# An Investigation of Parameter Dimension Reduction Optimization of PMA-Synrm
## 3 Parameter Dimension Reduction Optimization Design of the PMA-Synrm
### Multi-Objective Optimization Design of PMA-Symm  
The cross-section of a permanent magnet-assisted synchronous reluctance motor is shown in Figure 10. In the figure, it can be seen that the design parameters of this motor are d-axis magnetic barrier thickness \(w_{d}\), five-layer ferrite length L1-L5, and circumferential magnetic bridge Rid. Among them, the synchronous reluctance motor is optimized in the previous section, and the optimal values of C1, G1, and D1 are obtained, which are 0.625, 0.589, and 0.599 respectively. Therefore, \(w_{q}\), \(h_{d}\), and \(h_{q}\) can be represented by C1, G1, D1, and \(w_{d}\). Table 6 shows the range of these seven optimization parameters. Due to the limited area of the magnetic barrier and ferrite arranged on the rotor, the value range of each parameter can be obtained according to the analysis. Before the optimization design of the permanent magnet-assisted synchronous reluctance motor, the sensitivity analysis of the main optimized parameters is carried out by means of the finite element model, and the correlation coefficient of each optimization parameter to different optimization objectives is obtained. In this paper, the Pearson correlation coefficient is used to represent the influence of each optimization parameter on different optimization objectives. The specific results are shown in Figure 11. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Optimal Results** \\ \hline \(w_{d}\) (mm) & 4.27 \\ C1 & 0.625 \\ G1 & 0.589 \\ D1 & 0.599 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimization results of synchronous reluctance motor. Figure 10: Section diagram of permanent magnet-assisted synchronous reluctance motor. Figure 12 shows the response surface fitting curve of the seven design parameters of the permanent magnet-assisted synchronous reluctance motor on the main electromagnetic performance of the motor. Among them, the width of the circumferential magnetic bridge Rid has a great influence on the performance of the motor. The main function of the circumferential magnetic bridge is to prevent magnetic flux leakage, so it needs to be designed emphatically. The increase in the thickness of \(w_{d}\) will increase the salient pole ratio of the motor and improve the performance of the motor, but when it is too large, it will lead to serious magnetic saturation of the motor and reduce the output torque, efficiency, and power factor of the motor, and will increase the torque ripple. L1-L5 is the length of five layers of ferrite. The increase in length means an increase in ferrite content. In a certain range, it can provide a stronger magnetic field to help improve the output torque, efficiency, and other performance of the motor. However, when the increase is too large, it will also lead to serious rotor magnetic saturation, which will increase the iron loss, reduce the efficiency of the motor, reduce the rotor salient ratio, and reduce the power factor of the motor. The influence of L1-L5 on the torque ripple of the motor is different. The increase in L1, L2, and L4 will make the torque ripple decrease first and then increase, and the variation range is 3%, 5%, and 4%, respectively. The increase in L3 and L5 will make the torque ripple decrease continuously, and the change ranges are 11% and 6%, respectively. The optimization objective of the permanent magnet-assisted synchronous reluctance motor is shown in Equation (3). Similarly, in order to achieve the performance index of the motor, the maximum efficiency of the motor and the minimum output torque ripple are required to ensure the stable operation of the motor. \[Objectives: \begin{cases}\max(\eta_{2})\\ \min(T_{r2})\end{cases}  \tag{3}\]  
where \(\eta_{2}\) is the efficiency of PMA-Synrm, and \(T_{r2}\) is the torque ripple of PMA-Synrm.