## 1 Introduction  
Permanent magnet synchronous motors (PMSMs) have been widely used in automotive traction drives due to their high performance, efficiency, and power density [1; 2; 3]. PMSMs should be operated within a specified range of temperature rise without any risk of demagnetization and stator winding failure [4; 5; 6]. So, it is essentially important to accurately predict and monitor motor temperatures [7; 8]. Currently, there are mainly four methods for the thermal analysis of motors, i.e., finite element method (FEM), estimation method based on the rotor flux, estimation method based on the rotor high frequency impedance, and lumped parameter thermal networks (LPTNs). FEM can simulate the electromagnetic field and temperature field of the motor by means of multi-physics coupling. A combination of thermal and electromagnetic analysis was applied to analyze the behavior of the motor through FEM [9; 10], and the minimum ferromagnetic analysis was used to determine the parameters of the equivalent circuit of the induction motor [10]. [PERSON] proposed the rotor temperature estimation method based on rotor flux linkage. This method is not computationally intensive and simple to conduct [11]. The rotor temperature estimation method based on high frequency injection was proposed in [12; 13; 14]. The temperature of the permanent magnet not only affected the magnetic flux of the permanent magnet but also changed the transient resistance of the rotor. If the transient resistance of the rotor can be obtained, the temperature of the rotor can be obtained indirectly. Therefore, when the rotor transient impedance was observed under the condition of high-frequency voltage, the rotor temperature information can be obtained by the relationship between the transient resistance and the temperature [12]. However, the above-mentioned methods have some drawbacks. FEM has high estimation accuracy, but this method depends on the motor geometry, material properties, and boundary conditions, resulting in complex calculation and longer computing times. Thus, it can only be used for off-line analysis in the motor temperature field. Although the motor rotor temperature estimation algorithm based on rotor flux linkage is simple and easy to conduct, it is only able to predict the rotor temperature. In addition, the estimation accuracy depends on the observation accuracy of the rotor flux linkage, and the change of the flux linkage caused by temperature is not completely linear. Therefore, it is difficult to obtain a more accurate estimation of the rotor temperature. Compared with the method based on the rotor flux observation, the advantage of the approach based on the high frequency injection is that the change in rotor transient impedance is easier to detect. However, the injected high frequency signal may bring additional rotor loss, causing an increase in temperature. A suitable alternative to monitor motor temperature is lumped parameter thermal networks (LPTNs). This thermal network model is a simplification of the motor physical model and its structure has obvious physical meanings, which can be applied to estimate the motor temperature online [15; 16; 17]. Three different methods for establishing LPTN have been proposed according to the number of the thermal model nodes [18]: Dark gray-box LPTN, light gray-box LPTN, and white-box LPTN. Dark gray-box LPTNs are strongly abstracted from the complicated motor thermal structure. In general, two to five nodes are selected to predict the temperature in the most dominant hear paths. The parameter identification of the thermal model is realized based on the experimental data from the sensor [18; 19; 20; 21; 22; 23; 24; 25]. Compared with the modelling of the dark gray-box LPTN, the light gray-box LPTNs take more heat paths into consideration. More thermal nodes (5-15 nodes) are set up to design the LPTN based on heat transfer theory [26; 27].