## 4 Results
### Comparison of Model Performance  
Figure 4 displays the distributions of actual and predicted values of the power output, estimated using a kernel density estimation technique. The solid black and red lines represent the distribution of the observation and prediction of SL, respectively. The remaining colored lines represent the distribution of the predicted values of the other machine learning models. All distributions exhibit a multimodal shape. The distributions of the machine learning models and SL are quite similar. However, it can be seen that the distribution of the models has relatively lower variability than the observed distribution. Figure 5 and Table 3 present the performance of each model in terms of RMSE and MAE for 10 validation folds, as well as their average performance. For each model, the black points represent the performance values for 10 validation folds, while the red plus sign indicates the average performance of 10 validation folds. Ensemble learning models performed better than traditional single models for all folds. Among all the models, SL achieved the best performance in terms of the average of RMSE and MAE. Except for Super Learner, XGB showed better average performance compared to the other base learners, followed by GBM and RF. Table 3 compares the average performance of the regression methods in our study and a previous article by [3]. KNN, RF, GBM, and XGB show better prediction skills than BREP on the average of RMSE and MAE. Furthermore, SL outperformed BREP by combining models that were either better or not better than BREP. This implies that SL is a stable model by combining the predictions of various models. SL demonstrated superior prediction skills compared to base learners, with the averages of RMSE and MAE at 3.1772 and 2.2537, respectively. Figure 6 presents the predictive performance of SL and base learners in terms of RMSE and MAE for each fold. If the points are distributed close to the 45-degree line for the model, it indicates that the model's performance is similar to SL. Ensemble learning models are more closely aligned with the line compared to traditional single models, with XGB demonstrating the highest resemblance to SL. However, SL outperforms the base learners on all folds. Figure 7 and Table 4 present the average RMSE and MAE obtained from two-fold cross-validation for five files. The machine learning models and SL demonstrate comparable performance across the files. Ensemble models exhibit significantly superior prediction performance compared to traditional machine learning models. Among the ensemble models, SL consistently achieves the lowest RMSE and MAE, followed by XGB, GBM, RF, KNN, SVR, and DT for all files. Figure 4: Kernel density estimation of the predicted values for each model and its corresponding actual values. In Figure 8, the distribution of actual and predicted values of SL, which had the model with the most successful prediction performance, is presented. The predicted values of SL closely follow the observed pattern, indicating that the model predicts the power output of the CCPP using the four variables (AT, V, AP, and RH) similarly. Figure 5: Comparisons of the prediction performances for each 10 validation folds and averaged performance in terms of RMSE and MAE. Figure 6: Comparison of the prediction performances of SL and base learners. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Regression Method** & **Average RMSE** & **Average MAE** \\ \hline BREP [3] & 3.787 & 2.818 \\ SL & 3.1772 & 2.2537 \\ XGB & 3.2188 & 2.2858 \\ GBM & 3.288 & 2.3356 \\ RF & 3.4176 & 2.4632 \\ KNN & 3.7613 & 2.7202 \\ SVR & 3.9336 & 2.8332 \\ DT & 4.1673 & 3.1356 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average RMSE and MAE for SL ensembles and BREP. Figure 8: The plot of the real value and predicted value with SL for 200 points.