## 6 Simulation Results and Discussion
### Case 3: BESS versus PHES with TADP DRP  
In this case, the prospects of TADP DRP in optimum component-sizing problem has been investigated. The renewable energy generation forecasting is a subset feature of the TADP DRP implementation. Hence, the GBRT prediction results for wind speed, solar irradiance and the consequent WT and PV powers are validated using error metrics (MAE, RSME and \(r^{2}\)) in order to determine the suitable forecasting condition based on the learning rates \(\alpha_{gbr}\). The total data set contained 17,520 data points with an hourly resolution; from which 75% of the data are adopted for training, and 25% are adopted for testing. Table 5 summarizes the forecasting results based on MAE, RSME and \(r^{2}\) for the GBRT forecasting model under three \(\alpha_{gbr}\) values i.e., \(\alpha_{gbr}\) = 0.1, 0.3, 0.5. As it can be noticed, the chosen value of \(\alpha_{gbr}\) significantly affects the precision of the GBRT forecasting model. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**BESS-Based Microgrid**} & \multicolumn{3}{c}{**PHES-Based Microgrid**} \\ \hline LPSP & **0\%** & **5\%** & **10\%** & **15\%** & **0\%** & **5\%** & **10\%** & **15\%** \\ \hline PV capacity (kW) & 1110 & 1027 & 958 & 1039 & 1826 & 1670 & 1754 & 1671 \\ WT capacity (kW) & 2165 & 2184 & 2054 & 1808 & 1561 & 1498 & 1230 & 1195 \\ ESS capacity (kWh) & 6436 & 1170 & 670 & 132 & 7789 & 7311 & 6986 & 6414 \\ \hline TPC (US 5) & \(\mathbf{1.37\times 10^{7}}\) & \(\mathbf{9.91\times 10^{6}}\) & \(\mathbf{9.00\times 10^{6}}\) & \(\mathbf{7.99\times 10^{6}}\) & \(\mathbf{9.02\times 10^{6}}\) & \(\mathbf{8.48\times 10^{6}}\) & \(\mathbf{7.78\times 10^{6}}\) & \(\mathbf{7.49\times 10^{6}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Techno-economic analysis for case 2. Figure 5: Pareto front for case 2. The best wind speed and wind power forecast results are realized when the \(\alpha_{gbr}\) value chosen equals 0.1. The least error values indicated by MAE and RMSE of 0.22 (m/s) and 0.27 (m/s) for wind speed prediction and 35.03 kW and 47.98 kW for wind power forecast respectively confirms the consequences of the \(\alpha_{gbr}\) value chosen. The results accuracy are further validated using the \(r^{2}\) metric; the highest value of \(r^{2}=0.96\) further establishes that the GBRT at \(\alpha_{gbr}=0.1\) is an appropriate model for wind speed and wind power forecasting. Figure 6. shows a comparison of the actual wind speed versus the predicted wind speed with one-hour-ahead rolling forecasting horizon using the GBRT model when \(\alpha_{gbr}\) is set to 0.1 (for the best \(\alpha_{gbr}\) value). Also, for solar irradiance and PV power prediction, the best results are obtained when the \(\alpha_{gbr}\) parameter is set to 0.1. The minimum error values indicated by MAE and RMSE of 15.36 (W/m\({}^{2}\)) and 29.62 (W/m\({}^{2}\)) for solar irradiance prediction and 17.43 kW and 33.60 kW for PV power forecast, respectively, validate the parameter selection. Also, the highest \(r^{2}\) metric of 0.99 shows the goodness of fit and suitability of the model selection as being appropriate. Figure 7 shows a comparison of the actual versus the predicted solar irradiances with one-hour-ahead rolling forecasting horizon using the GRBT model when \(\alpha_{gbr}\) is set to 0.1 (for the best \(\alpha_{gbr}\) value).