Analytical Modeling of Surface PMSM Using a Combined Solution of Maxwell–s Equations and Magnetic Equivalent Circuit

This paper presents a complete analytical model for surface-mounted permanent magnet synchronous machines (PMSMs). A new simple and fast technique was developed to obtain accurate results in the calculation of machine parameters electromotive force (EMF), torque, and losses. This technique is based upon the combined solution of two models. The first model generates an exact solution of Maxwell´s equations in the air gap area applied to a very simple geometry. The second model gives an accurate solution in the detailed parts with complex geometry, based on a magnetic equivalent circuit (MEC) to obtain fast and accurate results in a simple way. The machine´s global quantities are then obtained and validated using the results of a finite element model (FEM) for different loading conditions and geometries. Compared with FEM, the proposed combined solution has the advantage of flexibility in the geometrical machine parameters, significantly less CPU time and an accuracy for the considered PMSM up to 4.85% in the EMF, 4.41% in the torque, and 4.44% in the iron losses. Finally, the relation between grid refinement in the MEC (coarse or fine grid of reluctances) and accuracy is pointed out, showing that the EMF can be accurately computed with a rather coarse grid, while accurate loss computation requires a fine grid.