## 5 Conclusions  
This paper describes the design optimization of a high-speed single-phase flux reversal motor with asymmetric rotor. The optimization criterion was selected to maximize the efficiency, to reduce the torque ripple, and to avoid the negative torque in a wide range of powers at the fan load (quadric dependence of torque on speed). Two operating modes are considered. A one-criterion Nelder-Mead method is used to optimize the motor design.  
After two stages of optimization, the peak-to-peak torque ripple in the FRM in the rated loading mode decreased by 1.7 times, and in the mode with reduced load, by 2.7 times. In addition, in the FRM before optimization, the torque has sections with negative values, and in the FRM after optimization, the torque is positive over the entire electric period. Although losses in the rated mode increased by 4%, when underloaded, they decreased by 11%, which creates an additional advantage for applications that work most of the time with underload.  
**Author Contributions:** Conceptual approach, V.P. and V.D.; data curation D.G. and V.K.; software V.D. and V.P.; calculations and modeling, V.P and V.D. and V.K.; writing of original draft, D.G., V.P., V.D. and V.K.; visualization, D.G., V.D. and V.K.; review and editing, D.G., V.P., V.D. and V.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The work was partially supported by the Ministry of Science and Higher Education of the Russian Federation (through the basic part of the government mandate, Project No. FEUZ-2020-0060).  
**Acknowledgments:** The authors thank the editors and reviewers for careful reading, and constructive comments.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**After First Optimization (Figure 3b)**} & \multicolumn{2}{c}{**After Second Optimization (Figure 11)**} \\ \hline Speed, rpm & 14,400 & 18,000 & 14,400 & 18,000 \\ \hline Current, A (RMS) & 6.06 & 8.48 & 4.44 & 6.61 \\ \hline Efficiency, \% & 84.2 & 84.2 & 85.7 & 84.5 \\ \hline Total losses, W & 70.8 & 138.1 & 62.7 & 135 \\ \hline Mechanical power, W & 386 & 754 & 386 & 754 \\ \hline Electrical power, W & 448 & 877 & 440 & 874 \\ \hline Copper losses, W & 48 & 94.2 & 37.6 & 83.3 \\ \hline Stator core losses, W & 9.1 & 21.8 & 11 & 29.1 \\ \hline Rotor core losses, W & 4.1 & 6.5 & 4.5 & 7 \\ \hline Magnet losses, W & 0.4 & 0.8 & 0.4 & 0.8 \\ \hline Duty cycle & 0.205 & 0.425 & 0.297 & 0.672 \\ \hline Minimum torque, N-m & 0.081 & 0.089 & 0.0623 & 0.171 \\ \hline AMinDT, N-m & 0.175 & 0.311 & 0.193 & 0.229 \\ \hline PPTR, N-m & 0.381 & 0.668 & 0.374 & 0.602 \\ \hline PPTR, \% of the average value & 149 & 167 & 146 & 150 \\ \hline Objective function \(F_{2}\) & \multicolumn{2}{c}{0.00801} & \multicolumn{2}{c}{0.00601} \\ \hline \hline \end{tabular}
\end{table}
Table 6: The FRM characteristics before and after the second optimization.