Computationally-efficient finite-element-based thermal models of electric machines

Knowledge of the internal temperatures of an electric machine under real-time operating conditions would be extremely useful in order to determine its torque capabilities. This knowledge is also useful for full-scale electric vehicle simulation and optimization. In this paper we present a technique for developing computationally-efficient thermal models for electric machines that can be used for real-time thermal observers and vehicle-level simulation and optimization. The technique is based upon simulating the eigenmode of the system as determined by finite element analysis. The order of the model is then dramatically reduced in two ways. First, the extent of excitation of each mode is calculated, and only eigenmodes that are significantly excited are included in the dynamic model; other eigenmodes are treated as static modes. Second, only a few “hot spots” in various regions are chosen. The result is a thermal model that can accurately model internal temperatures of the machine while requiring the modeling of only a handful of states. Such a model can be used in vehicle simulations, or for real-time observers in actual vehicles. The computation time of the model presented in this paper is dramatically reduced compared with a typical full-order finite element model.