# Multi-Objective Optimization for Outer Rotor Low-Speed Permanent Magnet Motor
## 4 Multiple Objectives Comprehensive Optimization
### Optimization  
In the optimization, the response-surface expression and the NSGA-II algorithm are obtained through the optimization module of the Ansys Workbench. During the optimization process, the objective function is evaluated by Ansys Maxwell finite-element analysis software, and the feasible region of the Pareto optimal solution can finally be obtained through calculation. Figure 11 shows the relationship between the multi-objective performance achieved in the optimization process. In the multi-objective optimization, nearly the same thermal load is seen for multiple solutions under the same constraints, but with different efficiencies due to different design parameters. Among all the feasible solutions shown in the figure, the highest efficiency can reach 94.8%; in addition, the minimum thermal load is about 154.5 A\({}^{2}\)/mm\({}^{3}\). The three candidate points obtained by calculation are listed in Table 3 for comparison. In Table 3, the design parameters of the three candidate points are different, but a similar performance is obtained. The highest efficiency is 94.66% of candidate point 3, the minimum thermal load is 156.9 A\({}^{2}\)/mm\({}^{3}\) of candidate point 2, and the minimum copper loss is 10,684.6 W of candidate point 1. Figure 11: Relationship between multi-objective performances. (**a**) Relationship between phase back EMF, efficiency and thermal load; (**b**) relationship between power factor, efficiency and thermal load; (**c**) relationship between output power, efficiency and thermal load. In order to maintain a reasonable temperature distribution for this motor, a water-cooling channel is provided on the stator shell, as shown in Figure 12. To compare the motor temperature distribution of these three candidates, the FEA of the temperature is conducted by motor-CAD. The turbulence model, inlet velocity, inlet temperature and the corresponding losses of the three points are set in the FEA, and the motor speed is set to 56 rpm. The temperature distribution of the motor is obtained by solving the model. Figure 13 shows the simulation results of the temperature distribution of the three candidate points. As shown, the temperature in the stator area is significantly higher than that in the rotor area. This is because the stator core loss of the motor is much larger than the rotor core loss, so the stator part generates more heat and the temperature is higher. In addition, the highest temperature point of the motor appears on the motor winding, which is mainly due to the large working load of the LSPMM resulting in a large stator current, so that the copper loss generated by the motor winding is large, the thermal conductivity of the insulating material is relatively low, and the winding produces heat that is difficult to dissipate. Moreover, when the LSPMM works in the rated state, the temperature of the PM surface is low. On the one hand, the speed of the LSPMM is very low, and the PM eddy current loss generated by the motor is small. On the other hand, the inner surface of the PM is connected to the rotor core, and the thermal conductivity of the two is better; the heat generated by the PM can be quickly transferred out through the rotor core. In addition, the outer surface of the PM is in contact with the air gap, and the air flow caused by the rotor movement can take away more heat.