Analytical Electromagnetic Performance Calculation of Vernier Hybrid Permanent Magnet Machine

The analytical model of vernier hybrid permanent magnet machines (VHPMMs) with two different permanent magnet (PM) arrays is proposed in this paper. The working principles of VHPMM are discussed based on the magnetic field modulation theory, and the main rotating harmonics of air-gap flux density are determined. The subdomain method is adopted to obtain the no-load and on-load air-gap flux densities of the slotless model, and the relative permeance model is used to consider the effect of the slot opening. Using fast Fourier transformation, the amplitudes and phase angles of the rotating harmonics are obtained, and the flux linkage, back electromotive force, and electromagnetic torque are calculated. With the working principles and performance calculation model, the determination method of the rotor slot number is proposed, and feasible combinations of PM and rotor slot numbers are studied. The analytical model is verified via the finite-element method and prototype machine experiments.