Multiple Reference Frame-Based Extended Concentrated Wound PMSM Model Considering PM Flux Linkage and Inductance Harmonics

Permanent magnet (PM) synchronous machines (PMSMs) with concentrated windings (CW) exhibit high content of space harmonics leading to nonsinusoidal distribution of PM flux linkage and phase inductances in addition to the non-sinusoidal wave shape of the induced electromotive force. The ideal single reference frame-based PMSM model considers these parameters to be sinusoidal and does not include the effect of harmonics. Hence, computation of electromagnetic torque using ideal model can lead to deviation from the actual waveform. In this paper, a novel analytical model for electromagnetic torque has been derived using multiple reference frames (MRF) incorporating non-sinusoidal aspects of CW PMSM. Initially, the PM flux linkage and inductances in abc frame are extended by incorporating higher order harmonics. Then, the extended model is transformed into dqaxis using MRF rotating at speeds of dominant harmonics in PM flux linkages and inductances, the fundamental being the electrical rotor frequency. Based on this MRF model, a comprehensive electromagnetic torque model for the CW PMSM is derived. Simulation and experiments are conducted on a CW PMSM to validate the proposed model under different operating conditions.