Torque Improvement of Dual Three-Phase Permanent-Magnet Machine With Third-Harmonic Current Injection

This paper presents dual three-phase permanent magnet (PM) machines utilizing third-harmonic back electromotive force (EMF) and current to improve the output torque, but the torque ripple remains almost similar. The feasibility and practical issues of dual three-phase machines with third-harmonic EMF and current are first discussed, and the output torque is analytically derived. Furthermore, the optimal value of the third harmonic injected into a current waveform for maximum torque improvement is also analytically derived and validated by finite-element analysis (FEA) with the consideration of the constraints of both the peak and root-mean-square currents. For feasible dual three-phase PM machines, torque characteristics, including the average torque and the torque ripple, are compared without and with third-order harmonic injection. It is found that, for a dual three-phase machine without third-harmonic back EMF, the optimal third harmonic into the current is 1/6 of the fundamental current, and the average torque with the current having the optimal third harmonic injected can be improved by 15%. However, for the dual three-phase PM machines with third-harmonic back EMF, the optimal third harmonic into the current is dependent on the ratio of the third-harmonic back EMF to the fundamental back EMF, and the interaction of the third-harmonic current and the third-harmonic EMF results in the further improvement of the output torque. Finally, the experiments on a prototype are given to verify both the analytical and FEA methods.