Application of the Padé via Lanczos Method for Efficient Modeling of Magnetically Coupled Coils in Wireless Power Transfer Systems

This paper presents a method for determining the equivalent circuit parameters of magnetically coupled air-core coils used in wireless power transfer (WPT) systems. The proposed approach enables fast and accurate modeling of inductively coupled energy transfer structures, which is essential for the design and optimization of high-efficiency wireless energy systems. The equivalent circuit of the analyzed system was developed using Cauer circuits, while a two-dimensional (2D) axisymmetric electromagnetic field model was employed to derive the equations. The model was implemented in proprietary software based on the edge-element finite element method (FEM) using the A–V formulation. The A–V formulation combines the magnetic vector potential A and the electric scalar potential V, enabling simultaneous representation of magnetic field distribution and current flow in conducting regions. The eddy currents in the conductors were considered in the electromagnetic field analysis. Simulations were carried out for two operating states: short-circuit and idle. The results were used to determine the parameters of the horizontal and magnetizing branches of the equivalent circuit of considered system and to analyze the frequency dependence of the resistances and inductances of the coupled coil system. The proposed modeling approach provides an effective and energy-oriented tool for the design of wireless power transfer systems with improved efficiency and reduced computational cost. The proposed method reproduces impedance characteristics with an accuracy of 0.2 × 10−3% in the idle state and 1.4 × 10−3% in the short-circuit state compared to the full FEM model, while significantly reducing the computation time.