###### Abstract  
The irreversible demagnetization of permanent magnets causes the deterioration of the performance in permanent magnet synchronous motors (PMSMs), which are used for electric vehicles, NdFeB, which is the permanent magnet most commonly used in PMSMs for electric vehicles, is easily demagnetized at high temperatures. Because traction motors for electric vehicles reach high temperatures, and a high current can be instantaneously applied, permanent magnets of PMSM can be easily demagnetized. Therefore, it is important to study the demagnetization phenomenon of PMSMs for electric vehicles. However, since the demagnetization analysis procedure is complicated, previous studies have not been able to perform optimization considering demagnetization characteristics. In this study, we optimized the shape of a PMSM for electric vehicles by considering the demagnetization characteristics of permanent magnets using an automated design of experiments procedure. Using this procedure, a finite element analysis for each experimental point determined by a sampling method can be performed quickly and easily. The multi-objective function minimizes the demagnetization rate and maximizes the average torque, and the constraints are the efficiency and torque ripple. Various metamodels were generated for each of the multi-objective functions and constraints, and the metamodels with the best prediction performance were selected. By applying a multi-objective genetic algorithm, 1902 various optimal solutions were obtained. When the weight rate of the demagnetization rate to the torque was set to 0.1:0.9, the demagnetization rate and average torque were improved by 4.45% and 2.7%, respectively, compared to those of the initial model. The proposed multi-objective optimization method can guide the design of PMSMs for electric vehicles with high reliability and strong demagnetization characteristics. optimization; PMSM; electric vehicle; demagnetization; metamodel; MOGA +
Footnote †: journal: Applied Sciences  
determine where the permanent magnets were demagnetized. In [2], the demagnetization of 45 SH grade permanent magnets was examined after applying a demagnetization current three, five, and seven times higher than the rated current at a temperature of 100 \({}^{\circ}\)C. Changes in the magnetic flux density distribution and demagnetization rate according to the separated number of permanent magnets were examined. Other studies examined the change in the back electromotive force (EMF) and magnetic flux density distribution of a motor after applying a demagnetization current one and a half to four times higher than the rated current at temperatures of 100-160 \({}^{\circ}\)C [3; 4; 5]. Although the demagnetization of permanent magnets according to the temperature and current was partially analyzed, the optimal design of motors considering the demagnetization characteristics was not achieved. The reason that the demagnetization characteristics were not considered in the optimal design is that the analysis process is complicated. For optimal design, computational analysis of many experimental points must be performed. However, it is not easy to perform such analyses at each experimental point and use the results for optimal design. Moreover, it is almost impossible to consider demagnetization characteristics in the optimal design performed manually. On the other hand, many studies have been conducted on the optimal design with multi-objective functions [5; 6; 7]. For such designs, the weights of the multi-objective functions affect the optimal design results. However, in most previous studies, optimization was performed with fixed weights. In the case of using multi-objective functions, the optimal design result according to the change in weight should be carefully reviewed [8]. As an optimal design method, the use of metamodels is widely used.