Calculation method of mutual inductance of circular coils with bilateral convex toroidal magnetic medium in WPT system with horizontal misalignment

Accurately calculating mutual inductance is crucial for achieving efficient and reliable wireless power transfer systems. However, when horizontal displacement occurs in double-sided magnetic coils, the mutual inductance values are typically obtained using finite element software, lacking a simple analytical formula for calculation. Additionally, magnetic materials are costly, and there's still room for optimizing disc-type magnetic structures. Therefore, this paper proposes a magnetic vector potential position equivalent method and derives an analytical solution for mutual inductance of circular coils with bilateral convex toroidal bounded magnetic media. The magnetic vector potential in each region can be derived, based on Maxwell's equations and combined with boundary conditions. Utilizing the position equivalent method enables rapid calculation of mutual inductance for coaxial and horizontally displaced scenarios on the receiving end. Comparison between calculated mutual inductance values and finite element simulation, along with experimental measurements, demonstrates an error within 4.23% and a calculation speed 70 times faster than simulation. Experimental validation shows that the mutual inductance of the convex toroidal magnetic structure can reach more than 97.75% of the mutual inductance of the disc-type magnetic structure while saving 15% of magnetic material.