Abstract

Background: The winding function method, commonly utilized for calculating machine inductance, requires solving the integral involving the product of the winding function and air-gap flux density. However, obtaining an analytical result for inductance via the winding function method in a variable flux reluctance machine (VFRM) is challenging due to the complex airgap flux density in its doubly salient structure.

Objective: An analytical model of VFRM inductance is established with a comprehensive understanding of the influence of geometrical parameters.

Methods: This paper presents a novel approach to transform the product of the winding function and air-gap flux density into a cosine series. Then, the integral can be calculated with the aid of the periodicity of trigonometric functions.

Results: The analytical results of the winding inductance are validated by the finite element method (FEM) simulations and experimental measurements. The relative error for the three-phase peak self-inductances is 4.8% between analytical and FEM results and does not exceed 4.9% between analytical and experimental results.

Conclusion: With this approach, the Fourier series of inductance can be calculated analytically rather than numerically. The relationship between the harmonic amplitude/order of inductance and machine parameters is revealed. This analytical model can provide the preliminary basis for the inductance design of VFRMs.

Keywords: Variable flux reluctance machines (VFRMs), fourier series, winding function method, doubly salient, winding inductance, geometrical parameter.