Computationally Efficient Analytical Model of Interior Permanent Magnet Machines Considering Stator Slotting Effects

Subdomain modeling is among the most reliable and accurate analytical tools for designing and analyzing permanent magnet machines. However, the application of the two-dimensional (2-D) subdomain model is mainly limited to permanent magnet machines with homogeneous rotor structures (with uniform permeability), such as surface-mounted or surface-inset permanent magnet machines. Solving Maxwell's equations and applying 2-D boundary conditions on structures with permanent magnets embedded in the rotor core, such as interior permanent magnet machines, are quite complex. Given the importance of enabling the tangential field component to capture accurate results, a 2-D hybrid analytical solution is proposed and applied to a multilayer interior permanent magnet machine. For this purpose, the radial components of the permanent magnet flux and the armature flux are first calculated using the magnetic circuit and the magnetic islands methods, respectively. Next, their respective tangential flux components are computed by solving Poisson's equation and applying a 1-D boundary condition along the tangential direction. Meanwhile, the stator slotting effect is included via the theory of virtual surface current. Finally, the steady-state performance metrics of the motor are calculated and verified via finite-element and experimental measurement.