Finite Element Analysis of Inflection Point Occurrence in Power Loss vs. Torque Curve of Permanent Magnet Synchronous Machines Towards Optimal Torque Distribution in Electric Vehicles

The paper deals with a finite element analysis (FEA) of the occurrence of an inflection point in the power loss vs. torque curve of permanent magnet synchronous machines (PMSM), related to optimal torque distribution in multi-motor all-wheel drive electric vehicles. Simplified, analytical power-loss models of the electric motor suggest that the power loss curve is convex, and consequently, the equal front/rear torque distribution is optimal. On the contrary, experimental studies usually point to a non-convex power loss curve containing an inflection point, which leads to more complex torque distribution laws. With the aim of explaining the experimentally observed effects, a first-principle, FEA approach is applied to PMSMs of different types (interior vs. surface permanent magnets, IPM vs. SPM) and different vector control strategies (maximum torque per ampere vs. maximum efficiency). Additionally, the impact of vehicle transmission losses on the power loss curve inflection point occurrence is analyzed. The results demonstrate that in the IPM motors, the inflection point occurs more readily than in the SPM motors due to the greater reluctance torque capabilities, which can strongly saturate the q-axis even under flux-weakening conditions, thus creating a highly nonlinear iron loss torque dependency. Also, the rising transmission efficiency vs. torque curve contributes to the occurrence of an inflection point.