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

Solving two-dimensional (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 paper presents a general imaging solution to enable the 2-D open-circuit modeling of the family of IPM machines. Interior magnets are replaced/modeled with (i) virtual magnets on the surface of the rotor body (mapping interior magnets to the surface of the rotor body), and (ii) virtual volume current on the surface of the rotor body. The specifications of the virtual magnet (i.e., the remnant flux density) and the virtual volume current (i.e., current density level) are determined via magnetic circuit model. Next, the 2-D flux distribution of the transformed machines are 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.