## 4 Simulation and Analysis
### Transient Performance Analysis  
For the transient performance study, a short circuit of three lines to ground fault (3 LG) and two lines to ground fault (2 LG) on one of the circuits of the 66-kV transmission line is considered as disturbance. The location of the faults is shown in Figure 17. The faults occur at 0.1 s, and then the circuit breakers (CBs) on the faulted line are opened at 0.2 s to isolate the fault from the system. The CBs are recclosed at 1.0 s on the assumption that the fault has been cleared. During the simulation time of 5 s, the wind velocities of the WTGs are assumed to be constant at a rated velocity of 12 m/s.  
As the wind speed applied to each wind turbine generator is the same, the dynamic performances of each individual WTG in the transient conditions for 3 LG and 2 LG are represented by the dynamic performances of only WTG1, as presented in Figures 21 and 22, respectively. As the wind turbine generator is totally decoupled from the grid network by the back-to-back MMC, the short circuit on the grid network does not affect dynamic performances on the generator side in cases of 3 LG and 2 LG. The transient disturbances have almost no influence on the dynamic performances of the generator, such as rotor speed response, power outputs, and voltage profile. However, the transient disturbances affect the performances of the DC link circuit voltage, the power output of the grid-side  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Rated MVA & 10 MVA & Stator Winding Resistance & 0.017 pu \\ Rated Voltage (L-L) & 10 kV & Stator Leakage Reactance & 0.0364 \\ Rated Frequency & 50 Hz & _d-axis_ Unsaturated Reactance [\(X_{d}\)] & 0.55 pu \\ Magnetic Strength & 1.1 pu & _q-axis_ Unsaturated Reactance [\(X_{d}\)] & 1.11 pu \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of PMSG.  
Figure 18: Wind velocity data.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Rated Power & 10 MVA & SM Capacitor & 9.2 mF \\ Rated AC Voltage & 10 kV & Arm Inductance & 3.8 mH \\ Rated DC Voltage & 18 kV & Arm Resistance & 0.097 \(\Omega\) \\ Number of SMs per arm & 6 & Reactor Inductance & 0.773 mH \\ Carrier Frequency & 1000 Hz & Reactor Resistance & 0.019 \(\Omega\) \\ DC link Capacitor & 7.4 mF & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of MMC.  
MMC, and the current and voltage profiles at Bus BG1. In the DC link circuit, a transient DC voltage appears due to the 3 LG and 2 LG faults, but it can be controlled by the overvoltage protection system, and hence the DC voltage can be returned to the initial condition after the fault is cleared. It is also confirmed that the power output of the grid-side MMC and the voltage profile at Bus BG1 can be returned to the initial conditions after the fault. The performances of the total power output of the wind farm and the voltage profile at Bus 33 for the 3 LG and 2 LG cases are shown in Figures 23 and 24, respectively.  
From the simulation results, it can be confirmed that the dynamic performances of the detailed model and the average model have almost the same responses under the transient conditions. The different responses between the detailed and the average models appear in the DC link circuit voltage profile and the power output of the grid-side MMC. However, they are slight and disappear after returning to the steady-state condition after fault clearance.  
Figure 19: Dynamic Performances of WTG1 under steady-state condition: (**a**) Rotor speed response; (**b**) Voltage profiles at the terminal of the stator winding; (**c**) Active and reactive power output of the PMSG; (**d**) DC link circuit voltage profile; (**e**) Active and reactive power output of grid-side MMC; (**f**) Voltage profile at Bus BG1.