## 4 Simulation and Analysis
### Three-Phase-to-Ground Fault  
The performance of the DVR-based SMES in achieving the fault ride through of DFIG and improving the frequency offset of the fault current was first analyzed during a three-phase-to-ground symmetrical fault. As shown in Figure 8a, the three-phase-to-ground fault occurred in the 220 kV line near the DFIG at \(t=0.08\) s and was cleared at \(t=0.28\) s. The dip depth of three-phase fault voltage in the 220 kV line was 25%, the wind speed was set to 10 m/s, and the rotor speed of the DFIG is 1.12 pu. The voltage of the 35 kV line was affected by the voltage dips of the 220 kV line; thus, the phenomenon of voltage dips also occurred in the 35 kV line, as shown in Figure 8b. At this time, the voltage dips in the 35 kV line could be detected by the DVR, and the voltage dips could be compensated by controlling the VSC converter of the DVR, so that the fault voltage in the 35 kV line could resume at the normal value 35 kV. During the fault period, the voltage provided by the DVR of the 35 kV line is shown in Figure 8c. Figure 8d shows the voltage of the 35 kV line after the DVR compensates. It can be seen in Figure 8d that the fault voltage of the 35 kV line can return to the voltage state before the fault. Figure 8e shows the stator voltage of the DFIG after the DVR compensates. It can be observed that during the fault period, the stator voltage of the DFIG experienced no severe fluctuations after the DVR compensated. During the fault period, the DVR system ensures that the stator voltage of the DFIG is no longer affected by the fault, which can improve the stability of the DFIG during the fault period. Figure 8f shows the stator current of the DFIG, and it can be observed that the stator current value of the DFIG could not reach the \begin{table}
\begin{tabular}{c c} \hline \hline
**The 0.69/35 kV Transformer** & **Value** \\ \hline Rated power & 2.5 MW \\ Winding resistance & 0.001 pu \\ Winding reactance & 0.1 pu \\ Transformer base frequency & 50 Hz \\ Magnetizing losses & 0.00001 pu \\ Transformer rating & 0.69/35 \\ \hline
**The 35/6 kV Transformer** & **Value** \\ \hline Rated power & 2.5 MW \\ Leakage resistance & 0.001 pu \\ Leakage resistance & 0.05 pu \\ Transformer base frequency & 50 Hz \\ Transformer rating & 35/6 \\ \hline
**The 35/220 kV Transformer** & **Value** \\ \hline Rated power & 2.5 MW \\ Leakage resistance & 0.001 pu \\ Leakage resistance & 0.1 pu \\ Transformer base frequency & 50 Hz \\ Transformer rating & 35/220 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specific parameters of the used transformers. \begin{table}
\begin{tabular}{c c} \hline \hline
**DFIG Parameter** & **Value** \\ \hline Proportional factor Kp1 of PI1 & 20 \\ Integral factor Ti1 of PI1 & 0.01 \\ Proportional factor Kp2 of PI2 & 1 \\ Integral factor Ti2 of PI2 & 0.01 \\ Proportional factor Kp3 of PI3 & 5 \\ Integral factor Ti3 of PI3 & 0.02 \\ Proportional factor Kp4 of PI4 & 20 \\ Integral factor Ti4 of PI4 & 0.02 \\ Proportional factor Kp5 of PI5 & 2 \\ Integral factor Ti5 of PI5 & 0.01 \\ Proportional factor Kp6 of PI6 & 5 \\ Integral factor Ti6 of PI6 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: PI parameter of the VSC converter in the DVR. overcurrent value of 2 pu that would have triggered the crowbar circuit, which can enhance the stability of system. Figure 9 shows the system's responses with an adopted DVR-based SMES during a three-phase-to-ground fault (depth of 80%). Figure 9a shows the voltage condition in the 220 kV line when a three-phase-to-ground fault occurred in 220 kV line side, away from the DFIG, at \(t\) = 0.08 s, and the fault was cleared at \(t\) = 0.28 s. The dip depth of three-phase fault voltage in the 220 kV line was 80%. It can be seen in Figure 9b-d that the fault voltage in the 35 kV line can be compensated to a normal voltage value by the DVR-based SMES. Figure 9e shows that the stator voltage of the DFIG can be affected by the fault in the 220 kV line.