Abstract:Magnetically coupled resonant wireless power transfer (MCR-WPT) technology has received significant attention due to its ability to realize mid-range power transfer. However, the transmission characteristics of MCR-WPT systems are susceptible to variations in coupling coefficients and loads. Parity-time (PT) symmetry has been introduced into the WPT system (PT-WPT) to achieve constant power and high-efficiency transmission over medium distances. This paper provides a comprehensive review of the PT-WPT technology. First, the paper introduces the PT-WPT system’s basic structure and operating mechanism. It analyzes how the system balances energy gain and loss through the nonlinear saturated negative resistor, allowing it to maintain stable power transmission under varying coupling conditions. Coupled-mode and circuit models are used to construct the PT-WPT system. The two models’ similarities and differences in the energy transmission mechanism, PT symmetry conditions, and system characteristics are described. In addition, PT-WPT can be considered a novel wireless power transfer technology. Next, the paper discusses the construction methods of nonlinear saturated negative resistors, which can be divided into two categories based on the components used: operational amplifiers and power converters. While operational amplifiers provide a simple and low-cost solution, they are limited in power output. In contrast, power converters, such as half-bridge, full-bridge, and class E inverters, enable higher power output and efficiency but require more complex control strategies. Then, the advantages and disadvantages of these methods are discussed, and directions for improving the design of negative resistors are given. This paper introduces the different types of coupling mechanisms and the implementation of charging functions. Among the topologies of PT-WPT systems, single-transmitter-single-receiver is the most basic structure; high-order compensation networks and the introduction of relay coils are commonly used to extend the transmission distance of the PT-WPT system. Multi-transmitter/multi-receiver can also improve the system’s reliability and realize stable power transmission in multi-load systems. Furthermore, the charging control strategies are investigated to realize the constant power and constant current/voltage functions independent of the coupling coefficient and load variation, further promoting the practicalization of PT-WPT systems. Finally, this paper summarizes the existing research on PT-WPT systems and future research issues. PT-WPT technology is expected to find broader applications in the future and promote the development of wireless charging technology.
王思睿, 丘东元, 张波, 陈艳峰, 谢帆. 宇称-时间对称磁耦合无线电能传输技术研究进展[J]. 电工技术学报, 2025, 40(12): 3787-3802.
Wang Sirui, Qiu Dongyuan, Zhang Bo, Chen Yanfeng, Xie Fan. A Review of Parity-Time Symmetric Magnetic Coupling Wireless Power Transfer Technology. Transactions of China Electrotechnical Society, 2025, 40(12): 3787-3802.
[1] 黄学良, 谭林林, 陈中, 等. 无线电能传输技术研究与应用综述[J]. 电工技术学报, 2013, 28(10): 1-11. Huang Xueliang, Tan Linlin, Chen Zhong, et al.Review and research progress on wireless power transfer technology[J]. Transactions of China Electro-technical Society, 2013, 28(10): 1-11. [2] 王得安, 张剑韬, 朱春波, 等. 海洋环境对水下无线电能传输系统的影响机理研究进展[J]. 电工技术学报, 2025, 40(3): 653-675. Wang Dean, Zhang Jiantao, Zhu Chunbo, et al.Review of progress in the study of marine environment effects on underwater wireless power transfer systems[J]. Transactions of China Elec-trotechnical Society, 2025, 40(3): 653-675. [3] Kurs A, Karalis A, Moffatt R, et al.Wireless power transfer via strongly coupled magnetic resonances[J]. Science, 2007, 317(5834): 83-86. [4] 张波, 荣超, 江彦伟, 等. 分数阶无线电能传输机理的提出及研究进展[J]. 电力系统自动化, 2022, 46(4): 197-207. Zhang Bo, Rong Chao, Jiang Yanwei, et al.Proposal process and research progress of fractional-order wireless power transfer mechanism[J]. Automation of Electric Power Systems, 2022, 46(4): 197-207. [5] Yeo T D, Kwon D, Khang S T, et al.Design of maximum efficiency tracking control scheme for closed-loop wireless power charging system employing series resonant tank[J]. IEEE Transactions on Power Electronics, 2017, 32(1): 471-478. [6] Gati E, Kampitsis G, Manias S.Variable frequency controller for inductive power transfer in dynamic conditions[J]. IEEE Transactions on Power Elec-tronics, 2017, 32(2): 1684-1696. [7] Bender C M, Boettcher S.Real spectra in non-Hermitian hamiltonians having PT symmetry[J]. Physical Review Letters, 1998, 80(24): 5243-5246. [8] Dorey P, Dunning C, Tateo R.Spectral equivalences, Bethe ansatz equations, and reality properties in $ \mathcal{P} \mathcal{T}$-symmetric quantum mechanics[J]. Journal of Physics A: Mathematical and General, 2001, 34(28): 5679-5704. [9] Assawaworrarit S, Yu Xiaofang, Fan Shanhui.Robust wireless power transfer using a nonlinear parity-time-symmetric circuit[J]. Nature, 2017, 546(7658): 387-390. [10] Zhou Jiali, Zhang Bo, Xiao Wenxun, et al.Nonlinear parity-time-symmetric model for constant efficiency wireless power transfer: application to a drone-in-flight wireless charging platform[J]. IEEE Transa-ctions on Industrial Electronics, 2019, 66(5): 4097-4107. [11] 赵志友. 基于宇称时间对称的无线电能传输系统电路模型及分析[D]. 广州: 华南理工大学, 2018. Zhao Zhiyou.Circuit model and analysis of wireless power transmission system based on parity time symmetry[D]. Guangzhou: South China University of Technology, 2018. [12] 张波, 疏许健, 吴理豪, 等. 无线电能传输技术亟待解决的问题及对策[J]. 电力系统自动化, 2019, 43(18): 1-12. Zhang Bo, Shu Xujian, Wu Lihao, et al.Problems of wireless power transmission technology urgent to be solved and corresponding countermeasures[J]. Auto-mation of Electric Power Systems, 2019, 43(18): 1-12. [13] Rong Chao, Zhang Bo, Wei Zhihao, et al.A wireless power transfer system for spinal cord stimulation based on generalized parity-time symmetry con-dition[J]. IEEE Transactions on Industry Applications, 2022, 58(1): 1330-1339. [14] Chen P Y, Sakhdari M, Hajizadegan M, et al.Generalized parity-time symmetry condition for enhanced sensor telemetry[J]. Nature Electronics, 2018, 1: 297-304. [15] Wu Jiayang, Li Kerui, Zeng Junming, et al.On the limitations of the coupled mode theory and parity-time symmetry for near-field wireless power transfer research[J]. IEEE Transactions on Power Electronics, 2024, 39(5): 6433-6441. [16] Zhang Zheng, Zhang Bo.Omnidirectional and efficient wireless power transfer system for logistic robots[J]. IEEE Access, 2020, 8: 13683-13693. [17] 何德宇, 肖文勋. 具有高抗偏移特性的PT对称无线电能传输技术[J]. 电力电子技术, 2023, 57(9): 54-57, 78. He Deyu, Xiao Wenxun.PT symmetric wireless power transmission technology with high anti-misalignment characteristics[J]. Power Electronics, 2023, 57(9): 54-57, 78. [18] Sun Shubin, Zhang Bo, Rong Chao, et al.A multireceiver wireless power transfer system using self-oscillating source composed of zero-voltage switching full-bridge inverter[J]. IEEE Transactions on Industrial Electronics, 2022, 69(3): 2885-2895. [19] 贾亚辉, 王智慧, 肖静, 等. 磁耦合无线电能传输系统宽范围零电压开关实现方法[J]. 电工技术学报, 2024, 39(22): 6952-6964. Jia Yahui, Wang Zhihui, Xiao Jing, et al.Imple-mentation method of wide range zero voltage switching in magnetic coupling wireless power transfer system[J]. Transactions of China Electro-technical Society, 2024, 39(22): 6952-6964. [20] 李争, 于治昊, 高世豪, 等. 基于有源整流的无线电能传输系统双边LCL零电压软开关控制策略[J]. 电工技术学报, 2025, 40(8): 2380-2392. Li Zheng, Yu Zhihao, Gao Shihao, et al.Two-sided LCL zero voltage switching control strategy based on active rectifier for wireless power transfer system[J]. Transactions of China Electrotechnical Society, 2025, 40(8): 2380-2392. [21] Wu Lihao, Zhang Bo, Jiang Yanwei.Robust parity-time-symmetric WPT system with reduced switching-frequency and improved step-down conversion ratio[J]. IEEE Transactions on Transportation Elec-trification, 2023, 9(2): 2090-2103. [22] Assawaworrarit S, Fan Shanhui.Robust and efficient wireless power transfer using a switch-mode implementation of a nonlinear parity-time symmetric circuit[J]. Nature Electronics, 2020, 3: 273-279. [23] He Liangzong, Huang Xiayi, Cheng Bing.Robust class E2 wireless power transfer system based on parity-time symmetry[J]. IEEE Transactions on Power Electronics, 2023, 38(4): 4279-4288. [24] 张波, 赖立, 林靖扬, 等. 基于量子力学的PT对称无铁芯变压器机理提出及研究进展[J]. 中国电机工程学报, 2024, 44(18): 7479-7491. Zhang Bo, Lai Li, Lin Jingyang, et al.Mechanism proposal and research progress of PT-symmetric coreless transformers based on quantum mechanics[J]. Proceedings of the CSEE, 2024, 44(18): 7479-7491. [25] Wei Zhihao, Zhang Bo.Transmission range extension of PT-symmetry-based wireless power transfer system[J]. IEEE Transactions on Power Electronics, 2021, 36(10): 11135-11147. [26] Qu Yuhu, Zhang Bo, Gu Wenchao, et al.Distance extension of S-PS wireless power transfer system based on parity-time symmetry[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2023, 70(8): 2954-2958. [27] Gu Yu, Wang Jiang, Liang Zhenyan, et al.A wireless in-flight charging range extended PT-WPT system using S/single-inductor-double-capacitor compensation network for drones[J]. IEEE Transactions on Power Electronics, 2023, 38(10): 11847-11858. [28] Hamam R E, Karalis A, Joannopoulos J D, et al.Efficient weakly-radiative wireless energy transfer: an EIT-like approach[J]. Annals of Physics, 2009, 324(8): 1783-1795. [29] Sakhdari M, Hajizadegan M, Chen P Y.Robust extended-range wireless power transfer using a higher-order PT-symmetric platform[J]. Physical Review Research, 2020, 2: 013152. [30] Zeng Chao, Sun Yong, Li Guo, et al.High-order parity-time symmetric model for stable three-coil wireless power transfer[J]. Physical Review Applied, 2020, 13(3): 034054. [31] Zeng Chao, Guo Zhiwei, Zhu Kejia, et al.Efficient and stable wireless power transfer based on the non-Hermitian physics[J]. Chinese Physics B, 2022, 31(1): 010307. [32] Shu Xujian, Zhang Bo, Wei Zhihao, et al.Extended-distance wireless power transfer system with constant output power and transfer efficiency based on parity-time-symmetric principle[J]. IEEE Transactions on Power Electronics, 2021, 36(8): 8861-8871. [33] Zhang Li, Yang Yihao, Jiang Zhao, et al.Demonstration of topological wireless power transfer[J]. Science Bulletin, 2021, 66(10): 974-980. [34] Qu Yuhu, Zhang Bo, Gu Wenchao, et al.Wireless power transfer system with high-order compensation network based on parity-time-symmetric principle and relay coil[J]. IEEE Transactions on Power Electronics, 2023, 38(1): 1314-1323. [35] 王兆延, 丘东元, 张波, 等. 具有恒功率恒效率输出特性的三线圈WPT系统[J]. 中国电机工程学报, 2022, 42(20): 7332-7342. Wang Zhaoyan, Qiu Dongyuan, Zhang Bo, et al.Three-coil wireless power transfer system with constant output power and constant transfer efficiency characteristics[J]. Proceedings of the CSEE, 2022, 42(20): 7332-7342. [36] 罗成鑫, 丘东元, 张波, 等. 多负载无线电能传输系统[J]. 电工技术学报, 2020, 35(12): 2499-2516. Luo Chengxin, Qiu Dongyuan, Zhang Bo, et al.Wireless power transfer system for multiple loads[J]. Transactions of China Electrotechnical Society, 2020, 35(12): 2499-2516. [37] Zheng Weibin, Xie Fan, Xiao Wenxun, et al.Plane-omnidirectional wireless power transfer system based on vector-controlled flux linkage[J]. IEEE Access, 2021, 9: 105651-105666. [38] Chen Hao, Qiu Dongyuan, Rong Chao, et al.A double-transmitting coil wireless power transfer system based on parity time symmetry principle[J]. IEEE Transactions on Power Electronics, 2023, 38(11): 13396-13404. [39] 徐兴鹏, 郭锋, 何禧煜. 基于线圈切换的PT对称空间无线电能传输系统[J/OL]. 电源学报, 2024: 1-13. [2024-04-26]. https://kns.cnki.net/kcms/detail/12.1420.tm.20240426.1422.081.html. Xu Xingpeng, Guo Feng, He Xiyu. PT symmetric space wireless power transmission system based on coil switching[J/OL]. Journal of Power Supply, 2024: 1-13. [2024-04-26]. https://kns.cnki.net/kcms/detail/12.1420.tm.20240426.1422.081.html. [40] Wu Lihao, Zhang Bo, Zhou Jiali.Efficiency improvement of the parity-time-symmetric wireless power transfer system for electric vehicle charging[J]. IEEE Transactions on Power Electronics, 2020, 35(11): 12497-12508. [41] Luo Chengxin, Qiu Dongyuan, Gu Wenchao, et al.Multiload wireless power transfer system with constant output power and efficiency[J]. IEEE Transactions on Industry Applications, 2022, 58(1): 1101-1114. [42] 李小飞, 蒋光利, 李志恒, 等. 基于互感与负载识别的AGV无线电能传输系统闭环恒流与效率优化控制方法[J/OL]. 电工技术学报, 1-13 [2025-01-07]. https: //doi.org/10.19595/j.cnki.1000-6753.tces.240790. Li Xiaofei, Jiang Guangli, Li Zhiheng, et al. A closed-loop constant current and efficiency opti-mization control method for AGV wireless power transfer system based on mutual inductance and load identification[J/OL]. Transactions of China Electro-technical Society, 1-13 [2025-01-07]. https://doi.org/10.19595/j.cnki.1000-6753.tces.240790. [43] Chen Jintao, Xie Fan, Zhang Bo, et al.Transmission range extension strategy of parity-time-symmetry-based wireless power transfer system by a Boost converter[J]. International Journal of Circuit Theory and Applications, 2023, 51(2): 510-524. [44] Zhu Huanjie, Zhang Bo, Wu Lihao.Output power stabilization for wireless power transfer system employing primary-side-only control[J]. IEEE Access, 2020, 8: 63735-63747. [45] Wu Lihao, Zhang Bo, Jiang Yanwei, et al.A robust parity-time-symmetric WPT system with extended constant-power range for cordless kitchen appli-ances[J]. IEEE Transactions on Industry Applications, 2022, 58(1): 1179-1189. [46] Wu Ziliang, Huang Jiasheng, Wang Pinhe, et al.Parity-time-symmetry-based WPT systems with homogenous transmitter coils for drone appli-cations[C]//2024 IEEE Applied Power Electronics Conference and Exposition (APEC), Long Beach, CA, USA, 2024: 2933-2939. [47] 李中启, 张晨曦, 王建斌, 等. 基于变频重构S/SP拓扑的无线电能传输系统恒流恒压研究[J]. 电工技术学报, 2024, 39(15): 4718-4732. Li Zhongqi, Zhang Chenxi, Wang Jianbin, et al.Research on constant current and constant voltage of WPT system based on variable frequency reconfi-guration S/SP topology[J]. Transactions of China Electrotechnical Society, 2024, 39(15): 4718-4732. [48] 陈永洪, 黎祎阳, 杨斌, 等. 基于多中继线圈结构的无线电能传输系统恒流/恒压输出方法[J]. 电力系统自动化, 2022, 46(20): 147-154. Chen Yonghong, Li Yiyang, Yang Bin, et al.Constant-current/constant-voltage output method for wireless power transfer system based on multi-relay coil structure[J]. Automation of Electric Power Systems, 2022, 46(20): 147-154. [49] Wu Lihao, Zhang Bo, Jiang Yanwei.Position-independent constant current or constant voltage wireless electric vehicles charging system without dual-side communication and DC-DC converter[J]. IEEE Transactions on Industrial Electronics, 2022, 69(8): 7930-7939. [50] Liu Jinghang, Qu Xiaohui, Li Yundi, et al.Investi-gation of PT-symmetric frequency and compensation for IPT coupling-independent CC/CV and efficiency in wide load range[J]. IEEE Transactions on Power Electronics, 2023, 38(11): 13353-13362. [51] Dong Wenjie, Li Changsheng, Zhang He, et al.Wireless power transfer based on current non-linear PT-symmetry principle[J]. IET Power Electronics, 2019, 12(7): 1783-1791. [52] Hao Xianglin, Yin Ke, Zou Jianlong, et al.Frequency-stable robust wireless power transfer based on high-order pseudo-Hermitian physics[J]. Physical Review Letters, 2023, 130(7): 077202. [53] Cui Hongjian, Dong Zhenya, Kim H J, et al.High-efficiency selective wireless power transfer with a bistable parity-time-symmetric circuit[J]. Physical Review Applied, 2022, 18(4): 044076. [54] Rong Chao, Zhang Bo.A robust simultaneous wireless power and information transfer system for charging battery with wide charging region[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2024, 12(4): 3302-3314. [55] Ying Yue, Yu Yanlan, Dong Shurong, et al.A flexible wireless sacral nerve stimulator based on parity-time symmetry condition[J]. Electronics, 2024, 13(2): 292.