## 4 Batch Simulation and Verification
### Effectiveness Analysis and Verification of the Proposed Protection Method
Consider that the rotor speed of a variable-speed pumped storage unit has a certain range of variation, usually \(s\in[-0.1,0.1]\)[32]. Therefore, all possible faults with slip ratios s of \(-0.1\), 0.05, \(-0.05\), 0.01 and \(-0.01\) are simulated. The simulation calculation results are shown in Figures 10-14. The overall distribution trend of calculation results \begin{table}
\begin{tabular}{c c c c c} \hline  & **Faults in the Same Branch** & **Faults between Two** & **Faults between** & **Total** \\  & **with Different Short Turns** & **Branches in the Same Phase** & **Phases** & \\ \hline In-slot faults & 252 & 42 & 0 & 294 \\ End faults & 1584 & 1944 & 8232 & 11,760 \\ Total & 1836 & 1986 & 8232 & 12,054 \\ \hline \end{tabular}
\end{table} 
Table 5: The number of possible internal short-circuit faults in rotor windings. Figure 9: When \(s=0.1\), the simulation results of all possible internal short-circuit faults in rotor windings: (**a**) in-slot faults; (**b**) end faults in the same branch with different short turns; (**c**) end faults between two branches in the same phase; (**d**) end faults between phases. of protection action values is almost the same under different slip ratios. In general, the minimum value of the protection action value in all faults is 0.0368 p.u. in Figure 13d. However, the protection action value of most faults is still greater than 0.1 p.u. ; the number of faults whose action value is greater than 0.1 p.u. is shown in Table 6. It can be found that most faults with different rotor speeds have obvious fault characteristics. Therefore, the protection setting value \(I_{set}\) can be selected flexibly, which verifies the effectiveness of the protection method. The protection action value is positively correlated with the fault degree. Even if the protection action value of a very few faults is less than the setting value and cannot be applied, the fault degree of this kind of rejection fault is extremely weak and will not cause serious harm to the unit in a short time. Therefore, it is acceptable to set the protection value to 0.1 p. u.  
Figure 11: When \(s=0.05\), the simulation results of all possible internal short-circuit faults in rotor windings: (**a**) in-slot faults; (**b**) end faults in the same branch with different short turns; (**c**) end faults between two branches in the same phase; (**d**) end faults between phases. Figure 10: When \(s=-0.1\), the simulation results of all possible internal short-circuit faults in rotor windings: (**a**) in-slot faults; (**b**) end faults in the same branch with different short turns; (**c**) end faults between two branches in the same phase; (**d**) end faults between phases. Figure 12: When \(s=-0.05\), the simulation results of all possible internal short-circuit faults in rotor windings: (**a**) in-slot faults; (**b**) end faults in the same branch with different short turns; (**c**) end faults between two branches in the same phase; (**d**) end faults between phases. Figure 13: When \(s=0.01\), the simulation results of all possible internal short-circuit faults in rotor windings: (**a**) in-slot faults; (**b**) end faults in the same branch with different short turns; (**c**) end faults between two branches in the same phase; (**d**) end faults between phases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Slip Ratio** & **Number** & **Proportion** \\ \hline \(0.1\) & 11,875 & 98.52\% \\ \(-0.1\) & 11,858 & 98.37\% \\ \(0.05\) & 11,767 & 97.62\% \\ \(-0.05\) & 11,780 & 97.73\% \\ \(0.01\) & 11,577 & 96.04\% \\ \(-0.01\) & 11,546 & 95.79\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of faults whose action value is greater than 0.1 p.u. It is worth mentioning that the fault corresponding to the protection action value 0.0368 p.u. in Figure 13d is a short-circuit fault between the 2 nd turn coil of branch A2 and the 1 st turn coil of branch B2, as shown in Figure 15. That is, the short-circuit fault occurs between F1 and F2. F2 is the equipotential with the neutral point \(o\).