Modeling of Mutual Inductance for Hexagonal Coils with Horizontal Misalignment in Wireless Power Transfer

The mutual inductance is an essential parameter to design and optimize a wireless power transfer (WPT) system. In this paper, an extended analytical model of mutual inductance for hexagonal coils with horizontal misalignment is presented using Biot-Savart law. The hexagonal coil is simplified into a set of superposed multiple concentric hexagonal filaments, and a integral method is described for simplifying the calculation. Besides, the coordinate axis rotation method is introduced to obtain the magnetic flux density of primary hexagonal filaments. Based on above all, the mutual inductance is derived by the integrals of magnetic flux density of primary hexagonal filaments on the surface of secondary filaments. The proposed model can predict the mutual inductance of two hexagonal coils at various coaxial distances and horizontal misalignments, and also lays foundation for parameters optimization in WPT. Both the experimental and simulation results demonstrate the validity of this model.

I. Introduction

As a reliable and convenient power transmission method without physical contact, WPT technology has drawn increasing attention of researchers from various, industrials ranging from portable electronic equipment, electric vehicles and biomedicine [1]–[3]. In general, the primary and secondary coil of a WPT system are separated from each other with air, and the power transferred with mutual inductance between them. Thus, the mutual inductance between coils is a crucial parameter to estimate the power link's performances before giving a proper WPT system design.