A Novel Analytical Model for Mutual Inductance Calculations Between Two Nonidentical N-Sided Polygonal Planar Coils Arbitrarily Positioned in 3-D Space for Wireless Power Transfer

Abstract

Mutual inductance (MI) calculation is of great importance, because there are many systems that operate on the principle of inductive coupling. This article presents a novel analytical model that calculates the MI between two nonidentical n-sided polygonal planar coils located in an arbitrary position in 3-D space. The model depends upon the misalignment of both the primary and the secondary coils of a wireless power transfer system operating based on inductive coupling. The polygonal coils used in this model may differ from each other in terms of size, shape, and turns number. The misalignment cases considered in the proposed model include lateral, angular, lateral-angular, and vertical distance variation between the primary and secondary coils. Based on Stokes theorem, instead of using the magnetic flux density vector, the magnetic vector potential (MVP) is used to reach the required magnetic flux in the calculation of the MI. A single analytical solution function that can calculate the MI between two planar polygonal coils of any shape in a simple manner and short time duration is obtained by performing difficult mathematical operations through MVP. Results obtained from the developed new model are compared with finite element analysis, and experimental and other studies in the literature. The good agreement of the results of this study with the other results has proved the accuracy and validity of the proposed new analytical model.