# 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 Symm  
Figure 7 shows the synchronous reluctance motor model. From the diagram, it can be seen that after the hypothesis and the exploration of the relationship between the parameters, the design parameters of the synchronous reluctance motor are only \(w_{d}\), C1, G1, D1, and Rid. Considering the processing technology, the Rid is constant at 1 mm. Figure 8 shows the effects of G1, D1, and G1 on the electromagnetic performance of the motor. From Figure 8a, it can be seen that with the increase in C1, the output torque of the motor decreases continuously; with the increases in G1 and D1, the output torque of the motor also increases. Among them, G1 has the greatest influence on the output torque of the motor, and the variation range reaches 4.5 Nm. In Figure 8b, with the increases in C1 and D1, the torque ripple of the motor increases continuously, and the increase is close to 10%. However, with the increase in G1, the torque ripple of the motor decreases first and then increases, with a minimum of only 7% and a maximum of 33%. Therefore, G1  
Figure 6: Parameter dimension reduction optimization flow chart. has the greatest influence on the torque ripple of the motor. From Figure 8c, it can be seen that with the increases in C1 and D1, the power factor of the motor changes little; with the increase in G1, the power factor of the motor increases from 0.78 to 0.81, and G1 has the greatest influence on the power factor of the motor. The change in motor efficiency with C1, G1, and D1 is shown in Figure 8d. With the increase in C1, the motor efficiency decreases continuously, with a decrease of 0.2%. With the increases in G1 and D1, the efficiency of the motor increases first and then decreases, and G1 has the greatest influence on the efficiency of the motor. According to the above analysis, it can be seen that \(w_{d}\), C1, G1, and D1 have an impact on the performance of the synchronous reluctance motor, so wd, C1, G1, and D1 are selected as the optimization parameters. In addition, according to the arrangement space of the magnetic barrier on the rotor, the variation range of \(w_{d}\), C1, G1, and D1 is determined, as shown in Table 4.  
Figure 8: Influence of optimized parameters on motor performance. (**a**) Torque. (**b**) Torque ripple. (**c**) Power factor. (**d**) Efficiency. Figure 7: Cross-section of synchronous reluctance motor. Figure 9 shows the sensitivity of the four optimization parameters to the motor performance. It can be seen that \(w_{d}\) and G1 have the highest sensitivity to the main output performance of the motor, followed by C1 and D1. On the whole, these four parameters need to be optimized in the next step to obtain the optimal value. The optimization goal of the synchronous reluctance motor is shown in Formula (1), which requires the motor to achieve the highest efficiency and minimum torque ripple. Efficiency: Efficiency is one of the important performance indicators of the motor. In this paper, the amount of efficiency is calculated as the ratio of the output power of the motor to the input power, which is also a commonly used calculation method for motor efficiency testing. Torque ripple: The torque ripple of the motor will directly affect the stability of its output torque and the vibration noise. In this paper, the calculation method of motor torque ripple is the ratio of the difference between the maximum and minimum output torque to the average output torque. \[Objectives:\left\{ \begin{matrix}\max(\eta_{1})\\ \min(T_{r1})\end{matrix} \right. \tag{1}\]  
where \(\eta_{1}\) is the efficiency of synchronous reluctance motor; \(T_{r1}\) is the torque ripple of synchronous reluctance motor. The constraints of synchronous reluctance motor optimization are shown in Equation (2). The motor is required to achieve the rated torque, and the power factor should be greater than 0.8. Output torque: The output torque is the primary parameter of the motor.