Control-Oriented Voltage and Current Estimation of Dual Three-Phase PMSMs Considering Spatial Harmonics and Inter-Set Magnetic Coupling

Abstract

This paper investigates the effects of rotor-position-dependent spatial harmonics on voltage and current prediction in dual three-phase permanent-magnet synchronous motors (PMSMs) under two current-control strategies. A simplified machine model retains the operating-point-dependent magnetic-saturation state and average inter-set coupling but neglects the spatial harmonics of the inductance and permanent-magnet flux linkage. Analysis of the voltage equations shows that parameter averaging removes nonfundamental voltage components arising from the rotor-position-dependent inductance and PM flux-linkage variations. Under two individual current control, these omitted voltage components excite harmonic currents in both winding sets, causing substantial current-harmonic prediction errors. Under vector space decomposition (VSD) current control, the dominant harmonic currents are actively suppressed in the $DZQZ$ subspace, and omission of the same voltage sources instead leads to underestimation of the harmonic controller-voltage demand. To isolate the effects of spatial harmonics, the simplified and detailed models are constructed from identical finite-element-analysis-based parameters obtained using the frozen-permeability method. Simulation and experiments using a prototype dual three-phase PMSM show that the simplified model substantially underestimates the dominant current harmonics under two individual current control and the harmonic voltage demand under VSD current control. These results demonstrate that the prediction limitations caused by spatial-harmonic omission depend strongly on the applied current-control strategy.