Precise Analytical Modeling of Litz-Wire Rectangular WPT Coil With Ferrite Core and Lateral Misalignment for Inductance Estimation

Generally, inductive wireless power transfer (WPT) coils are built with litz wire to minimize the skin and proximity effects. However, the complex stranding, twisting, and bundling effect of the litz wire makes precise parameter estimation extremely challenging. The analytical models are preferred over the finite element analysis (FEA) method for extracting coil parameters, as they are faster and require less computational effort. The existing analytical approach overlooks important geometrical features, such as stranding, twisting, and the bundling effect in the litz wire. These models rely on the outer envelop radius of twisted bundles of strands, leading to significant errors in calculating self-inductance. For mutual inductance calculations, the existing model oversimplified the original rectangular WPT coil structure, resulting in erroneous results. Addressing these limitations, this paper proposes an equivalent bundle radius and geometric mean distance (GMD) for bundles of strand distribution. The proposed model precisely calculates self- and mutual inductances for both air-core and ferrite-core configurations, including lateral and in-plane angular misalignment. The proposed analytical model achieves an accuracy of$>$99% for an air-core coil and$>$97% for a ferrite core-based coil. All mathematical analyses are verified through FEA simulation results and experimental measurements from various rectangular coil prototypes.