II. Introduction
Electric vehicles or hybrid electric vehicles require a thermal and energy management to ensure safety, efficiency and lifetime requirements. In the automotive industry, different thermal arrangements are investigated by co-simulation tools in order to achieve lower emissions [1]. Therefore, the optimization of power and torque density for electrical drive trains considering real driving cycles requires tools to predict the thermal behavior of electrical machines in addition to their electromagnetic behavior. In electric vehicles and hybrid electric vehicles, PMSMs are widely used due to their high efficiency and power density; they also require low maintenance and are relatively easy to control [2]. The changing characteristics of the permanent magnets, caused by temperature rise, and the stator winding temperature have significant impact on energy consumption and torque density. For this reason, thermal networks are coupled to the electromagnetic calculations of PMSMs to predict the efficiency maps for electrical machines quickly [3]. Recently, several researchers have proposed different thermal networks of PMSMs based on detailed machine data [4]–[5]. The white box approach can be used during the machine design stage. However, it is not the best approach in case the PMSM is available as hardware. In some cases, the geometry and winding data of available PMSMs are even unknown. Besides, particular difficulties in the parameterization of the thermal models arise from the fact that important parameters, such as the thermal resistance between stator winding and stator core, have to be identified experimentally, because they strongly depend on details of the manufacturing process [6]. For this reason, it is favorable to approach the thermal behavior of a PMSM by using a grey box model which is based on a thermal network. Thus, the thermal parameters are solely identified by observations and experiments conducted on an available PMSM.