Analytic power factor calculation for vernier machines with concentrated windings

It is well-known that the power factor of Vernier machines is small compared to permanent magnet machines. However, the power factor equations already derived show a huge deviation to the finite-element analysis (FEA) when used for Vernier machines with concentrated windings. Therefore, this paper develops an analytic model to calculate the power factor of Vernier machines with concentrated windings and different numbers of flux modulating poles (FMPs) and stator slots. The established model bases on the winding function theory in combination with a magnetic equivalent circuit. Consequently, equations for the q-inductance and for the no-load back-EMF of the machine are derived, thus allowing the calculation of the power factor. Thereby, the model considers stator leakage effects, as they are crucial for a good power factor estimation. Comparing the results of the Vernier machine to those of a pm machine explains the decreased power factor of Vernier machines. In addition, a FEA confirms the results of the derived model.