Calculation of Mutual Inductance Between Rectangular Coils at Arbitrary Positions of Porous Magnetic Media for Wireless Energy Transmission Systems
Li Zhongqi1,2, Bao Minghan1, Kong Lingjun3, Hu Changxuan1, Huang Shoudao2
1. College of Railway Transportation Hunan University of Technology Zhuzhou 412007 China; 2. College of Electrical and Information Engineering Hunan University Changsha 410082 China; 3. College of Electrical and Information Engineering Hunan University of Technology Zhuzhou 412007 China
Abstract：For wireless power transfer (WPT) systems, mutual inductance is one of the core performance indicators. The system integration of magnetic medium materials can significantly enhance mutual inductance performance while effectively suppressing magnetic leakage phenomena. In practical engineering applications, relative positional deviations between transceiver devices of the system are inevitable, which directly affect energy transfer efficiency. Mutual inductance calculation methods that can save magnetic medium materials are rare. Therefore, studying the mutual inductance calculation method for rectangular coils with bilateral bounded porous magnetic media at arbitrary positions is of great significance. This paper constructs a mutual inductance calculation model for rectangular coils integrated with porous magnetic media at arbitrary positions in a wireless power transfer (WPT) system. By leveraging spatial cross-sectional analysis, the magnetic vector potential equations for each region of the 2D cross-section were derived. Maxwell's boundary conditions were then applied to solve for the unknown coefficients in each area. Combining the results from individual 2D planes, the mutual inductance formula under coaxial conditions was ultimately obtained. Additionally, an image constraint method was proposed using image coils to represent the influence of magnetic media on the coils equivalently. Through analyzing the patterns of image coefficients, mutual inductance expressions for arbitrary positional scenarios were derived, thereby resolving the challenge of calculating mutual inductance between coils at arbitrary positions. Theoretical calculations, numerical simulations, and physical experiments confirmed the effectiveness of the proposed method across four positional configurations: vertical offset, horizontal offset, angular deflection, and combined angular-horizontal dis- placement. The deviations between calculated mutual inductance values and simulated/experimental results under various relative positional configurations are presented below. (1) For vertical misalignment scenarios, maximum discrepancies observed between computational outcomes and experimental data, along with simulation results, reached 4.15% and 4.42% respectively. (2) For horizontal misalignment configurations, maximum discrepancies observed between computational outcomes and experimental data, along with computational outcomes and simulation results, were 4.38% and 3.82% respectively. (3) In the context of angular deflection, the maximum disparities between the computational results and the experimental findings, along with those between the computational results and the simulation outcomes, are 4.32% and 4.89% respectively. (4) In the case of angular deflection combined with horizontal offset in the same direction, compared with the experimental and simulation results, the calculation results’ maximum errors are 4.94% and 4.09%, respectively. (5) When angular deviation is accompanied by negative horizontal displacement, the maximum computational discrepancies to empirical findings and modeled predictions reach 4.96% and 3.47%. The calculated, simulated, and experimental values exhibit good agreement, effectively validating the accuracy of the proposed calculation approach. Under the same parameter conditions, the model structure in this paper saves 56.25% of the materials compared with the traditional rectangular magnetic medium, and the mutual inductance can reach 91% of that of the rectangular magnetic medium.
李中启, 包明晗, 孔令军, 胡昌轩, 黄守道. 无线电能传输系统多孔磁介质任意位置矩形线圈间互感计算方法[J]. 电工技术学报, 2025, 40(24): 7863-7878.
Li Zhongqi, Bao Minghan, Kong Lingjun, Hu Changxuan, Huang Shoudao. Calculation of Mutual Inductance Between Rectangular Coils at Arbitrary Positions of Porous Magnetic Media for Wireless Energy Transmission Systems. Transactions of China Electrotechnical Society, 2025, 40(24): 7863-7878.
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