Analytical Model of Electromagnetic Performance for Permanent-Magnet Vernier Machines Using Nonlinear Exact Conformal Model

This article investigates the air-gap field distribution of the permanent-magnet Vernier machine (PMVM) using a nonlinear exact conformal model (NECM) to account for slotting effect, flux modulation effect, and iron nonlinearity. The exact conformal model (ECM) based on the region of one-slot and one-flux-modulation-pole (OSECM) are introduced to show the effectiveness of the linear analytical model for PMVM. It can keep high calculation accuracy and significantly reduce the computational burden. Then, the NECM is developed from OSECM by introducing the equivalent saturation current into the air region and coil region. The lumped parameter magnetic circuit model (LPMCM) model is used to obtain the magnetic potential of the iron region and therefore calculate the equivalent saturation current. The NECM which combines LPMCM and OSECM can essentially improve the accuracy of the linear analytical model. The harmonic analysis of the air-gap field is performed to theoretically explain the component of electromagnetic torque. Both finite element model (FEM) simulation and test results are presented to validate the NECM.