Modeling of electromagnetic torque considering saturation and magnetic field harmonics in permanent magnet synchronous motor for HEV

•We derive an electromagnetic model of PMSM considering saturation and harmonics.•The electromagnetic characteristics evidently vary because of saturation.•The electromagnetic torque ripple can be predicted by spatial and time harmonics.•The model of electromagnetic torque is validated by FEM and experiment. Electromagnetic torque ripple of permanent magnet synchronous motor (PMSM) causes electro-mechanical coupling vibration and noise in hybrid electric vehicle (HEV). However, the traditional mathematical model of PMSM cannot absolutely reflect the reason of torque ripple and variation on the different operation performance of the motor for HEV. The purpose lies in the fact that electromagnet factor originated torque ripple and variation have been taken into account in the mathematic model of PMSM. Based on the classical Park's transformation theory and the Fourier series analysis of magnetic field, a general nonlinear mathematical model of PMSM considering saturation and magnetic field spatial harmonics and time harmonics is presented in this paper. The general analytical model cannot only taking into account the variation of electromagnetic parameters caused by electric vehicle operating, but also can explain the frequency and the order of torque ripple theoretically. The model's effectiveness is tested through finite element analysis simulations and some experimental results. The analytical model presented here can be used for the characteristic analysis, the drive system dynamic precise analysis and fault diagnose of PMSM for HEV.