Real and complex models of multi-phase permanent magnet synchronous motors

This paper deals with the modelling of multi-phase permanent magnet synchronous machines (PMSM) with an arbitrary number of phases and arbitrary shape of the rotor flux. The aim of the paper is to propose new dynamic models for the multi-phase electrical machines based on the use of real and complex state space transformations which are invariant with respect to power. The dynamic models of the motor are obtained using a Lagrangian approach in the frame of the power-oriented graphs technique. The obtained dynamic models can directly be implemented in Simulink whatever the number of phase is. The state space transformations presented in the paper (both real and complex) are compared to the main other transformations know in the literature. Some simulation results are finally presented.