Harmonic Rotating Magnetic Field Injection Methods for Torque Ripple Suppression in the Overmodulation Region of PMSMs

This paper proposes torque ripple reduction methods that inject a harmonic rotating magnetic field (RMF) in the overmodulation (OVM) region of permanent magnet synchronous motors (PMSMs). Two methods are proposed: one injects harmonic voltages at the output of a dq-axis current controller in the rotor reference frame (RRF), and the other superimposes a harmonic phase onto the rotor angle used during coordinate transformation. The dominant torque harmonics in the OVM region are derived from spatial harmonics and double Fourier series (DFS) of the inverter pole voltage, and are mitigated using multi-resonant (MR) controllers incorporating frequency pre-warping to compensate for discretization error under a limited sampling frequency. Additionally, their effects on inverter reference voltage vectors (RVVs) and output voltage vectors (OVVs) are analyzed both mathematically and graphically in the OVM region, and their feasibility is verified. The proposed methods are evaluated through experiments using a 160 kW interior PMSM (IPMSM) at 6,000 RPM under 40 and 60 N·m, which represent typical vehicle traction conditions. The experimental results show that the proposed 3rd- and 6th-harmonic voltage compensation (3&6HVC) method reduces torque ripple by 33.3% and 9.1% at 40 N·m and 60 N·m, respectively, while the 3rd- and 6th-harmonic phase compensation (3&6HPC) method achieves reductions of 31% and 16.7%. In addition, in terms of vibration, the 3&6HVC method achieves reductions of up to 60% and 35.6% in the 3rd- and 6th-order vibration components, respectively, while the 3&6HPC method achieves up to 40.8% and 45% reductions. These results validate the effectiveness and practicality of the proposed methods in reducing torque ripple and mechanical vibration in the OVM region, while maintaining the same average output torque without modifying the current reference.