Thermal Homogenization of Electrical Machine Windings Applying the Multiple-Scales Method

Low-order thermal models of electrical machines are fundamental for the design and management of electric powertrains since they allow evaluation of multiple drive cycles in a very short simulation time and implementation of model-based control schemes. A common technique to obtain these models involves homogenization of the electrical winding geometry and thermal properties. However, incorrect estimation of homogenized parameters has a significant impact on the accuracy of the model. Since the experimental estimation of these parameters is both costly and time-consuming, authors usually prefer to rely either on simple analytical formulae or complex numerical calculations. In this paper, we derive a low-order homogenized model using the method of multiple-scales (MS) and show that this gives an accurate steady-state and transient prediction of hot-spot temperature within the windings. The accuracy of the proposed method is shown by comparing the results with both high-order numerical simulations and experimental measurements from the literature.