## 4 Batch Simulation and Verification  
### Effectiveness Analysis and Verification of the Proposed Protection Method  
An internal short-circuit fault in rotor windings is mainly caused by insulation damage. It can be divided into in-slot and end faults according to the fault position. For the in-slot fault, as the name implies, the short-circuit fault occurs on two bar conductors in the same slot. The number of possible short-circuit faults is equal to the total number of slots in the rotor, denoted as \(Z\). For the end faults, a specific connection form of the rotor double-layer wave windings needs to be considered, as shown in Figure 8. A single-turn coil is composed of the upper bar conductor in slot \(n\) and the lower bar conductor in slot \(n+y_{1}\). The upper connecting line of the upper bar conductor in slot \(n\) is overlapped with the upper connecting line of the lower bar conductor in slot \((n+1)-(n+y_{1}-1)\), which may lead to a total of \((y_{1}-1)\) short-circuit faults. The lower connecting line of the upper bar conductor in slot \(n\) is overlapped with the lower connecting line of the lower bar conductor in the slot \((n-1)-(n-y_{2}+1)\), which may lead to a total of \((y_{2}-1)\) short-circuit faults. There are \((y_{1}+y_{2}-2)\) faults in total. Therefore, the number of possible short-circuit faults at the end of the whole rotor winding is \((y_{1}+y_{2}-2)\)\(Z\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fault Condition** & \
\begin{tabular}{c} **Protection Action Values Obtained by** \\ **Multi-Loop Method (p.u)** \\ \end{tabular} &
\begin{tabular}{c} **Protection Action Values Obtained by** \\ **Finite Element Method (p.u)** \\ \end{tabular} & **Relative Error (\%)** \\ \hline A1\_13 and A1\_30 & 0.355 & 0.368 & \(-\)3.46\% \\ A1\_15 and A2\_4 & 0.258 & 0.266 & \(-\)2.93\% \\ A1\_6 and B1\_21 & 0.751 & 0.779 & \(-\)3.71\% \\ B2\_11 and C2\_17 & 0.824 & 0.859 & \(-\)4.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Protection action values obtained by the multi-loop method and finite element method under various faults. Figure 8: Position of the possible end short-circuit faults. For the actual variable speed unit in Table 1, the number of possible internal short-circuit faults in rotor windings is shown in Table 5. Various faults can be simulated by using the modeling method described in Section 3. When the slip ratio is 0.1, the simulation results of all possible faults in Table 5 are as shown in Figure 9, which are divided into four parts: in-slot faults, end faults in the same branch with different short turns, end faults between two branches in the same phase, and end faults between phases. In the figure, each scattered point represents a fault situation, the abscissa is the turn difference of the short-circuit fault, and the ordinate is the simulation calculation result of the protection action value \(I_{op}\) obtained by Equation (8). The number of end faults is huge and the overlap of scattered points is serious. Therefore, a scatter density diagram is used in the display, and the scatter color changes are proportional to the scatter density. Figure 9a corresponds to the calculation results of in-slot faults, and the minimum protection action value is 0.1678 p.u. Figure 9b corresponds to the calculation results of end faults in the same branch with different short turns, and the minimum protection action value is 0.1281 p.u. Figure 9c corresponds to the calculation results of end faults between two branches in the same phase, and the minimum protection action value is 0.0535 p.u. Figure 9d corresponds to the calculation results of end faults between phases, and the minimum protection action value is 0.0473 p.u. Among them, 0.0473 p.u is the minimum value of the above protection action value. Therefore, the minimum protection action value can be determined to be 0.0473 p.u. In addition, the protection action value of most faults is greater than 0.1 p.u., indicating obvious fault characteristics.