Analytical Modeling and Optimization of Permanent Magnet Synchronous Machine With Hybrid Magnets

This paper proposes an analytical model for a surface-mounted permanent magnet synchronous machine (SPMSM) with hybrid magnets. Through the magnetization analysis of the SPMSM with hybrid magnets, the expression of the air gap flux density is derived using the Laplace equation and the quasi-Poisson equation in which the effects of the thickness of the magnets and the angle of the isolation are considered. The relative permeability of the machine and the air gap field distribution under the slot effect are calculated by conformal transformation. The back electromotive force (EMF) based on the armature winding function is obtained by analyzing the winding law of fractional slot distributed winding. To further improve the torque performance and reduce the magnet cost, the multi-objective optimization based on the analytical model and particle swarm optimization (PSO) algorithm is carried out. The stability of the optimized model is proved by demagnetization analysis. Finally, the prototype based on the optimization results is fabricated, and the tested electromagnetic performances are compared to the finite element and analytical results to verify the effectiveness of the proposed design.