## 4 Simulation and Analysis
### Discussion  
The purpose for the development of the wind turbine generator models in this paper was to simulate and analyze the dynamic behaviors of a grid-connected wind farm under steady-state and transient conditions. To verify the accuracy of the proposed models, the simulation results should be validated by real field data. However, real field data is not easy to access. In addition, the implementation of an MMC-controlled PMSG-based wind turbine is a new topology concept for a wind turbine generator that has not yet been realized practically. Therefore, the detailed model is presented in this study because its dynamic behavior is close to real field conditions. To obtain a real system situation, the wind farm model shown in Figure 17 is adopted and simulated as the proposed detailed model. As a consequence, the simulation involved extensive computation time.  
It is very important to understand that the proposed average model is an approach method to approximate the detailed model by reducing the complexity of the MMC circuit, where some parts, such as the switching phenomena and power electronic IGBTs of the submodules, are omitted in the simulation. In the steady-state analysis, both models have almost the same responses. In the case of a transient condition with a short circuit fault, there are slight differences in the simulation results in the DC voltage response and the active and reactive power response overshoot between the detailed model and the average model after the CB is opened.  
As a real wind farm can consist of hundreds of wind turbine generators, the simulation study cannot be performed by the detailed model. To solve this problem, the average model is presented in this paper. The average model can be used as an individual or an aggregated wind turbine generator models in simulation analyses.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Simulation**} & \multicolumn{2}{c}{**Computation Time**} \\ \cline{2-3}  & **Detailed Model** & **Average Model** \\ \hline Time step & 10 μs & 100 μs \\ Duration & 840 h & 11 min \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computation time of each model for 300 sec steady-state analysis.  
Figure 20: Power output and voltage performances of the wind farm under steady-state condition: (**a**) Total active power and reactive power outputs of the wind farm; (**b**) Voltage profile at Bus B33.  
Figure 21: Dynamic performances of WTG1 in the case of 3 LG: (**a**) Rotor speed response; (**b**) Voltage profiles at the terminal of the stator winding; (**c**) Active and reactive powers 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; (**g**) Waveform of current at the grid-side MMC; (**h**) Waveform of voltage at the grid-side MMC.  
Figure 22: Dynamic Performances of WTG1 in the case of 2 LG: (**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; (**g**) Waveform of current at the grid-side MMC; (**h**) Waveform of voltage at the grid-side MMC.