# An Investigation of Parameter Dimension Reduction Optimization of PMA-Synrm
## 3 Parameter Dimension Reduction Optimization Design of the PMA-Synrm
### Exploration of Parameter Dimension Reduction Optimization Method  
It can be seen from the previous section that the rotor of the motor has 26 design parameters, and these design parameters are mutually coupled and influenced by each other, which is very unfavorable for the optimal design of the permanent magnet-assisted synchronous reluctance motor. Therefore, this section explores the parameter dimension reduction optimization method. Figure 3 shows the influence of d-axis five-layer magnetic layer thickness (DH1-DH5), d-axis five-layer magnetic barrier thickness (h1-h5), q-axis five-layer magnetic layer thickness (QH1-QH5), and q-axis five-layer magnetic barrier thickness (h6-h10) on the output torque of the motor. It can be seen from the figure that the influence of each design parameter on the torque is not the same, but the change in the output torque is not more than 1.5 Nm, so the influence of these 20 design parameters on the output torque is small. Figure 3: \(Cont.\)  
Figure 2: Design parameter diagram of permanent magnet-assisted synchronous reluctance motor rotor. (**a**) DH1–DH5, QH1–QH5 and Rid. (**b**) h1–h5, h6–h10 and L1–L5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Meaning of Parameter** \\ \hline DH1-DH5 & Thickness of d-axis five-layer magnetic layer \\ QH1-QH6 & Thickness of q-axis five-layer magnetic layer \\ h1-h5 & Thickness of d-axis five-layer magnetic barrier \\ h6-h10 & Thickness of q-axis five-layer magnetic barrier \\ L1-L5 & Length of five-layer ferrite \\ Rid & Length of circumferential magnetic bridge \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Interpretation of rotor design parameters of permanent magnet-assisted synchronous reluctance motor. Based on the above analysis, two motors are designed, as shown in Figure 4. Figure 4a shows the motor models with different values of DH1-DH5, QH1-QH5, h1-h5, and h6-h10. Figure 4b shows the motor models with equal DH1-DH5, equal QH1-QH5, equal h1-h5, and equal h6-h10. The above two motors are excited by the same current source, and the calculation results are shown in Figure 5. It can be seen that the output torque of the motor with the same thickness (WA) is only 0.2 Nm different from that of the motor with different thicknesses (WB), but the torque ripple of the motor with the same thickness (WA) is only 10.6%, which is 9.5% lower than that of the motor with different thicknesses (WB). In addition, the difference in the rotor saliency ratio between the two motors is only 0.05. Figure 4: Cross-sectional view of two motors. (**a**) The values of DH1–DH5, QH1–QH5, h1–h5, and h6–h10 are different. (**b**) DH1–DH5 equal, QH1 QH5 equal, h1–h5 equal, and h6-h10 equal. Figure 5: The torque characteristics and inductance characteristics of the two motors. (**a**) Torque characteristic. (**b**) Inductance characteristics. Figure 3: The influence of rotor design parameters on the output torque. (**a**) DH1–DH5. (**b**) QH1–QH5. (**c**) h1–h5. (**d**) h6–h10. According to the analysis of the influence of DH1-DH5, QH1-QH5, h1-h5, and h6-h10 on the output torque and the finite element analysis results of the above two motors, the hypothesis and the realization process of the parameter dimension reduction optimization design of the permanent magnet-assisted synchronous reluctance motor can be proposed, as shown in Figure 6.  
Step 1: Assume that the thickness of the five magnetic barriers of the D axis is equal to \(w_{d}\); it is assumed that the thickness of the magnetic layer between the magnetic barriers on the D axis is equal to \(h_{d}\); suppose that the thickness of the five layers of the Q-axis magnetic barrier is equal to \(w_{q}\); suppose that the thickness of the magnetic layer between the magnetic barriers on the Q axis is equal to \(h_{q}\);  
Step 2: Define C1, G1, D1, where C1 = \(w_{q}/w_{d}\); G1 = \(h_{d}/h_{q}\); D1 = \(h_{d}/w_{d}\). Then, \(w_{q}\), \(h_{d}\), and \(h_{q}\) can be expressed by \(w_{d}\).