Analytical Prediction of the Unsaturated Inductance Profile of a Switched Reluctance Machine Using a Flux-Tube-Based Method

The unsaturated inductance profile of a switched reluctance machine (SRM) is an important characteristic for performance evaluation and simulations. The complete inductance profile can be accurately predicted using inductances at three specific rotor positions, in addition to the aligned and unaligned inductances. This paper presents an analytical method to accurately predict the unsaturated inductance at these three rotor positions in terms of the machine dimensions and the unsaturated permeability of the magnetic material. A closed-form expression for the air-gap permeance is derived for each of these rotor positions, following a flux-tube-based approach. Unlike other analytical methods, this approach can incorporate the impact of rotor pole height, which is essential in high-speed SRMs. Additionally, the proposed method yields accurate results for SRMs with significantly different stator and rotor pole arc angles. The obtained permeances are validated through finite element analysis (FEA)-based simulations. The superiority of the proposed method is demonstrated by comparing it with two existing analytical methods that provide closed-form solutions. Finally, the inductances obtained by incorporating iron reluctance, as well as the derived complete inductance profile, are validated through FEA simulations and experiments performed on a 7.5 kW, 30,000 rpm, 3-phase switched reluctance machine prototype.