# Dynamic Frequency Support from a DFIG-Based Wind Turbine Generator via Virtual Inertia Control
## 6 Dynamic Simulation Results
### Case 2: Wind Speed = 8.0 m/s  
Figure 9 displays the simulation results, where the wind speed condition of the DFIG-based WTG is 8.0 m/s (partial load case). Thus, the kinetic energy available from the DFIG-based WTG is 1.66 s, which is 30% that of the total releasable kinetic energy and is 42% of the available kinetic energy in Case 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Strategies** & **Case 1** & **Case 2** & **Case 3** \\ \hline \multirow{3}{*}{Maximum rate of change of system frequency (Hz/s)} & MPPT operation & \(-\)0.503 & \(-\)0.505 & \(-\)0.502 \\  & Conventional strategy & \(-\)0.475 & \(-\)0.476 & \(-\)0.474 \\  & Proposed strategy & \(-\)0.390 & \(-\)0.421 & \(-\)0.388 \\ \hline \multirow{3}{*}{Frequency nadir (Hz)} & MPPT operation & 59.174 & 59.175 & 59.177 \\  & Conventional strategy & 59.194 & 59.196 & 59.202 \\  & Proposed strategy & 59.265 & 59.232 & 59.267 \\ \hline \multirow{3}{*}{Nadir-based frequency response (MW/Hz)} & MPPT operation & 108.96 & 109.09 & 109.36 \\  & Conventional strategy & 111.63 & 111.94 & 113.07 \\  & Proposed strategy & 122.45 & 117.19 & 122.78 \\ \hline \multirow{3}{*}{Released kinetic energy from the DFIG (s)} & Conventional strategy & 0.108 & 0.108 & 0.010 \\  & Proposed strategy & 0.563 & 0.329 & 0.017 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of numerical results for three cases.  
Figure 8: Results for Case 1: (**a**) system frequencies; (**b**) active powers; (**c**) rotor speeds; (**d**) control gains. MPPT: maximum power point tracking.  
Figure 9: Results for Case 2: (**a**) system frequencies; (**b**) active powers; (**c**) rotor speeds; (**d**) control gains.  
The maximum _df/dt_ for the proposed strategy is -0.421 Hz/s, which is smaller than those of the conventional strategy and the MPPT operation by 0.055 Hz/s and 0.084 Hz/s, respectively. The frequency nadir for the proposed strategy is 59.232 Hz, which is more than those of the conventional strategy and the MPPT operation by 0.036 Hz and 0.057 Hz, respectively (see Figure 9a). Comparing the results to Case 1, the performances of frequency nadir and the maximum _df/dt_ in the MPPT operation are almost the same as in Case 1, because the power injection is from synchronous generators. The performances of frequency nadir and the maximum _df/dt_ in the conventional strategy are the same as in Case 1 due to the same control gain of virtual inertia control. The performances of the frequency nadir and the maximum _df/dt_ for the proposed strategy are less than that of Case 1 because of the smaller control gain, as displayed in Figures 8 and 9.  
Further, as in Case 1, the proposed method ensures better nadir-based frequency response, which is more than those of the conventional method and the MPPT operation by 5.25 MW/Hz and 8.1 MW/Hz, respectively. The kinetic energy released for the proposed virtual inertia control strategy is more than that of the conventional strategy by 0.221 s. In addition, the kinetic energy released for the conventional method in Case 2 is the same as in Case 1 due to the same control gain.