Semi-analytical hybrid subdomain model for surface-mounted permanent magnet synchronous machines including nonlinear saturation effects

Purpose This paper aims to introduce an efficient hybrid model for surface-mounted permanent magnet synchronous machines (SPMSMs) that explicitly takes into account the magnetic nonlinearity in the ferromagnetic regions. Design/methodology/approach The approach combines an analytical subdomain (SD) formulation for the air-gap, magnet and slot regions with a nonlinear 2D magnetic equivalent circuit (MEC) representing the stator teeth and yoke. The SD formulation relies on the exact resolution of Poisson’s and Laplace’s equations using harmonic series. Both models are iteratively coupled through flux sources and a saturation coefficient derived from a variable local permeability scheme. Furthermore, an energetic principle evaluating the stored magnetic energy is introduced to characterize the saturation state. Findings The proposed methodology demonstrates fast numerical convergence and provides a highly detailed description of the magnetic field harmonic spectrum. It successfully quantifies the level of magnetic saturation through the aforementioned energetic principle. Finally, it is validated against time-consuming finite element analysis (FEA) simulations, demonstrating excellent agreement and high accuracy. Originality/value The originality of this work lies in the novel iterative coupling between a precise analytical SD technique and a saturated MEC model, as well as the innovative introduction of an energetic principle to explicitly quantify saturation levels in ferromagnetic circuits. This hybrid concept allows researchers and designers to achieve a substantial computational speed-up compared to purely numerical solutions while successfully preserving accuracy during heavy, localized magnetic saturation.