Space phasor theory and control of multiphase machines through their decoupling into equivalent three-phase machines

This paper, first, introduces the space phasor theory from a general mathematical viewpoint and, above all, from a physical one as well. The theory is then applied to the particular case of constant airgap multiphase machines (MM¿s) fed by arbitrary voltage waveforms. It is mathematically proven, and thereafter checked by simula-tions too, that these machines can be split into a set of equivalent three phase machines mechanically coupled but electrically fully independent. This electrical decoupling leads immediately to develop the very fast torque control schemes of the MM¿s. All of them boil down to a mere extension of those already used in the homologous three phase machines.