Optimization of the flux modulation poles for Vernier machines with concentrated windings

Vernier machines achieve high torque densities and fit the demands of direct drives due to the usage of the magnetic gearing effect. Unfortunately, Vernier machines suffer from a poor power factor. Thereby, in analytic models the power factor depends on the permeance coefficients of the ferromagnetic flux modulation poles (FMPs), thus the FMP shape influences the power factor. Therefore, this paper investigates the optimal FMP shape using a multi-objective genetic algorithm based optimization to gain the Pareto frontier. For that purpose, the algorithm creates the FMP shape autonomously. The results show that an S-shaped sideline of the FMP is beneficial.