Optimal Third-Harmonic Current Injection for Asymmetrical Multiphase Permanent Magnet Synchronous Machines

This article proposes a modeling approach and an optimization strategy to exploit a third-harmonic current injection for the torque enhancement in multiphase isotropic permanent magnet synchronous machines with nonsinusoidal back electromotive forces. The modeling approach is based on a proper vector space decomposition and on the associated rotational transformation, aimed to properly select a set of stator current space vectors to be controlled. It is presented for a generic (i.e., asymmetrical, with an arbitrary angular shift) winding configuration. The injection strategy is related to the choice of a constant synchronous current set aimed at minimizing the average stator winding losses for a given reference torque by using the first and the third spatial harmonics of the air-gap flux density. The optimal solution has been found analytically and has been developed in detail for a selected set of asymmetrical winding configurations. Both the numerical and experimental results are in good agreement with the theoretical analysis.