## 6 Experimental Verification
### Temperature Estimation Under Complex Conditions  
After the identification of the thermal model parameters, an independent continuous heating and cooling experiment at different speeds was carried out, and the duration of the experiment under the complex condition was about 4 h, as shown in Figure 9. The stator winding temperature, rotor temperature, and end cap temperature were investigated. The temperature directly measured by the temperature sensor, the temperature calculated by the motor state equation, and the temperature estimated based the Kalman filter algorithm were compared, which is shown in Figure 9. In Figure 9, V/Vn and T/Tn represent the ratio of the operating speed and rated speed and the ratio of the output torque and the rated torque, respectively. From Figure 9, the following conclusions can be made:  
1. By comparing the temperature estimation results, it was found that the stator, rotor, and end cap temperatures change with different operation conditions. Figure 9 shows that as the speed increases, the temperature of the rotor and end cap increases. During each period of torque change, the temperature will fluctuate, but the fluctuation range is not large within the range of 10 \({}^{\circ}\)C. Regarding the stator temperature variation, the temperature rises when the motor accelerates; but during each period of torque change, the temperature fluctuates greatly. When the range of torque change reduces, temperature fluctuations also decrease. Before 6000 s, the torque fluctuation changes in the range of 0-5 Nm, and the fluctuation range of the stator temperature exceeds 70 \({}^{\circ}\)C. After the moment of 6000 s, the temperature fluctuation range is reduced to 30 \({}^{\circ}\)C as the torque fluctuation decreases. It shows that the variation of the torque fluctuation range has a greater influence on the estimation of the stator temperature but has less impact \begin{table}
\begin{tabular}{c c} \hline \hline
**Duration (min)** & **Torque (Nm)** \\ \hline
5 & 0 \\
5 & 20 \\
7 & 40 \\
30 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental conditions at 7000 rpm. Figure 8: Temperature comparison at 7000 rpm. on the rotor and end cap temperature estimation. This is because when the torque is large, the current also becomes large. According to Equations (8) and (9), the change of the current and speed will result in variation of the stator and rotor loss. In addition, the change of working conditions will also lead to changes in the thermal resistance and capacity of the thermal model, so the motor temperature change is the result of multiple parameters. Thus, by establishing a lumped parameter network thermal model of the motor, the change in motor temperature can be accurately predicted. 2. From Figure 9, it can be seen that at the moment of sudden torque change, the temperature waveform will have a sharp peak, and the thermal model can quickly respond to the change of the working condition. The difference between the estimated temperature and the measured temperature will not exceed 10 \({}^{\circ}\)C at the moment of change. Therefore, the equivalent thermal model proposed in this paper has good robustness and observation accuracy. 3. For the temperature estimation in PMSMs, the rotor temperature is critical, since the rotor temperature is not easily available to sensors. The results show that the rotor temperature error is within a range of \(\pm\)5 \({}^{\circ}\)C in most cases, which indicates the improved prediction accuracy of the proposed model. Regarding the stator temperature estimation, at the moment, when the load condition changes, the error becomes large, but the proposed model can quickly follow the temperature change, resulting in a reduction of error. The rapid response ability shows that the proposed model has a better robustness. Besides, when the fluctuation of the load reduces, the accuracy will increase.