## 6 Conclusions  
In this article, we aim to address the inherent limitations associated with the design of WFSM systems tailored for vehicle traction applications. Specifically, our objective is to enhance key characteristics such as high power density and efficiency, critical for traction motors operating in demanding conditions. To achieve this goal, we propose a novel variant of the WFSM, termed PMA-WFSM, which integrates assisted permanent magnets into its design architecture. The incorporation of these permanent magnets holds the potential to significantly improve performance metrics. To systematically assess the anticipated effects of permanent magnet insertion, we employ mathematical formulations and conduct equivalent circuit analyses. Through these analytical methods, we forecast the potential impact on overall system performance and validate our projections through extensive FEM simulations. The reliability and accuracy of the FEM simulation results are verified through comparison with experimental data obtained from an existing WFSM model, with the observed back EMF data error between measured data and simulation results falling within an acceptable margin of 5.06%. Furthermore, in our efforts to enhance cost-effectiveness and minimize the utilization of rare-earth materials, we undertake comprehensive optimization efforts aimed at reducing magnet usage while maintaining optimal performance levels. To streamline the analysis process, we select OLHD during the design and analysis stages, within the framework of computer experiments on DACE sampling. Additionally, we leverage the MGA as the optimization algorithm, offering computational efficiency and effectiveness. Ultimately, our optimization endeavors yield a notable enhancement in efficiency, with the system's efficiency rating improving from 93.99% to 95.07% compared with that of the existing setup. When classified according to the International Energy Efficiency class (IE), the existing WFSM falls under the IE3 category, whereas the PMA-WFSM proposed in this paper achieves an IE4 rating. This improvement not only contributes to the economic viability of the system by reducing reliance on rare-earth materials, which are commonly utilized in traction systems, but \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **WFSM** & **PMa-WFSM** \\ \hline Stator Copper loss & 163.05 W & 163.05 W \\ Stator Current density & 3.85 A\({}_{\text{rms}}\)/mm\({}^{2}\) & 3.85 A\({}_{\text{rms}}\)/mm\({}^{2}\) \\ Rotor Copper loss & 123.69 W & 60.61 W \\ Rotor Current density & 3.24 A\({}_{\text{rms}}\)/mm\({}^{2}\) & 2.27 A\({}_{\text{rms}}\)/mm\({}^{2}\) \\ Average torque & 32.33 Nm & 31.84 Nm \\ Torque ripple & 11.15\% & 5.72\% \\ Core loss & 37.40 W & 35.97 W \\ Efficiency & 93.99\% & 95.07\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparing the characteristics of WFSM and PMa-WFSM. Figure 12: Comparing the output performance between WFSM and PMa-WFSM: **(a)** torque, and **(b)** load back EMF. also harnesses the inherent advantages of WFSM technology, particularly its capability for precise field current control. Considering these advancements, we assert that the proposed PMa-WFSM emerges as a compelling alternative to normal PMSM and WFSM systems. It embodies a potent blend of heightened performance, economic viability, and operational flexibility. Conceptualization, C.-B.P. and H.-W.L. ; methodology, H.-S.S. and S.-H.K. ; software, H.-S.S. and S.-H.K. ; validation, G.L. and Y.G. ; formal analysis, H.-S.S.; investigation, H.-S.S. and S.-H.K. ; writing--original draft preparation, H.-S.S.; writing--review and editing, G.L. and Y.G. ; visualization, H.-W.L. and C.-B.P. ; supervision, H.-W.L. and Y.G. ; project administration, C.-B.P. and G.L. ; funding acquisition, C.-B.P. and H.-W.L. All authors have read and agreed to the published version of the manuscript.