Thermal homogenisation 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 modelbased control schemes. A common technique to obtain these models involves homogenisation of the electrical winding geometry and thermal properties. However, incorrect estimation of homogenised 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 homogenised model using the method of multiple-scales 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.