# Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy
## 4 Discussion and Optimization Results
### Performance Evaluation by Experiments  
To further prove the effectiveness of the optimization method described above, an IPMSM prototype is tested on the experimental platform shown in Figure 9, which is based on the dSPACE controller. The magnetic powder brake is used to provide various load torques, and a dynamic torque sensor is used to measure dynamic torque and speed. The target motor is used to power an A0 class pure EV, which adopts UDDS as the main test specification for emissions certification and fuel economy performance testing. Therefore, L2 shown in Table 5 is chosen to be tested as the prototype, which is optimized under UDDS. Meanwhile, the UDDS driving cycle is carried out to conduct the motor performance evaluation. Firstly, the no-load performance of the proposed IPMSM is tested, and the results are shown in Figure 10. In Figure 10a, it can be observed that the IPMSM can quickly follow the given speed during the starting or speed switching process. And Figure 10b shows the torque ripple at no load is less than \(\pm\)0.2 N-m, which demonstrates the good design of cogging torque. From Figure 10c, it can be seen that its three-phase back EMFs are sinusoidal and symmetric. Moreover, the no-load current is smaller than 1A to provide no-load loss, as shown in Figure 10d. The changes in the above curves are consistent with the changes in motor working conditions, and the motor speed regulation effect shows the feasibility of the proposed control system. \begin{table}
\begin{tabular}{c c c c c} \hline  & & **L1** & **L2** & **L3** \\ \cline{3-5}  & **RPs** & & \(\mathbf{I_{\text{P}}}\) **(A), \(\mathbf{P_{\text{Fe}}}\) (W), \(\mathbf{P_{\text{Cu}}}\) (W), \(\mathbf{T_{\text{r}}}\) (\%)** & \\ \hline \multirow{4}{*}{UDDS} & 1 & 29.8, 39.35, 53.25, 21 & 31.56, 34.24, 59.76, 14 & \\  & 2 & 66.8, 355.11, 268, 35 & 53.37, 324.2, 171.24, 21 & \\  & 3 & 15.26, 178.09, 14, 42 & 16.32, 155.81, 16, 25 & none \\  & 4 & 92.74, 80.5, 515.9, 10 & 96.55, 76.14, 559.18, 8 & \\  & 5 & 52.6, 154.5, 165.8, 15 & 55.18, 140.78, 182.7, 11 & \\ \hline \multirow{4}{*}{HWFET} & 1 & 82.8, 381, 411.25, 38 & \multirow{4}{*}{none} & 82.75, 59.48, 325, 15 \\  & 2 & 71, 153.22, 303.4, 14 & & 71.11, 76.4, 135.76, 10 \\  & 3 & 34.39, 327, 71.27, 28 & & 34.39, 21.14, 296.67, 17 \\ \hline \multirow{2}{*}{Rated} & \multirow{2}{*}{97.3, 284, 567.9, 7.91} & \multirow{2}{*}{100.75, 274, 608.92, 6.1} & \multirow{2}{*}{103, 268.32, 638, 9.26} \\ \cline{3-5}  & & & \(\mathbf{x_{1}}\), \(\mathbf{x_{2}}\), \(\mathbf{x_{3}}\), \(\mathbf{x_{4}}\), \(\mathbf{x_{5}}\), \(\mathbf{x_{6}}\), \(\mathbf{x_{7}}\) & \\ \cline{1-1} \cline{2-5}  & 0.8, 5.5, 1.5, 36, 14, 8750, 6500 & 0.8, 5.5, 1.7, 33.5, 14.5, 7854, 6280 & 0.8, 5.5, 1.7, 32.5, 14.5, 7525, 7500 \\ \hline \end{tabular}
\end{table} 
Table 5: Objective performances and optimal variables. Figure 9: Experimentation platform of the IPMSM prototype. Moreover, the loaded performance of the proposed IPMSM under MTPA and flux weakening control is tested, and the results are shown in Figure 11. It can be seen from Figure 11a,b that the motor driving modes can be switched from MTPA mode to flux weakening mode at about 5 s to expand its high-speed carrying capacity. With the flux weakening control under constant power operation, more negative \(i_{\text{d}}\) is applied to the IPMSM to achieve the same torque requirements as the MTPA shown in Figure 11c. In Figure 11a, it can be seen that the IPMSM can quickly follow the given speed at starting, speed switching, or load-changing working conditions. Moreover, the torque ripple at 2000 rpm with 5 N\(\cdot\)m is about \(\pm\)1 N\(\cdot\)m; it is similar at 3500 rpm with 5 N\(\cdot\)m; and it is about \(\pm\)3 N\(\cdot\)m at 3500 rpm with 15 N\(\cdot\)m, which is shown in Figure 11b. Generally, torque ripples in the two modes are about 20%, which agrees with the results in Table 5. Furthermore, the three-phase currents shown in Figure 11c are sinusoidal and symmetric, which also shows the effectiveness of the proposed control system.