Combined Lumped-Parameter and Simplified 2-D Analytical Thermal Model of Totally Enclosed Water Cooled PM Machine

In this paper, a combined lumped-parameter (LP) thermal model and 2-D simplified analytical winding models is developed to predict the critical temperatures in an electrical machine, especially the average and maximum temperatures of active-winding and end-winding. The 2-D analytical active-winding and end-winding models are obtained by solving the Poisson's equation in polar coordinates and cylindrical coordinates with the Dirichlet boundary conditions, which are extracted from the LP thermal model. The analytical models are then simplified based on series expansions to reduce the computation time. Furthermore, the analytical models are used to calibrate the average active-winding and end-winding temperatures calculated by the LP thermal model and to estimate the maximum temperatures, which is suitable for real-time winding temperature estimation. The combined thermal model is applied to a medium size totally enclosed water cooled permanent magnet synchronous machine for electric vehicles, and validated by thermal analysis software Motor-CAD, 2-D and 3-D thermal finite-element analyses.