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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 or hybrid electric vehicle (EV/HEV) 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 EV/HEV powertrain-level simulation and optimization. The technique is based upon simulating eigenmodes of the thermal dynamics as determined by 3D finite element analysis. The order of the model is then dramatically reduced in two ways. First, the dynamic system is decomposed into two parts by using the orthogonality property of the eigenvectors. The extent of excitation of each eigenmode is calculated, and only eigenmodes that are significantly excited are included in the dynamic model; other eigenmodes are treated as static modes. Second, only the temperatures in few "hot spots" in various regions of the machine are chosen. By using the proposed model order reduction techniques, the computation time of the model is shown to be reduced by over five orders of magnitude, while maintaining sufficient accuracy. Experimental work also shows a good agreement between simulation results and measured data.

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