## 4 Topology of the Permanent Magnet Synchronous Motor
Figure 10 shows 1/12 of the overall form of the specific topology. Its final optimized geometric characteristics are given in detail in Table 5.  
Figure 8: Magnets Mass vs. changing D/L ratio. Figure 9: PMSM Efficiency vs. Changing D/L Ratio. The axial length of the motor L was equal to 1.5 m, with the internal D and the external diameter Do of the stator taking values being equal to 1.36 m and 1.75 m, respectively. Therefore, the D/L and Do/L ratios were equal to 0.91 and 1.173, respectively. The gap length was set to 6 mm. The height of the magnets was chosen to be within acceptable limits in an effort to keep the manufacturing complexity low. The ratio of magnet arc length to pole pitch \(\alpha_{p}\) was given by Equation (68), where \(LCM(Qs,2p)\) is the least common multiple of the number of poles \(2p\) and the number of stator slots \(Q_{s}\), and \(k\) is an integer coefficient that takes values ranging from 1 to \(LCM(Qs,2p)/2p-1\). The value of \(\alpha_{p}\) was  
Figure 10: Final Topology of the PMSM, (1/12 part) of the overall form. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantity** & **Symbol** & **Value** \\ \hline Outer diameter stator & D\({}_{\text{o}}\) & 1795.5 mm \\ Inner diameter stator & D & 1361.9 mm \\ Outer diameter rotor & D\({}_{\text{r}}\) & 1361.8 mm \\ Shaft diameter & D\({}_{\text{shaft}}\) & 1140.2 mm \\ Motor axial length & L & 1500 mm \\ Stator slots & Q\({}_{\text{s}}\) & 72 \\ Poles (Pair of Poles) & \(2p\) (\(p\)) & 60 (30) \\ Airgap length & L\({}_{\text{g}}\) & 6 mm \\ Stator opening width & H\({}_{\text{s}0}\) & 8 mm \\ Stator base width & H\({}_{\text{s}1}\) & 8 mm \\ Stator top width & H\({}_{\text{s}2}\) & 116.54 mm \\ Stator slot opening height & B\({}_{\text{s}0}\) & 20 mm \\ Stator tip height & B\({}_{\text{s}1}\) & 33.33 mm \\ Stator body height & B\({}_{\text{s}2}\) & 43.50 mm \\ Tooth width & w\({}_{\text{st}}\) & 27.51 mm \\ Stator yoke length & T\({}_{\text{bi}}\) & 66.26 mm \\ Ratio of magnet arc length & \(\alpha_{p}\) & 0.8533 \\ to pole pitch & \(w_{m}\) & 59.32 \\ Maximum magnet width & \(h_{m}\) & 22.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimized Design Variables for PMSM. set at 0.8533 in order to minimize the cogging torque, following the directions provided in [45]. This torque was a result of the interaction of the stator teeth with the permanent magnets. It was affected by the dimensions of the stator teeth and the \(\alpha_{p}\) size. It was one of the reasons why the motor showed ripple in the output torque. \[\alpha_{p}=\frac{(LCM(Q_{s},2p)\ /\ 2p)-k}{LCM(Q_{s},2p)\ /\ 2p} \tag{70}\]  
The operating characteristics of the motor at its rated load are summarized in Table 6. The motor output torque \(\mathrm{T_{avg}}\) was equal to 198.4124 kNm, absorbing a current equal to 1101.94 A. The stator winding density \(J_{s}\) was 2.75 A/mm\({}^{2}\). This value also guaranteed the satisfactory thermal behavior of the motor, ensuring that during its operation, a particularly high temperature would not develop near the gap, which would have negatively affected the permanent magnets. The output torque signal is given in Figure 11. Minimum \(\mathrm{T_{min}}\) and maximum \(\mathrm{T_{max}}\) of the torque were equal to 196.9841 and 199.7715 kNm, respectively. This implies that the torque ripple calculated from Equation (71) was equal to 1.40% of the output torque. This value was highly satisfactory and confirmed the effectiveness of the method followed in determining the \(\alpha_{p}\) value with the aim of minimizing the alignment moment. Also, the small value for the torque ripple could also be explained by the use of a concentrated double-layer winding, which resulted in the appearance of a smaller harmonic content for the magnetomotive force compared to the single-layer winding counterpart. Regarding the various forms of losses, the motor showed low copper losses considering its rated output power. This feature was due to the small resistance of the stator winding due to the large diameter of the conductors.