## 7 Conclusions  
This study proposed the utilization of the improved gray wolf optimization (I-GWO) method to determine the optimal sizing and placement of DSTATCOMs in radial distribution systems. To address the limitations of the conventional gray wolf optimization (GWO) method, the I-GWO incorporated a dimension learning-based hunting (DLH) strategy. This strategy helped maintain population diversity, balance exploration and exploitation, and prevent premature convergence. The effectiveness of this optimization approach was verified through tests on the IEEE-33 bus, IEEE-69 bus, and 85-bus radial distribution systems. Furthermore, this method was compared to other prevalent optimization techniques, such as BFOA, CSA, LSA, MOPSO, and MOSCA. The proposed method, designed as an offline approach, demonstrated its superiority in terms of reducing active losses and costs. Moreover, it enhanced the voltage profile and stability and improved the quality of the entire system. In the second phase of this study, the model considered the uncertainties associated with renewable energy generation and load fluctuations. Initially, the fast scenario reduction (FSR) method condensed wind and solar generation scenarios and loading levels into a limited number of scenarios. Following this, the I-GWO algorithm determined the optimum location and sizing for the DSTATCOMs, accounting for all the scenarios identified by the FSR method, thereby demonstrating its effectiveness even under the conditions of renewable energy and load uncertainty across various test systems. Further ResearchWhile this study proposes I-GWO as an offline method, it shares common limitations with any metaheuristic, such as time consumption, especially in the case of large-scale distribution networks. Therefore, a potential avenue for future research lies in enhancing this approach or exploring hybridization with other optimization techniques to effectively address these limitations. Conceptualization was performed by [PERSON]; [PERSON] and [PERSON] developed the methodology; [PERSON] and [PERSON] handled the software; [PERSON], [PERSON] and [PERSON] were responsible for validation; [PERSON] provided resources; [PERSON] took care of data curation; [PERSON] prepared the original draft; the writing was reviewed and edited by [PERSON], [PERSON] and [PERSON]; [PERSON], [PERSON], [PERSON] and [PERSON] managed the visualization; [PERSON] handled supervision. All authors have read and agreed to the published version of the manuscript. This research received no external funding. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Outputs** & \begin{tabular}{c} **BFOA** \\ **[9]** \\ \end{tabular} & \begin{tabular}{c} **MOPSO** \\ **[11]** \\ \end{tabular} & \begin{tabular}{c} **LSA** \\ **[7]** \\ \end{tabular} & \
\begin{tabular}{c} **MOSCA [11]** \\ \end{tabular} &
\begin{tabular}{c} **Proposed** \\ **Approach** \\ \end{tabular} \\ \hline Optimal size & 632.00 (12) & 679.21 (16) & 341 (14) & 733.41 (8) & 400.72 (13) \\ (kVAr) and & 487.00 (28) & 549.50 (29) & 516 (24) & 410.26 (16) & 554.87 (24) \\ location & 550.00 (31) & 722.03 (30) & 1013 (30) & 1029.04 (30) & 1089.27 (30) \\ Ploss (kW) & 144.38 & 152.44 & 138.35 & 150.27 & 132.16 \\ Vmin (p.u.) & 0.92400 & 0.95120 & 0.93010 & 0.9517 & 0.93774 \\ VSImin (p.u.) & 0.72280 & 0.81600 & 0.74230 & 0.81900 & 0.77327 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of results with existing methods in the case of an IEEE 33-bus system.