## 4 Simulation and Analysis
### Single Phase-to-Ground Fault  
In the power system, single phase-to-ground faults are the most commonly occurring. Therefore, this section verifies the performance of the adopted method in the case of single phase-to-ground faults. As shown in Figure 12a, the single phase-to-ground fault occurred in the 220 kV line near the DFIG at t = 0.075 s and was cleared at \(t\) = 0.275 s. Additionally, the depth of the single-phase voltage dip was 20% in the 220 kV line. The voltage of the 35 kV line is shown in Figure 12b. Due to the wiring method of the transformer, the two-phase voltage of the 35 kV line exhibited voltage dips. The voltage provided by the DVR of the 35 kV line during the fault period is shown in Figure 12c. Figure 12d shows the voltage of the 35 kV line after the DVR compensated. It can be seen in Figure 12d that the fault voltage of the 35 kV line can return to the voltage state before the single phase-to-ground fault. Figure 12e shows the stator voltage of the DFIG after the DVR compensated. It can be observed that  
Figure 11: Comparison of the DFIG output power when using an adopted DVR-based SMES at a voltage dip depth of 80%; an adopted DVR-based SMES at a voltage dip depth of 25%; crowbar circuit protection at a voltage dip depth of 80%; and crowbar circuit protection at a voltage dip depth of 25% when the three-phase-to-ground fault occurs. Figure 10: Comparison of the frequency of the fault current when using an adopted DVR-based SMES at a voltage dip depth of 80%; an adopted DVR-based SMES at a voltage dip depth of 25%; crowbar circuit protection at voltage dip depths of 80%; and crowbar circuit protection at voltage dip depths of 25% when the three-phase-to-ground fault occurs. during the fault period, the stator voltage of the DFIG exhibited no severe fluctuations after the DVR compensated. Figure 12f shows the stator current of the DFIG. Figure 13 shows the system's responses with a DVR-based SMES during the single phase-to-ground fault (depth of 70%). Additionally, the single phase-to-ground fault occurred in the 220 kV line, away from the DFIG, at \(t\) = 0.075 s and was cleared at \(t\) = 0.275 s. Additionally, the depth of the single-phase voltage dip was 70% in the 220 kV line, as shown in Figure 13a. Figure 13b-d shows the fault voltages on the 35 kV side, the compensating voltage of the DVR-based SMES, and the compensated fault voltages of the 35 kV side. It can be seen that the fault voltage of the 35 kV line can be compensated to return to the normal voltage value of 35 kV. Figure 12e shows the stator voltage of the DFIG after the DVR compensates. It can be observed that during the single-phase fault periods, the stator voltage of the DFIG exhibited no severe fluctuations. Figure 12f shows the stator current of the DFIG during the fault. Figure 14 shows a comparison of the frequency of the fault current with a DVR-based SMES and with conventional crowbar circuit protection when the two different single phase-to-ground faults occur. The two single phase-to-ground faults occurred at 0.22 s, and the fault duration was 0.2 s. It can be seen from Figure 14 that the DVR-based SMES compensated for the fault voltage, and the fluctuations in the current frequency were less than the current frequency with conventional crowbar circuit protection. Therefore, during the single phase-to-ground faults, the DVR-based SMES can also assist the DFIG in achieving the fault ride through and improving the frequency offset of fault currents. Figure 12: The system’s responses with DVR-based SMES during the single phase-to-ground fault (depth of 20%). (**a**) Fault voltages on the 220 kV side; (**b**) fault voltages on the 35 kV side; (**c**) compensating voltage of the DVR-based SMES; (**d**) compensated fault voltages on the 35 kV side; (**e**) stator voltage of the DFIG; (**f**) stator current of the DFIG.