White-Box High-Frequency Impedance Modeling of Permanent Magnet Synchronous Machines Using Small-Signal Time-Harmonic Finite Element Analysis

This article advances a two-dimensional (2-D) coupled field-circuit small-signal time-harmonic finite element analysis (THFEA) method for achieving comprehensive modeling of high-frequency (HF) impedances in permanent magnet synchronous machines (PMSMs). The model incorporates a frequency-dependent complex differential reluctivity tensor to simulate the impact of hysteresis, eddy currents, and saturation in electrical steel sheets on self-inductance, mutual inductance, and iron loss resistance of the machines. To efficiently account for eddy current effects without requiring excessive mesh refinement in winding regions, a homogeneous material with equivalent complex permeability is used to replicate the influence of eddy currents on winding resistance and slot leakage inductance. Additionally, a practical approach is proposed to determine this equivalent complex permeability. Subsequently, the 2-D axisymmetric THFEA is then performed to evaluate end leakage inductance and resistance at varying frequencies. Besides, when computing parasitic capacitances, the impact of dielectric loss is considered based on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Debye</i> model. The developed model not only accurately computes the HF impedances of PMSMs but also enables the prediction of overvoltage distribution at arbitrary locations within windings. Experimental validation was conducted on a PMSM with concentrated round-wire windings in the frequency domain and on a stator with distributed hairpin windings in the time domain.