Analytical determination of 3rd order harmonic current into five phase PM machine for maximum torque

This paper presents analytically derived optimal 3rd harmonic into phase current waveforms to improve the output torque of five phase surface-mounted PM (SPM) machines with the constraints of peak and rms values. The output torque with the 3rd harmonic current is analytically established and the optimal value of 3rd harmonic injected into the current waveform for maximum torque improvement is analytically derived and validated by finite element (FE) analyses. It is found that the optimal 3rd harmonic is dependent on the ratio of third harmonic back-EMF to the fundamental one but not 1/6 of the fundamental one as pulse width modulation in inverter. For the 10-slot/8-pole and 40-slot/8-pole five phase SPM machines having the same PM rotor, the electromagnetic performance including the back-EMF waveform, average torque, copper loss, and iron loss, are compared considering the 3rd harmonic current injection. The torque can be improved for both of the machines by injection third harmonic current under the peak current constraints, whilst only 40-slot/8-pole machine can have higher torque when 3rd harmonic current injection under the same rms value constraints.