Least squares based d-q model of non-ideal multiphase synchronous machine

Starting with the lumped parameter model for electrical machines with arbitrary M phase winding, by introducing a hypothesis of M spatial symmetrical winding sheets and spatial sinusoidal distributed flux density, the M × 1 phase flux linkage vector of the hypothesis can be expressed using 2 undetermined properties: d-q flux linkage and a M × 2 transformation matrix, which characterizes the symmetrical condition of the hypothesis and is determined by the position of the rotor. For invariant electromagnetic power, the phase flux linkage vector of this hypothesis is required to be equal that from FE calculation, which includes saturation and slotting effects. A linear equation system having M equations and two unknowns (d-q flux linkage) is obtained, and is solved by using least squares method. New formulas for calculating the parameters of the d-q model are developed. Furthermore, the error by using the classical d-q approach is discussed. The method is validated using the TOYOTA Prius IPM Motor.