A New Analytical Study on Mutual Inductance Calculations for Wireless Power Transfer Using Magnetic Vector Potential

This article presents a new analytical approach for the calculation of mutual inductance based on magnetic vector potential (MVP). To demonstrate the proposed mutual inductance calculation method, planar spiral coils of polygonal shape with an arbitrary number of sides are discussed. The coils considered in this work are coaxial and assumed to be composed of concentric filaments. The flux produced by the primary and linking the secondary is calculated by the line integral of the MVP. In order to simplify the calculation strategy, the MVP contribution of only one side of each single-turn filament of the primary is considered due to the symmetry of the coils’ shapes. Accordingly, coupling flux across the surface surrounded by each turn of the secondary is calculated by the line integral of the MVP over half path of the filament’s turn. The accuracy of the new analytical approach is confirmed by examining coil systems with a different primary and secondary in terms of the number of sides, the number of turns, and size. Results of the new approach are compared with those obtained from Ansys Maxwell, analytical studies in the literature, and experimental to demonstrate the validity of the proposed method. Results from this work are in good agreement with those obtained from simulation, studies in the literature, and experiment that proves the feasibility of formulas used in this work.