## 5 Power System Model  
The power system model used for transient stability analysis is shown in Figure 11. The model is composed of a nine-bus main system [29] and a WF. The main system is composed of three conventional power plants: two thermal power plants (SG1 and SG2) and one hydropower plant (SG3). Both SG1 and SG3 are operated under automatic generation control (AGC), and SG2 is operated under governor-free (GF) control. The parameters of the SGs are listed in Table 2. The IEEE type AC4A excitation system model shown in Figure 12 is considered for all SGs [30]. Table 3 lists the parameters taken from [30]. Figure 13 shows a block diagram of the reheat steam turbine governor system used in the thermal power plants (SG1 and SG2) [30]. The hydro turbine governor model system used for the hydropower plant (SG3) is shown in Figure 14 [30]. The parameters of both turbine systems are presented in Table 4 [30]. For AGC operation, an integral controller is installed on the governor system for both SG1 and SG3.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{\(d(el_{rd})\)/\(dt\)} \\ \cline{3-10}  & \(V_{rd}\)* & **PB** & **PM** & **PS** & **ZO** & **NS** & **NM** & **NB** \\ \hline \multirow{6}{*}{\(el_{rd}\)} & Positive Big (PB) & PB & PB & PM & PM & PS & ZO & ZO \\  & Positive Medium (PM) & PB & PM & PM & PS & ZO & NS & PS \\  & Positive Small (PS) & PM & PM & PS & ZO & NS & NM & PS \\  & Zero (ZO) & PM & PS & ZO & NS & NM & NM & PM \\  & Negative Small (NS) & PS & ZO & NS & NM & NM & NB & PM \\  & Negative Medium (NM) & ZO & NS & NM & NM & NB & NB & PB \\  & Negative Big (NB) & NS & NM & NM & NB & NB & NB & PB \\ \hline \hline \end{tabular}
\end{table}
Table 1: Fuzzy rules.  
Figure 10: Membership functions for the FLC: (**a**) Inputs (\(el_{rd}\), \(d[el_{rd}]/dt\))); (**b**) output (\(V_{rd}\)*).  
Figure 11: Power system model.  
Figure 12: IEEE type AC4A excitation system model.  
Figure 13: Steam turbine governor model.  
The integral controller on selected units for AGC is shown in Figure 15[30]. The output of the AGC supplies the power load reference of the governor system depending on the speed deviation of the SG (\(\Delta\omega_{sg}\)). The integral gain \(K_{i}\) is set to 6.  
A WF is connected to the main system at bus 5, as shown in Figure 11, and consists of one VSWT-DFIG and one FSWT-SCIG. In order to reduce computational time, each wind generator is represented as an aggregated equivalent single machine [31; 32]. The total capacity of the WF is 100 MW. A capacitor bank (C) is used for reactive power compensation of the SCIG. The value of C is chosen such that the power factor of the SCIG-based wind generator becomes unity at the rated operating condition. The base power of the system is 100 MVA, and the rated frequency is 50 Hz. The parameters of the DFIG and the SCIG are presented in Table 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Steam Turbine**} & \multicolumn{2}{c}{**Hydraulic Turbine**} \\ \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(R_{p}\) & 0.05 & \(R_{p}\) & 0.05 \\ \(T_{G}\) & 0.2 s & \(T_{G}\) & 0.2 s \\ \(T_{CH}\) & 0.3 s & \(R_{T}\) & 0.38 s \\ \(T_{RH}\) & 7.0 s & \(T_{R}\) & 5.0 s \\ \(F_{HP}\) & 0.3 & \(T_{W}\) & 1.0 s \\ \hline \hline \end{tabular}
\end{table}
Table 4: Typical values of turbine parameters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **SG1 (Thermal)** & **SG2 (Thermal)** & **SG3 (Hydro)** \\ \hline Rated Power & 150 MVA & 250 MVA & 200 MVA \\ Voltage & 16.5 kV & 18 kV & 13.8 kV \\ \(R_{a}\) & 0.003 pu & 0.003 pu & 0.003 pu \\ \(X_{l}\) & 0.1 pu & 0.1 pu & 0.1 pu \\ \(X_{d}\) & 2.11 pu & 2.11 pu & 1.20 pu \\ \(X_{q}\) & 2.05 pu & 2.