Comparative Evaluation of Mutual Inductance Calculation Methodologies for Circular Spiral Coils in Wireless Power Transfer Systems
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Elliptic Integrals, Finite Element Method (FEM), Mutual Inductance Calculation, Neumann Formula, Planer Spiral Coils, Wireless Power Transfer (WPT)
Abstract
Wireless power transfer (WPT) is rapidly evolving as a promising solution in modern power engineering. As accurate mathematical modeling of mutual inductance constitutes a cornerstone in designing these systems, this paper aims to evaluate and compare three methodologies for calculating the mutual inductance of perfectly aligned circular spiral coils: the Neumann Integral, the Elliptic Integrals, and the Power Series methods. The experimentally validated results of the finite element method (3D-FEM) were adopted in the reference literature as a proven experimental benchmark. in the near-field region, while the study was extended to the far-field to analyze convergence behavior. Results demonstrated that both Neumann and elliptic integral methods achieved high agreement with reference values (average error < 2%), with the elliptic method exhibiting superior computational speed. Conversely, the Power Series method showed significant deviation in the near-field (average error >33%) but demonstrated dramatic accuracy improvement in the far field (distance >> 30 mm). The study concludes that the elliptic integrals method represents the optimal engineering choice for general design of this coil type, while the power series is recommended for rapid estimations at larger separation distances.
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