Estimation of Magnet Temperature for Synchronous Motors via Duhamel’s Integral Thermal Model

In the permanent-magnet synchronous machines (PMSMs), the temperature of the permanent magnets (PMs) is hard to estimate, because the heat transfer involving the rotor includes speed-dependent heat convection processes. This article presents Duhamel’s integral thermal model for estimating the PM temperature of a water-cooled PMSM. In the present model, the PM temperature transient under highly varying driving cycles is presented as the superposition of the responses to all the major unit-step excitations. The accurate response of the PM temperature to each unit-step excitation can be directly obtained by numerical simulations of the corresponding auxiliary problem with the aid of a high-fidelity computational fluid dynamics (CFDs) model of the PMSM. The present PM temperature estimation model features a universal functional formula, of which the parameterization procedure does not involve the solution nonuniqueness of an inverse identification method. Therefore, it can be easily parameterized for the common radial-flux water-cooled PMSMs.