## 5 Results: Impact of Faults in LSHT Machines
### Evaluation of Faults Specific to PMSMs: Partial Demagnetization  
Table 8 shows the variation in the performance metrics of the 10-pole LSHT machines after applying the different levels of demagnetization, as outlined of Section 3.2.3. The results for the 10-pole machine indicate that demagnetization levels 1 and 2 have a low impact on the performance of the PMSM, with torque reductions below 5%. Specifically for level 2, where \(\Delta B_{\rm r,total}=5\%\), the torque reduction is directly associated with this change in remanence. At level 3, with \(\Delta B_{\rm r,total}=10\%\), the mean torque is reduced by 8.6% and losses decrease by 3.2%. This reduction in losses can be attribu \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **Symbol** & **Healthy** & **Level 1** & **Level 2** & **Level 3** \\ \hline Mean Torque & \(\rm T_{mean}\;[\rm Nm]\) & 700.1 & 700.5 & 700.0 & 684 \\ Torque Ripple & \(\rm T_{rp}\;[\%]\) & 3.9 & 6.4 & 10.5 & 20.5 \\ Efficiency & \(\rm\eta\;[\%]\) & 94.2 & 94.1 & 94.1 & 94.0 \\ Active Losses & \(\rm L_{cp+fe+edd}\;[W]\) & 2699 & 2703 & 2708 & 2719 \\ Power Factor & pf \([-]\) & 0.78 & 0.78 & 0.77 & 0.73 \\ \hline \end{tabular}
\end{table} 
Table 6: Main performance data comparison of optimized 10-pole SCIM LSHT machines including broken bars. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **Symbol** & **Healthy** & **Level 1** & **Level 2** & **Level 3** \\ \hline Mean Torque & \(\rm T_{mean}\;[\rm Nm]\) & 640.1 & 639.5 & 636.0 & 629.6 \\ Torque Ripple & \(\rm T_{rp}\;[\%]\) & 10.8 & 12.5 & 15.4 & 24.2 \\ Efficiency & \(\rm\eta\;[\%]\) & 90.7 & 90.7 & 90.6 & 90.5 \\ Active Losses & \(\rm L_{cp+fe+edd}\;[W]\) & 2543 & 2545 & 2550 & 2558 \\ Power Factor & pf \([-]\) & 0.63 & 0.63 & 0.62 & 0.60 \\ \hline \end{tabular}
\end{table} 
Table 7: Main performance data comparison of optimized 16-pole SCIM LSHT machines including broken bars. remanence, which leads to a decrease in magnet losses and a reduction in iron losses. Iron losses are influenced by both frequency and flux density as established by [67]:  
\[dP_{\rm iron}=k_{\rm h}fB_{\rm m}^{2}+\frac{\sigma d_{\rm I}^{2}}{12}\left(\frac{ dB(t)}{dt}\right)^{2}+k_{\rm e}\left(\frac{dB(t)}{dt}\right)^{1.5} \tag{7}\]  
where \(B(t)\) is the flux density in the iron core, \(B_{\rm m}\) is the amplitude of \(B(t)\), \(f\) is the electrical frequency, \(\sigma\) is the iron conductivity, \(d_{\rm I}\) is the lamination thickness, and \(k_{\rm h}\) and \(k_{\rm e}\) correspond to coefficients of hysteresis loss and excess loss, respectively. When a group of magnets has a reduced remanence, then there are regions of the stator core that will have a lower flux density magnitude, hence reducing \(B_{\rm m}\) and \(dB/dt\), which translates into lower losses as per (7). Frequency is not altered by partial demagnetization. As a result, although torque can be significantly reduced, efficiency remains largely unaffected. If the torque needs to be restored to its original rated value, a logical operating point at a rated load, the increased losses will exceed the rated levels, intensifying the thermal stress on the motor and amplifying the demagnetization effect. The same trend observed for level 3 is obtained for level 4, where a 20% total demagnetization leads to a 16.7% reduction in torque capacity and a 6.3% decrease in losses. Furthermore, a relatively linear relationship is observed between the total demagnetization \(\Delta B_{\rm r,total}\) and the reduction in torque capacity. Another trend observed is the variation in torque ripple across different demagnetization levels. Significant changes are noted, with level 3 showing the most pronounced effect. This is due to the high symmetry and periodicity of the faulty machine associated with this level, which significantly influences cogging torque.