# Multi-Objective Optimization for Outer Rotor Low-Speed Permanent Magnet Motor
## 5 Performance Evaluation  
Through the above multi-objective optimization analysis and combined with the actual situation, candidate point 3 is determined as the final design scheme. The comparison between the initial and optimized schemes is listed in Table 4. In Table 4, the optimized design has a larger pole arc coefficient, PM thickness and stator outer diameter, and it has a smaller number of conductors per slot and a smaller air gap length. The core length does not change much from the initial design considering the actual machining and installation process.  
The comparison of the initial and optimized electromagnetic performance can be obtained by finite-element analysis. The comparison of the no-load back EMF, output torque, core loss and copper loss is shown in Figure 15.  
In Figure 15, the amplitude of the no-load back EMF of the optimized scheme is basically the same as that of the initial scheme, while the no-load back EMF waveform of the optimized motor scheme is more sinusoidal than that of the initial scheme. In Figure 15, the output torque of the initial and optimized schemes is almost the same, which meets the design requirements. In Figure 15, compared with the initial scheme, the optimized core loss is approximately doubled. Since the pole arc coefficient and PM thickness in the optimized scheme are increased compared with the initial scheme, the magnetic flux density of the optimized motor increases, resulting in an increase in the core loss. In Figure 15, the copper loss is reduced from the initial 15,572.8 W to the optimized 10,708.1 W. In the optimization process considering the motor temperature distribution, the highest temperature point of the LSPMM appears on the stator winding, and the copper loss has a direct impact on the winding temperature. In addition, due to the low-speed and high-torque characteristics of the LSPMM, the copper loss is about 10 times larger than the core loss. Therefore, in the optimization process, the minimum copper loss is set as the main goal, while a quantitative increase in the core loss is acceptable.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Initial** & **Optimization** \\ \hline Pole arc coefficient \(\alpha_{\text{p}}\) & 0.7 & 0.89 \\ PM thickness \(TH_{\text{p}}\) (mm) & 11 & 14 \\ Stator outer diameter \(D_{\text{s}}\) (mm) & 863 & 877 \\ Core length \(L_{\text{ef}}\) (mm) & 930 & 932 \\ Conductors per slot N & 12 & 10 \\ Air gap length \(\delta\) (mm) & 3 & 2.3 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Initial and optimized parameters.  
Figure 14: Comparison diagram of winding temperature, rotor temperature, stator temperature and PM temperature of candidate points.  
Figure 16 shows a comparison of the initial and optimized temperature distributions. In Figure 16, the optimized maximum winding temperature is 106 \({}^{\circ}\)C, which is 17.9 \({}^{\circ}\)C lower than the maximum winding temperature before optimization.  
Figure 16: Temperature distribution map of initial and optimization. (**a**) Temperature distribution map of the initial; (**b**) temperature distribution map of the optimization.  
Figure 15: Performance comparison of initial and optimization. (**a**) Comparison of initial and optimized back EMF; (**b**) comparison of initial and optimized torque; (**c**) comparison of initial and optimized core loss; (**d**) comparison of initial and optimized copper loss.  
The performance comparison of the final initial scheme and the optimized scheme is listed in Table 5. In Table 5, compared with the initial scheme, the efficiency of the optimized scheme increased by 2.04%, and the thermal load and copper loss decreased by 76.1 A\({}^{2}\)/mm\({}^{3}\) and 4864.7 W, respectively. In addition, the power factor also increased from 0.910 to 0.982, the torque ripple decreased by 0.4%, and the air gap flux density increased from 0.84 T to 0.92 T.