Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics

A detailed model in direct-phase variables of a synchronous reluctance motor operating at mains voltage and frequency is presented. The model includes the stator and rotor slot openings, the actual winding layout and the reluctance rotor geometry. Hence, all mmf and permeance harmonics are taken into account. It is seen that non-negligible harmonics introduced by slots are present in the inductances computed by the winding function procedure. These harmonics are usually ignored in d–q models. The machine performance is simulated in the stator reference frame to depict the difference between this new direct-phase model including all harmonics and the conventional rotor reference frame d–q model. Saturation is included by using a polynomial fitting the variation of d-axis inductance with stator current obtained by finite-element software FEMAG DC®. The detailed phase-variable model can yield torque pulsations comparable to those obtained from finite elements while the d–q model cannot.