## 6 Simulation Results and Discussion
### Scenario (2)  
In this scenario, the RES were located at predefined locations, and both generation and load were uncertain. Data for the RES and their locations for each study case are provided in the Appendices. In this paper, the scenario reduction process was applied using the FSR method, as discussed in the previous section, to reduce the number of wind and solar generation scenarios and loading levels to 15. Subsequently, the proposed I-GWO method was used to find the optimal location and sizing of the DSTATCOMs, considering all these 15 scenarios. Table 6 presents the main results obtained--such as power losses, minimum voltage, VSI, cost of loss, cost of DSTATCOMs, and TACS--for each study case, using the developed I-GWO method. For these cases, the number of DSTATCOMs selected was 2 for both the 33-bus and 69-bus test systems, and 3 for the 85-bus test system. Within Table 6, each study case is represented by two columns: the first column shows metrics before the installation of DSTATCOMs, and the second column displays metrics after their installation. Figure 12: Effect on voltage profile for the 85-bus system. Figure 13: (**a**) Convergence behavior for the IEEE 33-bus network; (**b**) convergence behavior for the IEEE 69-bus network; (**c**) convergence behavior for the IEEE 85-bus network. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Outputs**} & \multirow{2}{*}{**Base Case**} & \multicolumn{4}{c}{**Number of DSTATCOMs**} \\ \cline{3-5}  & & **Single** & **Two** & **Three** \\ \hline \hline \multirow{2}{*}{VSImin (p.u.)} & 0.57631 & 0.75373 & 0.82171 & 0.82499 \\  & Cost of loss (USD/yr) & 166,189.63 & 120,419.81 & 105,163.24 & 100,131.51 \\  & Cost of DSTATCOMs (USD/yr) & & 11,403.52 & 18,225.65 & 18,845.46 \\  & TACS (USD/yr) & & 34,366.30 & 42,800.74 & 47,212.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._As illustrated, Table 6 reveals the significant impact of DSTATCOMs on reducing power losses across the IEEE 33-bus, 69-bus, and 85-bus systems. Specifically, for the 33-bus system, power losses were reduced from 135.84 to 55.17, achieving a reduction of 59.39% after installing 2 DSTATCOMs. The 69-bus system experienced a decrease in losses from 124.08 kW to 48.74 kW, translating to a 58.18% reduction with the installation of 2 DSTATCOMs. Lastly, the 85-bus system saw its power losses decline from 171.75 kW to 64.66 kW, amounting to a 62.35% reduction upon the integration of 3 DSTATCOMs. These reductions signify the pivotal role that DSTATCOMs play in enhancing the overall efficiency and reliability of radial distribution systems. Figures 14-16 present heatmaps that visualize voltage profiles for the three test systems, namely, 33-bus, 65-bus, and 85-bus, in the presence of renewable energies and load uncertainty. Before the installation of DSTATCOMs, these heatmaps partially display red areas that are indicative of low voltage levels below 0.95 p.u. Following the application of the proposed IGWO method for DSTATCOM sizing and placement, a noticeable shift to green can be observed in these figures. This color change signifies improved voltage levels, closer to 1 per unit, across all 15 scenarios. The transition clearly emphasizes the effectiveness of the optimal allocation and sizing of DSTATCOMs using the proposed IGWO method, in terms of improving voltage levels. The optimal locations for DSTATCOMs in the tree test systems are illustrated in the one-line diagrams found in Appendix D.