Modeling spatial harmonics and switching frequencies in PM synchronous machines and their electromagnetic forces

This paper shows how electromagnetic air-gap forces in permanent magnet synchronous machines (PMSM) fed with non-sinusoidal currents can be efficiently simulated under arbitrary operating conditions based on a time-domain force interpolation approach. To account for spatial harmonics in the stator currents, a generic non-linear PMSM model including spatial harmonics is introduced. Additional switching frequency components from the inverter are generated with common modulators. The spatial harmonic machine model itself is applicable beyond modeling the acoustic behavior of electric drives wherever the effect of spatial harmonics and the respective torque fluctuations are of interest. The second part of the paper then deals with the air-gap force decomposition and interpolation. The authors finally analyze the influence of switching frequencies and spatial current harmonics on the force excitation.