Analytical Magnetic Circuit Modeling and Parameter Estimation of a PMSM for Spatial Harmonics and Radial Forces Characterization

This paper presents an analytical model for three-phase Permanent Magnet Synchronous Motors (PMSMs) based on Magnetic Equivalent Circuits (MECs). The approach combines a reduced magnetic network, formulated in the complex domain to simplify the mathematical development, with an offline parameter estimation procedure systematically applied for different harmonic orders. This enables the model to capture the spatial dependence of permeance variations and reproduce inductance and magnetic flux nonlinearities, while maintaining generality, physical interpretability, and computational efficiency. Numerical simulations are compared with Finite Element (FE) results to validate the model’s ability to predict current and torque harmonics and the resulting radial electromagnetic forces, demonstrating its suitability for fast Noise, Vibration, and Harshness (NVH) analysis and vibroacoustic optimization.