Analysis and simulation of five-phase synchronous reluctance machines including third harmonic of airgap MMF

In this paper, the winding function method in conjunction with the coupled magnetic circuit approach are used to develop the dynamic equations of a five-phase synchronous reluctance machine in the natural frame of reference (a-b-c-d-e). The effect of the third harmonic of the airgap MMF is included in this development. A five-phase transformation from the (a-b-c-d-e) system to a (d₁-q₁-d₃ -q₃-n) system is introduced. This transformation removes the angular dependency of the inductances. Using this transformation, equations for a five-phase synchronous reluctance machine, including the third harmonic of the airgap MMF, were obtained. The resulting equations are compared with the equations in the natural (a-b-c-d-e) system. Simulation traces are used to confirm the validity of the model. Finally, the developed equations are compared to experimental results and their similarities and discrepancies are identified