## 4 Simulation Validation
### Validation 2: Available Power Estimator  
The simulation employing the available power estimation algorithm was conducted using the same model, under simulation conditions of wind speeds lower than the rated wind speed (8 m/s) with a Class A standard turbulence model. The analysis was performed for 600 s in a dynamic simulation environment with different wind speed estimation algorithms applied.  
Figure 8 illustrates the results of the dynamic simulation, presenting rotor speed, pitch angle, generator torque, generator output, and available power. Additionally, Figure 9 displays a representation of generator output and available power. Available power functions as a function of estimated wind speeds, exhibiting trends similar to those of estimated wind speeds. Table 4 shows the comparison results between generator output and estimated available power, indicating mean errors of \(-0.58\%\) and \(7.29\%\), and standard deviation errors of \(4.07\%\) and \(8.37\%\), respectively. Furthermore, Table 5 presents the comparison results of root mean square error (RMSE), mean square error (MSE), and mean absolute error (MAE) between generator output and available power. The drive train model method shows lower RMSE compared to the Kalman filter method, and similar trends are observed in MSE and MAE. Specifically, for the drive train model method, the RMSE, MSE, and MAE values are \(0.2061\) MW, \(0.0425\) MW, and \(0.1672\) MW, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multicolumn{3}{c}{**Rotor Speed [rpm, \%]**} & \multicolumn{3}{c}{**Electrical Power [MW, \%]**} \\ \cline{2-9}  & **Mean** & **Diff.** & **Std.** & **Diff.** & **Mean** & **Diff.** & **Std.** & **Diff.** \\ \hline Baseline & 12.10 & - & 0.2482 & - & 5.00 & - & 0.1035 & - \\ DTM & 12.10 & 0 & 0.2332 & \(-6.04\) & 5.00 & 0 & 0.0945 & \(-8.70\) \\ EKF & 12.09 & \(-0.08\) & 0.2431 & \(-2.05\) & 5.00 & 0 & 0.1015 & \(-1.93\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of simulation results with the application of the feed-forward control algorithm.  
Figure 7: Dynamic simulation results with the application of the feed-forward control algorithm.  
For the extended Kalman filter method, the same values are 0.2332 MW, 0.0544 MW, and 0.1818 MW, respectively. The simulation results indicate a slight advantage of the drive train model method in estimating available power, additionally demonstrating that the accuracy of available power estimation varied depending on the applied wind speed estimation methods, leading to the conclusion that more accurate wind speed estimation is needed to improve the estimation accuracy for available power.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Electrical Power (MW, \%)**} \\ \cline{2-5}  & **Mean** & **Error** & **Std.** & **Error** \\ \hline Generator Power & 1.9041 & - & 0.6533 & - \\ \hline Available Power-DTM & 1.8930 & \(-\)0.58 & 0.6799 & 4.07 \\ \hline Available Power-EKF & 2.0429 & 7.29 & 0.7080 & 8.37 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of power output and available power using wind speed estimation method.  
Figure 8: Dynamic simulation results with the application of the available power estimator.