A Hybrid Lumped-Parameter and Two-Dimensional Analytical Thermal Model for Electrical Machines

The lumped-parameter thermal network (LPTN) has been widely used in the thermal analysis for electrical machines. Nevertheless, since the thermal resistances are defined based on the one-dimensional (1-D) heat transfer equation, it will cause the misestimation of the average temperatures when the thermal model extends to two dimensions or three dimensions. In this article, a hybrid thermal model utilizing the synergies of LPTN and 2-D analytical thermal models is developed to address this issue and to predict accurate critical temperatures, especially the average and maximum temperatures of the active and end windings. The 2-D analytical thermal models are obtained by solving the Poisson's equations with the Dirichlet boundary conditions extracted from the LPTN. The derived analytical solutions are expressed as the Fourier series, which can be further simplified by utilizing the first term only to represent average and maximum temperatures with sufficient accuracy and short computation time. The hybrid thermal model is applied to a totally enclosed forced convection permanent magnet synchronous machine and validated by numerical techniques and experiments.