## 3 Four Kinds of Machine Performance and Comparison  
The induction motor used as a reference in this article is a standard induction motor with IE4 energy efficiency. Through the above analysis, the SynRM, ferrite-assisted SynRM and IPM will be optimized. The variation ranges of the optimized design parameters are listed in Table 2.  
The efficiency and torque ripple performance are important for four types of motor.  
\[\text{Objective:}\left\{\begin{matrix}\max(\eta)\\ \min(T_{r})\end{matrix}\right. \tag{1}\]  
where \(\eta\) is the efficiency, and \(T_{r}\) is the torque ripple.  
In this optimization process, the constraints include the output torque, power factor, torque ripple and output power.  
\[\text{Constraints:}\left\{\begin{matrix}235.6 Nm\leq T\\ 0.75\leq\varphi_{1},0.94\leq\varphi_{2}\\ 37,000W\leq P_{out}\end{matrix}\right. \tag{2}\]  
where \(T\) is the output torque, \(\varphi_{1}\) is the power factor of the SynRM and ferrite-assisted SynRM, \(\varphi_{2}\) is the power factor of the IPM, and \(P_{out}\) is the output power.  
The response surface expression and genetic algorithm (GA) are obtained using the optimization module of the Ansys Workbench. After optimization, the design parameters of the SynRM, ferrite-assisted SynRM and IPM are determined. To ensure the fairness of the comparison, the only difference between the four motors is the rotor structure. Structural diagrams of the four motors are shown in Figure 12. The rotor design parameters of the SynRM, ferrite-assisted SynRM and IPM are listed in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimization Parameter** & **Range (SynRM/** & **Range** \\  & **Ferrite-Assisted SynRM)** & **(IPM)** \\ \hline Bridge width Rid/U (mm) & [0.5, 3] & [0.5, 3] \\ Magnet Length S1/S2/S3, C (mm) & [30, 70] & [30, 70] \\ Width of each barrier in circumferential & [4, 8] & [4, 10] \\ direction W4/W5/W6, D (mm) & & \\ Width of each barrier in radial direction & [5, 15]/[5, 15]/[5, 10] & – \\ W1/W2/W3 (mm) & & \\ Skew slot (deg) & [0, 10] & [0, 10] \\ Angle of magnetic poles G (deg) & – & [100, 170] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Optimization parameters and variation range.  
Figure 11: Responses of (**a**–**c**) output torque, (**d**–**f**) torque ripple and (**g**–**i**) power factor with width of C, G, D and U.  
Figure 12: Cross section of the four machines. (**a**) Induction machine, (**b**) SynRM, (**c**) ferrite-assisted SynRM, (**d**) IPM.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter Name** & **SynRM** &
\begin{tabular}{c} **Ferrite-Assisted** \\ **SynRM** \\ \end{tabular} & **IPM** \\ \hline Number of barriers & 3 & 3 & 1 \\ Bridge width Rid/U (mm) & 1 & 1 & 1 \\ Magnet Length S1/S2/S3, C (mm) & \(-\) & 68.94/66.16/54.82 & 46 \\ Width of each barrier in circumferential & 6 & 6 & 6 \\ direction W4/W5/W6, D (mm) & 10/8/6 & 10/8/6 & \(-\) \\ Width of each barrier in radial direction & 10/8/6 & 10/8/6 & \(-\) \\ W1/W2/W3 (mm) & 6 & 6 & \(-\) \\ Width of each iron layer in circumferential & 6 & 6 & \(-\) \\ direction L2/L3 (mm) & 6 & 6 & \(-\) \\ Width of each iron layer in radial direction & 6.5 & 6.5 & \(-\) \\ H2/H3 (mm) & 7.5 & 7.5 & 7.5 \\ Skew slot (deg) & \(-\) & \(-\) & 120 \\ Angle of magnetic poles G (deg) & \(-\) & \(-\) & 120 \\ Type of magnet & \(-\) & Y30 & N42 UH \\ Type of iron & & DW310-35 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimized design parameters of the SynRM, ferrite-assisted SynRM and IPM.