Current and Torque Harmonics Analysis of Dual Three-Phase Permanent-Magnet Synchronous Machines with Arbitrary Phase Shift Based on Model-in-the-Loop 2023-01-0527

Dual three-phase permanent magnet synchronous machines (DTP-PMSM) are becoming increasingly popular in automotive electric powertrains due to their reduced phase currents and fault tolerance. The unique advantages of specific phase shift angles (such as 0°, 30°, 60°, etc.) between dual three-phase windings have been extensively studied. In this paper, the current and torque harmonics induced by the inverter are analyzed and the corresponding harmonics suppression strategy are proposed for a DTP-PMSM with different phase shift angles. In addition, this paper analyzes the effect of the phase shift angle between the dual three-phase windings on the torque ripple and phase losses, and proposes a novel optimal phase shift angle 80°. First, a mathematical vector space decomposition (VSD) model for a DTP-PMSM with arbitrary phase shift angles is derived. Second, a theoretical derivation of the torque harmonics based on phase current and induced electromotive force harmonics is carried out, and the effects of current and rotor flux-induced electromotive force harmonics of (6k ± 1)^thorders on torque ripple are obtained. For torque ripple suppression, the mapping of the phase current harmonics in VSD synchronous coordinate system with arbitrary phase shift angles is derived. Furthermore, a model-in-the-loop (MiL) simulation is set up using a mathematical model of an ideal electrical machine and a non-ideal 6-phase inverter model implemented in PLECS, and the VSD-based field-oriented control algorithm implemented in Matlab/Simulink. The simulation results for different phase shift angles show that the dq current, dqz current, dc-link current and torque harmonics vary periodically with the phase shift angle for (6k)^th orders. In addition, the proposed 80° configuration has relatively lower losses and torque ripple after weighing both aspects over all the phase shifts. Finally, the harmonics suppression method is validated in the MiL.