Abstract：Submarine currents are prone to cause multi-directional offsets in the coupling coils of the wireless charging system for AUVs, leading to a decrease in efficiency and power value, and even affecting the normal operation of the system. Recently, some offset-resistant coupling coils have been proposed to solve with these issues, but these methods have certain defects. To address these issues, this paper proposes a misalignment-compensated arc coil structure. By compensating the magnetic field, the anti-offset performance of the coil is effectively improved. Firstly, the analytical model for the spatial magnetic field of the arc coil was built based Biot-Savar law, and the analytical equation of the mutual inductance of the arc coil was obtained. Secondly, a simulation model of the arc coil was developed. An anti-offset optimization strategy for a single coil was designed based on the analysis of the spatial magnetic field of the arc coil. The influence of structural parameter changes on the spatial magnetic field distribution was also considered in the design process. Furthermore, a misalignment compensation structure for the arc coil was designed using the superposition theorem of magnetic fields, along with the spatial magnetic field distribution of the arc coil. Finally, a flowchart for the misalignment compensation arc coil was developed, taking into account the effects of the turn numbers Np1, Np2 and the misalignment distance l on mutual inductance. Through an iterative search of different values for the turn numbers and misalignment distance, the optimal parameter design was determined. Under various offsets, the calculated values of mutual inductance of the arc coil are compared with the experimental and simulated values, and the errors are less than 5%. From the simulation results, when the horizontal offset is 100 mm, the mutual inductance retention coefficient of the misalignment-compensated arc coil still reaches 0.57. In contrast, the arc coil only achieves a retention coefficient of 0.34. The arc coil also demonstrates strong offset resistance under rotating offsets. From the experimental results, the misalignment-compensated arc coil structure shows significant improvements in mutual inductance retention. When the horizontal offset is 50 mm, its retention coefficient increases by 13.29% compared to the ordinary arc coil structure. At an 80 mm horizontal offset, the retention coefficient rises by 19.23% relative to the ordinary design. The output voltage fluctuation of the load is 0.78% when the coil is horizontally offset by 30 mm, while the voltage fluctuation of the uncompensated arc coil is 7.7% under the same condition. These findings demonstrate the effectiveness of the misalignment-compensated design in maintaining mutual inductance under varying offset conditions. The following conclusions are drawn from calculations, simulations and experimental analyses: (1) The magnetic field distribution of the arc coil is mainly concentrated in the central region. The spatial magnetic field approaches zero as the distance from the center increases. (2) The proposed analytical model of mutual inductance is correct in all dimensions of the offsets. (3) The misalignment-compensated arc coil structure effectively compensates for misalignment in critical regions and demonstrates better offset resistance than other coil designs. (4) The proposed misalignment-compensated arc coil structure has lower output voltage fluctuation than the unipolar arc coil when the coils are subjected to the same offsets in a wireless power transmission system.
白龙雷, 刘一鸣, 罗博, 游江, 历程龙. 适用于水下感应式电能传输系统的抗偏移错位补偿弧形线圈设计方法[J]. 电工技术学报, 2025, 40(14): 4369-4381.
Bai Longlei, Liu Yiming, Luo Bo, You Jiang, Li Chenglong. Design Method of Anti-Offset Misalignment Compensation Arc Coils for Underwater Inductive Power Transfer Systems. Transactions of China Electrotechnical Society, 2025, 40(14): 4369-4381.
[1] 刘宇鑫, 高飞, 刘鑫, 等. 深海无人航行器双向无线充电系统的涡流损耗分析与效率优化[J]. 电工技术学报, 2024, 39(18): 5599-5609. Liu Yuxin, Gao Fei, Liu Xin, et al.Eddy current loss analysis and efficiency optimization of two-way wireless charging system for deep-sea unmanned aerial vehicle[J]. Transactions of China Electro- technical Society, 2024, 39(18): 5599-5609. [2] Sun Yushan, Chai Puxin, Zhang Guocheng, et al.Sliding mode motion control for AUV with dual- observer considering thruster uncertainty[J]. Journal of Marine Science and Engineering, 2022, 10(3): 349. [3] Kan Tianze, Mai Ruikun, Mercier P P, et al.Design and analysis of a three-phase wireless charging system for lightweight autonomous underwater vehicles[J]. IEEE Transactions on Power Electronics, 2018, 33(8): 6622-6632. [4] 何克成, 贾宏杰, 穆云飞, 等. 基于信息间隙决策理论的卡车式移动充电站协同调度策略[J]. 电力系统自动化, 2024, 48(15): 44-53. He Kecheng, Jia Hongjie, Mu Yunfei, et al.Collaborative scheduling strategy of truck mobile charging station based on information gap decision theory[J]. Automation of Electric Power System, 2024, 48(15): 44-53. [5] 顾文超, 丘东元, 张波, 等. 水下无线输电技术研究综述[J]. 电源学报, 2023, 21(3): 125-138. Gu Wenchao, Qiu Dongyuan, Zhang Bo, et al.Review of underwater wireless power transfer technologies[J]. Journal of Power Supply, 2023, 21(3): 125-138. [6] Li Wanjing, Zhu Jinwei, Wang Yadong, et al.Modeling and characteristic analysis of magnetic coupling mechanism in seawater environment[J]. IEEE Transactions on Magnetics, 2022, 58(9): 8402006. [7] 程志远, 宋晓逸, 吴晓婷, 等. 无线充电系统旋转式电磁耦合器损耗计算及热点温度研究[J]. 电工技术学报, 2024, 39(7): 1932-1942, 1956. Cheng Zhiyuan, Song Xiaoyi, Wu Xiaoting, et al.Loss calculation and hot spot temperature research of rotary electromagnetic coupler in wireless charging system[J]. Transactions of China Electrotechnical Society, 2024, 39(7): 1932-1942, 1956. [8] 唐丁源, 周玮, 黄亮, 等. 具有恒压输出特性的电场耦合式动态无线电能传输技术[J]. 电工技术学报, 2023, 38(20): 5385-5397. Tang Dingyuan, Zhou Wei, Huang Liang, et al.Dynamic electric-filed coupled wireless power transfer system with constant voltage output characte- ristics[J]. Transactions of China Electrotechnical Society, 2023, 38(20): 5385-5397. [9] 谢诗云, 杨奕, 李恋, 等. 基于双极性耦合磁场调控的高抗偏移偏转无线电能传输系统[J]. 电工技术学报, 2023, 38(18): 4838-4852. Xie Shiyun, Yang Yi, Li Lian, et al.Wireless power transfer system with high misalignment tolerance based on bipolar coupling magnetic-field control[J]. Transactions of China Electrotechnical Society, 2023, 38(18): 4838-4852. [10] 杨云虎, 贾维娜, 梁大壮, 等. LCC-LCC/S自切换恒流-恒压复合型无线电能传输系统[J]. 电工技术学报, 2023, 38(18): 4823-4837, 4852. Yang Yunhu, Jia Weina, Liang Dazhuang, et al.A self-switching wireless power transfer system based on hybrid topology of LCC-LCC/S with constant current and constant voltage[J]. Transactions of China Electrotechnical Society, 2023, 38(18): 4823-4837, 4852. [11] 张杰, 赵航, 许知博, 等. 磁耦合谐振式无线电能传输系统变电容调谐控制方法研究[J]. 电源学报, 2023, 21(6): 102-110. Zhang Jie, Zhao Hang, Xu Zhibo, et al.Variable capacitance tuning control method for magnetically coupled resonant wireless power transfer system[J]. Journal of Power Supply, 2023, 21(6): 102-110. [12] 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 recon- figuration S/SP topology[J]. Transactions of China Electrotechnical Society, 2024, 39(15): 4718-4732. [13] 张鹏飞, 龚立娇, 马欣欣, 等. 具有可变增益恒压特性的双线圈无线电能传输系统补偿网络设计与分析[J]. 电工技术学报, 2024, 39(5): 1256-1269, 1283. Zhang Pengfei, Gong Lijiao, Ma Xinxin, et al.Analysis and design of compensation network for two-coil wireless power transfer system with variable constant voltage gain characteristics[J]. Transactions of China Electrotechnical Society, 2024, 39(5): 1256-1269, 1283. [14] 闫争超, 胡谦宇, 赵晨旭, 等. 水下航行器感应式无线电能传输技术研究综述[J]. 中国电机工程学报, 2023, 43(24): 9668-9682. Yan Zhengchao, Hu Qianyu, Zhao Chenxu, et al.Review on inductive wireless power transfer technology for underwater vehicles[J]. Proceedings of the CSEE, 2023, 43(24): 9668-9682. [15] 林志远, 李中启, 胡昌轩, 等. 无线电能传输带凸字环形有界磁屏蔽任意位置圆形线圈互感计算方法[J]. 电工技术学报, 2024, 39(16): 4918-4930. Lin Zhiyuan, Li Zhongqi, Hu Changxuan, et al.Mutual inductance calculation method of arbitrarily positioned circular coils with convex ring type finite magnetic shielding in wireless power transfer[J]. Transactions of China Electrotechnical Society, 2024, 39(16): 4918-4930. [16] 张滨山, 张泽恒, 杨斌, 等. 基于钳位电路的LCC-S补偿型感应电能传输系统抗偏移方法[J]. 电工技术学报, 2024, 39(8): 2388-2399. Zhang Binshan, Zhang Zeheng, Yang Bin, et al.LCC-S compensated inductive power transfer system against misalignment with a clamp circuit[J]. Transactions of China Electrotechnical Society, 2024, 39(8): 2388-2399. [17] Yang Lei, Zhang Yuanqi, Li X, et al.Comparison survey of effects of hull on AUVs for underwater capacitive wireless power transfer system and under- water inductive wireless power transfer system[J]. IEEE Access, 2022, 10: 125401-125410. [18] Wu Shuai, Cai Chunwei, Wang Aobo, et al.Design and implementation of a uniform power and stable efficiency wireless charging system for autonomous underwater vehicles[J]. IEEE Transactions on Industrial Electronics, 2023, 70(6): 5674-5684. [19] Shi Jianguang, Li Dejun, Yang Canjun.Design and analysis of an underwater inductive coupling power transfer system for autonomous underwater vehicle docking applications[J]. Journal of Zhejiang University SCIENCE C, 2014, 15(1): 51-62. [20] Cai Chunwei, Zhang Yanyu, Wu Shuai, et al.A circumferential coupled dipole-coil magnetic coupler for autonomous underwater vehicles wireless charging applications[J]. IEEE Access, 2020, 8: 65432-65442. [21] Kan Tianze, Zhang Yiming, Yan Zhengchao, et al.A rotation-resilient wireless charging system for light- weight autonomous underwater vehicles[J]. IEEE Transactions on Vehicular Technology, 2018, 67(8): 6935-6942. [22] Budhia M, Boys J T, Covic G A, et al.Development of a single-sided flux magnetic coupler for electric vehicle IPT charging systems[J]. IEEE Transactions on Industrial Electronics, 2013, 60(1): 318-328. [23] Zaheer A, Covic G A, Kacprzak D.A bipolar pad in a 10-kHz 300-W distributed IPT system for AGV applications[J]. IEEE Transactions on Industrial Electronics, 2014, 61(7): 3288-3301. [24] Yan Zhengchao, Zhang Yiming, Zhang Kehan, et al.Underwater wireless power transfer system with a curly coil structure for AUVs[J]. IET Power Electronics, 2019, 12(10): 2559-2565.
2025, Vol. 40 
