The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023): Volume I (Lecture Notes in Electrical Engineering, 1158) 9819708729, 9789819708727

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Lecture Notes in Electrical Engineering 1158

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 I

Lecture Notes in Electrical Engineering

1158

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 I

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 978-981-97-0872-7 ISBN 978-981-97-0873-4 (eBook) https://doi.org/10.1007/978-981-97-0873-4 © 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

Research on Surface Flashover of Vacuum Insulator with High-Voltage Insulation and Wireless Power Transfer Capabilities . . . . . . . . . . . . . . . . . . . . . . . . Li Gui, Yanling Li, Weilesi, and Rui Jing Efficiency Improvement by Electromagnetic Metasurface in Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conghui Lu, Lei Fan, Keling Song, Renjun Jiang, QingLv, Xunyi Dang, and Pingping Wang

1

10

An H-Shape Magnetic Coupler of the WPT Systems for the Cervical Vertebral Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jing Li, Ruikun Mai, Yang Chen, Yuner Peng, and Li Zheng

20

Research on Three-Phase Bipolar Magnetic Coupling Mechanism for Wireless Charging of Electric Ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaofei Lv, Kechen Wu, Ming Gu, and Di Wu

29

Fast Optimal Frequency Tracking for S-S Compensation WPT Battery Charger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fei Xu, Yuxiang Ren, and Xian Zhang

40

Research on Rotary Compact Wireless Power Transfer System . . . . . . . . . . . . . . . Longlong Zhang, Xiaojing Zhao, Feiling Zheng, Xiao Qin, and Jingcheng Zhao

48

Universal Wireless Power Transfer System for AUV Based on Flexible Magnetic Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ben Zhang, Xudong Wang, Changbo Lu, Wanli Xu, and Yong Lu

59

Port Shore Wireless Power System Using Frequency Bifurcation for Multi-power Levels Interoperability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kai Hu, Shiqiang Li, Jiatong Li, and Lei Zhao

68

Design of Power Supply for Three Core Cable Wireless Monitoring Network Based on Space Magnetic Field Energy Harvesting . . . . . . . . . . . . . . . . . Lu Xu, Hu Ran, Tian Jie, Zhifeng Xu, and Tang Feng

77

An Efficient and Simple Battery Wireless Charging System with Re-configurable Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Youzheng Wang, Hongchen Liu, Huiying Yu, Shuyu Wang, and Shuo Wang

87

vi

Contents

A 6.78 MHz Class-E Amplifier Based Capacitive Power Transfer System with Approximate Constant Current Output Characteristic . . . . . . . . . . . . . . . . . . . Zelin Chen, Dingyuan Tang, Zhiqiang Li, and Wei Zhou

95

Effects of T-Type/
-Type Resonant Networks on Harmonics of Inverter Currents in WPT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Chao Cui, Shumei Cui, Qianfan Zhang, Ying Liu, and Chunbo Zhu The Fault-Tolerant Multi-coil WPT System with Coil Parameter Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Jiantao Zhang, Zhan Gao, Jianyu Lan, Shuai Wang, Fuze Chen, Hao Dong, and Chunbo Zhu Comparison of Distributed Coil Connections for Medium and High Distance-to-Diameter Ratio IPT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Fuze Chen, Guo Wei, Long Jia, Gang Li, De’an Wang, Zhan Gao, Jiantao Zhang, and Chunbo Zhu Vertical Self-coupling Plates Design for Capacitive Power Transfer System . . . . 136 Jiantao Zhang, Shunyu Yao, Shuai Wang, Liangyi Pan, Ying Liu, and Chunbo Zhu Design of Wireless Power Transfer System for Mobile Devices Based on Class E Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Qiang Zhou and Ruikun Mai Research on Dynamic Wireless Power Transfer Technology for Maximum Equivalent Energy Transmission of Embedded Sensors . . . . . . . . . . . . . . . . . . . . . 158 Qi Wang, Yuner Peng, Yang Chen, and Ruikun Mai Power Distribution of Multi-load WPT System Based on Active L-type Equivalent Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Dongxiao Huang, Zequan Hong, Xianhong Lin, Weidong Huang, and Fengxiang Wang Output Current Identification Based on the Kalman Filtering Algorithm for Magnetic-Coupling Excitation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Dongxiao Huang, Xianhong Lin, Zequan Hong, Xinhong Yu, and Fengxiang Wang A Passive Fractional-Order Capacitor to Realize Wide Region ZVS for Improving Efficiency in WPT System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Houxuan Liu, Bing Cheng, and Liangzong He

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Electric-Field Coupled Power Transfer System with Constant Current and Constant Voltage Output Based on Switchable Secondary Side of LCL-LLC/S Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Li Ji, Jiaqi Zhang, Jianghong Zhang, and Fuchen Ge Influence of Turn Number of Tesla’s Low-Voltage Coil on the Performance of Single-Wire Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Xin Jin, Xiyou Chen, Jinhui Zhao, and Fengquan Yu Parameter Design for Power Maximization in Inductive Wireless Power Transfer Systems with Consideration of Frequency Splitting . . . . . . . . . . . . . . . . . 213 Yangxin Zheng and Fan Feng Adaptive Switching Control for Wireless Power Transfer Systems Based on Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Shuaiqi Li, Zhifan Li, Xiaolong Wang, Peng Luo, Qiming Huang, Qijun Deng, Jiangtao Liu, and Udaya Madawala Frequency Characteristics Analysis of Wireless Power Transfer System in Seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Weiyu Xu, Liming Shi, and Zhenggang Yin Coil Optimization Design of RWPT System Based on Response Surface Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Shishuo Zhang and Ruiqing Ma A UUV Underwater Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . 259 Jialu Li, Jiantao Zhang, Wei Lu, Jian Zhao, and Shumei Cui A Single-Ended WPT Circuit with Automatic CC-CV Transition . . . . . . . . . . . . . 270 Jingyu Wang and Zhicong Huang A Modeling and Parameter Identification Method of LCC-S Wireless Power Transfer for Railway Transits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Jianxi Xu, Yuhao Peng, Xinyi Zhao, Meng Wang, and Ruifeng Ma Research on Segment Compensation Bipolar Power Rail for EV DWPT System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Xingjian Zhou, Xin Gao, Dongxue Li, and Chunbo Zhu Research on Bilateral LCC Compensation Network of Underwater Wireless Charging System with Multi-resonance Point Switching . . . . . . . . . . . . 298 Yongqin Zhou, Qiaobei Wang, Minghu Qiu, and Xiaoyu Zhang

viii

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Low-Frequency Vibration Wireless Power Transmission System Based on Dynamic Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 Hang Lu and Jiyao Wang Reconfigurable Topology Design on the Secondary Side of Rotary WPT Systems for Ensuring Stable Power Transmission over Large Coupling Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Li Ji, Jianghong Zhang, Jiaqi Zhang, and Fuchen Ge Research on Transmission Performance of Wireless Power Transfer System Under System Mistuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Bing Cheng, Houxuan Liu, and Liangzong He Overview of Ship Shore Power Automation Docking Methods . . . . . . . . . . . . . . . 346 Chunlai Yu, Haolun Ding, Hao Zhu, Jinda Zhu, Yancheng Liu, Siyuan Liu, Qinjin Zhang, and Haohao Guo Optimization of the Ferrite Bars in Power Pads for Inductive Power Transfer Systems Based on Penalty Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Li Shuohan and Zhou Yan Effects of Coil Geometries on the Performance of Electromagnetic Halbach Array Wireless Power Transfer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 Tamuno-omie Gogo and Dibin Zhu Multi Frequency and Multi Load IPT System for CP Charging of Supercapacitors with Maximum Efficiency Tracking . . . . . . . . . . . . . . . . . . . . . 378 Shui Pang, Jiayi Xu, Zhong Zhu, Jiwei Xu, Hengchi Zheng, Yifan Jiang, and Hongyu Li Research on Energy Decoupling Control Strategy for Multi-coil Insulators on Transmission Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Mingrong Duan, Wei Wang, Kairui Li, Siyuan Sheng, and Chenjin Xu Overview of Wireless Charging System for Ship Shore Power . . . . . . . . . . . . . . . . 398 Chunlai Yu, Zhikai Wang, Hao Zhu, Jinda Zhu, Yancheng Liu, Siyuan Liu, Qinjin Zhang, and Haohao Guo A Repeater-Based Dynamic Wireless Power Transfer System Using Controllable Detuning Rate for Constant Output Power . . . . . . . . . . . . . . . . . . . . . 408 Wenjing Xiong, Jiawei Tan, Zixi Liu, Qihui Yu, Qi Zhu, and Min Liu Simulation Research on the Three-Coil Wireless Power Transfer System Based on High Temperature Superconducting Relay Coil . . . . . . . . . . . . . . . . . . . . 417 Zhiqiang Zheng, Yujia Zhai, Tingkun Weng, and Zhuo Li

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Design of an AUV Underwater Magnetic Resonant Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Zhaoqun Wang, Hai Huang, Yize Sun, Lingqi Zhang, and Yunfei Zhang Wireless Charging for AGV: An Analysis to the Existing Solutions and a Novel Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 Yongkai Liao, Qing Jiang, and Dong Guo Commutated-Phase Resonance Suppression in Synchronous Rectification Mode for Bidirectional Bridgeless PFC Converters . . . . . . . . . . . . . . . . . . . . . . . . . 445 Cheng Chen, Linlin Tan, Yongfeng Yu, and Xinguo Li A Novel Wireless-Power-Transfer-Based Snubber Circuit for Suppressing High-Frequency Oscillation of SiC Power MOSFETs . . . . . . . . . . . . . . . . . . . . . . . 455 Binhong Cao, Bowang Zhang, Youhao Hu, and Wei Han Protection Strategy for WPT Standby Mode Switching Based on LCL-S Topology Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Lianbin Cheng, Guo Wei, Jiantao Zhang, and Chunbo Zhu Wireless Power Transmission Based on Optimized Coupling Structure . . . . . . . . 474 Xin Geng, Zhijie Zhou, and Jie Xu Generation of Off-Axis Different-Order Bessel Beams Using a Transmissive Metasurface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Nan Wang, Hongzhou Meng, Haixia Liu, Hao Xue, and Long Li Design and Development of Temperature Wireless Test System Based on NFC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Zhigang Zhang, Shuai Luo, and Xiaoxia Yu Design and Efficiency Optimization of Asymmetric Magnetic Coupled Resonant Wireless Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 Xiaobo Wan, Zimeng Zhou, Sen Yang, Li Zhao, Xu Zeng, and Ming Tang Design of Axial DD Magnetic Coupling Structure Based on Rotary Steerable Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Li Ji, Fuchen Ge, Jianghong Zhang, and Jiaqi Zhang The Application Progress of Wireless Power Transfer in Space Utilization Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520 Yandong Hu, Xiang Li, Wenbo Dong, Hanxun Zhang, and Xiaoli Wang

x

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Research on Power Regulation of WPT System Based on Bilateral Collaborative Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 Zicheng Wang, Fasheng Huang, Xinkang Li, Dong Guo, and Dan Li A Wireless Power Supply System Based on a Receiving End of Mountain-Type Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 Xinkang Li, Fasheng Huang, Zicheng Wang, Dong Guo, and Dan Li Application Potential Extension of PSDF Buildings Based on Output-Parallel EV Wireless Charging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Xuli Wang, Zhifan Li, Hui Zhang, Ru Ling, and Qijun Deng Detection Method of Lithium Plating of Lithium-Ion Battery Based on Complex Morlet Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 571 Kai Lyu, Xinwei Liu, Siwen Chen, Shiyou Xing, Yilong Guo, and Jinlei Sun Living Object Detection of Electric Vehicle Wireless Charging Systems Based on a Single Motion Feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Wenhao Li, Hui Jiang, Jindong Tian, and Yong Tian A Real-Time Positioning Strategy for Dynamic Wireless Power Supply System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 Xinguo Li, Linlin Tan, Xiaoqi Shen, Cheng Chen, and Zhijun Wu Progress of Low-Dimensional Metal Sulfide Electromagnetic Wave Absorption Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 Qi Li, Dazhong Liang, Lin Ling, and Ming Qian Primary Side Control Method of Wireless Power Transmission System Based on Load Resistance Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Qiang Qian, Zijian Zhao, Wenxi Liang, and Zicheng Cai Parameter Design of Dual Frequency Constant Voltage Output in Wireless Power Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 Yiming Zhang, Guo Wei, Jiantao Zhang, and Chunbo Zhu Design and Experimentation of Coupling Mechanism for Wireless Power Transfer of UAVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622 Wu Maopeng, Li Ning, Chen Jianxun, Qu Ganghui, Wu Donghua, Cheng Yan, Duan Xiaoli, and Song Shoujun Sub-harmonic Control Applied to LCC Compensation Topology Variants for Inductive Power Transfer System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 Xiaoqiang Wang, Xin Zhang, Minrui Leng, Liangxi He, and Hao Ma

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Research on the Anti-offset Performance of a Wireless Power Transfer System with Asymmetric Coupling Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642 Xiangyang Shi, JianWei Kang, Deyu Zeng, and Yang Shi A Pilot Study of Electrical Impedance Tomography for Dynamic Monitoring of Human Cerebral Perfusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 Yu Wang, Xiaoheng Yan, Weichen Li, Weice Wang, Kun Li, and Xuetao Shi Load Aggregator Demand Response-Based Electricity Sales Strategy Considering WPC-CERI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 Sian Chen, Dan Xia, Tongtong Zhang, Jian Gao, Liu Bo, Weixi Ji, and Jie Yu Research on MPPT Algorithm Based on Variable Step Conductance Increment Method and Sliding Mode Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Jiaojiao Xu, Minghao Zhou, William Cai, Xingguo Wu, and Rui Li A Survey of Global Information Fusion Optimization Algorithms Based on Distributed Precise Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 Yifan Zhang and Shi Liu Elastic-Plastic Analysis and Evaluation Method for the Research Reactor Irradiation Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689 Rui Liu and Xuede Chen Study of Magnetic Field Focusing Characteristics of Active Electromagnetic Metamaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 Xiaokuo Liu, Chao Zhang, Guoqiang Liu, and Yannan Tian Simulation of Magneto-Acousto-Electrical Tomography Based on Approximately Realistic Numerical Breast Model . . . . . . . . . . . . . . . . . . . . . . . 706 Wenwei Zhang, Guoqiang Liu, Hui Xia, Yuanyuan Li, Shiqiang Li, and Xiaonan Li Modeling Analysis of Wireless Power Transmission (WPT) System with LCCL-LCL Compensation Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714 Xiongting Zhu, Yukun Tang, and Guozhen Hu Anisotropic Electrical Impedance Imaging Technology Based on Transforming Medium Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 Yannan Tian, Jianjun Xu, Chao Zhang, Guoqiang Liu, and Xiaokuo Liu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733

Research on Surface Flashover of Vacuum Insulator with High-Voltage Insulation and Wireless Power Transfer Capabilities Li Gui, Yanling Li(B)

, Weilesi, and Rui Jing

Southwest Jiaotong University, Chengdu 611756, China [email protected]

Abstract. The integrated insulator device with multiple magnetic coupling coils provides continuous and stable power supply for online monitoring equipment. Nevertheless, how the introduction of high-frequency magnetic field effects the surface flashover of the insulator is still unrevealed. Based on the surface flashover hypothesis theory in vacuum, finite element analysis (FEA) method was used to simulate the motion trajectory of initial electron near the insulator in different positions and magnetic field configuration, and the insulation performance was studied by analyzing the electron movement under the influence of electric field and high-frequency magnetic field. It is found that the electron with initial kinetic energy will impact the insulator surface at certain positions and magnetic field configurations, resulting in secondary electron emission (SEE) and continuous accumulation of positive charge on the insulator surface. The movement of secondary electrons towards the anode increases the electric field intensity, which promotes the process of secondary electron emission and positive charge accumulation until the formation of flashover along the surface. In other cases, the electron is deflected by the Lorentz force and leave the surface, so as to inhibit the flashover along the insulator surface. Keywords: Integrated Insulator · Wireless Power Transfer · Surface Flashover · Electron Movement

1 Introduction High-voltage transmission line (HVTL) online monitoring equipment can effectively monitor the operation status of the line, providing strong assurance for its normal operation. However, traditional power supply methods such as solar energy and battery power have disadvantages such as high maintenance costs and susceptibility to weather conditions. Wireless Power Transfer (WPT) technology, which enables energy transfer under electrical isolation conditions, has become a hotspot in recent years. In the field of HVTL monitoring equipment charging, domestic and foreign researchers have mainly focused on the design of wireless power supply devices and techniques to improve power efficiency. Firstly, based on the non-embedded deployment of power transfer coils, [1] and [2] have found that the position of the coil outside © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 1–9, 2024. https://doi.org/10.1007/978-981-97-0873-4_1

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the insulator has a minimal impact on the surface electric field distribution. [2] also theoretically calculated that the induced current generated by the magnetic field in the transmitting coil can be neglected, demonstrating the feasibility of the non-embedded deployment method. However, the coil size in this method is too large and installation is inconvenient. On the other hand, the embedded coil deployment does not alter the external structure of the insulator and has better application prospects. [3] and [4] have developed integrated insulators suitable for voltage levels of 220 kV and 110 kV, and the electric field simulation results show that the distribution of the insulator’s electric field is basically unaffected before and after coil embedding. [5–8] mainly optimize the power transfer characteristics of wireless power supply systems, without considering the design of devices that integrate coils with insulators. The above-mentioned studies have macroscopically demonstrated that the presence of coils has little effect on the distribution of the insulator’s electric field, but they have not analyzed the movement of charged particles around the insulator under the comprehensive action of electromagnetic fields from a microscopic perspective. Some researchers have simulated the movement of metal particles in 1100 kV gasinsulated transmission lines and successfully captured metal particles by setting particle traps, thereby improving the insulation reliability of the equipment [9]. Other scholars have studied the effect of the circuit’s self-magnetic field on the insulation characteristics of insulators based on the vacuum surface flashover hypothesis. They found that when the magnetic field direction promotes the movement of electrons away from the insulator surface, a flashover inhibition effect (Magnetic Flashover Inhibition, MFI) occurs, which can increase the surface flashover field strength of the insulator [10, 11]. However, there is still limited research on the impact of the self-excited magnetic field generated by power transfer coil of the insulator on surface flashover. This paper focuses on the study of insulators with embedded coils at the 35 kV level and investigates the motion characteristics of electrons under the combined action of magnetic and electric fields. It analyzes the impact of the introduction of high-frequency magnetic fields in WPT systems on the movement of electrons around the insulator, providing a direction for improving the insulation characteristics of integrated insulator.

2 Insulator Model and Simulation Analysis 2.1 Integrated Insulator Model The integrated insulator studied in this article is shown in Fig. 1. Its structure mainly includes line end, ground end, weather sheds and core rod. The multi-relay magnetic coupling coils are embedded in weather sheds. The reference direction of the coil excitation current and the direction of the electric field have been marked. The electrons near the ground end move in the positive direction of the X-axis and are subjected to the electric field force Fe and the Lorentz force Fm . The combined force of the two is Ft . Under different magnetic field configurations, initial positions, and velocity conditions, the electrons will deviate from the original trajectory and move away from or closer to the insulator surface, thereby affecting the flashover field strength along the insulator surface.

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Fig. 1. Electron movement of the integrated insulator

2.2 Simulation and Analysis Model Building and Initial Condition Setting Around the insulator, the energy of electrons typically ranges from tens to hundreds of electron volt. In this study, a 7-weather shed integrated insulator with a voltage rating of 35 kV is taken as an example. A simulation model is established in finite element software to simulate the trajectory of charged particles around it. The initial positions of the electrons are placed near the line end, the middle, and the ground end, respectively. Under the influence of the initial kinetic energy E0 , the electron will move in the positive direction of the X-axis. The schematic diagram is shown in Fig. 2.

Fig. 2. Initial energy and moving direction of electron

The WPT system starts from the transmitter coil, and the current phase of the subsequent coils can be approximately considered to lag behind the previous coil by 90° [5]. In this paper, the initial phase of the transmitter coil is selected as three typical phases of 0°, 45° and 90°. The initial phase settings of the other coils are shown in Table 1, which is close to the actual working conditions of the WPT system, so as to obtain more accurate magnetic field distribution. Obtaining the motion laws of electrons in different magnetic field configurations is convenient. The other model parameters are set in Table 2.

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Configuration

Coil1

Coil2

Coil3

1 2 3

Coil4

Coil5

Coil6

Coil7

0°

−90°

−180°

−270°

0°

−90°

−180°

45°

−45°

−135°

−225°

45°

−45°

−135°

90°

0°

−90°

−180°

−270°

0°

−90°

Table 2. Model parameter settings Frequency

Initial energy

Turns of Coil

Voltage of Line end

Voltage of Ground end

1e6 Hz

800 eV

16

35000 V

0V

Simulation of Electrostatic Field and Magnetic Field Firstly, the electrostatic field simulation is carried out to obtain the surface potential and electric field distribution of the integrated insulator, as shown in Fig. 3. It can be seen that the surface potential of the insulator uniformly transitions from the top of the high potential to the low potential, and the potential near the two ends changes obviously, and the electric field strength is large, where the electron is affected by the electric field force, and will move from the initial position to the area near the high field strength.

Fig. 3. Voltage potential and Electrical field intensity of the insulator

Before conducting the magnetic field simulation, it is necessary to study the motion of electrons under the action of electric field force (EFF) only. Figure 4 shows the motion trajectory of electrons at the line end only under the EFF. It can be seen that electrons are slightly close to the negative direction of the Y-axis, tend to move towards the region of high field strength and move in a straight line after hitting the insulator surface. The simulation results are consistent with the above analysis. Next, the magnetic field frequency domain simulation is carried out. The magnetic flux distribution under the three configurations is shown in Fig. 5, where the arrow indicates the direction of the magnetic field line. It can be seen that due to the different initial phase of the excitation current of each coil, the magnetic flux around the insulator presents a clockwise or counterclockwise distribution, in which the electron is subjected

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Fig. 4. Moving trajectory of electron applied EFF only

to the Lorentz force, and the initial motion direction will be deflected to the direction of the force.

Fig. 5. Magnetic flux density of all configurations

Electronic Motion Trajectory Analysis On the basis of solving the electrostatic field and magnetic field, a single electron is placed in different initial positions around the integrated insulator, and its trajectories under different magnetic field configurations are obtained and briefly analyzed. Firstly, the results of three trajectories of electrons emitted from the line end are analyzed, as shown in Fig. 6, Fig. 7, Fig. 8. As can be seen from Fig. 6, the electron moves towards the direction of high field strength and cuts the magnetic field line at the same time, moving counterclockwise by Lorentz force. The closer the place is to the surface of the insulator, the greater the force and the smaller the motion radius. Finally, the direction of motion is directly reversed without colliding with the insulator surface.

Fig. 6. Moving trajectory at the top, configuration 1

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The motion trajectory of electron under the configuration 2 is similar. As shown in Fig. 7, the electron is also deflected counterclockwise by Lorentz force and do not collide with the insulator.

Fig. 7. Moving trajectory at the top, configuration 2

But the electron trajectory is different in configuration 3. The reason is that in the first two configurations, the magnetic field line around the line end starts from the top and pulls the beam down, while in the third configuration, the beam pulls up from the bottom. Therefore, it can be seen from Fig. 8 that the electron moves in a clockwise direction, hit the surface of the insulator and are bounced.

Fig. 8. Moving trajectory at the top, configuration 3

Next, the motion of the electron subjected to Lorentz force when its initial position is near the middle of insulator is analyzed. The trajectories under different magnetic field configurations are shown in Fig. 9, Fig. 10, Fig. 11. As can be seen from Fig. 9, in the case of configuration 1, the direction of electron movement is basically parallel to the magnetic field line, and it is less affected by Lorentz force, and the surface of the insulator is bounced back when the electron collides.

Fig. 9. Moving trajectory near the middle, configuration 1

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The deflection of electron trajectory under the influence of magnetic field is obvious, and the electron keeps moving counterclockwise away from the insulator surface.

Fig. 10. Moving trajectory near the middle, configuration 2

The electron is deflected clockwise under the configuration 3, but does not touch the insulator surface.

Fig. 11. Moving trajectory near the middle, configuration 3

Finally, Fig. 12, Fig. 13, Fig. 14 show the motion of electron under three magnetic field configurations near the ground end. As can be seen from Fig. 12, the electron moves counterclockwise and does not collide with the insulator surface, because the magnetic field lines near the ground end are drawn up from the bottom, but the magnetic flux density is different, resulting in different angles of electron deflection.

Fig. 12. Moving trajectory at the bottom, configuration 1

The motion trajectories of electron under all the above conditions are summarized in Table 3 below. Because the excitation current is sinusoidal alternating current, the direction of the magnetic field line changes with time, and the direction of the Lorentz force applied to the electron also changes from time to time, which is conducive to the electron leaving the insulator surface at some times, and will accelerate the electrons

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Fig. 13. Moving trajectory at the bottom, configuration 2

Fig. 14. Moving trajectory at the bottom, configuration 3

hitting the insulator surface at other times. In addition, the insulator we studied is in the vacuum domain, in actual circumstances, electron will be affected by other forces besides electric and magnetic forces, such as air resistance, friction, etc., and the movement will be more complicated. Table 3. Electron trajectory of all cases Position of electron

Line end

Middle

Ground end

Configuration1

No collision

Collision

No collision

Configuration2

No collision

No collision

No collision

Configuration3

Collision

No collision

No collision

3 Conclusion In this paper, the electromagnetic field simulation model of 35 kV integrated insulator with multistage magnetic coupling coil is established by finite element simulation method. The initial kinetic energy, direction and position of electrons are given, and the motion laws of electrons around the insulator are studied under three given magnetic field configurations. In summary, electrons with certain initial kinetic energy accelerate the impact on the insulator surface under certain initial positions and magnetic field configuration, which promotes the occurrence of flashover along the insulator surface. In other cases, it is deflected away from the insulator surface by the Lorentz force, which helps to restrain flashover along the insulator surface.

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Acknowledgments. This work is supported by Sichuan Science and Technology Program (24NSFSC1332) and the Funding of Chengdu Guojia Electrical Engineering Co., Ltd (NEEC2022-B06).

References 1. Wang, W., Yang, S., Yang, J., et al.: Optimization analysis of wireless charging system for monitoring sensors overhead the HVPLs based on impedance matching. IEEE Trans. Electromagn. Compat. 61(4), 1207–1216 (2019) 2. Cai, C., Wang, J., Liu, R., et al.: Resonant wireless charging system design for 110-kV high-voltage transmission line monitoring equipment. IEEE Trans. Industr. Electron. 66(5), 4118–4129 (2019) 3. Gu, P., Liu, Z., Guan, H., et al.: A 2.5m long-range IPT system based on domino cylindrical solenoid coupler compensated respectively in layers. IEEE Trans. Ind. Electr. 70(2), 1409– 1420 (2023) 4. Zhang, C., Lin, D., Tang, N., et al.: A novel electric insulation string structure with highvoltage insulation and wireless power transfer capabilities. IEEE Trans. Power Electron. 33(1), 87–96 (2018) 5. Guan, Y., Xiao, Y., Cui, Y., et al.: Analysis and optimal design of mid-range WPT system based on multiple repeaters. IEEE Trans. Ind. Appl. 58(1), 1092–1100 (2022) 6. Liu, M., Lyu, L., Li, J., et al.: A practical Z-parameter two-port modeling method to evaluate long-distance and high-efficiency wireless power-relay systems. IEEE Trans. Ind. Appl. 58(1), 1081–1091 (2022) 7. Dong, Z., Liu, S., Li, X., et al.: A novel long-distance wireless power transfer system with constant current output based on domino-resonator. IEEE J. Emerg. Sel. Top. Power Electr. 9(2), 2343–2355 (2021) 8. Shu, X., Zhang, B., Wei, Z., et al.: Extended-distance wireless power transfer system with constant output power and transfer efficiency based on parity-time-symmetric principle. IEEE Trans. Power Electron. 36(8), 8861–8871 (2021) 9. Zhang, B., Liu, Y., Du, Y., et al.: Research on the dynamic capture by particle trap in 1100 kV gas insulated transmission line for metal particles. In: The 3rd IEEE Conference on Energy Internet and Energy System Integration, pp. 779–783. IEEE, Changsha (2019) 10. Li, F., Wang, M., Yang, Z., Ren, J., Kang, J.: Surface flashover character of insulator in vacuum under self-magnetic field. High Power Laser Part. Beams 24(12), 2925–2929 (2012). (in Chinese) 11. Li, F., Wang, M., Ren, J., Kang, J., Yang, Z., et al.: Coaxial insulator surface flashover character in different self-magnetic field conditions. High Power Laser Part. Beams 25(11), 3055–3059 (2013). (in Chinese)

Efficiency Improvement by Electromagnetic Metasurface in Wireless Power Transfer System Conghui Lu(B) , Lei Fan, Keling Song, Renjun Jiang, QingLv, Xunyi Dang, and Pingping Wang China North Vehicle Research Institute, Beijing 100072, China [email protected]

Abstract. The electromagnetic parameters of the electromagnetic metasurface (EMMS) can affect the performance of the wireless power transfer system. However, the method of the effective medium theory can not reveal the intrinsic physical properties of the system. The theory of EMMS with dual-frequency has not been investigated. And the EMMS apply to the wireless power transfer is hard to analyze and optimize. Therefore, this article proposed the circuit method to optimize the structure of EMMS. The mutual inductance between the unit cells in the arbitrary position is calculated. Additionally, the effective permeability of the EMMS with dual-frequency is deduced by the numerical calculation. The calculation results are consistent with the simulation results. And the magnetic field of the wireless power transfer system with EMMS can be enhanced. The experimental results show that the designed EMMS can improve the efficiency at two frequencies. Additionally, the design structure can adjust the electromagnetic field to achieve different performance. It is important to understand the working mechanism of the EMMS with dual-frequency. Keywords: Electromagnetic metasurface · Effective permeability · Mutual inductance · Circuit model · Wireless power transfer

1 Introduction Metasurface is a kind of new artificial material which is composed of natural materials, such as metal, plastic, and printed circuit board. It is the arrangement with certain rules. The electromagnetic metasurface (EMMS) has the development potential in the fields of military, aerospace, and wireless power transfer [1, 2]. The EMMS with different structures has unique characteristics. The expected electromagnetic parameters of the EMMS can be adjusted by changing the physical size. The wireless power transfer with EMMS can improve the performance of the system [3]. As we all know, the EMMS has negative permeability, negative permittivity, and zero permeability, which can realize the energy improved and shield the magnetic field. Based on the most studied, the structure of the EMMS is very important [4–6]. Thus, the electromagnetic parameters of the EMMS should be optimized and considered. Currently, the effective electromagnetic parameters of the EMMS are extracted by the effective theory and simulated calculated [7, 8]. The application of the two methods needs © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 10–19, 2024. https://doi.org/10.1007/978-981-97-0873-4_2

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electromagnetic wave theory. However, the EMMS in the kHz frequency belongs to the quasi-static electromagnetic field. The electric field and magnetic field are decoupled, and the energy can be not transferred in the form of an electromagnetic wave. Also, the above methods are not matched to the low frequencies of EMMS. Additionally, the EMMS is composed of the most unit cell. It is needed to build the model of the whole system to calculate the electromagnetic parameters. However, the numerical simulation always relays the parameters scanning. The method is time-consuming and the modeling is complicated with the multiple iteration optimization. It can not be applied to the unit cell with complex structure and complex array combination. Based on the shortcoming of the above method, it needs to study the method of the equivalent circuit to acquire the electromagnetic parameters [9, 10]. The working mechanism of the EMMS in low frequency can be explored by the circuit theory. However, the circuit model is studied in the single-frequency of the EMMS. The electromagnetic parameters of the EMMS with dual-frequency should be investigated. The circuit parameters are important to analyze the performance of the EMMS. The effective permeability of the EMMS is in relationship to the mutual inductance, selfinductance, and resistance [11–13]. Additionally, the variation of mutual inductance can directly affect the transfer performance of the wireless power transfer system. It is very significant to study the mutual inductance of the unit cell with different positions. Currently, the mutual inductance between the unit cell is adopted by the tables and element simulation [14]. However, these methods need to conduct the parameters of the EMMS and difficult to analyze the mutual inductance of the unit cell in the other positions. The calculated method of mutual inductance in the arbitrary position is proposed [15]. However, the coordinate needs to be redefined when the relative position of the unit cells is changed. To address this problem, a circuit model of the EMMS with dual-frequency is proposed in this paper. The mutual inductance of the unit cell in the different positions and the formulates of the electromagnetic parameters for the EMMS with dual-frequency are established in Sect. 2. Section 3 develops the mutual inductance of the simulation and calculation results, and presents the calculation electromagnetic parameters. The magnetic field of the wireless power transfer with EMMS is simulated, and the efficiency of the system is calculated to verify the effectiveness of the designed EMMS in Sect. 4. Section 5 concludes the study of this paper and presents the future work from this study.

2 Theory Model of the EMMS 2.1 Model of the Mutual Inductance Figure 1 shows the mutual inductance model of square unit cells in the arbitrary position. The model is constructed with the Square1 and Square 2. The center of Square 1 and Square 2 are located on the axis of Oxyz and O´xyz, respectively. For example, the segment of the square unit cell, the coordinate of any point on the S i segment of Square 1 is (x 1 , y1 , 0), and the coordinate of any point on the S j segment of Square 2 is (x 2 , y2 , 0).

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Fig. 1. Square 1 and Square 2 in different positions.

Since the unit cells are composed of multiple line segments, the mutual inductance between the S i and S j can be calculated by Neumann’s formula [16]. The mutual inductance between the two segments can be written as: ⎞ ⎛  dx1 dx2  ⎟ ⎜ c1 c2 (x2 − x1 )2 + (y2 − y1 )2 + z22 ⎟ μ0 ⎜ ⎟ ⎜ (1) MSi ,Sj = ⎟ ⎜   dy1 dy2 ⎟ 4π ⎜ ⎠ ⎝+  c1 c2 (x2 − x1 )2 + (y2 − y1 )2 + z22 For the two segments in the two unit cells, the formula is written as follow: Square 1 :

x1 − ak0 y1 − bk0 z1 − ck0 = = = tk mk nk rk

(2)

Square 2 :

x2 − af0 y2 − bf0 z2 − cf0 = = = tf mf nf rf

(3)

where t k and t f represents the values of Square 1 and Square 2, (ak0 , bk0 , 0) and (af0 , bf0 , zf0 ) are the arbitrary point on the Square 1 and Square 2. Assuming the total number of segments, length, and thickness of the unit cells are N’x , wm , t m , where x = p represents the Square 1, x = s represents the Square 2. The electric parameters of mutual inductance is expressed as follows: 

Mtot =

N

Ns p



MSi ,Sj

(4)

i=1 j=1

Based on the formula of electromagnetic parameters, the circuit parameters of the wireless power transfer system and EMMS can be calculated. The calculated method of the mutual inductance is verified in Sect. 3 2.2 Numerical Calculation of Equivalent Permeability To qualitatively analyze the working mechanism of the metasurface, it is necessary to accurately obtain the equivalent permeability of the metasurface. Assuming the magnetic field incident the metasurface is under the condition of the wave, as shown in Fig. 2. Here, the magnetic flux density incident on the metasurface and generated the induced current in each turn of the metasurface. Figure 3 shows the equivalent circuit model of

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Fig. 2. Magnetic field incident on the unit cell of EMMS.

the metasurface. It should be noted that the induced current of the metasurface is the key to controlling the magnetic field. The effective permeability of the metasurface can be deduced as: μr1 μ0 μr = 1 + (5) μr2 Vunit where μr1 and μr2 are the formula of the effective permeability of the first frequency and second frequency, V unit is the volume of the metasurface. The detailed formula will be presented in another articles. According to Sect. 2.1, the electric parameters of the metasurface can be calculated. The effective permeability is varied with the frequency change. It can show the relationship between the electromagnetic response of the unit cells and thte metasurface.

3 Analyzed and Calculated To verify the correctness of the proposed mutual inductance calculation method and effective permeability formula, a 3 × 3 array metasurface is selected to analyze. The wireless power transfer system is shown in Fig. 3 (a). The model of the metasurface is shown in Fig. 3 (b).

Fig. 3. Wireless power transfer system and EMMS (a) Structure of the wireless power transfer system (b) Model of the EMMS.

The metasurface is located in the middle of the wireless power transfer system. The circuit model with the EMMS is developed, as shown in Fig. 4.

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M tr

Ct

M tml1 ( M tmh1 ) M ml1ml2 ( M mh1mh2 )

+ U t Lt −

Rml,1 ( Rmh,2 )

X mlr-1 ( X mhr-1 ) Lml,1 ( Lmh,1 )

HGJH M tml2 ( M tmh2 )

M ml2ml3 ( M mh2mh3 ) M M tml3 ( M tmh3 )

Rt

Ir

FHQWHU I ml1 ( I mh1 )

Lml,2 ( Lmh,2 ) ( M mh,2mh,2 )

Cr

I ml2 ( I mh2 )

Rml,2 ( Rmh,2 ) X mlr-2 ( X mhr-2 )

ml,2ml,2

M rml1 ( M rmh1 )

L

M rml2 ( M rmh2 )

M ml1ml3 ( M mh1mh3 )

Lr

Req

FRUQHU I ml3 ( I mh3 ) M rml3 ( M rmh3 )

Rml,3 ( Rmh,3 )

X mlr-3 ( X mhr-3 )

Lml,3 ( Lmh,3 )

L

Rr

Fig. 4. Equivalent circuit of the proposed system.

According to the symmetry of structure, the mathematical model of the wireless power transfer system with metasurface is derived as: ⎤⎡ ⎤ ⎡ ⎤ Ut It Zt jωMtr jωMtml jωMtmh ⎢ jωMtr ⎥⎢ Ir ⎥ ⎢ 0 ⎥ Z jωM jωM r rml rmh ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎣ jωMT jωMT Zml + jωMmlml ⎦⎣ Iml ⎦ = ⎣ 0 ⎦ jωMmlmh tml rml jωMTtmh jωMTrmh jωMmlmh Zmh + jωMmhmh Imh 0 ⎡

(6)

where the Im , Mtm , Mrm , Mmm , Zm are represented by matrix. The efficiency of the system can be written as:      V  R 1/2 2  V 2 R  L     S η = |S21 |2 = 2  = 4 2L S    VS Req  VS Req 

(7)

where VS and VL are the input voltage of the transmitter coil and the voltage across the receiver coil. The mutual inductance model of the metasurface and wireless power transfer is built. For example, the top layer pattern of the metasurface is used to calculate the mutual inductance. Put the center unit cell as the reference, the mutual inductance between the center and edge, corner unit cell are analyzed. Figure 5(a) shows the mutual inductance of calculated and simulated. The results show that the circuit method to calculate the EMMS is accurate. Figure 5(b) shows the mutual inductance of the wireless power transfer system. The size of the coils is the same as the Table 1. When the secondary coil is displacement along the y axis, the curve of the mutual inductance is obtained. The distance between the coils is from 100 mm to 200 mm. The coupling between the coils is gradually reduced. It shows that the mutual inductance between the coils is decreased with the increased distance. The simulated results are consistent with the calculated results. Based on the formula (4), (6) and (7), the structure of the EMMS is obtained. The size of the EMMS and wireless power transfer system are listed in Table 1. The top layer pattern and bottom layer pattern are different. The square spiral is made of copper. The material of the substrate is FR-4 and the thickness is 0.4 mm. The frequency of the metasurface is adjusted by changing the lumped capacitance. The turn-to-turn space, width, and copper outer length are defined as S, W, and Dm. The turns of the top layer

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Fig. 5. Mutual inductance (a) unit cell of EMMS (b) system coils.

and bottom layer are N m1 and N m2 , respectively. The turns of the transmitter coil and receiver coil are N p and N s , respectively. The outer length of the coils is Dp and Ds, respectively. The cross-section diameter and the spacing between the turns are W 0 and S 0 , respectively. Table 1. The parameters of the wireless power transfer system and EMMS. S

W

N m1 /N m2

Dm

Np

Ns

2 mm

3 mm

4/2

130 mm

8

5

Dp

Ds

Wp

Sp

Ws

Ss

200 mm

100 mm

3 mm

2 mm

2 mm

2 mm

Additionally, the effective permeability is calculated by (5). Figure 6 displays the curve of the effective permeability and the frequency. The real permeability of the EMMS is negative at 13.56 MHz and 19 MHz.

Fig. 6. Permeability of the EMMS.

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4 Simulation and Experimental Verification Furthermore, the design EMMS is applied to the wireless power transfer system. The distance between the coils is 20 cm. Figure 7 shows the magnetic field of the system at two frequencies. When the wireless power transfer system with EMMS, the magnetic field is enhanced compared with the system at 13.56 MHz. When the wireless power transfer system at 19 MHz, the EMMS can enhance the magnetic field of the system.

Fig. 7. Magnetic field of the wireless power transfer system with and without EMMS (a) System at 13.56 MHz (b) System at 19 MHz.

A wireless power transfer system operating at 13.56 MHz and 19 MHz is built to experimentally validate the effectiveness of the EMMS. The photograph of the measurement setup for the wireless power transfer system with the proposed EMMS can be seen in Fig. 8. The parameters of the wireless power transfer system are consistent with the Table 1.

Fig. 8. Measurement setup of the wireless power transfer system integrating with EMMS.

To the best of our knowledge, the position of the EMMS is critical to the efficiency of the wireless power transfer system. Thus, we investigate the variation of efficiency with the distance of EMMS. When the EMMS is applied in the wireless power transfer system, the distance of D1 is fixed at 20 cm, and the distance between the EMMS and transmitter coil is changed from 13 to 18 cm in steps of 1 cm. The effect of the EMMS positions on the performance of wireless power transfer system are provided in Table 2. It can be clearly seen that the WPT system has the maximum improvement efficiency when the

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EMMS is located at 17 cm. The efficiency is increased by 30.5% and 38.2% compared to the wireless power transfer system without EMMS. Therefore, the efficiency can be improved by adjusting the distance of EMMS. Table 2. Efficiency versus with the position of EMMS. Distance(cm)

13

14

15

16

17

18

Efficiency at 13.56 MHz

10.59%

13.31%

16.6%

21.61%

30.5%

26.24%

Efficiency at 19 MHz

14.76%

18.52%

21.98%

27.35%

38.2%

34.57%

In a subsequent study, to examine the optimal operating distance of the wireless power transfer system, the measured efficiencies versus distance D1 are shown in Fig. 9. The distance between the coils are varied from 12 cm to 26 cm when the EMMS is at the optimum position. From these results, it can be seen that the efficiency of the wireless power transfer system is significantly improved, especially at long distances. Meanwhile, it can be observed that the wireless power transfer system has the highest efficiency at the distance of 14 cm and the maximum improvement efficiency at the distance of 20 cm.

Fig. 9. Measured results with D1.

The EMMS can enhance the magnetic field strength of the wireless power transfer system which has been described in different distance. Here, we put the emphasis on analyzing the variation of the efficiency with the receiver coil offset misalignment. The efficiency of the wireless power transfer system with EMMS is shown in Fig. 10. When the receiver coil is longitudinal misalignment y = 5 cm, the efficiency of the system are increased by 24.65% and 22.78%, respectively.

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Fig. 10. Misalignment of the EMMS in the wireless power transfer system.

5 Conclusion In this paper, a novel method of the EMMS with dual-frequency for the effective permeability was proposed. The mutual inductance calculation between the unit cell of the EMMS is proposed. It can obtain the mutual inductance when the EMMS at arbitrary positions. The simulation and calculation results verified the mutual inductance method. In order to optimize the EMMS, the circuit model of the EMMS can calculate the effective permeability. The result shows that the effective permeability of the EMMS is negative at 13.56 MHz and 19 MHz. The wireless power transfer system with EMMS is simulated in this paper. The magnetic field strength is increased when the wireless power transfer system with EMMS. Meanwhile, the experiment results show that the efficiency is improved when the system with EMMS at different distances and different offset positions. The proposed method can be used to design the structure of the EMMS, which can improve the transfer performance of the wireless power transfer system.

References 1. Sun, K., Fan, R., Zhang, X., et al.: An overview of metamaterials and their achievements in wireless power transfer. J Mater. Chem. C 6(12), 2925–2943 (2018) 2. Wang, B., Yerazunis, W., Teo, K.H.: Wireless power transfer: metamaterials and array of coupled resonators. Proc. IEEE 101(6), 1359–1368 (2013) 3. Adepoju, W., Bhattacharya, I., Sanyaolu, M., Bima, M.E., Banik, T., Esfahani, E.N.: Critical review of recent advancement in metamaterial design for wireless power transfer. IEEE Access 10, 42699–42726 (2022) 4. Puccetti, G., Stevens, C.J., Reggiani, U., Sandrolini, L.: Experimental and numerical investigation of termination impedance effects in wireless power transfer via metamaterial. Energies 8(3), 1882–1895 (2015) 5. Zhao, C., Zhu, S., Zhu, H., Huang, Z., Luo, X.: Accurate design of deep sub-wavelength metamaterials for wireless power transfer enhancement. Prog. Electromagn Res. C 83, 195– 203 (2018) 6. Das, R., Basir, A., Yoo, H.: A metamaterial-coupled wireless power transfer system based on cubic high-dielectric resonators. IEEE Trans. Industr. Electron. 66(9), 7397–7406 (2018)

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7. Shan, D., Wang, H., Cao, K., Zhang, J.: Wireless power transfer system with enhanced efficiency by using frequency reconfigurable metamaterial. Sci. Rep. 12(1), 1–11 (2022) 8. Corrêa, D.C., Resende, U.C., Bicalho, F.S.: Experiments with a compact wireless power transfer system using strongly coupled magnetic resonance and metamaterials. IEEE Trans. Magn. 55(8), 1–4 (2019) 9. Rong, C., Lu, C., Hu, Z., et al.: Analysis of wireless power transfer based on metamaterial using equivalent circuit. IET J. Eng. 2019(16), 2032–2035 (2019) 10. Gong, Z., Yang, S.: Metamaterial-core probes for nondestructive Eddy current testing. IEEE Trans. Instrum. Meas. 70, 3505209 (2021) 11. Liu, S., Su, J., Lai, J., Zhang, J., Xu, H.: Precise modeling of mutual inductance for planar spiral coils in wireless power transfer and its application. IEEE Trans. Power Electron. 36(9), 9876–9885 (2021) 12. Raju, S., Wu, R., Chan, M., Yue, C.P.: Modeling of mutual coupling between planar inductors in wireless power applications. IEEE Trans. Power Electron. 29(1), 481–490 (2014) 13. Schormans, M., Valente, V., Demosthenous, A.: Practical inductive link design for biomedical wireless power transfer: a tutorial. IEEE Trans. Biomed. Circuits Syst. 12(5), 1112–1130 (2018) 14. Grover, F.W.: Inductance Calculation: Working Formulas and Tables. Dover, New York, NY, USA (1946) 15. Liu, F., Yang, Y., Jiang, D., Ruan, X., Chen, X.: Modeling and optimization of magnetically coupled resonant wireless power transfer system with varying spatial scales. IEEE Trans. Power Electron. 32(4), 3240–3250 (2017) 16. Ramo, S., Whinnery, J.R., Duzer, V.T.: Fields and Waves in Communication Electronics. Wiley, New York (1965)

An H-Shape Magnetic Coupler of the WPT Systems for the Cervical Vertebral Fusion Jing Li(B) , Ruikun Mai , Yang Chen , Yuner Peng , and Li Zheng School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China [email protected], [email protected], [email protected], [email protected]

Abstract. The adjacent segment degeneration after cervical spine fusion can severely impact the surgical efficacy. Therefore, it is necessary to monitor the stress of the adjacent segments and prevent degenerative diseases caused by excessive pressure. In this paper, a small magnetic coupler with a receiver of only 1.65 cm3 is proposed. And the power can be transferred to the stress transducer in the cervical spine through placing receiver in implants. First, an H-shape magnetic core is proposed to constrain the magnetic field, and the transmitting coil turn is increased to enhance the mutual inductance. Then, the magnetic sheets thickness, magnetic rod diameter and magnetic rod position are optimized by the finite element analysis software. Finally, the proposed structure is compared to existing structure, the mutual inductance is increased by 15 times, and the volume and core loss are basically unchanged. The experiment fully proves the feasibility and superiority of the proposed structure. Keywords: Cervical fusion · wireless power transfer · magnetic coupler · mutual inductance

1 Introduction In recent years, wireless charging technology for implantable medical devices has become a research focus both domestically and internationally [1, 2]. Compared to traditional battery-powered methods, wireless charging can completely avoid the risk of wound infection caused by battery replacement surgery, eliminate health hazards caused by harmful elements in the battery, and reduce additional medical costs [3]. The magnetic coupler is a key component of the wireless charging system for implantable medical devices, and its design directly affects the charging efficiency and quality [4]. Therefore, designing a magnetic coupler suitable for the wireless charging system of implantable medical devices is of great significance. In traditional wireless charging systems, the design of magnetic couplers mainly considers factors such as transmission distance, efficiency, and anti-misalignment ability. However, in the wireless charging system for implanted medical devices, the design of magnetic couplers is more complex and special due to factors such as space limitations and safety considerations [5]. Cervical fusion is a common surgery used to treat cervical © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 20–28, 2024. https://doi.org/10.1007/978-981-97-0873-4_3

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disc damage. By removing degenerated discs from the anterior part of the neck, implanting intervertebral fusion devices, and using plates and screws to fix adjacent vertebrae, cervical deformities can be improved and nerve compression can be alleviated [6, 7]. To monitor the stress on adjacent vertebrae during fusion and prevent new degenerative diseases caused by excessive pressure, this article proposes a magnetic coupler where the receiver coil can be placed inside the cervical fusion device to achieve wireless power supply for sensors inside the cervical spine (Fig. 1).

Fig.1. Installation of cervical fusion cage.

Currently, the commonly used coils in implantable medical device wireless charging systems include planar spiral coils [8] and spatial spiral coils. In planar spiral coils, a circular coil with the same wire length and outer diameter produces a more uniform magnetic field than a rectangular coil, and at the same time, due to the greater number of windings, the mutual inductance between the coils is also greater [9]. Compared to planar spiral coils, spatial spiral coils require less space to obtain the same mutual inductance, but in cases where the wire length and outer diameter are the same, planar spiral coils can provide a larger coupling coefficient [10]. It is worth noting that most implantable medical devices have a titanium alloy shell that acts as an electromagnetic shield in the face of high-frequency magnetic fields, impeding the transmission of energy in wireless charging systems. Therefore, how to reduce the impact of titanium alloy on energy transmission is an important issue that cannot be ignored in designing magnetic couplers [11]. Overall, the choice of coils for implantable wireless charging systems should not only consider the characteristics of the coils themselves but also take into account the specific implants and application scenarios. A micro-miniature magnetic coupler with an H-shape magnetic core has been proposed for cervical fusion implants based on their size, material, and application scenarios. In the proposed structure, the transmitting coil is located outside the body without any size limitations and a multi-layer planar spiral coil is selected. The receiving coil is located inside the cervical fusion implant and a spatial spiral coil is chosen. Ferrite magnetic bars pass through the receiving coil and connect to magnetic sheets outside the titanium alloy, greatly increasing the mutual inductance between the coils. Then, the receiver of the proposed magnetic coupler is optimized using finite element simulation

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software. Finally, the optimized structure is compared with existing structures to fully verify the correctness of the proposed magnetic coupler.

2 Proposed System Structure 2.1 Magnetic Coupler The magnetic coupler proposed is shown in Fig. 2. The transmitter consists of two seriesconnected planar rectangular coils spaced 160 mm apart and symmetrically placed on both sides of the receiver. The currents generated by the coils produce magnetic fields in the same direction, and the main magnetic flux passes from one transmitting coil, travels through the receiving coil, and arrives at the other transmitting coil. Based on the actual application scenario, the outer side length of the transmitting coil is set to 155 mm, the width is 83 mm, and the wire diameter is 2 mm. Each transmitting coil has 4 layers and 8 windings per layer. The transmitting coils are located on both sides of the cervical spine, and the receiving coil is implanted inside the body.

p p

Fig. 2. Diagram of the magnetic coupler.

As shown in Fig. 3, the receiver includes the outer shell, magnetic core, and receiving coils. The outer shell is 16mm × 16mm × 6mm which wall thickness is 0.5 mm. It is the support structure of the rectifier, dc/dc module, sensor, and other components, serving as a support structure. The outer shell is made of titanium alloy. The magnetic core includes two magnetic sheets and a cylindrical magnetic bar. The magnetic sheets are attached to both sides of the titanium alloy outer shell, and the magnetic bar passes through the outer shell and connects to both magnetic sheets, forming an H-shape structure that focuses the magnetic flux and enhances the coupling. The receiving coil is wound around the magnetic bar and located inside the titanium alloy outer shell. 2.2 Topology The topology of the implantable WPT system is shown in Fig. 4, in order to reduce the volume of the implant and reduce the number of components at the receiver, the S-S topology and half-bridge rectifier structure are adopted. In Fig. 4, U in is the input voltage, Q1~Q4 is the MOSFET switch, L p and L s represent the self-inductance of the

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Fig. 3. Diagram of the receiver.

transmitting coil and the receiving coil respectively, M is the mutual inductance between the coil, C p and C s are the series compensation capacitors of the transmitting coil and the receiving coil, R is the load resistance, and the output voltage is U out . 2

1

3

p 2

4

1

1

p

Fig. 4. Circuit topology.

In the structure shown in Fig. 4, the resonant conditions of the transmitting circuit and receiving circuit can be expressed as: jωLp +

1 1 = 0, jωLs + = 0, jωCp jωCs

(1)

where ω is the system operating frequency. Excluding the losses on the inverter and rectifier modules, the system output voltage can be expressed as Uout =

4RUin ωM π2

(2)

The output power can be expressed as Po =

16R(Uin ωM )2 π4

(3)

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3 Magnetic Coupler Optimization In order to enhance the coil coupling and increase the mutual inductance, the finite element simulation software Maxwell is used to optimize the thickness of the magnetic sheet, the diameter of the magnetic rod and the position of the magnetic rod at the receiver. In order to fit the actual model of the coupling structure, the gap between the magnetic sheet and the magnetic rod is set to 0.2 mm during simulation. The receiver is located in the middle of the two receiver coils, the receiver coil wire length is 300 mm, the wire diameter is 0.21 mm, and the system operating frequency is 500 kHz. 3.1 Magnetic Rod Position The magnetic rod is fixed at the bottom of the box, and the distance between the center shaft of the magnetic rod and the bottom plate of the box is x. When the magnetic sheet thickness is 0.6 mm and the magnetic rod diameter is 1.8 mm, the change curve of mutual inductance between the coils with x is shown in Fig. 5. From Fig. 5, the mutual inductance is maximum when the magnetic rod is located in the middle of the box.

Mutual inductance( H)

1.5 1.45 1.4 1.35 1.3 1.25 1.2 -6

-4

-2

0

2

4

6

Magnetic rod position(mm)

Fig. 5. Simulation results of mutual inductance versus magnetic column position.

3.2 Magnetic Sheet Thickness (mm) and Rod Diameter The receiver is implanted in the body, the volume should be as small as possible, the magnetic sheet thickness is not more than 1.4 mm. The magnetic rod diameter does not exceed 3 mm. According to Fig. 6, when the magnetic sheet thickness is 0.6 mm and the magnetic rod diameter is 1.8mm, the mutual inductance is 1.49 μH and reaches the highest point.

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1.5 1.4 1.3 1.2 1.1 3 2.5 2 1.5

0.2

0.4

0.6

0.8

1

1.2

Fig. 6. Simulation results of mutual inductance versus magnetic sheet thickness and magnetic column diameter.

4 Comparison with Existing Magnetic Coupler It is particularly important for implantable WPT systems to design the receiver. Table 1 shows the comparison results between the proposed structure and the existing structure. In both structures, the titanium alloy shell is a cuboid box of 16 mm*16 mm*6 mm, and the thickness of the box is 0.5 mm. Among them, the outer part of the structure 1 titanium alloy is wrapped with a U-shape core with a thickness of 0.3 mm, and the two receiving coils are connected in series with each other, respectively located on both sides of the core. The receiving coil is a double-layer flexible PCB board with a thickness of 0.235 mm, a length and a width of 15 mm and 5 mm, respectively. Table 1. Comparison of the original structure and proposed structure. Existing structure

Proposed structure

Total volume

1669mm3

1651mm 3

Ferrite volume

134.4mm 3

155.9mm3

Core loss

22.1mW

21.85mW

Mutual inductance

98.17nH

1.49μH

Shape

Both structures utilize flux direction for enhanced coupling, differing in the mounting location of the receive coil. The existing structure adopts flexible PCB coil mounted on both sides of the titanium alloy, and the number of coil turns is limited; The proposed structure places the coil inside the titanium alloy, and the number of turns is much

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larger than the existing structure, and the coupling is stronger. According to Table 1, the total volume of the two structures is basically equal to the core loss, but the proposed structure has obvious advantages in mutual inductance, and the mutual inductance of the proposed structure is 1.49 μH, while the mutual inductance of the existing structure is only 98.17 nH. Considering that the size difference between the transmit coil and the receiving coil of the coupling mechanism is large, the error may be caused by the inaccurate segmentation of the finite element software. Therefore, further verification by experiments is required.

5 Verification As shown in Fig. 7, the wireless power transfer system is constructed. In order to reduce the voltage difference between adjacent coils, the transmit coils are connected in a layered compensation circuit. When the existing structure and the proposed structure are used as the magnetic coupler, the current and voltage on the transmitting coil and the receiving coil are tested separately, during the test, the transmission coil current and load are fixed, and the circuit basically maintains a resonant state, the relevant parameters are shown in Table 2, and Fig. 8 is the corresponding experimental waveform.

Fig. 7. Experimental diagram.

As shown in Fig. 8, the current on the transmit coil is 0.6 A, and when the existing structure is adopted, the voltage and current waveforms on the receiving coil are close to straight lines, and the oscilloscope readings are 0.25 V and 2.89 mA, respectively, indicating that the mutual inductance of the existing structure is very small, and the energy can hardly be transmitted to the receiving side; When adopting the proposed structure, the voltage at both ends of the receiving coil is 2.15 V and the current is 30.26 mA, which is significantly larger than the existing structure, and the output power is 60 mW to meet the power supply requirements of the sensor. In summary, the proposed magnetic coupler has greater mutual inductance than the existing structure, and the output power meets the design requirements, which can realize the non-contact power supply for the cervical internal stress sensor.

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Table 2. Circuit parameters Parameter

Existing structure

Proposed structure

L s /μH

31.30

1.15

C s /nF

3.24

88.14

L p /μH

28.5

28.5

C p /F

46.4

46.4

ip /A

0.6

0.6

R/

180

180

f /kHz

500

500

Fig. 8. Experimental waveform. (a) Existing structure, (b) Proposed structure.

6 Conclusion In this paper, a micro-small magnetic coupler at the receiver is proposed, which uses the H-shape core to constrain the magnetic field, which increases the mutual inductance between the transceiver coils. The finite element simulation software Maxwell is used to optimize the thickness of the magnetic sheet, the diameter of the magnetic rod and the position of the magnetic rod, so that the receiver can maximize mutual inductance in the limited space and consumables range. The total volume and core loss of the two structures are basically the same as that of the magnetic coupler and the existing structure, but the mutual inductance of the proposed structure is about 15 times that of the existing structure, which meets the non-contact power supply of the cervical internal stress sensor, and the experiment fully verifies the superiority of the magnetic coupler proposed in this paper.

References 1. Sonmezoglu, S., Fineman, J.R., Maltepe, E., et al.: Monitoring deep-tissue oxygenation with a millimeter-scale ultrasonic implant. Nat. Biotechnol. 39(7), 855–864 (2021) 2. Khan, A.N., Cha, Y.-o., Giddens, H., et al.: Recent advances in organ specific wireless bioelectronic devices: perspective on biotelemetry and power transfer using antenna systems. Engineering 11(4), 27–41 (2022)

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3. Xu, L., Bai, X., Xu, L.: Design of microwave WPT system for implantable medical treatment. Transducer Microsyst. Technol. 41(10), 64–66+70 (2022) 4. Haoyu, Z., Wei, W., Guozheng, Y.: Omnidirectional wireless power transfer system using modified saddle-shaped coil pair for implantable capsule robots. IEEE Trans. Power Electron. 38(9), 11664–11672 (2023) 5. Cao, X., Sato, H., Xu, K.-D., et al.: A systematic method for efficient wireless powering to implantable biomedical devices. IEEE Trans. Antennas Propag. 71(3), 2745–2757 (2023) 6. Tu, Q., Sun, H., Chen, H., et al.: The surgical treatment strategy for adjacent segment disease after anterior cervical discectomy and fusion of multi-segments. Chinese J. Clin. Ana. 41(2), 218–223 (2023) 7. Zhang, J., Xuan, A., Ruan, D.: Research progress of risk factors of adjacent segment degeneration after anterior cervical discectomy and fusion. China J. Orthopaed. Traumatol. 35(11), 1104–1108 (2022) 8. Guan, Y., Xiao, Y., Wang, Y., et al.: Design of a self-compensating multi-relay wireless power transmission system based on PCB planar spiral coil. Proc. CSEE 42(24), 8984–8995 (2022) 9. Xiao, S., Ma, D., Zhang, H., et al.: The coil model of coupled magnetic resonance wireless power transmission system. Trans. China Electrotech. Soc. 30(S1), 221–225 (2015) 10. Zierhofer, C.M., Hochmair, E.S.: Geometric approach for coupling enhancement of magnetically coupled coils. IEEE Trans. Biomed. Eng. 43(7), 708–714 (1996) 11. Chen, W., Liu, Z., Li, Z., et al.: Research on multi coil reactive shielding of resonant wireless energy supply cardiac pacemaker. Trans. China Electrotech. Soc. 37(11), 2673–2685 (2022)

Research on Three-Phase Bipolar Magnetic Coupling Mechanism for Wireless Charging of Electric Ships Xiaofei Lv(B) , Kechen Wu, Ming Gu, and Di Wu NARI Technology Co., Ltd., No.19 Chengxin, Nanjing, China [email protected]

Abstract. The use of wireless charging for electric ships can solve the problem of insufficient safety and convenience, which was caused by conductance connection. And it was suitable for ferries, pleasure boats, official ships and other frequent entry and exit vessels especially. Compared with the wireless charging of electric vehicles, Marine high-power wireless charging devices not only require higher power density and specific power, but also need to take into account the electromagnetic radiation of the magnetic coupling mechanism. Therefore, the current wireless charging technology widely studied in the academic community needs to further improve the power density, specific power, and reduce electromagnetic radiation. In this paper, a three-phase bipolar topology is proposed based on the application scenario of wireless charging for electric ships. The compensation capacitance calculation method is designed according to the cross-coupling of multiphase magnetic coupling devices(MCD), and the compensation capacitance is compared with conventional magnetic coupling mechanisms such as single-phase monopole and single-phase bipolar in terms of electrical stress, power density and electromagnetic radiation. The simulation results show that the three-phase bipolar magnetic coupling mechanism has obvious advantages in the above aspects, which is suitable for the field of wireless charging of electric ships. Keywords: Wireless charging · Three phase bipolar magnetic coupling mechanism

1 Introduction In recent years, energy conservation, emission reduction and environmental protection has become more and more important internationally, and more and more attention was paid to the energy conservation and environmental protection [1]. Shore-based charging piles can effectively control pollution and reduce energy consumption during the docking of ships, and have been actually applied in some ports at home and abroad [2]. The current ship-shore connection method is that the ship is connected to the dock shore power box through conduction cable [1]. There are many shortcomings in the cable connection mode, such as cable wear, large footprint, connection reliability testing before charging, insufficient flexibility in charging mode, low degree of automation, and difficulty in charging under bad weather conditions [3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 29–39, 2024. https://doi.org/10.1007/978-981-97-0873-4_4

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Wireless charging technology can realize the wireless transmission of electric energy, truly realize the complete electrical isolation of the ship and shore, and avoid the safety accident caused by the potential difference between the ship and shore during the charging process [4]. Therefore, wireless charging technology has become an effective supplement to conductive charging in many fields such as electric vehicle charging [5] and robot charging [6]. Wireless charging of electric ships will be an important way to promote the development of electric ships, especially for vessels that frequently enter and leave ports, such as ferries, pleasure ships and official ships, and can solve the problem of insufficient safety and convenience of conductive cable connection [7]. There are few researches on 100-kilowatt wireless charging which was suitable for Marine wireless charging. Marine high power wireless charging device not only needs high power density and specific power, but also needs to take into account the electromagnetic radiation on the ship side [8, 9]. Most of the wireless charging systems studied at present were single-phase [10, 11]. However, due to the need to consider safety design constraints, the design of single-phase wireless charging systems becomes more and more difficult as the system power increasing. On account of the multiphase wireless charging system can achieve the more uniform magnetic field distribution, in the case of electromagnetic field radiation limitation, the multiphase can achieve higher power transmission capacity. At present, most of the research related to multiphase wireless charging system was applied to the dynamic wireless charging of electric vehicles. Some scholars have studied an EV wireless charging system with a three-phase single-pole coil at the transmitting end and a single-phase single-pole or single-phase bipolar coil at the receiving end, and optimized the size and phase of the current in the transmitting end, and increased the coupling coefficient of the magnetic coupling system. However, the literature assumes that the primary coils were ideally decoupled from each other, which was inconsistent with the actual situation [12]. Literature [13] studied a wireless charging system with multi-phase receiving end, which makes up for the disadvantage of large induced voltage fluctuation of single-phase receiver with multi-pole power rail. In the case of the same transmission capacity and parallel connection, the more the number of phases, the higher the cost of the cable and the smaller the loss, but the electromagnetic radiation effect was not considered in detail. Multiphase wireless charging system was also used in the wireless charging of UAV (Unmanned Aerial Vehicle). Literature [14] studies the equivalent model of a three-phase resonant wireless charging system, deduces the mutual inductance formula of transmitting coil and receiving coil, and analyzes the relationship between output power, transmission efficiency and angular misalignment in detail. However, the overall volume of this coil structure is large. Affect the flexibility and cost of wireless charging system installation. It can be seen from the literature analysis that wireless charging technology has not been fully applied in the field of Marine wireless shore power, and there are some problems to be solved. The traditional single-phase magnetic coupling device has the problems of low power density and large electromagnetic radiation, so it was necessary to design a new multiphase magnetic coupling device according to the practical characteristics of shore power engineering. In addition, the current compensation capacitance calculation method widely used in wireless charging system cannot compensate

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31

the reactive power of the system when the multi-phase magnetic coupling device was cross-coupled, resulting in the efficiency loss of the multi-phase system. To solve the above problems, this paper first selects the three-phase bipolar as the magnetic coupling mechanism topology based on the application of ship shore power. The theoretical model of the three-phase bipolar magnetic coupling mechanism was derived and a new compensation capacitance selection method was designed. Finite element analysis was performed using ANSYS-Maxwell to verify the power output and EMF capability of the design topology.

2 Topology Selection As the core part of wireless charging system, magnetic coupling mechanism not only affects the power transmission capacity and efficiency of the system, but also affects the level of electromagnetic radiation. The magnetic field distribution of the magnetic coupling mechanism with different polarity was different, and the more concentrated magnetic field distribution was beneficial to reduce the magnetic leakage of the magnetic coupling mechanism. Figure 1 was a simulation cloud image of the magnetic field of the unipolar and bipolar magnetic coupling mechanism. The magnetic field of the unipolar magnetic coupling mechanism diffuses outwards from the left and right half coils respectively. The magnetic induction intensity at the center of the magnetic coupling mechanism was almost 0 due to magnetic field cancellation, and the overall magnetic field was divergent and the magnetic leakage was large. The magnetic field of the bipolar emitter was diffused outwards from the central position of the magnetic coupling mechanism. The magnetic induction intensity at the central position was large, the overall magnetic field was convergent and the magnetic leakage was low. Therefore, in order to more easily meet the requirements of the electromagnetic radiation limit of ship shore electricity, the bipolar magnetic coupling mechanism was adopted in this design.

Fig. 1. Magnetic field simulation nephogram of unipolar and bipolar magnetic coupling mechanism

For the two-phase system, two vertical windings can be used to simplify the system architecture and control complexity. However, from the design of the magnetic coupling mechanism, due to the limited flexibility of the litz wire, a large amount of space needs to be allocated to facilitate the transition between the two layers, which reduces the spatial efficiency of the magnetic coupling mechanism. In addition, the three-phase system has

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a connection mode of third harmonic elimination, which can reduce electromagnetic radiation and reduce the loss caused by the third harmonic. Five-phase, seven-phase, and higher-phase systems have the advantage of reducing DC current ripple, but as the number of phase increases, so does the volume of the magnetic coupling mechanism, the power electronic devices, and the control complexity. At the same time, according to the Fourier transform, it can be seen that the third order harmonic was the largest and the phase number was greater than three in the harmonic cancellation was the best. Therefore, three-phase magnetic coupling mechanism was adopted in this design.

3 Modeling and Compensation Capacitance Analysis Figure 2 shows the three-phase wireless charging S-S compensation topological circuit. The input voltage was 750 V DC commonly used for shore power at present. That was inverted into the high-frequency voltage source with the angular frequency of ω by the three-phase inverter. The three-phase amplitude was the same and the phase difference was 120°. R1 , R2 , R3 , R4 , R5 , R6 represent the internal resistance the per phase, Re represents equivalent load resistance, M 14 , M 25 , M 36 represent mutual inductance of ship side coil directly corresponding to shore side coil, M 12 , M 13 , M 23 , M 45 , M 46 , M 56 represent cross-coupled mutual inductance between shore and ship side at the same side coil, M 15 , M 16 , M 24 , M 26 , M 34 , M 35 represent the mutual inductance between the shore side coil and the misaligned ship side coil; C 1 , C 2 , C 3 , C 4 , C 5 , C 6 represent the compensation capacitance per phase; I 1 , I 2 , I 3 , I 4 , I 5 , I 6 represent the current per phase; U S1 , U S2 represent the midpoint voltage of shore side and ship side.

Fig. 2. Topological circuit diagram of three phase wireless charging S-S compensation

According to KVL: In the formula (1), U 1N , U 2N , U 3N represent the shore phase voltage, and Re ’ represents the load resistance equivalent to the pre-phase of three-phase rectification. In order to facilitate analysis and derivation, the three-phase system was assumed to be completely symmetric, namely: M 14 = M 25 = M 36 = M, M 12 = M 13 = M 23 = M 45 = M 46 = M 56 = M’, M 15 = M 16 = M 24 = M 26 = M 34 = M 35 = M”, R1 = R2 = R3 = Rs , R4 = R5 = R6 = Rp , U S1 = U S2 = 0. The compensation idea of traditional S-S topology is to compensate the self-inductance of the coil itself, which was:

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⎧ I1 ⎪ + I1 R1 + Us1 U1N = (I1 L1 + I2 M12 + I3 M31 + I4 M14 + I5 M15 + I6 M16 )jω + jωC ⎪ 1 ⎪ ⎪ I2 ⎪ ⎪ U = (I M + I L + I M + I M + I M + I M )jω + ⎪ 1 12 2 2 3 23 4 24 6 26 2N 5 25 jωC2 + I2 R2 + Us1 ⎪ ⎪ ⎪ ⎨ U = (I1 M31 + I2 M23 + I3 L3 + I4 M34 + I M + I6 M36 )jω + I3 + I3 R3 + Us1 3N 5 35 jωC3 I4  ⎪ 0 = (I M + I M + I M + I L + I M + I M )jω + ⎪ 1 14 2 24 3 34 4 4 6 46 5 45 jωC4 + I4 (R4 + Re ) + Us2 ⎪ ⎪ ⎪ I5  ⎪ ⎪ 0 = (I1 M15 + I2 M25 + I3 M35 + I4 M54 + I5 L5 + I6 M56 )jω + jωC + I5 (R5 + Re ) + Us2 ⎪ ⎪ 5 ⎪ ⎩ 0 = (I M + I M + I M + I M + I M + I L )jω + I6 + I (R + R ) + U 1

16

2

26

3

36

4

Ci =

64

5

65

6 6

jωC6

6

1 , i = 1, 2, · · · , 6 ω2 Li

6

e

(1)

s2

(2)

By putting the above formula into Eq. (1) and solving it, the system efficiency expression can be obtained as follows: η=

(I42 + I52 + I62 )Re Re ω2 (M − M  )2    =   (Re + RS ) ω2 (M − M  )2 + RP (Re + RS ) + RP ω2 M 2 P 2 + Q2 (3)

From formula (3), it can be seen that the system efficiency has a certain loss compared with the single-phase system because the cross-coupled mutual inductance M  between the same side coils on shore and ship side was 0. The mutual inductance M  between the shore side coil and the wrong side coil was coupled with the mutual inductance M of the ship side coil directly corresponding to the shore side coil, which was a common design idea in single-phase coil, can be guided into the difference M-M  between the mutual inductance M  and the mutual inductance M of the ship side coil directly corresponding to the shore side coil. The efficiency expression of single-phase series compensation topological system was as follows: η=

Re ω2 M 2  (Re + RS ) ω2 M 2 + RP (Re + RS ) 

(4)

According to the above analysis, it can be seen that the three-phase system also needs to compensate the cross-coupled mutual inducers between the shore and the ship side coils. According to the system efficiency formula (3), the essence of improving the system efficiency was to reduce the reactive power in the system to 0, and the expressions of the ship side phase voltage U4N and U5N were as follows: U4N = (R4 + Re ) · I4 + jωL4 · I4 + jωM45 · I5 1 +jωM45 .I6 + jωC · I4 + US2 4 U5N = (R4 + Re ) · I5 + jωM45 · I4 + jωL5 · I5 1 +jωM56 .I6 + jωC · I4 + US2 5

(5)

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Then the expression of ship side line voltage U 45 was: U45 = U4N − U5N = (R4 + Re ) · I4 − (R4 + Re ) · I5 +jω(L4 − M45 ) · I4 + jω(M45 − L5 ) · I5 1 1 +jω(M46 − M56 ) · I6 + jωC · I4 − jωC · I5 4 5

(6)

Due to the three-phase star connection, so: I4 + I5 + I6 = 0

(7)

U45 = (R4 + Re ) · I4 − (R4 + Re ) · I5 +jω(L4 − M45 − M46 + M56 ) · I4 −jω(L5 − M45 − M56 + M46 ) · I5 1 1 + jωC · I4 − jωC · I5 4 5

(8)

Enter the formula (6) to obtain:

In order to eliminate the reactive power of each phase of the three phases, the imaginary part of formula (8) must be 0, so: jω(L4 − M45 − M46 + M56 ) · I4 + jω(L5 − M45 − M56 + M46 ) · I5 +

1 jωC4 1 jωC5

· I4 = 0 · I5 = 0

(9)

The value of ship side compensation capacitance was obtained as follows: C4 =

1 (L4 −M45 −M46 +M56 )·ω2

C5 =

1 (L5 −M45 −M56 +M46 )·ω2

(10)

In the same way, the compensation capacitance values of shore side and ship side can be obtained: Ci =

1 (Li − Mij − Mik + Mjk ) · ω2

(11)

i, j, k = 1, 2, 3 or 4, 5, 6

4 Simulation Analysis 4.1 Electromagnetic Model Construction Given modeling constraints: P ≥ 100 kW, ω = 2*pi*20000, U dc input was 750 V, U dc output interval was 650 V–960 V. The design idea was shown in Fig. 3:

Research on Three-Phase Bipolar Magnetic Coupling Mechanism Input of parameters

Selection of inside diameter

Calculation of current and mutual inductance

Design of coils and ferrites

Selection of litz diameter

Simulation calculation of mutual inductance

Selection of turns and inside diameter

35

Error of M Rp Rs and ω2 M 2 > Rp Rs , Rp and Rs can be neglected. Thus, we can obtain      Zin = 8π 2 k 2 L2S RL ωωr5 − j ωr2 − 1 −64R2L ωr2 + π 4 L2S ω2 k 2 − 1 ωr4 + 2ωr2 − 1 (2) where ωr is defined as a per-unit operation frequency given by ωr = ω/(L p C p )1/2 . Supposing the input impedance angle is ϕin which can be calculated as Im[Zin ] 180 180 arctan arctan =− ϕin = π Re[Zin ] π       ωr2 − 1 −64R2L ωr2 + π 4 L2S ω2 k 2 − 1 ωr4 + 2ωr2 − 1

(3)

8π 2 k 2 L2S RL ωωr5

2.2 Implementation of Resonant Frequency Tracking When the WPT system is operated at the natural resonant frequency point, i.e., ω = 1/(L p C p )1/2 , the input impedance of the WPT converter presents a pure resistance characteristic and the impedance phase angle is always zero, i.e., ϕ in = 0°. Therefore, the new resonant frequency can be tracked by detecting the phase difference between vp and vp , i.e., ϕ d . A fast hill-climbing search method is introduced to determine the new resonant frequency of the WPT charger when there are variation of gap distance and misalignment. By gradually increasing the operating frequency from a minimum boundary value f min with a step of f , ωn can be determined when ϕ d is approaching to zero. Theoretically, when the resonant frequency is tracked, the detected phase difference ϕ d is zero. However, due to the discrete change of operating frequency and phase detection error in the hardware, ϕ d is not equal to zero in practice. Therefore, we set a tolerance error ξ. When the detected phase difference is less than the preset error

Fast Optimal Frequency Tracking

43

angle, i.e., ϕ d < ξ, it is considered that the system resonant frequency is tracked. In this letter, ξ is set to 8◦ . The above method has been programmed in DSP TMS320F28335 as the micro-controllers for the resonant frequency tracking scheme. The implementation diagram is depicted in Fig. 2, where the phase difference ϕ d is detected in every switching cycle. Here, ϕ d is taken as a parameter to update the switching frequency. In order to search the resonant frequency fast, the operating frequency is set to sweep from a minimum resonant frequency of 85.02 kHz (under 3.5 cm air gap distance) with a step of f = 0.25 kHz (N = 5).

p

p

1

2

2

1

1

2

1

4

2

3

1

4

2

3

1

1

Fig. 2. Control diagram of the proposed resonant frequency tracking scheme implemented in DSP.

Figure 3 depicts the hardware design of the phase difference detection for resonant frequency tracking. First of all, the current ip is sampled by a high-frequency current transformer. The sampled signal ip1 is then sent to a sampling adjustment circuit. Then, the output signal ip2 is further fed to a high-speed ultra-fast low-power precision comparator TL3016 to perform zero-crossing detection. Next, the output signal ipz of TL3016 and the control signal G1 are sent to a XOR logic operator, where the control signal G1 indicates the phase of output voltage vp . If the signals of G1 and ip1 are in phase, so are vp and ip . The pulse width of the output signal of XOR indicates the phase difference between G1 and ipz . N p (N) is the counted pulse width of the output signal of XOR. The duty ratio of the output signal of XOR is d p (N) which is calculated by multiplying N p (N) and the switching frequency f p (N). The pulse width of the output signal of XOR is detected and represented as a digitized signal d p (N). If the pulse width is smaller than the previous duty cycle (i.e., Dp (N) < Dp (N-1)), the operating frequency will increase. This process will continue until Dp (N) approaches zero when the natural resonant frequency is reached.

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Fig. 3. Hardware design of current sampling and resonant frequency tracking diagram.

3 Experimental Verification An experimental prototype is built with the same schematic shown in Fig. 1 to verify the effectiveness of the proposed method. The system parameters are listed in Table 1. Table 1. Parameters of experimental prototype Parameters

Values

C p , C s , Rp , Rs

18.74 nF, 16.73 nF, 0.12 , 0.14 

V in , I N , RL

50 V, 2 A, 40 

The experimental waveforms of the resonant frequency tracking process at position A (under 6.5 cm air gap distance) and position B (under 4.5 cm air gap distance) are shown in Fig. 4. The start minimum operating frequency of the WPT charger is set to 85.02 kHz. It can be observed that when the receiving coil is at position A, the operating frequency sweeps from 85.02 kHz with a search step change of f = 0.25 kHz and the operating frequency will increase to the new natural resonant frequency 88.27 kHz after 60 ms, as shown in Fig. 4(a). Besides, it can also be observed from Fig. 4(b) that there are large voltage spikes under f = 85.02 kHz because the operating frequency is lower than the resonant frequencies of positions A and B. Thus, the input impedance presents capacitive characteristic which means that ip no longer lags vP and ZVS is not achieved. During the frequency sweeping process, the voltage spikes of vp caused by hard switching gradually decrease because the input phase angle ϕ in gradually approaches to the zero.

Fast Optimal Frequency Tracking

45

Fig. 4. Experimental waveforms of vp , ip and vfDA during search of the resonant frequency at position A and positions B, respectively. (a) shows the tracking process of the operating frequency sweeping from the minimum boundary f = 85.02 kHz to system resonant frequencies, (b) (c) shows the enlarged steady-state waveforms.

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Table 2 shows the comparison of theoretical resonant frequency and the determined operating frequency at positions A and B. It can be observed that the tracked operating frequencies are close to the natural resonant frequencies and the errors are all less than 0.5%. Table 2. Table captions should be placed above the tables. Air gap distances

Theoretical

Measured

Error

4.5 cm position A

86.58 kHz

86.77 kHz

0.22%

6.5 cm position B

88.01 kHz

88.27 kHz

0.30%

4 Conclusion To achieve fast resonant frequency tracking for an S-S compensation WPT battery charger for the compatibility of variations of gap distance and misalignment, a hillclimbing search method has been proposed in this letter. By detecting the input phase angle, the system resonant frequency can be tracked and determined accurately when there are variation of gap distance and misalignment of the magnetic coupler change. The effectiveness of the proposed method is validated by experimental results. It is shown that the system resonant frequency is well tracked with less than 0.5% error under significant variation of the gap distance of the magnetic coupler. The content of this letter provides guidance for the practical engineering design for system resonant frequency in an S-S compensation WPT system.

References 1. Qu, X., Chu, H., Wong, S., Tse, C.K.: An IPT battery charger with near unity power factor and load-independent constant output combating design constraints of input voltage and transformer parameters. IEEE Trans. Power Electron. 34(8), 7719–7727 (2019) 2. Zhong, W.X., Hui, S.Y.R.: Maximum energy efficiency tracking for wireless power transfer systems. IEEE Trans. Power Electron. 30(7), 4025–4034 (2015) 3. Hui, S.Y.R., Yang, Y.: A wireless battery charging system and method for battery charging and handshaking. US Provisional Patent Application 62(906), 180 (2021) 4. Yang, Y., Tan, S.C., Hui, S.Y.R.: Fast hardware approach to determining mutual coupling of series-series-compensated wireless power transfer systems with active rectifiers. IEEE Trans. Power Electron. 35(10), 11026–11038 (2020) 5. Nguyen, B., et al.: An efficiency optimization scheme for bidirectional inductive power transfer systems. IEEE Trans. Power Electron. 30(11), 6310–6319 (2015) 6. Xu, F., Wong, S.C., Tse, C.K.: Overall loss compensation and optimization control in singlestage inductive power transfer converter delivering constant power. IEEE Trans. on Power Electron. 37(1), 1146–1158 (2022) 7. Huang, Z., Wong, S.C., Tse, C.K.: Design of a single-stage inductive power-transfer converter for efficient EV battery charging. IEEE Trans. Veh. Tech. 66(7), 5808–5821 (2017)

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8. Huang, Z., Wong, S.C., Tse, C.K.: An inductive-power-transfer converter with high efficiency throughout battery-charging process. IEEE Trans. Power Electron. 24(10), 10245–10255 (2019) 9. Dai, X., Li, X., Li, Y., Hu, A.P.: Maximum efficiency tracking for wireless power transfer systems with dynamic coupling coefficient estimation. IEEE Trans. Power Electron. 33(6), 5005–5015 (2018) 10. Xu, F., Wong, S.C., Tse, C.K.: Inductive power transfer system with maximum efficiency tracking control and real-time mutual inductance estimation. IEEE Trans. Power Electron. 37(5), 6156–6167 (2022)

Research on Rotary Compact Wireless Power Transfer System Longlong Zhang(B) , Xiaojing Zhao, Feiling Zheng, Xiao Qin, and Jingcheng Zhao China University of Petroleum (East China), Qingdao 266555, China [email protected]

Abstract. Rotary wireless power transfer system has drawn more attention with the advantage of eliminating the mechanical slip ring to increase reliability and lifetime. It can also adapt to different types of rotating equipment and complex motion trajectories, which could be applied to unmanned aerial vehicle, unmanned ground vehicle, unmanned underwater vehicle and other fields. This paper proposes a compact wireless power transfer system with the optimization of the rotary magnetic structure in ANSYS Maxwell software, gives the circuit model of the wireless power transmission system with the S-S compensation scheme in PSIM 9.1.The efficiency of the rotary wireless power transfer system can be up to 95% according to the analysis. Keywords: Wireless Power Transfer · Rotary · Loosely coupled transformer

1 Introduction Traditional cable power transmission requires physical contact or connection. For rotary applications, brush and slip ring wear leads to decrease in lifetime [1]. In order to overcome these limitations, rotary loosely coupled transformers have gradually become the focus of research and application. The rotary loosely coupled transformer adopts a loosely coupled magnetic coupling method. The energy is transmitted from the fixed component to the rotating component through the rotating component, which realizes contactless, brushless and wireless energy transmission and power conversion [2]. The University of Stuttgart in Germany proposed a replacement system for the slip ring of electrically excited synchronous motor (EESM) [3]. Compared with the slip ring of EESM, the thermal limit of the wireless energy system of the rotary loosely coupled transformer is higher than that of the slip ring surface, allowing higher excitation current in the rotor winding and higher speed of the rotor. It verified the feasibility of inductive power transmission using a rotary loosely coupled system. Chongqing University has developed a rotating casing device for a wireless power supply system that can be used for drilling. The device includes an inner cylinder and an outer cylinder that can rotate freely with each other, and can transmit electric energy between the inner and outer cylinders. On this basis, the real-time transmission of digital signals between the inner and outer cylinders can be realized, and the transmission efficiency of the system can reach at least 65% [4]. Additionally, Chongqing University have designed a rotary loosely © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 48–58, 2024. https://doi.org/10.1007/978-981-97-0873-4_6

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49

coupled transformer, which is suitable for wireless power transmission of satellite solar array drive assembly (SADA). Compared with the traditional sliding ring structure, this rotary coupling mechanism can effectively reduce the loss caused by friction to the device, which has potential application value for the wireless power supply system inside the satellite [5]. Southwest Jiaotong University has designed a rotary wireless power transmission system. The coupling coil is cylindrical and spiral. The structure of the primary side transmitter and the secondary side receiver is the same. Through the rotation of the bearing, the contact friction between the primary and secondary sides is avoided, and the expensive confluence ring is not needed and the system cost is saved. At the same time, an aluminum shielding layer is provided to reduce eddy current loss and improve the transmission efficiency of the system [6]. Harbin Institute of Technology designed a magnetic coupler for a wireless power transmission system driven by a spacecraft solar wing that can be applied to rotating conditions. The experimental results show that the transmission power of the magnetic coupler can reach 7 kW [7]. Also, they proposed a free-rotation asymmetric magnetic coupling structure for Unmanned Aerial Vehicle (UAV) wireless charging platform, which could solve the problems of rotation misalignment and horizontal offset of UAV [8]. As a key component of the wireless energy transmission system, the loosely coupled transformer has an important influence on the transmission power, transmission efficiency and other parameters of the WPT system [9]. Therefore, this paper mainly designs the rotary loosely coupled transformer, simulates the electric field distribution and magnetic field distribution in the working process of the rotary loosely coupled transformer, and extracts the important parameters such as self-inductance, mutual inductance and coupling coefficient of the transformer. Finally, the circuit model of the magnetically coupled resonant wireless power transmission system is established to verify the feasibility of the design scheme.

2 Magnetic Structure Design The key to magnetically coupled resonant wireless power transmission is the design of a loosely coupled transformer composed of a transmitting coil and a receiving coil. Finite element simulation can be used to calculate parameters such as self-inductance, mutual inductance, and coupling coefficient. In this paper, ANSYS Maxwell software is used to design the loosely coupled transformer. The ferrite of the material library is selected as the magnetic core part, and the copper of the material library is selected as the coil part [10]. The geometric parameters of the primary and secondary sides of the rotary loosely coupled transformer are set as shown in Table 1. According to the design parameters in Table 1, the modeling of the rotary loosely coupled transformer is carried out in ANSYS Maxwell software. The 3D model of the loosely coupled transformer and the subdivision model along the central axis are shown in Fig. 1. The gray part represents the magnetic core of the rotary loosely coupled transformer, and the orange part represents the coil of the rotary loosely coupled transformer. After adding excitation to the loosely coupled transformer, the field distribution cloud diagram of the transformer can be simulated.

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L. Zhang et al. Table 1. Geometric parameters of rotary loosely coupled transformer

Parameter

Numerical value

Inner diameter of primary magnetic core

22/mm

Outer diameter of the primary magnetic core

34/mm

Inner diameter of secondary magnetic core

7/mm

Outer diameter of the secondary magnetic core

13/mm

Coil diameter

1.3/mm

Primary magnetic core height

75/mm

Secondary magnetic core height

64/mm

The turn ratio of primary coil to secondary coil

20/20

Fig. 1. Loosely coupled transformer model

2.1 Extraction of Self-Inductance and Mutual Inductance Parameters Table 2. Parameter numerical table Turn ratio

Primary self-induction(L1 )

Secondary self-induction(L2 )

Mutual inductance (LM )

10:10

28.825uH

27.811uH

25.254uH

10:15

28.848uH

58.062uH

36.829uH

15:10

58.911uH

27.534uH

36.372uH

15:20

59.633uH

95.752uH

69.463uH

20:15

97.145uH

57.511uH

68.817uH

20:20

97.934uH

95.718uH

89.926uH

30:30

186.92uH

183.30uH

174.38uH

The difference in the number of turns of the primary coil and the secondary coil has a certain influence on the self-inductance and mutual inductance of the transformer. The simulation compares the multi-group data values after the change of the number of turns.

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And the data of the relationship between the number of turns and the self-inductance and mutual inductance of the transformer are shown in Table 2. It can be seen from the Table 2 that the self-inductance of the primary side and the secondary side and the mutual inductance will decrease with the decrease of the number of turns, and the corresponding coupling coefficient will also decrease when the number of turns of the transformer is n:n. When the number of turns of the transformer is n:m type, with the decrease of the number of turns of m, the self-inductance of the primary side or the secondary side and the mutual inductance will also decrease. The conversion formula between self-inductance, mutual inductance and leakage inductance, excitation inductance of transformer model is as follows: L1 = Lp + Mt

(1)

L2 = Ls + Mt n21

(2)

LM = n21 · Mt

(3)

n21 = n2 /n1

(4)

The self-inductance and mutual inductance parameters obtained by substituting them into the simulation model can calculate the leakage inductance and excitation inductance of the primary and secondary sides of the model. The calculation results are shown in Table 3. Table 3. Calculation result table Turn ratio

Secondary coil leakage inductance (Lp )

Secondary coil leakage inductance (Ls )

Magnetizing inductance (Mt )

10:10

3.571uH

2.557uH

25.25uH

10:15

4.295uH

2.819uH

24.55uH

15:10

4.433uH

3.286uH

54.56uH

15:20

7.536uH

3.135uH

52.10uH

20:15

5.389uH

5.898uH

91.76uH

20:20

8.008uH

5.792uH

89.93uH

30:30

12.540uH

8.920uH

174.40uH

Considering the production size of the transformer, combined with the table data, the turn ratio of the primary side and the secondary side is finally set to 20:20. The following experimental simulation cloud images are based on the transformer model established by the turns ratio of 20:20. The coupling coefficient of the shaft loosely coupled transformer can be calculated according to Formula k =

M L1

·

M L2

=

√M . L1 L2

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2.2 Analysis of Simulation Cloud Image The distribution of transformer current vector is as shown in Fig. 2, which gives the obvious current flow direction. It can be seen that the primary winding current and the secondary winding current flow direction are opposite, because the transformer is essentially a coupling coil. Due to the existence of electromagnetic induction, the current direction is determined according to the homonymous end. If the current flows from the homonymous end of the primary coil, the mutual inductance voltage of the secondary winding is ‘ + ’ at the homonymous end. If the secondary side is connected to the load, the secondary side current should flow from ‘ + ’.

Fig. 2. Current flow

The magnetic field line is a closed curve, which always starts from the N pole of the magnetic field, enters its nearest S pole and forms a closed loop curve. Whether it is a permanent magnet or an energized solenoid (coil), it satisfies this law. The trend of the magnetic field line can be judged according to the Ampere ’s rule (right-handed spiral rule). The distribution of magnetic field lines is as shown in Fig. 3. The primary side coil current is clockwise, then the primary side magnetic field according to the right-handed spiral rule shows that the negative direction of the Z-axis is the N-pole of the primary side coil, so the magnetic field line is from N to S-pole, that is, from bottom to top to form a loop. The current induced by the secondary coil is counterclockwise. According to the right-handed spiral rule, the secondary magnetic field shows that the positive direction of the Z-axis is the N-pole of the secondary coil, and the direction of the magnetic field line forms a loop from top to bottom. The magnetic flux density distribution cloud picture is as shown in Fig. 4, which can be seen that the magnetic induction intensity is mainly concentrated around the magnetic core near the coil, and the magnetic induction intensity of the part farther away from the coil gradually decreases. At the same time, due to the existence of magnetic flux leakage, the magnetic induction intensity of the primary side core in the middle is larger than that of the secondary side core in the periphery. The magnetic field intensity cloud picture is as shown in Fig. 5. It can be seen from Fig. 5 that the magnetic field intensity is mainly distributed in the air gap between the primary coil and the secondary coil, with an average of 41.3862 A/m. There is also a certain magnetic field intensity in the air gap around the coil, which is about 13.7954 A/m. The magnetic field intensity on the core is very small, almost 0.

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Fig. 3. Distribution of magnetic force line

Fig. 4. Magnetic flux density cloud

Fig. 5. Magnetic field intensity cloud diagram

3 Design of Rotary Wireless Power System According to the different connection modes of capacitance and inductance on the transmitting side and the receiving side, four basic compensation networks can be formed, namely: series/series type (S/S type), series/parallel type (S/P type), parallel/parallel

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type(P/P type), parallel/series type (P/S type) [11]. When the resonant frequency of the circuit is equal to the operating frequency, both S/S type compensation network and S/P type compensation network can achieve constant voltage and constant current output. In this paper, the S/S compensation network is adopted. The inductive reactance of the resonant inductor can offset the capacitive reactance of the resonant capacitor. At this time, the total impedance of the circuit is zero. 3.1 Experimental Verification of Rotary Magnetic Structure The physical shaft loosely coupled transformer is as shown in Fig. 6. According to the T-type equivalent circuit of the transformer, the open circuit experiment and the short circuit experiment are carried out to measure the primary and secondary leakage inductance and excitation inductance of the physical transformer. The data are shown in Table 4.

Fig. 6. Shaft loose coupling transformer physical object

Table 4. Practical comparison Value

Turn ratio

Secondary coil leakage inductance (Lp )

Secondary coil leakage inductance (Ls )

Magnetizing inductance (Mt )

Measured data

20:20

13.801uH

1.421uH

44.58uH

Simulated data

20:20

8.008uH

5.792uH

89.93uH

It can be seen that there is an error between the measured data and the simulation data of the physical transformer. The main reason for this situation is that the magnetic core is LP9 wide-temperature low-power ferrite material developed by Nanjing NEW CONDA Company, which is different from the magnetic core parameters in the ANSYS material library to some extent. In the physical construction, the magnetic core is composed of multiple annular magnetic cores stacked, and the bonding place is bonded with silicone

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55

rubber, which will increase the height of the magnetic core to a certain extent, and there is an air gap at the bonding place of the magnetic core, which will produce a large magnetic flux leakage. 3.2 Simulation of the Rotary Wireless Power Transfer System The schematic diagram of the resonant wireless energy transmission system is as shown in Fig. 7.

Q1

D1

Q2 C1

Vin Q3

L1

L2

D2

C2 C3 D3

Q4

R

D4

Fig. 7. Principle diagram of resonant wireless power transmission system

For the receiving circuit part, when the transmitting end transmits energy to the receiving end, the energy will have a series resonance effect between L2 and C2 . The bridge rectifier circuit formed by four diodes realizes the transformation from AC to DC, and the capacitor C3 plays a filtering role. If and only if the resonant frequencies of the transmitter and the receiver are equal, the transmission efficiency of the system reaches the maximum [12]. The circuit model of the resonant wireless power transmission system is built with PSIM software as shown in Fig. 8. The calculation formula of the compensation capacitance of the primary and secondary side compensation network is as follows: C=

1 4f 2 π 2 L

(5)

It can be seen that the capacitance of the compensation capacitor is related to the switching frequency and the resonant inductance. In addition, the maximum power point tracking module is added to the PSIM simulation, and the frequency point of the maximum output power is automatically found by the program, which simplifies the tedious manual modification of the frequency. The simulation results are shown in Fig. 9, It can be clearly seen that the primary side current and the secondary side current of the transformer form a good resonance. At the same time, the output voltage is about 38 V, and the output power is about 320 W. With the maximum power point module for maximum output power tracking control, the optimal frequency is about 43 kHz.

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Fig. 8. Circuit model of resonant wireless power transmission system

Fig. 9. Simulation result

3.3 Theoretical Efficiency Analysis Results According to the voltage stress and current stress, the MOSFET and diode are selected. The device parameters of Infineon are shown in Table 5 and Table 6. Table 5. Device Specifications Device

Model

Vdss

Id

Pd

MOSFET

IRFR024NTRPBF

55 V

17 A

45 W

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57

Table 6. Device Specifications Device

Model

Vr

Io

Vf

Ir

Trr

Fast recovery diode

DPG20C200PB

200 V

10 A

1.45 V@20 A

1 uA@200 V

35 ns

Through simulation experiments, the output power of the wireless power transmission system can reach 319.7 W, and the power loss is 16.178 W. Consequently, the ideal transmission efficiency of the system is about 95%.

4 Conclusion In this paper, ANSYS Maxwall software is used to design the rotary loosely coupled transformer. The key parameters such as self-inductance, mutual inductance and coupling coefficient are extracted, and the electric field distribution and magnetic field distribution of the rotary loosely coupled transformer are simulated. At the same time, the PSIM software is used to build the circuit model of the wireless power transmission system for verification. The design model of rotary loosely coupled transformer in this paper provides an effective method for the design and optimization of underwater wireless power transmission system. The efficiency of the rotary wireless power transfer system can be up to 95% according to the analysis.

References 1. Detka, K., Gorecki, K.: Wireless power transfer—a review. Energies 15(19), 7236 (2022) 2. Su, Y., Liu, J., Wang, Z., et al.: Influence analysis of metal in the same plane with pickup coil on magnetic coupler and suppression method. Trans. China Electro. Techn. Soc. 37(03), 578–588 (2022) 3. Maier, D., Kurz, J., Parspour, N.: Contactless energy transfer for inductive electrically excited synchronous machines. In: 2019 IEEE pels workshop on emerging technologies - wireless power transfer (WOW), pp. 191–195 (2019) 4. ReadNews: http://www.wptchina.com.cn/ReadNews.asp?rid=866, last accessed 15 July (2023) 5. Liu, X., Wang, Z., Tang, C., et al.: Rotary coupling mechanism for satellite SADA wireless power supply. CN202210746407 3 (2022) 6. Zhang, H., Xu, J., Wang, X., et al.: A rotary wireless power transmission system, CN111049279A (2020) 7. Song, K., Ma, B., Yang, G., et al.: A rotation-lightweight wireless power transfer system for solar wing driving. IEEE Trans. Power Electr. 34(9), 8816–8830 (2019) 8. Zhi, B., Zhang, J., Song, K., et al.: A free-rotation asymmetric magnetic coupling structure of UAV wireless charging platform with conformal pickup. IEEE Trans. Power Electr. 69(10), 10154–10161 (2022) 9. Zhang, J., Cao, B.: Magnetic circuit and simulation of EE type loosely coupled transformer. Electr. Desi. Eng. 21(11), 81–84 (2013)

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10. Liu, H., Zhang, Z., Song, T., et al.: ANSYS Maxwell + Workbench 2021 Multi-physical field coupling finite element analysis of motor, 1st edn. Chemical Industry Publishing House, Beijing (2022) 11. Cheng, C., Lu, F., Zhou, Z., et al.: A Load-Independent LCC-Compensated Wireless Power Transfer System for Multiple Loads With a Compact Coupler Design. IEEE Trans. Industr. Electron. 67(6), 4507–4515 (2020) 12. Aditya, K., Williamson, S.: Design guidelines to avoid bifurcation in a series-series compensated inductive power transfer system. IEEE trans. Indus. Electr. 66(5), 3973–3982 (2019)

Universal Wireless Power Transfer System for AUV Based on Flexible Magnetic Couplers Ben Zhang1 , Xudong Wang2 , Changbo Lu2 , Wanli Xu2 , and Yong Lu1(B) 1 College of Power and Energy Engineering, Harbin Engineering University,

Harbin 150001, China [email protected] 2 Institute of Systems Engineering, Academy of Military Sciences, Beijing 100091, China

Abstract. To ensure efficient energy replenishment for underwater autonomous vehicles (AUVs), this paper introduces a universal wireless power transfer system based on flexible magnetic couplers. The designed flexible magnetic couplers can adjust the transmitter diameter according to different AUV models, enhancing the universality of the charging platform. Dynamic tuning is achieved by integrating variable capacitance and variable inductance technologies to maintain the system’s resonance state. The designed experimental prototype can transmit 1.08 kW of power while retaining a DC-DC transmission efficiency of 91.55%. Keywords: Autonomous underwater vehicles · Flexible magnetic couplers · Universal · Wireless power transfer

1 Introduction Autonomous Underwater Vehicles (AUVs) are defined as a class of unmanned underwater robots equipped with the capability of autonomous navigation, perception, and decision-making, enabling them to execute various tasks in underwater environments, such as ocean surveys, environmental monitoring, and underwater pipeline maintenance [1]. While AUVs exhibit promising applications in ocean exploration, they face a critical challenge – the reliance on limited battery power. During prolonged missions or tasks at remote distances, energy scarcity could lead to mission interruptions and, more critically, to the inability to accomplish assignments [2]. Wireless Power Transfer (WPT) is a technology that transfers energy through electromagnetic fields without physical contact, based on the principles of electromagnetic induction and resonance phenomena [3]. This technology utilizes the transmitter’s electromagnetic fields to induce electromagnetic energy in the receiver’s coils, converting it into electrical energy, thus achieving energy transmission. Compared to traditional energy supply methods, wireless power transfer offers multiple advantages for AUV energy replenishment. It can enhance AUV autonomy and adaptability to various complex environments, reduce maintenance costs, and bolster emergency response capabilities. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 59–67, 2024. https://doi.org/10.1007/978-981-97-0873-4_7

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The WPT technology applied to AUVs has been extensively researched. Wu et al. [4] introduced a Uniform Power and Stable Efficiency Wireless Charging System utilizing a novel magnetic structure with overlapped orthogonal transmitters and dipole receivers. The constructed experimental prototype achieved a transmission efficiency of around 90% while transmitting a power of 1.2 kW. Zeng et al. [5] proposed a hybrid transmitter consisting of conical and planar helical coils, significantly enhancing error tolerance and transmission performance. Experimental results indicated a transmission efficiency of approximately 86% at a distance of 20 mm. Yan et al. [6] presented a freely rotating WPT system with two decoupled transmitters and a segmented arc electromagnetic receiver to enhance AUV rotation and axial misalignment tolerance. Experimental outcomes demonstrated less than 5% power fluctuation at an output power of 700 W. Wang et al. [7] introduced a curved underwater wireless power transmission magnetic coupler suitable for underwater vehicles with curved hulls. Prototype results indicated a transmission efficiency of 91.9% while transmitting 3 kW power. Cai et al. [8] proposed a conformal, lightweight cross-coupled magnetic coupler. Testing on a 600g receiver showed an efficiency of 95.1% while transmitting 1 kW power. Although current WPT systems for AUVs exhibit good performance in transmission power and efficiency, considering the cost of AUV charging platforms and flexibility in choosing charging positions, designing a versatile wireless power transmission system becomes crucial. In this article, we present a versatile wireless power transmission system for AUVs based on flexible magnetic couplers, as depicted in Fig. 1. Firstly, we designed a flexible magnetic coupler with adjustable transmitter dimensions. Secondly, the system incorporates dynamic tuning capability to ensure efficient energy transmission. Finally, we validate the system’s functionality by constructing an experimental prototype.

Fig. 1. System framework diagram

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2 Design and Simulation of Flexible Magnetic Couplers 2.1 Proposal of Structure and Magnetic Field Analysis The inclusive charging platform features a simple structure and does not require any modifications to the AUV’s design, as shown in Fig. 2. Moreover, it effectively safeguards the AUV during the charging process, making it a prevailing solution for underwater AUV charging. The enclosure dimensions of the inclusive charging platform are fixed, limiting its ability to replenish multiple AUV models efficiently. To ensure smooth entry and exit of AUVs, there is a distance between the charging station and the AUV, which might affect the wireless power system’s transmission performance.

Fig. 2. Inclusive charging platform schematic diagram

It is building on our previous work [9, 10]. We proposed a flexible magnetic coupler to adjust the transmitter diameter. This adjustable diameter reduces the gap between the transmitter and receiver, enabling it to conform to the AUV’s surface. This enhances the system’s transmission performance and broadens its applicability. The structure of the flexible magnetic coupler is depicted in Fig. 3, consisting of eight curved rectangular coils for both the transmitter and receiver, with magnetic cores covering the outer side of the transmitter and the inner side of the receiver.

Fig. 3. Structure diagram of flexible magnetic coupler.

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The operational principle of the flexible magnetic coupler is illustrated in Fig. 4. The flexible magnetic coupler stretches to its full size before the AUV accesses the charging platform, giving enough room for the AUV to enter. Once the AUV is on the platform, the flexible magnetic coupler contracts to closely to the external surface of the AUV. At this stage, the contracted eight curved transmitter coils form a circular enclosure around the AUV. After the charging process, the flexible magnetic coupler re-expands to its maximum size, allowing the AUV to depart.

Fig. 4. Working principle of flexible magnetic coupler.

ANSYS Maxwell was used for the flexible magnetic coupler’s finite element analysis. With the flexible magnetic coupler’s transmitter and receiver separated by 20 mm and aligned in the centre, a 10 A excitation was applied to the coil windings. Taking a cross-sectional view from the top of the flexible magnetic coupler, the magnetic flux distribution is shown in Fig. 5, and the magnetic field intensity distribution is illustrated in Fig. 6. It can be observed that the magnetic fields generated by the current in the same direction within each pair of opposing coils form closed loops. Eight teams of opposing coils create sixteen magnetic flux loops. The magnetic field directions within these closed loops alternate between positive and negative phases.

Fig. 5. Magnetic field line distribution

Fig. 6. Magnetic field strength distribution

2.2 Parameter Simulation We performed a parameter simulation of the flexible magnetic coupler using ANSYS Maxwell. With 3 mm copper wires, the receiver and transmitter coils consist of 6 turns.

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A current of 10 A was applied to the coil cross-sections. A 2 mm thick nanocrystalline magnetic core material was placed on the outer side of the transmitter and the inner side of the receiver. Initially, the receiver diameter was 280 mm, and the transmitter diameter was 300 mm. To validate the necessity of the flexible magnetic coupler, we conducted a simulation analysis of the coupler’s coupling efficiency during the variation of the transmitter diameter from 300 mm to 320 mm. The results are shown in Fig. 7. As the transmitter diameter increases, the spacing of the magnetic coupler also increases, leading to a weaker coupling capability. This trend is relatively gradual when the spacing is not too large, but coupling efficiency significantly decreases when the transmitter diameter surpasses 304 mm. The self-inductance of the transmitter coil decreases initially with the increasing spacing, reaching a minimum value, and then slightly rises due to the enlargement of coil size. Similar to mutual inductance, the receiver coil exhibits a slow decreasing trend and then significantly reduces. Under the parameters above, we optimized the nanocrystalline magnetic core thickness, as shown in Fig. 8. It can be observed that with the increase in nanocrystalline material thickness, the self-inductance of both the transmitter and receiver coils increases, resulting in a slight enhancement of coupling efficiency. The increase in coupling efficiency is insignificant when the nanocrystalline thickness reaches five times the initial value. Considering the high cost of nanocrystalline materials, a thickness of 2 mm was chosen as the optimal thickness for the nanocrystalline magnetic core in the prototype design.

Fig. 7. Impact of transmitter diameter variation on coupling performance

Fig. 8. Influence of nanocrystalline magnetic core thickness on coupling performance

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3 System Dynamic Tuning When the AUV is recharging energy, its attitude may be unstable due to the interference of ocean currents. However, the LCC-S resonant compensation network has a wide range of coupling coefficient adaptability, can achieve stable power output in a wide range, and has excellent offset resistance. Therefore, it becomes the preferred system resonant network solution. When the charging platform provides energy supply for different types of AUVs, the flexible magnetic coupler will adjust the transmitter’s diameter according to the AUV’s size. Such adjustments will cause changes in the mutual inductance value. However, due to changes in the mutual inductance value, the system impedance no longer maintains a matching state, affecting transmission efficiency. Once the AUV model is determined, the coupling parameters of the WPT system receiver are also specified. Therefore, when setting the resonance compensation network of the receiver, it is only necessary to perform resonance calculation according to the coil parameters and configure the required capacitance value accordingly. In this case, only the resonant adjustment of the transmitter circuit is needed. To optimize the transmission performance of the system, we also need to adjust the value of the compensation inductance. Therefore, we use a capacitor matrix and a phase control inductor in the transmitter circuit to form a dynamic tuning circuit, as shown in Fig. 9. The capacitance matrix comprises several capacitors connected in series and parallel. By changing the combination form of the series-parallel capacitor matrix and adjusting the capacitance value to perform impedance compensation, impedance matching can be realized again. Phase-controlled inductors are composed of capacitors, inductors and bidirectional thyristors. Among them, the inductor is connected in series with the thyristor and then joined in parallel with the capacitor of fixed capacity. By detecting the current and voltage values in real-time and calculating the control angle of the circuit, we can control the on-off of the thyristor and realize the phase-shift control of the inductor current. In this way, the entire parallel circuit can be continuously adjusted from the capacitive to the inductive range to discover the flexible change in the value of the compensation inductance. For the capacitance matrix, to quickly find the best combination of series and parallel, it is necessary to use a search algorithm to complete the calculation. The capacitor matrix dynamic tuning circuit workflow is shown in Fig. 10. When the magnetic coupler’s mutual inductance changes, the analogue signal of the transmitter circuit current is recognized and transformed into a digital signal via digital-to-analogue conversion. Based on these digital signals, the microcontroller calculates the required capacitance for the resonant state and reconfigures the switches in the capacitance matrix.

4 Experimental Prototype Verification We constructed a 1 kW prototype to verify the flexible magnetic coupler’s performance and system functionality. The flexible magnetic coupler has a transmitter diameter of 300 mm and a receiver diameter of 280 mm while operating. The transmitter and receiver were composed of eight curved rectangular coils, and a nanocrystalline magnetic core

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Fig. 9. System circuit diagram with dynamic tuning capability

Fig. 10. Dynamic capacitance matrix tuning circuit workflow

material was applied on the outer side of the transmitter and the inner side of the receiver. The eight curved rectangular coils could slide in a lower track to simulate the change in diameter from the initial state to the operational state. Each curved rectangular coil was wound with six turns of Litz wire 3 mm in diameter. When the flexible magnetic coupler was in operation, the parameters were as indicated in Table 1. Table 1. Magnetic coupler parameters Parameters

Description

Value

Lp

Transmitter coil inductance

36 µH

Ls

Receiver coil inductance

32 µH

M

Mutual inductance

15 µH

k

Coupling Coefficient

0.44

The system’s primary side circuit employs a full-bridge inverter to generate four channels of 100 kHz square waves with a 50% duty cycle. It incorporates a variable capacitance matrix and phase-compensating inductance to maintain real-time resonance. In the experimental setup, with an input voltage of 120 V, a frequency of 100 kHz, and a compensating inductance of 8 µH, the environment is depicted in Fig. 11. The system

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Fig. 11. Experimental environment

Fig. 13. Primary and secondary coil current and voltage waveforms

Fig. 12. Power analyzer data display

Fig. 14. Inverter output and rectifier input current and voltage waveforms

data was monitored using a power analyzer. The results are illustrated in Fig. 12. It is evident that the system achieved a DC-DC efficiency of 91.55%, transmitting a power of 1.08 kW, meeting the design expectations. The current and voltage waveforms of the primary and secondary side coils are depicted in Fig. 13. The secondary side current and voltage lag the primary side by 90 degrees, indicating a favourable resonant state. The current and voltage waveforms of the inverter output and rectifier input are shown in Fig. 14. The voltage is a 50% duty cycle square wave, aligning with the design expectations.

5 Conclusion The proposed universal wireless power transmission system based on flexible magnetic couplers provides efficient energy replenishment for different AUV models. The introduction of flexible magnetic couplers eliminates the gaps between couplers and enhances the charging platform’s versatility. The system can maintain real-time resonance when combined with variable capacitance and variable inductance technologies. By constructing a 1 kW experimental prototype, the system achieved a power transmission of 1.08 kW with a DC-DC efficiency of 91.55%, meeting the design expectations.

References 1. Teeneti, C.R., Truscott, T.T., Beal, D.N., Pantic, Z.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Ocean. Eng. 46(1), 68–87 (2021) 2. Zhang, Z., Pang, H., Georgiadis, A., Cecati, C.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019)

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3. Zhang, B., Xu, W., Lu, C., Lu, Y., Wang, X.: Review of low-loss wireless power transfer methods for autonomous underwater vehicles. IET Power Electron. 15(9), 775–788 (2022) 4. Wu, S., Cai, C., Wang, A., Qin, Z., Yang, S.: Design and implementation of a uniform power and stable efficiency wireless charging system for autonomous underwater vehicles. IEEE Trans. Ind. Electron. 70(6), 5674–5684 (2023) 5. Zeng, Y., et al.: Misalignment insensitive wireless power transfer system using a hybrid transmitter for autonomous underwater vehicles. IEEE Trans. Ind. Appl. 58(1), 1298–1306 (2022) 6. Yan, Z., et al.: Free-rotation wireless power transfer system based on composite antimisalignment method for AUVs. IEEE Trans. Power Electron. 38(4), 4262–4266 (2023) 7. Wang, D., Cui, S., Zhang, J., Bie, Z., Song, K., Zhu, C.: A Novel Arc-shaped lightweight magnetic coupler for AUV wireless power transfer. IEEE Trans. Ind. Appl. 58(1), 1315–1329 (2022) 8. Cai, C., Wu, S., Zhang, Z., Jiang, L., Yang, S.: Development of a fit-to-surface and lightweight magnetic coupler for autonomous underwater vehicle wireless charging systems. IEEE Trans. Power Electron. 36(9), 9927–9940 (2021) 9. Zhang, B., Wang, X., Lu, C., Lu, Y., Xu, W.: A wireless power transfer system for an autonomous underwater vehicle based on lightweight universal variable ring-shaped magnetic coupling. Int. J. Circuit Theory Appl. 51(6), 2654–2673 (2023) 10. Zhang, B., et al.: High-power-density wireless power transfer system for autonomous underwater vehicle based on a variable ring-shaped magnetic coupler. IEEE Trans. Transp. Electrif. Early Access

Port Shore Wireless Power System Using Frequency Bifurcation for Multi-power Levels Interoperability Kai Hu1 , Shiqiang Li1 , Jiatong Li2(B) , and Lei Zhao2 1 Zhejiang Zhoushan Marine Power Transmission Research Institute Co., Ltd.,

Zhejiang 316000, China 2 Chongqing University, Chongqing 400044, China

[email protected]

Abstract. With the continuous development of “green ports”, more and more electric ships are being used in various industries. Wired charging of electric ships not only requires high manpower, but also has safety hazards such as leakage in the humid environment of the port. Therefore, the wireless charging system at the port have a great significance for the development of electric ships. The existing wireless charging systems can only output a single power level to charge one type of ship. But for electric boats of different sizes, they need to correspond to different charging power levels. This article proposes a method for achieving high power output near 20 kHz and low power output near 85 kHz in the same wireless charging system by adjusting the system frequency. The system can also achieve zero phase angle on two frequencies simultaneously. This method improves the interoperability of the port shore power wireless charging system, reduces the size of the wireless charging system equipment, and makes ship wireless charging more convenient. Keywords: Magnetic Coupling Wireless Power Transfer · Frequency bifurcation · Power interoperability

1 Introduction Wireless Power Transfer (WPT) technology can achieve non-contact transmission of electrical energy from the power grid or batteries to electrical equipment. Due to its advantages of convenience, flexibility, safety, and efficiency, it solves many problems under traditional electrical contact power supply methods and has received widespread attention and research from experts and scholars at home and abroad. Wireless power transfer systems have many advantages in providing power for a wide range of applications such as electric vehicles, consumer electronics, industrial field equipment, underwater equipment, and implantable medical devices. Its non-contact power transmission has the advantages of safety, reliability, cleanliness, aesthetics, and convenience [3–5]. With the increasing number of electric ships, the demand for charging electric ships has also increased. At present, the charging method for electric ships is wired charging, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 68–76, 2024. https://doi.org/10.1007/978-981-97-0873-4_8

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which is subject to weather conditions, high economic and labor costs, and the interface is prone to corrosion and aging. There is also a risk of cable damage, which can pose great safety hazards. The wireless charging system does not have the aforementioned safety hazards, providing a more convenient and safe option for the charging of electric ships. However, most existing wireless charging devices can only output a single power, and different electric ships have different power levels. When ships of different sizes dock and require different power levels for charging, different wireless charging devices are required, which will increase costs and reduce the convenience of charging. Nowadays, the common high-power wireless charging for large electric boats should not exceed a charging frequency of 20 kHz. For low-power wireless charging of small electric boats, the charging frequency is required to be around 85 kHz. Therefore, it is necessary to study how to make the same wireless charging device output two different powers at two frequencies. Many experts and scholars have conducted a series of studies on improving the interoperability of multiple power levels. L. Zhao et al. proposed a hybrid WPT system that integrates series connected (SS) and LCL-LCL topologies to compensate for power fluctuations, despite the need to produce multiple coils and asymmetric geometries of pads [6, 7]. C. Xia et al. explored the application of harmonics in inductively coupled transmission (ICPT) systems to achieve stable power transmission, but this method faces the challenge of separately controlling independent frequency branches and multiple pairs of coils [8, 9]. In addition, R. Mai et al. introduced dual resonant coils to counteract coil misalignment and achieve stable power output, but the calculation of converter current in this system is very complex [10]. Similarly, E. Lee et al. proposed a dual matching scheme that is robust to distance variation, but requires two different frequency input sources, which increases the complexity of modulation and zero phase angle (ZPA) implementation [11]. Reference [12] proposes a wireless charging system controller for high-power electric ships, which models the sensitivity of magnetic field coupling and load changes in the WPT system, improving the ship’s ability to resist misalignment and distance interference. The article proposes an adaptive controller based on a bidirectional LCC topology structure to achieve fast charging. When the coupling coefficient is between 0.25 and 0.35, the system efficiency can reach 91% to 94%. However, the system has low power and is only an experimental prototype system that needs further optimization before practical application. The wireless energy transmission device developed by German IPT Technology Company for shore power in reference [13] has a fixed coil position at the transmitting end and manipulates the position of the ship to align the receiving end with the transmitting end on shore, with a power of 100 kW and a maximum transmission efficiency of 92%. This article proposes a wireless charging system based on SS topology structure. By utilizing the characteristics of the SS type topology structure, constant voltage outputs of 20 kHz and 85 kHz were achieved in the same SS radio energy transmission system while maintaining zero phase angle. The output power of the system at 20 kHz and 85 kHz corresponds to 22 kW and 1 kW, respectively. This system provides a feasible way for dual band wireless charging, improves efficiency and compatibility, and promotes the widespread application of wireless charging technology.

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2 Model Analysis In order to study the characteristics of the SS type wireless energy transmission line system, the SS type WPT system is first analyzed. Figure 1 shows the overall circuit diagram of the SS type radio energy transmission system, Udc as a DC input, Q1 − Q4 as a full bridge inverter, and D1 − D4 as a full bridge rectifier. C1 and C2 are the resonant capacitance of the primary and secondary sides of the system.

Fig. 1. SS type WPT system circuit diagram

Analyzing its working principle, Fig. 1 can be equivalent to the system circuit diagram shown in Fig. 2.

Fig. 2. Equivalent circuit of SS type WPT system

In Fig. 2, R1 represents the internal resistance of the primary coil (including winding loss, core loss, shielding loss, etc.), R2 represents the internal resistance of the secondary

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coil, RL represents the load, and M is the mutual inductance between the primary and secondary coils. ⎧ 1 ⎪ ⎪ Z1 = jωL1 + + R1 ⎪ ⎪ ⎪ jωC2 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ Z2 = jωL2 + + R2 + RL ⎪ ⎪ ⎪ jωC 2 ⎪ ⎪ ⎨ (ωM )2 (1) Zr = ⎪ Z ⎪ 2 ⎪ ⎪ ⎪ ⎪ Z1 Z2 + RL Z1 + (ωM )2 ⎪ ⎪ Z = ⎪ in ⎪ ⎪ Z2 + RL ⎪ ⎪ ⎪ ⎪ 8RL ⎪ ⎩ Req = π2 Among them, Z1 is the primary impedance of the system, Z2 is the secondary impedance of the system, Zr is the reflection impedance of the secondary edge of the system to the primary edge, and Zin is the input impedance of the system. Req is the equivalent load of the system. According to the KVL equation, it can be obtained that: ⎧ VG − jωMI2 ⎪ I = ⎪ ⎪ 1 ⎨ 1 jωL1 + jωC + R1 1 ⎪ ⎪ ⎪ ⎩ I2 =

jωMI1 jωL2 +

1 jωC2

(2)

+ R2 + RL

where VG is the equivalent voltage of the DC input: √ 2 2 Udc VG = π

(3)

By analyzing Zin , we can achieve zero phase angle of Zin at 20 kHz and 85 kHz by designing parameters, which means that the imaginary part is zero. Then, we can determine other parameters of the system. The imaginary part expression of the input impedance of the system is as follows: 1 1 ωC1 ) + R1 (ωL2 − ωC1 )) 1 2 (ωL2 − ωC ) + 4R2eq 1 1 1 1 (2R1 Req + ωM 2 − (ωL1 − ωC )(ωL2 − ωC ))(ωL2 − ωC ) 1 1 1 − 1 2 (ωL2 − ωC ) + 4R2eq 1

Im(Zin ) =

2Req (2Req (ωL1 −

(4)

The output power of the system can be obtained from the above equation: Pout = I22 Req

(5)

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3 Design Method for Dual Frequency and Dual Power Level Output Parameters Based on SS Type WPT System Based on the analysis in sect. 1, the article proposes to first analyze the relationship between the input impedance and operating frequency of the SS type WPT system under different load conditions by utilizing the characteristics of the SS type WPT system, as shown in the following figure.

Fig. 3. The relationship between input impedance and frequency of the system under different loads

Figure 3 shows the variation of input impedance relative to operating frequency under different load conditions. Due to the tuning of both the primary and pickup compensation networks to 85 kHz, when the system operates at a frequency of 85 kHz, Zin is purely resistive, as shown in phase 00 . Under tuning conditions, as shown in Fig. 3, if the equivalent load resistance Req is high, the compensation network exhibits a lower input impedance. This can be explained by the current source output characteristics exhibited by the pickup circuit. Therefore, a higher Req corresponds to a heavier load. In fact, the system may not be able to operate accurately at the tuned frequency. Under heavy loads, when the operating frequency is slightly higher than the designed tuning frequency, Zin becomes inductive, making it easier to achieve ZVS. If the system needs to operate at a fixed frequency, then Zin can be made inductive by using a larger compensation capacitor. Under light load conditions, it can be seen from the above figure that there are three different zero crossing frequencies in the phase of the input impedance, which is called frequency classification and occurs under the following conditions: Req ≤ kωL2

(6)

When frequency bifurcation occurs, if the operating frequency fluctuates slightly above the designed resonant frequency of the system, it will lead to capacitive performance of the system. If a variable frequency controller is used, it will cause unstable operation of the system because the operating frequency may deviate from the designed resonant frequency and turn to the other two zero crossing frequencies. This phenomenon is frequency bifurcation because the coupling coefficient between the transmitting coil and the receiving coil is very high. So we can use this feature to select two zero crossing

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frequencies and design the system parameters to achieve high gain output at one frequency and low gain output at the other frequency, corresponding to two different ship types (Fig. 4).

Fig. 4. Parameter design flowchart

4 Simulation Verification To verify the effectiveness of the proposed method, a wireless energy transmission system with an output power of 25 kW at 20 kHz and 1.4 kW at 85 kHz was constructed based on the SS type WPT system. The circuit parameters of the system are shown in Table 1:

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Parameter

Value

Primal self perception L1

100 μH

Secondary self perception L2

100 μH

Primary capacitance C1

0.3406 μF

Secondary capacitor C2

0.3406 μF

Input voltage VG

770 V

Equivalent load Req

5

Frequency f

28 kHz

Coupling coefficient k Internal resistance of transmitting coil and receiving coil R1 , R2

0.9 0.2 

Under the above parameter conditions, the following simulation results can be obtained:

Fig. 5. Plot of phase angle and input impedance versus system frequency

Figure 5 only shows the input impedance and phase angle of the system with a load of 5 . It can be seen that the input impedance of the system is zero phase angle at frequencies of 20 kHz and 85 kHz. The output power of the system is shown in the following figure (Fig. 6):

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Fig. 6. Relationship between system output power and frequency

According to the simulation verification results, it can be seen that using the characteristics of the SS type WPT system itself and by designing the system parameters, only adjusting the frequency in the same set of wireless energy transmission equipment can realize the zero phase angle output of two kinds of power, and can realize the high-power wireless energy transmission with the output power of 25 kW at 20 kHz and 1.3 kW at 85 kHz.

5 Result In order to solve the problem of the same radio energy transmission system outputting two power levels, this article first studied the characteristics of the SS system. Through the study of the system characteristics, it was found that the SS system has frequency bifurcation characteristics. By designing the parameters of the SS system, the output power can be 25 kW at 20 kHz and 1.3 kW at 85 kHz in the same system. The system only needs to change the frequency of the system to achieve zero phase angle output of two types of power in the same device. It improves the interoperability of WPT systems with multiple power levels and achieves the requirement of outputting two types of power from the same device, thereby improving the compatibility of wireless energy transmission systems with multiple power levels and enabling better promotion of wireless energy transmission technology.

References 1. Ji, L., Wang, L., Liao, C., Li, S.: A simultaneous wireless power and bidirectional information transmission with a single-coil, dual-resonant structure. IEEE Trans. Ind. Electron. 66(5), 4013–4022 (2019) 2. Huang, C.C., Lin, C.L., Wu, Y.K.: Simultaneous wireless power/data transfer for electric vehicle charging. IEEE Trans. Ind. Electron. 64(1), 682–690 (2017)

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3. Wu, J., Zhao, C., Lin, Z., Du, J., Hu, Y., He, X.: Wireless power and data transfer via a common inductive link using frequency division multiplexing. IEEE Trans. Ind. Electron. 62(12), 7810–7820 (2015) 4. Li, X., Tang, C., Dai, X., Deng, P., Su, Y.: An inductive and capacitive combined parallel transmission of power and data for wireless power transfer systems. IEEE Trans. Power Electron. 33(6), 4980–4991 (2018) 5. Yan, Z., Xiang, Z., Wu, L., Wang, B.: Study of wireless power and information transmission technology based on triangular current waveform. IEEE Trans. Power Electron. 33(2), 1368– 1377 (2018) 6. Zhao, L., Thrimawithana, D.J., Madawala, U.K.: Hybrid bidirectional wireless EV charging system tolerant to pad misalignment. IEEE Trans. Industr. Electron. 64(9), 7079–7086 (2017) 7. Zhao, L., Thrimawithana, D.J., Madawala, U.K., et al.: A misalignment tolerant series-hybrid wireless EV charging system with integrated magnetics. IEEE Trans. Power Electron. 34(2), 1276–1285 (2018) 8. Xia, C., Jia, R., Wu, Y., et al.: WPIT technology based on the fundamental harmonic component for a single-channel and two-coil ICPT system. IET Power Electronics 12(10), 2608–2614 (2019) 9. Xia, C., Ren, S., Ma, N., et al.: Inductively coupled power transfer system with fundamental wave and harmonic wave two-path parallel transmission. Automation of Electric Power Systems 41(7), 93–100 (2017) 10. Mai, R., Yan, Z., Chen, Y., et al.: A hybrid transmitter based efficiency improvement controller with full-bridge dual resonant tank for misalignment condition. IEEE Trans. Power Electron. 35(1), 1124–1135 (2019) 11. Lee, E., Kang, W., Ku, H.: A magnetic resonance wireless power transfer system robust to distance variation using dual-matching scheme. J. Electr. Eng. Technol. 14(1), 2097–2103 (2019) 12. Haque, M.S., Mohammad, M., Choi, S.: Sensitivity Analysis and Controller Design of High Power LCC-LCC Compensated Wireless Battery Charging For Electric Ship Applications. In: 2020 IEEE Applied Power Electronics Conference and Exposition (APEC), p. 32003207 (2020). https://doi.org/10.1109/APEC39645.2020.9124536 13. “Wireless charging system suits electric ferries,” IPT-Technology, Efringen-Kirchen, Germany. Accessed on: Feb. 24, 2022. [Online]. Available: https://ipt-technology.com/ships-fer ries

Design of Power Supply for Three Core Cable Wireless Monitoring Network Based on Space Magnetic Field Energy Harvesting Lu Xu(B) , Hu Ran, Tian Jie, Zhifeng Xu, and Tang Feng China Southern Power Grid Shenzhen Power Supply Co., Ltd., Shenzhen 518000, China [email protected]

Abstract. In order to ensure the normal operation of power cable wireless monitoring network, it is first necessary to solve the energy supply problem. In response to the problem of traditional power supply failure caused by uneven spatial magnetic field distribution in three core cable, this paper proposes a calculation model for spatial magnetic field distribution in three core cable based on the idea of spatial magnetic field energy harvesting, to guide the design of power supply. Firstly, based on the spatial magnetic field distribution calculation model of three core cable, the characteristics of magnetic field distribution around the three core cable were analyzed, and a split winding type energy harvesting coil was designed accordingly; Then, by solving the output voltage of energy harvesting coil, the circuit of energy harvesting module and energy management module were further designed, thus achieving the overall design of the power supply; Finally, experimental tests were conducted on the designed power supply with load, and the experimental results showed that the power supply can meet the actual load requirements. Keywords: Three core cable · Wireless monitoring network · Power supply · Magnetic field energy harvesting

1 Introduction The underground cable ducts have been in a semi closed state for a long time, with poor air flow, abundant harmful gases, and low oxygen concentration, which pose a threat to the lives of workers. Therefore, wireless monitoring devices are needed to measure various parameters of cables [1]. In order to achieve reliable power supply for various wireless monitoring network systems in underground cable ducts, it is necessary to design an energy supply that can operate stably for a long time. Existing research has shown that the power supplies of wireless monitoring network mainly include solar energy, wind energy, lasers, ultrasound, batteries, and spatial magnetic field [2]. Due to the power cables being located in underground cable ducts, wind and solar energy cannot be utilized; Laser and ultrasonic power supply are stable, but the power supply is small and expensive; Batteries can achieve stable power supply, but due to their location in pipelines, charging issues are difficult to solve. Considering © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 77–86, 2024. https://doi.org/10.1007/978-981-97-0873-4_9

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that there is abundant magnetic field energy in the surrounding space during the operation of power cables, researchers tend to use spatial magnetic field energy harvesting to design the power supply for wireless monitoring networks [3]. However, the design of the above-mentioned power supply is mainly aimed at single core cable. For three core cable, the superposition of three-phase current magnetic fields leads to uneven distribution of overall magnetic field [4]. If we continue to use the traditional power supply mentioned above, it will be difficult to effectively extract energy from the space magnetic field. In response to the problem of energy harvesting difficulties caused by uneven spatial magnetic field around three core cable, this paper designs a split winding type energy harvesting coil based on the distribution characteristics of the spatial magnetic field of three core cable. Based on this, the energy harvesting module circuit and energy management module circuit of the power supply are designed, achieving reliable energy supply for the wireless monitoring network of three core cable.

2 The Principle of Space Magnetic Field Energy Harvesting and Design of Energy Harvesting Coil for Three Core Cable 2.1 The Principle of Space Magnetic Field Energy Harvesting The spatial magnetic field energy harvesting is mainly achieved by placing induction coils in a changing magnetic field [5, 6]. According to Faraday’s law of electromagnetic induction, a changing magnetic field will generate an induced electromotive force in the coil, thereby achieving the collection of magnetic field energy in space. From this, it can be seen that the study of the changes in the spatial magnetic field is particularly important in the process of obtaining energy from the three core cable spatial magnetic field. Therefore, this paper proposes a calculation model for the spatial magnetic field distribution around a three core cable, as shown in Fig. 1. Simplify the three-phase current carrying wire as an infinite line current located at the center of each phase wire, and according to Biot-Savart’s law, the magnetic induction intensity BA , BB and BC generated by the three-phase current I A , I B and I C at the field point P(r,φ)can be obtained as follows: ⎧   ⎪ a sin φ ⎪ BA = μ0 IA eφ r−a cos φ ⎪ − e ρ 2 2 2 2 ⎪ 2π r +a −2ar cos φ r +a −2ar cos φ ⎪ ⎨   r+a cos(π / 3−φ) a sin(π / 3−φ) μ0 IB (1) B e = − e B φ ρ 2π ⎪ r 2 +a2 +2ar cos(π / 3−φ) r 2 +a2 +2ar cos(π / 3−φ) ⎪ ⎪   ⎪ ⎪ sin(2π / 3−φ) ⎩ BC = μ0 IC eφ r−a cos(2π / 3−φ) + eρ r 2 +a2a−2ar 2π r 2 +a2 −2ar cos(2π / 3−φ) cos(2π / 3−φ) where, a is the distance from the center of cable to the center of wire, eφ and eρ are respectively tangential and radial unit vectors. By calculating Eq. (1), the spatial magnetic field distribution around the three core cable can be obtained. Considering the power frequency alternating current in the threephase wire, the variation of magnetic induction intensity at field point P with time can also be obtained.

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Fig. 1. The calculation model for spatial magnetic field distribution around a three core cable.

2.2 The Design of Harvesting Energy Harvesting Coil 2.2.1 Determination of Coil Layout Method Taking the common 10 kV three core cross-linked polyethylene cable in the distribution network as an example [7, 8], its type is YJLV22–8.7/10 kV–3 × 50 mm2 . Considering that the magnetic field generated by the coil cross-section is mainly the component of the field point magnetic field in the tangential direction, the determination of the coil layout mainly depends on the changes around the cable. When a three-phase alternating current with an effective value of 100 A is introduced into a three core cable, the magnetic field distribution around the cable is calculated using Eq. (1) and COMSOL software, respectively. The calculation results are shown in Fig. 2.

Fig. 2. The modulus and phase of tangential magnetic flux density Bφ at each point on the cable surface.

From Fig. 2, it can be seen that the trend of change calculated by Eq. (1) and COMSOL software is basically consistent, thus verifying the accuracy of the calculation model in Sect. 2.1. In addition, the tangential magnetic induction intensity around the three core cable has an extreme value at three positions, and rapidly decays after reaching the extreme value along the circumference of the cable. By rotating the extreme point by 30°, it decreases to half of the extreme value. In order to improve energy collection efficiency while considering the space required for coil winding, the gap distance between the iron core and the cable should be minimized as much as possible, and the center angle corresponding to the coil domain should be determined as 30°. That is, taking the extreme

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point as the benchmark, offset 15° to the left and right respectively, and at this time, only 12.5% decrease. The final designed the split winding type energy harvesting coil is shown in Fig. 3.

Fig. 3. The split winding type energy harvesting coil.

2.2.2 Determination of Coil Turns and Wire Diameter In order to determine the optimal number of turns of the energy taking coil and the diameter of the conductor, continue to use the cable parameter settings in Sect. 2.2.1, and use the layout in Fig. 3 to establish the COMSOL simulation model, as shown in Fig. 4 (a). Considering that the number of coil turns is determined by the coil domain thickness and conductor diameter, the coil domain thickness and conductor diameter can be set respectively in the simulation model, and the output power of the coil can be calculated through simulation calculation, as shown in Fig. 4 (b).

Fig. 4. COMSOL simulation model and coil output power calculation results.

It can be seen from Fig. 4 (b) that with the increase of coil domain thickness, that is, the number of turns of the coil increases, the output power of the coil increases significantly, that is, the output voltage of the induction coil increases. Under the same coil thickness, increasing the wire diameter will reduce the number of turns of the coil,

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even if the internal resistance of the coil is reduced, the output power of the coil will also be reduced. When determining the number of coil turns, it is necessary to consider not only the power required by the load, but also the structural size of the whole device. The thickness of the coil domain should be reduced as much as possible to reduce the cost. Therefore, after comprehensively considering the output power and structural size of the energy taking coil, the coil domain thickness is 5 mm and the wire diameter is 0.5 mm, and the number of turns of the coil is 514.

3 The Circuit Design of Power Supply 3.1 The Circuit Design of Energy Harvesting Module In sect. 2, the split winding type energy harvesting coil is designed, which needs the circuit of the energy taking module to transfer the power to the energy management module, and then supply power for the wireless monitoring network. It can be seen from Fig. 3 that the energy harvesting module has three induction coils. The circuit model of each induction coil is shown in Fig. 5. The circuit includes the induced voltage E, coil resistance RS , coil inductance L S and compensation capacitance C S of the coil, U OUT is the output port voltage.

Fig. 5. The circuit model of energy harvesting module.

After determining the structural parameters of the energy harvesting coil, the coil resistance and coil inductance can be determined, which are the parameters of the induction coil itself. In addition, in order to improve the output power of the coil, it is necessary to connect a capacitor C S in series at the output end of each coil, so that the series capacitor and the inductance L S of the coil will have series resonance at power frequency, compensate for the power loss caused by the self-inductance of the dropped coil, and improve the output power [9, 10]. 3.2 The Circuit Design of Energy Management Module 3.2.1 The Design of Rectifier Boost Circuit Considering that the energy harvesting module contains three induction coils, the output voltage of each induction coil is a power frequency sinusoidal waveform, and the phase difference is 120°. Therefore, a half wave rectifier boost circuit can be used to realize AC rectification and boost at the same time by using a circuit topology. The circuit topology is shown in Fig. 6. The circuit topology uses half wave rectification to rectify the output

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voltage of each induction coil to obtain the DC output voltage, and then the output voltages of the three induction coils are superimposed in series to improve the output voltage of the whole power supply. Compared with the three-phase rectifier circuit, the circuit topology contains only three diodes, which reduces the complexity of the circuit topology and the voltage loss of electrical components.

Fig. 6. Half wave rectifier boost circuit.

3.2.2 The Design of Energy Management Chip Under actual working conditions, the ampacity of the cable will change with the load. When the load current increases or decreases, the output voltage of the rectifier boost circuit will also increase or decrease, and the load of the power supply requires stable DC output. In order to solve the above problems, we need to use energy management chip. The following describes an energy management chip LTC-3331, as shown in Fig. 7. When the chip input voltage changes within the specified range, the output voltage can be stabilized at the set value, so as to meet the load demand.

Fig. 7. LTC-3331 circuit topology.

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The energy management chip LTC-3331 has a dual input, single output DC/DC converter with an input prioritizer. The energy collection input is a 3 V–18 V step-down DC/DC converter, and the main battery input is a 1.8 V–5.5 V step-down boost DC/DC converter. It can realize the stable output of the power supply under the condition of a wide range of cable load current. LTC-3331 energy management chip includes two input ports, one of which is input by energy collection. The energy collection input port has a buck DC/DC converter, and the collected magnetic field energy can be input through this port. The other can be input by a rechargeable battery. This port has a buck boost DC/DC converter, which is used as a backup power supply in case of failure of the energy collection input port. Each input port can provide independent power for the output port. Under the condition that the energy collection input can effectively drive the chip, the battery basically has no current leakage, and only when the energy collection disappears can it supply power to the VOUT . 3.2.3 Voltage Stabilization Design Scheme As mentioned above, the condition for the normal operation of the energy collection input terminal of the energy management chip is that the input voltage of the environmental energy collection is 3–18 V DC voltage, so the output voltage of the half wave rectifier boost circuit is required to meet the requirements of 3–18 V DC voltage. According to the energy taking coil designed in sect. 2, a half wave rectifier boost circuit is connected on this basis, and the output voltage is calculated using Faraday’s law of electromagnetic induction. The results are shown in Fig. 8. It can be seen from Fig. 8 when the cable current is higher than 200 A, the output voltage of the half wave rectifier boost circuit can meet the input requirements of the energy management chip.

Fig. 8. Output voltage of rectifier boost circuit under different load currents.

Therefore, the voltage output of the rectifier boost circuit used in this paper can be used as the input voltage of the energy management chip, and no additional voltage stabilizing circuit is needed. Thus, the circuit topology of the entire energy management module is shown in Fig. 9.

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Fig. 9. The circuit topology of energy management module.

4 Experimental Test of Power Supply According to the coil layout, coil turns and wire diameter determined in sect. 2, the energy harvesting coil is made, and the experimental circuit is built according to the circuit topology of the energy harvesting module and the energy management module determined in sect. 3. Finally, the experimental platform of the energy supply with load is built as shown in Fig. 10.

Fig. 10. Experimental platform of power supply with load.

In order to obtain higher output voltage of the energy harvesting module, two energy harvesting coils are arranged around the cable and connected in series. When the cable load current is rated at 500 A, the output voltage of the two energy harvesting modules in series is shown in Fig. 11(a). It can be seen from the figure that the output voltage amplitude of the induction coil is about 2.6 V, which is about twice as high as that of a single energy harvesting module. Connect the pure resistance load, and study the output power of the power supply. Under laboratory conditions, change the load current in the cable and calculate the load power. The results are shown in Fig. 11(b). Under the condition of cable rated current, the output power of the power supply is about 170 mW. When the cable current is 300 A and above, the output power of the power supply is more than 50 mW, which can meet the actual load demand.

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Fig. 11. Output voltage of the energy module and output power of the power supply.

5 Conclusion In response to the problem of energy harvesting difficulties caused by uneven spatial magnetic field around three core cable, this paper designs a split winding type energy harvesting coil based on the distribution characteristics of spatial magnetic field of three core cable. Based on this, the energy harvesting module circuit and energy management module circuit of the power supply are designed, thus achieving the design of the wireless monitoring network power supply for three core cable. In addition, experimental tests were conducted on the designed power supply, and the experimental results showed that the power supply can meet the actual load requirements. Acknowledgments. This work is supported by Research on Live Detection Technology of Distribution Network Cable Insulation State Based on Harmonic Component Characteristics (Project NO. 090000KK52220013).

References 1. Yinbai, X., Chenbin, W., Li, L.: Research on sensing and monitoring technology of complicated cable tunnel based on wireless Ad-Hoc network. In: 2021th international conference on power and energy systems, pp. 467–471 (2021) 2. Xin, C., Guixiang, Z.: Co-simulation research based on electromagnetic induction of wireless power transfer. J. Electr. Measure. Instrum. 28(4), 434–440 (2014). (in Chinese) 3. Yong, Z., Zhiming, W., Li, Y., et al.: Optimized design and simulation study of helical core suitable for non-invasive energy harvesting. In: 16th IEEE Conference on Industrial Electronics and Applications, pp. 1016–1019 (2021) 4. Juan, C.del-P.-L.: Evaluation of the power frequency magnetic field generated by three-core armored cables through 3D finite element simulations. Electric Power Systems Research 213 (2021) 5. Navau, C., Jordi, P.-C., Alvaro, S.: Magnetic energy harvesting and concentration at a distance by transformation optics. Physical Review Letters 109(26) (2012) 6. Xiangyong, Z., Haipen, L., Yunli, H.: Analysis of the influence of ferromagnetic material on the output characteristics of halbach array energy-harvesting structure. Micromachines 12(12) (2021) 7. Oilong, W., Xiangrong, C., Guohai, W.: Thermo-electric coupling simulation for 10 kV AC XLPE cable in DC operation. J. Southw. Jiaotong Univ. 57(01), 46–54 (2022). (in Chinese)

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8. Jingzhe, Y., Chen, X., Meng, F.: Numerical analysis of thermo-electric field for AC XLPE cables with different service times in DC operation based on conduction current measurement. IEEE Trans. Dielectr. Electr. Insulat. 27(03), 900–908 (2020) 9. Oktay, A., Baris, K.: A new approach to limit fault current with series-parallel resonance strategy. Electrical Engineering 102(03), 1287–1296 (2020) 10. Micheal, D., Chandra, S.N.: On resonance and frequency response characteristics of electrical circuits. Int. J. Electr. Eng. Edu. 50(04), 368–383 (2014)

An Efficient and Simple Battery Wireless Charging System with Re-configurable Rectifier Youzheng Wang , Hongchen Liu(B)

, Huiying Yu , Shuyu Wang, and Shuo Wang

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China [email protected]

Abstract. Wireless charging technology (WCT) is mostly used in the domain of power battery packs. The battery wireless charging system (BWCS) should provide the required constant outputs for the power battery packs. The existing charging conversion methods have the defects of more components, low transfer efficiency and poor reliability. To solve above issues, this paper proposes an efficient and simple BWCS with re-configurable rectifier. The BWCS can implement smooth switching between series-series (SS) circuit with natural loadindependent CCO and series/inductor-capacitor-capacitor (S/LCC) circuit with load-independent CVO by controlling the MOSFETs in the rectifier. The BWCS works at a fixed frequency with a few components, eliminating the wireless link between the two sides, and simple control method. The operating principle of the presented BWCS is described in detail, and a 250V/4A experimental platform is set up to validate the good performance of the presented BWCS. Keywords: Battery wireless charging system (BWCS) · Re-Configurable rectifier · Smooth switching

1 Introduction Compared with conventional plug-in charging technology, wireless charging technology (WCT) can break away from the constraints of cables and realize energy transfer at a certain spatial distance [1]. The WCT is convenient, safe and reliable, and has a wide range of applications in many fields, for instance implantable medical devices [2], underwater charging devices [3] electric vehicles [4], and so on. Currently, the WCT is mostly used to charge the batteries. The popular means of power battery packs charging is constant current output (CCO) and constant voltage output (CVO). That means the power battery packs are charged in CCO mode firstly, and then it is converted to CVO mode. It is noteworthy that the equivalent resistance of the power battery packs is not always fixed in the whole charging process, which inevitably increases the difficulties for designing a battery wireless charging system (BWCS). At this stage, domestic and foreign scientific researchers have done a lot of useful work in CCO-CVO charging method, which can be roughly divided into four categories. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 87–94, 2024. https://doi.org/10.1007/978-981-97-0873-4_10

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1) Multistage Power Transfer for CCO-CVO Charging: [5] and [6] proposes to cascade the Buck or Boost converter at the two sides to realize the system gain regulation or impedance transformation function and then satisfy the battery charging demand. However, this way will increase system cost and control complexity. The charger efficiency is also low. 2) Frequency Switching for CCO-CVO Charging: The variation from CCO to CVO is achieved by changing system operating frequency [7]. The way of switching the system frequency can minimize the number of components and reduce the cost due to no additional components are added. However, under the condition of the large misalignment or light load, the operating frequency is far away from the resonance point and the reactive power of the wireless charger is high. Besides, the parameter design of this method is relatively difficult. 3) Clamping Circuit for CCO-CVO Charging: [8] utilizes the two rectifier of the receiver to have the function of clamping each other to achieve CCO-CVO charging. Therefore, when the load resistance is lower than boundary resistance, the BWCS can be simulated by SS topology; When the load resistance is higher than boundary resistance, the BWCS can be simulated by S/LCC topology. Although this method has the merits of simple control and low difficulty in design, it requires additional coil and rectifier, causing higher system costs and poor anti-offset ability. 4) Topology Switching for CCO-CVO Charging: Switching from the topology with CCO feature to the circuit with CVO feature is implemented by two mode change-over switches [9–11]. The method is easy to realize, simple to control, and doesn’t require frequency switching, so it is a better scheme to implement CCO to CVO. Nevertheless, the proposed BWCSs contain a large number of components, which can affect system efficiency. To minimize the amount of components and achieve high efficiency charging, [12–14] proposed to adopt a relay in the transmitter and a small number of compensation components to implement CCO to CVO. However, this way has poor system dynamic characteristics and large current spikes. Moreover, the relay also bear a high voltage stress, and the wireless communication link should also be constructed. In view of the above existing problems, this paper presents a simple and efficient BWCS with re-configurable rectifier. In terms of the same switching compensation circuits as [11] and [15], the proposed BWCS only includes one inductor, three capacitors and an active rectifier. Besides, all the compensation capacitors are fully utilized, that is to say, there are no idle capacitors in both charging modes. Thus, the proposed BWCS has the superiorities of low cost and high efficiency. Compared to [12–14], the relay in the BWCS can be saved by power switch tubes through device multiplexing method. Besides, current spikes at the switching instantaneous are effectively suppressed and without constructing wireless communication between two sides. Thus, the proposed BWCS has the superiorities of high reliability.

2 Derivation and Operating Principle of the Proposed BWCS The circuit structure of the presented BWCS is depicted in Fig. 1. The transmitter is composed of the H-bridge inverter (Q1 –Q4 ), capacitor C P and transmitting coil P. V DC represents the input DC voltage of the system. vAB and iP respectively represent the output

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voltage and current of the inverter. L P represents the self-inductance of transmitter coil P. The receiver is composed of the receiver coil S, compensation inductor L 1 , compensation capacitors C S and C S1 and re-configurable rectifier. iCS , iCS1 and iL1 represent the current of C S , C S1 and L 1 , respectively. L S represents self-inductance of the receiver coil S. Q5 , Q6 , D1 , D2 and filter capacitor C O constitute re-configurable rectifier. iBAT and vBAT represent the system output current and output voltage, respectively. M PS represents mutual inductance (MI) between the two coils.

Q1

Q3

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MPS iCS

iP

CP

CS1

CS LP

VAB

VDC

LS

C CO VCD

D V D2 CE

iL1 Q6

Q4

+

Q5

L1

B Q2

iBAT

D1

vBAT

-

E

Fig. 1. The topology of the proposed BWCS.

The expression for V AB is as follows √ VAB = 2 2VDC /π

(1)

The proposed BWCS is in resonance mode during normal operation, and the working frequency ω can be indicated as: √ CS + CS1 1 1 = √ =√ (2) ω= √ LP CP LS CS CS1 L1 CS1

2.1 CCO Mode With respect to the CCO mode, Q6 doesn’t operate. The classical SS circuit driven by the high frequency inverter and the active rectifier, as depicted in Fig. 2(a). The phase-shift between two sides is π/2. RBAT represents the equivalent resistance of power battery packs. The equivalent circuit under the CCO mode is also given in Fig. 2(b). REQ represents the equivalent ac resistance of the rectifier. Write the circuit matrix equation for Fig. 2(a)      LP − ω21C MPS IP VAB P (3) = jω REQ 0 ICS MPS LS − C2S +CS1 + jω ω CS CS1

Combining (2) and (3), we can get (4) and (5) IP = VAB REQ /(ωMPS )2

(4)

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Q3

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iP

CP

VDC

LS

C Q5

vBAT

-

D

iL1 Q6

Q4

+ RBAT

CO

L1

B Q2

CS1

CS LP

iBAT

D1

D2 E

(a)

IP

CP LP

VAB

CS

MPS ICS

CS1

LS

REQ

VCD

(b)

Fig. 2. Proposed BWCS under the CCO mode. (a) Topology. (b) Equivalent circuit.

ICS = VAB /(ωMPS )

(5)

Therefore, the expression of I BAT can be indicated as:   IBAT = 4VDC / ωπ 2 MPS

(6)

2.2 CVO Mode With respect to the CVO mode, Q5 and Q6 are always ON. The S/LCC circuit driven by the H-bridge inverter and half-bridge rectifier, as depicted in Fig. 3(a). The relationship between V CE and V BAT is as follows √ VCE = 2VBAT /π (7) Write the circuit matrix equation for Fig. 3(a) ⎡ ⎡ ⎤ MPS LP − ω21C VAB P ⎢ ⎣ 0 ⎦ = jω⎣ MPS1 + 21 LS − 21 + ω CS1 ω CS 0 − ω2 1C − ω21C S1

1 ω2 CS1

S1

Combining (2) and (8), we can get (9)–(11)   2 IP = VAB L21 / REQ MPS

⎤⎡

0 0 −L1 −

REQ jω

⎤ IP ⎥⎣ ⎦ ICS ⎦ IL1

(8)

(9)

ICS = VAB /(jωMPS )

(10)

  IL1 = VAB L1 / REQ MPS

(11)

An Efficient and Simple Battery Wireless Charging System Q1

Q3

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iP

iCS

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vBAT

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D

iL1 Q6

Q4

+ CO

L1

B Q2

C

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iCS1 CS1

CS

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D2 E

(a)

IP

L1 IL1

MPS ICS CS

CP

ICS1 LP

VAB

LS

CS1

REQ

VCE

(b)

Fig. 3. Proposed BWCS under the CVO mode. (a) Topology. (b) Equivalent circuit.

3 Experimental Verification The 1 kW experimental device is set up to test the proposed scheme, whose picture is illustrate in Fig. 6. The key parameters of the presented BWCS is listed in Table 1. The desired charging current and charging voltage of the system are 4 A and 250 V, respectively. The operating frequency of the system is 100 kHz. Both two coils are square in shape [16, 17]. The spatial dimension of the coupler is 300 × 300 × 100 mm3 (length × width × height). The turns of two coils are 23 (Fig. 4). Transmitter

Receiver

DSP TMS320F28335 Coupler Drive circuit

H-bridge inverter

S6 S5 D1 L1 C D 2 S1 CS2

CP

Fig. 4. Experimental setup of the proposed BWCS.

Figure 5 displays the experimental waveforms in the CCO mode. Figure 5(a) displays the earlier stage of constant current charging with RBAT = 10 . In this case, iBAT = 4.02 A and vBAT = 40.21 V. Figure 5(b) displays the later stage of constant voltage charging with RBAT = 50 . In this case, iBAT = 3.96 A and vBAT = 197.53 V. It can be noticed

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Value

Transmitting coil P

193.7 μH

Receiving coil S

190.3 μH

MI M PS

40.32 μH

InductorL 1

20.2 μH

Capacitor C P

13.5 nF

Capacitor C S

14.9 nF

Capacitor C S1

125.4 nF

that under CCO mode, the current deviation between Fig. 5(a) and Fig. 5(b) is 1.5%, and the output current fluctuation is small, meeting the charging need. Furthermore, Q1 –Q4 can implement ZVS.

Fig. 5. Experimental results in the CCO. (a) RBAT = 10 . (b)RBAT = 50 .

Figure 6 displays the experimental waveforms in the CVO mode. Figure 6(a) displays the earlier stage of constant voltage charging with RBAT = 80 . In this case, iBAT = 3.09 A and vBAT = 248.62 V. Figure 6 (b) displays the later stage of constant voltage charging with RBAT = 250 . In this case, iBAT = 1.01 A and vBAT = 252.05 V. It can be noticed that under the CVO mode, the voltage deviation between Fig. 6(a) and Fig. 6(b) is 3.77%, and the output voltage fluctuation is small, meeting the charging need.

Fig. 6. Experimental results in the CVO. (a) RBAT = 80 . (b)RBAT = 250 .

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Figure 7 displays the transient experimental waveform of the BWCS. It mainly includes the waveforms of vAB , iP , I BAT , V BAT and the drive voltage vGQ6 of Q6 . It can be noticed from Fig. 7 that the current spike of iP at the switching moment is very small. V BAT and I BAT also change slightly. Therefore, the proposed BWCS achieves smooth switching from CCO to CVO.

Fig. 7. Transition process results from CCO to CVO.

4 Conclusion This paper has presented a simple and efficient BWCS with re-configurable rectifier. The concept of switching CCO and CVO by configuring the rectifier is proposed. On basis of the experimental, the conclusions are summarized as follows: 1) With simple control and a small amount of elements, smooth switching of the CCO mode and CVO mode at a fixed system frequency can be implemented to satisfy the battery charging needs. 2) The approximate zero phase angle input and ZVS can be obtained in both CCO and CVO modes. 3) At the moment of mode switching, the inverter output current spike is suppressed and the fluctuation rate of output current and voltage is also small. Acknowledgments. This work is supported by the National Key R&D Plan Project (Sub-project) under Grant 2018YFE0309102.

References 1. Wang, Y., Liu, H., Yu, H., Wheeler, P.: A battery wireless charger with full load range softswitching operation and zero-switching-loss inverter. IEEE Trans. Indu. Electr. https://doi. org/10.1109/TIE.2023.3306411, to be published. 2. Liu, H., Wang, Y., Yu, H., Wu, F., Wheeler, P.: A novel three-phase omnidirectional wireless power transfer system with zero-switching-loss inverter and cylindrical transmitter coil. IEEE Trans. Power Electron. 38(8), 10426–10441 (2023)

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3. RamRakhyani, A.K., Mirabbasi, S., Chiao, M.: Design and optimization of resonance-based efficient wireless power delivery systems for biomedical implants. IEEE Trans. Biomed. Circuits Syst. 5(1), 48–63 (2011) 4. Mai, J., Wang, Y., Yao, Y., Sun, M., Xu, D.: High-Misalignment -Tolerant IPT Systems With Solenoid and Double D Pads. IEEE Trans. Industr. Electron. 69(4), 3527–3535 (2022) 5. Wang, Y., et al.: A misalignment-tolerant hybrid coupler for electric vehicle IPT charging systems. IEEE Transactions on Vehicular Technology. https://doi.org/10.1109/TVT.2023.327 7834, to be published 6. Li, H., Li, J., Wang, K., Chen, W., Yang, X.: A maximum efficiency point tracking control scheme for wireless power transfer systems using magnetic resonant coupling. IEEE Trans. Power Electron. 30(7), 3998–4008 (2015) 7. Li, H.Z., Zhu, C., Jiang, J., Song, K., Wei, G.: A 3-kW wireless power transfer system for sightseeing car supercapacitor charge. IEEE Trans. Power Electron. 32(5), 3301–3316 (2017) 8. Qu, X., Chu, H., Wong, S., Tse, C.K.: An IPT battery charger with near unity power factor and load-independent constant output combating design constraints of input voltage and transformer parameters. IEEE Trans. Power Electron. 34(8), 7719–7727 (2019) 9. Wang, Y., Liu, H., Yu, H., Wheeler, P., Zhou, Q., Zhao, S.: A hybrid battery wireless charger for self-adapting battery charging curve and anti-misalignment. IEEE J. Emerg. Select. Topi. Indu. Electron. 4(4), 1192–1203 (2023) 10. Wang, D., Qu, X., Yao, Y., Yang, P.: Hybrid inductive-power-transfer battery chargers for electric vehicle onboard charging with configurable charging profile. IEEE Trans. Intell. Transp. Syst. 22(1), 592–599 (2021) 11. Chen, Y., Yang, B., Kou, Z., He, Z., Cao, G., Mai, R.: Hybrid and reconfigurable IPT systems with high-misalignment tolerance for constant-current and constant-voltage battery charging. IEEE Trans. Power Electron. 33(10), 8259–8269 (2018) 12. Wang, Y., Liu, H., Wu, F., Wheeler, P., Zhou, Q., Zhao, S.: Research on a three-coil hybrid IPT charger with improved tolerance to coupling variation and load-independent output. IEEE J. Emerg. Select. Topi. Indu. Electron. 4(2), 625–636 (2023) 13. Zhang, Y., Shen, Z., Pan, W., Wang, H., Wu, Y., Mao, X.: Constant current and constant voltage charging of wireless power transfer system based on three-coil structure. IEEE Trans. Industr. Electron. 70(1), 1066–1070 (2023) 14. Zhang, Y., et al.: Misalignment-tolerant dual-transmitter electric vehicle wireless charging system with reconfigurable topologies. IEEE Trans. Power Electron. 37(8), 8816–8819 (2022) 15. Wang, Y., Liu, H., Yu, H., Wheeler, P., Wu, F.: An efficient soft-switching wireless battery charger with low-loss auxiliary circuit. IEEE Trans. Transportat. Electrifi. https://doi.org/10. 1109/TTE.2023.3295794, to be published. 16. Wang, X., Xu, J., Ma, H., Zhang, Y.: A reconstructed S-LCC topology with dual-type outputs for inductive power transfer systems. IEEE Trans. Power Electron. 35(12), 12606–12611 (2020) 17. Wang, Y., Liu, H., Wheeler, P., Wu, F.: Implementation and analysis of an efficient soft switching battery wireless charger with re-configurable rectifier. IEEE Trans. Indu. Electron. 71(5), 4640–4651 (2024)

A 6.78 MHz Class-E Amplifier Based Capacitive Power Transfer System with Approximate Constant Current Output Characteristic Zelin Chen, Dingyuan Tang, Zhiqiang Li, and Wei Zhou(B) School of Electrical Engineering, Southwest Jiaotong University, Chengdu, China {zelinchen,tdy,1064595677}@my.swjtu.edu.cn, [email protected]

Abstract. Increasing the operating frequency of capacitive power transfer (CPT) systems is conducive to reducing the system volume and the port voltage of the coupler. Class-E power amplifier (PA) is a typical circuit suitable for high-frequency inverter because of fewer components and higher reliability. However, Class-E amplifier is extremely sensitive to the load, and changes in load may cause the Class-E amplifier to lose its zero-voltage switching (ZVS) operation and withstand a current spike. In this paper, a 6.78 MHz Class-E amplifier based capacitive power transfer (CPT) system with approximate constant current (ACC) output characteristic is proposed. The model of the capacitive coupler is established and a series-parallel (SP) compensation network is selected. The influence of load resistance variation on the system operation is analyzed, and the ACC output and wide-range ZVS characteristics of the system is proved. A 145 W prototype is built and the experimental results verified the theoretical analysis. Keywords: Class-E amplifier · Capacitive power transfer · Approximate constant current · Load variation

1 Introduction The CPT technology, as one of wireless power transfer (WPT) technologies using the high-frequency electric field between metal plates as the transmission medium, has been more and more studied in recent years [1–4]. Compared with inductive power transfer (IPT) system, CPT system has many advantages, such as flexible and light coupler and small eddy current loss. CPT technology has been applied in consumer electronics, special power supply and electric vehicles (EV). However, in order to compensate the capacitive reactance of the coupler of CPT system, large compensation inductors are used, which seriously affect the overall size and weight of the system, making CPT technology difficult to be widely applied. Enhancing the operating frequency of CPT system can effectively solve this problem. The Class-E amplifier [5–8] is the simplest and most common circuit to realize high frequency inverter. Generally, the switch realizes both zero-voltage and zero-current turn-on at the optimal load. However, the soft-switching operation is sensitive to load variation. Although © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 95–105, 2024. https://doi.org/10.1007/978-981-97-0873-4_11

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feedback control is a potential solution to adjust the switching behavior at various loads, it requires a complex design for reliable operation [9, 10], which seriously affects the ZVS and ACC characteristics of the system circuit. Therefore, this paper proposes a 6.78 MHz Class-E amplifier based capacitive power transfer system with approximate constant current output characteristic. Models of the Class-E rectifier, coupler and compensation network are established. System characteristics are analyzed and ACC and wide-range ZVS are demonstrated.

2 System Modelling The overall structure of the system is shown in Fig. 1, which includes Class-E amplifier, four-plate capacitive coupler, series-parallel (SP) compensation network and full-bridge rectifier. The Class-E amplifier consists of two inductors L pd and L x , a shunt capacitor C q and a MOSFET Q. Two external capacitors C pe and C se are installed on the coupler and two compensating inductors L p and L s are connected in series and parallel at the primary and secondary sides successively. The imaginary part of the input impedance Z ac of 6.78 MHz full-bridge rectification is compensated by the inductor L sr . o pd x

1

p

2

q d

3

4

Fig. 1. Structure of the proposed system.

2.1 Analysis of Capacitive Coupler and Compensation Network d3

1

13

p

4

d2 d1

h

3 1

p

2

3 23

12

34 14

2

24

4

Fig. 2. Capacitive coupler. (a) Structure and (b) circuit.

As shown in Fig. 2 (a), the coupler consists of four plates P1-P4. All the coupling capacitances C 12 , C 13 , C14 , C 23 , C 24 and C 34 between any two plates are considered.

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Two external capacitances are also treated as a part of the coupler, and its equivalent circuit is shown in Fig. 2 (b). In Fig. 2(b), the capacitive coupler is a two-port network. According to the two-port network theory, the relationship between the port voltage and current can be expressed as:       1/jωCpH Km Up I = (1) · p H Is Us −Km jωCs where CpH and CsH represent the self-capacitance of the coupler, Km indicates the coupling gain, and ⎧

2 CpH = CpY , Km = CmY /CpY , CsH = CsY − CmY /CpY ⎪ ⎪ ⎪ ⎨ +C14 )·(C23 +C24 ) CpY = C12 + Cpe + (CC13 13 +C14 +C23 +C24 (2) +C (C 23 )·(C14 +C24 ) ⎪ CsY = C34 + Cse + C13 ⎪ 13 +C14 +C23 +C24 ⎪ ⎩ C13 C24 −C14 C23 CmY = C13 +C14 +C23 +C24 According to Eq. (2), its equivalent circuit is shown in Fig. 3(a).

1

p p

3

CpH

1

H s

C K mI p

K m Us

p

3

CpH

p

2

4

K mI p

CsH 4

2

Fig. 3. Coupler equivalent circuit (a). Equivalent circuit with Reflected Impedance Z ref (b).

p

CpH

p

p

CsH p

p

K mI p

K mI p

Fig. 4. (a) Combination of the equivalent circuit of the capacitive coupler, compensation network and the full-bridge rectifier. (b) Its simplified circuit.

Similar with the concept of reflected impedance widely used in inductive power transfer systems, the voltage-controlled voltage source at the primary side of the coupler can also be replaced by a reflected impedance Z ref in Fig. 3(b). When L p , CpH and L s , CsH are fully tuned in series and parallel as shown in Fig. 4(a), Z ref can be simplified as: Zref = Km2 (Zac + jωLs1 )

(3)

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2.2 Analysis of 6.78 MHz Full-Bridge Rectifier In order to analyze the input impedance Z ac of the high frequency rectifier as shown in Fig. 5, a circuit-model-based simulation is carried out in a widely-used RF software ADS [11, 12]. The rectifier is built with the model of the diode SCS304AM which comes from ROHM semiconductor, and the SCS304AM will be used in the final experimental system. In the simulation, the rectifier is excited by a constant AC current source I Zac at 1.9 A, and the DC load RL is varied from 10  to 150 . Figure 6 shows that the real and imaginary parts of the input impedance Z ac change accordingly when the load RL changes, where Zac = Rac + jXac Rac = real{Zac },Xac = imag{Zac }

6.78

1

2

(4)

o

d

3

4

Fig. 5. A 6.78 MHz full-bridge rectifier.

90 60 30 0 30 60 0

30

60

90

120

150

Fig. 6. Rectifier input impedance Z ac (Rac and X ac ) for different load RL .

At low frequency, Rac is almost linearly with RL , and X ac is negligible compared to Rac . At high frequency, the relationship between Rac and RL becomes more nonlinear. The main reason is the presence of the shunt capacitors in the diode model. At low frequency, the transient time of the shunt capacitor is much less than the switching period. When the diode is on, the input impedance can be treated as a resistor; when the diode is off, it can be treated as an open circuit due to the infinite diode reverse resistance.

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Therefore, the input impedance is almost purely resistive. But as the frequency increases, the transient time will be compatible with the switching period. This means that shunt capacitors behave more like AC components, introducing a non-negligible imaginary part to the rectifier’s input impedance [11]. 2.3 Analysis of Class-E Amplifier According to the analysis above, the proposed system can be simplified to the circuit shown in Fig. 7(a), where the inductance L pd is a choke coil. The role of L x is to provide a certain inductive reactance. Z ref is the reflected resistance. The Q is driven by a 6.78 MHz square wave. The voltage and current waveforms of important branches or components are shown in Fig. 7 (b).

u



pk



pk

0

0 

 0

0 pk

u pk

u

0

0 1

0

2

2

1

1

0

2

2

1

Fig. 7. Class-E Rectifier Circuit (a). Time-varying waveforms of voltage or current under ideal operating conditions for a Class-E amplifier (b). Time-varying waveform of voltage or current under non-ideal operating conditions within the designed load range(c).

Define θ = ω · t. As shown in Fig. 7 (b). The Q is turned on when the voltage across the parasitic capacitor is zero, the product of the Q voltage and current is always zero. By observing the waveforms, when θ is between −α1 and α2 , Q is turned on, so the conduction angle φon of Q can be expressed as: φon = α1 + α2

(5)

Define m=

Irf Idc

(6)

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From Fig. 7 (b), i(θ ) can be expressed as: i(θ ) =Irf cosθ + Idc → i(θ ) =Idc (1+mcosθ )

(7)

When θ = −α1 , i(θ ) equal to zero. The following formula can be obtained. 1+mcosα1 = 0 → cosα1 = −1/m

(8)

In one period, the average value of the current flowing through the Q is equal to the input current I dc , so 1 α2 · ∫ Idc (1 + m cos θ )dθ = Idc 2π −α1 Equation (10) can be obtained by Eq. (9). 

2π − α1 − α2 2π − φon − sinφon 2 m= = 1+ sinα1 + sinα2 1 − cosφon

(9)

(10)

When the Q is turned off, the voltage u(θ ) is the integral of the current on the capacitor C q , which is expressed as: u(θ ) =

∫θα Idc (1+m cos θ)dθ 2 ωCq

=

Idc ·[θ−α2 +m(sin θ−sin α2 )] ωCq

α2 < θ < −α1

(11)

use the Fourier formula to decompose u(θ ) orthogonally, and decompose it into two parts: active U c and reactive U s in Eq. (12). ⎧ 2π −α1 ⎪ ⎪ Uc = 1 · ∫ u(θ ) cos θ d θ → Uc = Idc · fc (α1 , α2 ) ⎨ π α2 (12) 2π −α1 ⎪ 1 ⎪ ⎩ Us = π · ∫ u(θ ) sin θ d θ → Us = Idc · fs (α1 , α2 ) α2

From Eq. (12), the reactive component of the voltage on Q can be cancelled by the inductance L x , and the active component will act on the reflected impedance, which is purely resistive when the secondary side is fully tuned (RL0 = Z ref ). From Eq. (3) and (4), Eq. (13) can be obtained.  RL0 = Km2 · Rac (13) ωLs1 + Xac = 0 Under ideal working conditions, the ideal load resistance RL0 and the ideal inductive reactance of L x can be calculated.  Uc RL0 = UIrfc = mI = fc (αm1 ,α2 ) dc (14) f (α Us 1 ,α2 ) XL = UIrfs = mI = s m → Lx = XωL dc

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The DC input power is equal to the load power consumption. Pdc = Udc Idc =

2 Irf2 m2 Idc · RL0 = · RL0 2 2

The input current I dc and the loop current I rf is calculated as:  dc Idc = m2U 2R L0 2Udc Irf = mRL0

(15)

(16)

the rectifier input current I Zac can be calculated as: IZac = Km · Irf

(17)

So far, the parameter design of the Class-E amplifier under ideal working conditions is completed. But when the load changes, the Class-E amplifier will no longer operate under ideal conditions. Suppose the load decreases from RL to Rac , Observing Fig. 6, the real part of the input impedance Z ac will decrease and the imaginary part will increase.  , where Suppose Z ac changes to Zac   = Rac + jXac Zac

From Eq. (3), the following Eq. (19) can be obtained:

 



  = Km2 Zac + jωLs1 = Km2 Rac + j Xac + ωLs1 Zref Define



RL0 = Km 2 · Rac 

 + ωL XL = j XL + Km2 Xac s1

(18)

(19)

(20)

According to Eq. (10) and (14), when RL0 and XL are known, α1 and α2 can be solved as equations about RL0 and XL .

   α1 = f1 RL0 , XL  (21) α2 = f2 RL0 , XL  and I  can also be solved From Eq. (10) and (21), m can be obtained. Further Idc rf  changes accordingly. m , I  , I  and φ  can be in Eq. (15). The conduction angle φon on dc rf expressed as: ⎧ 2π −α1 −α2 ⎪ ⎪ m = sinα  +sinα  ⎪ ⎪ 1 2 ⎪ ⎨ I  = 2U dc  dc m 2 RL0 (22) ⎪ I  = 2Udc ⎪   ⎪ rf m RL0 ⎪ ⎪  ⎩ φon = α1 + α2  can be calculated in Eq. (23). The rectifier input current IZac  = Km · Irf IZac

(23)

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3 Performance Analysis 3.1 Zero-Voltage Switching Characteristic When the Q turn off, the system circuit can be regarded as an RC first-order circuit. When the load is smaller than the ideal load, the time constant τ = RC will become small, the capacitor C q will discharge faster, and the voltage across the Q will drop to 0 in advance. In this case, the Q still satisfies ZVS. When the load is larger than the ideal load, the system circuit will no longer satisfy the ZVS, and the Q will have a serious current spike. According to the theoretical analysis in Section 2, the change of load will cause the change of α1 and α2 . From Fig. 7 (b) and (c), the voltage across the Q will drop to zero in advance, which is equivalent to α1 + α2 > φon , the system satisfies the ZVS. A system with the input voltage of 72 V and the input power of 145 W. As shown in Fig. 8, the rectifier input current I Zac is calculated.

2.0 1.5 1.0 0.5 0 0

15

30

45

60

75

90 105 120 135 150

Fig. 8. The rectifier input current I Zac .

Bring the value of I Zac into the RF software ADS circuit model for simulation, the output current I o can be obtained as shown in Fig. 9.

o

1.2

o

0.8 0.4 0

0

15

30

45

60

75

90 105 120 135 150

Fig. 9. The output current I o .

In total, the system satisfies ZVS and ACC characteristics within the designed load range.

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3.2 Experimental Analysis

Fig. 10. Experimental prototype of 6.78-MHz CPT system.

A 145 W experimental prototype was built as shown in Fig. 10. Figure 11(a) and (b) show the waveforms of the Q and I o when the load is reduced from 135  to 20  (Ideal load RL0 is 135 ), which proves that the system has always been ZVS. The efficiency curve and output current curve are shown in Fig. 12 when the load RL changes from 10  to 135 , which further verifies the ACC characteristic of the designed system. As the load increases, the efficiency also rises, and the efficiency get the highest point when the load is the optimal load. The highest efficiency is 87%.

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o

o

o o

o

o

o o

Fig. 11. Class-E rectifiers are at ZVS during load shedding (a) and (b)

80

1

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0.25

0

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o

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0 150

Fig. 12. The efficiency and output current curves when the load RL changes between 10  and 135 .

4 Conclusion This paper proposes a 6.78 MHz Class-E amplifier based capacitive power transfer system with approximate constant current output characteristic. Based on the two-port network theory, the coupler model is established, and a series-parallel (SP) compensation network is selected. The relationship between the port voltage and current of the two-port

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network is analyzed, and the current-controlled current is realized. At the same time, the Class-E amplifier model is established to analyze the effect of load resistance changes on system operation. Finally, a 145 W prototype was built, achieving an efficiency of 87%, verifying the ACC output and wide-range ZVS characteristics of the system. Acknowledgments. This work was supported in part by the National Natural Science Foundation of China under Grant 51907170, in part by Sichuan Science and Technology Program under Grant 2021YFH0039.

References 1. Liu, Y., Wu, T., Fu, M.: Interleaved capacitive coupler for wireless power transfer. IEEE Trans. Power Electron. 36(12), 13526–13535 (2021) 2. Lian, J., Qu, X.: Design of a double-sided LC compensated capacitive power transfer system with capacitor voltage stress optimization. IEEE Trans. Circ. Systems II: Exp. Brie. 67(4), 715–719 (2020) 3. Liu, Z., Su, Y.G., Zhao, Y.M., Hu, A.P., Dai, X.: Capacitive power transfer system with double T-type resonant network for mobile devices charging/supply. IEEE Trans. Power Electron. 37(2), 2394–2403 (2022) 4. Liu, M., Fu, M., Ma, C.: Parameter design for a 6.78-MHz wireless power transfer system based on analytical derivation of Class E current-driven rectifier. IEEE Trans. Power Electron. 31(6), 4280–4291 (2016) 5. Grebennikov, A.: High-Efficiency Class-E power amplifier with shunt capacitance and shunt filter. IEEE Trans. Circu. Systems I: Regu. Pape. 63(1), 12–22 (2016) 6. Du, J.C., Wang, Z.G., Xu, J., Yang, Y.F.: A current-injection Class-E power amplifier. IEEE Microw. Wirel. Compon. Lett. 30(8), 775–778 (2020) 7. Liu, S., Liu, M., Yang, S., Ma, C., Zhu, X.: A novel design methodology for high-efficiency current-mode and voltage-mode Class-E power amplifiers in wireless power transfer systems. IEEE Trans. Power Electron. 32(6), 4514–4523 (2017) 8. Afanasyev, P., Grebennikov, A., Farrell, R., Dooley, J.: Analysis and design of outphasing transmitter using Class-E power amplifiers with shunt capacitances and shunt filters. IEEE Access 8, 208879–208891 (2020) 9. Li, Y., Ruan, X., Zhang, L., Dai, J., Jin, Q.: Optimized parameters design and adaptive dutycycle adjustment for Class E DC–DC converter with on-off control. IEEE Trans. Power Electron. 34(8), 7728–7744 (2019) 10. Liu, M., Qiao, Y., Liu, S., Ma, C.: Analysis and design of a robust Class E2 DC–DC converter for megahertz wireless power transfer. IEEE trans. Power Electron. 32(4), 2835–2845 (2017) 11. Fu, M., Tang, Z., Liu, M., Ma, C., Zhu, X.: Full-bridge rectifier input reactance compensation in Megahertz wireless power transfer systems. In: 2015 IEEE PELS Workshop on Emerging Technologies: Wireless Power (2015 WoW) (2015) 12. Fu, M., Tang, Z., Ma, C.: Analysis and optimized design of compensation capacitors for a megahertz WPT system using full-bridge rectifier. IEEE Trans. Indus. Info. 15(1), 95–104 (2019)

Effects of T-Type/
-Type Resonant Networks on Harmonics of Inverter Currents in WPT Systems Chao Cui1,2

, Shumei Cui1,2 , Qianfan Zhang1,2 and Chunbo Zhu1,2(B)

, Ying Liu1,2 ,

1 School of Electrical Engineering and Automation, Harbin Institute of Technology,

Harbin 150006, China [email protected] 2 Zhengzhou Research Institute of Harbin Institute of Technology, Zhengzhou 450003, China

Abstract. For wireless power transfer (WPT) systems, T-type/-type compensation networks have the advantage of converting the voltage source input to a constant-current output. However, the higher order harmonics in the output current can reduce the power factor of the inverter as well as shift the zero-crossing point of the inverter current, which increases the switching losses of the inverter. This problem is especially prominent under light load conditions. The existing solution is to add extra series power filters. There is still a lack of solutions that utilize the harmonic suppression capability of the T-type/-type topology, even less the comparison of the harmonic suppression capability of various types of compensation. In this paper, the higher order harmonic suppression capability for the inverter current of different T-type/-type compensation networks are systematically analyzed. An evaluation method based on the ratio of harmonic and fundamental of current is proposed, and the mapping of the third harmonic content of the inverter current in different compensation networks is obtained by using the ratio of the input and output fundamental currents of the topology as the independent parameter. On this basis, selection guides of T-type/-type compensation networks in WPT systems are given. The related experiments verify the correctness of the analytical results. Keywords: Harmonics suppression · resonant networks · LCC compensation · wireless power transfer (WPT)

1 Introduction Compensation topologies are critical sections of the WPT system. The basic order compensation network are adopted to compensate the reactive component from the transformer and to improve the power factor of the inverter, while the higher-order compensation network is used to realize certain system characteristics. The T-type/-type compensation networks are preferred in WPT systems because of their ability to convert the voltage-source input to a constant-current output which is load independent. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 106–118, 2024. https://doi.org/10.1007/978-981-97-0873-4_12

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In addition to the ability of reactive power compensation, the compensation network of a WPT system has a filtering function. However, the filtering capability of the T/-type compensation to higher order harmonics is relatively weak, and a considerable amount of odd harmonics is included. This issue is especially serious under light load conditions [3–6], which will have an impact on the WPT system. First, the output power factor of inverters will be reduced, which consequently increases the system’s requirement for inverter capacity. Second, the zero crossing points of the inverter voltage and current are no longer coincide, even though their fundamental waves are in phase. The property of zero crossing point of the current lagging behind the voltage contributes to realize the ZVS of the inverter [1, 2]. However, too much phase lag leads to increased switching losses of the inverter, which subsequently reduces the system efficiency. Thirdly, the distortion of the current waveform also increases the difficulty of sampling and detecting, especially when the WPT operates at higher frequencies, and hence affects the control capability of the system. Despite these issues, the T-type/-type compensation is still irreplaceable because of its constant-current and load-independent characteristics. To address the harmonics issues, the approach of adding LC filters for LCC networks is proposed in literature [4, 6, 7]. In addition, utilizing coupled inductors instead of the traditional T-network is adopted in literature [5]. However, the results are still not satisfactory at light loads. Thus, there are still lots of questions that required to be addressed, for example, how does the compensation topology affect the harmonic characteristics of the system? How to find a compensation network with good harmonic suppression in the full frequency domain? In addition to the LCC topology mentioned above, are there other T/-type networks with excellent load characteristics that have better harmonic suppression? What is the best choice of compensation topology for different characteristics and loads? To address the above issues, the mechanism of harmonic suppression of compensating topologies is revealed in this paper. A general method to evaluate the harmonic suppression power of compensating topologies is studied and given. A novel method that can quickly, intuitively, and conveniently determine the harmonic suppression ability of a topology is proposed. On this basis, the T-type/-type compensation topologies will be studied and compared, and their advantages and disadvantages will be analyzed to provide the compensation scheme for the system’s optimal harmonic suppression as well as the precautions for application in various scenarios.

2 Harmonics of Inverter Currents in WPT Systems with T-type/
-type Networks In this paper, the WPT system shown in Fig. 1 is studied for example. Typical T-type/type compensation networks are selected as shown in Fig. 2. The system parameters are shown in Table 1. The T-LCL network is simulated as an example and its inverter current and harmonics are obtained as shown in Fig. 3. It can be seen that the inverter current contains odd harmonics. The waveform distortion is especially serious at lighter loads. The Bode plot of the ratio of inverter current to inverter voltage of the WPT system in the case of LC series (S-type), T-LCL and T-CLC networks is shown in Fig. 4. It can be

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Fig. 1. Schematic diagram of the structure of the WPT systems used in this paper.

Fig. 2. Typical T-type/-type compensation networks.

Table 1. WPT system parameters used in this paper Symbol

Parameter

Value

Symbol

Parameter

Value

Vs

DC-link voltage

100 V

Lr

Resonant inductance

6.9 uH 6.9 uH

f0

operating frequency

85 kHz

Cr

Resonant capacitance

506 nF

Lp

Transmitter coil inductance

48.4 uH

Lr-CMC

Transformer Self inductance of the M type system

23.0 uH 22.3 uH

Ls

Receiver coil inductance

47.9 uH

Cr-CMC

Resonant capacitance of the M type system

151 nF 156 nF

Cs

Receiver coil compensation capacitor

73 nF

MT-CMC

Transformer Mutual inductance of the M type system

7.0 uH

M

Coupling mechanism mutual inductance

28.4 uH

Cp-CLC

Transmitter coil compensation capacitor of the CLC topology

63 nF

RL

Load Resistance

72 

Cp-CMC

Transmitter coil compensation capacitor of the CMC topology

49 nF

seen that the ratio of the high-order harmonics to the fundamental of the output current of the T-type topology is greater than that of the S-type topology, which means that the T-type topology is not as good as the S-type in filtering the high-order harmonics, which leads to the harmonic problems.

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Fig. 3. Inverter output waveform and spectrum maps under T-type LCL network

Fig. 4. Bode plot of inverter current versus voltage on S-type and T-type resonant networks

3 The Third Harmonic Gain of the T/
Topologies 3.1 Theoretical Derivation Analytical calculations are performed for the four topologies shown in Fig. 2. On the basis of the KVL equation, the input and output current expressions for each topology of Fig. 2 are obtained by ignoring the internal resistance, as shown in Table 2. In the table, V in and I in are the input voltages and currents of the topology, V out and I out are the output voltages and currents, L, C, and M are the inductance, capacitance, and mutual inductance values of the resonant elements used in the topology, Z out is the equivalent load on the output side of the topology, ω0 is the resonance frequency of the topology, and ω is the actual frequency or the harmonic frequency of the voltage or current. The expressions in Table 2 are simplified for ease of comparison. The expressions simplified to about two independent variables k and n are shown in Table 3. where the order of the harmonics n = ωωn1 , and gn is the ratio of output impedance to inductive reactance at the nth-order harmonic frequency.   Zout_n  gn = , n = 1, 2, 3, · · · (1) |jωn Lr |

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where

 Lr =

M , In T - CMC topologies L, In T - LCL, T - CLC or  - LCL topologies

(2)

Table 2. Input and output current expressions for four WPT system T/ resonant topologies over the full frequency range

Based on the expressions for the input and output currents at resonant frequency for each topology in Table 2, it can be known that for the topologies in the Tables 2 and 3, the impedance ratio at resonant frequency     Zout_1  Iin_1   (3) g1 = = Iout_1  |jω1 Lr | which can also represent the ratio of the input current to the output current amplitude of the topologies at the fundamental frequency. Using the expressions in Table 3, it is possible to compare the relative gain or rejection capability of these four topologies for the nth harmonic. It may be assumed that the structure of the system is shown in Fig. 1, and the gain curves of the four topologies for inverting the third harmonic of the current are plotted according to the expressions of Table 3 as shown in Fig. 5. |Z | |I | = |I in_1 | in the graph represents both the The horizontal coordinate g1 = ωout_1 1L out_1 ratio of the inverter current to the coil current and the level of load carried by the inverter.

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Table 3. Harmonic current gain of four WPT systems with T/ resonant topologies

LCL T CLC

T LCL

T CMC,k 0.7

T CMC,k 0.3 Fig. 5. The gain ratio of third harmonic to fundamental for each topology, k is the coupling coefficient of T-CMC type resonant transformer

3.2 Analysis and Comparison of Harmonic Suppression of T/
Topologies Comparison of Characteristics. The following conclusions can be drawn from the expressions in Table 2 and Fig. 5: 1. For inverter currents, the T-CMC type topology using a loosely coupled transformer has better harmonic rejection, followed by the T-LCL, T-CLC, and -LCL type topologies in order. 2. The slopes of the curves for the T-CMC and the T-LCL topologies are similar, and it is possible to take g1 = 0.5, n = 3, to solve that when the coupling coefficient of

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the T-CMC type topology, k = 0.584, its gain curve is similar to that of the T-LCL, and at this time, the third harmonic suppression capability of these two topologies is basically the same. 3. In conclusion, the loosely coupled T-CMC type (coupling coefficient k < 0.584) is the optimal choice when only the third harmonic filtering performance is considered. The above conclusion on the high harmonic suppression of the T/-type topology is analyzed mechanistically as follows: First, The two topologies that are less effective in filtering: the T-CLC and the -LCL type, the reason why they are not as effective as the other two is because of their series capacitors, parallel inductors connection, which makes the series impedance decrease, the parallel impedance increase, and the total impedance is a tendency to decrease when the frequency is higher than the resonance point. That is, the capacitor’s resistance to through-crossing and the inductor’s resistance to through-crossing characteristics are reflected. Second, The excellent filtering effect of the T-CMC type topology is due to the fact that it can actually be equated to a T-CLC plus two LC filters in series, and therefore it can achieve better filtering with ostensibly the same number of components (Fig. 6).

C

C L

L

-XL

XL-M XM

XL-M -X L

XM-XL XL-XM

-XM

-XM

L-M X -X M L

XM

Fig. 6. Equivalence of T-CMC type topology

3.3 Cost Analysis of Different Topologies Compare the T-CMC and T-LCL models for the same gain ratio as follows. Capacitors. Since both the T-CMC and LCC topologies have two capacitors, the capacitors are not taken into account in the cost comparison. Inductors. Generally the size of a loosely coupled transformer is larger than the size of two inductors. What’s more, the T-LCL type topology can be turned into a typical LCC topology by combining it with a coil compensation capacitor to save a back-end inductor. Although some filtering performance is lost, the size and cost of an inductor are saved. The costs of inductors and transformers for the two topologies are compared only by the amount of cores and wires used (Fig. 7). T-LCC and T-CMC topologies satisfy the following relationship when the fundamental wave characteristics are consistent: ⎧ ⎨ LT −LCC = MT −CMC (4) M ⎩ LT −CMC = T −CMC kT

Effects of T-type/-type Resonant Networks T-LCL + Series Compensation

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LCC Compensation

Fig. 7. A T-LCL type topology can be changed to a typical LCC topology.

Among them, LT −LCL is the inductance of the resonant inductor in the T-LCL topology. LT −CMC and MT −CMC are the self-inductance and mutual inductance of the resonant mutual inductor in the T-CMC topology, respectively. kT is the coupling coefficient of the resonant mutual inductor. Since the inductance of an inductor as well as the self-inductance of a mutual inductor is proportional to the square of the number of turns. √ L ∝ N 2, N ∝ L (5) The core size of an inductor is affected by the saturation magnetic density. The magnetic density of an inductor is directly proportional to the number of turns and inversely proportional to the cross-sectional area of the core. B∝

N ·I N ·I ,S ∝ S Bm

(6)

Therefore, with the core shape unchanged, i.e., the length of the path is basically unchanged, the volume of the core is directly proportional to the number of turns of the inductor in order to maintain the inductor’s magnetic density without saturation. From this we believe that we can characterize the volume and price cost of inductors and transformers in terms of their number of turns. Iin_3,T −CMC T −CMC Then the inductor cost ratio Cost CostT −LCC and the third harmonic gain ratio Iin_3,T −LCC for the T-LCC and T-CMC topologies, with respect to the coupling factors of the mutual inductors of the T-CMC topology are shown in Fig. 8.

Fig. 8. Cost and harmonic gain ratio of T-LCC and T-CMC topologies versus coupling factor of the T-CMC topology

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For the T-CMC topology to achieve better performance than the T-LCC topology, its coupling factor needs to be less than 0.584, which means that its inductor cost is at least 2.6 times that of the T-LCC topology. From Fig. 8, it can be seen that a small k T for a T-CMC topology will result in a high cost, while a large k T will make the performance of the T-CMC topology have no advantage over that of the T-LCC topology. The T-CMC topology is more cost-effective in the range of the coupling factor, k T ∈ (0.3–0.5). In summary, if the system is more cost sensitive, the T-LCC (LCL) topology is a better choice, and if the system requires more harmonic suppression capability, the T-CMC topology with small coupling factor is recommended.

4 Simulation and Experimental Verification 4.1 Simulation Verification The correctness of the conclusions is verified by simulation below. The WPT system is constructed as shown in Figs. 1 and 2. T-CLC, T-LCL and T-CMC (k = 0.2) are chosen as the resistive third order resonant networks in the system respectively. The system parameters are shown in Table 1. When the load resistance RL is 72 , the current gain g1 = 0.85, which corresponds to the heavy load condition of the system. Then the waveforms of the inverter output current I in of the T-LCL topology and T-CMC topology systems are shown in Fig. 9.

(a) T-CLC type

(b) T-LCL type

(c) T-CMC type

Fig. 9. Inverter current for various topologies when the system is heavily loaded (g1 = 0.85)

When the load resistance RL is 720 , the current gain k = 0.085, which corresponds to the light load condition of the system. Then the inverter output current I in for the T-LCL topology and T-CMC topology systems are shown in Fig. 10. From Figs. 9 and 10, it can be seen that the high-order harmonics filtering capability of the T-CMC-type topology is stronger than that of the T-LCL, stronger than that of the T-CLC in both light-load and heavy-load conditions. The advantage of the T-CMC-type topology is especially obvious in light-load conditions. The correctness of the conclusion of Fig. 5 is proved.

Effects of T-type/-type Resonant Networks

(a) T-CLC type

(b) T-LCL type

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(c) T-CMC type

Fig. 10. Inverter current for various topologies at light load (g1 = 0.085)

4.2 Experimental Verification The experimental platform of the system is shown in Fig. 11. The circuit topology of the experimental system is shown in Figs. 1 and 2. The parameters of the components in the system are shown in Table 1.

Fig. 11. Experimental system

When the load RL = 72 , the system is under heavy load and the output voltagecurrent of each topology inverter are shown in Fig. 12. Referring to the dynamic wireless charging application of electric vehicles, simulate the working conditions before or after the receiving side of the vehicle directly faces the transmitting side. The load of the receiving side is removed so that the system is in a light load state. The output voltage and current waveforms of each topology inverter are shown in Fig. 13. The T-CMC topology performs best, followed by the T-LCL topology, and this advantage is especially significant at no-load conditions. In addition, the measured inverter efficiencies of each topology system are shown in Fig. 14, which shows that the T-CMC topology improves the inverter efficiency due to its strong harmonic suppression. At heavy load, the inverter efficiency is improved by 2.6% compared to the inverter efficiency with the T-LCL topology. At no load, the

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Fig. 12. Experimental waveforms of inverter voltage and current under heavy loads.

Fig. 13. Experimental waveforms of inverter voltage and current under light loads.

Inverter Efficiency(%)

advantage of the T-CMC topology efficiency is even more pronounced and the inverter efficiency is improved by 7.3% compared to the T-LCL topology.

Fig. 14. Inverter efficiency for different topology systems

5 Conclusion In this paper, the suppression capability of load-independent T-type/-type compensation networks with constant-current characteristics, which are widely used in wireless energy transmission systems, on the higher order harmonics of inverter currents is investigated. The main conclusions are as follows: (1) An evaluation method of harmonic suppression capability based on the relationship between a certain harmonic content of the inverter current and the ratio of the inputoutput fundamental current of the T/-type topology is proposed, which can quickly and conveniently determine the harmonic suppression capability of the topology. The gain derivation and design methods are given. A theoretical tool is provided for analyzing, comparing, and selecting various compensation topologies.

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(2) The harmonic suppression capabilities of various topologies are discussed. The results indicate that the harmonic suppression capabilities of the loosely coupled T-CMC topology, the T-LCL topology, the strongly coupled-T-CMC topology, the T-CLC topology, and the -LCL topology are reduced in order, and increased with the increase of the ratio of the topology’s input-to-output fundamental currents. This means that the harmonics are less easily suppressed at light loads. (3) It is pointed out that the loosely coupled T-CMC type topology has the best harmonic suppression capability, and the loosely coupled T-CMC topology is recommended to be used when harmonic suppression power is required by the system. Especially when there are higher requirements for light loads. However, due to the cost disadvantage of the T-CMC type topology, the T-LCL type topology and his variant LCC topology are recommended when the system is cost sensitive. Simulations and experiments demonstrate the advantages of the loosely coupled T-CMC type topology. Simulation results show that the loosely coupled T-CMC topology has 10% lower harmonics at full load and 85% lower harmonics at no load than T-LCL. Experiments show that the efficiency of the T-CMC topology inverter with a coupling factor of 0.3 increases from 93.3% in the T-LCL topology to 95.9% in the loaded state. In no-load state, this enhancement is from 85.7% to 93%. It is clear that the loosely coupled T-CMC topology has excellent harmonic suppression and can significantly improve the inverter efficiency, which provides a new idea for the design optimization of WPT systems.

References 1. Liu, Y., Gao, F., Liu, H., Li, H.: Harmonic analysis and ZVS implementation in doubleside LCC WPT system. In: 2021 IEEE Sustainable Power and Energy Conference (iSPEC), pp. 3619–3624 (2021) 2. Wang, X., Xu, J., Mao, M., Ma, H.: An LCL-based SS compensated WPT converter with wide ZVS range and integrated coil structure. IEEE Trans. Industr. Electron. 68(6), 4882–4893 (2021) 3. Feng, H., Zhang, X., Cai, T., Duan, S., Zhao, J.: Optimization of LCL resonant inverter in inductive power transfer systems based on high-order harmonics analysis. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 1301–1305 (2015) 4. Huang, T., Tan, L., Wang, R., Li, C., Li, H., Huang, X.: Research on suppression of higher harmonics in wireless power transmission system. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 228–232 (2020) 5. Dai, X. et al.: Improved LCL resonant network for Inductive Power Transfer system. In: 2015 IEEE PELS Workshop on Emerging Technologies: Wireless Power (WoW), pp. 1–5 (2015) 6. Xia, C., Chen, R., Liu, Y., Liu, L., Chen, G.: Inhibition of current harmonics in LCL/LCC wireless power transfer system. In: 2017 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 1–6 (2017) 7. Xia, C., Chen, R., Liu, Y., Chen, G., Wu, X.: LCL/LCC resonant topology of WPT system for constant current, stable frequency and high-quality power transmission. In: 2016 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 110–113 (2016) 8. Namadmalan, A., Alonso, J.M., Iqbal, A.: Accurate fundamental harmonic modeling of inductive power transfer battery chargers. IEEE Trans. Transport. Electrific. 8(1), 627–635 (2022)

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9. Zhang, W., Mi, C.C.: Compensation topologies of high-power wireless power transfer systems. IEEE Trans. Veh. Technol. 65(6), 4768–4778 (2016) 10. Yao, Y., Wang, Y., Liu, X., Xu, D.: Analysis, design, and optimization of LC/S compensation topology with excellent load-independent voltage output for inductive power transfer. IEEE Trans. Transp. Electrific. 4(3), 767–777 (2018) 11. Wang, Y., Dongye, Z., Kheirollahi, R., Zhang, H., Zheng, S., Lu, F.: Review of loadindependent constant-current and constant-voltage topologies for domino-type multiple-load inductive power relay system. IEEE J. Emerg. Sel. Top. Ind. Electron. 3(2), 199–210 (2022)

The Fault-Tolerant Multi-coil WPT System with Coil Parameter Consistency Jiantao Zhang1,2 , Zhan Gao1,2 , Jianyu Lan3 , Shuai Wang4 , Fuze Chen1,2 , Hao Dong1,2 , and Chunbo Zhu1,2(B) 1 School of Electrical Engineering and Automation, Harbin Institute of Technology,

Harbin 150001, China [email protected] 2 Harbin Institute of Technology, Zhengzhou Research Institute, Zhengzhou 450003, China 3 hanghai Institute of Space Power-Sources, State Key Laboratory of Power-Sources Technology, Shanghai 200200, China 4 College of Safety Science and Engineering, Liaoning Technical University, Fuxin 123000, Liaoning, China

Abstract. Wireless Power Transfer (WPT) solves the friction problem of contact slip rings by its non-contacting characteristics. If WPT is to be applied in spacecraft, the WPT system must be designed for fault tolerance and redundancy to improve the stability and reliability of the system. Currently, fault-tolerant designs in WPT systems focus on anti-offset ability. This paper designs the high-reliability WPT system with redundancy, proposes the fault-tolerant control method for the disconnection fault of the transmitting coil, a parameter-consistent multi-coil magnetic coupling mechanism, and a multi-coil circuit decoupling method based on compensation capacitors are proposed for the effect of coupling between multiple coils. The parametric consistency of the novel coils and the decoupling process of multiple coils are experimentally verified. Keywords: Wireless Power Transfer (WPT) · Slip Ring · Magnetic Coupling Mechanism · Redundancy · Fault Tolerant

1 Introduction Nowadays, energy for both space satellites and space stations is mainly transmitted by satellite solar wings via contact slip rings. Under microgravity conditions in space, the suspension of metal particles generated by friction between contacts in contact slip rings can cause short-circuit accidents in the device, which can seriously cause damage to the device and affect the reliability and life of the entire spacecraft. With its non-contact, safe, and reliable characteristics, wireless power transmission technology can fundamentally solve the many problems caused by contact slip ring friction. Due to the particular application environment of spacecraft, once a failure occurs, it will generate a lot of human and material losses. Traditional slip rings usually use the cascade method of multiple outputs to improve the system’s reliability. If you © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 119–127, 2024. https://doi.org/10.1007/978-981-97-0873-4_13

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want to apply wireless power transmission technology in spacecraft, you must carry out a fault-tolerant design for the system. Current fault-tolerant designs in wireless power transmission technologies focus on anti-offset ability. Southwest Jiaotong University proposes a structure in which two transmitter coils are connected in reverse series, and the mutual inductance difference of the two coils to the receiving coil is the equivalent mutual inductance, and the offset adaptability is improved by keeping the mutual inductance difference unchanged in the offset situation [1]. KyungHee University in South Korea proposes a dynamic adaptive WPT system that can achieve a center offset of 35 mm and a rotational offset of 60°, under which the system continues to work [2]. Northwestern Polytechnical University proposes a magnetic coupling mechanism with a perpendicular flux direction of two receivers. The relative constant total mutual inductance and decoupling characteristics in the case of rotation offset are ensured [3]. The Dalian University of Technology proposes a new type of multi-coil array magnetic coupling mechanism with six transmitter coils uniformly distributed in a circular array, which significantly improves the system’s resistance to deflection under rotational operation, and the system can continuously supply power to 5 W loads [4]. Harbin Institute of Technology proposes a multi-coil WPT system, which realizes long-distance power transmission through a multi-coil structure, and the coil realizes zero voltage between layers through double-layer segmented compensation [5]. In research on non-contact slip rings, the University of Auckland develops a multiphase non-contact slip ring that can transmit 1000 W over a distance of 3 mm [6]. Fraunhofer Institute for Integrated Systems and Device Technology in Germany proposed a non-contact slip ring with a transmission power of 20 W at a transmission distance of 1 mm with a system efficiency of 89.7% [7]. Shanghai Jiao Tong University proposes a magnetic coupling mechanism with a spiral tube coil, with a U-shaped core and symmetrical arrangement, which can realize a system efficiency of 80% at an output of 165 W [8]. Harbin Institute of Technology proposes a redundancy WPT system based on the position of coil arrangement, which can be derated when coil failure occurs [9, 10]. More research needs to be done on the fault tolerance and redundancy characteristics of wireless power transmission technologies for aerospace slip rings. In this paper, a fault-tolerant multi-coil WPT system is demonstrated. In Sect. 2, the influence of mutual coupling between multiple coils is analyzed, and the decoupling condition and fault-tolerant control method of multiple coil circuits are proposed. In Sect. 3, a new magnetic coupling mechanism with redundancy and high reliability is designed. In Sect. 4, the theoretical analysis was verified by experiments.

2 Fault-Tolerant WPT Systems Figure 1 Illustrates a multi-coil WPT system with redundancy characteristics, where the power collected by the satellite solar wing is transmitted to the inverter. The AC power output from the inverter is transmitted through the transmitting coil and resonant circuit to the receiving coil and resonant circuit. It is supplied to the battery load through the rectifier circuit. The transmitting coil has three parallel coils, and the receiving coil is one.

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Fig. 1. Schematic diagram of fault-tolerant multi-coil WPT system

1 1 1

1 1

2 2 1 3 2 3 3

3

Fig. 2. Multi-coil WPT system

Based on Fig. 2, the Kirchhoff equation can be presented in eq. (1). ⎧ 1 ⎪ ⎪ U˙ 1 = I˙ P1(jωLP1 + + RP1 ) + I˙P2 jωMP1P2 + I˙P3 jωMP1P3 + I˙S jωMP1S ⎪ ⎪ jωC ⎪ P1 ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎪ ⎨ U˙ 1 = I˙ P1jωMP1P2 + I˙P2 (jωLP2 + jωC + RP2 ) + I˙P3 jωMP2P3 + I˙S jωMP2S P2 1 ⎪ ˙ ⎪ ⎪ U = I˙ P1jωMP1P3 + I˙P2 jωMP2P3 + I˙P3 (jωLP3 + + RP3 ) + I˙S jωMP3S ⎪ ⎪ 1 jωC ⎪ P3 ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎩ U˙ 2 = I˙ P1jωMP1S + I˙P2 jωMP2S + I˙P3 jωMP3S + I˙S (jωLS + + RS ) jωCS (1) where, L P1 , L P2 , L P3 for the three transmitter coil self-inductance, L S for the receiver coil self-inductance, M P1S , M P2S , M P3S for the mutual inductance of the transmitter coil and receiver coils, M P1P2 , M P1P3 , M P2P3 for the mutual inductance of the three transmitter coils, C P1 , C P2 , C P3 for the three transmitter coil compensation capacitors, C S for the receiver coil compensation capacitance, RP1 , RP2 , RP3 for the internal resistance of the transmitter coils, RS for the internal resistance of the receiver coils, I P1 , I P2 , I P3 for the current of the transmitter coil, I S for the current of the receiver coil. Equating the load to the front end of a rectifier circuit: ⎧ ⎨R = 8 R e L π2 (2) ⎩ U2 = IS Re The receiver side resonance condition is: jωLS +

1 =0 jωCS

(3)

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Substituting into Eq. (1) gives: I˙ P1jωMP1S + I˙P2 jωMP2S + I˙P3 jωMP3S = −I˙S (Re + RS )

(4)

When the three transmitting coils have parameter consistency: M1S = M2S = M3S = MS LP1 = LP2 = LP3 = LP M12 = M13 = M23 = MP RP1 = RP2 = RP3 = RP 1 IP1 = IP2 = IP3 = IP 3

(5)

Then Eq. (1) reduces to: U1 = IP1 (jωLP1 +

1 (ωMS )2 + RP1 + + jωMP1P2 + jωMP1P3 ) jωCP1 Re + RS

U1 = IP2 (jωLP2 +

1 (ωMS )2 + RP2 + + jωMP1P2 + jωMP2P3 ) jωCP2 Re + RS

U1 = IP3 (jωLP3 +

1 (ωMS )2 + RP3 + + jωMP1P3 + jωMP2P3 ) jωCP3 Re + RS

(6)

From Eq. (6), it can be seen that the resonant capacitance of the three transmitter coils eliminates the coupling effect of the other coils on the same side. Part of the capacitance is used to compensate for the self-inductance of the respective coils. The other part is used to compensate for the other two coils on the coupling of this coil, thus realizing the decoupling between the three transmitter coils on the circuit. ⎧ 1 ⎪ CP1 = 2 ⎪ ⎪ ⎪ ω (LP1 + MP1P2 + MP1P3 ) ⎪ ⎪ ⎨ 1 CP2 = 2 (7) ⎪ ω (LP2 + MP1P2 + MP2P3 ) ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎩ CP3 = ω2 (LP3 + MP1P3 + MP2P3 ) When one of the transmitter coils has a circuit breakage fault, the system can continue to work by switching the compensation capacitors of the other two coils because the three coils are connected in parallel. At this time, the compensation capacitor only needs to compensate for its self-inductance and the mutual inductance of the remaining coil. Similarly, when two of the coils are disconnected, switch the compensation capacitor of the remaining coil. At this time, the compensation capacitor only compensates for its selfinductance.The system’s fault-tolerant control of disconnection faults of the transmitter coil is realized by the redundancy design of the transmitter coil.

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3 Magnetic Coupling Mechanism To consistently parameterize the three transmitter coils. A conventional stacked multicoil magnetic coupling mechanism model is shown in Fig. 3(a). The three transmitting coils are the same, stacked up and down sequentially and coaxially distributed with the receiving coils. The parallel-wound multi-coil magnetic coupling mechanism model is shown in Fig. 3(b). The three transmitter coils are wound in the same plane, which ensures that all three coils are the same distance from the core and reduces the variability of the parameters of the three coils. The upper and lower cores are disc-shaped, and the material is ferrite. Receiver Core

Receiver Core

Receiver Coil Receiver Coil

oil 1

Transmitter Coil

oil 2 oil 3

Transmitter Core

Coil 1

Transmitter Coil Coil 1

Coil 2

Coil 2

Coil 3

Coil 3

Transmitter Core

(a) Superimposed Coils (b) parallel-wound (c) Staggered Archimedes coil Fig. 3. Multi-coil magnetic coupling mechanism

The structure of the transmitting coil is shown in Fig. 3(c). To realize the parameter consistency of the transmitting coil. This paper proposes a staggered Archimedes coil structure. The three coils are designed based on the Archimedes curve. All three coils are the same length, spatially separated by 120°, and wound in alternating order. The three coupling structures differ only in design, and the other main parameters are consistent, as shown in Table 1. This paper selects the multi-stranded Leeds wire with a strand diameter of 0.05 mm to reduce the coil’s skin effect and proximity effect under high frequency. Table 1. Parameter of the magnetic coupling mechanism Parameter

Value

Coil Diameter

200 mm

Coil Wire Diameter

3.6 mm/4.8 mm

Core Length/Thickness

200 mm/5 mm

Transmission distance

200 mm

Transmitting coil turns/layers

14/2

Receiving Coil Turns/Layers

48/3

The simulation results of the three coupling mechanisms are shown in Table 2, the physical parameters of the three coupling mechanisms are consistent, and the electrical

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parameters are somewhat different due to different structures. The staggered coil proposed in this paper not only solves the problem of the coil distance from the core and the secondary coil distance, but also makes the length of the three coils precisely the same. Table 2. Coil Simulation Results Parameter

Superimposed Coils (µH)

Parallel-wound coils (µH)

Staggered Coil (µH)

L P1

58.56

27.07

31.27

L P2

52.63

24.34

31.31

L P3

46.61

22.68

31.41

LS

352.73

359.46

353.84

M P1S

5.23

4.07

4.84

M P2S

5.29

3.7

4.84

M P3S

5.39

3.34

4.85

M P1P2

52.63

24.34

29.43

M P1P3

46.61

22.68

29.48

M P2P3

47.86

21.86

29.49

4 Experimental Verification The experimental diagram, shown in Fig. 4, uses electronic loads instead of batteries.

Fig. 4. Prototype of the proposed WPT system

The transmission distance of the magnetic coupling mechanism is 200 mm, and the coil diameter and core diameter are both 200 mm, which realizes the pitch-to-diameter ratio of the magnetic coupling mechanism to be one. The resonant frequency of the

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Table 3. System Circuit Parameters Parameter

Value

Parameter

Value

Parameter

Value

L P1 L P2

25.45 µH

C P1

8.87 nF

M P1P2

22.926 µH

25.109 µH

C P2

8.9 nF

M P1P3

23.05 µH

L P3

25.196 µH

C P3

8.88 nF

M P2P3

23.095 µH

LS

325.91 µH

C S1

6.12 nF

M P1S

4.612 µH

U in

200 V

C S2

6.7 nF

M P2S

4.608 µH

f

200 kHz

C S3

6.19 nF

M P3S

4.56 µH

resonant circuit is the same as the switching frequency of the inverter circuit, and the rest of the circuit parameters are shown in Table 3. The current and voltage waveforms of the three transmitter coil branches are shown in Fig. 5, and the voltages of the three coil branches are the inverter output voltages, which can be seen in the figure that the three current phases are slightly lagging behind the voltage phase. There are slight differences in the magnitude and phase of the three currents, mainly due to subtle differences in the parameters of the three transmitting coil loops caused by differences in the physical coil windings and the length of the terminals. U

Fig. 5. Voltage and current waveforms of the three transmitter coils

Fig. 6. 5kW Experimental Results

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The inverter voltage and current waveforms are shown in Fig. 6. It can be seen that the current phase is slightly lagging behind the voltage phase, which realizes the decoupling between the three transmitter coils and makes the system work in the ZVS mode. The experimental results when the system works at full power are shown in Fig. 8. When the system is working at full power, the system efficiency is 88%, the inverter efficiency is 98.8%, the transmission efficiency of the magnetic coupling mechanism and the resonant circuit is 92.6%, and the rectifier circuit efficiency is 96.1%.

5 Conclusion A multi-coil circuit decoupling condition based on the consistency of coil parameters and a fault-tolerant control method for transmitter coil breakage faults are proposed, a redundant “staggered Archimedes” coil is designed, and the parameter differences of three different structures of coils are compared. An experimental prototype was built, and the parameter consistency of the three transmitter coils was verified. The coupling effect between the three transmitting coils was successfully solved using the multi-coil circuit decoupling method. The system can realize the maximum power output of 5kW with 92% transmission efficiency. Acknowledgment. This work was supported in part by the National Natural Science Foundation of China under Project 52107002. And Civil Space Technology Advance Research Program of China.

References 1. Chen, Y., Mai, R., Zhang, Y., He, Z.: Improving misalignment tolerance for IPT system using a third-coil. IEEE Trans. Power Electron. 34(4), 3009–3013 (2019) 2. Thuc, P.D., Lee, J.: A dynamically adaptable impedance-matching system for midrange wireless power transfer with misalignment. Energies 8(8), 7593–7617 (2015) 3. Yan, Z., Song, B., Zhang, Y.: A rotation-free wireless power transfer system with stable output power and efficiency for autonomous underwater vehicles. IEEE Trans. Power Electron. 34(5), 4005–4008 (2018) 4. Li, T., Chen, X., Lang, Z., Jin, X., Qi, C., Wang, Y.: Wireless power transfer system for long-term sensor on rotating plane. In: 2021 IEEE Industrial Electronics and Applications Conference (IEACon), pp. 136–140 (2021) 5. Gu, P., et al.: A 2.5 m long-range IPT system based on domino cylindrical solenoid coupler compensated respectively in layers. IEEE Trans. Ind. Electron. 70(2), 1409–1420 (2023) 6. Abdolkhani, A.: A contactless slipring system based on axially traveling magnetic field. IEEE J. Emerg. Sel. Topics Power Electron. 3(1), 280–287 (2015) 7. Ditze, S., Endruschat, A., Schriefer, T., Rosskopf, A., Heckel, T.: Inductive power transfer system with a rotary transformer for contactless energy transfer on rotating applications. In: 2016 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1622–1625 (2016) 8. Feng, X., Fu, Z., Hao, G., Wang, K., Weng, Y.: Modeling and implementation of a new non-contact slip ring for wireless power transfer. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference, pp. 106–111 (2020)

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9. Wang, D., Cui, S., Bie, Z., Zhang, J., Song, K., Zhu, C.: A redundancy design of wireless power transfer system for satellite slip ring with high reliability. In: 2021 IEEE 4th International Electrical and Energy Conference (CIEEC), pp. 1–6 (2021) 10. Miwa, K., Kaneda, J., Kikuma, N., Hirayama, H., Sakakibara, K.: Consideration of use of arrayed transmitting coils in wireless power transfer with magnetically coupled resonance. In: 2012 International Symposium on Antennas and Propagation (ISAP), pp. 451–454 (2012)

Comparison of Distributed Coil Connections for Medium and High Distance-to-Diameter Ratio IPT Systems Fuze Chen1,3 , Guo Wei1,3 , Long Jia2 , Gang Li2 , De’an Wang1,3 , Zhan Gao1,3 , Jiantao Zhang1,3(B) , and Chunbo Zhu1,3 1 School of Electrical Engineering and Automation, Harbin Institute of Technology,

Harbin 150001, China [email protected] 2 Beijing Aerospace Automatic Control Institute, Beijing 100854, China 3 Zhengzhou Research Institute of Harbin Institute of Technology, Zhengzhou 450003, China

Abstract. Large voltage stresses exist on the coupling pads and compensation capacitors in the medium to high distance-to-diameter ratio induction power transmission applications at more significant power levels. The existing solution uses distributed compensation to reduce the voltage stresses on the system components. Most studies have connected the distributed coils in series and have yet to analyze the various connections in detail. However, different ways of connecting distributed compensation coils will result in different output power, output efficiency, and current stresses in each branch within the system. This paper will analyze the characteristics of each of the four distributed coil connections for the S-S compensation topology. It will also discuss the most suitable distributed coil connections for the medium to high distance-to-diameter ratio conditions in wireless power transmission application scenarios at more significant power levels. Keywords: Induction Power Transfer (IPT) · medium to high DDR · distributed compensation · connections

1 Introduction Wireless power transfer (WPT) has gained much attention in the past decades as a flexible way to charge electronic devices. IPT is one of the most commonly used WPT methods in which the transmitter and receiver coils are inductively coupled close to each other [1]. IPT has the advantages of isolation, safety, and convenience and has promising applications in electric vehicles [2], industrial IoT, and implantable medicine [3]. However, IPT has the disadvantage that the coupling coefficient becomes significantly smaller when the two coils are relatively far away, i.e., when the DDR is relatively high. This dramatically affects the output power and efficiency. There are many schemes to solve this problem. Literature [4] has constructed a low reluctance loop and utilizes magnetic materials to wrap the coupling pads to reduce the magnetic circuit reluctance. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 128–135, 2024. https://doi.org/10.1007/978-981-97-0873-4_14

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However, this solution is not compatible with the flexible power supply of WPT. Another solution is to increase the system frequency [5]. This enables power transfer with less mutual inductance, but there is an increase in losses. Also, the smaller size makes the system heat dissipation a severe problem, so such systems generally operate under a low power level. Other solutions contain the use of relay coils [6]. Domino coils [7] belong to this category, and this solution can significantly increase the DDR of the coil transmission, but the usage scenarios are limited. An easy solution is to increase the mutual inductance value by increasing the number of turns in the winding. But transmitting higher power will make the voltage stress on the individual coils unacceptable. Therefore, a segmented compensation is needed to reduce the coil voltage stress [8]. One of the most widely used connections is to connect all distributed coils in series with the corresponding compensation capacitors [9]. But other connections may have better performance[10]. In this paper, the equivalent electrical parameters of the four distributed coil connections are derived in Sect. 2. Section 3 analyzes and compares the characteristics of the four connection methods under the scenario of transmitting enormous power with a medium to high DDR. Section 4 uses a simulation example to validate the theoretical analysis in Sects. 2 and 3. Section 5 summarizes the whole paper and draws conclusions.

2 Equivalence of Distributed Compensation Coils for Four Connection Methods This paper will use an S-S compensation topology with two distributed coils in each transmitter and receiver pad for computational simplicity. Then the four coils will be connected in different ways. The characteristics of each connection will be discussed. To facilitate the comparison of the four distributed compensation coils, the four circuits with different connections will be equated to the circuit shown in Fig. 1.

u

u

Fig. 1. Equivalent circuit schematic

2.1 Primary and Secondary Distributed Coils Connected in Series (S-S/PSSS) The schematic diagram of the primary and secondary distributed coil series connection circuit is shown in Fig. 2. The following is a description of the symbols in Fig. 2. M P1P2 and M S1S2 is the mutual inductance between the two coils at the transmitting and receiving side; M P1S1 , M P1S2 , M P2S1 , and M P2S2 are the mutual inductance between the distributed coil at the transmitting and receiving side; L P1 , L P2 and L S1 , L S2 are the self-inductance of the

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u

Fig. 2. Schematic diagram of series connection circuit of primary and secondary distributed coils

distributed coil at the transmitting and receiving side. C P1 , C P2 and C S1 , C S2 are the compensation capacitances of the distributed coil at the transmitting and receiving side. RP1 and RP2 are the sums of the internal resistances of the transmitter distributed coil and the corresponding compensation capacitors; RS1 and RS2 are the sums of the internal resistances of the receiver distributed coil and the related compensation capacitors. Based on Fig. 2, the Kirchhoff equation can be presented in (1). 

U1



0

 =

ZP1 + ZP2 iω(MP1S1 + MP1S2 + MP2S1 + MP2S2 ) ZS1 + ZS2 + Req iω(MP1S1 + MP1S2 + MP2S1 + MP2S2 )



I1P I1S



(1)

1 1 where ZPi = iωC + iωLPi + iωMP1P2 , ZSi = iωC + iωLSi + iωMS1S2 , i = 1,2. Pi Si Considering the matched-resonant capacitor in complete resonance with the distributed coil, i.e., satisfying the following Eq. (2). Based on Eq. (2), we can obtain the Eq. (3).

ZP1 = ZP2 = ZS1 = ZS2 = 0 I1P =

Req U1 ω2 (MP1S1 + MP1S2 + MP2S1 + MP2S2 )2

, I1S = −

iU1 ω(MP1S1 + MP1S2 + MP2S1 + MP2S2 )

(2) (3)

Based on Eq. (3), we can find the equivalent mutual inductance of this topology, the system output power and the system efficiency. In the high-power usage scenario, distributed compensation reduces the voltage stress on the coil and the compensation capacitor. Therefore, the distributed coils should be kept as consistent as possible so that the voltage on the distributed coils is as uniform as possible and there is no breakdown problem due to high voltage stress. Therefore the analysis can be considered to satisfy the following conditions as Eq. (4). RP1 ≈ RP2 , RS1 ≈ RS2 , MP1S1 ≈ MP1S2 ≈ MP2S1 ≈ MP2S2 = Mi

(4)

Substituting into Eq. (4) and simplifying gives: MS - S/PSSSeq ≈ 4M1 , PS - S/PSSSout ≈

Req U12 16ω2 M1

, ηS - S/PSSS ≈

8ω2 M12 Req   R2eq RP1 + 8ω2 M12 Req + 2RS1

(5)

2.2 Primary Distributed Coils in Parallel with the Secondary Distributed Coils in Series (S-S/PPSS) The circuit diagram of the primary distributed coil in parallel with the secondary distributed coil in series is shown in Fig. 3.

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Based on Fig. 3, the Kirchhoff equation, as in Eq. (6), can be presented: ⎤ ⎡ ⎤⎡ I ⎤ U1 2P1 ZP1 + RP1 iωMP1P2 iω(MP1S1 + MP1S2 ) ⎥ ⎢ ⎥ ⎣ ⎢ iωMP1P2 ZP2 + RP2 iω(MP2S1 + MP2S2 ) ⎦⎣ I2P2 ⎦ ⎣ U1 ⎦ = iω(MP1S1 + MP1S2 ) iω(MP2S1 + MP2S2 ) ZS1 + ZS2 + Req 0 IS (6) ⎡

where ZPi =

1 iωCPi

+ iωLPi , ZSi =

1 iωCSi

+ iωLSi + iωMS1S2 , i = 1,2.

u

Fig. 3. Circuit diagram of the primary distributed coil in parallel with the secondary distributed coil in series

Consider a matched-resonant capacitor in complete resonance with the distributed coil. The parameters of the two distributed coils on the primary side are close enough to be considered as I2P1 ≈ I2P2 . Substitute into Eq. (4) and simplify, we can get: MS - S/PPSSeq ≈ ηS - S/PPSS

2Req U1 a+b = 2M2 , I2P ≈ 2 Req RP1 + 8ω2 M22

8ω2 M22 Req 4iωM2 U1   , I2S ≈ − ≈ 2 2 2 Req RP1 + 8ω M2 Req + 2RS1 Req RP1 + 8ω2 M22

(7)

2.3 Primary-Side Distributed Coils in Series and Secondary-Side Distributed Coils in Parallel (S-S/PSSP) The circuit diagram of the primary-side distributed coil in series and the secondary-side distributed coil in parallel is shown in Fig. 4.

Fig. 4. Circuit diagram of the primary-side distributed coil in series and secondary-side distributed coil in parallel

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Based on Fig. 4, the Kirchhoff equation, as in Eq. (8), can be presented: ⎤ ⎡ ⎤⎡ I ⎤ U1 3P ZP1 + ZP2 iω(MP1S1 + MP2S1 ) iω(MP1S2 + MP2S2 ) ⎥ ⎢ ⎢ ⎥ ⎣ iωMS1S2 + Req ⎦⎣ I3S1 ⎦ ⎣ 0 ⎦ = iω(MP1S1 + MP2S1 ) ZS1 + Req + RS1 iω(MP1S2 + MP2S2 ) iωMS1S2 + Req ZS2 + Req + RS1 0 I3S2 (8) ⎡

1 1 + iωLPi + iωMP1P2 , ZSi = iωC + iωLSi , i = 1,2. where ZPi = iωC Pi Si Consider a matched-resonant capacitor in complete resonance with the distributed coil. The parameters of the two distributed coils on the secondary side are close enough to be considered as I3S1 ≈ I3S2 . Substitute into Eq. (4) and simplify, we can obtain:

MS - S/PSSPeq ≈

8ω2 M32 Req a2 + b2

= 2M3 , ηS - S/PSSP ≈   2 2Req + RS1 2Req RP1 + RP1 RS1 + 4ω2 M32   2Req + RS1 U1 iU1 I3P ≈ , I3S ≈ 2ωM3 8ω2 M 2

(9)

3

2.4 Parallel Connection of the Primary-Side Distributed Coils with the Secondary-Side Distributed Coils (S-S/PPSP) The circuit diagram of the parallel connection of the primary-side distributed coils with the secondary-side distributed coils is shown in Fig. 5. Based on Fig. 5, the Kirchhoff equation, as in Eq. (10). ⎡ ⎤ ⎡ ⎤⎡ I4P1 ⎤ U1 iωMP1S2 ZP1 + RP1 iωMP1S1 iωMP1S1 ⎢U ⎥ ⎢ ⎥⎢ I4P2 ⎥ iωMP2S2 ⎥ ⎢ 1 ⎥ ⎢ iωMP1S1 ZP2 + RP2 iωMP2S1 ⎥⎢ ⎥ ⎢ ⎢ ⎥=⎣ ⎦ iωMP1S1 iωMP2S1 ZS1 + RS1 + Req iωMS1S2 + Req ⎣ I4S1 ⎦ ⎣0 ⎦ iωMP1S2 iωMP2S2 iωMS1S2 + Req ZS2 + RS2 + Req 0 I 4S2

(10) where ZPi =

1 iωCPi

+ iωLPi , ZSi =

1 iωCSi

+ iωLSi , i = 1,2.

Fig. 5. Circuit diagram of parallel connection of the primary-side distributed coils with the secondary-side distributed coils

Consider a matched-resonant capacitor in complete resonance with the distributed coil. The parameters of the two distributed coils on the primary and secondary sides are

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close to each other, which can be considered as I4P1 ≈ I4P2 , I4S1 ≈ I4S2 . By substituting into the simplified conditional Eq. (4), we can figure out Eq. (11).   2 2Req + RS1 U1 4iωM4 U1 I4P ≈ , I4S ≈ − 2 2 2Req RP1 + RP1 RS1 + 4M4 ω 2Req RP1 + RP1 RS1 + 4M42 ω2 (11) 8M42 Req ω2   MS - S/PPSPeq ≈ M4 , ηS - S/PPSP ≈  2Req + RS1 2Req RP1 + RP1 RS1 + 4M42 ω2

3 Connections for More Significant Power Levels and Medium to High DDR Scenarios In the comparison, the morphology and the number of turns of the primary and secondary coupling pads do not change significantly, i.e. MP1S1 ≈ MP1S2 ≈ MP2S1 ≈ MP2S2 , RP1 ≈ RP2 , and RS1 ≈ RS2 these conditions still hold while MP1P2 and MS1S2 remain unchanged. In the comparison, the distance of the coupling pads with different connections changes, i.e. MP1S1 ≈ MP1S2 ≈ MP2S1 ≈ MP2S2 = Mi , the mutual inductance between the four coils of M i changes. To achieve the same output power, the following conditions need to be satisfied: MS - S/PSSSeq = MS - S/PPSSeq = MS - S/PSSPeq = MS - S/PPSPeq

(12)

Combined with the above Equation, we can figure out: 4M1 = 2M2 = 2M3 = M4

(13)

The comparison results show that the required value of M 1 is the smallest. Therefore, for the S-S compensation topology, the connection of both the primary and secondary distributed coils in series can achieve the maximum DDR at the specified power.      2 2 Req > −2RP1 RS1 + RP1 RS1 RP1 RS1 + 36M2 ω /(3RP1 ) (14) Comparing the efficiency at the same output power while varying the output power by changing the load. Substituting M 2 = 2M 1 into η S-S/PSSS and η S-S/PPSS yields η S-S/PPSS > η S-S/PSSS . There also exists M 4 = 2M 3 , substituting it into η S-S/PSSP and η S-S/PPSP yields η S-S/PPSP > η S-S/PSSP . When inequality eq. (14) holds, there is η S-S/PPSS > η S-S/PSSP .

4 Simulation Verification In the following, a simulation example will be presented to verify the theoretical analysis presented above. Considering the application scenario of the medium to high DDR wireless power transmission for high power levels, we will design a wireless power transmission system with a DDR of 1 and an output power of 3 kW. The input voltage is set to 200 V, and the load resistance is set to 10 . The size of the coupling pads is set to be within 300 mm × 300 mm. We want to achieve a transmission distance of 300 mm. Through simple calculation, the number of turns of the primary and secondary side coils is set at 15 turns per layer, and the primary and secondary side coupling pads are both two layers. Each layer is an independent distributed coil.

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A plot of the system’s mutual inductance parameters corresponding to the transmission distance calculated by Maxwell is shown in Fig. 6.(a). S-S/PSSS S-S/PSSP

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Fig. 6. (a) Plot of mutual inductance parameters corresponding to the transmission distance (b) Curves of output power variation with transmission distance for different connections (c) Plot of efficiency versus equivalent load for specified conditions

Combined with Fig. 6(a), we can get the transmission distances corresponding to various connections to achieve the requested condition. The structure with primary-side distributed coils connected in series and secondary-side distributed coils connected in series is able to achieve the maximum distance-to-diameter ratio at the required power. The output power curves of different connection methods with the transmission distance are discussed as the distance changes, as shown in Fig. 6(b). In the S-S compensation topology, the topology with primary and secondary distributed coils connected in series has the smoothest output power with the least fluctuation in transmission distance. The output power is minimized for the same transmission distance. Figure 6(c) shows the calculation example, which can be seen in using the same transmitting pad and receiving pad to output the same power conditions, connecting to the same load. The primary-side and secondary-side of the distributed coil in series connection has the lowest system efficiency. The primary-side and secondary-side in parallel connection has the highest system efficiency. In the same input voltage and output power, the current flowing through the circuit trunk is basically the same. The parallel connection can be shunted, so the current flowing through the parallel branch circuit is about half of the series branch circuit current. Therefore, using the parallel connection method has higher system efficiency.

5 Conclusion In this paper, we derive the equivalent electrical parameters of the four distributed coil connections and then discuss the characteristics of the four connections using the S-S compensation topology for scenarios with medium to high distance-to-diameter ratios. The topology where both primary and secondary distributed coils are connected in parallel maintains high system efficiency. Still, due to the low equivalent mutual inductance, the output power fluctuates wildly, which is unsuitable for medium to high DDR application scenarios. The topology in which both primary and secondary distributed coils are connected in series can achieve the maximum DDR at the required power. The output

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power is minimized at the same transmission distance. The output power fluctuation is minimized with the change in transmission distance. Although there is the problem of low system efficiency, it is still relatively the most suitable for the application scenario of medium to high DDR and enormous output power. Acknowledgment. This work was supported in part by the National Natural Science Foundation of China under Project 52107002. And Civil Space Technology Advance Research Program of China.

References 1. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019) 2. Mahesh, A., Chokkalingam, B., et al.: Inductive wireless power transfer charging for electric vehicles–a review. IEEE Access 9, 137667–137713 (2021) 3. Kim, H.-J., Hirayama, H., et al.: Review of near-field wireless power and communication for biomedical applications. IEEE Access 5, 21264–21285 (2017) 4. X Tech, https://www.xjishu.com/zhuanli/60/202110163443.html 5. Li, Z., Lu, R., Zhu, C., et al.: Research on performance optimization of long-distance lowpower wireless power transmission system. Trans. China Electrotech. Soci. 30(S1), 209–214 (2015). (in Chinese) 6. Saha, C., Anya, I., Alexandru, C., Jinks, R.: Wireless power transfer using relay resonators. Appl. Phys. Lett. 112(26), 263902 (2018) 7. Gu, P., et al.: A 2.5 m long-range ipt system based on domino cylindrical solenoid coupler compensated respectively in layers. IEEE Trans. Ind. Electron. 70(2), 1409–1420 (2023) 8. Kim, J.H., et al.: Development of 1-MW inductive power transfer system for a high-speed train. IEEE Trans. Ind. Electron. 62(10), 6242–6250 (2015) 9. Mai, J., et al.: A multi-segment compensation method for improving power density of longdistance IPT system. IEEE Trans. Ind. Electron. 69(12), 12795–12806 (2022) 10. Zhou, M., Liu, F., Li, S., et al.: A 1-kW and 100-cm distance magnetically coupled resonant WPT system achieving 80% efficiency. IEEE Trans. Transport. Electrific. 8(3), 4001–4013 (2022)

Vertical Self-coupling Plates Design for Capacitive Power Transfer System Jiantao Zhang1,2 , Shunyu Yao1,2 , Shuai Wang3 , Liangyi Pan1 , Ying Liu1(B) , and Chunbo Zhu1 1 School of Electric Engineering and Automation, Harbin Institute of Technology,

Harbin 150001, China {jiantaoz,zhuchunbo}@hit.edu.cn, [email protected] 2 Harbin Institute of Technology, Zhengzhou Research Institute, Zhengzhou 450003, China 3 Fushun China Coal Technology Engineering Testing Center Co., Ltd., Fushun 113122, China

Abstract. Capacitive power transfer (CPT) technology has become a research hotspot of wireless power transfer technology by the advantages of its low cost, lightweight, and no eddy current loss. In CPT systems, the port capacitance in parallel with the coupling capacitance contributes significantly to the reduction of system component voltage stresses and system inductance volume. However, the existing coupling mechanism suffers from small equivalent port capacitance values, low utilization of the coupling area of the port capacitance to the plate, and inability to be adjusted accurately, which constrains the development of CPT systems. In this paper, a vertical self-coupling mechanism is proposed, which improves the utilization of port capacitance to the coupling plate. Without external capacitors, it can generate a larger port capacitance by relying on its own structure and has a certain degree of adjustability, which provides a new solution to improve the value of port capacitance, and thus reduce the value of the system inductance and the voltage stress on the components. Keywords: coupling mechanism · port capacitance · voltage stress · adjustability

1 Introduction With the development of the electric power industry, the conventional contact power transfer method relying on wires has shown its drawbacks in many fields. Therefore, it is crucial for the further development of the electric power industry to vigorously develop wireless power transfer technology so that electric power can be realized through noncontact transfer. A few common types of wireless power transfer are inductive power transfer (IPT) [1], capacitive power transfer (CPT) [2], microwave power transfer (MPT) [3], and optical power transfer (OPT) [4]. Among them, capacitive power transfer has a greater development prospect due to the advantages of high transfer efficiency, the easy-to-change shape of the coupling mechanism, and the low price of the coupling mechanism.

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 136–144, 2024. https://doi.org/10.1007/978-981-97-0873-4_15

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In a CPT system, the port capacitance is connected in parallel with the coupling capacitance port. The increase of port capacitance value can effectively reduce the resonant inductance value of the system and the voltage stress of the system components, thus reducing the system’s cost and weight and improving the system’s safety. To increase the system port capacitance value, the parallel capacitance scheme is used in [5], although this scheme effectively increases the port capacitance value, the capacitor’s voltage withstand value is limited, and it is easy to be broken by excessive voltage when the power rises, thus failing to meet the demand of high-power scenarios. A vertical coupling mechanism was proposed in [6], which does not require external capacitors and can generate a large port capacitance only by the coupling mechanism itself. However, this structure has low utilization of the plates and poor adjustability of the capacitance value, which still has much room for improvement. This paper introduces the calculation of port capacitance in Sect. 2, the defects of existing coupling mechanisms in enhancing the value of port capacitance in Sect. 3, and proposes a vertical self-coupling coupling mechanism in Sect. 4, which generates a large port capacitance without the need of external capacitors and has a certain degree of adjustability. In Sect. 5, the performance of the proposed vertical self-coupling mechanism is compared with the conventional vertical coupling mechanism through simulation to verify the superior performance of the proposed vertical self-coupling mechanism.

2 Introduction to Port Capacitance in Coupling Mechanisms In the existing CPT system, the coupling mechanism can be roughly divided into parallel and vertical coupling mechanisms. The coupling mechanism is often composed of four plates, which can be divided into two groups, one of which plays the role of power transfer, and the other group plays the role of power return [7]. The four plates’ mutual coupling, a total of six coupling capacitances can be generated, the schematic diagram is shown in Fig. 1.

1

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1 12 2

23 14 13

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14

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23 3

34

4

4

34

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(a)

(b)

Fig. 1. Six-capacitance coupling model of the CPT system(a) Parallel type, (b) Vertical type

The six-capacitance model in the form of a two-port network of these six capacitances is shown in Fig. 2(a). The six-capacitance model has a complex structure, which is not easy to carry out the analysis and can be decoupled according to the method in [4], which simplifies the six-capacitance model into a π-type network model containing only three equivalent capacitances [7], As shown in Fig. 2(b). Where each parameter of the π-type

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network is calculated as shown in Eq. (1). ⎧ (C13 +C14 )(C23 +C24 ) ⎪ ⎪ C1 =C12 + − CM ⎪ ⎪ C13 +C14 +C23 +C24 ⎪ ⎪ ⎨ (C13 +C23 )(C14 +C24 ) C2 =C34 + − CM ⎪ C13 +C14 +C23 +C24 ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ CM = C24 C13 −C14 C23 C13 +C14 +C23 +C24

1

12

(1)

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14 24

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23 3

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(a)

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(b)

Fig. 2. Equivalent model of the coupling mechanism (a) Six-capacitance model, (b) π-network model

Among the three equivalent capacitances which form the π-type network, C M is the power transfer capacitance and C 1 and C 2 are connected in parallel with the port, which are the port capacitances. The port capacitances C 1 and C 2 play an important role in improving the performance of the CPT system. Taking the double-sided LCL-type resonance compensation network as an example, as the port capacitances increase, the system’s resonant inductors value and component voltage stress will decrease [8, 9].

3 Defects of Conventional Vertical Coupling Mechanism In the conventional parallel coupling mechanism, the opposite area between the plates on the same side is small and the distance is far, resulting in a small value of the coupled self-capacitance C 12 and C 34 , which results in a small value of the port capacitance C 1 and C 2 in the equivalent π-network model [10]. In the vertical coupling mechanism, the distance between the pole plates on the same side is closer and the coupling area is larger, so the values of its self-capacitance C 12 and C 34 are larger, which in turn makes the port capacitance C 1 and C 2 have larger values, and the system’s demand for the port capacitance can be satisfied even if there are no external compensation capacitors [6, 9, 11]. The schematic diagram of the vertical coupling mechanism is shown in Fig. 3(a), where the power transfer distance refers to the distance between the plates P2–P4. However, the coupling pole plates of the vertical coupling mechanism intersect with each other, making its coupling capacitance to the coupling pole plate utilization rate decline, and difficult to accurately adjust the value of its port capacitance. For the purpose of analysis, the vertical coupling mechanism is divided into five parts according to the different positions, as shown in Fig. 3(b).

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(b)

Fig. 3. Vertical coupling mechanism schematic diagram (a) Three-dimensional view of the structure, (b) Schematic diagrams of the partitions of the vertical coupling mechanism

4 Vertical Type Self-coupling Mechanism Structure In order to overcome the defects of the conventional vertical coupling mechanism, structural improvement can be made to form a vertical type self-coupling mechanism. For P1 , it is split into two parts, P1a and P1b , which remain electrically connected. The two parts of P1 in area 1 and areas 3 and 4 are disassembled, and the area of P1 in area 1 is slightly reduced to form “P1a ” in the self-coupling mechanism; similarly, the same operation is applied to P3 to form “P3a ” in the self-coupling mechanism. The portion of P1 in regions 3 and 4 is shifted downward, kept level with P2 , and the area of the portion close to region 1 is slightly removed to form P1b . Similarly, the portion of P3 in regions 3 and 4 is shifted upward, kept level with P4 , and the area of the portion close to region 2 is slightly removed to form P3b . At this time, the distance between P1a and P3b has been minimized to be the distance between the plates P2-P4 distance, which is the vertical coupling mechanism power transfer distance. P2 and P4 remain unchanged, thereby forming a vertical type self-coupling structure, as shown in Fig. 4. In operation, the vertical type self-coupling coupling mechanism is electrically maintained between P1a and P1b , and similarly, P3a and P3b are electrically maintained between them.

1a

2

1

3 4 3a

(a)

(b)

Fig. 4. Schematic diagram of vertical self-coupling mechanism (a) Schematic diagram, (b) Circuit connection diagram in operation

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5 Simulation Verification In order to verify the performance of the vertical type self-coupling plates, a simulation model is built in Maxwell for verification. As shown in Fig. 5. Among them, the model schematic of the vertical type coupling mechanism is shown in Fig. 5 (a)–(c), and the definition and values of each parameter are shown in Table 1. Table 1. Definition and values of the parameters of the vertical coupling mechanism Parameters

Definition

Values (mm)

L1

P1 , P3 length and width

100

L2

P2 , P4 length and width

40

H1

distance between P1 and P3

30

H2

distance between P2 and P4

20

H3

distance between P1 and P2 (P3 and P4 )

(a)

5

(b)

(c) 1

1a

1

2 1

4

4 3

4

1a

3a

4

3a

2

3

3a

2

1 2

3

3

2

2

1a

3

3

(d)

(e)

(f)

Fig. 5. Schematic diagram of Maxwell simulation model and its parameters (a) Vertical mechanism three-dimensional view, (b) Vertical mechanism main view, (c) Vertical mechanism top view, (d) Self-coupling mechanism three-dimensional view, (e) Self-coupling mechanism main view, (f) Self-coupling mechanism top view

The model schematic of the vertical type self-coupling mechanism is shown in Fig. 5 (d)–(f), and the definition and values of each parameter are shown in Table 2.

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Table 2. Definition and values of the parameters of the self-coupling mechanism Parameters

Definition

Values (mm)

L1

P1b , P3b length width of the outer ring

100

L2

P2 , P4 length and width

L3

distance between P1b (P3b ) inner ring and P2 (P4 )

L4

P1a , P3a length and width

30

H1

distance between P1a and P3a distance between P2 (P1b ) and P4 (P3b )

30

H2 H3

40 5

20

distance between P1a and P1b (P2 ) distance between P3a and P3b (P4 )

5

5.1 Verification of Coupled Plates Area Utilization To verify the advantage of the vertical type self-coupling plates in the utilization of plates area, the coupling capacitance values of the two coupling mechanisms were derived by simulation through Maxwell. The coupling capacitance values per unit area (in pF/mm2 ) for the two structures are shown in Fig. 6.

1.931 10

2.095 10 4

4

1.5×10-4

2.0×10-4

1.931 10 (

2.150 10 4 (

4

1.5×10-4

8.5%

-4

11.3% -4

1.0×10

1.0×10

5.0×10-5 0.0

C oupl i ng capaci tance val ue per uni t ar ea-C 2

C oupl i ng capaci tance val ue per uni t ar ea-C 1

2.5×10

2.5×10-4 2.0×10-4

-4

5.0×10-5

Vertical-coupling mechanism

(a)

Self-coupling mechanism

0.0

Vertical-coupling mechanism

(b)

Self-coupling mechanism

C oupl i ng capaci tance val ue per uni t ar ea-C M

vr-M cate g lin p u o C

C catevrg lin p u o 2

C vr-1 cate g lin p u o

2.5×10-5 2.0×10-5

2.180 10 5 (

10 5 1.974 (

1.5×10-5

10.4%

1.0×10-5 5.0×10-6 0.0

Vertical-coupling mechanism

Self-coupling mechanism

(c)

Fig. 6. Comparison of coupling capacitance values per unit area for two structures (a) C 1 , (b) C 2 , (c)C M

According to Fig. 6, the coupling capacitance values per unit area of the three equivalent coupling capacitances of the vertical type self-coupling mechanism are improved compared with the conventional vertical type coupling mechanism. It means that the vertical type self-coupling plates have a higher plate area utilization and can produce a larger equivalent coupling capacitance with the same plate area, and conversely, a smaller plate area is required under the condition of producing the same equivalent coupling capacitance.

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5.2 Adjustability Validation To verify the advantages of the vertical type self-coupling plates in terms of adjustability, the two coupling mechanisms were adjusted based on Fig. 5, as shown in Fig. 7, respectively. 6

6

0 4

0 4

4 0

4 0 6

6

(a)

(b)

Fig. 7. Verification of adjustability of two coupling mechanisms (a) Vertical coupling mechanism, (b) Self-coupling mechanism

Self-coupling mechanism V er tical-coupling mechanism

16.0 12.8 9.6 6.4 3.2 -4

-2

0

2

Offset V alue

(a)

4

6

19.2

Self-coupling mechanism V er tical-coupling mechanism

16.0

C apacitance Offset V alue C M (pF )

19.2

C apacitance Offset V alue C 2(pF )

C apacitance Offset V alue C 1(pF )

In Fig. 7(a), for the vertical type coupling mechanism, along the vertical direction, P1 and P3 are dynamically adjusted, in which P1 is adjusted from 4 mm (−4) down to 6 mm (+6) up, and P3 is adjusted from 4 mm (−4) up to 6 mm (+6) down. In Fig. 7(b), for the vertical type self-coupling mechanism, P1a and P3a are dynamically adjusted along the vertical direction, in which P1a is adjusted from 4mm (−4) downward to 6mm (+6) upward, and P3 is adjusted from 4mm (−4) on upward to 6mm (+6) on downward. During the movement of the pole plate, the three capacitances of the equivalent π-type network change as shown in Fig. 8.

12.8 9.6 6.4 3.2 -4

-2

0

2

Offset V alue(mm)

(b)

4

6

M ax=0.438 M ax=0.494

0.50 0.48 0.46 0.44

Self-coupling mechanism V er tical-coupling mechanism

0.42 0.40

-4

-2

0

2

4

6

Offset V alue(mm)

(c)

Fig. 8. Variation of equivalent capacitance of π-type network (a) Amplitude of C 1 variation, (b) Amplitude of C 2 variation, (c) Amplitude of C M variation

From Fig. 8(a), (b), it can be seen that the port capacitances C 1 and C 2 change significantly with the movement of the plates, which proves that both structures can significantly change the value of the self-capacitance by adjusting the distance between the plates. However, from Fig. 8(c), during the process of changing the port capacitance, the power transfer capacitance C M of the vertical coupling mechanism produces a large offset, with a maximum offset value of 0.083pF and a maximum offset rate of 20.11%. This makes it impossible to accurately regulate the self-capacitance, that is, to adjust

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the port capacitance, because the other capacitances of the system also produce more obvious changes. In the self-coupling mechanism, with the movement of the pole plate, the maximum offset value of the power transfer capacitance C M is only 0.004pF, which is approximated to be 1/21 of the vertical structure, and the maximum offset rate is only 0.96%, which is also approximated to be 1/21 of the vertical structure, which indicates that when the self-capacitance is being adjusted, other capacitances of the system are almost unchanged. The precise adjustment of self-capacitance and the port capacitance can be realized, and the coupling mechanism is adjustable.

6 Conclusions In this paper, for the problem of improving the port capacitance of the CPT system, firstly, the composition and calculation method of the port capacitance value are introduced, and then, the important role of port capacitance is presented as an example of a doublesided LCL-type resonance compensation network. To deal with the shortcomings of the existing coupling mechanism in improving the capacitance value of the system port, a vertical type self-coupling mechanism is proposed, which has a higher plate utilization as well as adjustability, and uses simulation to validate it. Under the simulation parameters set in this paper, the plate utilization of the vertical type self-coupling mechanism is improved by 10% compared with the conventional vertical type coupling mechanism, and the stability of the power transfer capacitance of the vertical type self-coupling mechanism is improved by 20 times compared with that of the conventional vertical type coupling mechanism in the process of adjusting the distance of the plates to adjust the port capacitance. Acknowledgments. This work was supported in part by the National Natural Science Foundation of China under Project 52107002. And Civil Space Technology Advance Research Program of China.

References 1. Vishnuram, P., Panchanathan, S., Rajamanickam, N., Krishnasamy, V., Bajaj, M., Piecha, M.: Blaze SS charging system: magnetic materials, coil configurations, challenges, and future perspectives. Energies 16(10), 4020 (2023) 2. Regensburger, B., Sinha, S., Kumar, A., Afridi, K.K.: A 3.75-KW high-power-transferdensity capacitive wireless charging system for EVS utilizing Toro Idal-interleaved-foil coupled inductors. In: 2020 IEEE Transportation Electrification Conference & Expo (ITEC), pp. 839–843. IEEE, Chicago, IL, USA (2020) 3. Eteng, A.A., Goh, H.H., Rahim, S.K.A., Alomainy, A.: A review of metasurfaces for microwave energy transmission and harvesting in wireless powered networks. IEEE Access 9, 27518–27539 (2021) 4. Mohsan, S.A.H., Qian, H., Amjad, H.: A comprehensive review of optical wireless power transfer technology. Front. Inform. Technol. Electron. Eng. 24(6), 767–800 (2023) 5. Lian, J., Qu, X.: Design of a double-sided LC compensated capacitive power transfer system with capacitor voltage stress optimization. IEEE Trans. Circuits Syst. II 67(4), 715–719 (2020)

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6. Vu, V.-B., Dahidah, M., Pickert, V., Phan, V.-T.: An improved LCL-L compensation topology for capacitive power transfer in electric vehicle charging. IEEE Access 8, 27757–27768 (2020) 7. Lecluyse, C., Minnaert, B., Kleemann, M.: A review of the current state of technology of capacitive wireless power transfer. Energies 14(18), 5862 (2021) 8. Zhang, H., Lu, F., Hofmann, H., Liu, W., Mi, C.C.: Six-plate capacitive coupler to reduce electric field emission in large air-gap capacitive power transfer. IEEE Trans. Power Electron. 33(1), 665–675 (2018) 9. Zhang, H., Lu, F., Hofmann, H., Liu, W., Mi, C.: A 4-plate compact capacitive coupler design and LCL-compensated topology for capacitive power transfer in electric vehicle charging applications. IEEE Trans. Power Electron. 31(12), 8541–8551 (2016) 10. Lu, F., Zhang, H., Hofmann, H., Mi, C.C.: A double-sided LC-compensation circuit for loosely coupled capacitive power transfer. IEEE Trans. Power Electron. 33(2), 1633–1643 (2018) 11. Zhang, J., Yao, S., Pan, L., Liu, Y., Zhu, C.: A review of capacitive power transfer technology for electric vehicle applications. Electronics 12(16), 3534 (2023)

Design of Wireless Power Transfer System for Mobile Devices Based on Class E Amplifier Qiang Zhou1 and Ruikun Mai2(B) 1 Mingyang Smart Energy Group Co., Ltd., Zhongshan 528400, China 2 Southwest Jiaotong University, Chengdu 611756, China

[email protected]

Abstract. This paper addresses the dynamic impact of pickup relocation or removal on the topological configuration of the Electric field Coupled Power Transfer (ECPT) system, potentially leading to adverse transistor effects and operational anomalies. The study analyzes the ECPT system’s core characteristics using the class E amplifier model, investigating the causes behind transistor current and voltage surges triggered by pickup detachment. A parameter design strategy is then proposed to achieve wide-load zero-voltage switching (ZVS) operation while maintaining a fixed operating frequency. To sustain ECPT system functionality in a post-pickup removal standby mode, a novel power regulation technique integrated into the DC/DC converter is presented. Through simulations and experiments, the feasibility and effectiveness of the proposed methods are verified. Keywords: Wireless power transfer(WPT) · Electric field coupled · Class E aplifier · Parameter design · ZVS

1 Introduction Wireless Power Transfer (WPT) is a technology that utilizes soft media such as magnetic fields, electric fields, lasers, microwaves, and ultrasound to transmit energy between the power supply and the load without any physical connection. Magnetic-field Coupled Wireless Power Transfer (MC-WPT) and Electric field Coupled Power Transfer (ECPT), as two main wireless power transfer technologies [1, 2], have the advantages of convenience, flexibility, safety, and reliability. This technology has attracted great attention in the field of the power electronics, and has become a hot research direction of many enterprises, universities and scientific research institutions at home and abroad [3–5]. The power transmission system based on electric field coupled has the advantages of simple structure and light weight; Under working conditions, it has very little electromagnetic interference to the surrounding environment; The high-frequency electric field does not generate eddy current losses in the surrounding metal devices, and the system also has good anti-offset properties [6]. Based on the above characteristics of ECPT technology, electric field coupled wireless power transmission technology has been preliminarily applied in the fields of consumer electronic devices, special power supplies, and electric vehicles [7–10], reflecting certain advantages. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 145–157, 2024. https://doi.org/10.1007/978-981-97-0873-4_16

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In the practical application of ECPT technology, the pickup of the movable load devices often needs to be removed or relocation from the wireless power supply system, such as mobile phones, mobile robots, household appliances and electric vehicles. The load switched changes the topology of the ECPT system, causing a wide range of changes in the system load and resulting in significant changes in the operating characteristics of the ECPT system. Usually causing severe current and voltage surges, it is easy to damage the transistor and resonant network components. At the same time, the high input power of the system after the pickup is removed, and the system cannot enter the standby state, resulting in power waste. In view of the shortcomings of the existing ECPT system in the wireless power supply for mobile devices, this paper analyzes the causes of transistor current and voltage surges caused by the removal of the pickup, and uses the characteristics that the equivalent circuit form of the system is basically the same before and after the load is removed, a parameter design method is proposed to enable the system to achieve ZVS operation over a wide load range at a fixed operating frequency. To achieve the operation of the ECPT system in standby mode after the pickup is removed, a power regulation method integrated into the DC/DC converter is presented. Simulation and experimental results have verified the feasibility of the method.

2 ECPT System Based on Class E Amplifier 2.1 Principle of Class E Amplifier The circuit topology of the classic class E power amplifier is shown in Fig. 1. The circuit consists of a DC power supply Edc , a MOS transistor S, a choke inductor Lf , a bypass capacitor C1 , a resonant inductor L, a resonant capacitor C, and a load resistor R.

Lf

L iS

II

Edc

S

iC1 uS

C

i C1

R

Fig. 1. Basic topology of class E amplifier.

When the transistor is turned on, the current flows through it, and the resonant circuit includes L, C, R, the resonant frequency at this time is: fo1 =

1 √

2π LC

(1)

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When the transistor is turned off, the bypass capacitor C1 is charged, and the resonant circuit is composed of C1 and L,C,R in series connection, since C1 and C are connected in series, the equivalent capacitance value is: Ceq =

CC1 C + C1

(2)

At this time, the resonant frequently of the loop is: fo2 =

1  2π LCeq

(3)

The operating frequency of the amplifier should meet the following conditions: fo1 < f < fo2

(4)

When class E amplifier reaches its optimal operating state, two conditions should be met when the transistor is switched: zero voltage switching (ZVS) and zero derivative switching (ZDS), namely  us (2π ) = 0 (5) dus d (ωt) |ωt=2π = 0 According to the basic characteristics of class E amplifier, the load resistance R is called the optimal load [11], namely:R = Ropt . When and only when R = Ropt , Class E amplifier reaches its optimal operating state. When 0 ≤ R ≤ Ropt , class E amplifier can only achieve ZVS. 2.2 Analysis of ECPT System Based on Class E Amplifier The topology of the ECPT system based on class E amplifier studied in this paper is shown in Fig. 2. In Fig. 2, the coupled mechanism of ECPT system is composed of four metal plates, and CS1 , CS2 represent the capacitance values of these two equivalent capacitors respectively. The two plates connected to the main circuit are called emitter plates, the remaining two plates, together with the load resistor RL , form the pickup, so the removal of the pickup can be equivalent to the removal of the load resistor RL . The DC input of the ECPT system passes through the class E amplifier and the resonant network at the transmitting terminal to obtain high-frequency alternating current. Under its action, a high-frequency alternating electric field is excited between the transmitting and receiving plates. Under the action of the alternating electric field, the displacement current is generated between the plates, and power transfer across the tissue layers is achieved through the displacement current between the plates.

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Lf

L

iS

II

Edc

S

CS1

iC1 uS

u C1

RL

C2

C1

CS2

Fig. 2. The topology of ECPT system based on class E amplifier.

3 Equivalent Circuit Analysis of ECPT System and ZVS Operating Conditions 3.1 Analysis of Voltage and Current Waveforms of the Transistor in ECPT System According to the topology of the ECPT system based on Class E amplifier and parameters in reference [12], a simulation model can be established, and the voltage and current simulation waveforms of the transistor can be obtained as shown in Fig. 3.

(a) Waveforms of the transistor voltage

(b) Waveforms of the transistor current

Fig. 3. Simulated waveforms of the transistor voltage and current when the pickup is removed

It can be seen from Fig. 3 that after the pickup is removed, the terminal voltage waveform of the transistor will be severely distorted, and the current flowing through the transistor will generate serious peaks. The above problems are mainly related to the operating characteristics of class E amplifier itself. The key difficulty in solving this problem is how to ensure that class E amplifier can operate in the zero voltage switching state before and after the pickup is removed.

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3.2 Analysis of System Equivalent Circuit Before and After Removal of the Pickup Figure 4 shows the equivalent circuit of the ECPT system after the pickup is removed. In the actual circuit, the internal resistance of the resonant inductor exists objectively. Therefore, in the case of considering the inductance resistance, comparing Figs. 4 and 1, it can be seen that the basic circuit form of the equivalent circuit in Fig. 4 is consistent with that of class E amplifier.

Lf

L

iS

II

Edc

iC1 uS

S

u C1

C2

C1

Fig. 4. Equivalent circuit of ECPT system with no-load

Based on the foregoing analysis, it can be seen that the operating state of class E amplifier is closely related to the load resistance. In practical applications, the load carried by the system usually cannot meet the efficient operation requirements of the system. Therefore, impedance matching is required to equivalently transform the actual load into a load that can meet the efficient operation of the system. Figure 5 shows the equivalent transformation network of series and parallel impedances, the resonant network of the ECPT system shown in Fig. 2 can be transformed into a series L-C-R resonant circuit through impedance equivalent transformations.

L C1

L

CS

C2

(a) Equivalent circuit of resonant network

RL

C1

L

C2

CP

RP

CSS

C1

(b) Series impedance CS - RL (c) Parallel impedance CP - RP equivalent to parallel imped- equivalent to Series impedance CP - RP ance CSS - RS

Fig. 5. Equivalent conversion of series-parallel impedance.

RS

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The series impedance in Fig. 5(a) is equivalently transformed into the parallel impedance shown in Fig. 5(b), and the related expressions can be deduced as: R2L + XC2S

Rp =

(6)

RL

RCP =

R2L + XC2S

(7)

RCS

The parallel impedance in Fig. 5(b) is equivalently transformed into the series impedance shown in Fig. 5(c), and the related expressions can be deduced as: RS = RCSS = X

XC2 R2P + XC2

RP

R2P R2P + XC2

(8)

XC

(9)

X

Among them, XC = XCCP+XCC2 . P 2 From Fig. 5(c), it can be seen that the equivalent circuit of the ECPT system before and after the removal of the pickup is basically the same in terms of circuit form. According to Eqs. (6), (7) and (8), the change curve of equivalent series resistance RS and load resistance RL can be obtained as shown in Fig. 6. When the optimal operating point of the system appears, that is: RL = Ropt , if RS = RSmax is established at this point, then the ECPT system can realize ZVS operation under any load resistance value RL , because no matter how RL changes, RS ≤ RSmax is established.

RS RSmax

Ropt

RL

Fig. 6. The curve of RS versu RL .

According to the previous analysis, it can be seen that the ECPT system based on class E amplifier can ensure that the amplifier is still running in ZVS state after the pickup is removed without changing the operating frequency of the system, completely avoiding the voltage and current surge phenomenon of the transistor as shown in Fig. 3.

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4 ECPT System Parameter Design and Power Regulation Method 4.1 System Parameter Design Method According to Fig. 1, when the load quality factor QL ≥ 2.5[11], the current flowing through the series resonant circuit is sinusoidal function, and its expression is: i = Im sin(ωt + ϕ)

(10)

Among them, Im is the amplitude of the resonant current i, and ϕ is the initial phase of the resonant current i. According to Kirchhoff’s current law: iS + iC1 = I1 − i = I1 − Im sin(ωt + ϕ)

(11)

According to Fig. 2, when 0 ≤ ωt ≤ π , the transistor is turned on; when π ≤ ωt ≤ 2π , the transistor is turned off. Therefore, when the transistor is turned off, the terminal voltage of bypass capacitor C1 and transistor can be expressed as:  ωt 1 1 {I1 (ωt − π ) + Im [cos(ωt + ϕ) + cos ϕ]} uC1 = uS = iC1 d (ωt) = ωC1 π ωC1 (12) According to formula (5) and formula (12), the DC input voltage can be obtained as: Edc =

1 2π



2π

π

uS d (ωt) =

I1 π ωC1

(13)

According to the equivalent transformation of series-parallel impedance, the calculation expressions of the main parameters of the ECPT system can be obtained. Among them, the relational expression between the equivalent capacitive reactance XCS of the coupling mechanism and the equivalent series resistance RS is:    2 2 1 2 π π − 4 XCS = = RS RL QL − (14) 16 + 1 − RL ωCS The relationship between the inductance L and the series resistance RS is: L=

QL RS ω

(15)

The relationship between the bypass capacitor C1 and the series resistance RS is: ωC1 RS =

8  π π2 + 4

(16)

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The relationship between the C2 reactance XC2 and the series resistance RS is:

 XC2 =

1 = ωC2

RS RL

   2 2 QL − π π − 4 16 + 1



        2  2 −4 2 −4 2 π π π π  RL QL − 16 − RS RL QL − 16 + 1 − RL 

(17)

Since the values of the resonant inductance L and the bypass capacitor C1 do not change before and after the pickup is removed, when the values of the capacitor C2 and the capacitor CSS are approximately equal, the ECPT system can ensure that the transistor still operates in ZVS state at a fixed operating frequency after the pickup is removed. It can be seen from the above expressions that the main parameters of the ECPT system are jointly determined by the four variables RL ,CS ,QL and f , and the influence curves of these four variables as shown in Fig. 7.

Fig. 7. The effect of variables on ZVS.

It can be seen from Fig. 7 that the change of the load resistance RL , the equivalent capacitance CS and the operating frequency f of the system have a relatively large effect on the difference between the capacitance C2 and CSS , so the effect of them is mainly considered in parameter design. Figure 8 is the flowchart of the system main parameters design. Usually, set the value of RL according to the load requirements, the values of Lf ,QL and f are set according to experience, set initial values of CS and Edc based on the space restrictions of the usage site, and then follow the parameters design process shown in Fig. 8 to finally

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calculate the values of all parameters. At the same time, the load judging condition |RS − RSmax | < δ is added, where δ is a preset threshold. The frequency constraint is fo1no - load < f , fo1no - load represents the natural resonant frequency of the resonant circuit when the transistor is turned on after the pickup is removed, and f is the operating frequency of the system before the pickup is removed.

Set the values of

,

,

,

according

to the output power and experience

Set initial parameters

and

Calculate the main parameters Calculate the values of

,

,

and

,

and

according to the

formula equivalent transformation of series-parallel impedance

No

The load limit conditions are met Yes No

The frequent limit conditions are met Yes

Obtain the system parameters

,

,

,

and

satis-

fying the conditions Fig. 8. The flowchart of the system parameters design.

4.2 Buck Power Regulation Method The system parameters design method proposed in the previous section to enable the ECPT system to achieve ZVS operation over a wide load range, and effectively suppresses the voltage waveform distortion and the current peak of the transistor. However, it cannot achieve the operation of the ECPT system in standby state after the pickup is removed. In order to ensure that the ECPT system can provide required power for

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the load and operate in a stable state after the pickup is relocated, and operate in the standby state after the pickup is removed, this paper presents a method to achieve above functions by adjusting duty ratio of front-stage Buck chopper circuit. Figure 9 shows the structural of the ECPT system integrated into DC/DC converter, which identifies the removal or relocation of the pickup by detecting the current of branch where coupling mechanism is located. The detected current signal is processed by conditioning circuit and then transmitted to controller MCU. The MCU outputs the corresponding drive signal according to characteristics of the current signal transmitted by conditioning circuit, and then drive circuit drives transistor to turn on or off.

Lf

LB

EB

iS

II

SB

CB

L

S

iC1 uS

u C1

C1

VD

CS1

C2

RL CS2

Current detection Drive circuit

MCU

Conditioning circuit

Fig. 9. The ECPT system structure with regulation loop

When the pickup is removed, detect the current at the corresponding position in Fig. 9 to identify the removal of the pickup, and then adjust the duty ratio of the frontstage Buck chopper circuit, under this duty ratio, the input power of the system will be significantly reduced, and the system will work in a low-power standby state; When the pickup is relocated, the identification of the moving behavior of the pickup is completed through current detection, and the duty ratio of the Buck circuit is adjusted to the duty ratio of the previous Buck circuit when the ECPT system is operating under load, so as to transmit the required power for the load.

5 Simulation and Experimental Verification 5.1 Simulation Verification In order to verify the feasibility and effectiveness of the ECPT system design methods proposed in this paper, a system simulation model was built on the MATLAB simulation platform according to the ECPT system topology shown in Fig. 2. First calculate the values of all parameters according to the system parameters design process shown in Fig. 8, and obtain the main parameters values of the system as shown in Table 1. The simulation results obtained through simulation shown in Fig. 10. Figure 10 shows the simulation waveform of voltage and current of the transistor before and after the pickup is removed in the ECPT system without the Buck circuit. Although the system resistance is significantly reduced after the pickup is removed, the

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Table 1. System parameters. System parameters

Value

System parameters

Value

Edc /V

28

CS1 ,CS2 /nF

1

f /MHz

1

C1 /nF

1.464

Lf /mH

0.5

C2 /nF

1.18

L/µH

22.24

RL /

500

system can also achieve ZVS. The voltage waveform distortion and the current waveform peaks of the transistor in Fig. 3 are completely suppressed, the results indicate that ECPT system design method proposed in this paper is feasible and effective.

(a) The pickup is placed

(b) The pickup is removed

Fig. 10. Simulated voltage and current waveforms of the transistor with pickup-removed

5.2 Experimental Verification On the basis of theoretical analysis and simulation research, an experimental circuit is built to further verify the feasibility and effectiveness of the proposed method. Figure 11 shows experimental waveforms of the voltage and current of transistor and load voltage before the pickup is removed, and Fig. 12 shows experimental waveforms of the voltage and current of transistor after the pickup is removed. It can be seen that the voltage waveform of the load resistor is a regular sinusoidal, the transistor of amplifier achieves ZVS operation before and after the pickup is removed. The input power of the system is about 15.5 W, and the output power of the system is calculated to be about 13.5 W. Therefore, the power transmission efficiency of the experimental circuit of the ECPT system has reached more than 85%. Figures 13 and 14 are the Experimental waveforms of the transistor voltage and the inductor current when the pickup is removed or relocated. It can be seen from Fig. 13 that voltage of CB in Fig. 9 decreases through the regulation of Buck circuit after the pickup is removed, and the transistor voltage and the resonant inductor current decrease accordingly. The system input power is about 0.5 W, which is in a low-power standby state; when the pickup is relocated, the voltage of CB increases, and the voltage of the

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Fig. 11. Experimental waveforms of the voltage and current of transistor and load voltage

Fig. 12. Experimental waveforms of the voltage and current of transistor with no-load

Fig. 13. Experimental waveforms of transistor and inductor when the pickup is removed

Fig. 14. Experimental waveforms of transistor and inductor when the pickup is placed

transistor and the current of the resonant inductor also increase accordingly. The system stabilizes the transmission of power to the load again. In summary, through simulations and experiments, the feasibility and effectiveness of the proposed design scheme of the wireless power transfer system for mobile devices based on class E amplifiers are verified in this paper.

6 Conclusion On the basis of the current research on the ECPT technology, this paper focuses on the change of the topological structure of the ECPT system caused by the random shift-in and removal of the pickup, which usually leads to sudden changes in the voltage of the transistor terminal and the current flowing through the transistor, causing significant impact or even damage to the switch, and then making the system unable to work normally. This paper analyzes the basic characteristics of the ECPT system based on the class E amplifier, and uses the characteristics that the equivalent circuit form of the system is basically the same before and after the pickup is removed, and proposes a

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system design method that can effectively suppress the current and the voltage surge of amplifier transistor caused by the removal of the pickup, improves the adaptability of the ECPT system based on the class E amplifier for wireless power supply of mobile devices. To reduce the input power of the ECPT system after the pickup is removed, and make the system operate in a standby state, a power regulation method integrated into the DC/DC converter is presented. Simulation and experimental results have verified the feasibility and effectiveness of the system design method and the power regulation method proposed in this paper.

References 1. Qing, X., Su, Y.: An overview of electric-filed coupling wireless power transfer technology. Trans. China Electrotech. Soc. 36(17), 3649–3663 (2021). (in Chinese) 2. Lu, F., Zhang, H., Hofmann, H., et al.: A double-sided LCLC-compensated capacitive power transfer system for electric vehicle charging. IEEE Trans. Power Electron. 30(11), 6011–6014 (2015) 3. Qing, X., Wang, Z., Su, Y., et al.: Parameter design method with constant output voltage characteristic for bilateral LC-compensated CPT system. IEEE J. Emerg. Selected Topics Power Electron. 8(3), 2707–2715 (2020) 4. Liao, Z., Zhou, L., Wu, Z., et al.: An electric-field coupled power transfer system with constant voltage and constant current output based on changeable LC-CLCL resonant circuit. Proc. CSEE 41(17), 6039–6050 (2021). (in Chinese) 5. Wang, S., Liang, J., Fu, M.: Analysis and design of capacitive power transfer systems based on induced voltage source model. IEEE Trans. Power Electron. 35(10), 10532–10541 (2020) 6. Su, Y., Liu, J., Wang, Z., et al.: Influence analysis of metal in the same plane with pickup coil on magnetic coupler and suppression method. Trans. China Electrotech. Soc. 37(3), 578–588 (2022). (in Chinese) 7. Su, Y., Qian, L., Liu, Z., et al.: Underwater electric-filed coupled wireless power transfer system with rotary coupler and parameter optimization method. Trans. China Electrotech. Soc. 37(10), 2399–2410 (2022). (in Chinese) 8. Wu, S., Cheng, X., Meng, X., et al.: An electric-field coupled wireless power transfer system with misalignment-tolerance and light-weight characteristics for unmanned aerial vehicle applications. In: Proceedings of the CSEE, pp. 1–11 (2022). (in Chinese) 9. Zhu, J., Ban, Y., Xu, R., et al.: An NFC-CPT-combined coupler with series-none compensation for metal-cover smartphone applications. IEEE J. Emerg. Select. Topics Power Electron. 9(3), 3758–3769 (2021) 10. Liu, Z., Su, Y., Zhao, Y., et al.: Capacitive power transfer system with double T-type resonant network for mobile devices charging/supply. IEEE Trans. Power Electron. 37(2), 2394–2403 (2022) 11. Kazimierczuk Marian K. RF Power Amplifiers. Wiley (2008) 12. Su, Y., Xu, J., Xie, S., et al.: A tuning technology of electrical-field coupled wireless power transfer system. Trans. China Electro-Tech. Soc. 28(11), 189–194 (2013). (in Chinese)

Research on Dynamic Wireless Power Transfer Technology for Maximum Equivalent Energy Transmission of Embedded Sensors Qi Wang(B)

, Yuner Peng , Yang Chen , and Ruikun Mai

School of Electrical Engineering, Southwest Jiaotong University, Sichuan, China {wangqi2022,pengyuner}@my.swjtu.edu.cn, {yangchen, mairk}@swjtu.edu.cn

Abstract. To address the issue of long-term reliable power supply for embedded sensors in subgrade along the rail transportation system, this paper proposes a method utilizing a detection vehicle to provide power to the subgrade sensors through bottom-mounted transmitting coils. Furthermore, an optimization approach for the DD transmitting coils is presented, with the constraint of the detection vehicle clearance as the limiting factor, aiming to maximize the output power of the dynamic wireless power transfer system. By comprehensively considering the variables associated with DD coils along with the clearance height, a comprehensive equivalent circuit model incorporating the reinforcing bars is constructed. Through magnetic field calculations of the hollow coils and analysis of the impact of various parameters on the system’s output power, corresponding conclusions are derived and elaborated upon regarding how to leverage these findings to enhance the output power. Finally, the validity of the proposed method is validated through theoretical calculations. The dimensions of the transmitting coil are 150 mm × 150 mm, with the auxiliary coil closely wound around a 12 mm diameter rebar. When the height is set at 150 mm, and an example speed of 7 m/s is considered, the optimized coil parameters result in a 50% increase in output power, achieving 0.14 W·s, thereby meeting the power supply requirements of multiple sensors. Keywords: Embedded sensors · Dynamic wireless power transfer · Coil design · Maximum Power

1 Introduction Sensors are widely used in civil engineering, transportation, implantable medical treatment and other fields [1–3]. Among them, embedded sensors play a huge role in structural health monitoring, which can not only obtain key state information such as temperature, humidity and settlement in real time, but also provide important data support for the early warning of potential hazards, which is crucial for the maintenance and management of large civil engineering such as tunnels and Bridges, and important structures such as roadbed and rail along rail transit. Continuous and reliable power supply is the basic premise for the normal operation of embedded sensors, and the existing power © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 158–166, 2024. https://doi.org/10.1007/978-981-97-0873-4_17

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supply methods are divided into wired and wireless power supply. The wired power supply mode is easy to be damaged and difficult to maintain. In recent years, the rapid development of radio energy transmission technology [4] has provided new ideas for solving the problems existing in wired power supply. In the field of rail transit, conditions along the railway line are not conducive to manual monitoring [5], and dynamic wireless power supply can well avoid these problems. The University of Auckland [6] proposed an energy transfer system using array inductors, which can provide 3.3 kW charging power for electric vehicles in mobile state. The output efficiency of the final designed system is higher than 80%, which is limited by the maximum allowable magnetic field range and mass factor. Due to its low power consumption and small size [7], the research of embedded sensors is gradually emerging in the fields of biomedicine [8] and rail transit [9]. Therefore, the size of the receiving end is limited, and the received energy is also limited. Periodic dynamic wireless power supply for the embedded sensor in the track plate is carried out by the detection vehicle during the driving process. Due to the fast driving speed of the detection vehicle, it is an urgent problem to improve the energy obtained by the embedded sensor in a limited time. In this paper, a transmitting coil optimization method for a single transmitting multireceiving dynamic radio energy transmission system is proposed. The distance between the two subcoils of DD coil and the direction of current flowing into the two subcoils are determined by calculating the height of the receiving end as the constraint condition, so that the receiving end can obtain maximum energy.

2 System Structure 2.1 System Parameter Modeling Combined with the characteristics of rebar, each rebar grid is regarded as a loop. The rebar loop can be regarded as a receiving coil, as shown in Fig. 1(a), where L R represents the self-inductance of the rebar ring and RR represents the internal resistance of the rebar ring. As shown in Fig. 1(b), the rebar is laid in the lower track plate, mainly considering the energy obtained by the coupling of the transmitting coil between the rebar loop and the lower rebar network. The coil design is square and consistent with the size of the

Fig. 1. The position of receiving coil and diagram of the proposed system

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rebar ring. Based on the previous research results [10], the receiving wire trap obtains energy on the steel bar.

h

h

Fig. 2. Diagram of mutual inductance calculation between rebar array and transmit coil

2.2 System Parameter Modeling In Fig. 2, Tx1 and Tx2 represent the transmitting coils, Ri (i = 1,2,3,…,9) indicates the reinforcement loop, and the transmitting coil is opposite the reinforcement ring R5 and R6 . M i (i = 1,2,3,…,9) denotes the corresponding mutual inductance between the transmitting coil and the reinforcement loop, I i (i = 1,2,3,…,9) represents the current coupled to each rebar ring. In the established reference coordinate system, h1 is the ordinate of the rebar ring; h2 is the ordinate of the transmitting coil; l2 is half the length of the inner square side of the bar ring; l1 is half the length of the inner square side of the transmitting coil; The center O1 of the rebar ring R5 overlaps with the Z axis; Transmitting coils Tx1 and Tx2 have centers O3 and O4 on the YZ plane; G is the distance between DD coils; h1 and h2 are the distances of the rebar ring and the transmitting coil to the XOY plane of the reference coordinate system, respectively. The expression of mutual inductance between single-turn square coils is shown in Eqs. (2) and (3) [11]:   B · ds  ∞ ∞ 1 ejl1 ξ − e - jbl1 ξ D M15 = = (C + C ) z y I1 4π 2 I1 −∞ −∞ jξ ×

ej(l1y +l1 )η − ej(l1y −l1 )η −kh2 e dξ dη jη

Table 1. Dimensions of simulation Coil

Length/mm

Width/mm

Diameter/mm

Number of turns

Tx1

150

150

4.2

3

Tx2

150

150

4.2

3

Ri

150

150

12

1

(1)

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  B · ds M25 =

D

I2

1 = 4π 2 I2



∞



∞

−∞ −∞

(Cz + Cy )

161

ej(l1 −GT )ξ − e - jb(l1 −GT )ξ jξ

ej(l1y +l1 )η − ej(l1y −l1 )η −kh2 e dξ dη × jη

(2)

The mutual inductance between multi-turn square coils is calculated as: M =

N1  N2 

Mmn

(3)

m=1 n=1

where N 1 is the number of turns in Rx and N 2 is the number of turns in Tx ; m is the m turn of Rx and n is the n turn of Tx . When the size of coil and rebar is shown in Table 1, h1 = 0 mm, h2 = 150 mm, and the height difference between the transmitting coil and the rebar ring is recorded as H, H = h2 −h1 = 150 mm. 2.3 Influence of I d1 and I d2 in the Same/Different Direction The system adopts DD coil as the transmitting coil, as shown in Fig. 2. As shown in Fig. 3, α(α = 1,2,3,…) Represents multiple points when the primary transmitting coil corresponds to different moving distances during the moving process, M (α) can be obtained from Eq. (5). When G = 60 mm and H changes, as shown in Fig. 3(a), the opposite direction coil is better, and as shown in Fig. 3(b), the same direction coil is better. Then the direction of I d1 and I d2 will affect the size of M (α) , and then affect the energy acquired by the secondary side. 1 10

10

4 2

0.5 0

0

0.5

2 0.4 0.2

0 0.2 0.4 0.6

1

0.4 0.2

0 0.2 0.4 0.6

Fig. 3. The curve of M (α) variation with different direction of I d1 and I d2

2.4 The Effect of Coil Spacing G The difference of the distance G between the two coils in the transmitting coil will also affect the magnetic field coupling between the two coils. As shown in Fig. 4(a) and Fig. 4(b), when H = 300 mm, the mutual inductance of the codirectional coil is greater when G = 0 mm, and the mutual inductance of the cross-directional coil is greater when G = 200 mm, then the change of G will affect the size of M (α) , and then affect the energy obtained by the secondary side.

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0.5

10

10

162

0.5 0

0

0.5

0.5 0.4 0.2

0

0.2 0.4 0.6

0.4 0.2

0

0.2 0.4 0.6

Fig. 4. The curve of M (α) variation with different G

2.5 Simulation Proof

3 2 1 0 1 2 3

10

10

Maxwell simulation is used to obtain the mutual inductance value between the steel bar ring and the receiving coil, and the mutual inductance value calculated by the formula is compared with the mutual inductance value calculated by the formula, as shown in Fig. 5. The calculated value is basically consistent with the simulation value, which verifies the accuracy of the calculated value. The output power can be calculated by using the calculated value.

5 0 5

400 200 0 200 400 600

400 200 0 200 400 600

Fig. 5. Calculated and simulation value of M (α) with different H, direction of I d1 and I d2 under G = 20 mm

3 Circuit Analysis The proposed system adopts LCC-S topological circuit as shown in Fig. 6. In the Fig., L P and L S are respectively the self-inductance of the transmitting and receiving coils; L 1 , C 1 , C 2 constitute the primary LCC compensation; C S is the series resonant capacitance of the receiving coil; C O is the rectifier bridge output filter capacitor; RS is the internal resistance of the receiving coil; U IN is the input constant voltage source; I P and I S are transmitting coil and receiving coil currents respectively. I IN and V P are inverter output current and voltage respectively. V S is the input voltage of the receiving rectifier circuit. Four power MOSFET(Q1 −Q4 ) constitute the inverter; Diodes D1 and D2 constitute halfbridge rectification. Req is the equivalent resistance from the front end of the bridge, the bridge output is connected to the load RL , I O and U O are the bridge output current and voltage respectively. Ignoring the influence of the distance of the steel bar, the steel mesh of the nine grids was selected for analysis, and the I i was taken in the clockwise direction.

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Fig. 6. The topology of the proposed system

According to Kirchhoff’s voltage law, the system is analyzed, and the equation can be obtained as shown in Eq. (6). jωIP · [M ](α) = [Z] · [I ] ⎧

T (α) ⎪ ⎪ = [M ] M M · · · M 0 ⎪ 1 2 9 ⎨ ⎪ ⎪ ⎪ ⎩



[I ] = I1 I2 · · · I9 IS

T

⎡

Z11 ⎢ Z21 ⎢ ⎢ , [Z] = ⎢ ⎢ ⎣ Z91 ZS1

(4) Z12 Z19 Z22 · · · Z29 . M .. Z92 Z99 ZS2 ZS9

⎤ Z1S Z2S ⎥ ⎥ ⎥ ⎥ ⎥ Z9S ⎦ ZSS

(5)

By solving Eq. (6), the subside current I S (α) can be obtained, and the output power Pout (α) can be obtained by substituting Eq. (8). (α)



(α)

(α)

Pout = IS · I S · Req

(6)

(α)

Including, Req = (2 π 2 )RL , I S denotes the conjugation of I S (α) . The equivalent power output of the secondary coil in the whole moving process P out can be obtained by Eq. (9). 2

P out =

ω2 IP · I P · Req 2 1  (α)2 Pout = ( ) Meq n (Req + RS )2 n

(7)

α=1

Including, Meq

  n  1 4 =  M (α)4 n

(8)

α=1

(α)

I P represents the conjugation of I P (α) , and M eq represents the equivalent mutual inductance of the transmitting and receiving coils. As can be seen from Eq. (9), P out and M eq are positively correlated, then M eq can be used to reflect the size of P out .

4 Coil Design For different application scenarios, the limit of the detection vehicle is different, so H is taken as a measurement basis for the design of the transmitting coil. Through the design of the same/different direction of I d1 and I d2 and the coil spacing G, the energy obtained by the receiving coil at the target H is maximized, and P out is maximized.

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2 1.5 1 0.5 0 100

80

60

40

20

0 300

250

200

150

Fig. 7. The curve of M (α) variation with different G and H

By comparing the M eq of I d1 and I d2 when the two variables H and G are changed in the same direction and in different directions, the data calculated by Eq. (10) are drawn into two surfaces, as shown in Fig. 9. As can be seen from Fig. 7, when G is smaller (about 225 mm), the mutual inductance value obtained by the coil with the same direction of I d1 and I d2 is larger. On the contrary, the mutual inductance value obtained by I d1 and I d2 coils is larger.

5 Computational Verification Maxwell was used to obtain the self-inductance parameters of the primary secondary side coil, the parameters of the steel bar were measured, and the rest parameters of the system were calculated, as shown in Table 2. As shown in Fig. 10, Pout (α) in different directions of I d1 and I d2 is compared when G = 20 mm and H is changed. Figure 10(a) shows that H = 150 mm, and the Pout (α) of I d1 and I d2 in different directions, it can be seen that selecting I d1 and I d2 in different directions at this time can increase the power output of the secondary side. Figure 10(b) shows that H = 300 mm, and the Pout (α) of I d1 and I d2 in different directions, it can be seen that selecting I d1 and I d2 in the same direction at this time can increase the power output of the secondary side. Table 2. System parameters Parameter

Value

Parameter

Value

Parameter

Value

f 0 /kHz

250

C 2 /nF

1.5

L S /µH

55.6

I P /A (H = 150 mm)

2.7

L R /µH

356

RS /

0.7

I P /A (H = 300 mm)

4.5

RR/

0.068

C S /nF

7.2

L 1 /µH

2.3

L P /µH (Same)

266.1–277.1

RL /

50

C1/nF

166.2

L P /µH (different)

252.7–261.5

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3

0.3

2

0.2

1

0.1

0 400 200

0

200 400 600

165

0 400 200 0 200 400 600

Fig. 8. Calculated value of Pout (α) with different H, direction of I d1 and I d2 under G = 20 mm

As shown in Fig. 8, during the whole moving process, I d1 and I d2 can only have output power when the moving distance is −400–600 mm, regardless of the opposite direction or the same direction. For the different directions of I d1 and I d2 , Pout (α) shows asymmetry between the left and right peaks, which is related to the position of the receiving coil. As shown in Fig. 2, the receiving coil is not placed in the middle during the analysis, but near the edge, resulting in asymmetric received energy. 

L/V

Weq = 0

(α) Pout dt =

1  (α) L Pout · j V j

(9)

α=1

Formula can be used to obtain the energy W eq that can be obtained by the second side of the detection vehicle when it travels at a certain speed V through a distance of length L. If the detection vehicle moves 1m at the speed of 7 m/s (about 25 km/h), when H = 150 mm, the W eq of the different coil can reach 0.14 W·s, and the W eq of the homotropic coil is only 0.07 W·s, then the energy received by the secondary side can be increased by 50% by optimizing the coil.

6 Conclusion Through theoretical calculation and deduction, combined with the difference of H in practical engineering application, adjusting the current direction and G of the primary transmitting coil can make the secondary side obtain more energy. The experimental principle prototype was built to verify the accuracy of the calculation, and it was found that at a certain height (150 mm for example) and speed (7 m/s for example), the same and different direction selection of the optimized coil could increase the energy obtained by the secondary side by 50%, meeting the power supply demand of multiple sensors on the secondary side, which may not be met without optimization. Finally, it is proved that the energy obtained by the secondary side can be increased by using this optimization method.

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References 1. Tokognon, C.A., Gao, B., Tian, G.Y., et al.: Structural health monitoring framework based on Internet of Things: a survey. IEEE Internet Things J. 4(3), 619–635 (2017) 2. Jie, Y., Anping, W., Jinglin, W., et al.: Aeroengine bearing fault diagnosis based on convolutional neural network for multi-sensor information fusion. Proc. CSEE 42(13), 4933–4942 (2022) 3. Jia, Y., Qu, D., Lin, L., et al.: Coordinated speed control of connected mixed traffic flow based on trajectory. J. Jilin Univ. (Eng. Technol. Edn.) 51(06), 2051–2060 (2021) 4. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019) 5. Wang, L., Xu, S., Qiu, J., et al.: Automatic monitoring system in underground engineering construction: review and prospect. Adv. Civil Eng. 2020, 1–16 (2020) 6. Jafari, H., Olowu, T.O., Mahmoudi, M., et al.: Optimal design of IPT bipolar power pad for roadway-powered EV charging systems. IEEE Can. J. Electr. Comp. Eng. 44(3), 350–355 (2021) 7. Abdulkarem, M., Samsudin, K., Rokhani, F.Z., et al.: Wireless sensor network for structural health monitoring: a contemporary review of technologies, challenges, and future direction. Struct. Health Monit. 19(3), 693–735 (2020) 8. Zhenling, S., Dongyun, W., Xiaomin, Q., et al.: Development of a flexible embedded neurostimulator for animal robots. J. Biomed. Eng. 40(02), 327–334 (2023) 9. Yanjuan, W., Ding Guoping, Y., Yi.: Research on forming process of CFRP pantograph upper frame with embedded FBG sensor. Comp. Sci. Eng. 01, 107–111 (2023) 10. Peng, Y.E., Wang, Q., Chen, Y., et al.: Wireless sensor power supply based on eddy currents for structural health monitoring. IEEE Trans. Industr. Electron. (2023). https://doi.org/10. 1109/TIE.2023.3299043 11. Zhongqi, L., Shangyou, L., Jing, L., et al.: Mutual inductance calculation and 0ptimization of multi-receiver positive and negative series coil structure in dynamic wireless powertransfer systems. Trans. China Electrotechnical Soc. 36(24), 5153–5164 (2021)

Power Distribution of Multi-load WPT System Based on Active L-type Equivalent Network Dongxiao Huang1(B)

, Zequan Hong1,2 , Xianhong Lin1,3 , Weidong Huang2 , and Fengxiang Wang1

1 National Local Joint Engineering Research Center for Electrical Drives and Power

Electronics, Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences, Quanzhou 362000, China {dongxiao.huang,fengxiang.wang}@fjirsm.ac.cn, [email protected], [email protected] 2 Fujian Key Laboratory of Intelligent Machining Technology and Equipment, Fujian University of Technology, Fuzhou 350118, China [email protected] 3 Fuzhou University, Fuzhou 350108, China

Abstract. Instead of achieving the power distribution of the specific load in the constant voltage mode, most of the existing single-input multiple-output Magnetic Coupled Wireless Power Transfer (MC-WPT) systems for multi-load simultaneous charging focus on the resonant frequency tracing or misalignment tolerance enhancement with active impedance matching network. A novel single-input multiple-output multi-load MC-WPT system combining the LCC-S impedance matching topology and the active L-type equivalent network applied the phasecontrolled switched capacitors is proposed. By applying the double closed loop PI controller, the system can adjust the power that distributed to each load. The simulation result of the triple-load MC-WPT system proves that the proposed method can achieve the real-time power distribution of three secondary sides with fast load transient response. Keywords: MC-WPT · Power distribution · Equivalent Network · Switched Capacitor

1 Introduction Due to the merits of high efficiency and high coil misalignment tolerance [1–3], the single-input multiple-output Magnetic Coupled Wireless Power Transfer (SIMO MCWPT) system is widely applied to the multi-target simultaneous charging of electronic products [4, 5] and electric vehicles [6, 7]. These years, the researches mainly focus on the resonance point tracing [8–11] or the misalignment tolerance enhancement [12–14]. As a matter of fact, the stability of power distribution is also crucial in practical application. C. Luo [3] proposed a novel multi-load WPT system combining the parity-time symmetry principle and time-sharing control strategy to maintain constant power for each load © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 167–177, 2024. https://doi.org/10.1007/978-981-97-0873-4_18

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against the transient of coupling condition. K. Baba [15] proposed a power distribution method that combines a phase-controlled capacitor with a DC-DC converter in each secondary side for dual-load WPT system working at the same frequency. F. Liu [16] proposed a configuration that achieve the synchronous drive of transmitting resonant tank with multiple inverters operating at the different frequencies and a novel multi-frequency superposition methodology is presented to achieve the power distribution. X. Tian [11] proposed a multi-frequency multi-load WPT system that can simultaneously deliver power to different pickups with arbitrary power requirements and resist the disturbance in transmission. In this paper, a novel SIMO MC-WPT system applied the LCC-S impedance matching topology with the active L-type equivalent network using Phase-Controlled Switched Capacitor (PCSC) is proposed for multi-load WPT power distribution. The proposed system is communication-free and each secondary side is controlled independently. Applied in each secondary side, the active L-type network can change the equivalent impedance of the load side circuit by adjusting the PWM signal of PCSC. The double closed loop PI controller is applied in the control of PCSC to maintain the constant voltage value of each load and achieve the power distribution.

2 System Configuration Analysis 2.1 Circuit Structure of the Proposed System Based on the theory of optimal number of receiving coils [17], a SIMO triple-load MCWPT system configuration with the LCC-S impedance matching topology and active L-type equivalent network is introduced in Fig. 1. CS(1) LT(1)

Lf (1) C0

Q1 LS(1) C (1) (1) 0 (1) RLs Q2

(1) MPS

Lr

MS(12)

CP2

CS(2) LT(2)

(2)

U

MPS 0

CP1

Rr

LP RP

LS(2) C0(2) (2) Q2 RL(2)s

(13)

MS (3)

MPS

PCSC (2) Q1

UL

IL(1) RL(1)

UL

IL(2) RL(2)

UL

IL(3) RL(3)

(1)

Cf

(1)

Lf C0

(2)

Cf

(2)

(23)

MS

CS(3) LT(3)

Lf (3) Q1 C0

(3)

LS(3) RL(3)s

C0(3)

(3)

Q2

Cf

(3)

L-type Equivalent Network

Fig. 1. Circuit structure of the proposed triple-load MC-WPT system

As is shown in Fig. 1, i (=1,2,3) is used to number the same components exist in all secondary sides. The LCC-S topology network contains an inductor L r with a parallel

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capacitor C P1 and a series capacitor C P2 in the primary side and a capacitor C S (i) in secondary sides. L P , L S (i) stands for the self-inductance of the coils. Rr and RP stands for the resistance of the compensation inductor, RS (i) stands for the resistance of L S (i) . RL (i) , U L (i) , I L (i) stands for the resistance, voltage and current of each load. M PS (i) is the mutual inductance between the transmitting coil and the ith receiving coil. M S (ij) ( j = 1, 2, 3, i = j) is the mutual inductance between receiving coils. The L-type equivalent network contains a PCSC and a constant inductor L T (i) , each PCSC contains two antiparallel MOSFETs Q1 (i) , Q2 (i) that series with a constant capacitor C 0 (i) separately. The second-order filter between the rectifier and the load is composed of L f and C f . 2.2 Principle of the Phase Controlled Switched Capacitor Served as an adjustable capacitor in the circuit, the equivalent capacitance C T (i) of the PCSC in a system period T can be adjusted by changing the duty D1 (i) , D2 (i) of the MOSFETs Q1 (i) , Q2 (i) [18]. Assuming that α (∈[0, π/2]) is the cut-off angle that D1 (i) , D2 (i) reflects on T, the relationship of C T (i) , α and C 0 is (i)

CT =

[4 − 2 cos(α) + sin(α)(π − 2α)] · C0 (i = 1, 2, 3) 2

(1)

Assuming that V 1 (i) , V 2 (i) is the electrical level of C 0 (i) in series with Q1 (i) , Q2 (i) , The waveform of V 1 (i) , V 2 (i) and switching states of Q1 (i) , Q2 (i) is shown in Fig. 2. V1(i) Vα θ

0 2π-α

2π-α

D1(i) 1 ON OFF

ON

OFF

ON θ

0 V2(i)

θ

0 -Vα

ON 0

2π-α

2π-α

D2(i) 1

OFF

ON

OFF ON θ

Fig. 2. Waveform of V 1 (i) , V 2 (i) and the corresponding switching states

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2.3 Principle of the L-type Equivalent Network The simplified circuit applying an ideal L-type equivalent network is shown in Fig. 3(a), which can be converted into the equivalent circuit shown in Fig. 3(b) by adjusting the value of C T (i) and L T (i) basing on the theory of impedance conversion. LT(i) R1 Uin

(i)

LT(i)Ď CT(i)

R2

CT(i)Ď

R1(i)Ď Uin

(i)

R2(i)Ď

(a)

(b)

Fig. 3. Impedance equivalent conversion of the proposed L-type network

The converting process of proposed configuration can be expressed as 1 (i) 1/jωCT

+

1 (i) R2

=

1 (i) 1/jωCT

(i)

+ R2

,

(2)

and the equivalent resistance R2 (i)’ can be derived as (i)

R2 =

(i)

R2

   (i)  CT  1 + (  (i)  )2 R1 

(i)

< R2 ,

(3)

where |C T (i) |/|R1 (i) | stands for the ratio of the value of C T (i) and R1 (i) , the difference of unit between them is ignored. Figure 3 and (3) indicate that it is practicable to adjust the equivalent resistance by changing the value of C T (i) in L-type network. However, (3) is difficult to establish accurately in actual system due to the complexity of the synchronous control of C T (i) and L T (i) at a high frequency, so the proposed system uses a constant inductor L T0 instead. In addition, the accurate value of R1 (i) is also difficult to measure or calculate, so the double closed loop PI controller is applied to the control of C T (i) through the PCSC.

3 Modelling and Control Strategy 3.1 Mathematical Modelling of the Proposed System Given that the cross-coupling affect is restrained to a degree that M S (ij) can be negligible, the equivalent configuration of proposed system is shown in Fig. 4(a), where Req (i) stands for the equivalent resistance of the rectifier and load, REQ (i) stands for the resistance after conversion. By reflecting the secondary impedance to the primary side, the circuit can be further converted into the one in Fig. 4(b), where Z r (i) stands for the reflected secondary impedance that can be adjusted by PCSC.

Power Distribution of Multi-load WPT System CS

(1)

LS

(1)

MPS(1) Lr Uin

CP2 LP

CP1 Rr

MPS(2)

RP

CS

(2)

(2) LS (2)

CS

(3)

LS

CS

REQ

Lr CP1 Z2

CP2 LP Zr(1) Z3 Z (2) r Zr(3) Z4 RP

+ .

UP

Zin

(3)

(3)

CS

+ Rr . Z1 Uin

(2) Req

LT

(3)

(3)

(2) REQ

(2)

(3)

RS

(1) Req

LT

(2)

RS MPS(3)

CS

(1)

(1) RS

(1) REQ

LT

(1)

171

(3) Req

(a)

(b)

Fig. 4. Equivalent configuration of proposed triple-load MC-WPT system

By analyzing of the circuit in Fig. 4(b), the system input impedance Z r (i) can be     1   Z1 Z2   Rr + jω0 Lr  jω C 0 P1 = (4) Z =  , (1) (2) (3) 1   jω C + jω0 LP Zr + Zr + Zr + RP  Z3 Z4 0 P2

and the power of each secondary side can also be derived as (i)

(i)

(ωi MPS Uin )2 REQ (i) PS =   ,  (i) 2 (Z11 · Z4 + Z12 )Zr 

(5)

which indicates that the power distributed to each load is in direct proportion to the reflected impedance, verifying the effectiveness of L-type equivalent network. 3.2 Control Strategy of the Proposed System The schematic diagram of the proposed control strategy is shown in Fig. 5. Accordingly, QI ~QIV stands for the controlling signal sent to the inverter. Q1 (i) , Q2 (i) stands for the controlling signal sent to the PCSC. U ref (i) stands for the reference voltage of each load. U L (i) and I L (i) stands for the nominal voltage and current of each load, U T (i) and I T (i) stands for the transient voltage and current signal of each load. Considering the complexity of SIMO system modelling, the double closed loop PI algorithm is suitable for the real-time adjustment of PCSC in disturbance rejection. The block diagram of proposed controller is shown in Fig. 6(a) and the control process of power distribution against load transient is shown in Fig. 6(b).

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CS(1) LT(1) L

(1) S

U0

QII

Lr CP1

 

QIII

Rr

QIV

CP2 LP RP

MPS(2) MPS(3)

Q Q Q Q I

II

III

Gate Driver PWM Generator

IV

Secondary Side DSPs

(1)

CS

(2)

L(2)S RS

(1) Q1,2

Lf

LT(2)

CT

(3)

(2) Q1,2

Lf

LT

(3)

CT(3)





IL(2)

Cf UL(2)

(2)

(2)

CS(3) L(3)S RS

Cf UL(1)

CT(1)

 

IL(3)

Cf UL(3)

(3) Q1,2

 

Gate Driver Current Sensor

PWM Generator

D1,2(i)



MPS(1) QI

RS

IL(1)

Voltage Sensor

IT(i)

UT(i)

 

Voltage-Loop PI Controller



Current-Loop PI Controller

(i) Uref

Fig. 5. Control strategy of proposed triple-load MC-WPT system

4 Simulation and Analysis To verify the power distribution control strategy in Fig. 5, a simulate model is built in MATLAB/simulink. The corresponding parameters is designed in Table 1 according to the condition of resonance and six controlled simulations (Case ➀ to ➅) are designed in Table 2 for different situations caused by load transient. For example, Case ➃ stands for the situation that RL (2) steps from 25  to 23.5  at the 0.5 s after the entry of steady state and RL (1) , RL (3) remain unchanged, the same applies to other cases. The waveform of output voltage and current of the L-type equivalent network before and after the transient of RL (i) in Case ➃ is shown as a demonstration in Fig. 7, proving that the proposed system can work close to the resonant frequency and thus achieve a high level of system efficiency, the same applies to other cases. The results of controlled simulations are shown in Table 3 and Fig. 8. According to (5) and the result in Table 3, the proposed method is proved to be practicable for the power distribution of any load in CV mode, but the extra power consumption will cause the decline of the system efficiency. By comparing the waveform in Fig. 8, the proposed method is proved to be effective in maintaining the value of load voltage against all cases of load transient that may happen in the triple-load MC-WPT system.

Power Distribution of Multi-load WPT System io

(i)

173

1 Z (s)

RL

(i)

UT

IT

(i)

VoltageLoop PI

Uref

(i)

CurrentLoop PI

K PWM

(i)

1 sL

1 sC

(a) Block diagram of proposed double closed loop controller Interrupt Entry

Interrupt Exit UT

(i)

Current Sampling

Voltage Sampling

IT

RL(i)

(i)

UL(i)

Signal Conversion

PCSC D

(i)

ADC(I)

ADC(U)

CurrentLoop PI

VoltageLoop PI

ePWM α PCSC Controller (i) Uo (i)

Uref

(i)

(b) Process of double closed loop PI control against load transient

Fig. 6. Control principle and process of proposed power distribution method

Table 1. Electrical Parameters of the Proposed System Parameter

Value

Parameter

Value

U in

380 V

U ref

(i)

100 V

f0

100 kHz

L S (i)

30 μH

LP

108.5 μH

0.005 

RP

0.015 

Lr

120 μH

Rr

0.01 

RS (i) L T (i) C 0 (i) C S (i)

C P1

20 nF

C P2

20 nF

20 μH 10 nF 85 nF

Uo

(i)

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D. Huang et al. Table 2. Resistance Transient of Each Load in Controlled Simulations

Simulation Case

Resistance of each load/ RL (1)

RL (2)

RL (3)

➀

25

25

25

➁

25

33.5

25

➂

25

30

30

➃

25

23.5

25

➄

25

23.5

23.5

➅

25

23.5

33.5

Table 3. Steady-state Power of Each Load After Transient in different cases Simulation Case

Power of each load (RSM) /W PL (1)

PL (2)

PL (3)

Efficiency η /%

➀

419.8

420.1

420.1

94.1

➁

413.1

329.1

413.4

87.9

➂

465.9

409.2

408.7

93.4

➃

413.9

451.8

414.3

92.5

➄

398.6

415.4

414.9

90.3

➅

348.8

362.7

306.6

85.7

After transient

Before transient 5 0 -5

100 0 -100

5 0 -5

100 0 -100

100 10

5 0

0

Current(A)

Voltage(V)

50

-5

-50

-10 -100

0.4998

0.4999

0.5000

0.5001

0.5002

Time(s)

Fig. 7. Waveform of output voltage and current of the L-type equivalent network

Power Distribution of Multi-load WPT System 35

120

UL

(2)

80 0.45

0.55

0.65

20

Voltage(V)

Voltage(V)

25

100

110 100

(1)

80 0.45

0.55

0.65

35

UL ,UL

0.65

0.75

(1)

(3)

90

20

Voltage(V)

Voltage(V)

25

RL

35

15 0.85

30

110 (1) UL(2),UL(3) RL

25

100

RL(2),RL(3) 90

80 0.45

0.55

0.65

UL

(1)

0.75

20

Resistance( )

UL(2)

100

0.55

15 0.85

120

Resistance( )

30

110

80 0.45

0.75

Time(s) (b) Case III

120

(2)

(3)

20

Time(s) (a) Case II

RL(1),RL(3)

25

UL , U L

90

15 0.85

0.75

30

UL(2)

RL(1)

Resistance( )

UL(1),UL(3)

Resistance( )

30

110

90

35

120

RL(2),RL(3)

RL(2)

RL(1),RL(3)

175

15 0.85

Time(s) (d) Case V

Time(s) (c) Case IV 35

120

30

110 100

90 80 0.45

0.55

RL(1)

UL(2)

RL(2)

UL(1)

0.65

0.75

25

UL(3)

20

Resistance( )

Voltage(V)

RL(3)

15 0.85

Time(s) (e) Case VI

Fig. 8. Waveform of voltage and corresponding load transient of each simulation

The results above show that the proposed system is capable to resist the load transient in secondary side to a certain extent and ensure that the voltage U L (i) can recover to the value that close to the reference voltage U ref (i) , which proves that the proposed system can work in the CV mode by applying the proposed L-type network, but the range of the load transient response remains to be expanded.

5 Conclusion A novel SIMO MC-WPT system combining the LCC-S topology network with the active L-type equivalent network is proposed in this study. By applying the principle of equivalent impedance conversion, the proposed system can achieve the multi-load power distribution without a communication between the primary side and secondary sides. In addition, the proposed system can achieve the fast load transient response in CV mode with the application of double closed loop PI controller to the adjustment of PCSC in proposed L-type network. The simulation results verify the feasibility of proposed system in power distribution and disturbance rejection. Acknowledgments. This research was supported by Quanzhou Science and Technology Program (2021C020R).

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References 1. Liu, Y., Liu, C., Huang, R., Song, Z.: Primary multi-frequency constant-current compensation for one-to-multiple wireless power transfer. IEEE Trans. Circuits Syst. II Express Briefs 70(6), 2201–2205 (2023) 2. Li, K., Ding, W.: An improved one-to-three WPT system with tunable compensation network and enhanced pulse density voltage control. IEEE J. Emerg. Sel. Topics Power Electron. 11(3), 3586–3596 (2023) 3. Luo, C., Qiu, D., Gu, W., et al.: Multiload wireless power transfer system with constant output power and efficiency. IEEE Trans. Ind. Appl. 58(1), 1101–1114 (2022) 4. Tang, W., Zhu, Q., Yang, J., et al.: Simultaneous 3-D wireless power transfer to multiple moving devices with different power demands. IEEE Trans. Power Electron. 35(5), 4533– 4546 (2020) 5. Li, J., Qin, R., Sun, J., et al.: Systematic design of a 100-W 6.78-MHz wireless charging station covering multiple devices and a large charging area. IEEE Trans. Power Electron. 37(4), 4877–4889 (2022) 6. Wang, R., Tan, L., Li, C.: Analysis, design, and implementation of junction temperature fluctuation tracking suppression strategy for SiC MOSFETs in wireless high-power transfer. IEEE Trans. Power Electron. 36(1), 1193–1204 (2021) 7. Wu, L., Zhang, B., Zhou, J.: Efficiency improvement of the parity-time-symmetric wireless power transfer system for electric vehicle charging. IEEE Trans. Power Electron. 35(11), 12497–12508 (2020) 8. Gong, W., Xiao, J., Chen, S., et al.: Research on parameter configuration of C-C and C-V of WPT system based on LCL-LCC compensation network. In: Proceedings of 2021 IEEE 4th International Electrical and Energy Conference, Wuhan, China, pp. 1–6 (2021) 9. Zhang, Z., Yang, H., Analysis methodology for multiple resonators in wireless power transfer systems. In: Proceedings of 2022 IEEE 5th International Electrical and Energy Conference, Nangjing, China, pp. 4871–4876 (2022) 10. Huang, Y., Liu, C., Xiao, Y., et al.: Separate power allocation and control method based on multiple power channels for wireless power transfer. IEEE Trans. Power Electron. 35(9), 9046–9056 (2021) 11. Tian, X., Chau, K.T., Pang, H., Liu, W.: Power adaption design for multifrequency wireless power transfer system. IEEE Trans. Magn. 58(8), 1–5 (2022) 12. Zhang, Y., Pan, W., Wang, H., et al.: Electric vehicle wireless power transfer system employing reconfigurable topology for misalignment tolerance. In: Proceedings of 2022 IEEE 5th International Electrical and Energy Conference, Nangjing, China, pp. 1150–1154 (2022) 13. Darvish, P., Mekhilef, S., Illias, H.A.B.: A novel S-S-LCLCC compensation for three-coil WPT to improve misalignment and energy efficiency stiffness of wireless charging system. IEEE Trans. Power Electron. 36(2), 1341–1355 (2021) 14. Zhang, P., Saeedifard, M., Onar, O.C., et al.: A field enhancement integration design featuring misalignment tolerance for wireless EV charging using LCL topology. IEEE Trans. Power Electron. 36(4), 3852–3867 (2021) 15. Baba, K., Miyaura, T., Nakamura, S.: Efficiency improvement of SIMO WPT using capacity control in addition to load control. In: 2022 IEEE/SICE International Symposium on System Integration (SII), Narvik, Norway, pp. 718–723 (2022)

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16. Liu, F., Yang, Y., Ding, Z., et al.: A multifrequency superposition methodology to achieve high efficiency and targeted power distribution for a multiload MCR WPT system. IEEE Trans. Power Electron. 33(10), 9005–9016 (2018) 17. Lu, L.: Research on the cross-coupling effect and the power distribution of multi-receiver MCWPT. Taiyuan University of Science and Technology, Shangxi, China (2019). (in Chinese) 18. Feng, P.: Tuning strategy research on magnetically coupled resonant WPT system. Chongqing University of Posts and Telecommunications, Chongqing, China (2017). (in Chinese)

Output Current Identification Based on the Kalman Filtering Algorithm for Magnetic-Coupling Excitation System Dongxiao Huang1(B)

, Xianhong Lin1,2 , Zequan Hong1,3 , Xinhong Yu1 , and Fengxiang Wang1

1 National Local Joint Engineering Research Center for Electrical Drives and Power

Electronics, Quanzhou Institute of Equipment Manufacturing, Hai xi Institutes, Chinese Academy of Sciences, Quanzhou 362000, China {dongxiao.huang,xinhong.yu,fengxiang.wang}@fjirsm.ac.cn, [email protected] 2 Fuzhou University, Fuzhou 350108, China 3 Fujian Key Laboratory of Intelligent Machining Technology and Equipment, Fujian University of Technology, Fuzhou 350118, China [email protected]

Abstract. Magnetic-coupling excitation system is one of the research highlights in the field of brushless Electrically Excited Synchronous Motor (EESM), which contains the primary energy emission device and a secondary receiving device that rotates synchronously with the motor rotor. Primary-side control estimation is widely applied in Wireless Power Transmission (WPT) system to detect the output current of the secondary device to reduce the weight of rotor and achieve the merit of communication-free. A magnetizing current estimation method based on the Kalman filter algorithm is proposed for a novel system combined with EESM and WPT. The proposed method adopts the Kalman filter algorithm to the magnetizing current estimation model, which eliminates the higher-order harmonics in the sampling of inverter current and transmitting coil current. In addition, the output current control is achieved by applying the PI controller. The simulation result of proposed system in Matlab/Simulink proves the enhancement of proposed method on the accuracy, the transient response speed and the tracking performance of magnetizing current estimation. Keywords: Wireless Power Transmission · Electrically Excited Synchronous Motor · Magnetizing Current Estimation · Kalman Filter Algorithm

1 Introduction With the development of electric vehicles, the electric motor has attracted significant attention as a sentient load. Especially, the Permanent Magnet Synchronous Motor (PMSM), faces many issues such as the demagnetization at high temperatures and the uncontrollable power generation during operation [1]. To circumvent such demerits, the Electrically Excited Synchronous Motor (EESM) is applied as the driving component © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 178–186, 2024. https://doi.org/10.1007/978-981-97-0873-4_19

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with the advantages of controllable rotor magnetic flux [2–4] and low demagnetization risk. In the categories of EESM rotor excitation, the brushed excitation structure is limited in applications due to the issues of wear and sparks on the brushes and collector rings [5]. On the meanwhile, the Wireless Power Transmission (WPT) technology is becoming a research highlight of the power electronics [6]. Therefore, the novel wireless EESM brushless excitation system is proposed by adopting the WPT technology [7, 8]. The principle of the proposed system based on the energy transmission via the electromagnetic field. The primary side of WPT system is fixed on the stator side while the secondary side is fixed on the rotor side. However, due to the rotation of the brushless excitation structure’s rotor with the motor, magnetizing current is difficult to be measured for the constant output control of secondary current, which is proposed to be estimated by sampling the primary current [9]. Shanghai Electric Power University proposed a novel online identification method for the key parameters of inductance and load in WPT systems based on the Unscented Kalman Filter [10]. By sampling the instantaneous voltage values on the primary side, real-time value of key parameters like inductance and load can be acquired. Chongqing University introduced an identification method for the response to the transient of the mutual inductance and load in the operation of MCR-WPT system, which is not suitable for the case that inductive load resistance is unstable while the accurate load parameter is required [11]. Tongji University proposed a novel method to establish the accurate current model of the unstable inductive load in secondary side, which also optimizes the current model by further analyzing the higher order harmonics of the inverter voltage signal [12]. In the estimation of the magnetizing current, the estimated value of the load current deviates significantly from the actual value due to the high-order harmonics in the inverter output current, which reduces the accuracy of the magnetizing current [13]. This paper proposed a magnetizing current estimation method based on the Kalman Filter Algorithm for the proposed system combined with EESM and WPT. By applying the Kalman Filter Algorithm to the optimization of the inverter current sampling, the high-order harmonics and Gaussian White Noise are eliminated, which improves the accuracy of the estimated value of magnetizing current and the performance of the output current PI controller.

2 System Configuration Analysis 2.1 Excitation Current Estimation Model This paper focuses on the magnetically coupled excitation system. Due to the fixation of the secondary receiving coil to the rotor end, which rotates as the motor operates, it is imperative to simplify the topology and circuit on the secondary receiving coil during system design. Consequently, the secondary side adopts a series topology. For this reason, during system design, an LCL-S topology structure is utilized. This topology boasts constant current characteristics for the transmitting coil and constant voltage output characteristics decoupled from the load on the receiving side. The WPT system structure, as shown in Fig. 1, comprises two parts: the primary input side and the secondary output side. The primary input side includes an inverter, compensation inductor, compensation

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capacitor, and transmitting coil. The secondary output side consists of a receiving coil, compensation capacitor, uncontrollable rectification, and excitation winding.

Fig. 1. Magnetically Coupled Excitation System

The equivalent circuit of the system is shown in Fig. 2. Here, U in represents the output voltage of the inverter. I in and I 1 denote the primary input side current and the transmitting coil current, respectively. L 1 and C 1 are the compensation inductance and capacitance on the primary input side, while L P signifies the inductance of the primary input side coil. L S symbolizes the inductance of the coil on the secondary output side, C 2 stands for the compensation capacitor, and M represents mutual inductance. I 2 denotes the current on the secondary output side, and RLe is the equivalent impedance of the excitation winding. 1

1

2

2

p

1 p

Fig. 2. System Equivalent Circuit

Based on the rectifier bridge, the equivalent load on the secondary output side is represented as: RLe =

8 ZLe π2

(1)

Where Z Le is the equivalent impedance of the excitation winding. Since the excitation current is independent of the load parameters, the equivalent impedance Z Le in this paper is formed by the series connection of inductance and resistance, simulating the inductive load of the motor for analytical research.

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According to the equivalent circuit and Kirchhoff’s Voltage Law (KVL), the system’s mathematical model is:         −jωM Uˆ in jωL1 ˆ jωLP + RP ˆ = Iin + I1 + (2) Iˆ 1 + RLe 2 RS + jωLS + jωC jωM Iˆ1 0 0 2 Here, Uˆ in , Iˆin , Iˆ1 and Iˆ2 represent vectors of voltages and currents. RP and RS signify the resistances of the primary input side coil and the secondary output side coil, respectively, and ω denotes the system’s operating angular frequency. 1 = 0. When the system operates at the resonant frequency, jωLS + jωC 2 ˆ ˆ From formula (2), the relationship between I1 and I2 can be derived as: Iˆ2 =

jωM Iˆ1 (RS + RLe )

(3)

Through formula (3), it’s evident that the secondary output side current Iˆ2 will change with variations in Iˆ1 and Z Le . Therefore, to achieve real-time output current control on the primary input side, using Kirchhoff’s Current Law (KCL), the expressions for currents Iˆin and Iˆ2 can be determined as: (jωLP + RP )Iˆ1 − jωM Iˆ2 Iˆin = Iˆ1 + 1/jωC1

(4)

Thus, the secondary side output current can be expressed as: Iˆin − jωC1 RP Iˆ1 Iˆ2 = ω2 MC1

(5)

Consequently, the excitation current IˆL can be represented by the primary side input parameters as: π π(Iˆin − jωC1 RP Iˆ1 ) IˆL = √ Iˆ2 = √ 2 2 2 2ω2 MC1

(6)

From formula (6), it is evident that the excitation current is independent of load characteristics. The process for estimating the excitation current is as follows: Acquire the primary input side currents Iˆin and Iˆ1 through current sampling. Inserting these into formula (5) yields the secondary output side current Iˆ2 , which, when applied to formula (6), provides an estimate of the excitation current. This method enables the estimation of the secondary excitation current using primary side information. 2.2 Optimization of Excitation Current Estimation Based on Kalman Filter Due to the high-order harmonics in the inverter output current, the estimation accuracy is affected. This paper proposes an optimization method for excitation current estimation based on the Kalman filter, which filters out the high-order harmonic current of the

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Fig. 3. Flow Chart of Excitation Current Control Based on Kalman Filter

inverter output, enhancing the estimation accuracy of the excitation current value IˆL . Combined with the primary control strategy for the output current, it achieves a constant current output for the secondary excitation current, as shown in Fig. 3. By sampling the primary input side current Iˆin and Iˆ1 parameters, the secondary load current can be estimated. Through formula (6), the feedback current value in the closed-loop system can be calculated. This value is then compared with the given load current value, and a constant current control on the secondary side is achieved through PI control. Based on this, a Kalman filter is added. After each discrete compensation calculation, the covariance matrix is updated before entering the next iteration process. The Kalman Filter Algorithm is a control algorithm based on state estimation. The algorithm formulas include the state prediction equation, error prediction equation, and state update equation. By observing the system input and output data, an optimal estimate of the state is made. State prediction equation: x(k|k − 1) = Fx(k − 1|k − 1) + Bu(k)

(7)

Where x(k|k − 1) represents the predicted state value at step k, A represents the state transition matrix, B represents the input matrix, and u(k) represents the control input at step k. Error prediction equation: P(k|k − 1) = FP(k − 1|k − 1)F  + Q

(8)

Where P(k|k − 1) represents the error prediction of the state at step k, and Q denotes the system noise covariance matrix. State update equation: ⎧   ⎪ ⎨ K(k) = P(k|k − 1)H /(HP(k|k − 1)H + R) x(k|k) = x(k|k − 1) + K(k)(z(k) − Hx(k|k − 1)) (9) ⎪ ⎩ P(k|k) = (I − K(k)H )P(k|k − 1) Where K(k) represents the Kalman gain, z(k) denotes the current Iˆin measurement value, H represents the measurement matrix, and R stands for the measurement noise covariance matrix.

3 Simulation and Analysis While the motor is operating, the winding resistance may change slightly due to heating during operation. Issues such as coil moisture, excessive dust and carbon compounds, and overheating aging can also cause slight changes in load resistance. Furthermore, the

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presence of back EESM during motor operation can also result in load variations. To verify the effectiveness of the estimation model proposed in this paper and the estimation accuracy, dynamic response, and tracking performance of the Kalman Filter Algorithm in the motor, a simulation system was built using Matlab/Simulink for comparative verification. Simulation parameters are shown in Table 1. Table 1. Electrical Parameters of the Proposed System Parameter

Value

Parameter

Value

Ui

24 V

C1

22 nF

f

1 MHz

C2

15 nF

LP

1.0047 µH

LS

0.005 

RP

0.0656 

RS

20 µH

L1

1 µH

M

1.1854 µH

3.1 Excitation Current Estimation With a given excitation current reference value of 2 A, a simulation comparing the actual current and estimation error waveforms during start-up with and without the Kalman Filter Algorithm was designed. The results are depicted in Fig. 4. In Fig. 4(a), without Kalman filtering, the actual excitation current stabilizes at 1.97 A, with an oscillation amplitude of the error around 0.75 A. In contrast, Fig. 4(b) shows that the proposed algorithm stabilizes the actual excitation current at 2.00 A, with the error’s oscillation amplitude around 0.66 A. This proves that the proposed method can effectively reduce error fluctuations.

1

E rr (A)

0 2 0

-1 0

0.01

0.02

2 1

0.04

0.05

0.06

0

(a) Estimation without Kalman filtering

-2

Err

0.10 0.05 0.00 -0.05 -0.10

1

-1

0.03 Time(s)

IL ILest

2.04 2.02 2.00 1.98 1.96

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0 2

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E rr (A)

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0.03 Time(s)

0.04

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(b) Kalman filter estimation

Fig. 4. Excitation Current Estimation Error

3.2 Output Load Impedance Change Working Condition To validate the impact of load changes on excitation current estimation, this paper designed a load change simulation with a variation range from 9  to 11 . The results

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are presented in Fig. 5. When the load R is set to 9 , 10 , and 11 , respectively, the system in Fig. 5(a) without Kalman filtering reaches a steady state in 11 ms, 12 ms, and 14 ms. In Fig. 5(b), with the addition of Kalman filtering, the system reaches a steady state in 10 ms, 11 ms, and 14 ms. As the load resistance increases, the time required for the system to stabilize also increases. Moreover, introducing the Kalman filter algorithm reduces the system stabilization time. Once the system stabilizes, the maximum absolute error of the load current in Fig. 5(a) is less than 0.05 A, with a relative error of 2.5%. In contrast, the proposed algorithm in Fig. 5(b) produces a maximum absolute error less than 0.03 A after stabilization, with a relative error of 1.5%, a relative reduction of 40%. The results demonstrate the capability of the proposed method to enhance estimation accuracy.

2

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Fig. 5. Comparison of Current Waveforms Under Load Changes

3.3 Excitation Current Sudden Change Working Condition With a given excitation current reference value of 2 A, a simulation comparing the actual current and estimation error waveforms during start-up with and without the Kalman filter Algorithm was designed. The results are depicted in Fig. 6(a), without Kalman filtering, the actual excitation current stabilizes at 1.97 A, with an oscillation amplitude of the error around 0.75 A. In contrast, Fig. 6(b) shows that the proposed algorithm stabilizes the actual excitation current at 2.00 A, with the error’s oscillation amplitude around 0.66 A, which proves that the proposed method is effective. 3.4 Simulate Back Electromotive Force Conditions To validate the effectiveness of the proposed algorithm under conditions where there is back EMF in an inductive load, the load uses a 10  resistor in series with a 3 mH inductor, and a 0-2 V DC source is used in series to simulate back EMF for verification. Figure 7 depicts the simulation results of the excitation current when back EMF undergoes step changes. When the back EMF jumps from 0 to 1 V and 1 to 2 V, the stabilization times without Kalman filtering are 7.85 ms and 10.91 ms, with steady-state errors of about 40 mA and 20 mA, respectively. With Kalman filtering, the stabilization times are 6.14 ms and 10.15 ms, with steady-state errors of about 10 mA and 50 mA. This proves that

Output Current Identification Based on the Kalman Filtering Algorithm IL

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1.8

1.78A

1.4 1.2 1

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6.21ms 2.00A

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(a) Estimation without Kalman filtering

8.23ms

1.80A

2.04 2.02 2.00 1.98 1.96

1.6 1.4

0.03 Time(s)

IL

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9.76ms 1.98A 9.95ms

IL (A)

IL (A)

2

185

0.01

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0.03 Time(s)

0.04

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0.06

(b) Kalman filter estimation

Fig. 6. Load Current Sudden Change

the proposed method, when inductive load has back EMF, can estimate the excitation current, and introducing the Kalman filter enhances control accuracy and response speed. 3

1V

1

0V

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0V

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1

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Fig. 7. Reverse Electromotive Force Sudden Change

4 Conclusion To address the excitation current estimation of magnetically coupled electrically excited synchronous motors and mitigate the effects of high-order harmonics, this paper proposes an excitation current estimation method based on the Kalman filter. Firstly, a mathematical estimation model linking the primary input side information to the secondary output side excitation current was established. Subsequently, by sampling information from the primary input side, including the current on the primary input side and the transmitting coil current, the excitation current is estimated through the estimation formula. Given that the inverter output current contains high-order harmonics, this introduces certain errors to the current estimation model. By incorporating the Kalman Filter Algorithm, the estimation model is optimized, filtering out high-order harmonics to enhance estimation accuracy. Ultimately, the effectiveness of the proposed method is validated through simulation results, demonstrating that it can enhance system control precision and dynamic performance.

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References 1. Maier, M., Parspour, N.: Operation of an electrical excited synchronous machine by contactless energy transfer to the rotor. IEEE Trans. Ind. Appl. 54(4), 3217–3225 (2018) 2. Sun, L., Kang, J., Liu, Y., Mao, Z., Zhong, Z.: Wireless power transfer based contactless excitation of electrically excited synchronous. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference, China, pp. 1091–1097 (2020). 3. Kuo, J., Gao, Q., Teng, Y., et al.: Speed sensorless model predictive control for load commutated inverter-fed electrically excited synchronous motor. Trans. China Electrotech. Soc. 36(01), 68–76 (2021) 4. Raminosoa, T., Wiles, R.: Contactless rotor excitation for traction motors. In: 2018 IEEE Energy Conversion Congress and Exposition, Portland, USA, pp. 6448–6453 (2018) 5. Fu, X., Jiang, Z., Lü, H., et al.: Review of the blushless excitation and torque density improvement in wound field synchronous motors. Trans. China Electrotech. Soc. 37(07), 1689–1702 (2022) 6. Xue, M., Yang, Q., Zhang, P., Guo, J., Li, Y., Zhang, X.: Application status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(8), 1547–1568 (2021) 7. Zhong, Z., Gou, Y., Lü, H., et al.: Research on electrically excited synchronous motor based on MCR-WPT. Motor Control Appl. 45(08), 39–44 (2018) 8. Fu, X., Qi, Q., Tan, L.: Design and analysis of brushless wound field synchronous machine with electro-magnetic coupling resonators. IEEE Access 7(2), 173636–173645 (2019) 9. Kang, J., Liu, Y., Sun, L., et al.: A reduced-order model for wirelessly excited machine based on linear approximation. IEEE Trans. Power Electron. 36(11), 12389–12399 (2021) 10. Cheng, Z., Zhang, Z., Sui, Q., et al.: Online identification of key parameters of secondary edges in underwater WPT system based on unscented Kalman filtering algorithm. Chinese Society for Electrical Engineering, China, pp. 1–14 (2023) 11. Hu, J.: Research on mutual inductance and load identification method and output control strategy for LCC-S type dual excitation MC-WPT system. Chongqing University, China (2022) 12. Kang, J., Liu, Y., Sun, L., et al.: A primary-side control method of wireless power transfer for motor electric excitation. In: 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA), Xi’an, China, pp. 2423–2428 (2019) 13. Qiao, Z., Wei, Z., Yang, Y., et al.: Influence analysis of traction current harmonic on receiving voltage of track circuit. China Railway, China, pp. 103–109 (2023)

A Passive Fractional-Order Capacitor to Realize Wide Region ZVS for Improving Efficiency in WPT System Houxuan Liu, Bing Cheng, and Liangzong He(B) Electrical Engineering Department, Xiamen University, Xiamen 361005, China [email protected]

Abstract. High frequency inverter is essential for wireless power transfer (WPT) system, of which the loss cannot be ignored. Thus, zero voltage switching (ZVS) should be realized to improve the transmission efficiency. The phase shift (PS) control of the inverter can achieve controllable output, while it is under a hardswitching state. Because of their higher degrees of freedom, fractional-order components received attention in WPT system. In implementation, the passive fractional-order capacitor (P-FOC) can adaptively achieve variable capacitance with order of 1 or –1. In this paper, the phase angle of P-FOC is controlled to lag behind the phase-shifting angle of inverter by 90°, which can adaptively maintain the ZVS of the inverter in a wide region. Compared with the switch controlled capacitor (SCC) or variable inductor (VI), the proposed P-FOC has a larger range of impedance matching and a simpler control scheme. Especially, when P-FOC and inverter share the same processor, there is no need for additional feedback circuits. Finally, the system is theoretical analyzed and experimental verified. Keywords: Wireless Power Transfer · Phase Shift Control · Zero Voltage Switching · Fractional-Order

1 Introduction Power can be transmitted from the transmitter to receiver via wireless power transfer (WPT) technology. Owing to its safety, reliability and convenience, it has been paid more attentions in aeronautic, astronautic and automobile industry [1–3]. The power loss in the high frequency inverter (HFI), including conduction loss and switching loss, accounts for a considerable proportion of the total power loss of the WPT system. The switching loss dominates mostly in the power losses of HFI part, especially under hard-switching state during the turn-on process [4]. Hence, zero voltage switching (ZVS) should be realized to improve the transmission efficiency. For WPT system, constant output is required under variable mutual inductance and load conditions. Many different control methods, including adding a dc-dc converter, frequency modulation or phase shift (PS) modulation, are proposed to keep the output constant. However, additional components in dc-dc converter will increase the system © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 187–194, 2024. https://doi.org/10.1007/978-981-97-0873-4_20

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cost and install space [5]. Wide range frequency regulation can lead to frequency splitting, which will bring unstable output [6]. By comparison, stable output can be realized by PS modulation without additional components. However, hard switching will lead to the reduction of transmission efficiency [7]. A lot of researches have been done for the realization of ZVS in PS WPT. The input impedance angle is adjusted by regulating the operation frequency to guarantee the realization of ZVS operation under PS modulation strategy [8]. However, the coupling efficiency will reduce due to the resonance tank on the secondary side being in a mistuning state [9]. Other researches focused on the regulation of input impedance angle by changing the network parameters, including variable inductance (VI) [10] or switch controlled capacitor (SCC) [11]. However, limited adjustment range and complex control scheme bring inconvenience in practical. The concept of the fractional-order capacitor (FOC) can be defined as [12] iCα = Cα

d α uCα dt α

(1)

where d α / dt α is defined as the fractional-order derivative and α is the order. Compared with traditional integer-order circuits, fractional-order circuits have higher degrees of freedom [13]. A passive fractional-order capacitor (P-FOC) has been proposed to achieve variable capacitance with order of 1 or -1, and the control scheme needs no closed-loop circuit [14]. Thus, this paper applied a P-FOC to realize wide region ZVS in PS WPT system for improving efficiency. By fixing the angle difference between the phase shift angle of the inverter and P-FOC to 90°, the ZVS operation of the inverter can be ensured in a wide region. Compared to existing schemes, the impedance matching range is expanded and simpler control strategy requires no feedback circuits.

2 Analysis of Phase-Shift Control Scheme in the Primary Side 2.1 Structure and Operational Principle The configuration of the WPT system based on a series-series (SS) topology is shown in Fig. 1. The DC input voltage V I is inverted into AC voltage uP by an inverter with switches Q1 – Q4 . In the secondary side, the voltage uS is rectified to DC voltage V O by the rectifier with a filter capacitor C f . The transmitting coil L P and receiving coil L S are coupled by mutual inductance M, wherein the resistances RSP and RSS respectively represent the coil losses. Meanwhile, the capacitors C P and C S are resonant with the coils L P and L S respectively and satisfied with ω2 L P C P = ω2 L S C S = 1. Controllable constant output under the variable load and mutual inductance is an important index in the WPT system. Taking constant current (CC) output as an example, the phase shifting modulation waveforms are shown in Fig. 2 and then the output current I O can be controlled.

A Passive Fractional-Order Capacitor to Realize Wide Region ZVS Q1

Q3

CP i P

Vin



uP

RSP



Q2

IO

D1 D3

M

iS

CS 

LP

LS

RSS

Q4

uS

Cf

189



VO

CS M IS

CP

IP

RL

UP

LP

LS

Req



RSP

D2 D4

RSS



Fig. 1. Structure and equivalent circuit of traditional PS WPT System.

Q1 Q2 Q3 Q4 uP

u P ,1

iP

t 2

Fig. 2. Switching waveforms and key output waveforms of the inverter in PS WPT system.

2.2 Circuit Analysis In Fig. 1, the equivalent PS WPT system is shown and the fundamental frequency equivalent voltage source U P can be expressed as [11] √ 2 2 θ θ Vin cos  (− ) (2) U˙ P = π 2 2 The KVL equations of transmitter and receiver can be given by ⎧ 1 ⎪ ⎪ ⎨ U˙ P = (jωLP + jωC + RSP )I˙P + jωM I˙S = RSP I˙P + jωM I˙S P 1 ⎪ ⎪ ⎩ 0 = (jωLS + + RSS + Req )I˙S + jωM I˙P = (RSS + Req )I˙S + jωM I˙P jωCS

(3)

The relationship between the current I O and phase shift angle θ can be derived as IO =

ωMVin cos(θ/2) ω2 M 2 + RSP (RSS +

8 R ) π2 L

(4)

When the load or mutual inductance changes, I O can be controlled by adjusting θ. The larger the angle θ, the lower the output current is. Then the current I P is ahead of the

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rising zero crossing of the voltage U P by an angle of θ /2, thus the ZVS of the inverter losses and brings higher switching losses.

3 Wide Region ZVS by a Passive Fractional-Order Capacitor 3.1 Concept of Fractional-Order Capacitor Before introducing the P-FOC, the concept of the FOC should be shown in this paper. Considering that the WPT system can be approximated as a sinusoidal steady-state system, the time domain expression of FOC can be changed to ZCα =

1 ωα Cα

1 π π cos( α) − j α sin( α) 2 ω Cα 2

(5)

where α is the order of FOC and C α is the capacitance of FOC. When α changes, the impedance of FOC can be realized arbitrarily, even negative resistance. To simplify the analysis, [−2, 2] can be chosen as the range of order α. 3.2 Implementation of Proposed Passive Fractional-Order Circuit The proposed passive fractional-order circuit is shown in Fig. 3. The structure of PFOC replaces the power supply with an energy-storage capacitor C V . The capacitor C V is connected with a LC filter after passing through the half-bridge inverter, and then connected in parallel with a capacitor C C . The LC filter consists of L F and C F , and meets ω2 L F C F = 1. Thus, only the fundamental frequency current is allowed to pass through. An extended region of ZVS will be implemented. The phase of switch Q5 is set to lag 90° behind switch Q4 as shown in Fig. 4. The turn-on time of switches Q5 and Q6 are set to half a cycle and complementary. The voltage of P-FOC can be expressed as √ 2  ˙ ˙ UV ϕ (6) UCα = UF = π In the proposed system, P-FOC is used as an adaptively variable capacitor with order of 1. When the angle of voltage U Cα is fixed, the inflow current I Cα must be 90° ahead of U Cα , and then the equivalent input impedance of the system has a unique solution. Thus the rise time of voltage uP and zero crossing point of current uP are consistent and the ZVS of the inverter can be achieved. In addition, when P-FOC and inverter share the same processor, there require no additional communication or feedback circuits due to the fixed angle of their control signals. It is worth noting that the voltage U Cα will also reach the certain voltage level by adaptively charging and discharging. 3.3 Analysis of Proposed Passive Fractional-Order Circuit The equivalent model of the proposed topology is shown in Fig. 5. The KVL equations of the primary and secondary sides need to be changed to ⎧ ˙ ⎨ UP = (jωLP − jXCα + RSP )I˙P + jωM I˙S (7) 1 ⎩ 0 = (jωLS + + RSS + Req )I˙S + jωM I˙P = (RSS + Req )I˙S + jωM I˙P jωCS

A Passive Fractional-Order Capacitor to Realize Wide Region ZVS

U CV

+

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+

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M CC

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+ uF -

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+

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+

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D4

Q5 , Q6

-

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I0

I0

I ref Fig. 3. Diagram of proposed fractional-order circuit.

Q1 Q2 Q3 Q4 Q5 Q6 uP

iP uF

u P ,1

90

u F ,1 (uC )

t

Fig. 4. Key waveforms of proposed system.

The equivalent impedance X Cα and DC output current I O can be expressed as XCα = ωLP − (RSP +

ω2 M 2 θ ) tan( ) RSS + Req 2

(8)

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C

IP UP

RSP

M IS LP

LS

CS

Req

RSS

Fig. 5. Equivalent circuit of proposed WPT system.

IO =

ωMVin cos3 (θ/2) ω2 M 2 + RSP (RSS + Req )

(9)

The impedance of the system is inductive and the impedance angle is θ / 2. The impedance range of proposed P-FOC can theoretically adaptively be (0, ωL P ). Thus, the ZVS region of the system has be expanded significantly. Although the introduction of P-FOC brings additional devices, the MOSFETs in P-FOC can achieve ZVS and the loss is low enough compared to the hard-switching of the inverter.

4 Implementation 4.1 Parameters Design For the LC filter, it is advisable to select L F and C F with a higher quality factor to filter out higher harmonics as much as possible. The energy storage capacitor C V can be selected as a microfarad level capacitor to provide a stable voltage. In order to realize the ZVS of P-FOC, the impedance of capacitor C C should be greater than the required impedance X Cα of P-FOC. The required impedance of P-FOC gradually decreases with the increase of phase shift angle θ, and C C can be selected as C C < C P . The experimental platform parameters built in this article are shown in Table 1. Table 1. Experimental parameters of the proposed system. Symbol

Value

Symbol

Value

V in

72 V

CV

120 µF

f

85 kHz

LF

112 µH

LP , LS

100.4 µH, 105.2 µH

CF

31 nF

RSP , RSS

0.2 , 0.2 

CC

31 nF

CS

33.5 nF

IO

1.6 A

4.2 Experimental Results The experimental results are shown in Fig. 6. The inverter achieves phase shifting operation in order to maintain a CC output in the proposed system. The voltage uCα of the

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proposed P-FOC lags behind the rising edge of the inverter output voltage uP by 90°. Thus, the zero crossing of current iP is synchronized with the zero crossing of voltage uP . It is worth noting that the current iP and voltage uCα are approximately sine waves in Fig. 6. This is because the impedance matching network is not in a resonant state, which will lead to an increase in higher-order harmonics.

uP

iP

uF uC

Fig. 6. Experimental oscillograms of the inverter and P-FOC.

As shown in Fig. 7, the hard-switching of phase shift control is solved in the proposed structure. Both the inverter and P-FOC have achieved ZVS, thus the feasibility of the proposed scheme has been confirmed.

u DS

ZVS

(a)

uGS

u DS

ZVS

uGS

(b)

Fig. 7. Enlarged experimental oscillograms of ZVS. (a) P-FOC. (b) Inverter.

5 Conclusion In this paper, a method for extending the ZVS region in PS-WPT is proposed for improving the efficiency. Existing P-FOC have adaptive variable capacitance with order 1 or −1 without additional auxiliary power supply. Compared with the switched controlled capacitor (SCC) or variable inductance (VI), P-FOC has a higher regulation range and a simpler control scheme. There requires no additional closed-loop control circuit when it shares the same processer with the inverter. The principle of proposed system is analyzed and experimentally verified.

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References 1. Covic, G.A., Boys, J.T.: Inductive power transfer. Proc. IEEE 101(6), 1276–1289 (2013) 2. Makhdoom, R., Maji, S., Sinha, S., Etta, D., Afridi, K.: Multi-MHz in-motion capacitive wireless power transfer system for mobile robots. In: 2022 Wireless Power Week (WPW), pp. 1–5. IEEE Press, Bordeaux, (2022). https://doi.org/10.1109/WPW54272.2022.9853940 3. Zhang, Z., Pang, H., Georgiadis, A., Cecati, C.: Wireless power transfer—an overview. IEEE Trans. Ind. Electron. 66(2), 1044–1058 (2019) 4. He, L., Xu, X., Chen, J., Sun, J., Guo, D., Zeng, T.: A plug-play active resonant soft switching for current-auto-balance interleaved high step-up DC/DC converter. IEEE Trans. Power Electron. 34(8), 7603–7616 (2019) 5. Jou, H.-L., Wu, J.-C., Wu, K.-D., Kuo, C.-Y.: Bidirectional DC–DC wireless power transfer based on LCC-C resonant compensation. IEEE Trans. Power Electron. 36(2), 2310–2319 (2021) 6. Jiang, Y., Wang, L., Wang, Y., Liu, J., Wu, M., Ning, G.: Analysis, design, and implementation of WPT system for EV’s battery charging based on optimal operation frequency range. IEEE Trans. Power Electron. 34(7), 6890–6905 (2019) 7. Li, Y., et al.: Analysis, design, and experimental verification of a mixed high-order compensations-based WPT system with constant current outputs for driving multistring LEDs. IEEE Trans. Ind. Electron. 67(1), 203–213 (2020) 8. Fang, Y., Pong, B.M.H.: Multiple harmonics analysis for variable frequency asymmetrical pulse width-modulated wireless power transfer systems. IEEE Trans. Ind. Electron. 66(5), 4023–4030 (2019) 9. Jiang, Y., Liu, J., Hu, X., Wang, L., Wang, Y., Ning, G.: An optimized frequency and phase shift control strategy for constant current charging and zero voltage switching operation in series-series compensated wireless power transmission. In: 2017 IEEE Energy Conversion Congress and Exposition, (ECCE), pp. 961–966. IEEE Press, Cincinnati (2017). https://doi. org/10.1109/ECCE.2017.8095889 10. Li, Y., et al.: Extension of ZVS region of series-series WPT systems by an auxiliary variable inductor for improving efficiency. IEEE Trans. Power Electron. 36(7), 7513–7525 (2021) 11. Tian, J., Hu, A.P.: A DC-voltage-controlled variable capacitor for stabilizing the ZVS frequency of a resonant converter for wireless power transfer. IEEE Trans. Power Electron. 32(3), 2312–2318 (2017) 12. Rong, C., Zhang, B., Jiang, Y., Shu, X., Wei, Z.: A misalignment-tolerant fractional-order wireless charging system with constant current or voltage output. IEEE Trans. Power Electron. 37(9), 11356–11368 (2022) 13. Jiang, Y., Zhang, B.: A fractional-order wireless power transfer system insensitive to resonant frequency. IEEE Trans. Power Electron. 35(5), 5496–5505 (2020) 14. Liu, H., He, L., Cheng, B., Li, L.: A passive fractional-order capacitor to realize zero angle phase input for wireless transfer system. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), pp. 3896–3901. IEEE Press, Hefei (2023). https://doi.org/10.1109/CIE EC58067.2023.10166459

Electric-Field Coupled Power Transfer System with Constant Current and Constant Voltage Output Based on Switchable Secondary Side of LCL-LLC/S Structure Li Ji(B)

, Jiaqi Zhang, Jianghong Zhang, and Fuchen Ge

College of Information Science and Engineering, China University of Petroleum, Beijing 102249, China [email protected], {2022216006,2019011617, 2021216007}@student.cup.edu.cn

Abstract. In the practical application of electric-field coupled power transfer (EC-WPT) technology, the battery type load requires the power supply system to provide constant current or constant voltage output under load changes and the function of instant switching between the two output modes. This paper proposes an electric field-coupled power transfer system with constant current/constant voltage output based on LCL-LLC/S topology with switchable secondary side, and the system automatically enters the low power state when the battery is charged and removed. Firstly, the basic structure and switching strategy of the system are introduced, and the equivalent model of the system is set up. Then the principle of constant current/constant voltage and load adaptive is analyzed, and the parameter conditions and optimal switching point of the system are derived, and the parameter design method of the system is given. Finally, a simulation model is built to verify the feasibility and reliability of the proposed EC-WPT system’s constant current/constant voltage output characteristics and its parameter design method. Keywords: Wireless power transfer · EC-WPT system · Constant current output · Constant voltage output · Resonant network

1 Introduction Wireless Power Transfer (WPT) technology is a combination of modern power electronics technology, circuit theory and modern control technology, using magnetic field, electric field, microwave and other carriers to achieve wireless transfer of electric power. The current commonly used wireless power transfer technology is mainly magnetic field coupled wireless power transfer technology. Compared to the magnetic field coupled method, EC-WPT technology has the advantages of low cost, light weight and low eddy current loss. At present, domestic and foreign researchers have carried out various researches on EC-WPT technology and achieved rich results [1, 2]. Nowadays, WPT technology is mostly used for lithium battery or lead battery power supply. The charging © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 195–203, 2024. https://doi.org/10.1007/978-981-97-0873-4_21

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process of the battery consists of two stages: constant current stage and constant voltage stage [3, 4]. So the WPT system needs to have the function of switching between the two output modes. In literature [5–8], different compensation networks were designed to achieve a constant output of the system, but only a single constant current or constant voltage output could be achieved. [9] proposes a F-F/T structure compensation network to realize constant current/constant voltage output of the system, but the compensation structure was complicated. Based on LC-CLC resonant network, [10] proposes a method to achieve constant current/constant voltage output of the system by changing the frequency, but this method needs to change the output frequency of the inverter, so it needs to add the communication process between the primary and secondary sides. This paper propose an EC-WPT system with LCL-LLC/S secondary side switchable compensation topology, which realizes output mode switching between constant current and constant voltage by controlling two switches on and off. When the load changes in a large range, the system has a good constant current or constant voltage output characteristics, and the system can achieve ZPA in both constant current mode and constant voltage mode, which effectively improving the efficiency of the system. When the load is removed in the constant voltage mode, the system automatically enters the state of low-power consumption, realizes the self-adaptability of the load.

2 System Structure and Coupling Structure Analysis 2.1 System Structure and Working Principle The structure of the LCL-LLC/S secondary side switchable constant current and constant voltage EC-WPT system proposed in this paper is shown in Fig. 1. The primary and secondary parallel capacitors C p1 and C p2 are used to improve the transmission capacity of the coupling structure and reduce the inductance value of the compensation network. When S 1 and S 2 switch on, L s2 is short-circuited, L 2 is connected to the circuit, the system works in the constant current output mode of the LCL-LLC topology, the load changes within a certain range, and the current value flowing through the load basically remains basically constant. When S 1 and S 2 switch off, L s2 is connected to the circuit, L 2 is cut off, the system works in the constant voltage output mode of the LCL-S topology, and the voltage values at both ends of the load do not change with the load.

Electric-Field Coupled Power Transfer System

197

Fig. 1. LCL-LLC/S secondary side switchable constant current and constant voltage type ECWPT system.

2.2 Electric Field Coupling Structure Equivalent Model The coupling structure in Fig. 1 is composed of four metal plates, in which a coupling capacitor is formed between two plates on the transmitting side and two plates on the receiving side to form a power transfer loop. By cross-coupling between the four plates, a six-capacitance coupling model can be obtained, as shown in Fig. 2(a).

Fig. 2. Coupling structure equivalent model (a) Six-capacitance model, (b) Equivalent π model.

By simplifying the six-capacitive coupling model, the equivalent π model shown in Fig. 2(b) can be obtained, and the mathematical model is expressed as: ⎧ C24 C13 − C14 C23 ⎪ ⎪ ⎪ CM = C + C + C + C ⎪ 13 14 23 24 ⎪ ⎪ ⎨ C13 C23 + C14 C24 + 2C14 C23 (1) Cs1 = C12 + ⎪ C13 + C14 + C23 + C24 ⎪ ⎪ ⎪ ⎪ C C + C23 C24 + 2C14 C23 ⎪ ⎩ Cs2 = C34 + 13 14 C13 + C14 + C23 + C24 2.3 System Equivalent Circuit Analysis The equivalent capacitors C s1 and C s2 in the π model are connected in parallel with the capacitors C p1 and C p2 respectively, to form new equivalent capacitors C x1 and C x2 , and the mathematical relationship among the three is: Cx1 = Cs1 + Cp1 Cx2 = Cs2 + Cp2

(2)

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Fig. 3. Controlled source model equivalent circuit diagram of the system.

According to the analysis in [11], the π model of the coupling structure is transformed into the controlled source model of the coupling structure, the equivalent circuit diagram of the controlled source model of the system is shown in Fig. 3. In the equivalent circuit, the inverter and rectification processes in the system are omitted, and R is the AC equivalent resistance. Where the induced voltage sources V α and V β and the equivalent capacitors Cα and Cβ can be expressed as: V˙ α =

I˙s jω(Cx1 + Cx2 + Cα = Cx1 +

Cx1 Cx2 CM )

Cx2 CM Cx2 + CM

V˙ β =

I˙p jω(Cx1 + Cx2 +

Cβ = Cx2 +

Cx1 CM Cx1 + CM

Cx1 Cx2 CM )

(3) (4)

3 Analysis of System Output Characteristics Switches S 1 and S 2 are on, the system is in constant current output mode. When the system is in a resonant state, the relationship between the resonant frequency and the parameters of each component in the circuit is as follows:  C2 − Cβ 1 1 1 = =√ = (5) ω= √ L L1 C1 L C (Lp − L1 )Cα s1 C2 Cβ 2 2 The current gain GVI and input impedance Zin-CC of the system in constant current mode are as follows:   Cx2 2 (Cx1 + Cx2 + Cx1  I˙out  ωC1 C2 CM ) = Z = (6) GVI =  in−CC Cx2 U˙ in  Cx1 + Cx2 + Cx1 ω2 C12 C22 R CM Switches S 1 and S 2 are off, the system is in constant voltage output mode. When the system is in a resonant state, the relationship between the resonant frequency and the parameters of each component in the circuit is as follows:  C2 + Cβ 1 1 (7) = = ω= √ C2 Cβ (Ls1 + Ls2 ) L1 C1 (Lp − L1 )Cα

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The voltage gain GVV and input impedance Zin-CV of the system in constant voltage mode are as follows:   Cx2 2 (Cx1 + Cx2 + Cx1  U˙ out  C1 CM ) = Z = R (8) GVV =  in−CV Cx2 U˙ in  Cx1 + Cx2 + Cx1 C12 CM It can be seen from Eq. (6) and (8) that the system can realize the constant current or constant voltage output characteristic independent of load, the input impedance of the system Zin-CC and Zin-CV has no imaginary part, the system has ZPA characteristic in both constant current output mode and constant voltage output mode. When the system works in the constant voltage output mode to supply power to the battery load, R tends to infinity if the load is removed after charging is completed, at this time the input impedance of the system is large according to Eq. (8), the output current of the inverter will quickly drop to a small value, and the system will automatically enter the state of low power consumption, that means the system has load adaptability.

4 System Working Mode Switching Point and System Parameter Design 4.1 System Working Mode Switching Point Design To protect battery loads, it is necessary to minimize the fluctuation of the output voltage and output current before and after the system switching mode, so GVI and GVV needs to meet the following conditions, R0 is the resistance of the load at the time of switching. GVI =

π 2 GVV 8R0

(9)

4.2 System Parameter Design In this paper, four square aluminum plates are used as the coupling structure parameter design. 3D Maxwell simulation software was used to simulate the coupling capacitors between the coupling structure, the simulation results were shown in Table 1. Table 1. Coupling structure simulation and equivalent capacitance value Simulated capacitance value (pF) Equivalent capacitance (pF)

C 12 = 3.05

C 13 = 36.32

C 14 = 2.25

C 23 = 2.24

C 24 = 36.40

C 34 = 3.05

C M = 17.06

C s1 = 5.29

C s2 = 5.29

According to the analysis of the third part, the relationship between the parameters of each component of the system and the parameters of the coupling structure such as

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capacitance, current gain and voltage gain is as follows: ⎧ GVI − ωGVV Cβ 1 GVV ⎪ ⎪ Ls1 = ⎨ L1 = ω2 G C L2 = ωG ω2 GVI Cβ VV 0 VI ⎪ 2GVV 1 1 1 ⎪ ⎩ Ls2 = Lp = 2 ( + ) ωGVI ω GVV C0 Cα Cx1 Cx2 GVI C0 = Cx1 + Cx2 + C1 = GVV C0 C2 = CM ωGVV

(10)

(11)

Fig. 4. Flowchart of system parameter design.

According to Eq. (2) and Eq. (4), when the coupling structure, current gain, voltage gain and operating frequency of the system are determined, the parameter value of the component in the circuit only depends on the size of the capacitors C p1 and C p2 . The parameter design flow chart of the system is shown in Fig. 4.

5 System Simulation Verification In order to verify the correctness of the constant current/constant voltage working characteristics and parameter design method of the system proposed in this paper, the corresponding simulation model is built based on the circuit structure shown in Fig. 1 with the help of MATLAB/Simulink software, the results of Table 1 are used for coupling structure parameters. The parameter design are carried out according to the process in Fig. 4, the theoretical calculation results are shown in Table 2. In this paper, the simulation system is set to switch from constant current output mode to constant voltage output mode when the load value reaches 60. In order to analyze the constant current and constant voltage operating characteristics of the system and the fluctuation of the output when the working mode is switched, three resistance

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Table 2. Design parameters of each component Parameter

Value

Parameter

Value

Parameter

Value

E dc /V

110

L 2 /μH

15.45

C 1 /nF

5.88

f /kHz

500

L p /μH

337.74

C 2 /nF

6.56

RL /

30~100

L s1 /μH

305.04

C p1 /pF

294.70

L 1 /μH

17.24

L s2 /μH

30.90

C p2 /pF

294.71

Fig. 5. System output simulation waveform (a) output current, (b) output voltage.

values 45, 60 and 100 are selected as samples to observe the changes of the output current and output voltage when the load changes and the working mode is switched. The output waveform of the system is shown in Fig. 5. At t 2 , the system switches from constant current output mode to constant voltage output mode, the system can quickly and stably switch the output mode. At t 1 and t 3 , the load changes, and the output current or output voltage basically remains constant after the load changes, so the system has good constant current and constant voltage output characteristics. Figure 6(a) shows the simulation waveform of inverter output current before and after the load cut off and access in constant voltage output mode. When the load is cut off at t 1 , the inverter output current rapidly drops, and the system works in a low power consumption state. When the load is access at t 2 , the inverter output current recovers. Therefore, the EC-WPT system proposed in this paper has good load adaptability. The curve of the system’s output power Pout and transmission efficiency η with the load RL is shown in Fig. 6(b). The system’s transmission efficiency can remain at above 80% in the range of 30 ~ 100 . Based on the above analysis, regardless of constant current or constant voltage output mode, the system has relatively high transmission efficiency.

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Fig. 6. (a) Inverter output current when load in and out at constant voltage mode, (b) System output power and transmission efficiency changes with load.

6 Conclusion At first, this paper put forward a LCL-LLC/S topology with switchable secondary side, which realizes the constant current or constant voltage output of the system and the conversion between the two output modes under the condition of load change by using switch, and the system has load adaptability under the constant voltage output mode. Then, the component parameter conditions of the system are deduced, and the system parameter design method is given. Finally, through MATLAB/Simulink software simulation, the feasibility and stability of the system are preliminarily verified.

References 1. Wang, Z., Zhang, Y., He, X., Luo, B., Mai, R.: Research and application of capacitive power transfer system: a review. Electronics 11(7), 1158–1181 (2022) 2. Yu, Z., Xiao, W., Zhang, B., Qiu, D.: Development status of electric-field coupled wireless power transmission technology. Trans. China Electrotech. Soc. 37(5), 1051–1069 (2022). (in Chinese) 3. Mai, R., Chen, Y., Li, Y., Zhang, Y., Cao, G., He, Z.: Inductive power transfer for massive electric bicycles charging based on hybrid topology switching with a single inverter. IEEE Trans. Power Electron. 32(8), 5897–5906 (2017) 4. Yao, R., Qu, X., Yu, J., Wang, G., Chen, W.: Three-coil wireless battery charger with selfadaptation to battery charging curve. Autom. Electr. Power Syst. 46(7), 170–177 (2022). (in Chinese) 5. Lian, J., Qu, X.: Design of a double-sided LC compensated capacitive power transfer system with capacitor voltage stress optimization. IEEE Trans. Circuits Syst. II-Exp. Briefs 67(4), 715–719 (2020) 6. Qing, X., Wang, Z., Su, Y., Zhao, Y., Wu, X.: Parameter design method with constant output voltage characteristic for bilateral LC-compensated CPT system. IEEE J. Emerg. Sel. Topics Power Electron. 8(3), 2707–2715 (2020) 7. Su, Y., Xie, S., Tang, C., Chen, L., Wu, X.: An electric-field coupled power transfer system with constant voltage output based on T-Pi mixed resonant circuit. Trans. China Electrotech. Soc. 33(8), 1685–1695 (2018). (in Chinese)

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8. Zhao, Y., Wang, Z., Su, Y., Qing, X., Wu, X.: Load adaptive technology of constant voltage electric-field coupled power transfer system based on T-CLC resonant network. Trans. China Electrotech. Soc. 35(1), 106–114 (2020). (in Chinese) 9. Su, Y., Xie, S., Wang, Z., Wu, X., Zhao, Y.: An electric-field coupled power transfer system with constant voltage and constant current output based on F-F/T changeable resonant circuit. Trans. China Electrotech. Soc. 34(6), 1127–1136 (2019). (in Chinese) 10. Su, Y., Yan, Z., Hu, H., Sun, Y., Liu, Z., Liu, S.: Electric-field coupled power transfer system with constant current/constant voltage output characteristics based on frequency switching. In: Proceedings of the Chinese Society of Electrical Engineering, pp. 1–13 (2023). (in Chinese) 11. Wang, Y., Zhang, H., Lu, F.: Review, analysis, and design of four basic CPT topologies and the application of high-order compensation networks. IEEE Trans. Power Electron. 37(5), 6181–6193 (2022)

Influence of Turn Number of Tesla’s Low-Voltage Coil on the Performance of Single-Wire Power Transfer System Xin Jin(B)

, Xiyou Chen, Jinhui Zhao, and Fengquan Yu

School of Electrical Engineering, Dalian University of Technology, Dalian 116024, China [email protected]

Abstract. In the single-wire power transfer (SWPT) system, electrical energy can be transmitted efficiently through only one wire over long distances. In this paper, under the structure of multilayer Tesla’s coil, the effect of the number of turns of the low-voltage coil (LVC) on the transmission performance of the system at different transmission distances is studied. Firstly, a circuit model of the SWPT system is built. Then, the effects of changing the number of turns of the LVC on various circuit characteristics such as input current, voltage gain and transmission efficiency are analyzed through the circuit model. Finally, at the 50 m experimental site, the power of 500 W can be delivered with an efficiency of 89.8% in the system with fewer LVC turns. After the number of turns is increased, the input current is reduced and the efficiency is improved. The SWPT system can transmit 5 kW at 5 km. Keywords: Single-wire power transfer · Transmission performance · Tesla’s coil · Number of turns

1 Introduction At present, two or more wires are required in existing power transmission methods. In the nineteenth century, wireless power transfer (WPT) was proposed by Nikola Tesla. Although WPT can get rid of the constraints of wires, the transmission performance of this technology drops significantly as distance increases. Therefore, single-wire power transfer (SWPT) has sparked interest among some researchers. SWPT was proposed by Nikola Tesla in 1897. In 2002, Strebkov used the SWPT system to transmit 20 kW power at 1.2 km [1]. [2] established a model of SWPT system and constructed an experimental prototype in 2017. When the Tesla’s coil works, a high voltage of 10,000 V is generated near the top conductor. By short-circuiting both ends of the high-voltage coil, the safety and efficiency of the system can be improved [3]. To reduce the sensitivity of transmission efficiency to distance, the traditional highfrequency power supply was replaced by an improved power supply [4]. To raise the transfer capacity of the system, a large-sized coil was produced, and a distributed parameter circuit model was built [5]. At 70 m, 300 W was transmitted with an efficiency of © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 204–212, 2024. https://doi.org/10.1007/978-981-97-0873-4_22

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42%. In [6], the theory of electromagnetic surface waves was used to reveal the working mechanism of a long-distance large-scale SWPT system. In an experiment of 200 m, 135 W was transmitted with an efficiency of 23%. For the purpose of improving system performance, a multilayer structure Tesla’s coil was fabricated, and an accurate circuit model was established [7]. In an experiment with a distance of 70 m, 1150 W power was transmitted with efficiency of 90%. Some researchers have applied SWPT systems in special scenarios. SWPT can be used to power aerial platforms such as wireless communication balloons and fixedposition drones [8]. Since wireless sensor networks have the characteristics of flexible distribution and non-directionality, SWPT systems are used to power their batteries [9]. A capacitive WPT is constructed through a single-wire coupling interface to wirelessly charge electric vehicles, and an output power of 3.3 kW is achieved in SPICE software simulation [10]. When a capacitor is connected in series on a single-wire, the single-wire capacitive power transfer system is formed. This system can be used to transmit power across metal barriers [11]. In existing research, the SWPT system composed of Tesla’s coils has better transmission performance, and the number of LVC turns of will affect the performance of the system. Therefore, in this paper, a model of SWPT system is obtained, and transmission characteristics before and after the number of LVC turns are changed are analyzed. Experimental sites with transmission distances of 50 m and 5 km were set up, and the influence of the number of LVC turns on the transmission performance was studied at different distances.

2 SWPT System and Modeling The SWPT system can be seen in Fig. 1.

Fig. 1. SWPT system.

There is a Tesla’s coil on both the power transmitting side and the power receiving side. Tesla’s coil consisting of LVC and HVC is a magnetically coupled air-core resonant transformer that can convert low-voltage electrical energy into high-voltage electrical energy. For the purpose of improving efficiency, a multilayer structure is applied. The HVC is wound with seven layers on the coil bobbin, and the LVC is tightly wound on

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the outermost layer of the HVC. The top ends of the HVC on both sides are connected by an overhead line, and the bottom end is connected to the real soil. Based on the multilayer coil structure, this paper increases the number of turns of the LVC to study the impact of its changes on the transmission performance of the system. It is worth noting that in order to maintain a high coupling coefficient between the LVC and the HVC, the increased number of turns is connected in series with the original coil and wound on the outermost layer, so that the LVC forms a double-layer structure. The multilayer Tesla’s coil is the main part of the SWPT system, so the model of the coil should be gotten first. After the number of turns is changed, the HVC has a 7-layer structure and the LVC has a 2-layer structure. The model of the multilayer Tesla’s coil is depicted in Fig. 2. M d12 M d17 Rd1 * Ld1

us M d

Ls7

* Ld2 Rw7

Rd2

C67

*

M d11

C23

Ls2

Ls1

*

Ctt7

Rw2

Ctt2 Rw1

Ctt1

C12

M d27 M d22

*

M 12

M 27 M 17

M d21

Fig. 2. The model of Tesla’s coil.

In Fig. 2, Rd1 and Ld1 are the resistance and self-inductance of the original LVC. Rd2 and Ld2 are the resistance and self-inductance of the increased number of turns. Rw1 , Rw2 , …, Rw7 are the resistance of each layer of the HVC. The resistance value of the coil can be calculated from (1) and (2): sinh(2T) + sin(2T) cosh(2T) − cos(2T)   π 0.75 d di i T= 4 ddep p

Rw = Rwdc T

(1) (2)

where Rwdc is the DC resistance of the coil. di represents the inner diameter of the wire, ddep denotes skin depth. p is the turn spacing of coil. Ls1 , Ls2 , …, Ls7 are inductances of each layer of the HVC respectively, as: KN μ0 Nm2 Sc μlw + lc 3π 1 KN ≈ 1 + 0.45Dc /lc

Ls =

(3) (4)

where μ0 is the magnetic permeability in vacuum, Nm is the number of turns in each layer of the coil. Dc , Sc and lc denote the diameter, cross-sectional area, and length of the coil. lw denotes the wire length of each layer.

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In Fig. 2, M12 , …, M17 represent the interlayer mutual inductance of the HVC, respectively. Md11 , …, Md17 indicate mutual inductances between Ld1 and the HVC, respectively. Md21 , …, Md27 indicate mutual inductances between Ld2 and the HVC, respectively. The mutual inductance values are obtained through electromagnetic field simulation in this paper. C12 , C23 , …, C67 are the interlayer capacitance of the HVC, they can be expressed as the parallel connection of basic capacitors. A basic interlayer capacitor consists of cable insulation capacitor dCci , air gap capacitance dCair and insulating paper capacitance dChp connected in series. dCci , dCair and dChp are calculated as: εr1 ε0 lt dθ ln(do /di ) ε0 lt do dCair = dθ 2x(θ ) εr2 ε0 lt do dChp = dθ 2dhp dCci =

(5) (6) (7)

M 12

*

Rd1 * M d21 Ls2 Ld1 C M d22 23 us M d * M 27 Ld2 C67 M d17 Rd2 Ls7 M d27

Rw2 M 17

*

Rw1 C12

Rline

Cline 2

C12 Cline 2

M 12

Ls2

M 27 Ls7

Rw7

RG

Rw1

Ls1 *

Ls1

*

M d12

*

M d11

*

where εr1 and εr2 are the relative dielectric constants of cable insulation materials and insulation paper. ε0 is the dielectric constant in vacuum. dhp is the thickness of the insulating paper, x(θ ) ≈ [do (1 − cos θ ) + 1](mm). On the basis of model in Fig. 2, the SWPT system is modeled as detailed in Fig. 3. Rline is the resistor of single-wire, Cline represents capacitance between single-wire and earth. Through experimental measurements, the earth is equivalent to a series connection of resistance RG and inductance LG .

Rw2 C23 M 17

C67 Rw7

* Rd1 Ld1 M d RL * Ld2

uo

Rd2

LG

Fig. 3. Model of the SWPT system.

3 Circuit Characteristics Analysis The model of the system is used to analyze the impact of changes in the number of LVC turns on the system characteristics. For the convenience of description, the system with increased turns is called a two-layer system, and the system without an increase is called a one-layer system.

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The frequency characteristic curves of input impedance of the two systems are depicted in Fig. 4.

Fig. 4. Characteristic curve of input impedance. (a) Amplitude-frequency curve. (b) Phase frequency curve.

Changes in the number of LVC turns has little effect on the trend of the frequency characteristic curve. In Fig. 4(a), when the frequency is between 5–40 kHz, the input impedance amplitude has a maximum value point and a minimum value point. Increasing the number of LVC turns will increase the amplitude of the input impedance. In Fig. 4(b), the phase angle first decreases and then increases. There are two frequencies such that the phase angle is zero. Figure 5 is the frequency characteristic of voltage gain. The trends of the two curves are basically the same, but the voltage gain of the two-layer system at each frequency is smaller than that of the one-layer system.

Fig. 5. Characteristics curve of voltage gain.

The working frequency of the system is usually selected at the frequency when the input impedance phase angle is zero. To obtain the maximum output power, from Fig. 4 and Fig. 5, the working frequency of one-layer system is 19.1 kHz, the working frequency of two-layer system is 17.9 kHz. The load characteristic of input current and efficiency are shown in Fig. 6. In Fig. 6(a), the input current of the two-layer system is smaller than that of the onelayer system at various resistance values. Therefore, the copper loss in the system can be reduced. In Fig. 6(b), the efficiency of the one-layer system decreases significantly

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Fig. 6. (a) Load characteristics of input current. (b) Load characteristics of transfer efficiency.

with the increase of the resistance value. The efficiency of the two-layer system first increases and then decreases, and both are higher than those of the one-layer system.

4 Experimental Results 4.1 System Test Before Number of Turns Changes The SWPT system was constructed according to Fig. 1 to provide conditions for experimental research. A Tesla’s coil with a LVC of 1 layer with 21 turns and a HVC of 7 layers with a total of 966 turns was first produced. 500 W power can be transmitted at 50 m with 89.8% efficiency. At this time, the peak-to-peak value of the system input current is only 30 A. The 5 km experimental site is shown in Fig. 7. When the load is 25 incandescent lamps connected in parallel, 500 W power can be transmitted with efficiency of 80%, but the peak-to-peak input current is close to 100 A at this time. Compared with the experiment of 50 m, the increase in distance leads to an increase in the input current of the system, which in turn reduces the transmission efficiency.

Fig. 7. The 5 km experimental site.

For the purpose of analyzing the impact of load value on transmission performance, the number of incandescent lamps is changed. When the input voltage is constant, the curves of input current and output power are described in Fig. 8. Since the incandescent

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Fig. 8. Variation of input current and output power with load in the one-layer system.

lamps are connected in parallel, the load value is inversely proportional to the number of incandescent lamps in the load. It can be seen from Fig. 8 that the input current will decrease as the load decreases. When the number of incandescent lamps is five, the peak-to-peak input current is close to 90 A, but the output power at this time is only 110 W. Although the increase in the number of incandescent lamps can reduce the input current, it does not increase the output power. 4.2 System Test After Number of Turns Changes The LVC is increased from one layer of 21 turns to two layers of 39 turns here. When the number of incandescent lamps changes, the curves of input current and output power are depicted in Fig. 9. After the number of turns increases, the input current still decreases as the load decreases. However, compared with Fig. 8, the output power has been significantly improved.

Fig. 9. Variation of input current and output power with load in the two-layer system.

The experimental results with an output power of 5 kW are shown in Fig. 10. Figure 10(a) is the waveforms on the transmitting side. It can be seen that the output voltage and output current of the inverter are in the same phase. When the load is 25 incandescent lamps, the curves of efficiency and load resistance changing with output power are shown in Fig. 10(b). The highest efficiency is 89%, and the average efficiency is about 86%. After the number of turns increases, the input current of the system decreases significantly, which can further improve the output power and efficiency.

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Fig. 10. Experimental results at 5 km. (a) Waveforms on the transmitting side. (b) Curves of efficiency and load as a function of output power.

When the distance is 5 km, the RMS values of the single-wire current on the transmitting side and the receiving side are simultaneously measured at different frequencies, as shown in Fig. 11. The currents on both sides are not completely equal. This is caused by Cline . Changes in frequency will change the capacitive reactance, which in turn affects the current on the capacitor branch, causing the current on the transmitting side and the receiving side to deviate with frequency.

Fig. 11. Currents of single-wire.

5 Conclusions The effect of changes in the number of low-voltage coil turns in multilayer Tesla’s coils on the performance of SWPT systems is studied in this paper. When the number of LVC turns is small, the SWPT system can transmit 500 W power with an efficiency of about 90% within a hundred meters. However, when the transmission distance increases to 5 km, the input current increases significantly at the same output power, reducing the transmission efficiency. When the number of LVC turns increases, the input impedance of the system increases and the voltage gain decreases at the same frequency. When transmitting the same power, the input current is reduced and the efficiency is improved. In the experiment with a transmission distance of 5 km, compared with the system without increase in turns, the output power of the system is greater. In the end, this system can transmit kilowatt-level power with an average efficiency of 86%.

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References 1. Strebkov, D.S., Nekrasov, A.I., Nekrasov, A.A.: Resonant methods for electric power transmission and application. Mach. Energ. J. Rural Prod. Res. 9(2), 37–43 (2018) 2. Chen, X., Chen, J., Li, G., Mu, X., Qi, C.: Electric-field-coupled single-wire power transmission — analytical model and experimental demonstration. In: 2017 International Symposium on Power Electronics (EE), pp. 1–6. IEEE Press, Serbia (2017) 3. Chen, X., Lan, Y., Qi, C., Mu, X.: Single-wire power transmission using shorted highvoltage coupling coils. In: IEEE 46th Annual Conference of the Industrial Electronics Society, pp. 3930–3935. IEEE Press, Singapore (2020) 4. Liu, G., Zhang, B.: Analytical model of a 25–50 m robust single-wire electric-field coupling power transfer system using a limiter. IEEE Trans. Circuits Syst. II: Exp. Briefs. 66(6), 978–982 (2019) 5. Li, T., Chen, X., Lang, Z., et al.: Modeling and analysis of single-wire power transfer system using distributed parameter resonant coil. In: IEEE Industrial Electronics and Application Conference, pp. 141–145. IEEE Press, China (2021) 6. Jin, X., Chen, X., Qi, C., et al.: Investigation on the electromagnetic surface waves for singlewire power transmission. IEEE Trans. Industr. Electron. 70(3), 2497–2507 (2023) 7. Jin, X., Chen, X., Qi, C., et al.: Modeling and construction of single-wire power transmission based on multilayer tesla coil. IEEE Trans. Power Electron. 38(5), 6682–6695 (2023) 8. Wang, S., Ludois, D.C.: A capacitively-coupled single-wire earth-return power tether for aerial platforms. In: 2022 IEEE Energy Conversion Congress and Exposition, pp. 1–7. IEEE Press, USA (2022) 9. Li, Y., Li, Y., Wang, R., et al.: Electromagnetic safety analysis on single wire power transfer system based on wireless sensor networks. Trans. China Electrotech. Soc. 37(04), 808–815 (2022). (in Chinese) 10. Muharam, A., Mostafa, T.M., Nugroho, A., et al.: A single-wire method of coupling interface in capacitive power transfer for electric vehicle wireless charging system. In: 2018 International Conference on Sustainable Energy Engineering and Application, pp. 39–43. IEEE Press, Indonesia (2018) 11. Zou, L.J., Hu, A.P., Su, Y.-G.: A single-wire capacitive power transfer system with large coupling alignment tolerance. In: IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 93–98. IEEE Press, China (2017)

Parameter Design for Power Maximization in Inductive Wireless Power Transfer Systems with Consideration of Frequency Splitting Yangxin Zheng(B) and Fan Feng(B) School of Ocean Engineering and Technology, Sun Yat-Sen University, Zhuhai 519000, China [email protected], [email protected]

Abstract. Wireless Power Transfer (WPT) is expected to have a significant positive impact on both industry and daily lives. However, the maximal load power is prone to be reduced due to excessive coupling coefficient, which results in frequency splitting phenomenon. This paper provides design guidelines for WPT systems to ensure the maximal output power operation. From the point of view of the load power, this paper establishes the mathematical model of the frequency splitting phenomenon first, creating the connection between frequency splitting and extreme points of load power. Then we deduce the relationship between the coupling coefficient and frequency splitting, a discriminant is proposed to check whether there is frequency splitting. Analytical solutions of splitting frequencies are derived by solving zero points in the derivative of the load power over the operation angular frequency. Finally, the maximal load power under different coupling coefficient is attained. The theoretical analysis is validated by simulation. Keywords: WPT · Load power · Frequency splitting · Over coupling

1 Introduction WPT has been a research hot spot in the last decade, and significant progress has been made. Owing to distinguished merit, which is able to transfer power wirelessly, WPT enables convenient and safe charging. Moreover, WPT has high-density and controllable output power, hence, it can be applied to power various electronic devices. At present, WPT are used to charge Electric Vehicles (EVs) [1], Autonomous Electric Vehicles (AEVs) [2], and Autonomous Underwater Vehicles (AUVs) [3, 4]. The performance of the WPT system is restricted by the parameters, which should be properly designed to reach the best performance. In [5], a two-coil model is analyzed to maximize the system efficiency. To achieve higher efficiency, the ratio of internal resistance of the source to the equivalent series resistance should be small as possible. And the ratio of the load to the equivalent series resistance should be large as possible. An optimized parameters design method is proposed in consideration of efficiency [6]. The proposed method synthetically considers charging current, capacitor voltage and inductor current, and quality factor to obtain optimal operation frequency range. The © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 213–221, 2024. https://doi.org/10.1007/978-981-97-0873-4_23

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analytical function of efficiency is derived based on mutual inductance coupling theory [7]. Some key parameters are simplified with Fourier series and linearization in order to analyze the optimal coil turns for maximum efficiency. In [8], the efficiency is improved by optimizing the parameters of coils, in this way, the AC loss is reduced and the inductance is increased. A negative-impedance converter is applied to an additional coil to improve the maximum load power in [9], for the reflected impedance could be eliminated by the negative coil. To reach the maximal load power, the mutual impedance is properly changed in different distance [10]. Most of existing literatures concentrate on parameters design to improve the efficiency, however, the maximal output power, i.e., load power is equally important. In practical situations, sufficient maximum output capability is necessary to drive the load. One of the most significant parameters which impact the load power is coupling coefficient. The load power is prone to be influenced by the coupling coefficient, which is essentially influenced by the frequency splitting phenomenon brought by over-coupling. On the one hand, if the designed coupling coefficient exceeds the critical value, the maximum value of the load power won’t occur at the resonant point and the practical load power will be lower than the designed value. On the other hand, the transfer distance might decrease in the practical operation, which also induces an increase in the coupling coefficient. In this paper, we focus on maximizing the load power while dealing with frequency splitting. In the first place, we establish the mathematical model of the frequency splitting by the derivative of load power over operation angular frequency. Based on the deduced quartic function, the relationship between the frequency splitting and the coupling coefficient is mathematically explained. By substituting known resonant point into the equation, the splitting frequencies are solved. Finally, a piecewise function is attained to show the relationship between the coupling coefficient and maximal load power. The theoretical analysis validated by simulation.

2 Modeling 2.1 Load Power The equivalent circuit of a typical WPT system based on S-S compensation is shown in Fig. 1. U˙ IN is the equivalent voltage source, C p (C s ) is the compensate capacitor, L p (L s ) is the inductor, R1 (R2 ) is the equivalent series resistance, k is the coupling coefficient, and RL is the load. Based on Kirchhoff’s Law, equivalent current I˙P and I˙S can be calculated as: • Ip

• Is

•

=

UIN (R1 + jX1 ) +

ω2 M 2 (R2 +RL +jX2 )

(1)

•

−j UIN ωM = (R1 + jX1 )(R2 + RL + jX2 ) + ω2 M 2

(2)

where X 1 and X 2 denote the reactance of the primary side and secondary side: X1 = (ωLp −

1 ) ωCp

(3)

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X2 = (ωLs −

1 ) ωCs

215

(4)

In this way, the load power could be calculated as: PL = Is2 RL =

2 ω2 M 2 R UIN L 2 2 2 (R1 (RL + R2 ) + ω M − X1 X2 ) + ((RL + R2 )X1 + R1 X2 )2

(5)

Fig. 1. Equivalent Circuit

2.2 Frequency Splitting When frequency splitting doesn’t occur, the function PL (ω) has one extreme point, i.e. resonant point ω0 . Three extreme points appear while frequency splitting occurs. Extreme points could be solved by finding zero points in derivative of PL (ω) over ω. When the derivative only has one zero point, the frequency splitting disappears. But if there are three zero points, the frequency splitting occurs. The derivative of PL (ω) over ω is calculated and set to zero. dPL =0 dω

(6)

To simplify the equation, the equivalent series resistance R1 and R2 are set to be zero. Thus, the ω in (6) could be calculated in: a

ω6 ω4 ω2 ω8 + b + c + d +3=0 ω08 ω06 ω04 ω02

(7)

The coefficients are: a = −(k 2 − 1)2

(8)

b=0

(9)

c = 6 − 2Cs2 R2L ω02 − 2k 2

(10)

d = 2Cs2 R2L ω02 − 8

(11)

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wherein, k is the coupling coefficient, whose value is between (0,1). To obtain an analytical solution of (7), the degree of (7) has to be reduced. The variable Q is set to be used to substitute for ω, where: Q=(

ω 2 ) ω0

(12)

After substituting (12) into (7), the octave equation is turned into a quartic equation. aQ4 + bQ3 + cQ2 + dQ + 3 = 0

(13)

The situation of the roots in (13) is determined by the discriminant Δ. Given the coefficient b is zero, Δ is calculated as:  = 6912a3 − 1152a2 c2 + 432a2 cd 2 − 27a2 d 4 + 48ac4 − 4ac3 d 2

(14)

If Δ is larger than zero, which means the Eq. (13) has two real roots and two complex conjugate non-real roots. And if Δ is smaller than zero, the roots of (13) are all real or none is. Given Eq. (12), the roots of (13) should be real and larger than zero to make sure the ω in (7) is meaningful. When the frequency splitting occurs, Eq. (7) has only three positive roots so that Eq. (13) has at least three positive roots, corresponding to a negative Δ. Inversely, Eq. (7) has only one positive root when there is no frequency splitting, corresponding to a positive Δ. Consequently, the critical coefficient k 0 could be calculated by setting Δ equal to zero. 2.3 Solutions of Extreme Points (ω)0 is the unique extreme point of PL (ω) without frequency splitting, as well as one of three extreme points with frequency splitting. Based on this, Eq. (13) has a root, whose value is one. To solve the other two extreme points, (13) could be modified as: a(Q − 1)(Q3 + uQ2 + vQ + w) = 0

(15)

where u, v, and w are the coefficients. Expand Eq. (15): aQ4 + (au − a)Q3 + (av − au)Q2 + (aw − av)Q − aw = 0

(16)

By comparing the coefficients between (13) and (16), u, v, w could be deduced as: u=1 v=

(17)

(a + c) a

(18)

3 −a

(19)

w=

Thus, the three remaining roots could be calculated by solving a cubic equation: Q3 + Q2 + vQ + w = 0

(20)

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where 1 − 3v Q1 = −  1 −  3 2 4(1−3v)3 +(−9v+27w+2)2 9v 27w 3 −2 + 2 + − +1 2 (21)   3 2 3 2 4(1−3v) +(−9v+27w+2) 27w − 9v +1 1 2 + 2 + − 2 − 3 3 1 − 3v Q2 = −  1 − √   27w 3 + (−9v + 27w + 2)2 /2 + 1 3 3 − 21 − 23i − 9v + + −4(1 − 3v) 2 2 (− 21 −

√

3i 2 )

 − 9v 2 +

27w 2

+



1 3 −4(1 − 3v)3 + (−9v + 27w + 2)2 /2 + 1 3

−

1 3 (22)

Q3 = −  3 − 21 + (− 21 +

√

3i 2 )

√

3i 2

 − 9v 2 +



− 9v 2

27w 2

+

+ 

27w 2

+



1 − 3v −4(1 − 3v)3

+ (−9v + 27w

+ 2)2 /2 + 1

1 3 −4(1 − 3v)3 + (−9v + 27w + 2)2 /2 + 1 3

−

1 − 3

1 3 (23)

Q1 is smaller than zero, so the final roots are Q2 and Q3 . The other two extreme points in (7) with frequency splitting can be calculated by Q2 and Q3 . The extreme points are ω0 , ω1 , and ω2 respectively. ω1 , ω2 are calculated in (24) and (25). The cases of the roots are shown in Table.1.  ω1 = ω0 Q2 (Q2 < 1) (24)  ω2 = ω0 Q3 (Q3 > 1)

(25)

Table 1. Roots in equations Δ

Q

ω

WPT system

>0

2real 2non-real

1pos 3neg 4non-real

no splitting

k0

3 Simulation Results

Table 2. Simulation Parameters Parameter

Value

Lp

6.0598 μH

Ls

12.74 7μH

U IN

28 V

Cp

3.74 nF

Cs

1.91 nF

f0

1.02 MHz

RL

10 

R1

0.02 

R2

0.02 

The critical coupling coefficient could be calculated according to (14). In the WPT system whose parameters are designed as Table.2, the critical value is 0.09256. To validate the accuracy of calculated ω1 and ω2 , we sweep ω from 0 to 7.4 × 106 and calculate the load power, then use MATLAB internal command search for the peaks, and finally compare the resulting ω values with the theoretical ω values proposed in the article. Figure 2 shows the comparison of searched frequency and calculated frequency. The searched frequencies are ω1 (Matlab) and ω2 (Matlab), they are searched by the command which is to find the local maximum point. The results in Fig. 2 indicate that the calculated splitting frequencies based on the derived theory are correct. Load power at three different frequencies under various coupling coefficient is simulated in Simulink, and is plotted in Fig. 3. While k exceeds the critical value, the frequency splitting phenomenon occurs and the maximum load power is obtained at ω1 , rather than ω0 .

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Fig. 2. Scatter diagram of frequencies

Fig. 3. Load Power versus Coupling Coefficient

4 Conclusion In this paper, we explain the frequency splitting phenomenon mathematically first, associating it with the extreme points of PL (ω). The existence of three extreme points indicates the presence of frequency splitting, while one extreme point indicates its absence.

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A discriminant is proposed to indicate the number of extreme points, by setting the discriminant to zero, the critical coupling coefficient can be derived. And it suggests that the coupling coefficient should be kept less than the critical value in order to avoid frequency splitting. With the theoretical analysis, splitting frequencies are obtained by solving the zero points of the derivative of the load power over the operation frequency after substituting the resonant frequency. Compare the searched frequency with the calculated frequency, the proposed model in this paper is proved. Without the frequency splitting, the maximal load power is attained at the resonant frequency, but with the frequency splitting, the maximal load power is attained at the ω1 , which is lower than the resonant frequency. It is shown that if maximum load power is desired, the coupling coefficient should be designed lower than the critical coefficient to avoid frequency splitting. Notwithstanding, when frequency splitting does occur, lower operation frequency, which can be calculated by analytical solutions, will lead to maximal load power. Acknowledgments. This work is supported by National Key Research and Development Program of China (Grant No. 2021YFC2800700), and by Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515110891).

References 1. Nama, J.K., Verma, A.K., Srivastava, M., Tomar, P.S.: An efficient inductive power transfer topology for electric vehicle battery charging. IEEE Trans. Ind. Appl. 56(6), 6925–6936 (2020) 2. Lee, C.H., Jung, G., Hosani, K.A., Song, B., Seo, D.-k., Cho, D.: Wireless power transfer system for an autonomous electric vehicle. In: 2020 IEEE Wireless Power Transfer Conference, WPTC, pp. 467–470. IEEE, Seoul (2020) 3. Teeneti, C.R., Truscott, T.T., Beal, D.N., Pantic, Z.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Ocean. Eng. 46(1), 68–87 (2019) 4. Lopes, I.F., Valle, R.L., Fogli, G.A., Ferreira, A.A., Barbosa, P.G.: Low-frequency underwater wireless power transfer: maximum efficiency tracking strategy. IEEE Latin Am. Trans. 18(07), 1200–1208 (2020) 5. Zhang, Y., Zhao, Z.: Frequency splitting analysis of two-coil resonant wireless power transfer. IEEE Antennas Wirel. Propag. Lett. 13, 400–402 (2014) 6. Jiang, Y., Wu, M., Yin, S., Wang, Z., Wang, L., Wang, Y.: An optimized parameter design method of WPT system for EV charging based on optimal operation frequency range. In: 2019 IEEE Applied Power Electronics Conference and Exposition, APEC, pp. 1528–1532. IEEE, Anaheim (2019) 7. Ye, Z.-H., Sun, Y., Wang, Z.-H., Tang, C.-S., Su, Y.-G.: An optimization method of coil parameters for wireless charging system of electric vehicle. In: 2016 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer, WoW, Knoxville, TN, USA, pp. 221–223 (2016) 8. Varghese, B.J., Smith, T., Azad, A., Pantic, Z.: Design and optimization of decoupled concentric and coplanar coils for WPT systems. In: 2017 IEEE Wireless Power Transfer Conference, WPTC, Taipei, Taiwan, pp. 1–4 (2017)

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9. Jeon, S.-J., Seo, D.-W.: Maximum output power improvement using negative coil in overcoupled WPT system. IEEE Microwave Wirel. Compon. Lett. 30(8), 810–813 (2020) 10. Namin, A., Chaidee, E., Tanang, S., Chaikam, K., Jansuya, P.: Mutual impedance adaptation for maximum power point tracking on LED TV wireless power transfer vary with distance. In: 2018 15th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, ECTI-CON, Thailand, pp. 501–504 (2018)

Adaptive Switching Control for Wireless Power Transfer Systems Based on Identification Shuaiqi Li1(B) , Zhifan Li1 , Xiaolong Wang1 , Peng Luo1 , Qiming Huang1 Qijun Deng1 , Jiangtao Liu2 , and Udaya Madawala3

,

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

[email protected]

2 Hubei University of Education, Wuhan 430072, China 3 The University of Auckland, Auckland, New Zealand

Abstract. This paper focuses on the application of switching control methods to wireless power transfer (WPT) systems. The method addresses the nonlinear perturbations introduced by the inverter by switching a set of controllers as well as weighting the outputs. Firstly, the internal model controllers (IMC) set is designed based on the nonlinear characteristics specific to WPT. Secondly, controller switching rules are developed to ensure the selection of the appropriate controller set across variations in phase shift angles. Finally, a controller set weighting function design scheme is explored, incorporating PID controllers with diverse tuning rules and dynamically adjusting their output-weighted multipliers to enhance closed-loop response. The effectiveness of the proposed method is validated by simulations and experiments, which further substantiate the performance and reliability of the method in practical applications. Keywords: Wireless Power Transfer · System Identification · Internal Model Control · Switching Controllers

1 Introduction Wireless Power Transfer (WPT) technology is widely applied in underwater equipment [1, 2], electric vehicles, industrial robots, etc., owing to less physical contact and remarkable characteristics such as reliability, position free, and robustness. Modeling and control of magnetic resonance coupling WPT have been intensively studied since 2007, when researchers from MIT used strongly coupled magnetic resonance theory to achieve 60 W of transmitted power at a distance of 2 m [3]. To extend the application of the WPT, many valuable modeling and control methods have been proposed. The analytical modeling method such as coupled mode and state space averaging is implemented in control-oriented WPT system modeling [4, 5]. Modular parallel multi-inverters are developed to increase the power of WPT which also requests higher demands on controller design [6]. Particularly, data-driven modeling of the WPT system is investigated, which enables an accurate system model directly from experimental input-output data before each run © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 222–234, 2024. https://doi.org/10.1007/978-981-97-0873-4_24

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[7–9]. A new modeling approach based on system identification is proposed for the WPT system with time lag, and the corresponding internal-mode model is designed [8]. Nevertheless, the design of controller and the identification of model are irrelevant to different objectives. What is more, the controller is designed only based on the transfer function at a specific working point. In summary, the effects of the inherent nonlinear characteristics of the WPT and the parameter identification errors are not considered when designing the controller. Additionally, the performance of the closed-loop system is seriously affected by the uncertainty caused by load variations. To achieve accurate and constant output performance even under disturbances of uncertainty, many advanced control methods are applied to the WPT system. Zhifan Li et al. [8] introduced the internal model control (IMC) into the WPT achieving a setting time of 16 ms at a power level of 10 kW. Xin Dai et al. [10] explored a standard H ∞ controller for a CLC magnetic resonance coupling WPT system with a settling time of about 50 ms. Liang Y et al. [11] proposed a H ∞ mixed sensitivity robust control approach to achieve a stable output of the voltage under load variations, and mutual inductance. However, the effect of the nonlinear disturbance of the system itself is not considered in the above control methods. Therefore, the robustness of the system cannot be guaranteed. Predictably, modeling and control techniques for WPT have great potential to promote improved device applicability. The major contributions of this paper can be summarized as follows. 1) To address the perturbations caused by the inherent nonlinearities of the system, a multi-controller output-weighting adaptation control method has been proposed. A controller group is obtained and used for coordinated control of the WPT system, based on the system identification. 2) To guarantee closed-loop performance throughout the entire operating range of the system, a controller switching and weighting rule based on the nonlinear characteristics of the WPT is developed. 3) In order to obtain the system model and the corresponding controller at a low cost, a controller-oriented modeling and controller design methodology is introduced.

2 WPT System Analysis 2.1 The Topology of WPT A classical series-series compensated WPT system shown in Fig. 1 is considered for analysis, where Vd and Id are the voltage and current of the inverter DC source, vC1 and vC2 are the voltages of capacitors C1 and C2 , v1 and v2 are the input and output voltages of the resonant tank, i1 and i2 are the input and output currents of the resonant tank, Ir is the root mean square (RMS) value of the rectifier bridge output current, and Io and Vo are the load voltage and current, respectively. The S-S topology WPT circuit diagram as shown in Fig. 1 has been deeply researched in [1–5]. Therefore, only the basic fundamentals of the WPT system are given: L1

di1 di2 = vab − vc1 + M − i1 R1 dt dt

(1)

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Fig. 1. A typical WPT circuit

L2

di1 di2 =M − vc2 − v2 − i2 R2 dt dt

(2)

C1

dvc1 = i1 dt

(3)

C2

dvc2 = i2 dt

(4)

dVo Vo = Ir − dt Ro

(5)

Cf

For the WPT system shown in Fig. 1, the following assumptions are made: Assumption 1: 1) The switches and diodes are ideal components. 2) The switching frequency is fixed. 3) Both the sending and receiving resonators are at or sufficiently close to the resonant state. Remark 1: The purpose of assumption 1) is to simplify the expression of the model without considering the power loss. The second assumption is imposed to ensure that the frequency components of v1 and v2 are fixed in the frequency domain when the phase angle is determined. The last assumption allows only the first harmonic to pass through the resonant tank, guaranteeing the accuracy of the first harmonic approximation. In this paper, we suppose that true circuit parameters are fixed when the system starts working, the parametric values of the WPT system are listed in Table 1.

2.2 Excitation Signal for WPT To identify the ARX model, a 4th-order pseudorandom binary sequence (PRBS) signal is required to excite the dynamics of the WPT system. The process to be identified must be sufficiently excited by the PRBS signal within the dynamic range of the process of interest to ensure the accuracy of the identification results. The PRBS signal is determined by three parameters, namely the amplitude A, the shift time λ and the period length N.

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Table 1. Main parameters of the Simulink diagram in Fig. 1. Parameter

Explanation

Value

fs

Switching Frequency

92 kHz

Vd

DC Voltage

300 V

L1

Self-inductance of Primary coil

110 μH

L2

Self-inductance of Secondary coil

110 μH

C1

Primary resonant capacitance

26 nF

C2

Secondary resonant capacitance

25.4 nF

M

Mutual inductance

41 μH

Cf

Filter capacitance

600 μF

RL

Load resistance

35 

Ts

Sampling time

1 ms

According to [12], the A is chosen to be ±0.02, and the λ is chosen to be λ ≤ Ti /5, where Ti is the time constant of the RC loop. According to the design method of the PRBS signal and the prior knowledge of the WPT system obtained in Table 1. Design a 4th-order PRBS sequence with a shift time of 0.002 s and the PRBS period length N is calculated by 2^4−1. 2.3 Identification of WPT Systems To design controllers with superior performance, an accurate model of the WPT system is required. Therefore, the stochastic recursive least squares (SRLS) method [13] is employed for system identification. The model of a WPT (i.e. G(z)) is considered as the autoregressive model with exogenous inputs (ARX) form, which is assumed to have the following linear regression form:     (6) A z −1 z(k) = B z −1 u(k) + e(k) where the measurement  z(k) of output   voltage is assumed to be contaminated by Gauss white noise e(k), A z −1 and B z −1 are numerator and denominator polynomials of transfer function of G(z). 2.4 Internal Model Control Framework In order to obtain a corresponding controller based on the identified model, the Internal Model Control (IMC) method is adopted in this paper. The primary objective of the IMC framework is to integrate a reference model within the control system and establish a parallel connection with the controlled object. The design of the controller is predicated upon the inverse of the reference model, while further fortifying the system’s resilience is achieved through the inclusion of a filter in the control system.

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The fundamental principle of IMC involves incorporating a reference model, which represents the desired dynamic behavior, into the control system. This reference model is connected in parallel with the actual controlled object and obtained by identification. The design of the IMC controller is based on the inverse of the reference model, thereby ensuring that the controller mimics the desired dynamic response. By utilizing the inverse model, the controller can generate control signals that drive the controlled object towards the desired behavior. IMC controllers are widely used in power electronics and have also been introduced into the WPT system control. Therefore, in this paper, only the basic principles of IMC controllers are presented. By approximating the time-delay term to a first-order Taylor expansion form, the IMC controller can be represented as: Gc (s) =

a 1 1 + b(ζ + τ ) b(ζ + τ ) s

(7)

where a, b are parameters to be designed, τ is the time delay, and ζ is the controller performance parameter set by the user.

3 Control Realization of the WPT System 3.1 System Identification and Controller Design To verify the accuracy of the linear system identification over the normalized working interval of α ∈ [0 1] (i.e.α ∈ [0π]rad), this range has been divided into nine subintervals with the same Lebesgue metric (see Table 2). Prior to the identification process, it is essential for the system to be in a balanced state. The input can be decomposed into a ∼ static value and a small signal static input, represented as α = α+ α. When α = 0.6, the static voltage output is VO = 95 V. To obtain meaningful identification data, the input ∼ α is chosen as the PRBS signal designed in Chapter 2. At the working point of α = 0.6. ∼

∼

The small signal static input α and corresponding output voltage VO is depicted in Fig. 2. The model G6 at the working point α = 0.6 is obtained using the SRLS method based on the input-output data shown in Fig. 2. Subsequently, the identification process described above is repeated within nine subintervals, and the models in these small sub-intervals are presented in Table 2. Simultaneously, the corresponding IMC controller C1 ∼ C9 is also designed in accordance with the models. 3.2 Multi-controller Output-Weighting Adaptation System To mitigate the disturbances caused by the inherent nonlinearity in the WPT system, a multi-controller output-weighting adaptation system is proposed in this paper. The complete control system is comprised of two components: the multi-controller coordination system and the output-weighting adaption system, represented by Fig. 3(a) and Fig. 3(b) respectively. Based on the models established for different equilibrium points in Table 2, we utilize the IMC method to design the corresponding controllers, resulting in the controller set

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0.03 0.02 0.01 0 -0.01 -0.02 -0.03

0

50

100

k

150

200

250

VO

k

Fig. 2. The blue line represents small signal perturbations in the input phase shift angle, and the orange color represents the corresponding output voltage.

Table 2. The identified model and the designed IMC controller. Working point

Phase Shift

System Model

Discrete IMC Controller

0.1

[0.05 0.15]

−13.35 G1 = z−0.3971

C1 = −0.009781z+0.0007473 z−1

0.2

[0.15 0.25]

−26.74 G2 = z−0.6048

C2 = −0.005879z+0.002922 z−1

0.3

[0.25 0.35]

−39.36 G3 = z−0.6742

C3 = −0.004199z+0.002544 z−1

0.4

[0.35 0.45]

−50.68 G4 = z−0.7021

C4 = −0.003324z+0.002149 z−1

0.5

[0.45 0.55]

−60.26 G5 = z−0.7151

C5 = −0.00282z+0.0018741 z−1

0.6

[0.55 0.65]

−67.88 G6 = z−0.7213

C6 = −0.002514z+0.001692 z−1

0.7

[0.65 0.75]

−73.87 G7 = z−0.7235

C7 = −0.002313z+0.001564 z−1

0.8

[0.75 0.85]

−69.16 G8 = z−0.7246

C8 = −0.002472z+0.001676 z−1

0.9

[0.85 0.95]

−71.81 G9 = z−0.7278

C9 = −0.002386z+0.001628 z−1

Cs = C1 , C2 , . . . , Cn . This set includes all the controllers required to stabilize the system throughout the entire operating range. The size of the set is determined by the Lebesgue metric. The operational flow of the control system is as follows: Firstly, the controller set Cs is established based on the pre-identified models obtained for the entire operating range prior to each run. Secondly, switching rules are designed based on the system’s nonlinear characteristics and the system voltage adjustment setpoints. After that, the selection of an appropriate controller group Cg = {Cg1 , Cg2 } for coordinated control

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is performed in real time according to the switching rules. Lastly, the output-weighted adaptive control is applied based on the controller group Cg .

g1

ĂĂ

Ă g2 g

g1

g2 g

Fig. 3. System control block diagram. (a) The coordinated control system of the controllers. (b) The output-weighted adaptive control system.

The structure diagram of the closed-loop system and the switching system is illustrated in Fig. 3(b). Where Vref represents the reference voltage setpoint for the WPT system, and Wt1-Wtn are the weighted functions for the output of the WPT controller group. The outputs of the controller group are weighted by the supervisory unit to appropriately distribute the capabilities of each individual controller, thereby enhancing the response performance of the closed-loop system. The analysis of system nonlinearity is a critical aspect in designing the switching rules for the switching system and the supervisory rules for the coordinated control system. In the case of WPT systems, the nonlinearity is primarily introduced by the inverter and rectifier bridge. In Assumption 1, it is assumed that all diodes in the system are ideal devices, implying the equality of input and output powers in the rectifier bridge, often approximated by the constant π2 /8 [14]. Consequently, this study primarily focuses on investigating the nonlinearity introduced by the inverter. To obtain a larger range of adjustable control angles as well as ZVS soft-switching phase margins, the control strategy known as optimal ZVS is applied in this paper. The relationship between the α and V0 can be succinctly expressed as g(α) = V0 . Since g(α) does not have any memory term, assuming g(α) is invertible, the relationship between the inverter output voltage and the phase shift angle can be obtained as h(V0 ) = α. By uniformly sampling the α within the specified range, the corresponding inverter output voltage is obtained, as shown in Fig. 4.

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d

Fig. 4. The nonlinear characteristics of WPT system.

To design the switching rules to handle different operating points of the WPT system, Vref and system nonlinearity are incorporated into the switching rules. When Vref changes, the system deviates from the working point. The impact of system nonlinearity on the closed-loop system becomes more pronounced. In this context, the switching function s1 is represented as:  s11 = h(V  O ) (8) s1 = s12 = h Vref Then controller set Cg is selected as the controllers from at s11 and at the s12 working point. The selected Cg is maintained for a minimum duration of 1 s to avoid frequent controller switching and preserve system stability. At this point, Cg has been obtained and updated, and it is introduced into the plant as shown in Fig. 3(b). As the α changes from 0.1 π, to 0.3 π, the system model undergoes corresponding changes. The actual operating characteristics of the system may lie between G1 and G3 . Therefore, by designing a controller set, the capabilities of each corresponding controller in the set are shared in a suitable manner, resulting in improved response performance of the closed-loop system compared to using a single controller alone. Afterward, when the system operates to a steady state and Vref does not change, the switching system is only related to the α. In this case VO ≈ Vref , the switching function is transformed from s1 to s2 and is denoted as: s2 = (u(t) + u(t − 1))/2

(9)

In such scenarios, Cg is selected to include two controllers from the neighboring working point around s2 . The supervisory unit is designed to evaluate dual weights that simultaneously emphasize the output of one controller while relaxing the output of another controller. Additionally, the mechanism for updating the weights must ensure the stability response of the closed-loop system. Therefore, the Lyapunov function is constructed using the square of the response error [15]. V =

1 2 e 2

(10)

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de ∂e de du = e u˙ = e u˙ V˙ = e˙e = e du dt du ∂u

(11)

And the total control signal is obtained as: u˙ = −Qe

∂e ∂u

(12)

where Q is a positive constant. The time derivative of the Lyapunov function, denoted ˙ is always negative semi-definite. as V,     ∂e ∂e ∂e 2 V˙ = e −ke = −k e ≤0 ∂u ∂u ∂u

(13)

˙ remains negative, V will decrease, i.e., V(t) ≤ V(0). Consequently, As long as V e2 may decrease, and the response error will decay to a small value in the steady state. The total control signal can be realized by distinctly collecting outputs of each IMC controller. The composite control signal can be achieved by separately collecting the outputs of each controllers in the group Cg . u = Wt1 u1 + Wt2 u2

(14)

Wt1 = w1 /(w1 + w2 )

(15)

Wt2 = w2 /(w1 + w2 )

(16)

The denominator of Wt1 and Wt2 must be nonzero and both of the w1 , w2 have to be merely positive. By taking the time derivative of u and rearranging the terms, we obtain: u˙ =

w˙1 w2 (u1 − u2 ) − w1 w˙2 (u1 − u2 ) (w1 + w2 )

2

+

w1 w2 (u˙1 + u˙2 ) + w12 u˙1 + w22 u˙2 (w1 + w2 )

2

∂e ∂u (17)

= −Qe

The parameter tuning law is reformed into the integral type as below [15]:  t

(w1 + w2 )2 ∂e e w1 = −k dt + w1 (0) 0 w2 (u1 − u2 ) ∂u t   1 w1 w2 (u˙1 + u˙2 ) + w12 u˙1 + w22 u˙2 dt + w2 (0) w2 = 0 w1 (u1 − u2 )

(18)

(19)

where u˙1 and u˙2 are the differentials of u1 and u2 , w1 (0) and w2 (0) are the initial values of w1 and w2 , both set to 0.5.

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4 Simulation Results and Discussion Using MATLAB (2021a), the parameters shown in Table 1 and the controllers depicted in Table 2 are employed to conduct simulations. Specifically, the scenario of switching function s1 is simulated. In the vicinity of the operating point α = 0.55, the system load switches from 50  to 35  while maintaining a constant desired voltage value. Consequently, the switching function s2 is activated, leading to the transition of the operating point from α = 0.54, to α = 0.44,. The simulation results are presented in Fig. 5, where Fig. 5(a) illustrates the waveform of voltage variation during the load shedding, and Fig. 5(b) shows the corresponding change in α. It can be observed that the controllers exhibit adaptive and weighted outputs around the new operating point, resulting in a system settling time of less than 15 ms.

35 1

Fig. 5. Signals in Simulation during load shedding. (a) The blue line is output voltage waveform with load shedding, while the red line is reference voltage. (b) The control signal waveform with load shedding.

In the case of RL = 35 , the Vref are modified for the switching system using switching function s1 to select the appropriate group in the controller set. The controllers for operating points Vref = 100 V and Vref = 240 V are used to construct the controller group. Figure 6 illustrates the simulation waveforms under a step change in Vref , where Fig. 6(a) represents the voltage variation waveform and Fig. 6(b) shows the corresponding change in the α. The controller group demonstrates adaptive and weighted outputs, resulting in a system settling time of less than 15 ms. These simulation results further confirm the effectiveness of the proposed methodology. The proposed control method has been implemented on a WPT laboratory prototype. As shown in Fig. 7 an S-S compensated WPT prototype is settled. The prototype consists of a DC source, a full-bridge inverter, resonant coils, resonant capacitor banks, a rectifier, and a resistive load on the receiving side. In particular, an ARM and FPGA are used to run the control program and generate the precise MOSFET control signals, respectively, and the high-speed communication between them is performed by CAN protocol. Both resonant coils were made by winding 9 turns of Litz wire. The number of strands in the stranded bundle is chosen to be 3000 to reduce the inductive resistance and improve the quality factor of the coils.

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Fig. 6. Signals in Simulation during voltage step. (a) The blue line is output voltage waveform with voltage step, while the red line is reference voltage. (b) The control signal waveform with voltage step.

VZLWFK

Fig. 7. The prototype of the WPT system

Fig. 8. Experimental output voltage signal. (a) The output voltage waveform in load shedding experiment. (b) The output voltage waveform in voltage step experiment

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The experimental results are presented in Fig. 8. Figure 8(a) shows the load shedding experiment where the load abruptly changes from 50  to 35 , and the settling time is approximately 50 ms. Figure 8(b) displays the voltage step experiment where the load voltage undergoes a step change from 100 V to 130 V, and the settling time is also around 50 ms. However, due to factors such as communication delay and other influencing factors in the system, there may be some discrepancies between the experimental results and the simulations. Nevertheless, both sets of experiments demonstrate the stability of the system using the proposed control method, thereby validating its feasibility.

5 Conclusion This paper proposes a multi-controller output-weighted adaption system to address the disturbances caused by the inherent nonlinearity in the WPT system. By utilizing a simplified model obtained through identification, the complexity of modeling and controller design is reduced. The proposed approach incorporates a set of multi-controller selection and weighting rules to ensure robust performance at different working points. Simulation and experimental results demonstrate the effectiveness of the proposed method in improving system performance and stability.

References 1. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. IEEE Trans. Industr. Electron. 66(2), 1044–1058 (2018) 2. Kurs, A., Karalis, A., Moffatt, R., et al.: Wireless power transfer via strongly coupled magnetic resonances. Science 317(5834), 83–86 (2007) 3. Swain, A.K., Devarakonda, S., Madawala, U.K.: Modeling, sensitivity analysis, and controller synthesis of multipickup bidirectional inductive power transfer systems. IEEE Trans. Industr. Inf. 10(2), 1372–1380 (2014) 4. Hata, K., Imura, T., Hori, Y.: Dynamic wireless power transfer system for electric vehicles to simplify ground facilities-power control and efficiency maximization on the secondary side. In: 2016 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1731– 1736. IEEE (2016) 5. Aditya, K., Williamson, S.: Linearization and control of series-series compensated inductive power transfer system based on extended describing function concept. Energies 9(11), 962 (2016) 6. Deng, Q., Wang, Z., Chen, C., et al.: Modeling and control of inductive power transfer system supplied by multiphase phase-controlled inverter. IEEE Trans. Power Electron. 34(9), 9303– 9315 (2018) 7. Chen, F., Young, P.C., Garnier, H., et al.: Data-driven modeling of wireless power transfer systems with multiple transmitters. IEEE Trans. Power Electron. 35(11), 11363–11379 (2020) 8. Deng, Q., Li, Z., Liu, J., et al.: Data-driven modeling and control considering time delays for WPT system. IEEE Trans. Power Electron. 37(8), 9923–9932 (2022) 9. Li, Z., Deng, Q., Chen, F., et al.: Receding horizon D-optimal input design for identification of wireless power transfer systems. IEEE J. Emerg. Sel. Top. Power Electron. (2023) 10. Dai, X., Tang, C., Sun, Y., et al.: Investigating a H∞ control method considering frequency uncertainty for CLC type inductively coupled power transfer system. In: 2011 IEEE Energy Conversion Congress and Exposition, pp. 2022–2027. IEEE (2011)

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11. Liang, Y., Sun, P., Wu, X., et al.: H∞ robust control for ICPT system with selected weighting function considering parameter perturbations. IEEE Trans. Power Electron. 37(11), 13914– 13929 (2022) 12. Ljung, L.: System identification. Signal analysis and prediction, pp. 163–173. Birkhäuser Boston, Boston, MA (1998) 13. Young, P.C.: Recursive Estimation and Time-Series Analysis: An Introduction. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-21981-8 14. Deng, Q., et al.: Wired/wireless hybrid charging system for electrical vehicles with minimum rated power requirement for DC module. IEEE Trans. Veh. Technol. 69(10), 10889–10898 (2020) 15. Sangtungtong, W., Dadthuyawat, W.: The two parallel PID controllers with their outputweighting adaptation. In: 2013 10th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, pp. 1–5. IEEE (2013)

Frequency Characteristics Analysis of Wireless Power Transfer System in Seawater Weiyu Xu, Liming Shi(B) , and Zhenggang Yin Key Laboratory of Power Electronics and Electric Drive, Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China {xuweiyu,limings}@mail.iee.ac.cn.com

Abstract. Inductively coupled wireless power transfer (ICWPT) has become an effective solution for underwater power transfer. Since there is no direct electrical connection, safety hazards such as cable aging, leakage, and short circuit can be avoided, and the reliability, flexibility, and sealing performance of underwater equipment charging are improved. Although the ICWPT in air has been extensively studied, its transmission characteristics in seawater are still unclear. This paper first discusses the parameter changes when the transmission coil is placed in seawater, then mathematically derives the output characteristics of the series-parallel compensation network, primarily analyzing the system’s frequency response. Finally, an experimental platform is built to verify the frequency characteristics of the wireless power transfer (WPT) system in seawater. Frequency splitting and frequency offset phenomena in over coupled regime are analyzed. Keywords: Wireless Power Transfer · Coil in Seawater · Series-parallel Compensation · Frequency Characteristics

1 Introduction In the 21st century, inductively coupled wireless power transfer (ICWPT) has become an effective solution for underwater power transfer [1–3]. Since there is no direct electrical connection in this transmission technology, safety hazards such as cable aging, leakage, and short circuit are avoided. Meanwhile, the reliability, flexibility, and sealing performance of underwater equipment charging can be improved [4–7]. Reference [8] presents the use of underwater WPT for a data logger. The system consists of two circular coils with a diameter of 18 cm and achieves 70% efficiency with a coil gap of 1 cm in the frequency range of 295–555 kHz. Reference [9] discusses the development and implementation of an induction-based underwater wireless power transfer system for unmanned underwater vehicles. Reference [10] designs a UWPT system using ferrite-core coils to power an underwater detector and a 40 W light. Although wireless power transfer has been extensively studied in air, its application in seawater still faces numerous challenges. The seawater environment is complex and involves variables such as salinity and temperature, which may lead to the change in the characteristics of the coupling coil and the compensation network. This paper first © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 235–246, 2024. https://doi.org/10.1007/978-981-97-0873-4_25

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analyzes the parameter changes when the transmission coil is placed in seawater, then derives mathematically the frequency characteristics of the series-parallel compensation network. Based on the experimental platform in our lab, the frequency splitting and frequency offset in over coupled regime of WPT system in seawater are analyzed.

2 Parameter Changes of the Coil in Seawater As presented in Table 1, it illustrates a comparison of various media characteristics. While the magnetic permeability of seawater is similar to that of air, its electrical characteristics are quite different. The conductivity of seawater is between 4–4.81 s/m, and the relative permittivity is about 81. Table 1. Comparison of different media characteristics. Media

Relative permittivity

Relative permeability

Conductivity

Air

1.0006

1

0

Seawater

81

0.999991

4

The electrical properties of seawater can lead to variations in the parasitic effects of coupling coils. In the following study, the coil with Litz wires is shown as in Fig. 1, and the parameters are shown in Table 2.

Fig. 1. A coil made by winding Litz wires.

2.1 Self-inductance and Mutual Inductance of the Coil in Seawater The expression for the electric field of a single turn coil is obtained as follows [11]: jωμRI E1 = − 2

∞ 0

λ J1 (λR)J2 (λρ)e−u|z| d λeϕ u

(1)

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Table 2. Coil parameters for simulation. Parameter

Value

number of turns

15

Inner radius/mm

33

outer radius/mm

75

line width/mm

3

distance/mm

12

where J1 represents the first-order Bessel function of the first kind. R denotes the radius of the coil, and I is the root mean square (RMS) value of the current i(t) flowing through a single-turn coil. At the frequency of 100 kHz, the coil radius of 0.1 m and the 1 A current, the amplitude and phase of the electric field intensity in air and seawater respectively are plotted along the direction of the transmission distance (z direction) in Fig. 2. 0.5

0.4

E phase, air

-90.5 E phase, seawater

0.3

-91.0 0.2

E amplitude, air

E phase/°

E amplitude (V/m)

-90.0

-91.5 0.1

E amplitude, seawater -92.0

0.0 0.025

0.050

0.075

0.100

z/m

Fig. 2. The amplitude and phase of electric field intensity in seawater and air.

The induced voltage in the secondary coil in seawater can be obtained by:  Esea dl Vsea =

(2)

coil

where, N represents the number of turns of the coil, and the mutual inductance is expressed as the ratio of the induced voltage in the secondary coil to the total current in the primary coil: Msea =

Vsea jωI

(3)

From Fig. 2, it can be seen that there are differences in the amplitude and phase of the electric field in air and seawater. At low frequencies, the amplitude changes are not

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significant. The phase in seawater is less than −90°, while the phase of electric field intensity in air is always equal to −90°. Therefore, compared with mutual inductance in air, the expression for mutual inductance in seawater is written as follows. Msea = Mair · G

(4)

Here, an additional loss factor G has been introduced, and its expression is G = ke−jϕ . 0 < k < 1 represents a decrease in amplitude, e−jϕ represents the delay in phase ϕ = ϕair − ϕsea . The frequency is set 100 kHz, and the parameters of the primary and secondary coils are completely consistent. Through simulation and measurement, the parameters of the coil in air and seawater are listed in Table 3. It can be seen that the value changes of self-inductance and mutual-inductance are not significant in different media. Table 3. Coil parameters in air and seawater. Parameter

Self-inductance/μH

Mutual inductance /μH

Simulated value in air

93.23

51.84

Measured value in air

93.45

51.5

Simulated value in seawater

93.1

51.37

Measured value in seawater

93.36

51.12

2.2 Capacitance of the Coil in Seawater Due to the high permittivity and high conductivity in seawater environments, two conductors will behave capacitively when a potential difference exists between them. The impedance of single coil and double coil are measured respectively in air and seawater by LCR analyzer to observe the change of its self-resonant frequency. The results are displayed in Fig. 3. The self-resonant frequency of the coil in air is 2.225 MHz, while in seawater it is 2.0642 MHz. It is easy to conclude that the self-resonant frequency will be advanced for both single-coil and double-coil systems due to the effect of additional capacitance in seawater. By establishing the equivalent lumped parameter model of the coil, finding the frequency position of the attenuation of the impedance modulus 3 db to determine the quality factor, and the ordinate value of the Z max (maximum impedance) point, the following three equations can be written to obtain the equivalent inductance and capacitance.  R2 1 − 2 ω0 = (5) LC L f 2(f0 − fz=zmax /√2 )

=

ω0 L R

(6)

Frequency Characteristics Analysis of Wireless Power Transfer System 40

600

35

seawater

30

400

Impedance/M

Impedance/M

500

300 200 air

100

25

air

20

seawater

15 10 5

0 2.0

239

0

2.2

2.4

frequency/MHz

2.6

0

2.8

1

2

3

frequency/MHz

4

5

(b)

(a)

Fig. 3. Impedance characteristics of (a) single coil; (b) dual coils.

Zmax =

L RC

(7)

According to calculations, the capacitance of the tested coil increases by about 10 pF underwater. The following conclusions are drawn: In comparison to air, the change trend of the parasitic capacitance of the coil in seawater is to increase; at 100 kHz, the influence of the increase of capacitance is small. 2.3 Resistance of the Coil in Seawater Compared to air, seawater with higher dielectric constant and conductivity will increase the eddy current resistance of the coil, which can be obtained through experiments. First, place the primary coil and secondary coil in air, and resonate the primary circuit at the frequency of 100 kHz with the secondary circuit open-circuited. Then, adjust the RMS value of the primary current from 5 A to 10 A and record the power of the primary coil. Next, place the coils in seawater and repeat the above steps. The eddy current loss is the consumption of electric energy, which converts electric energy into heat and dissipates it. Therefore, the equivalent impedance should be pure resistance, denoted as Reddy1 . The number 1 stands for the primary side. According to the circuit principle, the following two formulas are established: 2 ∗ R1 P1air = I1air ∗ U1air = I1air

(8)

2 ∗ (R1 + Reddy1 ) P1sea = I1sea ∗ U1sea = I1sea

(9)

P1air and I 1air represent the primary power and current in air respectively; P1sea and I 1sea represent the primary power and current in seawater respectively. R1 represents the coil resistance. Keeping I 1air and I 1sea the same, then there is the calculation expression of eddy current loss: Peddy = P1air − P1sea = I 1sea 2 *Reddy1. The experimental results are obtained. As shown in Fig. 4, the P1sea is significantly higher than P1air , and the additional power in seawater is due to the eddy current losses. Divide the primary power by the square of the current to obtain the loss resistance. In

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air, the loss resistance is the coil resistance R1 , while in seawater, the loss resistance is the coil’s own resistance plus the loss resistance in seawater, which is R1 + Reddy. As the transmission distance increases, indicating an increase in the amount of seawater between the two coils, the Reddy also increases. 18

0.170 0.165

16

seawater-90mm seawater-75mm seawater-50mm seawater-25mm air

12

0.160

loss resistance/

Power/W

14

10 8 6

0.150 0.145

seawater-90mm seawater-75mm seawater-50mm seawater-25mm air

0.140 0.135 0.130

4 2

0.155

0.125 0.120

5

6

7

I1/A

8

9

5

10

6

7

8

9

10

I1/A

(b)

(a)

Fig. 4. (a) The primary power and (b) loss resistance at different transmission distance.

3 Topological Analysis of Series-Parallel Compensation for WPT System in Seawater 3.1 Series-Parallel Compensation The above research provides an explanation for the possible influence of different media on the electrical performance and coupling performance of the coil. The analysis of the current reveals the following influences of seawater as a medium: First, seawater will increase the additional eddy current resistance. Second, at low frequencies, the seawater medium has little effect on the inductance and capacitance of the coil. Thirdly, mutual inductance directly affects the characteristics and performance of WPT system, and the influence of seawater medium on mutual inductance cannot be ignored. Therefore, as shown in Fig. 5, a series-parallel (SP) model of WPT system is established specifically for the seawater medium. 1

2

1

2 1

2

2

1

Fig. 5. Topology of S-P WPT system in seawater.

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In Fig. 5, U s represents the AC power supply. L 1 denotes the inductance of primary coil, while L 2 corresponds to the inductance of secondary coil. R1 represents the internal resistance of the power supply and the primary coil, whereas R2 represents the internal resistance of the secondary coil. C 1 is the matching capacitance at the transmitting end, and C 2 is the matching capacitor at the receiving end. M sea represents the mutual inductance between the two coils. RL denotes the load. Let I 1 and I 2 represent the currents in the primary coil and the secondary coil, respectively. Additionally, ω represents the natural angular frequency at both sides. According to Kirchhoff’s law and mutual inductance principle, Z1 I1 − jωMsea I2 = Us

(11)

Z2 I2 − jωMsea I1 = 0

(12)

When the system is in resonance: 1 ω2 L2 L2  C1 = 2  2 ω L1 L2 − Msea C2 =

(13) (14)

The output voltage gain is: Gvsp =

Uo jωMsea RL = 2 2 Us (ω Msea + Z1 Z2 )(1 + jωC2 RL )

(15)

The efficiency of the system is: η= ∗

PL = Pin 2 + (ω2 Msea

2 R (ωL + jR ) −ω2 Msea L 2 L 2 +R L +R 2 2 (jωMsea 1 2 eddy L2 )(jω L2 +ωR2 L2 +ωReddy L2 +jR2 RL +jReddy RL ) ) L2 (ωL2 +jRL )

1 (1 + jωC2 RL )2 (jω2 L22 + ωR2 L2 + ωReddy L2 + jR2 RL + jReddy RL ) (16)

Set the effective value of the AC power supply voltage to 30 V, the resistance of the primary and secondary sides to 0.1 , the inductance values of the transmitting and receiving coils to be equal, both 95 uH. The voltage gains at close and long distances are depicted in Fig. 6(a) and Fig. 6(b) respectively. Based on the comparison of the amplitude and phase of electric field intensity in air and seawater, as the amplitude change is not significant, k = 1 is taken; ϕ represents the change in phase, where the value is 2°. At close distance, the mutual inductance is 50 μH, and it is obvious that the frequency curve in seawater shifts to the right. At long distance, the mutual inductance is 10 μH, and no frequency shift phenomenon is found at this time. Figure 6(c) demonstrates the efficiency of the system. It is evident that employing series-parallel compensation enables stable transmission efficiency in WPT systems, ensuring the stability and continuity of the charging process. This is particularly important in complex underwater environments, as the unpredictable effects of water flow in seawater can result in significant variations in coupling coefficients.

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2.0 air

1.8

air

80

seawater

1.4 1.2 1.0

6

efficiency/%

voltage gain

voltage gain

1.6

8

seawater

4

0.8

40

2

0.6

20

0.4 0.2 50000

60

100000

150000

0 50000

200000

100000

frequency/Hz

150000

frequency/Hz

(a)

0 0.0

0.2

(b)

0.4

k

0.6

0.8

1.0

(c)

Fig. 6. (a) Voltage gain at close distance; (b) voltage gain at long distance; (c) efficiency curve of S-P WPT system in seawater.

3.2 Frequency Splitting of WPT System in Seawater The phenomenon of frequency splitting is a critical issue that affects the transmission performance of WPT systems. When frequency splitting occurs, the frequency characteristics of the load power in the system will transition from a single peak to multiple peaks, resulting in instability in power transmission. For a SP WPT system in seawater, it is essential to avoid frequency splitting in order to achieve stable system operation and maximize power transmission. To achieve this, it is required that the input impedance of the system meet the requirement of having and only one solution when the imaginary part is zero. The subsequent explanation will be provided through mathematical derivation. Denote the input impedance as: Zin =Z1 +

(ω ∗ Msea )2 Z2

=R1 + Reddy + jωL1 +

1 (ω ∗ Msea )2 + jωC1 R2 + Reddy + jωL2 +

1 RL

1 + jωC2

(17)

Equation (17) can be rewritten into the plural form: Zin =

2 B 2 A ω2 Msea 1 ω2 Msea + i(ωL − − ) 1 B2 + A2 ωC1 B2 + A2

Zin = R1 + R1eddy + Among them: A = ωL2 −

(18)

2 B 2 A ω2 Msea 1 ω2 Msea + j(ωL − − ) 1 B2 + A2 ωC1 B2 + A2

ωC2 1 +ω2 C22 2 RL

, B = R2 + R2eddy +

1 RL (

1 +ω2 C22 ) R2 L

(19)

.

When the coupling coefficient is 0.5 and the load is 150  respectively, draw the relationship between the frequency at which the imaginary part of the input impedance is zero and the load and the coupling coefficient, as shown in Fig. 7. It can be seen that under the numerical conditions used, when the load is greater than 106 , the frequency splitting phenomenon occurs, that is, the load 106  is the critical point of frequency splitting. Similarly, the coupling coefficient k = 0.33 is the critical point of frequency splitting. When k > 0.33, frequency splitting occurs; When k < 0.33, it does not appear.

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3.5x105 1.3x105

3.0x105

1.1x105

RL=106

frequency/Hz

frequency/Hz

1.2x105

1.0x105 4

9.0x10

2.0x105 k=0.38

1.5x105 1.0x105

8.0x104 7.0x104

2.5x105

5.0x104 0

100

200

300

400

500

0.0

0.0

0.2

0.4

RL/

(a)

0.6

0.8

1.0

k

(b)

Fig. 7. Relationship between frequency splitting and (a) load; (b) coupling coefficient.

It can be concluded that the frequency splitting phenomenon of SP WPT system in seawater is related to the load and coupling coefficient. Specifically, the system with large load and short distance is more prone to frequency splitting phenomenon. In general, to ensure stable operation and avoid the phenomenon of frequency splitting, it can be achieved by decreasing the coupling coefficient (mutual inductance).

4 System Design and Experimental Analysis An experimental platform was built as shown in Fig. 8. It uses a 30 V DC power supply with a primary coil of 93 μH, a secondary coil of 82 μH, and a mutual inductance of 51 μH. The primary side is equipped with a series resonant capacitance of 33 nF, while the secondary side has a parallel resonant capacitance of 22 nF. Based on the above analysis, two layers of hollow disc coils are wrapped by using Litz wires and they are made waterproof.

Fig. 8. Experimental platform of SP WPT system in seawater.

The overall distribution law of seawater salinity is that it decreases from the subtropical sea area in the southern and northern hemisphere to the low latitude and high

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latitude, with an average salinity of 3.5%. Therefore, the salinity of seawater is 35ppt, and the temperature test is 21.7 °C. When the transmission distance is 21 mm (coupling coefficient k = 0.42) and 36 mm (coupling coefficient k = 0.28), and the load is RL = 67.5200 and 500 , the transmission power curves of the WPT system in air and seawater with frequency are tested and plotted, respectively. From Fig. 9, when the load is 200  and the distance is 36 mm, the output power is a single peak curve; When the distance is 21 mm, the output power is a double peak curve, that is, frequency splitting occurs at the distance of 21 mm. 60 50

seawater air

60

40

20

0

seawater air

40

Power/W

Power/W

80

30 20 10 0

60

80

100

120

140

160

180

60

frequency/kHz

80

100

120

140

160

180

frequency/kHz

(b)

(a)

Fig. 9. Transmission power of WPT system at R = 200 : (a) distance = 36 mm; (b) distance = 21 mm.

Comparing Fig. 10 and Fig. 11, it is known that the output power is a single peak curve when the load is 67.5 , but the output power is a double peak curve with load 500 . That is, if the load is greater than the critical value, the system become frequency splitting. 200

90 80

seawater air

70

Power/W

Power/W

150

100

seawater air

60 50 40 30

50

20 10

0

0

60

80

100

120

140

frequency/kHz

(a)

160

180

60

80

100

120

140

160

180

frequency/kHz

(b)

Fig. 10. Transmission power of WPT system at R = 67.5 : (a) distance = 36 mm; (b) distance = 21 mm.

Frequency Characteristics Analysis of Wireless Power Transfer System 120

70 seawater air

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(a)

160

180

60

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frequency/kHz

(b)

Fig. 11. Transmission power of WPT system at R = 500 : (a) distance = 36 mm; (b) distance = 21 mm.

In addition, as shown in Fig. 9 (b) and Fig. 11 (b), when distance is 21 mm, the phenomenon of frequency shift is observed. When the load is 500 , it can be obviously found that there is a frequency offset of 1–4 kHz in the WPT in seawater. When distance is 36 mm, no frequency shift is observed. Additionally, it is worth noting that the phenomenon of frequency shift is more pronounced when frequency splitting occurs. Therefore, as mentioned earlier, frequency shifting occurs in the tightly coupled region at short distances, rather than in the loosely coupled region at longer distances.

5 Conclusions This paper mainly analyzed the frequency characteristics of the WPT system in seawater. The parameters of the underwater coupling coil including their inductance, capacitance and resistance were analyzed. Based on this, a model of the SP WPT system was established in seawater and analyze its output characteristics. The frequency splitting and frequency offset characteristics are verified through experiments. Specifically, the system with large load and short distance is more prone to frequency splitting phenomenon, and the frequency shift occurs in the close coupling region at short distance, not in the loose coupling region at long distance. Acknowledgements. This work was supported by the National Natural Science Foundation of China [E011320101].

References 1. Cai, C., Wu, S., Zhang, Z., Jiang, L., Yang, S.: Development of a fitto-surface and lightweight magnetic coupler for autonomous underwater vehicle wireless charging systems. IEEE Trans. Power Electron. 36(9), 9927–9940 (2021)

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2. Feng, L., Zhu, C., Zhang, J., et al.: Research on key technology based on wireless charging technology for unmanned underwater vehicle. Ship Sci. Technol. 42(23), 159–162 (2020). (in Chinese) 3. Teeneti, C.R., Truscott, T.T., Beal, D.N., Pantic, Z.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Ocean. Eng. 46(1), 68–87 (2021) 4. Hasaba, R., Eguchi, K., Yamaguchi, S., Satoh, H., Yagi, T., Koyanagi, Y.: WPT system in seawater for AUVs with kW-class power, high positional freedom, and high efficiency inside the transfer coils. In: 2022 Wireless Power Week (WPW), Bordeaux, France, pp. 90–94 (2022) 5. Zhou, J., Yao, P., Chen, Y., et al.: Design considerations for a self-latching coupling structure of inductive power transfer for autonomous underwater vehicle. IEEE Trans. Ind. Appl. 57(1), 580–587 (2021) 6. Mostafa, A., Wang, Y., Zhang, H., Tangirala, S., Lu, F.: An ultra-fast wireless charging system with a hull-compatible coil structure for autonomous underwater vehicles (AUVs). In: 2022 IEEE Transportation Electrification Conference & Expo (ITEC), Anaheim, CA, USA, pp. 279–284 (2022) 7. Bobba, P.B., Rao, R.K., Chinthamaneni, S.S.V.: Wireless power transfer in autonomus underwater vehicles. In: 2022 IEEE 2nd International Conference on Sustainable Energy and Future Electric Transportation (SeFeT), Hyderabad, India, pp. 1–5 (2022) 8. Virgilio Tibajia, G., Caesar Talampas, M.: Development and evaluation of simultaneous wireless transmission of power and data for oceanographic devices. In: SENSORS, 2011 IEEE, Limerick, pp. 254–257 (2011) 9. Bana, V., Kerber, M., Anderson, G., Rockway, J.D., Phipps, A.: Underwater wireless power transfer for maritime applications. In: 2015 IEEE Wireless Power Transfer Conference (WPTC), Boulder, CO, pp. 1–4 (2015) 10. Zhou, J., Li, D.J., Chen, Y.: Frequency selection of an inductive contactless power transmission system for ocean observing. Ocean Eng. 60, 175–185 (2013) 11. Zhang, K., Du, L., Zhu, Z., Song, B., Xu, D.: A normalization method of delimiting the electromagnetic hazard region of a wireless power transfer system. IEEE Trans. Electromagn. Compat. 60(4), 829–839 (2017)

Coil Optimization Design of RWPT System Based on Response Surface Methodology Shishuo Zhang and Ruiqing Ma(B) School of Automation, Northwestern Polytechnical University, Xi’an 710072, China [email protected], [email protected]

Abstract. Wireless power transfer (WPT) technology is widely applied in daily life. However, in rotary wireless power transfer (RWPT) systems, performance is compromised due to coil misalignment. This paper analyzes the RWPT system using LCC-S compensation topology and optimizes the dimensions of the coupling coils using a fast and universal method. Specifically, a finite element model of the coupling coil is established and analyzed. Then, the sensitivity of the coupling coefficient to various parameters of the coupling coil in the RWPT system is analyzed using response surface methodology (RSM). The response surface results are optimized using evolutionary algorithms. A Pareto solution is selected, and joint simulations using Maxwell and Simplorer are performed to validate the effectiveness of this method. After optimization, the effective coupling range of the coil is increased by 46%, and the system robustness is significantly improved. Keywords: RWPT · Finite-element modeling · RSM · Pareto optimization

1 Introduction The traditional electric power transmission usually adopts the direct connection of wire for energy transmission, which has many potential security problems. Since the Wireless Power Transfer (WPT) technology was proposed in the 1980s, it has experienced decades of development, and now it has widely existed in daily life. WPT technology uses a high-frequency magnetic field for energy transmission, which is more suitable for harsh working environments and has higher flexibility and reliability. At present, its main application scenarios are consumer electronics [1], biomedical [2] and electrified transportation [3]. The research on static WPT has become relatively mature. However, in many usage scenarios, it is difficult to guarantee a constant relative position between the coupling coils. Therefore, dynamic wireless power transfer (DWPT) has become one of the current research hotspots. The rotary wireless power transfer (RWPT) system belongs to a type of DWPT technology. Unlike the more common DWPT systems in the field of electric vehicles, the RWPT system not only involves relative motion along a certain direction between the transmitting coil [4] and the receiving coil but also introduces angular displacement. Rotating components are not uncommon in both consumer and industrial products, ranging from car tires to aircraft engine blades. In order to provide power to © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 247–258, 2024. https://doi.org/10.1007/978-981-97-0873-4_26

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these rotating components or monitor their motion parameters, an RWPT system is often required. Compared to static WPT systems, the relative position of the magnetic couplers in DWPT systems is not fixed. Therefore, when the coupling coefficient dynamically changes, the power transfer performance of the system may fluctuate. To mitigate the impact of coupling variations, the research focus of DWPT lies in magnetic couplers, power converters, resonant compensation networks, and control schemes [5]. In a RWPT system, the coupling coefficient between the magnetic couplers continuously changes, and when the coupling coefficient is too small, power transmission becomes difficult. Based on the minimum coupling coefficient, there exists an effective coupling range boundary. For an RWPT system, the most important indicators are the power transmission within the effective coupling range and the robustness.

2 Rotary Wireless Power Transmission System 2.1 Introduction of RWPT System In certain scenarios, such as loosely coupled transformers, an RWPT system is described as a magnetic coupling mechanism that remains aligned but rotates around its axis. In this type of RWPT system, the relative position of the magnetic coupling mechanism remains unchanged. However, the focus of this paper is on RWPT systems where there is relative displacement between the magnetic coupling mechanisms. As shown in Fig. 1, Fig. 1 a) illustrates the relative position of the coupling coils in static wireless power transfer. Figure 1 b) depicts the relative position of the coupling coils in common dynamic wireless power transfer. Figure 1 c) displays the relative position of the coupling coils in rotating wireless power transfer.

Fig. 1. Diagram of the relative position between the coupling coils. a) the coupling coils in static WPT. b) the coupling coils in common DWPT. c) the coupling coils in RWPT.

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The overall structure of the RWPT system used in this paper is shown in Fig. 2. In this paper, the compensation network is also classified as part of the magnetic coupling mechanism. On the transmitter side, the DC power source is connected to the highfrequency inverter circuit. The power is transmitted wirelessly after compensation and is then rectified and filtered to provide power to the load. Additionally, the DC power source is regulated to supply power to the control section. On the receiver side, the receiver coil and subsequent circuits are located on the rotating component. The rotating component is connected to the motor, which is powered by a power supply. The motor drives the rotating component to rotate.

Fig. 2. The overall structure of the RWPT system

2.2 Mathematical Model of Compensation Topology WPT systems typically incorporate compensation networks in the circuit to achieve resonance. This helps to reduce reactive power and thereby improve the power transmission capacity and efficiency of the WPT system. The selection of an appropriate compensation circuit topology is crucial for WPT systems. Different compensation circuit topologies result in different power supply characteristics of the system. The four basic compensation topologies widely used are series-series (S-S) compensation, series-parallel (S-P) compensation, parallel-series (P-S) compensation, and parallel-parallel (P-P) compensation. In addition, higher-order compensation topologies are also being developed, including LCC-LCC, LCC-S, CCL-LC, LCC-LCCL, and other types [6]. Although the S-S compensation topology exhibits good transmission efficiency and power at low coupling coefficients and loads, it is prone to overcurrent on the primary side [7]. In this

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paper, the chosen compensation topology is the LCC-S type. As shown in Fig. 3, the mutual inductance model of the LCC-S compensation topology is depicted.

Fig. 3. The mutual inductance model of the LCC-S compensation topology

Uin is the voltage of the AC supply. Rf , Rp , Rs are internal resistances. Lf , Cp , Cp2 are resonant inductors and capacitors of the primary-side circuit. Cs is the resonant capacitor of the secondary circuit. RL is the resistance of the load. Lp and Ls are the inductances of the transmitting coil and receiving coil. M is the mutual inductance of them. As the capacitor Cp2 also participates in resonance, the following relationship can be derived: 1 1 = = ωLf (1) ωLp − ωCp2 ωCp Based on Kirchhoff’s voltage law, the system circuit equation can be formulated as follows: ⎧ ˙ ˙ ˙ ˙ ⎪ ⎨ Uin = (Rf + jωLf )If + (Rp + jωLf )I1 + jωM I2 1 ˙ ˙ ˙ ˙ (Rp + jωLf )I1 + jωM I2 = jωCp (If − I1 ) (2) ⎪ ⎩ U˙ = jωM I˙ + (R + jωL + 1 )I˙ = −R I˙ out

1

s

s

jωCs

2

L 2

The compensation capacitors are selected according to the following criteria to achieve resonance state in the system: ⎧ 1 ⎪ ⎪ Cp = ω2 Lf ⎨ Cp2 = 2  1  (3) ω Lp −Lf ⎪ ⎪ ⎩ Cs = ω21L s

The voltage gain and current gain of the system can be obtained as follows: ⎧ ω2 MLf ⎪ ⎪ Rs +RL RL ⎨ GV = U˙ out = ⎪ ⎪ ⎩ GA =

U˙ in

I˙2 I˙f

=

2

2

M ω2 L2f +Rf ( Rωs +R +Rp ) L 2 ω MLf ω2 M 2 +Rp (Rs +RL )

The output power and efficiency of the system can be expressed as: 2

ω2 MLf ˙  2 RL Rs +RL Uin GV U˙ in = Po =

2 2M 2 RL ω2 L2f + Rf ( Rωs +R + R ) p L

(4)

(5)

Coil Optimization Design of RWPT System

η = GV GA =

ω2 MLf Rs +RL

251

2 RL



2M 2 2M 2 ( Rωs +R + Rp ) ω2 L2f + Rf ( Rωs +R + Rp ) L L

(6)

Since RWPT is a type of DWPT, the mutual inductance M is variable. The mutual inductance can be characterized by a more intuitive coupling coefficient k. Therefore, it is generally desirable to achieve a stable coupling coefficient to enhance the robustness of the RWPT system.

3 Coil Optimization Design For the design of coil size and various parameters in WPT systems. The most widely used method is to establish a finite element model of the coupling coils and utilize commercial finite element software for optimization. This method is time-consuming. Another method is to consider the relationship between the geometric parameters of the coupling coils and the circuit parameters and establish a nonlinear programming mathematical model for optimization [8]. This method offers faster computation speed but also has some problems. For instance, it is difficult to establish mathematical expressions for self-inductance and mutual inductance for coils of various shapes, especially when non-axial displacement and deflection occur between the coils. The position relationship between the coil on the transmitting side and the coil on the receiving side in the RWPT system is often in the case of misalignment and angle offset. When the coupling coefficient of the coil is too small, it is difficult to transfer power. There is an effective coupling range boundary based on the minimum coupling coefficient. The optimization design method of the RWPT system coil used in this paper is shown in Fig. 4. The coil optimization method used in this paper is based on RSM. It combines the advantages of traditional finite element methods and direct mathematical model-based optimization methods. Evolutionary algorithms (EAs) are population-based methods that rely on mutation, recombination, and selection to evolve a collection of candidate solutions toward an optimal state. Differential Evolution (DE) is a typical evolutionary algorithm. Unlike other evolutionary algorithms with biomimetic characteristics, DE directly samples the population to drive mutation. As shown in Fig. 4, the initial population is distributed within a certain range. xi,j,g=0 = xlow + U(0, 1) ∗ (xhigh − xlow )

(7)

In Eq. 7, U (0,1) is a random number generator that returns a uniformly distributed value in the range (0,1). The variables xlow and xhigh are the lower and upper bounds. DE utilizes two distinct vectors in the population to perturb an existing vector, performing differential operations to achieve mutation. vi (g) = xr1 (g) + F ∗ (xr2 (g) − xr3 (g))

(8)

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Fig. 4. The optimization design method of RWPT system

xr1 (g), xr2 (g), and xr3 (g) are three randomly selected distinct individuals from the current population. F is the scaling factor, which is a constant. vi (g) represents the mutated individual in the g-th generation corresponding to the target individual xi (g). Each individual undergoes crossover with its corresponding mutated offspring vector, aiming to randomly select individuals.  v (g), ifU (0, 1) ≤ CR (9) ui,j (g) = i,j xi,j (g), otherwise In the Eq. 9, CR represents the crossover probability. It stochastically generates new individuals through probability. Employing different differential strategies, including the vectors involved in mutation, the number of differential vectors involved in mutation, and different crossover methods, can have varying effects on the performance of DE.

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Selection refers to choosing the more optimal individuals to be the next generation.  ui (g), iff (ui (g)) ≤ f (xi (g)) xi (g + 1) = (10) xi (g), otherwise By using DE, a Pareto solution set can be obtained, which can be filtered to get the desired optimal solution.

4 Simulation of RWPT System and Experiment Results 4.1 Coil Optimization To verify the effectiveness of the proposed optimization method, a coupled coil model was constructed in Maxwell software, and coupled electromagnetic and circuit simulations were performed using ANSYS Simplorer. The dimensions of the coupled coils before optimization were empirically selected. The following approach was used: the outer diameter of the receiving-side coil can be determined when the rotating component radius on the receiving side is known. To enhance the misalignment tolerance of the WPT system, the outer radius of the transmitting-side coil should be equal to that of the receiving-side coil, and the inner radius of the receiving-side coil should be larger than the inner radius of the transmittingside coil [9]. The inner radius of the transmitting-side coil is set to 40% of its outer radius [10]. The parameters are shown in Table 1. Table 1. Parameters of transmitting coil and receiving coil Coil

r/mm

R/mm

N

T /mm

L/µH

transmitting

24

60

15

2

32.96

receiving

40

60

15

2

19.84

The specific parameters include the inner radius of the coil r, the outer radius of the coil R, the number of turns in the coil N, the thickness of the coil T, and the self-inductance L. The finite element analysis results are shown in Fig. 5. The distance between the coupling coils is 15 mm. The rotation radius is twice the diameter of the receiving-side coil. When the minimum coupling coefficient is 0.1, the effective coupling range before optimization is ±13°. The selected parameters are r and R of the transmitting-side coil, r of the receivingside coil, and T. The R of the receiving-side coil is constrained to a fixed value, and the maximum R of the transmitting-side coil is no greater than twice R of the receiving-side coil. Due to the presence of a certain number of turns in the spiral coil, constraints were applied to the difference between the inner and outer radii of the coil. The sensitivity of the response value to each parameter can be obtained by using the response surface method, as shown in Fig. 6. The response surface results are shown in Fig. 7.

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Fig. 5. The magnetic field line results before optimization

The DE is applied to the function relationship fitted by the response surface to obtain the optimized Pareto solution set. The result is shown in Fig. 8. The optimization objective is to maximize the coupling coefficient when the coil on the rotating component rotates by 15°, while minimizing the difference between this condition and the alignment condition. In the three-objective optimization, the difference between the inner and outer radius of the transmitting-side coil is included. The final selected optimal solution in this paper is obtained by normalizing the results of the dual optimization objectives and then summing them with equal weights.

Fig. 6. The sensitivity of the response value to each parameter

The optimized coil parameters are shown in Table 2. The magnetic field line results are shown in Fig. 9.

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Fig. 7. The response surface of the coupling coefficient influenced by the inner and outer radius of the transmitting-side coil

Fig. 8. The result of Pareto solution set after optimization

Table 2. Parameters of transmitting coil and receiving coil Coil

r/mm

R/mm

N

T /mm

L/µH

transmitting

86.3

120

15

4

71.59

receiving

27.6

60

15

4

22.23

When the minimum coupling coefficient is 0.1, the effective coupling range after optimization is ±19°. 4.2 Performance Comparison The performance of the RWPT system during coil rotation was simulated using Maxwell software and ANSYS Simplorer (Fig. 10). The parameters of the compensating devices can be calculated using Eq. 3. The performance comparison before and after coil optimization is shown in Fig. 11.

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Fig. 9. The magnetic field line results after optimization WM1

+

WM2 Cp2

L1

Cs

W

W

gnd1 gnd_term

Winding2:snk

p

Winding1:snk

m

Winding2:src

Cp1

Winding1:src

Vin

+

Mx_SS1

Rload

gnd2 gnd_term

Fig. 10. The simulated circuit in Simplorer. Vin = 28 V, f0 = 85 kHz, L1 = 14 µH, Cp1 = 250 nF, Cp2 = 100 nF, Cs = 142 nF, Rload = 3 .

When the coupling coefficient is 0.1, the transmission efficiency between the magnetic coupling mechanisms is 90%. As the coupling coefficient further decreases, the transmission efficiency rapidly declines. WM1.I represents the current on the transmitting side, WM1.V represents the voltage on the transmitting side, WM2.I represents the current on the receiving side, and WM2.V represents the voltage on the receiving side. The transmission efficiency remains relatively constant within a certain coupling range. The power transmission of the coil before optimization is higher at small rotation angles but lacks robustness. At a rotation angle of 20°, the transmission efficiency of the coil before optimization is very low, while the transmission efficiency of the optimized coil can still be maintained above 85%.

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Fig. 11. Performance comparison results

5 Conclusion This paper optimizes the dimensions of the coupling coils using a fast and universal method. The RSM-based method outperforms the traditional finite element method in terms of computational speed and is more universal compared to directly establishing mathematical models. Simulation results demonstrate that this method can be used to optimize coils and enhance the robustness of RWPT systems. The effective coupling range is increased from ±13° to ±19°, resulting in a 46% improvement. This optimization process can also be applied to the optimization of RWPT systems with coils of different shapes.

References 1. Zhang, Y., Chen, S., Li, X., Tang, Y.: Design methodology of free-positioning nonoverlapping wireless charging for consumer electronics based on antiparallel windings. IEEE Trans. Ind. Electron. 69(1), 825–834 (2022) 2. Roy, S., Azad, A.N.M.W., Baidya, S., Alam, M.K., Khan, F.: Powering solutions for biomedical sensors and implants inside the human body: a comprehensive review on energy harvesting

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5.

6.

7.

8.

9.

10.

S. Zhang and R. Ma units, energy storage, and wireless power transfer techniques. IEEE Trans. Power Electron. 37(10), 12237–12263 (2022) Li, S., Mi, C.C.: Wireless power transfer for electric vehicle applications. IEEE J. Emerg. Sel. Top. Power Electron. 3(1), 4–17 (2015) Li, X., Hu, J., Wang, H., Dai, X., Sun, Y.: A new coupling structure and position detection method for segmented control dynamic wireless power transfer systems. IEEE Trans. Power Electron. 35(7), 6741–6745 (2020) Bagchi, A.C., Kamineni, A., Zane, R.A., Carlson, R.: Review and comparative analysis of topologies and control methods in dynamic wireless charging of electric vehicles. IEEE J. Emerg. Sel. Top. Power Electron. 9(4), 4947–4962 (2021) Venkatesan, M., et al.: A review of compensation topologies and control techniques of bidirectional wireless power transfer systems for electric vehicle applications. Energies 15(20), 7816 (2022) Wang, C.-S., Covic, G.A., Stielau, O.H.: Power transfer capability and bifurcation phenomena of loosely coupled inductive power transfer systems. IEEE Trans. Ind. Electron. 51(1), 148– 157 (2004) Tao, M., Yugang, S., Zichi, W.: Multi objective optimization technology for parameters of magnetic coupling mechanism in LCC-S type wireless power transmission system. J. Chongqing Univ. 46(4), 52–63 (2023). (in Chinese) Aditya, K., Sood, V.K., Williamson, S.S.: Magnetic characterization of unsymmetrical coil pairs using archimedean spirals for wider misalignment tolerance in IPT systems. IEEE Trans. Transp. Electrification 3(2), 454–463 (2017) Zierhofer, C.M., Hochmair, E.S.: Geometric approach for coupling enhancement of magnetically coupled coils. IEEE Trans. Biomed. Eng. 43(7), 708–714 (1996)

A UUV Underwater Wireless Power Transfer System Jialu Li1,2 , Jiantao Zhang1 , Wei Lu2 , Jian Zhao2 , and Shumei Cui1(B) 1 Harbin Institute of Technology, Harbin 150001, China

[email protected] 2 Tianjin Power Research Institute, Tianjin 300384, China

Abstract. The difficulty of fast and efficiently supplied of energy has become one of the key factors restricting the endurance of unmanned underwater vehicles (UUV). Underwater Wireless Power Transfer technology is proposed as a new approach to solve the problem which is efficiently supplied of energy for UUV. This paper focuses on the impact mechanism of seawater medium and underwater special environment on UUV Wireless Power Transfer systems. Firstly, detailed analysis is conducted, and optimization design methods for system parameters are provided, in terms of the impact of operating frequency on system performance. Then, a topology and primary-secondary bilateral control strategy with wide range regulation are proposed to achieve wide range regulation for stable output, which are suitable for underwater environments. Finally, an engineered prototype of UUV Wireless Power Transfer is developed, achieving stable wireless charging for 24 V battery pack with 6.5 cm transmitting distance, at 100 W transmitting power and 88% transmitting efficiency. Keywords: UUV · Underwater Wireless Power Transfer · Charging control

1 Introduction As an important carrier of marine operations, underwater unmanned equipment can perform operations in various complex environments and high-risk sea areas. As a typical representative of underwater unmanned equipment, UUV has been extensively studied by countries including China, the United States, Japan, Russia, and Germany, achieving rich achievements [1]. Currently, power sources of UUV include nuclear energy, fuel cells, and lithium batteries. The energy density of nuclear energy is extremely high, but the cost is high and the safety is poor. Fuel cells have a high energy density, but they are complex and technological maturity is low [2]. Lithium batteries have become the main power source of UUV due to their advantages such as light weight, safety, reliability, and long cycle life. With the continuous development of the operational demand for marine equipment towards deep and distant seas, it has put forward higher requirements for the endurance of UUV [3]. The existing ways of supplementing UUV energy are generally through salvage and battery swapping or wet plug charging. The salvage and battery swapping © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 259–269, 2024. https://doi.org/10.1007/978-981-97-0873-4_27

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method requires the UUV to surface and be manually salvaged by surface ships, with low automation and poor concealment, which make it difficult to apply to the application scenarios of UUV clusters. The wet plugging charging interface is exposed to seawater, and the electrical connector must adopt a complex and tight sealing design. This charging method requires the plug-in to be strictly aligned and requires a large installation torque to ensure the sealing effect of wet plugging. It has many problems in underwater environments, such as difficulty in docking, limited plugging and unplugging times, short service life, and significant safety hazards, which are difficult to meet the practical application needs of UUV [4, 5]. Underwater wireless charging system can achieve non-contact and automated real-time energy replenishment of UUV, avoiding the problems of salvage, battery swapping, and wet plug and unplug charging, greatly improving the endurance and operational capability of UUV. This paper analyzes the characteristics of power converters and compensation networks which are suitable for underwater environments. And a topology architecture based on LCC-S compensation topology is proposed. Then, the influence of frequency and pressure on the electrical parameters of the system in special underwater environments is analyzed and solutions are proposed. Furthermore, a coordinated control method based on wireless communication between the primary and secondary sides was proposed to achieve wide range power conversion and stable output control. Finally, an engineered prototype of UUV Wireless Power Transfer is developed, achieving stable wireless charging for 24V battery pack with 6.5cm transmitting distance, at 100W transmitting power and 88% transmitting efficiency.

2 Topology of Underwater Wireless Power Transfer System The block diagram of the UUV wireless charging system with an underwater base station is shown in Fig. 1. The high-frequency inverter converts direct current into high-frequency AC power, and drives the transmitting coil through a compensation network. The receiving coil senses high-frequency AC power, which is then output by the receiving electric energy conversion link to charge the battery after passing through the compensation network at the receiving side.

Fig. 1. Block diagram of UUV wireless charging system based on underwater base stations

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The compensation network is an important part of the wireless power transfer system, which determines the resonant form of the system and affects the electrical characteristics. It is necessary to choose a suitable compensation topology based on the actual working conditions (Fig. 2). M

R1 US

C1

L1 I1

R2 L2

I 2 C2

RL

Fig. 2. Series to Series (SS) Compensation Topology

The basic compensation topology consists of a single capacitor that resonates with the inductance coil. According to the connection method between the capacitor and the coil, four compensation methods can be obtained: series series (SS), series parallel (SP), parallel series (PS), and parallel parallel (PP). Among them, the series series (SS) compensation topology has the advantages of simple form and the resonance state is not affected by the load state, making it the most widely used [6]. Its circuit topology is shown in the following figure. The primary side is composed of series compensation capacitor C 1 and the transmitting coil L 1 . The secondary side is composed of series compensation capacitor C 2 and the receiving coil L 2 . Furthermore, U S is the input voltage, I 1 is the input current, I 2 is the output current. R1 , and R2 are the internal resistance of L 1 and L 2 . M is the mutual inductance between L 1 and L 2 . RL is the load of S-S compensation network. The current of the transmitting coil is shown in Eq. (1): I1 =

M 2 ω2

R2 + RL US + R1 (R2 + RL )

(1)

From Eq. (1), it can be seen that I 1 is the short-circuit current in the S-S compensation topology when the receiving side is open. When the mutual inductance M of the receiving and transmitting coils is small, the transmitting end current will also increase, posing a risk of overcurrent. During UUV operation, there will be frequent entry and exit of underwater base stations, and the charging process is affected by ocean currents. The relative position of the transmitting and receiving coils is not fixed, which is prone to open circuits at the receiving end and significant changes in mutual inductance parameters, leading to overcurrent at the transmitting end. Therefore, the S-S compensation topology is not suitable for UUV underwater wireless charging. On the basis of the basic compensation topology, increasing the number of resonant components forms a composite compensation topology, which can achieve inherent constant voltage or constant current electrical characteristics, such as the LCC-S compensation topology shown in Fig. 3 [7].

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The primary side is composed of series compensation inductance L 1 , series compensation capacitor C 1 , parallel compensation capacitor C 2 and the transmitting coil L 2 . The secondary side is composed of series compensation capacitor C 3 and the receiving coil L 3 . Furthermore, U S is the input voltage, I 1 is the current of transmitting coil, I 2 is the output current. R1 , R2 and R3 are the internal resistance of L 1 , L 2 and L 3 . M is the mutual inductance between L 2 and L 3 . RL is the load of LCC-S compensation network. I1 R1 US

L1

R2

C2

L2

C1

I2

R3

M L3

I3 C3

RL

Fig. 3. LCC-S compensation topology

Using this topology, the current at the transmitting side I 2 = U S /jωL 2 , this current is independent of mutual inductance and receiver resistance, meaning that the emission current is not affected by the load state. In addition, this topology is less sensitive to changes in resonant component parameters compared to S-S compensation topology. Therefore, LCC-S compensation topology is more suitable for complex underwater environments. Corresponding to the above block diagram, the topology of the underwater wireless power transfer system proposed is shown as Fig. 4.

Fig. 4. Topology of Underwater Wireless Transfer System

The primary high-frequency inverter adopts a full bridge inverter, which has low device stress and low output harmonic components. The secondary electric energy conversion adopts a cascade of full bridge uncontrolled rectification and a four switch Buck-Boost conversion, which has simple structure and superior performance.

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3 Analysis of the Influence of Seawater Medium on System Electrical Parameters The primary coil and secondary coil are coupled with each other, forming a coupling mechanism, which is an important part of wireless power transfer system. The circuit model in air is generally shown in Fig. 5. RP and RS are the internal resistances of the primary coil and the secondary coil, respectively. When the Wireless Power Transfer system is in a seawater environment, seawater as the transmission medium has significant differences in electrical parameters compared to air, especially in terms of conductivity. The conductivity of seawater is 4S/m while that of air is 0, which means that seawater has electrical characteristics. The specific differences in parameters between air, fresh water, and seawater are shown in Table 1 [8]. RP up

RS

M LP

IP

us

LS IS

Fig. 5. Circuit model of coupled mechanism in air

The seawater medium can have an impact on the parameters of Wireless Power Transfer systems. The equivalent circuit model of the coupled structure in air shown in Fig. 5, which cannot fully and accurately represent the characteristics of Wireless Power Transfer systems in seawater. Table 1. Differences in parameters of air, fresh water, and seawater media conductivity

relative permeability

relative dielectric constant

air

0

1.000004

1.0006

freshwater

0.01

0.999991

81

seawater

4

0.999991

81

On the one hand, alternating magnetic fields can generate eddy current losses in seawater medium. On the other hand, due to the relative dielectric constant of seawater being 81 times that of air, the bridging capacitance between the transmitting and receiving coils is many times larger than that in air, which cannot be ignored. In summary, the circuit equivalent model of the magnetic coupling mechanism in seawater medium can be described in Fig. 6. In the circuit model, the influence of harvester can be equivalent to a series of circuits of L sea and Rsea , where L sea has multiple indices M 1 with the primary coil and M 2 with the secondary coil, and the straight bridging capacity is C 1 and C 2 . This circuit model

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RS

MPS LP

IP

M2

M1 Lsea

us

LS IS

Rsea C2

Fig. 6. Circuit model of coupling mechanism in seawater

explains the mechanism of eddy current loss caused by seawater medium. Due to the presence of M 1 and M 2 , L sea and Rsea series circuits will reflect impedance towards the primary and secondary coil circuits, resulting in eddy current loss. The magnitude of the reflection impedance is proportional to the square of the coil excitation frequency. The larger the reflection impedance, the more severe the eddy current loss introduced by seawater. In the laboratory, simulating seawater with saline water can directly use an LCR meter to measure the coil resistance value, and the relationship between the magnitude of the reflection impedance in seawater medium and the coil excitation frequency can be measured, as shown in Fig. 7. As shown in Fig. 7, in seawater medium, the additional impedance of the coil increases rapidly with the increase of excitation frequency. After the excitation frequency exceeds 100 kHz, the additional impedance of the coil increases rapidly with the increase of excitation frequency. Therefore, the excitation frequency should be less than 100 kHz. In the paper, an excitation frequency of 85 kHz is used.

Fig. 7. Relationship between the magnitude of reflection impedance and coil excitation frequency in seawater medium

Additionally, high pressure is an important characteristic of deep-sea environments [9]. Systems in deep-sea high-pressure environments are also affected by surrounding pressure, resulting in changes in transmission characteristics. This is mainly due to the piezomagnetic effect of the ferrite core in the electromagnetic coupler, that is, when the Ferrite core of the soft magnetic material is in the deep sea, its magnetic domain will change under the high pressure of seawater, resulting in the initial permeability pair will decrease with the increase of pressure.

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The inductance and mutual inductance of electromagnetic couplers mainly depend on the high magnetic permeability of the magnetic core. The decrease in magnetic permeability can lead to changes in the coupler parameters, and in severe cases, it can reduce the degree of coupling between coils. This article solves the problem of electrical parameters being affected by pressure by coupling the mechanism shell under pressure.

4 System Stable Charging Control Strategy The stable charging characteristics of batteries are jointly influenced by the circuit topology and control strategy. The control strategies of wireless power transfer systems are mainly divided into primary control, secondary control, and bilateral control. The characteristics of different control strategies are shown in the Table 2. In underwater environments, there are a lot of challenges to the stable charging control of batteries. Simple primary control methods have limited output regulation capabilities and require communication with the receiving side. The fluctuation range of mutual inductance parameters in underwater environments is large, and it is not easy to achieve low delay communication, so the primary control method is not applicable. Due to fluctuations in mutual inductance parameters, the input voltage of the receiving side fluctuates significantly, making it difficult for the charging module to maintain efficient and stable operation, so the secondary control method is not applicable. Therefore, the primary-secondly bilateral control strategy is more suitable for complex underwater environments. The primary-secondly bilateral control strategy proposed includes phase shift control on primary side and control of additional DC/DC topology. Table 2. Characteristics of Three Control Methods primary control

secondary control

bilateral control

advantage

*Small volume and light weight for secondary side; *Less prone to overcurrent for primary side

*Fast control response speed; *Without need to communicate with primary side

*Stable control; *Fast control response speed; *Wide adjustment ability

disadvantage

*Limited adjustment ability; *Requiring communication with the secondary side; *Slow control response speed

*Additional topology on secondary side *Weak adaptability to input voltage fluctuations

*Requiring communication between the primary and secondary sides; *High complexity

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0

0

Fig. 8. Relationship between the Drive Signal of the Phase Shift Control Switch and the Inverter Output Voltage

The waveform of phase shift control is shown in Fig. 8, corresponding to the topology in Fig. 4. VT1 -VT4 are respectively the driving signals of switch tubes Q1 -Q4 , with a duty cycle of 50%. If the VT2 driving signal lags behind the VT1 driving signal with a phase shift angle θ, within the 180° range, the larger θ, the smaller the effective value of the output voltage [10]. Adjusting the angle of θ can change the effective value of the output voltage, thereby changing the current of the transmitting coil and adjusting the induced voltage at the receiving side. The additional DC/DC topology adopts a four switch Buck-Boost topology as shown in Fig. 4. The proposed four switch Buck-Boost topology controls the modulation signal of the switch to achieve smooth switching of the circuit in Buck, Boost and Buck-Boost modes by detecting the input and output voltage. The control method of using the primary phase shifting and secondary integrated charging module does not require high communication speed, and the adjustment ability of the primary inverter bridge, which will not increase the complexity of the system too much. It can also ensure that the integrated charging module at the receiving end remains at an efficient and stable working point, with fast output control response speed and high control loop stability, suitable for complex underwater conditions.

5 Experimental Verification A prototype of underwater wireless power transfer system has been developed as shown in Fig. 9. The receiving and transmitting coils are placed in a simulated seawater environment, and the secondary side transmits the input and output voltage and current signals of the charging module to the primary side through WIFI. The upper computer displays the signals, and experiments are conducted with a 56 V DC source as input and a 24 V battery pack as load. When the misaligned distance is 0 cm and the transmitting distance is 6.5 cm, overall efficiency is 86.99%, and the output waveforms of full bridge inverter and the input waveforms of full bridge rectifier are shown in the Fig. 10(a). It can be seen that the phase of the voltage and current is same for inverter and rectifier, which means that the system works under fully tuned condition. Furthermore, the phase shift angle θ is

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Fig. 9. Engineered Underwater Wireless Power Transfer Prototype Experiment

92°, which means that the phase shift control strategy is effective. Meanwhile, the input voltage V DC_in and output voltage V DC_out waveforms of are shown in the Fig. 10(b). Obviously, the four switch Buck-Boost converter works in Buck mode.

(a) Waveforms of inverter and rectifier

(b) Waveforms of four switch Buck-Boost converter

Fig. 10. Experimental waveform with 6.5 cm transmitting distance and 0cm misaligned distance

When the misaligned distance increases with 6.5 cm transmitting distance, the four switch Buck-Boost converter is about to work in Boost mode, the phase shift angle θ will increase to make Buck-Boost converter work in Buck mode. The waveforms with 5.3 cm misaligned distance and 7 cm misaligned distance are shown as Fig. 11(a) and Fig. 11(b), whose phase shift angle θ is 45° and 18° respectively. When the misaligned distance increases to 9.5 cm based on above conditions, the phase shift angle θ is 0° and four switch Buck-Boost converter works in Boost mode, as shown in Fig. 11(c). The overall efficiency is 88.16%, 87.95% and 78.7% respectively. The prototype has achieved stable wireless charging of 24 V battery pack with 6.5 cm transmitting distance at 100 W transmitting power and 88% transmitting efficiency.

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(a) 5.3cm misaligned distance

(b) 7cm misaligned distance

(a) 9.5cm misaligned distance Fig. 11. Experimental waveforms with different misaligned distance

6 Conclusions The paper focuses on the impact mechanism of seawater medium and underwater environment on UUV Wireless Power Transfer systems. Then, a system parameter optimization design approach is provided considering seawater environment. Furthermore, a wide range regulation system topology and an improved coordinated control strategy for primary and secondary sides are proposed to achieve wide range regulation and stable output control in seawater environments. What’s more, an engineered prototype is developed, which achieves technical indicators of transmitting distance reach up to 6.5 cm, transmitting power up to 100 W, and transmitting efficiency up to 88% respectively. The prototype can efficiently and stably charge for the battery pack in underwater environment, which has reference value for the subsequent design of underwater wireless power transfer systems.

References 1. Zhong, H.: Review and prospect of equipment and techniques for unmanned undersea vehicle in foreign countries. J. Unmanned Undersea Syst. 25(04), 215–225 (2017). (in Chinese) 2. Hasvold, O., Stqrkersen, N., Forseth, S., et al.: Power sources for autonomous underwater vehicles. J. Power. Sources 162(2), 935–942 (2006) 3. Wang, X., Shang, J., Luo, Z., et al.: Reviews of power systems and environmental energy conversion for unmanned underwater vehicles. Renew. Sustain. Energy Rev. 16(4), 1958–1970 (2012) 4. Zhou, D., Ren, B., Wang, S.: Review on lithium batteries for underwater weapons. Chin. J. Power Sources 39(4), 846–851 (2015). (in Chinese) 5. Niu, W.: The state of the art of underwater wireless power transfer. J. Nanjing Univ. Inf. Sci. Technol. (Nat. Sci. Ed.) 9(1), 46–53 (2017). (in Chinese)

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6. Li, W., Zhao, H., Deng, J., et al.: Comparison study on SS and double-sided LCC compensation topologies for EV/PHEV wireless chargers. IEEE Trans. Veh. Technol. 65(6), 4429–4439 (2016) 7. Zheng, G., Zhao, K., Wang, H., et al.: Small-signal model for inductive power transfer systems using LCC-S compensation. Trans. China Electrotech. Soc. 373(21), 5369–5376 (2022). (in Chinese) 8. Zeng, Y., Rong, C., Lu, C., et al.: Misalignment insensitive wireless power transfer system using a hybrid transmitter for autonomous underwater vehicles. IEEE Trans. Ind. Appl. 58(1), 1298–1306 (2022) 9. Teeneti, C., Truscott, T., Beal, D., et al.: Review of wireless charging systems for autonomous underwater vehicles. IEEE J. Oceanic Eng. 46(1), 68–87 (2021) 10. Zhu, G., Dong, J., Shi, W., et al.: A mode-switching-based phase shift control for optimized efficiency and wide ZVS operations in wireless power transfer systems. IEEE Trans. Power Electron. 38(4), 5561–5575 (2023)

A Single-Ended WPT Circuit with Automatic CC-CV Transition Jingyu Wang

and Zhicong Huang(B)

Shien-MingWu School of Intelligent Engineering, South China University of Technology, Guangzhou, China [email protected]

Abstract. A Single-ended wireless power transfer (WPT) circuit with the automatic transition of constant current (CC) to constant voltage (CV) output is proposed in this paper. The proposed circuit has a simple structure and no shootthrough problem compared with full-bridge or half-bridge WPT circuits. To achieve the automatic transition of CC-CV output without active control, the double-D quadrature (DDQ) coils are used to simplify the analysis. The corresponding compensation networks are proposed to achieve the automatic transition from the CC mode to CV mode. Extra mode switches and frequency switching control are not used in the proposed method. Moreover, the transfer gain does not rely on the parameters of the loosely coupled transformer (LCT), and more parameters design freedom can be achieved in the proposed circuit. Keywords: Constant-Current (CC) · Constant-Voltage (CV) · Single-ended · Wireless power transfer (WPT) · Automatic transition

1 Introduction In order to achieve the inherent constant current (CC) to constant voltage (CV) transition capability and remove the wireless communication and active control, a novel clamp coilassisted wireless power transfer (WPT) circuit is proposed in [1], the clamp coil is used to achieve the automatic switching from the CC to the CV. At the beginning of charging, the equivalent circuit is a series-series (SS) compensated WPT circuit, and the output current is constant. When the battery voltage is up to the rated value, the equivalent circuit will change with the operation of an extra clamping coil, and the output voltage of the circuit will be constant. Moreover, another WPT circuit with the automatic transition of CC-CV output is proposed in [2]. Two transmitting and receiving coils are used in this circuit, the switching of the charging mode is realized by cutting off one compensation circuit when the battery voltage is large enough. At present, the automatic transition of CC-CV output has only been discussed in full-bridge WPT circuits. The circuit structure and the drive and control circuits are. Complicated, the risk of the shoot-through problem cannot be ignored. Moreover, the adoption of the basic compensation circuit makes the design of transfer gain limited.

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 270–278, 2024. https://doi.org/10.1007/978-981-97-0873-4_28

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A Single-ended WPT circuit only uses one switch, there is no risk of shoot-through problems, the control strategy is simple, and the cost is low. Different from the Singleended WPT circuit discussed in [3–5], the structure has been revamped to generate a constant high-frequency voltage source in this paper. To remove cross-coupling between coils, the double-D quadrature (DDQ) coils are adopted in the proposed circuit. The compensation circuits used to achieve the automatic transition of CC to CV output are designed in this paper. Moreover, due to the compensation design in this paper, the design of transfer gain is not limited.

2 The Analysis of the Automatic CC-CV Transition in Single-Ended Circuit Figure 1 shows the proposed novel Single-ended WPT circuit. The switch Q and the devices L x and C x consist of a high-frequency voltage source, C 1 , C 2 and C 3 are the compensated capacitors, and L 1 and L 2 are the compensated inductors in the primary circuit. L p1 and L s1 are unipolar coils, and L p2 and L s2 are DD coils. M 12 and M 34 are their mutual inductance, respectively. L 3 , C 4 , C 5, and C 6 are devices in the receiving circuit. Figure 2 shows the structure of the LCT. This kind of structure has been discussed in [6, 7], the mutual inductance can be removed as shown in Fig. 2(a). The resonant relationship of the primary LCL Network As shown in (1), the ω is the switching frequency. jωL1 =

1 = jωL2 jωC1

(1)

When the Eq. (1) is satisfied, the output current of L 2 is constant, which could be expressed by (2). The equivalent input high-frequency voltage of the Single-ended ˙ in is the output voltage of a Single-ended circuit could be calculated as discussed in [8]. V inverter. V˙ in (2) I˙p = jωL1

Fig. 1. The proposed Single-ended circuit with automatic CC-CV transition.

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Fig. 2. The model and structure of the LCT. (a) The mutual inductance of LCT. (b) The design of the LCT.

As shown in Fig. 1, the I p consists of two parts as shown in (3). I˙p = I˙p1 + I˙p2

(3)

Figure 3 shows the two two-port networks in parallel after the inductor L 2 . The input voltage is expressed by V p , and I p1 and I p2 are the input currents of Network A and Network AI, respectively. Rac1 and Rac2 are the equivalent AC resistance of the two networks. The resonant relationships of the devices in Fig. 3 are shown in (4). ⎧ 1 ⎪ ⎪ jωLp1 = ⎪ ⎪ jωC ⎪ 2 ⎪ ⎪ ⎪ 1 1 ⎪ ⎪ ⎪ ⎨ jωL3 = jωC = jωLs1 − jωC 4 5 (4) 1 ⎪ ⎪ ⎪ jωL = p2 ⎪ ⎪ jωC3 ⎪ ⎪ ⎪ ⎪ 1 ⎪ ⎪ ⎩ jωLs2 = jωC6 As shown in Fig. 3, the two-port networks consist of T networks, which could be expressed by (5) according to the analysis in [9–11].     −M12 0 0 −jωM34 L 2 T = T1 · T2 = T  = T3 = (5) 1 3 0 0 ML12 jωM34 Based on above analysis, the Eq. (6) should be met. ⎧  · · T · · T ⎪ ⎪ = T V, − I ⎪ I ⎨ Vp , p1 o1 o1  T  ⎪ · · · · T ⎪ ⎪ ⎩ V, I = T V, − I p

p2

o2

o2

(6)

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Then, the relationship between the input and output could be expressed by (7). ⎧ · · L3 ⎪ ⎪ V =V ⎪ ⎪ p M12 ⎪ o1 ⎪ ⎪ ⎪ · ⎪ ⎪ ⎪ V ⎪ ⎪ · o1 ⎨ I = (7) Rac1 o1 ⎪ ⎪ · · ⎪ 1 ⎪ ⎪ ⎪ I = Vp ⎪ ωM34 o2 ⎪ ⎪ ⎪ · ⎪ · ⎪ ⎪ ⎩ V = I Rac2 o2

o2

Fig. 3. The two-port networks after L 2 of the proposed circuit. (a) Network A. (b) Network B.

The output voltage as shown in Fig. 3 could be expressed by ⎧ · · L3 ⎪ ⎪ ⎨ V = − Vp M o1

12

· R · ⎪ ⎪ ⎩ V = − V ac2 p jωM34 o2

(8)

The input impedance of the two-port networks in Fig. 3 (a) and (b) could be expressed by Z 1 and Z 2 , respectively. ⎧ 2R M12 ⎪ ac1 ⎪ ⎪ Z = 1 ⎨ 2 L3 (9) 2 2 ⎪ M ω ⎪ ⎪ 34 ⎩ Z2 = Rac2 According to the structure in Fig. 1, the equivalent load of the battery is shown in (10). RL =

π 2 Rac1 Rac2 8 Rac1 + Rac2

(10)

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When the voltage of the battery is very low, the equivalent resistance of the battery will also be small, as shown in (9), Z 1 < Z 2 should be satisfied. So that, I lp1 > I lp2 will occur. The Network A and Network B are both operating in this case. The voltage of the load will depend on the larger one of V o1 and V o2 . In Eq. (8), the V o1 is larger. The Network A in Fig. 3(b) is still working, V o1 = V o2 will be satisfied. The Rac2 is constant, which is shown in (11) ωM34 L3 (11) M12 Rac2 is constant when the voltage of the battery is low, the subscript peak is used to represent the amplitude of AC parameters, and the DC output current I BAT is

 2M12 IPpeak IP2peak ωM34 2 IP1peak M12 2

IBAT = = Io1peak + Io2peak = + (12) π π L3 Rac2 π L3 Rac2 =

where the V inpeak , I o1peak , I o2peak , I P1peak , I P2peak , and I Ppeak are peak values of corresponding parameters. According to Eqs. (2) and (12), the I BAT is shown in Eq. (13). 2M12 Vinpeak (13) π ωL1 L3 Obviously, the circuit could realize a load-independent constant current output when the voltage of the battery is low. As battery voltage increases, the RL will increase to π2 Rac2 /8, which makes the Rac1 ∞, and then the Network A is cutting off. Rac2 = 8RL /π2 . The Network B is still operating in this case. Therefore, V BAT is shown in (14) IBAT =

VBAT =

π M34 Vinpeak 4L1

(14)

Fig. 4. The trends of Rac1 and Rac2 as RL varies.

According to (13) and (14), the design freedom of the LCT could be achieved. The parameters of the proposed single-ended circuit are shown in Table 1. And the trends of Rac1 and Rac2 as RL varies are shown in Fig. 4.

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Table 1. Parameters of proposed circuit. Symbol

Definition

Value

LX

Primary-side compensation inductor

45.2 μH

CX

Primary-side compensation capacitor

45 nF

L1

Primary-side compensation inductor

45.52 μH

C1

Primary-side compensation capacitor

77.02 nF

L2

Primary-side compensation inductor

45.52 μH

C2

Primary-side compensation capacitor

69.12 nF

C3

Primary-side compensation capacitor

58.26 nF

C4

Secondary-side compensation capacitor

99.4 nF

C5

Secondary-side compensation capacitor

220.66 nF

L3

Secondary-side compensation inductor

15.89 μH

C6

Secondary-side compensation capacitor

99.4 nF

L P1

The inductance of primary unipolar coil

50.72 μH

L S1

The inductance of secondary unipolar coil

51.16 μH

M 12

Mutual inductance

23.04 μH

L P2

The inductance of primary DD coil

60.18 μH

L S2

The inductance of secondary DD coil

61.38 μH

M 34

Mutual inductance

26.4w1 μH

fs

System operation frequency

85 kHz

V inpeak

Calculated fundamental amplitude

158 V

V BAT

Output DC voltage

72 V

I BAT

Output DC current

6A

D

Duty cycle

0.55

Dzvs

ZVS margin

0.08

3 Experimental Verifications The photograph of the proposed Single-ended circuit with automatic CC-CV transition is shown in Fig. 5. The distance between the transmitting and receiving coils is about 3 cm. As shown in Fig. 5, the DC input, transmitting circuit, loosely coupled transformer, receiving circuit, oscilloscope, and electronic load are used to carry out the experimental verifications. Figure 6 (a) shows the waveforms of output voltage V BAT and output current I BAT when the load changes from 10  to 5  in CC mode, the result shows that I BAT changes from 5.85 A to 6.17 A, and the V BAT will change from 58.41 V to 30.85 V. As shown in Fig. 6 (b), when RL switches from 15  to 30 , the output voltage changes from 70.64 V to 71.55 V, and the result shows that the output voltage could realize 72 V constant voltage output. Figure 7 shows the experiment and simulation dates of

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Fig. 5. Photograph of the proposed Single-ended circuit.

Fig. 6. Waveforms of V BAT an I BAT . (a) Equivalent load changes in CC mode. (b) Equivalent load changes in CV mode.

Fig. 7. The experiment and simulation dates of the output.

the output current and the output voltage. The simulation results are obtained from the

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SABER simulation software. The above experimental results prove that the proposed Single-ended WPT could realize the automatic CC-CV transition. Figure 8 shows the efficiency condition of the proposed Single-ended WPT circuit. The maximum output power is about 378 W, and the maximum output power occurs when the RL is 12  meanwhile the maximum efficiency is about 91.4%.

Fig. 8. The efficiency condition of the proposed circuit.

4 Conclusion In this paper, a Single-ended WPT circuit with automatic CC-CV transition is proposed to achieve load-independent output. The transition from CC mode to CV mode could be achieved automatically, which improves the reliability of the charging system. Different from conventional full-bridge WPT converter, the high-frequency inverter is achieved by the Single-ended circuit, which has no shoot-through problem and further improves reliability. The volume of the circuit could also be reduced. To verify the characteristics of the proposed single-ended WPT circuit, a prototype is built to realize 6A constant current output and 72 V constant voltage output. The automatic CC-CV transition has been verified in the experiment. The proposed circuit is suitable for low-power wireless charging applications. Acknowledgments. This work was supported in part by the National Natural Science Foundation of China (52007067) and in part by the Natural Science Foundation of Guangdong Province (2022A1515011581, 2023A0505050124 and 2023A1515011623).

References 1. Huang, Z., Wang, G., Yu, J., Qu, X.: A novel clamp coil assisted WPT battery charger with inherent CC-to-CV transition capability. IEEE Trans. Power Electron. 36(8), 8607–8611 (2021)

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2. Li, G., Ma, H.: A hybrid WPT system with high-misalignment tolerance and inherent CC– CV output characteristics for EVs charging applications. IEEE J. Emerg. Sel. Top. Power Electron. 10(3), 3152–3160 (2022) 3. Yue, R., Wang, C., Li, H., Liu, Y.: Constant-voltage and constant-current output using P-CLCL compensation circuit for single-ended wireless power transfer. IEEE Trans. Power Electron. 36(5), 5181–5190 (2021) 4. Zhang, Q., et al.: Research on input-parallel single-ended wireless power transfer system with constant-current and constant-voltage output. IEEE Trans. Power Electron. 37(4), 4817–4830 (2022) 5. Ke, G., Chen, Q., Zhang, S., Xu, X., Xu, L.: A single-ended hybrid resonant converter with high misalignment tolerance. IEEE Trans. Power Electron. 37(10), 12841–12852 (2022) 6. Yuan, H., Wang, C., Xia, D.: Research on input-parallel single-ended WPT system with loadindependent constant voltage output. IEEE Trans. Transp. Electrification 9(1), 1888–1896 (2023) 7. Li, Y., Lin, T., Mai, R., Huang, L., He, Z.: Compact double-sided decoupled coils-based WPT systems for high-power applications: analysis, design, and experimental verification. IEEE Trans. Transp. Electrification 4(1), 64–75 (2018) 8. Yue, R., Li, H., Liu, Y., Wang, C.: A new IPT topology with load-independent constantvoltage and constant-current output based on single switch circuit. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference (IPEMC2020-ECCE Asia), Nanjing, China, pp. 995–1000 (2020). https://doi.org/10.1109/IPEMC-ECCEAsia48364.2020. 9367848 9. Wang, D., Qu, X., Yao, Y., Yang, P.: Hybrid inductive-power-transfer battery chargers for electric vehicle onboard charging with configurable charging profile. IEEE Trans. Intell. Transp. Syst. 22(1), 592–599 (2021) 10. Wang, J., Wang, C., Zhang, S., Yuan, H., Zhang, Q., Li, D.: Constant-current and constantvoltage output using hybrid compensated single-stage resonant converter for wireless power transfer. IEEE J. Emerg. Sel. Top. Power Electron. 10(5), 6371–6382 (2022) 11. Qu, X., Chu, H., Wong, S.-C., Tse, C.K.: An IPT battery charger with near unity power factor and load-independent constant output combating design constraints of input voltage and transformer parameters. IEEE Trans. Power Electron. 34(8), 7719–7727 (2019)

A Modeling and Parameter Identification Method of LCC-S Wireless Power Transfer for Railway Transits Jianxi Xu1(B) , Yuhao Peng2 , Xinyi Zhao2 , Meng Wang1 , and Ruifeng Ma1 1 China Energy Railway Equipment Company Limited, Beijing 100011, China

{11658299,20027251,20039711}@ceic.com

2 School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China

{22121492,23121522}@bjtu.edu.cn

Abstract. Wireless Power Transfer (WPT) technology has great potential in railway transit applications benefiting from the advantages including high reliability, safety, low maintenance cost, low labor cost and strong environmental adaptability. In order to improve the efficiency and stability of WPT system considering the complicated operation environment of railway vehicles, especially the coil misalignment during long slopes and turns, it is indeed necessary to accurately identify the system parameters and take control measures accordingly with the system parameters varying. In this paper, a new parameter identification method with accurate modeling based on Genetic Algorithm (GA) is proposed, and the equivalent relationship between load and mutual inductance is introduced. The proposed parameter identification method avoids the common problem that the genetic algorithm easily falls into local optimal. Besides, the optimization speed is effectively improved. A detailed accurate high harmonic modeling and optimization algorithm process steps is provided, and simulation results proved that the parameter identification error of the load and mutual inductance is less than 1%. Keywords: Railway Transits · Wireless Power Transfer · LCC-S · Parameter Identification · Generac Algorithm

1 Introduction Wireless power transfer (WPT) technology has increasing potential as the power supply infrastructure in railway transportation, especially for heavy-haul railway systems [1, 2]. In WPT technology, in order to compensate the reactive power in the coupling coil and improve the system efficiency, a resonance compensation network is required, and LCC-S type compensation is widely studied and used because of its unique features [3]. During the operation of railway vehicles, there is unavoidably changes and positional shifts between the transmitter-side and receiver-side coils of the WPT coupling coil, resulting in changes in the mutual inductance as well as the equivalent output impedance. These parameters variation makes the system deviate from the rated operating point, which reduces the system output power and efficiency, while increasing the difficulty © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 279–287, 2024. https://doi.org/10.1007/978-981-97-0873-4_29

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of controller design [4–6]. When the equivalent load resistance or mutual inductance changes, the controller must adjust the PWM gate signals accordingly to ensure that the system maintained in desired operating state and keep high transfer efficiency under complicated situations. Therefore, the instant load and mutual inductance identification of the system is crucial. At present, parameter identification for WPT system has been preliminarily studied, which is mainly based on auxiliary inverter, reconfigurable circuit, mathematical transformation, and numerical optimization searching, etc. There are also several parameter identification methods which switch the circuit topology so that the system operates in different modes. Paper [3] achieves simultaneous change of resonant states with variable switched capacitors and Bluetooth modules in the transmitter and receiver sides, which in turn identifies the mutual inductance and the self-inductance values on both sides of the LCC-S topology system using different sets of circuit resonance parameters. Nevertheless, the method of adopting switched capacitors [7] affects the output voltage and transmitted power of the system because it is necessary to switch the system state. Paper [8] uses two inverters and two matching transformers on the transmitter side to enable the system operating in different modes, then the load and mutual inductance values are obtained by solving the derived equations in different modes using the Ferrari method. In addition, the numerical method can also be used to solve the higher order nonlinear systems where multiple parameters are coupled to each other. Paper [9] identified the resonance parameters and mutual inductance of the system using a two-layer adaptive differential evolutionary algorithm. Paper [10] used the Pulse Density Modulation (PDM) based technique to extract effective information to establish a system identification model, and then used the least squares method to complete the parameter identification. Though several parameter identification methods for WPT system have been proposed, there are few methods identifying the parameters in the form of higher-order compensation, which degrades it identification accuracy considering the effect of highorder harmonics. In this paper, the accurate modeling taking into accounts the harmonics and parameter identification methods of the WPT system are investigated based on GA which effectively avoids the problem of algorithm falling into local optimization.

2 System Modeling Considering High-Order Harmonics Figure 1 presents the classical topology of LCC-S WPT system, where a full-bridge inverter is adopted to provide high-frequency alternating current for the transmitter side in the main circuit of the WPT system with LCC-S resonance compensation network with uncontrolled rectifier circuit connecting to the loads. To satisfy the resonance requirement of the compensation network at the transmitter and receiver sides, the following could be derived: ω2 =

1 1 1 1 = + = Lf Cf Lp Cp Lp Cf Ls Cs

(1)

A Modeling and Parameter Identification Method S

S

S

S

281

Fig. 1. Main circuit of the classical LCC-S type WPT system

The square wave voltage uin (t), which is the output voltage of the inverter circuit, can be expanded by Fourier transform as: uin (t) =

2k+1 4Udc  1 sin(nωt) k = 0, 1, 2, · · · π n

(2)

n=1

The inverter output current, i.e., the steady state current iin (t) generated by the system input current under the excitation of this square wave voltage can be expressed as: iin (t) =

2k+1 

iin_n (t) =

n=1

2k+1 

In sin(nωt + φn ) n = 1, 3, · · ·, 2k + 1, · · ·

(3)

n=1

It is obvious that: U˙ in_n I˙in_n = Zin_n

(4)

Neglecting the losses of the full-bridge inverter circuit and the uncontrolled rectifier circuit devices, the equivalent impedance of the load after passing through the rectifier bridge is: Re =

8 RL π2

(5)

It can be further deduced that the impedance of the circuit on the secondary side and its reflected impedance on the primary side can be expressed as: Zs_n = jμs + Rs + Re

(6)

where μs = nωLs − Zr_n =

1 nωCs

n2 ω2 M 2 Zs_n

(7) (8)

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Thus, the input impedance of the system can be found: Zin_n = jnωLf +

1 jnωCp

+ jnωLp + Rp + Zr_n

1 1 + jnωCf × ( jnωC + jnωLp + Rp + Zr_n ) p

(9)

Organizing (8) into the form of (9), it can be derived that: Zin_n = αn + jβn ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

αn = −

(10)

μp nωCf (Rp + Zr_n ) (μp nωCf − 1)2 + n2 ω2 Cf2 (Rp + Zr_n )2 (Rp + Zr_n )(μp nωCf − 1)

(μp nωCf − 1)2 + n2 ω2 Cf2 (Rp + Zr_n )2 μp (μnωCf − 1) ⎪ ⎪ βn = nωLf − ⎪ ⎪ ⎪ (μ nωC − 1)2 + n2 ω2 Cf2 (Rp + Zr_n )2 p f ⎪ ⎪ ⎪ nωCf (Rp + Zr_n )2 ⎪ ⎪ ⎪ − ⎩ (μp nωCf − 1)2 + n2 ω2 Cf2 (Rp + Zr_n )2

(11)

where μp = nωLp −

1 nωCp

(12)

Combining (3), (4), (5), and (11), it could be derived that: In =

4Udc  nπ αn2 + βn2

φn = arctan

βn αn

(13) (14)

The organizing transformation of Eq. (14) yields: αn2 + βn2 = n

(15)

4Udc 2 ) nπ In

(16)

where n = (

Equation (16) can be simplified to obtain the relationship about M 2 : M2 = −

Zs_n (Rp + F1 ) Zs_n (Rp − F1 ) − n2 ω2 n2 ω2

(17)

where F12 F22 = − F2 (μ2p n4 ω4 Cf2 L2f − n μ2p n2 ω2 Cf2 − 2μ2p n2 ω2 Cf Lf + μ2p −2μp n3 ω3 Cf L2f + 2n μp nωCf + 2μp nωLf + n2 ω2 L2f − n )

(18)

A Modeling and Parameter Identification Method

F2 = n4 ω4 Cf2 L2f − n n2 ω2 Cf2 − 2n2 ω2 Cf Lf + 1

283

(19)

Therefore, when the mutual inductance M of the system is given, the equivalent load value Re is also be uniquely determined if all other parameters are the same. There is a unique correspondence between the two, and this correspondence will keep unchanged with the variation of the harmonic number n. In the input current of the WPT system, the fundamental component has the greatest influence and is the easiest to be measured, so the fundamental wave is taken for measurement and calculation. At this time, M and Re corresponds to n = 1:  (Rs + Re )(Rp + F1 ) (Rs + Re )(Rp − F1 ) − (20) M = − ω2 ω2 After the system is stabilized, the value of a selected starting moment of a cycle is recorded as T0 , and T0 = mT (m = 1, 2, 3, …). At this time, according to (5), it can be derived from the system input current value of the time domain expression: iin (t) =

2k+1 

In sin(nωt + φn ) =

n=1

2k+1 

In sin φn

(21)

n=1

The relationship between mutual inductance M and equivalent load resistance Re for parameter identification is obtained, and these two parameters can be further reduced to one, i.e. the load parameter. The objective function is constructed through the relationship between Re and the input current of the system, and the optimization searching is carried out using genetic algorithm to complete the identification of Re , and finally the value of M is determined.

3 Algorithm and Parameter Identification Results 3.1 Flowchart of the Genetic Algorithm Genetic algorithm has been developed as a mature optimization algorithm [10]. Based on the accurate higher harmonic modeling mentioned above together with genetic algorithm, the parameter identification flow chart is shown in Fig. 2. The value of the fitness function can be calculated as: (If − If_mea )2 + (Uo − Uo_mea )2 (22) F(Re , M ) = 2

3.2 Parameter Identification Results The proposed modeling and parameter identification method is verified in MATLAB/Simulink simulation platform to testify the feasibility and accuracy of the above theoretical analysis. The simulation time is set to 5ms, and the system has been running stably within this period. The simulation parameters are shown in Table 1.

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U

Uo 0

Fig. 2. The flowchart of a GA

Table 1. The key system parameters in simulation Parameters

Values

Parameters

Values

Input Voltage U dc /V

375

Compensation capacitor C s /μF

100.17

Resonant inductance L f /μH

65.63

Primary parasitic resistance Rp /

0.1

Resonant capacitance C f /nF

53.42

Secondary parasitic resistance Rs /

0.1

Compensation capacitor C p /nF

47.14

Switching frequency f /kHz

85

Primary side inductance L p /μH

140

Rated coupling coefficient k

0.3

Secondary side inductance L s /μH

35

/

/

The number of termination iterations was set to 40 under multiple tests of combined recognition speed and recognition accuracy. The parameters of the model were set to a load value of 4.5  and a mutual inductance value of 21 μH. In this simulation model, the equivalent load resistance Re and mutual inductance M are firstly set to 4.5  and 21 μH, respectively. The results of the genetic algorithm for recognizing the Re and M are shown in Fig. 3. Since the algorithm has already converged under the first 20 iterations, only the results of the first 20 iterations are shown here. The Y-axis of the graph represents the value of the fitness function, and the X-axis is the number of iterations, i.e., number of generations of populations. Legend 1 represents the average of fitness function values of each generation of the population. Example 1 represents the average value of the fitness function value of each generation in the population, and Example 2 represents the optimal value of the fitness function value of each generation in the population. It can be seen that when the algorithm iterates to the 18th time, the fitness function value has approximately converged to the minimum, i.e., at this time, the optimal values of Re and t M are identified. The average fitness function value of the population decreases in the process of population reproduction and evolution, which indicates that the population is constantly optimizing the individual fitness function value, while the average fitness function is much larger than the optimal fitness function value, which indicates that the population has a good diversity. In other words, there are differentiated individuals in the population, which avoids the population from being dominated by the dominant individual to fall into the local optimum.

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As shown in Fig. 3, it can be seen that the algorithm starts to converge significantly in the 3rd generation, and the number of iterations is greatly reduced compared with that without the load-impedance relationship. Table 2 presents the best recognition results from the 11th generation to the 20th generation of the iterative evolution process of the population, and the analysis of the figure shows that the algorithm searches for the optimal solution for the equivalent load and mutual inductance at the 18th generation, in which the recognition result of the load resistance value is 4.486 , and the recognition result of the mutual inductance value is 20.94 μH. The relative errors of the identification of the equivalent load resistance and mutual inductance are 0.31% and 0.28%, respectively. It proves that the result obtained by this the algorithm with the proposed modelling method has a high identification accuracy.

6

5 4 3 2 1 0 0

0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Fig. 3. The curves of optimal and mean fitness values versus generation

Table 2. The optimum solutions of Re and M from the 11th to the 20th generation Number of iterations

Optimal solution of Re ()

Optimal solution of M (H)

Number of iterations

Optimal solution of Re ()

Optimal solution of M (H)

11

3.991

2.170 × 10–5

16

4.103

2.094 × 10–5

12

3.991

2.094 × 10–5

17

4.103

2.094 × 10–5

13

4.055

2.094 × 10–5

18

4.486

2.094 × 10–5

14

4.055

2.094 × 10–5

19

4.486

2.094 × 10–5

4.103

2.094 × 10–5

20

4.486

2.094 × 10–5

15

The accuracy and feasibility of the recognition algorithm is verified under different Re and M values. Only the recognition of Re values is analyzed because the mutual inductance M are more accurately recognized. Figure 4(a) shows the results of multiple identifications with the resistance set to 4.5 . Figure 4(b) shows the load identification error results of changing the Re and

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M values in the simulation model. Taking the first three times as a group, the mutual inductance is set to 21 μH, the load changes are 4.5 , 9 , and 13 , respectively; taking the last three times as a group, the mutual inductance value is set to 28 μH, and the load changes are still 4.5 , 9 , and 13 , respectively. 4.65 4.60 4.55 4.50 4.45 4.40 4.35

1

2

3

4

5

(a) Multiple identification results

1

2

3

4

5

6

(b) Load identification error

Fig. 4. The identification results of Re

The load parameter identification errors in the above identification results are less than 1%, confirming that the parameter identification method is feasible with good accuracy under different setting conditions. The parameter identification error is compared with existing works as presented in Table 3. It shows that the proposed method is competitive in terms of identification error. Table 3. Comparison with existing works Literature

Topology

Parameters for Identification

Identification Method

Identification Error

[3]

LCC-S

M, R

Based on switched capacitors

500 W, the “Power-supply-liked” solutions, which adopts contactless transformers to replace the common transformers in general power supplies, would be good candidates to improve the power loss on the coils by comparing to the “Qi-liked” solutions. WPT stage implements a voltage step-down, by setting a high turns ratio of the coils [9]. With AC input, a PFC circuit should be adopted to generate a high DC voltage, normally around 400 V, as the input of the WPT stage. A typical architecture is shown in Fig. 2. This is also a simple architecture, and good for the Rx volume. The power loss in the Tx coil can be also well controlled. The voltage step-down function in WPT stage requires low turns number of Rx coil, even 1 or 2. Several approaches can be adopted to minimize the DCR of the Rx coil,

Wireless Charging for AGV

439

N : 1

PFC

HV Inverter

Comp.

Comp.

LV Rectifier

LV Battery

Fig. 2. A typical architecture of the “Power-supply-liked” solutions

such as copper bar, multiple layers of copper foils, multiple strands of the litz wires, etc. However, due to the effects at high frequency such as skin effect, and as well, the magnetic field is not 3D uniformly distributed in the Rx coil, the AC loss of the Rx coil would be much higher than its DC loss. Meanwhile, the high tolerance in the dimension of the 1-turn or 2-turns Rx coil, from either manufacturing or installation, leads to high tolerance in the inductance, thus easy detuning of the resonant circuit. Another drawback of such solutions is the inflexibility when there is a need to adjust the Rx inductance. A common simple approach to change the inductance is to change the turns of coils, but for the Rx coil with low turns number, even a change in 1 turn is a high percentage. To keep the turns ratio unchanged, a same percentage of change in turns will lead to much higher DCR in Tx coil. 2.3 The Solutions with Post-Regulators As discussed in Subsect. 2.2, a WPT stage with high turns ratio by setting a very low turns number in Rx coil is with some drawbacks, especially at high frequency. To avoid these drawbacks, the contactless transformers’ turns ratio should be close to 1, indicating the WPT stage is with high voltage (HV) input and HV output. To implement the voltage transition to finally charge the LV batteries, post-regulators can be added [10]. And between the WPT stage and the post-regulator there should be electrolytic capacitors (Fig. 3). N1 : N2

PFC

HV Inverter

Comp.

Comp.

HV Rectifier

DC/DC N:1

LV Battery

Fig. 3. A typical architecture of the solution with post-regulators

The post-regulator should be a DC-DC converter with a high step-down ratio - almost 400 V input, and a 24 V or 48 V output. With an almost 0.1 or even lower duty ratio, typical buck circuit is not suitable for such application. Instead, a circuit with step-down transformer, such as LLC or phase-shift full-bridge is more proper. This kind of solution controls the power loss in Tx and Rx coil well. With the existence of the post-regulator, the load dynamic performance is good, but it becomes a serious challenge to achieve good Rx volume and system efficiency.

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2.4 A Comparison of the Existing Solutions Based on the analysis in Subsects. 2.1–2.3, a comparison of the existing solutions can be summarized in Table 1. Table 1. A comparison of the existing solutions Solution

Rx volume

Rx coil loss

Tx coil loss

Additional features or drawbacks

1. The “Qi-liked” solutions

Good

Fair

Bad

1. a pre-regulator is necessary, additional loss at Tx

2. The “powersupply-liked” solutions

Good

Bad

Good

1. high tolerance of Rx inductance 2. inflexibility when adjusting Rx inductance

3. The solutions with post-regulators

Bad

Good

Good

1. good load dynamic performance 2. additional loss at Rx

Per the analysis and comparison, based on the trends of rising AGV charging power and rising WPT frequency, a conclusion can be made that none of the existing solutions is completely suitable for AGV applications.

3 A Novel Architecture for AGV Wireless Charging For AGV’s charging with a voltage transition from 110 V/220 V AC to 24 V or 48 V LVDC battery, the essence of the differences between the 3 existing solutions which have been analyzed in Sect. 2 is the approach to implement the voltage step-down. The common problem for the “Qi-liked” solutions, which implements the voltage step-down before WPT stage, as well as the “power-supply-liked” solutions, which implements the voltage step-down at WPT stage, is that the power loss at Tx or Rx coils is too high. A HV-HV transition with WPT stage is good to improve the power loss at WPT coils, but a post-regulator which implements the voltage step-down after WPT stage leads to additional volume and loss. The post-regulator should at least include a HV inverter, a transformer with high turns ratio, and a LV rectifier. By simplifying the solution with post-regulators, a novel architecture can be derived. The HV rectifier in the WPT stage and the HV inverter in the post-regulator can be cancelled, together with the HV E-capacitors. The simplification of the solution in more details is shown in Fig. 4. And after the simplification, the step-down transformer will be cascaded with the compensated Rx coil, as shown in Fig. 5.

Wireless Charging for AGV N1 : N2 HV Inverter

PFC

Comp.

441

N : 1

Comp.

HV Rectifier

HV Inverer

LV Rectifier

LV Battery

Fig. 4. Simplification of the solution with post-regulators, in more details

PFC

HV Inverter

Comp.

Comp.

LV Rectifier

LV Battery

Fig. 5. A novel architecture with cascaded step-down transformer

With this novel architecture, the disadvantages of the solutions with the postregulators can be minimized, so that the Rx volume and the system efficiency can be improved. • Three key volume contributors (HV rectifier, HV E-capacitors, HV inverter) are removed. • Two key power loss contributors (HV rectifier, HV inverter) are removed. • The volume and the power loss of the step-down transformer can be further improved, due to an almost sinusoidal voltage is directly applied to this transformer. More advantages provided by the novel architecture lies on the design flexibility. The turns numbers of the contactless transformer and the step-down transformer can be finetuned, to optimize system efficiency. Moreover, in the view of product development, to generate another product variant with the same power level but a different output voltage level, the design efforts can be minimized, by keeping the WPT stage the same, and only changing the turns ratio of the step-down transformer.

4 Evaluations 4.1 Prototype with the Novel Architecture To verify the correctness of the analysis in Sect. 3, a prototype with the novel architecture has been built, with parameters or specifications listed in Table 2. The photograph of prototype is shown as Fig. 6. The Tx and Rx coils in the contactless transformer share the same design, thus simplify the design procedure and manufacturing. The tested efficiency of the prototype, from 400 V DC (PFC bulk voltage) to 48 V DC output, reaches 95% at 2 mm air-gap, and 90% at 22 mm air-gap. The step-down transformer is with small volume so that the DC resistance of the windings is much lower. Plus, it can be without any air-gap, so that the magnetic flux is more evenly distributed inside the transformer. These factors lead to the advantage of low power losses on the step-down transformer. With 2.5 Arms primary current and 25 Arms secondary current, the loss on the step-down transformer can be RC , so

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it is necessary to calculate the equivalent impedance RL2 less than the critical impedance at the corresponding RL power, RL2 = 3.174  by Eq. (10), and the corresponding phase shift value is calculated from Eq. (11) to obtain X = 51.28°. Phase shift is performed on the basis of phase shift value X = 51.28°, at which time the power curve is shown in Fig. 10, and the power decreases monotonically with phase shift.

Fig. 10. Optimize the power curve of simulation and theoretical calculation after phase shifting

5 Experimental Verification The prototype and experimental platform in this paper are shown in Fig. 11, the primary side uses frequency tracking to achieve soft switching, where the secondary side of Fig. 11(a) is a single-sided control system with passive rectification of diodes, and the secondary side of Fig. 11(b) is a bilateral control system with active rectification. The prototype parameters are shown in Table 2.

Coupling mechanism

inverter H-bridge

Resonant network

mechanism

Inverter H bridge

Resonant network '63

Driver 1

driver Diode rectifier bridge

'63

(a)

Driver 2

'63

MOSFET rectified H-bridge

(b)

Fig. 11. Prototype and experimental platform (a) single-sided control system of diode rectification (b) Bilateral control system for MOSFET active rectification

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Table 2. Parameters of WPT system prototype with bilateral collaborative control. Parameter

Value

Input DC voltage Vdc/V

35

Simulation operating frequency f /khz

85–89

Primary side resonant capacitor C T /nf

27.34

Secondary side resonant capacitor C R /nf

27.46

Primary coil inductance L T /μH

128.29

Secondary-side coil inductance L R /μH

128.44

mutual inductance M/μH

14.2

Primary coil internal resistance RT /

0.04

Internal resistance of the secondary side coil RR /

0.04

Other internal resistance of the line RE /

0.01–0.5

Load resistance R1 /

6–10

5.1 Efficiency Comparison of Bilateral Control System and Unilateral Control System Under the primary-side frequency tracking control, the efficiency of the bilateral control system using active rectification on the secondary side and the unilateral control system with passive rectification of diodes is shown in Fig. 12. The efficiency of bilateral control systems with active rectification has increased by an average of four percent.

Fig. 12. Comparison of active rectification efficiency and passive rectification

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5.2 Verification of Secondary Phase Shift at Deviating From the Primary Side Resonant Frequency According to the prototype parameters in Table 2, the primary side resonance frequency is 85 kHz, and when the frequency is traced to 89 kHz, it obviously deviates from the primary side resonance frequency, and the secondary side phase shift waveform is shown in Fig. 13(b), and the secondary side current I R becomes larger after phase shifting.

(a)

(b)

Fig. 13. The secondary side voltage and current waveform (a) before phase shift (b) after phase shift

The power data and theoretical calculation curves of the phase shift experiment are plotted in Fig. 14. Among them, the sum of the coil internal resistance and other internal resistance of the line in experiment 1 is about 0.5 , the sum of the coil internal resistance and other internal resistance of the line in experiment 2 is optimized to be about 0.15 , and the sum of the coil internal resistance and other internal resistance of the line in experiment 3 is optimized to be about 0.05 . Since Eq. (4) ignores the internal resistance of the line and the coil, the smaller the internal resistance optimization in the experiment, the closer it is to the theoretical curve P calculation.

Fig. 14. Experimental and theoretical phase-shift work adjustment curvest

The critical impedance RC = 3.256 , RL > RC is calculated by Eq. (5), RL2 = 1.308  is calculated by Eq. (10), and the corresponding phase shift value is calculated by

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Eq. (11) to obtain X = 66.29°, the experiment has a large error of influence on power due to the influence of internal resistance, but the curve change trend and critical impedance RC , initial phase shift value X, etc. are almost consistent with the theoretical calculation. The power curve after optimizing the power control strategy is shown in Fig. 15, and there is no overcharge phenomenon after optimization, and the power decreases monotonically with phase shift.

Fig. 15. Optimize the control strategy backward phase shift power adjustment curve

6 Conclusion In this paper, a bilateral collaborative control WPT system for primary side frequency tracking to realize soft switching and secondary side phase shift power regulation is proposed. The nonlinearity phenomenon of phase shift power deviating from the primary resonant frequency is analyzed theoretically, the critical conditions and solutions are obtained, and the control strategy is optimized. Simulation and experiments verify the accuracy of the analytical method. It provides a feasible scheme for the design and optimization of bilateral collaborative control system of primary frequency conversion and secondary side phase shifting. Acknowledgments. This research is supported by High-level Guidance Project of Wireless transmission mechanism and application verification of electric energy and information in complex marine environment of Harbin Engineering University (Grant No. KY10800230037).

References 1. Song, H., Lin, W.: Characteristics and analysis comparison of synchronous rectification technology. 23(3), 11–14 (2006). (in Chinese)

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2. Shen, S., Gao, Q., Li, Z.: Research on constant voltage output of WPT system based on phase shift control. Sci. Technol. Wind 2020(15), 5 (2020). (in Chinese) 3. Lu, K., Wang, Y., Wang, L., et al.: A novel efficiency-oriented frequency tracking method for WPT systems. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS) 4. Zhang, X., Cai, T., Duan, S., et al.: A control strategy for efficiency optimization and wide ZVS operation range in bidirectional inductive power transfer system. IEEE Trans. Ind. Electron. 66(8), 5958–5969 (2019) 5. Tang, Y., Chen, Y., Madawala, U.K., Thrimawithana, D.J., Ma, H.: A new controller for bidirectional wireless power transfer systems. IEEE Trans. Ind. Electron. 33(10), 9076–9087 (2018) 6. Zhang, Y.: Design and implementation of two-way wireless charging system for underwater autonomous vehicle. Harbin Institute of Technology (2020).(in Chinese) 7. Thrimawithana, D.J., Madawala, U.K., Neath, M.: A synchronization technique for bidirectional IPT systems. IEEE Trans. Ind. Electron. 60(1), 301–309 (2013) 8. Liu, F., Li, K., Chen, K., et al.: A phase synchronization technique based on perturbation and observation for bidirectional wireless power transfer system. IEEE J. Emerg. Sel. Top. Power Electron. 8(2), 1287–1297 (2020) 9. Jia, S., Chen, C., Liu, P., Duan, S.: A digital phase synchronization method for bidirectional inductive power transfer. IEEE Trans. Ind. Electron. 67(8), 6450–6460 (2020) 10. Tan, T., Chen, K., Jiang, Y., et al.: A bidirectional wireless power transfer system control strategy independent of real-time wireless communication. IEEE Trans. Ind. Appl. 56(2), 1587–1598 (2020)

A Wireless Power Supply System Based on a Receiving End of Mountain-Type Core Xinkang Li, Fasheng Huang, Zicheng Wang, Dong Guo, and Dan Li(B) Yantai Research Institute of Harbin Engineering University, Yantai 264010, China [email protected]

Abstract. Aiming at the problems of low coupling coefficient and low efficiency of magnetic coupling in rail dynamic wireless power supply system, this paper proposes a receiving end mountain core design, which has higher coupling coefficient and mutual inductance value than the traditional E, U, and S cores, and can provide higher power density and higher system efficiency at close weight and volume. Based on the characteristics of LCC-S primary coil current constant and secondary side output voltage constant, this paper builds a guide-rail dynamic wireless power supply experimental platform, the secondary side realizes constant voltage closed loop through synchronous buck, and it is verified that the system achieves 85.7% efficiency at 150 W output, compared with the traditional receiver core structure, the wireless power supply system designed in this design has higher coupling coefficient, mutual inductance and system efficiency under a small coupling area, which has significant advantages. Keywords: Dynamic wireless power supply with rail type · LCC-S · Synchronous buck

1 Introduction Dynamic wireless power transfer technology can transmit electrical energy to automated guided vehicles [1], electric vehicles [2, 3], rail vehicles [4] and other electrical equipment through non-contact means. Compared with traditional cable power supply, dynamic wireless power supply can eliminate cable damage caused by dragging cables, electric sparks at the interface, etc., in addition, the electrical equipment can take power while moving, which can greatly increase its battery life, and even achieve battery removal [5]. According to the different designs of the magnetic coupling mechanism, DWPT can be divided into two categories: segmented wireless power supply [6, 7] and long rail wireless power supply [8]. The transmitter coil of segmented wireless power supply is cascaded together by multiple transmitting coils, and the advantage of this structure of the transmitter end is that when the AGV travels on a certain set of transmitting coils, other transmitting coils can be in a shutdown state, so that the overall efficiency of the system is improved [9], but each set of transmitting coils needs to be configured with a set of inverters, too many coils will greatly increase the cost of the system, and the © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 547–559, 2024. https://doi.org/10.1007/978-981-97-0873-4_55

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complexity of control will be multiplied [10, 11]. The transmission coil of the long rail wireless power supply system is a long coil form, and the transmission coil is only coupled above a part of the transmission coil, and the advantages of this coupling form of long rail power supply system are simple structure and control, low cost, and suitable for long-distance laying. However, this coupling form often has the problem of low coupling coefficient and low overall system efficiency. Because the transmission coil is a long coil and the number of turns is less, the magnetic coupling coefficient of the long rail wireless power supply system mainly depends on the design of the receiving end, and the different core shapes of the receiving end can greatly affect the coupling performance, the current core shape research on the receiving end is mainly E-type, Stype, U-type and other structures, these core structures have good coupling performance, but there is still a lot of room for improvement in the field of dynamic wireless power supply. This paper uses finite element analysis software to model and analyze the coupling mechanism, proposes a receiving end mountain core design, and then builds a dynamic wireless power supply system prototype based on the design of the mountain core magnetic coupling mechanism, the system adopts LCC-S [12, 13] topology, and it is verified that the core design has significantly superior coupling coefficient and mutual inductance value compared with the traditional E, S [14] and U core shapes, and the system prototype can achieve 85.7% efficiency under 150 W output, which verifies the superiority of the core design.

2 Core Modeling and Design Considering the inconvenient installation of S-type cores and the low coupling coefficient of U-shaped cores, this paper establishes a mountain-type core model based on the Etype core and optimizes its size to obtain the optimal size selection rules on the basis of limiting the overall core mass and volume. Figure 1 below is a schematic diagram of the AGV power supply of a magnetic coupling equipped with a mountain-type core structure, in which the orbital wireless electromagnetic coupling mechanism of the mountain-type core structure is mainly composed of the following three parts: the transmitting rail (1), the receiving end core (2) and the receiving coil (3). Figure 2 shows the dimensions of the mountain-type core. Wherein the core length is l, the height of the columns on both sides is equal and both are h, the height of the middle column is hm , the width of the columns on both sides is equal and w1 , and the width of the middle column is w2 . This coupling mechanism is modeled and its dimensions are parametrically swept. In order to verify the regularity of the influence of each size on the coupling performance, some sizes are expressed in proportion to each other, and the general law of the mountain core design is obtained by studying the coupling performance change caused by the change of the scale coefficient (Fig. 3). Take the height of the middle column hm = c × l, the value of c value scanning results as shown in Fig. 4, with the increase of c value, the coupling coefficient shows a gradual slowdown growth trend, after c = 0.9, the coupling coefficient will increase

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Fig. 1. Schematic diagram of the power supply of an AGV equipped with a magnetic coupler with a mountain-type core structure.

Fig. 2. Mountain core size drawing.

Fig. 3. Magnetic field pattern and magnetic induction intensity distribution of magnetic core.

relatively slowly, considering the overall size of the core is small, the c value should not exceed 1, the value in this paper is 0.94. Take the height h = d × hm of the left and right columns of the mountain-type core, and scan the d value, and the result is shown in Fig. 5. In the case of the unchanged value of c value (that is, the unchanged hm value), the coupling coefficient increases rapidly with the increase of d and then tends to remain unchanged, and after calculation, when d = 1 decreases to d = 0.37, the coupling coefficient of the mountain magnetic coupling decreases by 15.0%, but the overall weight decreases by 51.8%, and the weight is reduced by more than half. Considering the overall weight of the core, it is more appropriate to take the d value between 0.3–0.6. In this example, the value of d is 0.37.

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Coupling coefficient

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0

0.25

0.5

0.75

c

1

1.25

1.5

Fig. 4. The coupling coefficient changes with the c value.

Coupling coefficient

0.8

0.7

0.6 c=0.7 c=0.9 c=1.1

0.5

0.4 0.25

0.375

0.5

0.625

0.75

0.875

1

1.125

d

Fig. 5. The coupling coefficient changes with the d value.

Take the width of the left and right columns of the magnetic core w1 = e × lm , where lm is the length of the core l minus the width of the columns on both sides w1 , and take the width of the middle column of the core w2 = f × w1 . The results of the value sweep of e and f are shown in Fig. 6 and 7. Figure 6 shows that with the increase of e, the coupling coefficient of the system increases obviously, so the larger the e, the better, but the increase of the e value will greatly increase the overall weight and volume of the core, and the highest yield can be obtained when e is taken from 0.3–0.5. The increase of the f -value shown in Fig. 7 can increase the coupling coefficient of the system by a small amount, so the f -value is more appropriate to take 0.3–0.5, and too large the f -value will cause the middle column of the core to be too close to the guide rail, reducing the degree of freedom of the equipment. In this example, the value of e is 0.37 and the value of f is 0.4. The final core size parameters are shown in Table 1. The coupling mechanism is made according to the dimensions shown in Table 1, as shown in Fig. 8. Table 2 below shows the coupling performance and volume comparison between mountain-type cores and traditional E-type cores when the transmitting cable is 2 turns and the receiving coil is 6 turns. Using the E-type core as a reference, the normalization process is performed, and the two cores are intuitively shown in Table 3 below.

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0.7

0.6

0.5 f=0.3 f=0.4 f=0.5

0.4

0.3 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

e

Fig. 6. The coupling coefficient changes with the e value.

Coupling coefficient

0.7

0.6

0.5 e=0.4 e=0.5 e=0.6

0.4

0.3 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

f

Fig. 7. The coupling coefficient changes with the f value.

Table 1. Table of parameters for each size of the core. Size

Value

Core length l

117

Height of columns on both sides h

41

Middle column height hm

110

Width of columns on both sides w1

25

Middle column width w2

10

Under the premise of only increasing the overall weight and volume by less than 5%, the coupling coefficient can be increased by 31.6% and the mutual inductance value can be increased by 75.4%, which means that the mountain core has significantly superior magnetic coupling performance.

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Fig. 8. Physical diagram of the mountain-type coupling mechanism.

Table 2. Performance comparison of coupling mechanism. Type of coupling mechanism

Size

Coupling coefficient

Mutual inductance

E-type

160000 mm3

0.339

3.46 µH

Mountain-type

167550 mm3

0.446

6.05 µH

Table 3. Normalization comparison of two coupling mechanisms. Type of coupling mechanism

Normalized Size

Normalized coupling coefficient

Normalize mutual inductance

E-type

1

1

1

Mountain-type

1.047

1.316

1.754

3 Analysis and Design of LCC-S The topology model of LCC-S is shown in Fig. 9. Where U in is the inverter output voltage, I in is the inverter output current, I p is the transmit coil current, RL is the equivalent load of the rectifier bridge and the load at the receiving end, I L is the current at the receiving end, L f1 is the series compensation inductor at the transmitter, C p1 is the parallel compensation capacitor at the transmitter, C p2 is the series compensation capacitor at the transmitter, L p is the self-inductance of the transmitting coil, M is mutual inductance, L s is the self-inductance of the receiving coil, and C s is the series capacitance at the receiving end.

Fig. 9. Equivalent circuit of LCC-S wireless power supply system.

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If the internal resistance of the coil and inductor is ignored, the impedance Z S at the receiving end is Zs = jωLs + jωCs + RL

(1)

where ω is the angular frequency of the system, according to the theory of mutual inductance, when the impedance of the receiving end is known, the receiving end can be regarded as an equivalent reactance Z r at the transmitting end, and the calculation formula is as follows [15]. Zr =

ω2 M 2 Zs

(2)

The total input impedance Z in at the transmitter is calculated as follows. Zin = jωLf 1 +

1 1

jωCp1 +

1

jωLp +Zr +

jωCp2

(3)

According to the current relationship of each branch, according to Kirchhoff’s current law, there is an input current. I˙in =

U˙ in Zin

(4)

The transmit coil current can be expressed as I˙p =

1 jωCp1 1 1 jωCp1 + jωCp2 +jωLp +Zr

I˙in

(5)

The current at the receiving end can be expressed as I˙L =

jωM I˙p Zs

(6)

In order for the transmitter and receiver of the LCC-S wireless power supply system to work in a resonant state, the following conditions should be met. ⎧ ⎪ Cp1 = ω21L ⎪ ⎨ f1 Cs = ω21L (7) s ⎪ ⎪ ⎩ Cp2 = 2 1 ω (L −L ) p

f1

Under the resonant conditions of substitution (7), the transmit coil current can be obtained. I˙p =

U˙ in jωLf 1

(8)

The output voltage U out can be expressed as U˙ out =

M U˙ in Lf 1

(9)

Through Eqs. (8) and (9), it can be obtained that the LCC-S wireless power supply system transmits coil current and output voltage during resonance without changing with the change of load, that is, it has the characteristics of constant current on the primary side and constant voltage on the secondary side, which is suitable for the rail wireless power supply system with changing load at the receiving end.

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4 Simulation and experimentation In order to verify the constant current and constant voltage characteristics of the primary coil and the constant voltage of the secondary side of LCC-S, the circuit model of the DWPT system is constructed according to the circuit structure of the compensation network topology shown in Fig. 9, as shown in Fig. 10.

Fig. 10. System circuit model.

The circuit parameters are shown in Table 4, where L f1 , C p1 , C p2 and C s are calculated according to the resonance conditions shown in Eq. (7), and L p , L s and mutual inductance are measured by the bridge after winding the coil, and then substituted into the model for simulation verification. Table 4. Values of circuit parameters. Parameter

Value

U in

25.5 V

f

85 k

L f1

6.206 µH

C p1

565 nF

C p2

232.3 nF

Lp

21.3 µH

Ls

18.47 µH

M

7.8 µH

Cs

215 nF

R1

7.5 

C1

190 µF

R0

9.4 m

Rp

59.7 m

Rs

15.8 m

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At this time, the output power of the system is 120 W, and the waveform of the primary coil current I p , the secondary side output voltage U L and the voltage U 1 and current I 1 output by the converter are shown in Fig. 11, the rms value of I p is 6.9A, the rms value of U L is 30 V, the rms value of U 1 is 25.5 V, and the rms value of I 1 is 6.5A. 10

ip 0

6.9A

-10 40 30V

uL 0 -40 30

u1

10 25.5V

-30

v1 5

10

6.5A

i1

0

0

i1

-10 15

t (μs)

20

25

Fig. 11. Waveform diagram of primary coil current, secondary output voltage, and inverter output.

After simulation verification, when the load resistance value increases from 5  to 55 , the load voltage value increases from 29.8 V to 31.3 V, and the transmit coil current is stable at 6.9A. According to the simulation parameters shown in Table 4, the experimental platform of the mountain-type wireless power supply system is built, as shown in Fig. 12(a), including the inverter part, rectifier part, coupling mechanism, LCC-S compensation network, synchronous buck module, electronic load, DC voltage source and other parts. Among them, the transmit coil is 3 turns and wound together, the length is 1.1 m, and the receiving coil is 6 turns. The inverter section consists of DSP 28335, a drive circuit, and a full-bridge inverter, as shown in Fig. 12(b). The rectifier section is an uncontrollable rectifier consisting of a rectifier bridge, as shown in Fig. 12(c). The synchronous buck section consists of DSP 28335, drive circuitry, and a pair of upper and lower side switches, as shown in Fig. 12(d). Set the input DC voltage U dc = 25.5 V, continuously change the load resistance without adding the buck module, measure the primary side current I p and the secondary side voltage U L , and plot the measurement data as shown in Fig. 13 and Fig. 14. It can be seen that U L fluctuates to a small extent with the resistance value, and in the process of RL change from 5 –50 , ΔU L is 3.68 V and ΔI p is 0.26A. In order to make the load voltage constant, it is necessary to increase the DC-DC circuit, this experimental platform adds a synchronous buck circuit in the later stage, conducts the same variable load experiment, records the data and makes the curve as shown in Fig. 15, it can be seen that the output voltage has been stable at 30 V with the change of load at this time, and the load voltage is constant. Record the output power of the above experiment and make the power change trend shown in Fig. 16. The input and output powers of the above experiment were recorded to make the efficiency curve shown in Fig. 17, and the maximum efficiency of the system was 85.7%.

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(a)

(b)

(c)

(d)

Fig. 12. Experimental platform of mountain-type wireless power supply system (a) overall experimental bench (b) inverter part circuit board (c) rectifier part circuit board (d) synchronous buck circuit board.

Primary current/A

Fig. 13. Trend plot of output voltage change with load. 8 7 6

5

10

15

20 25 30 35 Load resistance/

40

45

50

Load voltage/V

Fig. 14. Trend of primary current change with load. 30.2 30 29.8 5

10

15

20

25 30 35 Load resistance/

40

45

50

Fig. 15. Diagram of load voltage change after adding synchronous buck module.

Record the voltage and current waveforms output by the inverter via an oscilloscope, as shown in Fig. 18(a). It can be seen from the figure that the system is weakly inductive, the current is slightly hysteresis voltage, and the system has soft switching characteristics. Figure 18(b) shows the waveform of the primary coil current I p and the inverter output voltage U 1 , and it can be seen that the primary side current lags the inverter voltage by 90°.

Output power/W

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150 100 50 0

5

10

15

20

25

30

35

40

45

50

Load resistance/

Efficiency

Fig. 16. Trend of output power as a function of load. 1 0.9 0.8 0.7 0.6 0.5 5

10

15

20 25 30 35 Load resistance/

40

45

50

Fig. 17. Trend chart of system efficiency with load.

(a)

(b)

Fig. 18. (a) Waveform of voltage and current output by inverter (b) Waveform of primary coil current and inverter output voltage.

5 Conclusion In this paper, the mountain-shaped core structure at the receiving end of the dynamic wireless power supply system is first designed, and the superiority of the core structure of the design in the application of dynamic wireless power supply system is verified by comparing the coupling performance with the traditional core shape, and then the LCC-S compensation network is built in the system topology, and the secondary side is controlled by synchronous buck for closed-loop system control, and the experimental data are recorded and the constant voltage and constant current curve and efficiency curve are made. Simulation analysis and experimental verification show that the wireless power supply system equipped with mountain core has 85.7% efficiency, which can be well applied to the guide rail wireless power supply system. Acknowledgements. This research is supported by High-level Guidance Project of Wireless transmission mechanism and application verification of electric energy and information in complex marine environment of Harbin Engineering University (Grant No. KY10800230037).

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References 1. Matsumoto, H., Shibako, Y., Neba, Y.: Contactless power transfer system for AGVs. IEEE Trans. Ind. Electron. 65(1), 251–260 (2018). https://doi.org/10.1109/TIE.2017.2721913 2. Azad, A.N., Echols, A., Kulyukin, V.A., Zane, R., Pantic, Z.: Analysis, optimization, and demonstration of a vehicular detection system intended for dynamic wireless charging applications. IEEE Trans. Transp. Electrification 5(1), 147–161 (2019). https://doi.org/10.1109/ TTE.2018.2870339 3. Ahmad, R., Kumar, V., Bilal, M., Kumari, S.: Dynamic wireless power transfer (DWPT) for charging application of electric vehicle. In: 2022 1st International Conference on Sustainable Technology for Power and Energy Systems (STPES), SRINAGAR, India, pp. 1–6 (2022). https://doi.org/10.1109/STPES54845.2022.10 006610 4. L. Shuguang and Y. Zhenxing, Modeling and Analysis of Contactless Traction Power Supply System for Urban Rail Transit, 2020 Chinese Control And Decision Conference (CCDC), Hefei, China, 2020, pp. 5653–5657.https://doi.org/10.1109/CCDC49329.2020.9164286 5. Anyapo, C.: Development of long rail dynamic wireless power transfer for battery-free mobile robot. In: 2019 10th International Conference on Power Electronics and ECCE Asia (ICPE 2019 - ECCE Asia), Busan, Korea (South), pp. 1–6 (2019). https://doi.org/10.23919/ICP E2019-ECCEAsia42246.2019.8796909 6. Li, S., Wang, L., Tao, C., Li, F., Wang, L.: Designing of the transmitting coils and compensation network of a segmented DWPT system. In: 2019 IEEE 15th Brazilian Power Electronics Conference and 5th IEEE Southern Power Electronics Conference (COBEP/SPEC), Santos, Brazil, pp. 1–5 (2019). https://doi.org/10.1109/COBEP/SPEC44138.2019.9065907 7. Liu, S., et al.: An output power fluctuation suppression method of DWPT systems based on dual-receiver coils and voltage doubler rectifier. IEEE Trans. Ind. Electron. 70(10), 10167– 10179 (2023). https://doi.org/10.1109/TIE.2022.3217592 8. Anyapo, C., Intani, P.: Development of long rail dynamic wireless power transfer for highspeed train. In: 2019 16th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Pattaya, Thailand, pp. 565–568 (2019). https://doi.org/10.1109/ECTI-CON47248.2019.8955393 9. Shuguang, L., Zhenxing, Y., Jia, J.: Contactless power supply method for rail transit based on multi-parallel primary coils. In: 2020 39th Chinese Control Conference (CCC), Shenyang, China, pp. 5695–5700 (2020). https://doi.org/10.23919/CCC50068.2020.9188380 10. Li, X., Hu, J., Wang, H., Dai, X., Sun, Y.: A new coupling structure and position detection method for segmented control dynamic wireless power transfer systems. IEEE Trans. Power Electron. 35(7), 6741–6745 (2020). https://doi.org/10.1109/TPEL.2019.2963438 11. Lv, X., Dai, X., Jiang, C., Wang, S.: A cross double-D coil for electric vehicles dynamic wireless transfer system to reduce output power pulsation. In: 2020 8th International Conference on Power Electronics Systems and Applications (PESA), Hong Kong, China, pp. 1–5 (2020). https://doi.org/10.1109/PESA50370.2020.9344038 12. Hu, X., Wang, Y., Jiang, Y., Lei, W., Dong, X.: Maximum efficiency tracking for dynamic wireless power transfer system using LCC compensation topology. In: 2018 IEEE Energy Conversion Congress and Exposition (ECCE), Portland, OR, USA, pp. 1992–1996 (2018). https://doi.org/10.1109/ECCE.2018.8557494 13. Chen, Y., Zhang, H., Shin, C.-S., Seo, K.-H., Park, S.-J., Kim, D.-H.: A comparative study of S-S and LCC-S compensation topology of inductive power transfer systems for EV chargers. In: 2019 IEEE 10th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Xi’an, China, pp. 99–104 (2019). https://doi.org/10.1109/PEDG.2019.880 7684

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14. Elliott, G.A.J., Covic, G.A., Kacprzak, D., Boys, J.T.: A new concept: asymmetrical pickups for inductively coupled power transfer monorail systems. IEEE Trans. Magn. 42(10), 3389–3391 (2006). https://doi.org/10.1109/TMAG.2006.879619 15. Bo, Q., Zhang, Y., Guo, Y., Wang, L., Liu, Z., Li, S.: Sensitivity analysis to parameter variations in LCC-S compensated inductive power transfer systems. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), Seoul, Korea (South), pp. 233–237 (2020). https://doi.org/10.1109/WoW47795.2020.9291274

Application Potential Extension of PSDF Buildings Based on Output-Parallel EV Wireless Charging Xuli Wang1 , Zhifan Li2(B)

, Hui Zhang1 , Ru Ling1 , and Qijun Deng2

1 State Grid Anhui Economic and Technological Research Institute, Hefei 230000, China 2 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

Abstract. For PSDF (photovoltaic, storage, DC, flexible) new building power distribution system, EV wireless charging is a promising application case due to its bi-direction power transfer and control flexibility. To extend application of PSDF buildings, output-parallel wireless charging topology is proposed in this paper, which employees relatively low input voltages to achieve higher power transfer. This topology can greatly increase the charging power and enlarge the application fields from household EV to industrial fields, such as heavy-duty truck charging. Meanwhile, the method is able to increase the flexible load regulation margin of the PSDF building. To ensure the stability of the system, the output current from different modules should be consistent. However, differences in component parameters between channels can affect magnitude of the output current. Meanwhile, the circuit topology interaction between the channels tends to influence control performance. In this paper, a dual-channel output-parallel wireless power transfer system is established as a dual-input dual-output system, which then is estimated by the instrument variable method. Based on the identified separate and interaction models, the inverted decoupling method is developed to make up the vibration owing to interaction. Moreover, the internal model control is adopted to the decoupled system to realize the current control. Simulation and experiment results on WPT system demonstrate that the control error due to the interaction is reduced. Keywords: PSDF building · EV wireless charging · WPT · Inverted Decoupling · Data-Driven Modeling

1 Introduction The design of new building electrical distribution systems needs to meet the user experience, ensure the safety and reliability of electrical equipment, and also have the advantage of energy saving. In order to meet these demands, PSDF (photovoltaic, storage, DC, This work is supported by Science and Technology Projects of State Grid Anhui Electric Power Co. LTD under Grant B31209220002. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 560–570, 2024. https://doi.org/10.1007/978-981-97-0873-4_56

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flexible) technology is the key [1]. Figure 1 shows a typical building power supply and distribution system, which contains all the components of PSDF. P denotes the building photovoltaic. S refers to the distributed power storage such as battery resources. D is the DC power supply in the buildings, and F stands for the flexible power demand. To advance the development of PSDF, wireless power transfer (WPT) is adopted to power the load flexibly and efficiently. WPT has changed people’s life patterns in various applications, such as electric vehicles [2], portable electronic devices, implanted medical devices [3] and so on. A novel bi-directional WPT system has also been proposed to provide power for ac grid side power and mobile energy storage systems [4]. However, the limited output power of a single channel cannot meet the demand of high-power energy transmission scenes such as dynamic wireless power supply of high-speed rail [5], trams [6], fast charging of public buses. Using output-parallel topology with multiple inverters to increase the total output current is a feasible solution to increase the total output power. For domestic buildings, high power WPT can realize the fast charging needs of electric vehicles. In industrial scenarios, it can fast charge large industrial AGVs, duty trucks and other mechanical equipment to reduce time costs and improve work efficiency. Besides, output-parallel WPT is able to fully exploit the potential of wireless charging power enhancement. Thus, it increases the proportion of demand-side flexible loads and enhances the adjustable range of PSDF building power. Figure 2 shows the circuit topology of a dual-channel output-parallel WPT system. Compared to the conventional single power level WPT system which is designed for a single power to keep high transmission efficiency, the output-parallel WPT system is more suitable in situations demanding higher and more flexible output power, such as welding, inductive heating, lighting and so forth. By connecting modular power supplies, the user can flexibly and easily regulate the WPT output power level. Furthermore, each module can be produced in larger quantities to reduce the manufacturing cost without redesigning.

Electric Vehicle

Bus WPT System Photovoltaic

Battery Stack + 375V

- 375V

Fig. 1. PSDF Building power supply and distribution system.

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To ensure system stability and increase system life, it is necessary to keep the currents from different modules the same. However, in the output-parallel WPT system, the interaction caused by the circuit topology tends to degrade the current control performance. The coupling feature comes from the parallel current outputs of different modules. When the input of one of the modules is adjusted, the output of the other is affected simultaneously. To maintain a high level of control accuracy for WPT system, the interaction vibration between different modules should be compensated. Then, the loop control needs to be introduced when the decoupling module has eliminated the effect of the interaction dynamics. This paper shows an inverted decoupling method to decouple the dual-channel output-parallel WPT system that is regarded as a dual-input dual-output (DIDO) structure. Simulation results demonstrate that the inverted decoupling is simple to design and is able to obtain current control accuracy with internal model control.

2 Methods 2.1 System Modeling The circuit diagram of the series-series compensated output-parallel WPT system with two modules is depicted in Fig. 2. Each letter in the figure is labeled with a subscript j ( j = 1, 2.): j = 1 denotes it is a component from the module 1, while j = 2 denotes it is a component from the module 2. Each module is powered by a phase-shift-controlled full-bridge inverter. V dj is the dc voltage source. Then, energy is transferred through a resonant tank composed of series inductors and capacitors. L pj , C pj , Rpj denote the inductor, capacitor and parasitic resistance at the primary side, respectively. M j is the mutual inductance. L sj , C sj , Rsj denote the inductor, capacitor and parasitic resistance at the secondary side, respectively. C fj is the output filter capacitor, and RL denotes load resistance. To adjust the output current I 1 and I 2 , the phase shift α 1 and α 2 between S 1 -S 8 are considered as the control variables. When α j changes from 0 to π, I j decreases from the maximum to zero. For the controller design, the model needs to be linearized around the given point [7]. Therefore, the outputs and inputs should be decomposed as a static value plus a small signal as: Ij = I j + I˜j , αj = α j + α˜ j , j = 1, 2.

(1)

where I j and α j represent the static value, I˜j and α˜ j represent the small value. For brevity of explanation, the output current I˜j and the phase shift angle α˜ j will be replaced by yj and uj in the following. The output-parallel WPT system with two modules can be formulated as a dual-input dual-output (DIDO) structure. The block diagram of the DIDO structure for the outputparallel system is depicted in the dash-dotted box in Fig. 3, where G11 (s) and G22 (s) are the WPT models, G12 (s) and G21 (s) are the coupling models, which describe the dynamic behavior between the modules. C 11 (s) and C 22 (s) are the controllers. D21 (s) and D12 (s) are the decoupling modules.

Application Potential Extension of PSDF Buildings Cp1 M1 S1

Cs1

S3 Lp1

+

563

I1

Cf1

Ls1

Vd1 -

S2

S4

RL Cp2 M2 S5

Cs2

S7

+

Lp2

Ls2

I2 Cf2

Vd2 -

S6

S8

Fig. 2. Circuit topology for output-parallel WPT system.

Fig. 3. Inverted decoupling control for DIDO WPT system.

The transfer function of the DIDO model, G11 (s), G22 (s), G12 (s) and G21 (s), can be identified based on the data-driven modeling method [8]. Letting the system work at the given point, the dynamic response of the DIDO model can be derived by independent single loop test method, where one module is excited by the test signal while the other module is kept unchanged. By collecting the input-output data at the time instant tk = kTs , k ∈ N + , where T s is the sample time, the separate model is then estimated using instrument variable estimation algorithm. Take G11 (s) as an example, keep α 2 unchanged and superimpose an excitation signal α˜ 1 (usually PRBS) on α 1 . Based on sampled data {y1 (tk ), u1 (tk )}N k=1 , the instrument variable estimation algorithm is adopted to estimate θˆ (tk ), the parameters of G11 (s):   ˆ k ) = θˆ (tk − 1) + g(tk ) y(tk ) − φ T (tk )θ(t ˆ k − 1) (2a) θ(t

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 −1 ˆ k − 1)φ(t ˆ k − 1)φ(t ˆ k ) σ 2 + φ T (tk )P(t ˆ k) g(tk ) = P(t

(2b)

ˆ k ) = P(t ˆ k − 1) − g(tk )φ T (tk )P(t ˆ k − 1) P(t

(2c)

ˆ k ) is the estimated error covariance matrix and φ(t ˆ k ) is the instrumental vector where P(t selected by the user, which is uncorrelated with the noise but maximally correlated with φ T (tk ). Similarly, G22 (s), G12 (s) and G21 (s) can also be obtained. 2.2 Inverted Decoupling Control As Fig. 3 shows, the inverted decoupling module composed of D12 (s) and D21 (s) is adopted to cancel the effect of coupling. Then, the output-parallel WPT system with two modules can be decoupled into two individual single-input single output (SISO) system [9]. To meet decoupling requirement, the following equation holds:      −1 D12 G11 0 G11 G12 . (3) = G21 G22 D21 −1 0 G22 where the transfer matrix at the right-hand side is the diagonal decoupled plant. Therefore, the decoupled module is: D12 =

G12 G21 , D21 = G11 G22

(4)

After the decoupling modules are implemented, the feedback controllers C 11 (s) and C 22 (s) can be designed separately and independently without further troublesome redesign. To regulate the output current, internal model control (IMC) method is adopted [10]. It has the advantage of few adjustment parameters, simple structure, and so on. Besides, it can be easily converted to PID form [11], which is widely used in industrial practice. The internal model control structure is shown in Fig. 4:

R

+

G(s)

Q(s)

Y +

Gm(s)

Fig. 4. IMC basic structure.

where R is the set value, Y is the system output, G(s) is the controller object, Gm (s) is the internal model, and Q(s) is the internal model controller. Gm (s) can be decomposed into two parts, Gm- (s) and Gm+ (s). (Gm (s) = Gm+ (s)Gm- (s)) Gm- (s) is the minimum phase part of the internal model, Gm+ (s) is the non-minimum phase part, containing the right half-plane zeros and time-delay term. Q(s) can be designed as: −1 F(s) Q(s) = Gm−

(5)

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1 where F(s) is a low-pass filter, F(s) = (λs+1) r . r stands for the order of the filter, usually r = 1, and λ is the only adjustable parameter of the internal model controller. After the equivalent transformation of the structure diagram, the internal mode controller can be transformed into a conventional unit feedback PID controller C(s), which is shown in Fig. 5:

R

+

C(s)

+

Q(s)

G(s)

Y

Gm(s) Fig. 5. Equivalent IMC structure.

C(s) is as follows: C(s) =

Q(s) . 1 − Q(s)Gm (s)

(6)

3 Simulation Results 3.1 Inverted Decoupling Performance The inverted decoupling method was adopted on the dual-module WPT system. The simulation parameters are listed in Table 1. Firstly, let WPT system work at the stationary point. Set α 1 = α 2 = 0.8π . Then, keep α˜ 1 = 0 and let α˜ 2 be a M-sequence to excite the system. By collecting I˜1 and I˜2 , G12 (s) and G22 (s) are estimated based on (2). G11 (s) and G21 (s) can be acquired in a similar way. Then, the decoupling modules D12 (s) and D21 (s) are calculated by (3) and (4): D12 (s) =

−2.391e4s − 2.72e7 5.04e4s + 4.714e7

(7a)

D21 (s) =

−1.974e4s − 1.481e8 1.011e5s + 3.73e6

(7b)

Figure 6 shows the output current when u1 and u2 steps. When t = 0.004 s and 0.01 s, u1 changes. It can be seen that only I 1 is influenced. When u2 steps at t = 0.012 s, I 1 is not affected and only I 2 certainly changes, which verifies the effectiveness of the inverted decoupling method.

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Fig. 6. The output current when u1 changes. Table 1. Simulation Parameters. Parameter

Explanation

Value

Vd

Voltage of the dc source

100 V

L p1

Inductance of the primary side of module 1

114 μH

L p2

Inductance of the primary side of module 2

125 μH

L s1

Inductance of the secondary side of module 1

114 μH

L s2

Inductance of the secondary side of module 2

125 μH

C p1

Capacitance of the primary side of module 1

22 nF

C p2

Capacitance of the primary side of module 2

18 nF

C s1

Capacitance of the secondary side of module 1

22 nF

C s2

Capacitance of the secondary side of module 2

18 nF

M1

Mutual inductance of module 1

10 μH

M2

Mutual inductance of module 2

10 μH

Cf 1

Capacitance of the output filter of module 1

50 μF

Cf 2

Capacitance of the output filter of module 2

50 μF

fs

Working frequency

100 kHz

RL

Load Resistance

50 

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3.2 Internal Model Controller Performance The internal model controller C 1 (s) and C 2 (s) are designed based on the decoupled WPT system. The exact controller parameters are as follows: C1 (s) = −0.00587 − 9.88 C2 (s) = −0.0124 − 120

1 s

1 s

(8a) (8b)

The control period is the same as the sampling period T s . The controller performance can be seen in Fig. 7. When the reference output current changes from 6 A to 8 A at t = 0.014s, both output currents change from 3 A to 4 A, the setting time is about 10 ms. It can be seen the dynamic performance is satisfactory. Besides, the controller can well equalize the output current in each channel.

Fig. 7. Output current experiment when the reference voltage changes.

4 Experiment Verification To verify the effectiveness of the proposed decoupled and control methods, an experiment is conducted by means of the apparatus in Fig. 8. The experiment parameters are listed in Table 2. A Tektronix DPO 2004B oscilloscope is used to display the current of each channel, I 1 and I 2 . Firstly, let WPT system work at the working point. Set α 1 = α 2 = 0.8π . Then, excite each channel to acquire the corresponding models. Based on the estimated models, the decoupling modules are calculated and embedded in the hardware.

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Controller at the primary side

Inductive coil

Rectifier bridge at the second side Load

Fig. 8. Experimental apparatus.

Load voltage

I1 + I2 I2

I1

Fig. 9. Output current waveforms when the reference current of channel 1 steps.

It can be seen in Fig. 9 that when u1 steps, only I 1 , the cyan line, is changed. I 2 , the purple line, is not affected, which confirms the validity of the inverted decoupling method. Furthermore, performance of the internal model controller is depicted in Fig. 10. When the reference output voltage varies from 10 A to 15 A, I 1 and I 2 change from 5 A to 7.5 A. The setting time is about 30 ms. Besides, the output current is divided equally into each channel to ensure the system stability.

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I1 + I2 I2 I1

Fig. 10. Output current waveforms when the reference current changes.

Table 2. Experimental Parameters. Parameter

Explanation

Value

Vd

Voltage of the dc source

300 V

L p1

Inductance of the primary side of module 1

114 μH

L p2

Inductance of the primary side of module 2

110 μH

L s1

Inductance of the secondary side of module 1

98 μH

L s2

Inductance of the secondary side of module 2

100 μH

C p1

Capacitance of the primary side of module 1

22 nF

C p2

Capacitance of the primary side of module 2

20 nF

C s1

Capacitance of the secondary side of module 1

26 nF

C s2

Capacitance of the secondary side of module 2

24 nF

M1

Mutual inductance of module 1

55 μH

M2

Mutual inductance of module 2

55 μH

Cf 1

Capacitance of the output filter of module 1

50 μF

Cf 2

Capacitance of the output filter of module 2

50 μF

fs

Working frequency

100 kHz

RL

Load Resistance

25 

5 Conclusion A new method is developed for decoupling and control for the output-parallel WPT system fro PSDF new building power distribution system. This paper presents the internal model control based on inverted decoupling method. Simulation and experiment results on the dual-module WPT system verified the effectiveness of the proposed method.

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References 1. Dong, T., et al.: Load management approach for residential power system incorporating photovoltaics, electric storage and electric-vehicle charging. J. Chongqing Univ. 44(08), 45– 58 (2021). (in Chinese) 2. Zakerian, A., Vaez-Zadeh, S., Babaki, A.: A dynamic WPT system with high efficiency and high power factor for electric vehicles. IEEE Trans. Power Electron. 35(7), 6732–6740 (2020) 3. Wang, J., et al.: A 403 MHz wireless power transfer system with tuned split-ring loops for implantable medical devices. IEEE Trans. Antennas Propag. 70(2), 1355–1366 (2022) 4. Onar, O.C. et al.: 20-kW bi-directional wireless power transfer system with energy storage system connectivity. In: 2020 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 3208–3214 (2020) 5. Geng, Y., Yang, Z., Lin, F.: Design and control for catenary charged light rail vehicle based on wireless power transfer and hybrid energy storage system. IEEE Trans. Power Electron. 35(8), 7894–7903 (2020) 6. Zhiwei, W. et al.: A 600 kW wireless power system for the modern tram. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 214–217 (2020) 7. Chen, F., Garnier, H., Deng, Q., Kazimierczuk, M.K., Zhuan, X.: Control-oriented modeling of wireless power transfer systems with phase-shift control. IEEE Trans. Power Electron. 35(2), 2119–2134 (2020) 8. Chen, F., Young, P.C., Garnier, H., Deng, Q., Kazimierczuk, M.K.: Data-driven modeling of wireless power transfer systems with multiple transmitters. IEEE Trans. Power Electron. 35(11), 11363–11379 (2020) 9. Zheng, J., Guo, G., Wang, Y.: Feedforward decoupling control design for dual-actuator system in hard disk drives. IEEE Trans. Magn. 40(4), 2080–2082 (2004) 10. Saxena, S., Hote, Y.V.: Load frequency control in power systems via internal model control scheme and model-order reduction. IEEE Trans. Power Syst. 28(3), 2749–2757 (2013) 11. Liu, Y., Gao, J., Zhong, Y., Zhang, L.: Extended state observer-based IMC-PID tracking control of PMLSM servo systems. IEEE Access 9, 49036–49046 (2021)

Detection Method of Lithium Plating of Lithium-Ion Battery Based on Complex Morlet Wavelet Transform Kai Lyu, Xinwei Liu, Siwen Chen, Shiyou Xing, Yilong Guo, and Jinlei Sun(B) School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China [email protected]

Abstract. Lithium-ion batteries (LIBs) are widely used in electric vehicles (EVs) and energy storage systems for their high energy density, high power density and long service life. The phenomenon of lithium plating (LP) has always threatened the safe operation of LIBs, and the detection of LP by electrochemical impedance spectroscopy (EIS) has become the focus of industry and academia. Therefore, in order to solve the time-consuming problem of existing LP detection method, this paper proposes a method of EIS calculation and LP detection method based on complex Morlet wavelet transform (CMWT). Firstly, the boundary conditions of LP phenomenon in LIBs under different rates and ambient temperatures were investigated through LP induction experiments. Then, the EIS of the battery was extracted quickly by current excitation pulse and CMWT. Finally, the EIS variation rules in different SOC intervals after LP are studied, and the LP criterion is formed. The LP detection method in this paper can promote the reduction of EIS detection time. Keywords: Lithium Plating Detection · EIS · Complex Morlet Wavelet Transform · Lithium-ion Battery

1 Introduction EVs are expected to play a key role in enabling greener, more sustainable mobility. Due to the advantages of light weight, high energy density, long service life and low price, graphite-based LIBs have been widely used in the energy storage system of EVs [1]. One of the main challenges in the current development of EVs, compared to the refueling time of gasoline-powered vehicles, is the long charging time of LIBs. To address this challenge, the U.S. Department of Energy has emphasized that achieving fast, safe and reliable charging of EVs to 80%SOC in 15 min is a key goal [2]. However, rapid charging, especially at low temperatures, often brings inevitable side reactions to LIBs, one of the most important side reactions is LP. LP results in a reduction in the amount of recyclable lithium between electrodes, which is manifested as a reduction in battery capacity. In addition, the deposited lithium metal may grow in the form of dendrites and puncture the battery diaphragm, which may lead to an internal short circuit, and in serious cases may lead to thermal runaway [3]. Therefore, in order to ensure the safe use of LIBs, an © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 571–578, 2024. https://doi.org/10.1007/978-981-97-0873-4_57

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effective LP detection method is needed to detect whether LP occurs in LIBs during the charging process. In order to detect the phenomenon of LP, a variety of non-situ LP detection methods have been reported in the literature, such as nuclear magnetic resonance (NMR) [4], inductively coupled plasma photoemission spectrometry (ICP-OES) [5] and electrode visual inspection [6]. However, these methods require LIBs disassembly as part of the evaluation of the LP process and are not suitable for LP inspection of EV battery systems. Petzl [7] et al. estimated the amount of lithium metal precipitated according to the dV/dQ peak characteristics of the LIB under the condition of constant discharge. Tanim et al. [8] evaluated the LP of graphite NMC batteries by recording and analyzing the terminal voltage after charging. Schindler et al. [9] combined EIS with dOCV analysis to study the evolution of EIS collected during rest periods after whole cell rapid charging. They found that at a frequency of 5 Hz, the resistance dropped immediately after a quick charging “pulse” of a few minutes. Koleti et al. [10] used EIS data to obtain the minimum impedance change at low and medium frequencies, which can be used to detect the LP of LIBs. Based on the existing research, it can be found that the EIS test of LIB is a slow process, and generally requires expensive electrochemical testing equipment, so it is difficult to realize the rapid detection of EIS of LIB. Therefore, in order to obtain the EIS of LIB faster for LP, this paper proposes a method of EIS calculation and LP detection based on CMWT. The reminder of this paper is as follows. Section 2 is the impedance calculation method. Section 3 is about the experiments. Section 4 is the results and discussion. Section 5 is the conclusion.

2 Impedance Calculation Principle Based on Complex Morlet Wavelet Transform Wavelet transform (WT) is a method of waveform analysis of time-domain signals. Wavelet transform coefficient of original time domain signal f (t) can be obtained and is defined as: ∞ WTf (a, b) =

∗ f (t)ψa,b (t)dt

(1)

−∞ ∗ (t) is the complex conjugation of ψ (t); ψ (t) is a series of subwavelet where ψa,b a,b a,b basis functions, which can be expressed by the following equation:   t−b 1 (2) ψa,b (t) = √ ψ a a

where t is the time of the parent wavelet; a is the scale coefficient; b is the translation parameter. Both a and b are real numbers, and a is greater than zero. Complex Morlet wavelet is a complex-valued wavelet basis function regulated by Gaussian function, whose imaginary part is the Hilbert transform of the real part, satisfying complex-valued and non-orthogonal. Therefore, it is very suitable for EIS calculation.

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The complex Morlet wavelet basis is the product of Gaussian function and sinusoidal term with the following equation:     1 j2π fc (t − b) (t − b)2 (3) exp − 2 exp ψa,b (t) = g(t)h(t) =  a fb a π fb   1 (t − b)2 g(t) =  exp − 2 (4) a fb π fb   j2π fc (t − b) (5) h(t) = exp a fb is the frequency band parameter; fc is the center frequency; j is the imaginary unit. The relationship between the fb and the standard deviation σ in the Gaussian function is expressed as follows:  fb σ = (6) 2 In order to quickly and simply calculate the EIS of the LIBs through CMWT, it also needs to apply a current excitation signal i(t) containing as many frequencies as possible to the LIBs, and record the voltage response signal u(t) of the LIBs. Adjust the parameters a and b in the complex Morlet wavelet basis and calculate the wavelet transform coefficients of i(t) and u(t) at different frequencies. The calculation expressions are as follows:      ∞ 1 1 j2π fc (t − b) (t − b)2  I (a, b) = √ i(t)conj exp exp − 2 dt (7) a a fb a π fb −∞

1 U (a, b) = √ a

∞ −∞



   1 j2π fc (t − b) (t − b)2  u(t)conj exp exp − 2 dt a a fb π fb 

(8)

By dividing the wavelet transform coefficients of voltage and current at different frequencies, the simulated impedance values of the battery at different frequencies f can be obtained, and the calculation formula is as follows: Z(a, b) =

U (a, b) I (a, b)

(9)

The relationship between impedance frequencies f and fc and a is as follows: f =

fc a

(10)

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3 Experiments 3.1 Experimental Platform The research object is 2.6Ah ternary material (nickel-cobalt-manganese, NCM) 18650 cylindrical LIB. Figure 1 shows schematic of entire test system. Arbin BT-ML charges LIBs and provides excitation current. The sampling rate of data acquisition card (NI USB-6210, voltage range: ± 10 V, resolution: 16bit, accuracy: 20/216 = 306 μ V) is 10 kHz. Collect operating voltage of LIBs and voltage of shunt (75 mV/100 A, ± 0.5%). The current through LIBs can be obtained by dividing voltage by resistor of the shunt. The temperature box provides charging conditions for LIBs at different temperatures. IVIUM is used to measure the reference EIS. The EIS is recorded at a frequency of 10 points per tenfold in the range of 10 Hz to 0.1 Hz, and the AC amplitude applied by IVIUM is set to 0.2A. In addition, the data (current/voltage /EIS) is recorded using a host computer with an AMD Ryzen 7 5800H CPU and 16 GB RAM, and the program is run for calculation. Arbin BT-ML battery charging and discharging tester

NI USB-6210 data acquisition board

shunt

lithium battery

computer

thermotank

IVIUM electrochemical workstation

Fig. 1. LIBs test system structure diagram.

3.2 Experimental Design LP Induction Experiments. In order to explore the boundary conditions for LP of LIBs at different rates and ambient temperatures, Cells of 1, 2, 3 were placed at 25°C, 15°C and 5°C respectively and charged with different rates of charging current. LP detection method of voltage relaxation profiles (VRP) was used to detect LIBs. The steps of the experiment are as follows: 1. Put the Cell 1 in a 25°C temperature box for 2 h; 2. Cell 1 is charged with 0.5C, 0.75C, 1C, 1.25C and 1.5C respectively until it reaches 4.2 V; 3. Stand Cell 1 for 2 h, record the terminal voltage and determine whether lithium LP occurs by VRP; 4. Discharge Cell 1 with 0.5C rate until it reaches 2.75 V;

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5. Place Cells of 2, 3 at 15°C and 5°C respectively and repeat steps 2 ~ 4. LP Detection Experiment. In order to detect LP and record detection time, the LIB was fully discharged, and then charged to different SOCs with 1.5C at 15°C. Reference EIS was measured by IVIUM, and analog EIS was calculated by CMWT. Excitation currents in Fig. 2 were provided to the LIB. fc is 100 Hz; fb = 1.62 × 10−4 s2 . The steps of the experiment are as follows: 1. 2. 3. 4. 5. 6. 7.

A new LIB is pretreated in a cycle; After the LIB is fully discharged, it is placed at 15°C for 2 h; Charge the LIB to 20%SOC with 1.5C and stand for 2 h; Test the EIS with IVIUM and record the test time; Apply excitation current to the LIB, calculate the EIS and record the time; Charge the LIB to SOCs of 40%, 60%, 80%, 99% with 1.5C and repeat steps 3 ~ 5; Identifying the minimum impedance of EIS under different SoCs, the lithium plating criterion is extracted to determine whether LP occurs in the LIB.

Fig. 2. Excitation current.

4 Results and Discussion 4.1 Analysis of Experimental Results of LP Induction The VRPs and corresponding derivatives of Cells 1, 2, 3 are shown in Fig. 3. According to VRP, when the differential curve appears a hollow area in the early stage, it indicates that LP occurs during the charging process of the LIBs [10]. Therefore, LP occurs at 5°C, 15°C except 0.5C and does not occur at 25°C except 1.5C. 4.2 Analysis of Experimental Results of LP Detection In this section, before analyzing the detection results of LP, the calculation results of reference EIS (ZIVIEM ) and analog EIS (ZWT ) when the LIB is charged to 20%SOC with 1.5C at 15°C were first compared, as shown in Fig. 4(a).

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Fig. 3. The VRPs of Cells at different temperatures and their derivatives (a) and (b) Cell1 at 5°C, (c) and (d) Cell2 at 15°C, (e) and (f) Cell3 at 25°C.

Fig. 4. The LIB is at 20%SOC (a) EIS comparison, (b) Real part relative error and imaginary part relative error.

Figure 4(b) shows the relative error of ZIVIEM and ZWT , the relative error of the real part of the black line and the relative error of the imaginary part of the red line. In the frequency range from 0.1 Hz to 10 Hz, the maximum relative error of the real part is 0.41%, in which the maximum relative error of the negative imaginary part is 8.29%, and the relative error of both the real part and the imaginary part is within 9%. As shown in the Fig. 5, the EIS obtained by different methods at different SOCs. ZWT and ZIVIEM are represented by dashed and solid lines respectively. It can be seen from the figure that ZWT and ZIVIEM under different SOCs are basically consistent in shape and have obvious minimum points. As can be seen from Fig. 5, when the LIB is charged with 1.5C at 15°C, the minimum value ZWT _ min of the LIB EIS in the frequency range of 10 Hz ~ 0.1 Hz first decreases with the increase of SOC, then basically remains

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Fig. 5. Result comparison and criterion extraction (a) ZIVIEM and ZWT under different SOCs, (b) ZWT _ min under different SOCs.

unchanged, and finally decreases again. According to the judgment principle of LP in literature [10], the LP phenomenon occurred in the battery. The time required to calculate ZWT pass under five SOCs is the sum of time of data collection and time of program calculation, and the total time is 552.28 s. The time required to measure ZIVIEM at five SOCs is the sum of the time of five tests, and the total time was 752.5 s. It can be seen that the LP detection method based on CMWT is 26.61% faster in detection time than the LP detection method using IVIUM, and does not require expensive EIS testing equipment.

5 Conclusions A method of EIS calculation and LP detection based on CMWT is presented in this paper. Different from the conventional electrochemical workstation measurement of EIS, this paper calculates the applied excitation current and response voltage signals based on CMWT to extract EIS quickly. In order to obtain the boundary conditions of battery LP, this paper charged three different batteries at different temperatures and charging rates and determined whether LP occurred by VRP. The EIS at different SOCs were quickly calculated by CMWT under the condition of 15°C with 1.5C current, and then the LP criteria were extracted to determine whether LP occurred in the battery. Compared with the EIS measured by IVIUM for LP detection, the maximum relative error between the imaginary part and the real part of the EIS calculation proposed in this paper is less than 9%, and the detection time of LP is 26.61% faster. Acknowledgments. This study is supported by the National Natural Science Foundation of China (52007085).

References 1. Tran, M.K., Mevawalla, A., Aziz, A., et al.: A review of lithium-ion battery thermal runaway modeling and diagnosis. Processes 10(6), (2022)

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2. Neubauer, J., Wood, E.: The impact of range anxiety and home, workplace, and public charging infrastructure on simulated battery electric vehicle lifetime utility. J. Power. Sources 257, 12–20 (2014) 3. Li, Y.L., Gao, X.L., Feng, X.N., et al.: Battery eruption triggered by plated lithium on an anode during thermal runaway after fast charging. Energy 239 (2022) 4. Ge, H., Aoki, T., Ikeda, N., et al.: Investigating lithium plating in lithium-ion batteries at low temperatures using electrochemical model with NMR assisted parameterization. J. Electrochem. Soc. 164(6), A1050–A1060 (2017) 5. Zhang, Y.K., Li, X.Y., Su, L.S., et al.: Lithium plating detection and quantification in Li-ion cells from degradation behaviors. Failure Mode Mechanism Analyses 75(23), 37–50 (2017) 6. Bach, T.C., Schuster, S.F., Fleder, E., et al.: Nonlinear aging of cylindrical lithium-ion cells linked to heterogeneous compression. J. Energy Storage 5, 212–223 (2016) 7. Petzl, M., Danzer, M.A.: Nondestructive detection, characterization, and quantification of lithium plating in commercial lithium-ion batteries. J. Power. Sources 254, 80–87 (2014) 8. Paul, P.P., Cao, C.T., Thampy, V., et al.: Using in situ high-energy X-ray diffraction to quantify electrode behavior of Li-ion batteries from extreme fast charging. ACS Appl. Energy Mater. 4(10), 11590–11598 (2021) 9. Schindler, S., Bauer, M., Petzl, M., Danzer, M.A.: Voltage relaxation and impedance spectroscopy as in-operando methods for the detection of lithium plating on graphitic anodes in commercial lithium-ion cells. J. Power. Sources 304, 170–180 (2016) 10. Koleti, U.R., Dinh, T.Q., Marco, J.: A new on-line method for lithium plating detection in lithium-ion batteries. J. Power Sources 451 (2020)

Living Object Detection of Electric Vehicle Wireless Charging Systems Based on a Single Motion Feature Wenhao Li1 , Hui Jiang1 , Jindong Tian1,2 , and Yong Tian1(B) 1 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060,

China [email protected] 2 Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ), Shenzhen 518060, China

Abstract. The electromagnetic field generated during the wireless charging of electric vehicles is likely to cause electromagnetic injury to nearby living objects. Although some living object detection methods have been proposed, they are unable to accurately distinguish an organism from other non-living moving objects. In this paper, a method based on millimeter wave radar and motion feature is proposed to exactly detect the living objects rather than the moving objects. The standard velocity deviation is served as a single motion feature of moving objects. A machine learning model, namely support vector machine, is designed to classify the living objects and other non-living moving objects based on the selected single motion feature. Experimental results show that the average accuracy of human body identification is higher than 97%, and the false positive rate of foreign objects is about 10%. Keywords: Wireless charging system · MMW radar · living object detection · support vector machine

1 Introduction Electric vehicles (EVs) have been commercialized rapidly in the last two decades. However, how to supplement electric power for EVs safely, quickly and conveniently is still a challenging issue to be addressed, which restricts the development of EVs [1]. At present, the commonly used charging technology for EVs requires electric cables for physical connection, which is called wired charging. After frequent use, the charging connector is easy to loosen due to aging or generate sparks, even leading to fire. In addition, the charging device may cause safety accidents such as electric shock in humid environments [2]. Another “recharging” mode is to replace the battery, but it needs to solve the problem of battery matching from different manufacturers. Wireless charging, in contrast, overcomes these aforementioned problems and makes dynamic charging possible, and it has been widely concerned by both academic and industrial communities. With the development of wireless charging technology, the electromagnetic field generated © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 579–587, 2024. https://doi.org/10.1007/978-981-97-0873-4_58

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during the charging process has attracted attention due to the potential electromagnetic hazards to the living objects, such as human beings and animals [3]. To meet the requirements of International Commission on Non-Ionizing Radiation Protection, living objects in or near the wireless charging region need to be protected from excessive electromagnetic radiation, which refers to living object detection (LOD). There are mainly two ways for LOD. The first is to shield or weaken the electromagnetic field leakage around the charging region. Further, it can be divided into active shielding and passive shielding. The active shielding is to use the reverse magnetic field generated by the shielding coil to weaken the target magnetic field [4]. Nevertheless, it is difficult to design the appropriate shielding coils. The passive shielding is to adapt magnetic materials with high permeability for constraining the target magnetic field, and conductive materials for generating reverse magnetic fields to inhibit magnetic field leakage [5]. However, the addition of conductive materials will lower the coupling degree of the charging coils, thus reducing the efficiency of power transmission. The second method is based on extra sensors, including capacitance-based methods, thermal detection methods and motion detection methods [6–8]. Among them, capacitance-based methods are difficult to deal with the electromagnetic noise between the power transmitting coil and capacitance sensors, and it can only detect living objects which have entered on the charging coil. Thermal detection methods are unreliable in extreme weather, and the used sensors usually are expensive. Motion detection methods can detect moving objects outside the high-intensity electromagnetic field area, thus guiding the wireless charging system to reduce or even close the charging power in advance. Currently, sensors used for motion detection mainly include ultrasonic radars, laser radars and millimeter wave (MMW) radars. Among them, ultrasonic radars are susceptible to sand and dust weather, while laser radars are susceptible to rain and snow weather [9]. Compared with ultrasonic radars and laser radars, MMW radars have advantages such as high detection accuracy, strong anti-interference and penetration abilities, and moderate cost [10], so they are preferred for LOD of EV wireless charging systems. Unfortunately, current detection methods based on MMW radars can only distinguish moving objects from non-moving objects, but cannot accurately recognize the moving objects are human bodies or not [11]. When foreign objects that need not to be protected approach the charging area, such as moving beverage bottles caused by wind, the charging system will suffer from unexpected shutdowns due to false alarms. To address the aforementioned drawback of current MMW radar-based method, this paper newly proposed a LOD method based on a single motion feature. A 77 GHz MMW radar is applied to collect data. Then, standard velocity deviation is adopted to capture the motion feature of moving objects. Finally, a support vector machine (SVM) model is trained to distinguish the living objects from other moving non-living objects. Effectiveness of the proposed method is validated by experiments.

2 Dataset The MMW radar used in this paper is based on the frequency modulated continuous wave (FMCW) principle. It modulates the transmitting signal at a certain modulation rate, transmits the modulated signal via the transmitter antenna, and then receives the

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signal reflected by targets using the receiver antenna. After data processing, information such as distance, direction and speed of the target can be obtained. Specially, the TI IWR1642, which is a 77 GHz MMW radar was used in this paper. Main specifications of the TI IWR1642 radar include range resolution of 4 cm, velocity resolution of 0.24 m/s, horizontal detection angle of 120°, and vertical detection angle of 30°. The configuration of the MMW radar detection system is illustrated in Fig. 1, where the arrow indicates moving direction of the objects.

Fig. 1 Configuration of the MMW radar detection system

Three kinds of moving objects, including a free walking human body (age: 25 years old, height: 174 cm, weight: 61.5 kg), an ordinary plastic bottle with decelerating motion (15 cm in height and 6 cm in width) as shown in Fig. 2(a), and a slow-moving rubber ball (about 13 cm in diameter) as shown in Fig. 2(b), were used to collect data.

(a)

(b)

Fig. 2 Samples of common foreign object: (a) a plastic bottle, (b) a rubber ball

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3 Methods 3.1 Algorithm Overview Figure 3 shows the overview and workflow of the proposed method for human motion detection based on MMW radar.

Fig. 3 Workflow of the proposed algorithm for human motion detection

The specific steps are as follows: 1) Data preprocessing: two-dimensional spatial position information of moving objects is used for noise reduction based on point cloud density. 2) Feature extraction: the standard velocity deviation of the remaining points is calculated after removing noise points in each segment. 3) Target identification: the trained SVM model is employed to judge the object type. 3.2 Data Preprocessing The 77 GHz MMW radar is high-resolution, so multiple detection points will be generated when a human body freely moves one step. At the same time, noise points unrelated to the actual target will be generated, causing errors to the motion feature extraction. Therefore, it is imperative to reduce noise on the target points.

Fig. 4 Noise reduction based on point cloud density

Density-based spatial clustering of application with noise (DBSCAN) algorithm, as a commonly used clustering method based on point cloud density, has high clustering

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speed, simple principle and good effect. Hence, it is used in this paper for noise reduction, and the processing steps are summarized as follows: (1) The data is divided according to the time series: every ten groups of data is a paragraph, and each group of data points includes the position information and speed information of the moving object. (2) Calculating the number num in the neighborhood radius ε of each point in this data segment. (3) If num > MinPts, then this point is considered to be a core point, otherwise it is the noise point, as explicated in Fig. 4. where ε is the neighborhood radius of each point, MinPts is the minimum number of points in the neighborhood. In this paper, ε = 75 cm and MinPts is set to 5. 3.3 Motion Feature Extraction Usually, the normal walking process of human body is not a simple uniform motion, but a combination of multiple movements, including ankle joint rotation, knee joint rotation, leg and foot movement, arm swing and torso movement, etc. In addition, during a free walking, the movement speed of different body parts is inconsistent, and even the speed of the same part is different [12]. The decomposition of human free walking is shown in Fig. 5. In contrast, the movement of common foreign objects (plastic bottles and small balls) changes more smoothly than that of human body. In summary, the velocity dispersion degree of moving objects in a time period is chosen as a key feature to distinguish human movement and common foreign object movement. Since standard deviation, as a commonly used mathematical concept to describe the dispersion degree of data, has the advantages of simple calculation and ideal effect, it is selected in this paper to describe the velocity dispersion degree of different moving objects.

Fig. 5 The decomposition of free walking of a human body

The standard deviation is defined as:    n  (xi − x)2  i=1 s= n−1

(1)

where x is the mean value of velocity in the data segment after noise point removal; x i is the velocity value of each group of data; n is the remaining number of data points in the data segment; s is the standard deviation of velocity.

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Feature extraction is carried out based on preprocessed data. The standard deviation of velocity of three different moving objects is plotted in Fig. 6. It is evident that the plastic bottle and the rubber ball have a similar standard deviation of speed, and both are significantly different from that of the human body. Specially, the dispersion degree of human motion velocity is higher, indicating that the complexity of human motion is much higher than other foreign objects. It is also proved that with a section of data (ten data points), human motion and other foreign object motion can be distinguished using the degree of velocity dispersion. After the normalization of the preprocessed data, datasets of different object velocity dispersion are obtained. 150 Plastic Bottle Rubber Ball Hunman body

Standard deviation(m/s)

100

50

0 0

5

10

15

20

25

Number of segments

Fig. 6 The standard deviation of velocities of different moving objects

3.4 SVM Classifier As a classical supervised binary machine learning model, SVM is suitable for classification based on small datasets. The issue in this paper is single feature-based classification with a small amount of data, so SVM model is chosen. Besides, Gaussian kernel function is used in the SVM model, which is formulated as: f (x) = sign(

n 

yiλiK(x, xi) − b)

i=1

K(x, xi) = exp(−γ ||x − xi||2)

(2)

where K(x, x i ) is the kernel function, λi is the Lagrange multiplier, γ and b are the parameters to be trained, x i is the sample, and yi is the label.

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4 Results 4.1 Model Training The dataset was proportionally divided into training set and test set. The performance of the model is evaluated by accuracy η in Eq. (3), which gives the ratio of correct detection results to the total samples. η=

Ntrue × 100% N

(3)

where N true is the number of samples classified correctly, and N is the total sample in the training set or test set. The training results of SVM model are shown in Table 1. Table 1. Training results of the SVM model Classes

Human

Foreign object

Accuracy rate

Total samples

82

28

/

Training samples

57

13

100%

Test samples

25

15

100%

The tabular results show that even though the SVM model is trained only using a single feature, the accuracies of both the training set and the test set can reach 100%, which proves the rationality of choosing the standard deviation of the speed as the feature to distinguish human movement from common foreign object movement. 4.2 Real-Time Test Results In order to verify the generalization ability of the proposed method, the trained SVM model was used for real-time test. The designed algorithm and the trained model were transplanted into a personal computer with software Qt5, and the test objects move freely in sequence within the detection range of the radar. Meanwhile, the type of the moving object is judged in real time and the results are shown in Table 2. Table 2. Real-time detection results of different objects Test objects

Total samples

Human

Foreign object

Accuracy rate

Human body 1#

105

103

2

98.1%

Human body 2#

94

94

0

100%

Human body 3#

106

99

7

93.4%

Foreign object

86

9

77

89.5%

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The results in Table 2 show that the accuracy of different test objects are different to some extent, but the accuracy of all test human bodies is more than 93%, and the average accuracy is 97%. The false alarm rate of foreign object movement is about 10%. It is proved that the SVM model based on the single motion feature of standard velocity deviation has good generalization ability, especially for human body detection.

5 Conclusion This paper has proposed an algorithm based on a single motion feature to accurately protect living objects approaching the wireless charging region of EVs. A TI IWR1642 millimeter wave radar is employed to collect motion dataset of three moving objects. Based on statistical analysis results, the standard velocity deviation is chosen as the single motion feature for representing motion difference of different moving objects. Afterwards, a support vector machine model is designed to detect living objects based on the selected single motion feature. Experimental results show that the proposed method can well distinguish the human body from other two non-living moving objects. In particular, the accuracy of human movement detection reaches 97% in average, and the false positive rate of non-living foreign object detection is about 10%. In our future work, we will further investigate the influence of high wireless power transfer on the millimeter wave radar measurement, and thus on the accuracy of living object detection. Also, the recognition capability and accuracy of the proposed method will be evaluated with multiple smaller organisms. Acknowledgements. This research is supported by the Science and Technology Plan Project of Shenzhen (No. JCYJ20220818100012026).

References 1. Machura, P., Santis, V.D., Li, Q.: Driving range of electric vehicles charged by wireless power transfer. IEEE Trans. Veh. Technol. 69(6), 5968–5982 (2020) 2. Xue, M., Yang, Q., Zhang, P., et al.: Application status and key issues of wireless power transmission technology. Trans. China Electrotech. Soc. 36(8), 1547–1568 (2021). (in Chinese) 3. Tian, Y., Guan, W., Li, G., et al.: A review on foreign object detection for magnetic couplingbased electric vehicle wireless charging. Green Energy Intell. Transp. 1(2), 100007 (2022) 4. Hiles, M.L., Olsen, R.G., Holte, K.C., et al.: Power frequency magnetic field management using a combination of active and passive shielding technology. IEEE Trans. Power Deliv. 13(1), 171–179 (1998) 5. Kim, J., Kim, J., Kong, S., et al.: Coil design and shielding methods for a magnetic resonant wireless power transfer system. Proc. IEEE 101(6), 1332–1342 (2013) 6. Jeong, S.Y., Kwak, H.G., Jang, G.C., et al.: Living object detection system based on comb pattern capacitive sensor for wireless EV chargers. In: 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), pp. 1–6, Auckland (2016) 7. Sonnenberg, T., Stevens, A., Dayerizadeh, A., et al.: Combined foreign object detection and live object protection in wireless power transfer systems via real-time thermal camera analysis. In: 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 1547–1552, Anaheim (2019)

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8. Poguntke, T., Schumann, P., Ochs, K.: Radar-based living object protection for inductive charging of electric vehicles using two-dimensional signal processing. Wirel. Power Transf. 4(2), 1–10 (2017) 9. Zhou, T., Yang, M., Jiang, K., et al.: MMW radar-based technologies in autonomous driving: a review. Sensors 20(24), 7283 (2022) 10. Yang, D., Jiang, K., Zhao, D., et al.: Intelligent and connected vehicles: current status and future perspectives. China Technol 61, 1446–1471 (2018) 11. Tian, Y., Yang, H., Hu, C., Tian, J.: Moving foreign object detection and track for electric vehicle wireless charging based on millimeter-wave radar. Trans. China Electrotech. Soc. 38(2), 297–308 (2023). (in Chinese) 12. Boulic, R., Thalmann, N.M., Thalmann, D.: A global human walking model with real-time kinematic personification. Vis. Comput.Comput. 6, 344–358 (1990)

A Real-Time Positioning Strategy for Dynamic Wireless Power Supply System Xinguo Li, Linlin Tan(B) , Xiaoqi Shen, Cheng Chen, and Zhijun Wu School of Electrical Engineering, Southeast University, Nanjing 210096, China [email protected]

Abstract. In order to avoid the problem that traditional load detection system in dynamic wireless power supply system needs to be idle for a long time and cause a lot of loss, an improved real-time positioning strategy is proposed in this paper to support the switching of the system. Firstly, the magnetic field and mutual inductance of the segmented guide coil are analyzed, and the relationship between mutual inductance and three-dimensional coordinate of load is established. Secondly, the offset of the load perpendicular to the driving direction is calculated from the induced voltage of the sampling coil at the receiving end. The mutual inductance is calculated from the picking voltage of the receiving end, and the displacement of the driving direction is calculated according to the mutual inductance and the offset, so as to determine the coordinate of the load. Finally, it is verified by simulation that the proposed strategy can calculate the relative position of load and guide rail in real time, so as to avoid the no-load loss caused by the long standby of the transmitter due to the load detection, reduce the engineering cost and improve the system efficiency. Keywords: Dynamic wireless charging · magnetic field analysis · mutual inductance calculation · positioning strategy

1 Introduction With the global attention to the problem of energy shortage, new power storage components such as lithium-ion batteries have developed rapidly, and are widely used in mobile automation scenarios such as inspection robots and embedded workstations. Compared with the way of using cables to transmit power, dynamic wireless power supply technology has significant advantages, it is safer and more reliable, more unmanned and intelligent. Therefore, in the field of intelligent mobile load power supply for mobile robots, inspection robots and other technologies, dynamic wireless power supply technology (DWPT) is a major research focus. Wireless power supply technology can be divided into long guide rail and segmented guide rail according to the type of magnetic coupling mechanism. Although the system composition and control of the long-guide coupling mechanism are relatively simple, the mutual inductance fluctuation is small, but the no-load loss is too large. The segmented guide rail has a higher efficiency improvement space. Therefore, in the process of DWPT © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1158, pp. 588–597, 2024. https://doi.org/10.1007/978-981-97-0873-4_59

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technology towards industrialization, the application of segmented guide rail, with better control strategy, in order to reduce the loss is the main direction of research. For the segmented guide system, the switching area means the departure or access of the load, which requires the transmitter to have accurate positioning capability and the ability to accurately switch in a high-efficiency position. In order to optimize the load location strategy, the current conventional method is to install sensors at fixed positions for load detection. In reference [2], the method of arranging special detection coils is applied. The size of the detection coils in this method is almost the same as that of the transmitting coils, which requires an independent and huge signal processing system, which is not conducive to the popularization of the project. Reference [3] proposes a positioning strategy based on no-load current as the threshold value. The load needs to drive a certain distance away from the transmitting coil to reach the threshold value, and the response time is long, which is not suitable for the system where the transmitting coil is tightly arranged with high utilization rate at the transmitting end. Moreover, the prerequisite for the application of this method is that the transmitting coil must be turned on standby in advance, which has a large no-load loss. In summary, the above load identification methods do not consider the relative position between the load and the transmitting coil in real time, and the sensor for load detection needs to be installed at a specific position in each switching area, so there is room for optimization in terms of cost, response speed, no-load loss, etc. The positioning strategy proposed in this paper can calculate the relative position of the robot load and the transmitting coil in real time, so as to achieve real-time positioning, accurate switching, reduce no-load loss, and improve system efficiency.

2 Introduction 2.1 Coil Mutual Inductance Calculation Mutual inductance is mapped to the relative position between transmitting and receiving coils. The position of transmitting coil and receiving coil is shown in Fig. 1.

8 5

0, 0, 0

7

1

4

Coil2

0 3

6

2

Coil1

Fig. 1. Position diagram of transmitting and receiving coils.

Let the four sides of the transmitting coil be l1 , l 2 , l 3 and l 4 , The four sides of the receiving coil are l5 , l 6 , l 7 and l 8 , The length of l 1 and l 2 is 2a, the length of l3 and l 4 is 2b, the length of l5 and l 6 is 2c, and the length of l 7 and l 8 is 2d. There is no mutual inductance between the vertical wires, and the mutual inductance between the non-vertical wires

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can be calculated. Taking l1 and l5 as an example, the mutual inductance between them is    c a μ N N dl dl5 dx1 dx2 μ0 N1 N2 → 1 → = 0 1 5 Ml1 l5 =   4π 4π −c −a Rl1 l5  r1 − r5  l1 l5   dx1 dx2 μ0 N1 N5 c a  = (1) 4π −c −a (xcoil1 − xcoil2 )2 + (d − b)2 + h2 where μ0 is the permeability in vacuum and its value is 4π × 10−7 , N 1 and N 2 are the number of turns of transmitting and receiving coils respectively; x coil1 and x coil2 are the X-axis coordinates of the entries on l1 and l 5 . In the same way, the mutual inductance between the other non-perpendicular coil edges can also be calculated. Finally, the formula for calculating the mutual inductance between the transmitting coil and the receiving coil is Mi = Ml1 l5 + Ml1 l6 + Ml2 l5 + Ml2 l6 + Ml3 l7 + Ml3 l8 + Ml4 l7 + Ml4 l8

(2)

According to Eqs. (1) and (2), the mapping relationship between mutual inductance and three coordinates of load position can be constructed. Obviously, the smaller the offset of load position coordinates with respect to the X-axis, the greater the mutual inductance, and a monotone increasing function of the X-axis offset with respect to mutual inductance can be constructed.

3 Positioning and Switching Strategy 3.1 Calculation of Offset Perpendicular to the Direction of Operation Two inductive detector loops are installed on the chassis of the mobile robot with symmetrical driving direction. The detector loop will generate an induced electromotive force under the magnetic field stimulated by both the transmitting coil and the receiving coil. Since the magnetic field of the receiving coil is symmetric at P and Q, the difference of the effective value of the induced electromotive force at P and Q can eliminate the component of the receiving coil to the induced electromotive force, so that the electric potential difference is only related to the load position and the relative position of the transmitting coil. As shown in Fig. 2, the coordinates of the two inductive detector loops are P(x 1 , y1 , h) and Q(x 2 , y2 , h) respectively. According to Faraday’s law of electromagnetic induction, the expression of induced electromotive force is E=

dB(t) d ϕ(t) = NA μ dt dt

(3)

where ϕ(t) is the magnetic flux, N is the number of turns of the coil, A is the cross-section area of the coil, μ0 is the permeability in vacuum, μ is the magnetic core permeability, and B(t) is the magnetic induction intensity.

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1, 2,

4

0

1

2

3

Coil

Fig. 2. Position diagram of transmitting coil and detector loop

According to the Biot-Savart law, 



μ0 Id l × e dB = 4π |  r |2 

(4)

The magnetic field intensity stimulated by the transmitting coil at P is μ0 ( = 4π

BP1  +







Id l × e

−a

(b + y1 )2 + h2 + x2

1







b

Id l × e

−b

(a − x1 )2 + h2 + y2

3





a

dy +

dx +



a

Id l × e

−a

(b − y1 )2 + h2 + x2

2



dx



b

Id l × e

−b

(a + x1 )2 + h2 + y2

4

dy)

(5)

The magnetic field intensity stimulated by the receiving coil at P is

BP2 =  +

μ0 ( 4π





a

−a 





Id l × e 1

(b + y1 )2 + x2 



b

Id l × e

−b

(a − x1 )2 + y2

3

dy +

dx +



a

−a 



Id l × e 2

(b − y1 )2 + x2

dx



b

Id l × e

−b

(a + x1 )2 + y2

4

dy)

(6)

In the LCC topology, the coil current waveform is sine at resonant frequency, the angular frequency is ω0 , the initial phase is θ0 , and the transmitting coil current expression is I = Im sin(ω0 t + θ0 )

(7)

The magnetic field strength at P is BP = BP1 + BP2

(8)

By inserting Eqs. (14)–(17) into Eq. (12), the effective value of the induced electromotive force of the detection coil at P is

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  a Im μ0 x  EP = EP1 + EP2 = NAμω0 √ (arctan   2 2 4π 2 (a − y1 ) + h −a    a  b y x    + arctan + arctan    (a − y2 )2 + h2 −a (a − x1 )2 + h2 −b   b y  ) + EP2 + arctan   (a − x1 )2 + h2 −b

(9)

In the same way, the induced electromotive force of the Q point can be obtained, ignoring the small pose change, then y1 = y2 . The equations formed by the induced electric potential difference at P and Q and the distance between the detection coils are ⎧ ⎪ E = EP − EQ ⎪ ⎪ ⎪ ⎨ EP − EQ = K(arctan √ b − arctan √ b 2 2 ) (a−x1 )2 +h2 (a−x2 ) +h (10) ⎪ x − x = D ⎪ 1 2 ⎪ ⎪ ⎩ K = √1 NAμμ0 ω0 Im 2 2π

Combining the monotone interval of E P and E Q , we can solve the binary equation about x 1 and x 2 , and obtain the numerical solution of x 1 and x 2 . The offset of the load on the X-axis is x =

1 (x1 + x2 ) 2

(11)

3.2 Calculation of the Amount of Travel Parallel to the Running Direction This switching strategy is applicable to the scenario of single transmitting module power supply in the LCC-S compensation topology. As shown in Fig. 3, with the edge of the first transmitting coil as the coordinate starting point, the switch is performed when the midpoint of the receiving coil runs to the midpoint of the adjacent transmitting coil.

p

o

Fig. 3. Energy emission module

US

ip

12

i S S

Fig. 4. LCC-S topologically equivalent circuit

The equivalent circuit of the LCC-S topology is shown in Fig. 4. Among them, U S represents the square wave voltage output by the inverter; L f is the inductance value of the compensating inductance; r f is the internal resistance of the transmitting coil and the

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power supply; C f is the compensation capacitance; C p is the resonance capacitance; L p is the equivalent inductance of the transmitting coil; M 12 is the mutual inductance between the transmitting coil and the receiving coil; L s is the self-inductance of the receiving coil; C s is the compensation capacitance of the receiving end; r s is the equivalent internal resistance of the receiving end. After the rectifier, the output end of the rectifier is V bus . According to LCC-S resonance condition and KVL equation, the steady state condition can be deduced is =

M12 Us (rs + rL )Lf

(12)

The relationship between the effective value of the pick voltage and the bus voltage on the input side of the hybrid accumulator is √ Vout = 2(Vbus + is rs ) (13) At the same time, the pick voltage Vout is open circuit voltage. Then it is  rL M12 Us  M12 Us Vout = = (rs + rL )Lf rs