# Efficiency Optimization of the Main Operating Points of an EV Traction Motor
## 3 Optimal Design
### Sensitivity Analysis  
A sensitivity analysis was performed to select the design variables significantly affecting the objective and constraint functions. The number of experimental points for the analysis was determined using the Orthogonal Array (OA) method, a DOE technique designed to reduce the number of experimental points compared with the Full-Factorial Design (FFD) method. The experimental points were selected according to Equation (3) [24].  
\[\text{nEXP}\geq 1.5\times(\text{nDV}+1)\,(\text{nDV}+2)/2, \tag{3}\]  
where nEXP is the number of experimental points, and nDV is the number of design variables. According to Equation (3), the experimental points should be at least 42. To consider the nonlinear changes in the output and characteristics of the OA, each design variable was set at three levels, and 45 experimental points closest to the calculated number of experimental points in the OA table were selected. FEA was performed, and based on the results, an Analysis of Variance (ANOVA) was conducted to calculate the probability value (\(p\)-value) at a significance level of 0.05. This method was used to compare means between different groups to determine whether differences between groups were statistically significant. The results are presented in Table 5, where values below the significance level of 0.05 are shaded [25,26]. A \(p\)-value less than 0.05 indicates that the factor has a statistically significant impact on the results and affects the objectives.  
Although the X4_Notch angle is significant based on the \(p\)-value, its impact is lower than that of the other variables when the proportions are compared according to the Sum-of-Squares (SS) values, representing the magnitude of variation for each design variable; therefore, considering the number of experimental points and the accuracy of the metamodel, the X4 notch angle was excluded as a design variable. The SS values are summarized in Table 6. The five design variables X1, X2, X3, X5, and X6 significantly impact the objective and constraint functions; thus, the optimal design was determined using the selected design variables.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Items** & **X1** & **X2** & **X3** & **X4** & **X5** & **X6** \\ \hline MOP1 & 52.4 & 1.26 & 3.18 & 0.84 & 42.31 & 0.04 \\ MOP2 & 7.63 & 10.45 & 21.42 & 0.37 & 56.52 & 3.6 \\ MOP3 & 7.39 & 22.89 & 34.96 & 0.12 & 33.06 & 1.58 \\ \(THD_{Back-EMF}\) & 58.57 & 2.02 & 1.86 & 2.19 & 12.52 & 22.84 \\ \(T_{Max\_BaseRPM}\) & 11.36 & 1 & 3.5 & 2.39 & 79.41 & 2.34 \\ \(T_{Max\_maxRPM}\) & 72.31 & 9.74 & 2.61 & 4.44 & 10.12 & 0.79 \\ \(V_{line-to-line}\) & 50.02 & 20.98 & 17.54 & 3.69 & 3.27 & 4.5 \\ \(T_{ripple}\) & 41.6 & 0.36 & 1.84 & 1.26 & 37.87 & 17.06 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Analysis results of SS.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Items** & **X1** & **X2** & **X3** & **X4** & **X5** & **X6** \\ \hline MOP1 & 0 & 0.485 & 0.185 & 0.636 & 0 & 0.975 \\ MOP2 & 0.028 & 0.02 & 0.001 & 0.828 & 0 & 0.18 \\ MOP3 & 0.016 & 0 & 0 & 0.927 & 0 & 0.362 \\ \(THD_{Back-EMF}\) & 0 & 0.053 & 0.062 & 0.04 & 0.001 & 0 \\ \(T_{Max\_BaseRPM}\) & 0 & 0.405 & 0.05 & 0.129 & 0 & 0.132 \\ \(T_{Max\_maxRPM}\) & 0 & 0 & 0.092 & 0.022 & 0 & 0.474 \\ \(V_{line-to-line}\) & 0 & 0 & 0 & 0.006 & 0.006 & 0.003 \\ \(T_{ripple}\) & 0.039 & 0.967 & 0.849 & 0.89 & 0.043 & 0.219 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Analysis results of the \(p\)-value.