## 4 Simulation Analysis
### Performance Analysis under Different Fault Types  
To verify the applicability of this method to different types of faults, it is first necessary to determine what rotor winding short-circuit faults may occur in the generator-motor. Rotor winding short-circuit faults are mainly caused by insulation damage. They can be divided into in-slot faults and end faults according to the fault position. For in-slot faults, 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 9. 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 \((n+1)\sim(n+y_{1}-1)\), 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 \((n-1)\sim(n-y_{2}+1)\), 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 short-circuit faults at the end of the whole rotor winding is \((y_{1}+y_{2}-2)\)\(Z\). Figure 8: The action of the protection when the slip ratio \(s\) is \(0.01\). Figure 7: The action of the protection when the slip ratio \(s\) is \(0.05\). The above VSPSGM is still taken as an example. Through the statistical analysis, the number of rotor winding short-circuit faults that may occur in the unit is as shown in Table 2, and the total number of faults is 12,054. At present, the instantaneous over-current protection of the AC excitation system is used in engineering, as well as the rotor winding short-circuit-fault protection. The protection setting value is usually set to three times the peak value of the rated phase current of the rotor winding. When the slip ratio is 0.1, the actionable number of instantaneous over-current protections is shown in Table 3. The actionable protection number is 10,420, and the action rate is 86.44%. Among them, the action rate of interturn short-circuit faults (the faults in the same branch with different short turns + the faults between two branches in the same phase) is 63.99%, and the action rate of interphase short-circuit faults (the faults between phases) is 96.87%. The main reason for the large difference in the action rates of the two types of faults is that the fault characteristics of the interphase short circuit faults are generally more obvious and easier to protect. The number of actionable protections of the proposed method is 11,209, shown in Table 4, which is 789 more than that of the existing method. The sensitivity is higher, and the overall action rate is 92.98%. Among them, the action rate of interturn short-circuit fault is 85.46%, and the action rate of interphase short-circuit faults is 99.54%. Compared with the existing method, the proposed method can significantly improve the protection range of interturn short-circuit faults, and the protection action rate is increased by 21.47%. \begin{table}
\begin{tabular}{c c c c c} \hline
**Faults in the Same Branch** & **Faults between Two** & & \\
**with Different** & **Branches in the** & & & \\
**Short Turns** & **Same Phase** & & & \\ \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 2: The number of possible internal short-circuit faults in rotor windings.