A Two-Stage Analytical Modeling Approach for Consequent-Pole Surface Mounted Permanent Magnet Machines with Shaped Iron Poles

This paper presents an analytical solution to simplify the complexity of the subdomain model in Consequent-Pole Surface Permanent Magnet (CP-SPM) Machines with shaped iron poles. The original two-dimensional (2-D) problem is reformulated into a two-stage process, comprising a one-dimensional (1-D) analysis followed by a simplified 2-D problem with a single boundary condition. In the first stage, the radial flux density in the air gap is calculated using the Magnetic Equivalent Circuit (MEC) for the Permanent Magnet (PM) field and the Winding Function (WF) method for the armature reaction. The effect of stator slots in the radial flux is modeled using the flux path function method, while the influence of the non-uniform air gap, caused from the shaped poles, is captured through an appropriate analytical function. In the second stage, the tangential flux density is derived by solving a 2-D Laplace equation, subject to only a single boundary condition. The effect of stator slots on the tangential flux is accounted for using virtual surface currents placed along the lateral sides of the stator slots. The proposed hybrid approach reduces computational time while maintaining high accuracy, as confirmed through comparison with the subdomain model, finite element (FE) analysis, and experimental testing on the fully developed, production-ready version of the motor intended for the kitchen hood application.