Analysis of a Symmetrical Nine-phase Machine with Highly Non-Sinusoidal Back-Electromotive Force

In this paper a two-pole surface permanent magnet synchronous machine (PMSM) with a symmetrical nine-phase winding configuration is investigated. Magnets on rotor are shortened which causes production of highly non-sinusoidal back-electromotive force (EMF) in the stator windings. Analysis of the EMF reveals a third-harmonic component, which is almost equal in magnitude to the fundamental. These harmonics have been used by researchers in the past to increase the torque density of multiphase machines. In this paper, a specific rotor structure is designed and tested under third-harmonic current injection in order to analyse torque improvement. It is shown that optimal injection ratio and torque improvement are dependent on the ratio of third-harmonic back-EMF to the fundamental one. The so-called ‘same RMS value’ constraint method is used for calculation of the optimal level of the third-harmonic current injection. It is found that the torque can be increased by up to 36% for the studied machine. Obtained torque increase results are validated using finite element method (FEM) simulations. Finally, the results acquired with the described rotor structure are compared with those obtained for rotor with full magnets and near-sinusoidal back-EMF. It is shown that for approximately 4 times less magnet material in non-sinusoidal configuration and with third-harmonic current injection, the total electromagnetic torque is only 22% lower.