Estimation of 3-D Magnet Temperature Distribution Based on Lumped-Parameter and Analytical Hybrid Thermal Model for SPMSM

This paper presents a hybrid analytical thermal model by utilizing the synergies of the lumped-parameter thermal model (LPTM) and the analytical thermal model to estimate the 3-dimensional (3-D) permanent magnet (PM) temperature distribution as well as the hotspot for surface-mounted PM synchronous machines (SPMSMs). The hybrid analytical thermal model is firstly developed based on 2-dimensional analytical models in radial-circumferential and radial-axial planes, and then extended to three dimensions, in which the uneven distributions of PM eddy current loss are taken into account. The analytical solutions are obtained by solving the Poisson's equations under the Dirichlet and the convection boundary conditions, which are extracted from the synergized LPTM. The proposed hybrid thermal model is applied to a totally enclosed SPMSM and validated by the 3-D electromagnetic-thermal coupled finite element method and experiments.