# Clustering Optimization of IPMSM for Electric Vehicles: Considering Inverter Control Strategy
## 4 Discussion and Optimization Results  
### Optimization Results  
According to the optimization procedure shown in Figure 1, after determining the value of representative currents of RPs under different operating conditions, the system's performance could be evaluated based on the fitness function, and MOPSO is used to obtain the optimal design. To illustrate the optimistic effect, the optimized motor scheme designed by the proposed optimization method will be compared with that designed by the single operation point optimization method in this section. The results of multi-objective optimization are shown in Figure 7. Figure 7a-c shows the Pareto solution set optimized by the rated operation point optimization method and the proposed optimization method under UDDS and HWFET, respectively. The black curves in these three figures are the Pareto optimal fronts for each optimization design. Each solution in the Pareto front solution set is optimal. Hence, the optimal motor scheme could be selected from this Pareto front solution set by the decision maker. Based on the VIKOR model [37], which is a multi-attribute decision-making method, the optimal solution could be selected according to (14).  
\[\text{max}\;f(\mathbf{x})=v_{1}\frac{\eta-\eta_{\text{min}}}{\eta_{\text{max}}- \eta_{\text{min}}}+v_{2}\frac{T_{\text{r}}\;\text{max}-T_{\text{r}}}{T_{\text {r}}\;\text{max}-T_{\text{r}}\;\text{min}}, \tag{14}\]  
where \(\eta\) and \(T_{\text{r}}\) are the efficiency and torque ripple corresponding to the current scheme, and the subscript max and min represent the maximum and minimum values of the corresponding variables. \(v_{1}\) and \(v_{2}\) are weight coefficients of two objectives, which depend on the will and preference of decision-makers, and are 0.55 and 0.45, respectively, in this paper.  
In this way, three optimal motor schemes are selected and marked as red points in Figure 7. The motor scheme designed by the rated operation point optimization method is termed L1. The motor scheme designed by the proposed optimization method under UDDS is termed L2, and that optimized under HWFET is termed L3.  
The values of the optimal variables and objective performance of the three motor schemes are listed in Table 5. Furthermore, their performances under different driving cycles are shown in Figure 8. The area in the red dotted box in Figure 8 is defined as the sweet region with high efficiency and low torque ripple, where 92% \(<T_{\text{r}}<\) 98% and 5% \(<\eta<\) 30%. Figure 8a shows the performance evaluation of L1 and L2 under UDDS. It can be observed that the motor optimized at the rated point (L1) has about 40% of the operation points falling into the sweet region, and this ratio is about 90% for the motor optimized under UDDS (L2). Figure 8b shows the performance evaluation of L1 and L3 under HWFET. It can be seen that L1 has about 20% of the operation points falling into the sweet region, and this ratio is over 90% for the motor optimized under HWFET (L3). Therefore, it can be concluded that the sweet region can be expanded by the proposed system-scale optimization, considering driving cycles.  
Figure 8: Performance evaluations of three motor schemes under different working conditions. (**a**) UDDS. (**b**) HWFET. The area in the red-dotted box is the sweet region.  
Figure 7: Motor optimization results under different working conditions. (**a**) Underrated condition. (**b**) Under UDDS. (**c**) Under HWFET. The blue dots are optimization solutions and black curves are Pareto optimal fronts.