# On the Contribution of Wind Farms in Automatic Generation Control: Review and New Control Approach
## 5 Simulation Results
### Fourth Scenario: Sensitivity Analysis  
In the Fourth scenario, a sensitivity analysis is done to examine the robustness of the proposed controller under a wide variation in governor time constant of steam turbine (\(T_{sg}\)) and the synchronizing coefficient (\(T_{12}\)) separately. To do so, the \(T_{12}\) (as an indicator of active tie-line power between the areas) and \(T_{sg}\) are changed by \(\pm 25\%\) of nominal value regarding the first scenario condition. The dynamic responses for the case of DFIGs equipped with the SCA optimized FOPID controllers after applying uncertainties in \(T_{12}\) and \(T_{sg}\) are depicted in Figures 8 and 9, respectively. Furthermore, the system damping characteristics for both changes are listed in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Controller Type** & **Signal** & **MDR** & **PO** & **PT** & **ST** & **ITSE** \\ \hline \multirow{3}{*}{FOPID-based DFIG \& AGC} & \(\Delta f_{1}\) & & 0.0208 & 0.6997 & 14.1210 & \\  & \(\Delta f_{2}\) & 0.1910 & 0.0131 & 1.5054 & 14.8400 & 0.0026 \\  & \(\Delta P_{12}\) & & 0.0036 & 1.1957 & 21.0161 & \\ \hline \multirow{3}{*}{PID-based DFIG \& AGC} & \(\Delta f_{1}\) & & 0.0301 & 0.7311 & 17.0812 & \\  & \(\Delta f_{2}\) & 0.0658 & 0.0194 & 1.5536 & 18.3103 & 0.0041 \\  & \(\Delta P_{12}\) & & 0.0053 & 1.2089 & 23.4412 & \\ \hline \multirow{3}{*}{Without DFIG (Just AGC)} & \(\Delta f_{1}\) & & 0.0389 & 0.9309 & 28.1927 & \\  & \(\Delta f_{2}\) & 0.0498 & 0.0449 & 2.0776 & 27.1289 & 0.0333 \\ \cline{1-1}  & \(\Delta P_{12}\) & & 0.0073 & 1.3934 & 32.5925 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Frequency deviation and tie-line power characteristics of FOPID, PID and just AGC.  
Figure 6: Frequency deviation and tie-line active power change in second scenario, (**a**) frequency deviation in area 1; (**b**) frequency deviation in area 2; and (**c**) tie-line power deviation.  
Figure 7: Frequency deviation and tie-line active power change in second scenario, (**a**) frequency deviation in area 1; (**b**) frequency deviation in area 2; and (**c**) tie-line power deviation.  
Figure 8: Simulation results for \(\pm 25\%\) of synchronizing coefficient, (**a**) frequency deviation in area 1; (**b**) frequency deviation in area 2; and (**c**) tie-line power deviation.  
It can be seen from the Figures 8 and 9, and in Table 4 that in comparison with the nominal responses demonstrated in Table 2 and Figure 5, the considered severe variations have negligible  
Figure 9: Simulation results for \(\pm\)25% of time constant of steam turbine, (**a**) frequency deviation in area 1; (**b**) frequency deviation in area 2; and (**c**) tie-line power deviation.  
impacts on the system dynamic performance, since the damping ratios, performance indices and damping control measures deviate slightly from the nominal values so that the power system is still stable as before. Therefore, the adjustable parameters of the controllers are tuned for the nominal condition and it is not necessary to tune the parameters for the \(\pm 25\%\) change in the \(T_{12}\) and \(T_{gg}\) again.