Torque improvement in five-phase unequal tooth SPM machine by injecting third harmonic current

In order to increase the torque density of the fivephase machines, the third harmonic is commonly employed. In this paper, the optimal and critical ratios for the third harmonic current injection are analytically derived and validated by finite element (FE) analyses. It is found that the optimal and critical injection ratios along with the torque improvement are dependent on the ratio of the third harmonic back electromotive force to the fundamental one. In order to improve the electromagnetic torque contributed by the third harmonic component, this paper employs unequal tooth to increase both the fundamental and third harmonic winding factors. Meanwhile, the optimal unequal tooth width combination is deduced and demonstrated by the FE method. When the third harmonic current is injected under the same amplitude constraint, the output torque can be improved. When the third harmonic current is injected under the same RMS value constraint, for the ten-slot/eight-pole equal tooth machine, the output torque can barely be increased, whilst for the unequal tooth machine, the output torque can be increased by 2.1%. Finally, the ten-slot/eightpole machine with unequal teeth is prototyped and tested to prove the analyses.