Optimal Third-Harmonic Current Injection for an Asymmetrical Nine-phase PMSM with Non-Sinusoidal back-EMF

The paper investigates an optimal strategy to exploit the third harmonic current injection for the torque enhancement in a nine-phase permanent magnet synchronous machine (PMSM). The machine is with asymmetrical winding configuration and has a single isolated neutral point. The optimization follows the minimization of the average power losses for a given reference torque or, equivalently, the maximization of the developed torque for a given current RMS. It is shown that, in contrast to the situation for a symmetrical configuration, the optimal ratio between the fundamental and the third harmonic components does not correspond to the ratio between the corresponding back-EMF components. It is demonstrated that this is due to the fact that the phase currents have to sum to zero; consequently, the third harmonic current injection in different three-phase sets has to be different with regard to the magnitude and phase shift. The strategy is introduced using an entirely analytical approach and its effectiveness has been successfully validated through numerical simulations.