## 5 Comprehensive Optimization
### Optimization Objectives and Constraints  
In order to make the selection of optimization objectives and constraints more reasonable, it is essential to analyze and consider the characteristics of multiple physical fields, including mechanical strength, electromagnetic properties, and temperature distribution [27]. Due to small size and difficult heat dissipation conditions, the maximum motor efficiency is set as the first optimization goal to obtain a more reasonable temperature distribution.  
In addition, when the motor efficiency is the same, different loss distributions have a great impact on the motor temperature distribution of the high-speed IPM motor. The housing water cooling system is used for heat dissipation design. The heat dissipation conditions of the stator are good because it is close to the spiral waterway.  
On the premise of keeping the total iron loss constant at 4 kW, only the iron loss distribution ratio between the stator and rotor is adjusted. This change means that the iron loss of the stator or rotor may increase, while the iron loss on the other side will decrease accordingly, but the sum of the two will always be maintained at 4 kW. The effect of different rotor losses on motor temperature is shown in Figure 15. When the rotor core loss  
Figure 14: Flowchart of the optimization.  
increases, the temperature of the stator core remains basically unchanged. The temperature of the stator core decreases by 2%. However, the temperature of the rotor core and PM increased significantly, by 33.1% and 29.8%, respectively. It can be concluded that the influence of rotor core loss on temperature is serious. Therefore, the minimum rotor core loss is set as the second optimization objective to guarantee the lowest motor temperature.  
The constraints of the high-speed IPM motor optimization process include rotor stress, no-load line back-EMF, output torque, and power factor.  
Rotor stress: To ensure the mechanical reliability, the maximum stress of the rotor core must be less than the maximum yield strength of the rotor material (480 MPa) and leave a certain safety margin (85%).  
No-load electromagnetic characteristics: No-load line back-EMF is an important indicator of no-load performance. To achieve a higher power factor, the line back-EMF should be close to the rated voltage, which is limited to between 360 V and 380 V.  
Rated-load electromagnetic performance: Torque should be greater than the rated torque (74.2 N-m). In addition, the power factor is limited to above 0.95.  
Summarizing the above analysis, the two optimization objectives and four constraints of the IPM motor are listed as follows:  
\[\min:\left\{\begin{array}{c}f_{1}(x)=-\eta\\ f_{2}(x)=P_{rotor}\end{array}\right. \tag{2}\]  
\[\begin{split}\text{s.t.}\left\{\begin{array}{c}\sigma_{rotor} \leq 400\text{ MPa}\\ 360\text{ V}\leq E_{L}\leq 380\text{ V}\\ 74.2\text{ N-m}\leq T_{N}\\ 0.95\leq\cos\Phi\end{array}\right.\end{split} \tag{3}\]  
where \(\eta\) is the efficiency, and \(P_{rotor}\) is the rotor core loss. \(\sigma_{\text{rotor}}\) is rotor stress, \(E_{L}\) is the no-load line back-EMF, \(T_{N}\) the output torque, and \(\cos\Phi\) is the power factor.  
Genetic algorithm has been recognized as an effective optimization method, and this method has been verified in many related papers. Thus, in this paper, genetic algorithms are employed in order to obtain optimized solutions based on response surface models. The electromagnetic optimization uses the multi-objective genetic algorithm to obtain Pareto solutions. During multi-objective optimization, the optimal solution is a compromise between two objectives. The four subplots in Figure 16 all show the relationship between multi-objective performances during optimization.  
Figure 15: The influence of rotor loss on temperature. (**a**) Stator; (**b**) rotor.