## 4 Case Study
### Simulation Results  
The performances of the PMSG wind farms in three different cases are compared to verify the effectiveness of the proposed optimal strategy. Case 1: No frequency support control;  
Case 2: Frequency support control (5% de-loaded operation) without using the KE optimization method;  
Figure 11: Wind speed variations at each wind farm. Figure 10: Simulated small power system. Case 3: Frequency support control using the KE optimization method (proposed strategy). In Case 1, none of the wind farms utilize the reserve margin for supporting regulations with frequency control and active power. The PMSG wind turbines are operated only at the maximum aerodynamic efficiency and the pitch angle is then retained at the optimal value. In Case 2, the PMSG wind turbines participate in frequency regulations using a fixed 5% de-loaded operation based on frequency support control without using the KE optimization method. In Case 2, the active power outputs from all wind farms are subjected to the same power reduction according to a fixed de-loaded reference. To enhance the frequency contribution of the PMSG wind turbines, Case 3 implements an additional KE optimization method to maximize the total KE in the rotor. In this case, each individual wind farm operates in the de-loaded control mode to optimize the additional KE generated from the wind turbine under consideration. In this work, an initial system is considered where all synchronous units are operated in accordance with the parameters listed in Table 1. Here, the active load power is 270 MW. The steam turbine G1 maximizes the output from power generation as a base generator in a small power system. The overall capacity of the wind farms represents approximately 28% of the total installed generation capacity. It is assumed that at \(t=100\) s, the system operator requests the power output reference for all wind farms to be approximately 40 MW. The columns in Table 2 represent the wind speed, maximum power, optimal rotational speed, and de-loaded power reference of individual wind farms in the three cases. The power outputs in Case 2 and Case 3 satisfy the power reference requirement specified by the system operator. Table 3 presents a comparison of the results of the additional KE reserve values in wind farms for the three cases. The additional KE in Case 3 can supply a greater power output to the power system than the KE in Case 2. When PMSG wind turbines operate at a near-rated wind speed, the rotational speed is also restricted by the maximum value generated from the pitch angle control (1.2 p.u.). As shown in Table 3, the rotational speed of the WFI in Case 2 is limited to maximum rotational speed of 1.2 p.u. (\(\omega_{del}\)) through pitch angle control. Besides, the rotational speed of the WFI and WF5 in Case 3 are restricted by pitch angle control. The de-loaded power reference for Case 3 increases the KE reserve considerably. The application of the output control using the KE optimization method can enhance the capability of the frequency regulation. To evaluate the frequency contribution of the proposed optimal strategy, the loss of G2 is determined at \(t=250\)\(s\) in such a way that it promotes a change in the frequency of the power system. When the frequency drops owing to the loss of G2, wind farms are simulated to support the frequency regulation in the test system. Figures 12 and 13 illustrate the variations in the active power \begin{table}
\begin{tabular}{c c c c} \hline
**Unit** & **Generator Type** & **Generation (MW)** & **Capacity (MW)** \\ \hline G1 & Steam turbine & 80 & 100 \\ G2 & Gas turbine & 40 & 50 \\ G3 & Hydro turbine & 60 & 70 \\ G4 & Hydro turbine & 50 & 60 \\ Total & - & 230 & 280 \\ \hline \end{tabular}
\end{table} 
Table 1: Power output of individual generators. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Wind Farm** & \(\mathbf{S}_{w}\) **(m/s)** & \(\mathbf{\omega}_{m,opt}\) **(p.u.