Dual-method 3D FEM-based determination of d-q inductances in axial-flux permanent magnet synchronous generator taking saturation, magnet material and air-gap effects into account

Abstract

This paper presents a method for determining the d and q axis inductances (L_d, L_q) of a 4 kW axial-flux permanent magnet synchronous generator (AFPMG) using combined 2D and 3D finite element method (FEM) simulation in Ansys Maxwell.  The key contribution is a cross-validation framework employing two independent post-processing methods applied to the same FEM dataset: Method A, based on direct dq flux linkage extraction, and Method B, based on the phase inductance matrix (L_abc) combined with coordinate transformation. The d-q mathematical model, including voltage equations, flux linkages, and saturation effects, is first summarized. The complete 3D FEM simulation procedure is described, from geome-try construction to inductance extraction, covering both static and transient analyses. Re-sults demonstrate that both methods yield consistent inductance values, within a maximum deviation of approximately 7-8%. At rated current, L_d ≈ 6.8 mH and L_q ≈ 6.4 mH are ob-tained from 3D static simulation (Method A), confirming the reliability of the proposed simulation approach. The influence of magnetic saturation, magnet material, and air-gap length on L_d and L_q is also systematically investigated. The determined L_d and L_q values serve as essential parameters for field-oriented control (FOC) design of the AFPMG, ena-bling accurate torque and flux regulation.