# On the Contribution of Wind Farms in Automatic Generation Control: Review and New Control Approach
## 4 Proposed Wind Farm Control Technique in AGC  
### Wind Turbine Modeling in AGC  
DFIG is the most commercially used variable speed wind turbine and therefore it is used in this research to demonstrate the effect of wind turbine in AGC. The DFIG wind turbine participates in frequency control through releasing the stored kinetic energy in the turbine blades under sudden load changes. Extracting the stored kinetic energy and converting it into electric energy depends on the turbine inertia, and its control system. Figure 2 shows the block diagram of DFIG-based wind turbine used in this paper for the AGC issue. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & \multicolumn{3}{c}{**Generation Unit**} & \multirow{2}{*}{**System Configuration**} & \multirow{2}{*}{**Control Approach (AGC)**} & \multirow{2}{*}{**Optimization Techniques**} \\  & **Wind** & **Thermal** & **Gas** & **Hydro** & & & \\ \hline
[58] & \(\surd\) & \(\surd\) & & Single area power system & MPC & – \\ \hline
[59] & \(\surd\) & \(\surd\) & & Two area power system & MPC & – \\ \hline
[60] & \(\surd\) & \(\surd\) & & Three area power system & DMPC & – \\ \hline
[61] & \(\surd\) & \(\surd\) & & Four area power system & DMPC & – \\ \hline
[62] & \(\surd\) & \(\surd\) & & Two area power system with flywheel & PID controller & – \\ \hline
[63] & \(\surd\) & \(\surd\) & \(\surd\) & Dereguilated two area power system with SMES & Integral controller & CRPSO \\ \hline
[64] & \(\surd\) & \(\surd\) & \(\surd\) & Two area power system with RFB & PID controller &
\begin{tabular}{c} Grey Wolf Optimizer \\ Optimizer (GWO) \\ \end{tabular} \\ \hline
[65] & \(\surd\) & \(\surd\) & \(\surd\) & Dereguilated two area power system with SMES and TCPS & Integral controller & CRPSO \\ \hline
[66] & \(\surd\) & \(\surd\) & \(\surd\) & Two area power system with SMES and TCPS & Fuzzy logic-PID with derivative &
\begin{tabular}{c} Multi-Vers \\ Optimizer (MVO) \\ \end{tabular} \\ \hline
[67] & \(\surd\) & \(\surd\) & \(\surd\) & Dereguilated two area power system with CES and TCPS & Integral controller & – \\ \hline
[68] & \(\surd\) & \(\surd\) & \(\surd\) & Two area power system with RFB and 58 SC & Integral controller & GA \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 2: Block diagram of doubly-fed induction generator (DFIG) based wind turbine model. In this model, the extra signal \(\Delta P_{f}^{*}\) tries to adapt the set point power as a function of frequency deviation rate \(\Delta f\). Another signal, \(\Delta P_{\omega}^{*}\), attempts to maintain the speed of wind turbine at a desired value for producing the maximum output. In the considered model, \(e\) is error signal in speed of the wind turbine, \(\Delta\omega^{*}\) and \(\Delta\omega\) are the reference and actual deviations of wind turbine speed, respectively. In order to obtain \(\Delta\omega\), a mechanical equation can be stated as follows [37]:  
\[\frac{d\Delta\omega}{dt}=\
icefrac{{1}}{{2H}}(T_{m}-T_{e}), \tag{1}\]  
where \(T_{m}\) is the mechanical torque and \(T_{e}\) is the electrical torque. Equation (1) represents the swing equation, which shows that the change in generator speed result from a difference in the electrical torque and the mechanical torque. The equation can be rewritten based on the active power as follows:  
\[2H\times\frac{d\Delta\omega}{dt}=\Delta P_{NC,ref}-\Delta P_{NC}, \tag{2}\]  
where \(H\) and \(\Delta P_{NC,ref}\) are the inertia constant of the generator and the desired wind source output obtained using power versus wind speed characteristics with the wind speed as its input. A description of the related calculations of \(\Delta\omega\) is indicated in Figure 1. The wind turbine is specified by a time constant (\(T_{a}\)) as follows:  
\[\frac{1}{1+sT_{a}}, \tag{3}\]  
The effect of the conventional generators frequency changes on DFIG is determined by a filter with time constant \(T_{r}\). A governor droop (\(R\)) is added, which is the rate of change of frequency with respect to generator power change.