Computationally Efficient 3-D Finite-Element-Based Dynamic Thermal Models of Electric Machines

The performance of an electric machine is significantly constrained by temperature. Hence, in order to determine the torque and power capabilities of an electric machine under real-time operating conditions, dynamic knowledge of internal temperatures is required and needs to be estimated in a computationally efficient manner. 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 electrified vehicle powertrain-level simulation and optimization. The technique is based on simulating eigenmodes of the thermal dynamics as determined by 3-D finite-element analysis (FEA). The order of the FE model is then dramatically reduced. The full-order system is decomposed into two parts by using the orthogonality property of the thermal eigenmodes, and only eigenmodes, which are significantly excited, are included in the dynamic model; other eigenmodes are treated as static modes. A large 3-D FEA model can be thus reduced to a small reduced-order model without the necessity of calculating all the eigenmodes. Furthermore, the process of selecting the significantly excited eigenmodes is automatic based on a proposed normalized “extent of excitation” calculation. By using the proposed techniques, the computation time of the model can be dramatically reduced compared with the full-order model while maintaining sufficient accuracy. Experimental results show good agreement between simulation results and measured data.