD3/2 , results in a relatively small error.

Fig. 3. Schematic diagram of cesium atomic energy levels based on nDJ state.

For cesium atoms, using quantum defect theory [13] nD3/2 and nD5/2 energy level spacings, the Rydberg atom nDJ state has an energy given by: ωnDJ = −

RCs (n − δD )2

(3)

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RCS is the Rydberg constant of cesium atom, RCS = 3289828381.1149 MHz, n is the main quantum number, the quantum defect number of angular quantum number l = 2, obtained from the following formula: δD = δ0 +

δ2 δ4 δ6 δ8 + + + + ....... (n − δ0 )2 (n − δ0 )4 (n − δ0 )6 (n − δ0 )8

(4)

The parameters of the two Rydberg states of nD3/2 and nD5/2 are given in Table 1 below: Table 1. Quantum defect numbers of nD3/2 and nD5/2 . δ0

δ2

δ4

δ6

δ8

nD3/2

2.47545(2)

0.0099(40)

−0.43324

−0.96555

−16.9464

nD5/2

2.4663141(6)

0.01381(15)

−0.392(12)

−1.9(3)

−1.5532

Based on the EIT spectra peaks of 6S1/2 → 6P3/2 (F’ = 5) → nD2/3 and 6S1/2 → 6P3/2 (F’ = 5) → nD5/3 , and the energy difference between nD3/2 and nD5/2 Rydberg states given by: ω = ωnD5/2 − ωnD3/2

(5)

The horizontal axis scale of the oscilloscope is T, and the energy difference ω (MHz) corresponding to nD3/2 and nD5/2 is kT, as shown in Fig. 4. Then, convert the time scale axis to the frequency scale axis f  = ω/k.

Fig. 4. nDJ frequency calibration waveform.

3 Electric Field Measurement Experiment Based on nDJ State Frequency Shift Calibration The electric field measurement for cesium atom Rydberg atomic laser spectroscopy frequency calibration is demonstrated using the nDJ states, taking the 49D3/2 and 49D5/2 states as examples. At zero electric field, the two EIT peaks generated by 49D3/2 and

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49D5/2 are denoted as W3/2 and W5/2 , respectively, as shown in Fig. 5. Each grid spacing on the oscilloscope time axis is T, and there are a total of k = 6.42 T between the two EIT peaks. The inter-peak spacing is calculated as 592.615 MHz using quantum defect theory, thus providing the frequency scale f = 592.615/k = 92.931 (MHz).

Fig. 5. 49DJ Atomic EIT Spectrogram.

Taking the EIT spectrum measurement of the 49D3/2 state as an example, when a radio frequency (RF) electric field with a frequency of 10 MHz and a peak-to-peak amplitude of 2 V is applied to the 8 cm electrodes, the Stark effect causes the degeneracy of energy levels with different absolute magnetic quantum numbers in the 49D3/2 state to be lifted. The EIT spectrum peak splits into two peaks with magnetic quantum numbers |mj | = 1/2 1/2 and 3/2, respectively, and the peak frequency shift of EIT is f3/2 = 6.598 MHz and 3/2

f3/2 = 0.539 MHz relative to zero field. As shown in Fig. 6, the red line indicates the position of the 49D3/2 peak W3/2 at zero field. Compared to Fig. 5, the x-axis in Fig. 4 is magnified by a factor of 10.

Fig. 6. Schematic diagram of 49D3/2 state energy level splitting under the Stark effect.

Under the action of radio frequency electric field, the relationship between the frequency shift f (the frequency shift between the peaks of different magnetic quantum numbers after splitting and the peak of 49D3/2 state before splitting) and the external electric field [14] is:  −2f E= (6) −J (J +1) α0 + α2 3mJJ(2J −1)

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In the equation, α0 = −510.151 MHz·V−2 ·cm2 and α2 = 354.706 MHz·V−2 ·cm2 are the scalar and tensor polarizabilities of the nDJ states, respectively, and MJ is the 1/2 3/2 magnetic quantum number. The electric field values calculated from f3/2 and f3/2 are 0.092 V/cm and √ 0.083 V/cm, respectively, the errors between the two values and the actual values 2/16 V/cm are 4.09% and 6.1%, respectively. The average value of electric field is 0.0875 V/cm, and the error is 1.4%. So when we select the nDJ Rydberg state of the cesium atom to measure the electric field, we can calibrate the frequency axis of the time axis at the same time, the mean value of the electric field can be calculated by eliminating different frequency shifts by the stark effect degenerate energy level of the Rydberg state of the nDJ of cesium atom.

4 Conclusion In this study, we employ a frequency calibration method based on cesium atom nDJ Rydberg state laser spectroscopy. Firstly, the frequency calibration is performed using the two peaks of nD3/2 and nD5/2 without the need for introducing additional optical frequency combs for measurement. Secondly, when measuring the external electric field based on the nDJ states, the stark effect eliminates the degeneracy of energy levels with different absolute magnetic quantum numbers in the nDJ states. As a result, multiple sets of frequency shift values are obtained for nD3/2 or nD5/2 , allowing simultaneous calculation of corresponding field strengths and improving measurement accuracy by averaging the results. Acknowledgments. This work is supported by the funding program from China Southern Power Grid Guizhou Power Grid Co., Ltd. (GZKJXM20222158, GZKJXM20222147, GZKJXM20222200).

References 1. Kaiyu, L., Haitao, T., Xinding, Z., Hui, Y., Shiliang, Z.: Microwave sensing and communication based on Rydberg atoms. Sci. China Phys. Mech. Astron. 51(7), 7–20 (2021). (in Chinese) 2. Rosenbusch, P., Ghezali, S., Dzuba, V.A., Flambaum, V.V., Beloy, K., Derevianko, A.: AC Stark shift of the Cs microwave atomic clock transitions. Phys. Rev. A 79(1), 013404 (2009) 3. Blackmore, J.A., Sawant, R., Gregory, P.D., Bromley, S.L., Cornish, S.L.: Controlling the AC Stark effect of RbCs with DC electric and magnetic fields. Phys. Rev. A 102(5), 053316 (2020) 4. Marangos, J.P.: Electromagnetically induced transparency. Optica Acta Int. J. Opt. 45(3), 471–503 (1998) 5. Shuaiwei, C., Wenxin, P., Songnong, L., Yuan, J., Zhonghua, J., Yanting, Z.: Measurement of power frequency electric field based on Rydberg atoms. High Voltage Eng. 49(02), 644–650 (2023). (in Chinese) 6. Chungang, Z., Wei, L., Hao, Z., Mingyong, J., Linjie, Z.: Measurement of power frequency electric field based on modulated RF field electromagnetically induced transparency spectroscopy. Acta Photonica Sinica 50(06), 162–168 (2021). (in Chinese)

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7. Wei, L.: Measurement of Power Frequency Electric Field Based on AC-Stark Effect of Rydberg Atoms. Shanxi University (2021). (in Chinese) 8. Wenxin, P., et al.: Laser frequency locking of unmodulated Rydberg transitions based on electromagnetically induced transparency. Chin. J. Quant. Electron. 27(03), 246–252 (2021). (in Chinese) 9. Drever, R.W., et al.: Laser phase and frequency stabilization using an optical resonator. Appl. Phys. B 31, 97–105 (1983) 10. Jie, W.: Precision Measurement of Hyperfine Interaction Constant and Dual-Color MagnetoOptical Trap Based on Stepped Atomic System. Shanxi University (2016). (in Chinese) 11. Jian, Z., Yuxin, Z., Jiawen, Z., Yanxia, Y., Haoyu, W., Jie, Z.: Laser mode analysis based on Fabry-Perot cavity. Phys. Exp. 42(1), 10–14 (2022). (in Chinese) 12. Yuechun, J.: Electromagnetically Induced Transparency and Quantum Correlation Properties of Rydberg Atoms Controlled by External Fields. Shanxi University (2017). (in Chinese) 13. Min, D.: Applications of Quantum Trajectory Theory in Cold Atom Physics. Tsinghua University (2018). (in Chinese) 14. O’sullivan, M.S., Stoicheff, B.P.: Scalar and tensor polarizabilities of D2 Rydberg states in Rb. Phys. Rev. A 33(3), 1640 (1986)

Author Index

A Anmin, Tian 73

Dong, Kai 56 Du, Fei 145

B Bao, Weining 213 Bu, Fanpeng 45

F Fan, Jingsheng 239 Fan, Kuanjun 9 Fang, Yanzhao 36 Fang, Yongli 463 Feng, Fei 56, 426 Fu, Benzhao 371 Fu, Biao 102 Fu, Jianding 145 Fu, Kelin 493, 518

C Cai, Fenghuang 387 Cai, Jilin 197 Cao, Xu 250 Chai, Qianyi 137 Chang, Jinhai 239 Chen, Chuan 326 Chen, Chuanfang 615 Chen, Chuanren 250 Chen, Dan 535 Chen, Dezhi 653 Chen, Dong 564 Chen, Jia 272 Chen, Jun 197 Chen, Keyu 548 Chen, Kui 463 Chen, Liyan 564 Chen, Qiming 564 Chen, Wencong 169 Chen, Xiaomin 362, 379, 472 Chen, Xilong 362, 379, 472 Chen, Xingyun 371 Cheng, Jianping 371 Cheng, Ling 45 Cheng, Xingong 102 Chi, Xiangwen 272 Chu, Ning 169 D Dai, Xin 574 Deng, Dahan 509 Ding, Chao 669, 677 Ding, Yi 633 Ding, Yixing 197 Ding, Zemin 481

G Gai, Chao 272 Gao, Dong 395 Gao, Hongjian 145 Gao, Jinlong 342 Gao, Kun 287 Gao, Ming 353 Gao, Wei 326 Gao, Xin 593 Gao, Xingle 353 Gao, Xinyu 395, 426 Gao, Yang 25 Gao, Yinghui 250 Gao, Ze 287 Gao, Zheyuan 362 Gao, Zihan 45 Gu, Yun 197 Guan, Shili 448 Guo, Chunping 585 Guo, Jinzhi 556 Guo, Xingxin 92 Guo, Zhikang 509 H Hao, Rui 263, 304, 315 Hao, Xu 73 He, Chengye 17 He, Haoran 502

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1160, pp. 685–688, 2024. https://doi.org/10.1007/978-981-97-0865-9

686

Author Index

He, Jun 456 He, Yu 127 He, Yumin 493 He, Zhifei 56 Hu, Changbin 127 Hu, Shanshan 669, 677 Hu, Tongning 9 Hu, Xiaoyu 119 Huang, Jiancheng 92 Huang, Jiyao 371 Huang, Yeping 564 Huang, Yu 677 Huang, Zhanhua 17 Huang, Zhiming 493 Huo, Haoxiang 502 J Jia, Xinxin 239 Jiang, Jiaxin 602 Jiao, Chongqing 92 Jiao, Xuelei 615 Jiayu, Wang 73 Jiayuan, Ma 73 Jin, Heping 414 Jin, Li 295 Jin, Ningzhi 602 K Ke, Haojie 434 Kong, Xiaoguang

111

L Lai, Yuping 353 Li, Bowen 493 Li, Chao 326 Li, Chenghao 287 Li, Chengxiang 535 Li, Dan 625 Li, Dongxue 593 Li, Fengtai 326 Li, Guofeng 181 Li, Jiacheng 1 Li, Jinshan 342 Li, Long 25 Li, Ming 564 Li, Qi 1 Li, Qifan 119 Li, Qiu 231 Li, Shuaihu 414 Li, Siqi 36

Li, Weiwei 585 Li, Xiaodong 334 Li, Xiaofei 9 Li, Xingyun 213 Li, Xinyao 56 Li, Xudong 155 Li, Yubin 155 Li, Yueming 481 Li, Zhaohui 263, 304, 315 Li, Zihe 395, 426 Liang, Huidong 456 Liang, Xinzhao 387 Lin, Jingxuan 362, 379, 472 Lin, Wenyu 677 Lin, Xu 222 Ling, Hui 633 Liu, Baoling 456 Liu, Jian 644 Liu, Mingyang 287 Liu, Shuqi 653 Liu, Wei 326 Liu, Wenjie 633 Liu, Xiaobing 295 Liu, Xinguang 456 Liu, Yanbin 502 Liu, Yi 272 Liu, Yongbao 481 Lu, Fuchao 189 Lu, Jianghua 434 Lu, Ketong 548 Luo, Dan 181 Luo, Shanna 127 Luo, Yan 518 Lv, Qishen 17 M Ma, Qian 404 Ma, Siyuan 472 Mao, Chenxu 169 Meng, Fanshun 602 Meng, Guodong 17 Meng, Lingqiang 527 Meng, Ming 362, 371, 379, 472 Miao, Youzhong 556 Mu, Runzhi 404 P Pan, Bo 1 Pan, Jiekai 137

Author Index

687

Pan, Shenggui 493, 518 Peng, Minfang 353 Pu, Tingxu 295 Pu, Zengxin 677 Pu, Zengxing 669 Q Qian, Lingzhi 64 Qiang, Dandan 585 R Ren, Juguang

295

S Shen, Yangwu 414 Shen, Zhan 213 Shi, Xiaolin 371 Shuaiqi, Liang 73 Si, Donglin 205 Song, Hongtian 669, 677 Song, Liang 169 Su, Ning 342 Su, Yinsheng 404 Su, Yugang 574 Sun, Chao 556 Sun, Dongyang 602 Sun, Jieyi 414 Sun, Min 574 Sun, Shixiong 434 Sun, Yue 574 T Tan, Guojun 509 Tang, Cui 644 Tang, Jian 625 Tang, Jinhao 527 Tao, Xuezhi 472 Tian, Chunsun 287 Tian, Jiahui 155 Tian, Runze 82 Tian, Yun 1 Tong, Zhaojing 527 W Wang, Baoshuai 669, 677 Wang, Chunli 362, 379, 472 Wang, Jiarui 263, 304, 315 Wang, Jing 342 Wang, Jun 213, 379

Wang, Lixin 263, 304, 315 Wang, Longwei 145 Wang, Ming 205 Wang, Pingping 205 Wang, Shunchao 213 Wang, Xianri 371 Wang, Xiaolan 263, 304, 315 Wang, Xiping 371 Wang, Xuejian 395 Wang, Yang 92 Wang, Yanling 222, 231 Wang, Yanwen 342 Wang, Yi 556 Wang, Yingqiu 82 Wang, Yongtao 456 Wang, Yu 493, 518 Wang, Yucui 287 Wang, Zhanbo 45 Wang, Zhiqiang 181 Wang, Ziyu 1 Wei, Tenfei 263 Wei, Tengfei 304 Wei, Xutao 669 Wen, Feng 1 Wen, Tao 119 Wu, Hong 414 Wu, Jie 119 Wu, Jun 502 Wu, Peng 527 Wu, Xingwang 119 Wu, Xueying 574 Wu, Zhaoxiao 535 X Xia, Linghan 17 Xiang, Minjiang 102 Xiao, Dongping 669 Xiao, Zhuangsheng 36 Xie, Huasen 633 Xie, Yiming 119 Xie, Zhen 362, 379 Xing, Zhitong 169 Xu, Chenguan 82 Xu, Hang 102 Xu, Hongjie 9 Xu, Lei 189 Xu, Qi 644 Xu, Shizhou 239 Xu, Xing 353 Xu, Yanhui 155

688

Xu, Yaoqi 644 Xu, Yuan 404 Xuejun, Zhang 73 Y Yan, Jingdong 493 Yan, Ping 250 Yan, Suna 564 Yan, Wangpei 456 Yan, Yan 362, 379, 472 Yan, Yuting 17 Yan, Zhijiang 17 Yang, Haitao 119 Yang, Jing 602 Yang, Nan 334 Yang, Peng 155 Yang, Xiao 585 Yang, Zhicheng 127 Yang, Zhuo 111 Yao, Zhilei 448 Yi, Yongli 633 Yin, Hongxu 169 You, Zixuan 64 Yu, Huang 669 Yu, Junsong 564 Yu, Songnan 334 Yu, Xingpeng 36 Yu, Ying 17 Yu, Youhong 481 Yu, Zhongming 548 Yu, Zongmin 556 Yuan, Xiaocui 456 Yuan, Yaju 36 Yue, Meng 263, 304, 315 Z Zeng, Yifeng 9 Zhang, Di 287 Zhang, Donglei 145 Zhang, Genmi 633 Zhang, Hongmei 353 Zhang, Huaiqing 677 Zhang, Ji 353 Zhang, Jiexin 633 Zhang, Jing 45 Zhang, Jingwei 509 Zhang, Junjie 518 Zhang, Kai 272

Author Index

Zhang, Ke 625 Zhang, Li 295, 518 Zhang, Pengfei 213 Zhang, Ruiqing 213 Zhang, Sinan 615 Zhang, Sirui 45 Zhang, Tao 326 Zhang, Xiaotong 25 Zhang, Xiaoying 64 Zhang, Xin 17 Zhang, Xinyue 535 Zhang, Xu 102 Zhang, Yaowen 111 Zhang, Yu 548 Zhang, Yuqing 660 Zhang, Zhengwen 456 Zhang, Zhenquan 189 Zhao, Chenyang 82 Zhao, Chuncheng 205 Zhao, Dong 342 Zhao, Feng 556 Zhao, Ligang 404 Zhao, Meng 82 Zhao, Shengnan 102 Zhao, Wanyu 564 Zhao, Xingyu 633 Zhao, Xizheng 334 Zhao, Yao 181 Zhao, Yi 119 Zhao, Yuanzhi 334 Zhao, Zhenyu 395, 426 Zhao, Zhibin 660 Zhen, Hongyue 404 Zhen, Yawen 625 Zheng, Li 137 Zheng, Wenbin 137 Zheng, Wenzhang 272 Zhou, Feng 9 Zhou, Jie 556 Zhou, Tao 326 Zhou, Tinghui 404 Zhou, Xingjian 593 Zhou, Yan 535 Zhou, Yao 633 Zhu, Chunbo 593 Zhu, Guorong 434 Zhuo, Ran 518 Zu, Jiaao 222, 231