## 6 FaSynRM Optimization Parameters and Results
### FaSynRM Optimization Results  
As Figure 12 shows, the FaSynRM optimization process took 180 calls of the objective function, and its value was significantly reduced.  
Table 8 shows the characteristics of the initial and optimized FaSynRM designs. In the open-circuit coasting mode, the voltage at the motor terminals in the initial design and after optimization is 171 V and 207 V, respectively. The magnetic loss density is mainly concentrated in the stator magnetic core and is equal to 840 W and 490 W, respectively. Figure 13 shows the FaSynRM geometry and flux density amplitude at operating points 1-5 listed in Table 1. Figure 14 shows the geometry and flux density amplitude after the FaSynRM optimization. Figure 15 shows the demagnetizing field in the area of permanent magnets on the rotor before and after optimization.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Machine length excluding winding end parts \(L\), mm & 240 \\ \multicolumn{2}{c}{Stator outer radius, mm} & 250 \\ \multicolumn{2}{c}{Stator parameter \(h_{\text{stat1}}/\alpha_{\text{stat2}}\), mm} & 1 \\ \multicolumn{2}{c}{Stator parameter \(h_{\text{stat2}}/\alpha_{\text{m}}\)} & 3 \\ \multicolumn{2}{c}{Outer rotor ribs thickness \(h_{\text{control}}\), mm} & 1 \\ \multicolumn{2}{c}{Inner rotor ribs thickness \(h_{\text{inr},j}\), mm} & 1.5; 2.5; 3.5; 4 \\ \multicolumn{2}{c}{Rotor parameter \(h\), mm} & 3 \\ \multicolumn{2}{c}{Rotor parameter \(\varepsilon\)} & 0.8\(\cdot\alpha_{\text{cp}}\) \\ \multicolumn{2}{c}{Stator slot thickness ratio \(\alpha_{\text{stat1}}/\alpha_{\text{stat2}}\)} & 1.05 \\ \multicolumn{2}{c}{Rotor parameter \(a\)} & 0.4777\(\cdot\alpha_{\text{cp}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: FaSynRM parameters were unchanged during optimization.  
Figure 12: FaSynRM optimization progress.  
Figure 16 shows the calculated waveforms of the FaSynRM: torque ripples at operating points with minimum and maximum torque; cogging torque; back EMF at the operating point where its maximum amplitude is reached, and back EMF at costing.  
Comparing the characteristics of the FaSynRM before and after optimization, we can draw the following conclusions:  
1. Average losses were reduced by 100%(10.46 - 7.4)/10.46 = 29.3%;
2. Maximum armature winding current decreased by 100%(1402 - 839)/1402 = 40%;
3. Maximum torque ripple decreased by (33 - 10) = 23%;
4. The share of magnets \(\delta\)demag exposed to a demagnetizing field of more than 2 kOe decreased from 8.6% to almost zero (0.06%). As can be seen from Figure 15, the \(-\)2 kOe  
Figure 14: FaSynRM cross-section after optimization, with a plot of flux density modulus at saturation limit (>2 T) highlighted in white. (**a**) Operating point 1; (**b**) Operating point 2; (**c**) Operating point 3; (**d**) Operating point 4; (**e**) Operating point.  
Figure 15: The demagnetizing field in the area of permanent magnets of the PMaSynRM rotor. Areas with the strongest demagnetization (<\(-\)2 kOe) are highlighted in white. (**a**) Before optimization; (**b**) After optimization.  
level is reached only in the corners of the magnets, and it can be concluded that the demagnetization of this small share of magnets is not critical. Therefore, we can conclude that with a coercive force of 4 kOe, the optimized design has a large safety margin (\(4-2\)) = 2 kOe. The achievement of a higher resistance to demagnetization of the design after optimization, apparently, was facilitated by an increase in the thickness of the magnets, as well as an increase in the number of turns, and hence a decrease in the turn voltage and magnetic flux in the magnetic circuits.  
Figure 16: FaSynRM calculated waveforms. (**a**) Torque ripple at operating point 1; (**b**) Torque ripple at operating point 4; (**c**) Line-to-line back EMF at operating point 2 (maximum EMF amplitude); (**d**) Line-to-line back EMF at coasting (operating point 0); (**e**) Cogging torque.