General 2-D Analytical Framework for No-Load Analysis of Interior Permanent Magnet Machines

Solving 2-D Maxwell's equations in interior permanent magnet (IPM) motors is fairly complex due to the asymmetrical geometry of rotor magnets in the cylindrical coordinate system. This article presents a general imaging solution to enable the 2-D open-circuit modeling of the family of IPM machines (e.g., V-shape, U-shape, Spoke shape, Single-layer, multi-layer, and etc). Interior magnets are mapped to the surface of the rotor body with: 1) virtual magnets and 2) virtual volume current (VVC). The specifications of the virtual magnet (i.e., the remnant flux density) and the VVC (i.e., current density level) are determined via magnetic circuit model. Next, the 2-D flux distribution of the transformed machines is calculated by solving 2-D Maxwell's equations and considering relevant boundary conditions. Meanwhile, the effect of stator slots on flux profile is accounted by injecting proper amount of surface magnetizing current on the stator bore. Analytical results are supported via finite element method (FEM) and a series of experimental measurements.