Magnetic Equivalent Circuit Model of Interior Permanent-Magnet Synchronous Machine Considering Magnetic Saturation

This paper improves an analytical model for interior permanent-magnet synchronous machine (IPMSM) by a magnetic equivalent circuit (MEC) approach. The proposed MEC model consists of three major regions: the stator, the rotor, and the air gap. The conventional reluctance approach is applied to the first two regions. Since the magnetic field in air gap region is supposed to distribute unevenly, this model employs a function of rotor electrical angle to describe the flux density distribution. Firstly, the permeability of all iron is assumed to be infinite, so the reluctance of the iron core is close to zero and can be ignored. Then the air gap flux density in the direct-axis and quadrature-axis caused by armature currents are calculated in the d-q reference frame respectively, which are used to acquire the direct and quadrature axes inductances Ld and Lq. Open-circuit voltage E0 can be obtained by the air gap flux density caused by the magnets. A finite element model (FEM) is developed to validate the analytical model, and the comparison results indicate that the accuracy of the analytical model is acceptable only in the condition of low armature currents. When the armature currents exceed a certain value, magnetic saturation of the iron core must be taken into account. Therefore, a modification model considering the magnetic saturation is proposed by adding the reluctance of iron core parts to the previous one. The permeability of iron is nonlinear and presented as a function by fitting the BH-characteristic curve with a cubic polynomial. Finally, through numerical calculation, the air gap flux density is derived from the equations of the analytical model. The result of the modification model is validated with the FEM in the saturated condition.