Optimal multi-harmonic current injection strategy for an asymmetrical nine-phase PMSM

The paper develops a strategy to enhance the torque development for a nine-phase PMSM with an asymmetrical winding configuration and a single isolated neutral point. The approach is based on the simultaneous exploitation of different spatial harmonics of the magnetic flux density in the air-gap, which requires both a non-sinusoidal set of PM induced back-EMFs and a non-sinusoidal set of phase currents (thus implying the injection of multiple harmonics). By formulating the machine's mathematical model in a proper multiple synchronous reference frames, the electromagnetic torque is given by the superposition of different harmonic quadrature current component contributions: their simultaneous utilization allows to meet a set optimization goal. The proposed approach focuses on the minimization of the average stator losses for a given reference torque. The optimal solution is found analytically and validated numerically for a specific case study. With respect to the sole fundamental current exploitation, the proposed technique allows for a significant reduction of the average losses but, given the machine's configuration, it requires an uneven distribution of the third harmonic current component among the nine phases.