Torque Improvement Utilizing Third Harmonic Current in Five-Phase PM Machines with Unequal Tooth

The third harmonic current is commonly injected into the fundamental one to improve the output torque of the multi-phase machines. It can interact with the third harmonic back-EMF, contributing to positive torque. However, the output torque may not always be improved with the third harmonic current injection under the same rms value constraint. The optimal ratio of the third harmonic current to the fundamental one for maximum torque improvement is analytically derived and validated by finite element (FE) analyses in this paper. It is found that the optimal third harmonic current and the torque improvement are dependent on the ratio of the third harmonic back-EMF to the fundamental one. In order to improve the output torque, this paper employs unequal tooth width techniques to increase both the fundamental and the third harmonic back-EMFs. For the equal tooth machine, the output torque can barely be improved, while the unequal tooth machine can improve the torque by injecting the optimal third harmonic current under the same rms value constraint.