Fast Calculation of Electromagnetic Forces in IPMSMs Under PWM VSI Supply Based on Small-Signal Time-Harmonic Finite Element Method

This paper introduces a novel method for fast calculating the electromagnetic forces in interior permanent magnet synchronous machines (IPMSMs) under pulse width modulation (PWM) voltage source inverter (VSI) supply based on the small-signal time-harmonic finite element analysis (THFEA), which has been successfully utilized for fast calculating the PWM-induced losses in silicon steel sheets and permanent magnets. Based on the small-signal THFEA, the functional relationships between high-frequency harmonic voltages (HFHVs) and corresponding airgap flux densities are established, which are used for calculating the flux density spectra caused by each HFHV in the PWM voltage spectra. Then, the superposition principle is applied for calculating the flux density spectra caused by fundamental currents and all HFHVs, which are converted to the electromagnetic force spectra at last. The relative errors between the force density spectra calculated with the proposed method and those obtained from traditional time-stepping finite element analysis (TSFEA) using PWM voltages as input are within 3.1%, while the proposed method is 24 times faster than the traditional TSFEA.