In the paper two power-invariant real and complex state space transformations for modeling multi-phase electrical machines in a compact and general form are proposed. In particular the paper deals with the modeling of multi-phase permanent magnet synchronous machines with an arbitrary number of phases and an arbitrary shape of the rotor flux. The dynamic model of the motor is obtained using a Lagrangian approach and in the frame of the Power-Oriented Graphs technique. The obtained models are equivalent from a mathematical point of view and can be directly implemented in Simulink. The complex transformed model is quite compact and uses a reduced order state vector. Some simulation results end the paper.

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