## 5 Conclusions  
In this paper, a conventional PMA-SynRM is used as a reference for study. An asymmetric-rotor PMA-SynRM combined with a Halbach array is proposed using the same amount of permanent magnets. The torque characteristics of both models are theoretically analyzed by establishing a simplified analytical model of the conventional model and the proposed model, neglecting core saturation and cross-coupling. No-load simulation analysis reveals that the permanent magnet flux linkage of the proposed model is shifted, resulting in significantly increased air-gap magnetization compared to the conventional model. Load simulation analysis indicates that the proposed model achieves higher utilization of permanent magnet torque and reluctance torque utilization, leading to a notable improvement in average torque. Furthermore, through optimal design, sensitivity analysis, and multi-objective optimization, the average torque of the optimized model is increased and the torque ripple is reduced compared to the conventional model. Finally, the CPSR performance and anti-demagnetization performance of the three models are analyzed. CPSR comparison results demonstrate that both the proposed and optimized models exhibit superior performance. In the analysis of the anti-demagnetization performance, it is found that at a set temperature of 170 \({}^{\circ}\)C and under nine times the maximum rated current, all three models show minimal demagnetization, indicating robust anti-demagnetization capabilities. However, at 200 \({}^{\circ}\)C and under the same current conditions, the proposed model shows the most severe demagnetization rate of the permanent magnets, while the conventional model shows the lowest demagnetization rate of the permanent magnets. This highlights that the conventional model outperforms the other in terms of anti-demagnetization performance, whereas the proposed model demonstrates poorer anti-demagnetization performance. Compared with the conventional model, the permanent magnet of the proposed model is more prone to demagnetization at high temperatures. Therefore, in the subsequent research, the temperature rise design should be given focus to prevent the demagnetization of the permanent magnet at excessive temperature.  
Conceptualization, F.X.; methodology, F.X.; software, J.Z.; validation, J.Z.; formal analysis, J.Z.; investigation, F.X.; resources, C.Q.; data curation, J.Z. and M.Z; writing--original draft preparation, J.Z.; writing--review and editing, F.X.; visualization, J.Z.; supervision, C.Q.; project administration, F.X.; funding acquisition, M.Z. and C.Q. All authors have read and agreed to the published version of the manuscript.  
This research was in part supported by the Stable Funding Support for Universities in Shenzhen (GXWD20220817140906007) and the Start-up Funding for Newly Introduced Talents in Shenzhen (CA11409031).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Temperature** & **Unit** & **Conv. Model** & **Prop. Model** & **Opti. Model** \\ \hline
170 \({}^{\circ}\)C & \% & 0 & 0.98 & 0.44 \\
200 \({}^{\circ}\)C & \% & 17.21 & 92.66 & 79.84 \\ \hline \end{tabular}
\end{table}
Table 6: Maximum demagnetization rate of three models of permanent magnets under operating conditions at different temperatures and nine times the rated current.