Average Torque Separation in Permanent Magnet Synchronous Machines Using Frozen Permeability

This paper investigates the average torque separation in permanent magnet (PM) synchronous machines. In order to accurately separate the PM and armature fields, and, hence, the torque components accounting for the magnetic saturation and crosscoupling, the frozen permeability (FP) method is often employed, while the torque can be calculated by different methods, such as Maxwell stress tensor and virtual work principle. Although these two methods result in identical torques in normal finite element (FE) analyses when appropriate FE meshes are used, the average torques calculated by these two methods are found to be different when the FP method is employed due to the influence of equivalent rotational magnetic saliency in the stator, which causes a part of PM torque being improperly attributed to the reluctance torque when Maxwell stress tensor method is employed. However, by using the virtual work principle, this is eliminated, and, hence, the average torque components can still be appropriately separated and analyzed.