Calculation method of coupling coefficient for circular coils with bilateral double-layer bounded magnetic shielding

The calculation of the coupling coefficient between coils is crucial for optimizing the efficiency of wireless power transfer (WPT) systems. For bilateral double-layer bounded magnetic shielding circular coils under horizontal displacement conditions, the accurate calculation of coupling coefficients currently relies mainly on time-consuming large-scale finite element simulations. To address this problem, the coupling model is divided into subregions using boundary conditions, the magnetic vector potential in each region is solved through Maxwell's equations, and a formula for the coupling coefficient of coaxial double-layer bounded magnetically shielded circular coils is derived. Additionally, a double-layer boundary vector-equivalence method is proposed, and the coupling coefficient formula for a circular coil with bilateral double-layer bounded magnetic shielding under horizontal offset is derived using spatial geometric relationships. The reliability of the proposed method is corroborated by the calculated, simulated, and laboratory-obtained values. The errors between calculated and simulated values are not more than 3.95%, and between calculated and laboratory-obtained values are not more than 4.51%, which confirms the accuracy of the proposed method. Furthermore, a significant computational speed advantage is demonstrated by the proposed method compared to simulation.