## 5 Results and Discussion  
Tables 3 and 4 present the performance metrics obtained in both the grid-dependent and self-powered configurations of the 33-node test system. These results correspond to a 24 h evaluation horizon, during which the proposed optimization methodology was executed jointly with the load flow calculation using the SA method. The tables summarize the best and average outcomes, along with their respective standard deviations, for energy losses and CO\({}_{2}\) emissions. The results obtained through the proposed PMVO-based methodology are compared with the base case (without BESS scheduling) and with two alternative optimization approaches (CBGA and PVSA). In the grid-dependent configuration (Table 3), the PMVO algorithm yielded the best performance for all indicators. It achieved the lowest energy loss with a best value of 2374.8497 kWh and the lowest emissions at 9.8693 TonCO\({}_{2}\). Furthermore, its average values also surpassed the other methods, maintaining relatively low variability (0.3974% for energy and 0.0172% for emissions). Although the PVSA showed a comparable performance, particularly in its best-case scenario, its average results were slightly less efficient and more dispersed. A similar pattern is observed in the self-powered configuration (Table 4). The PMVO produced the most favorable outcomes again, reducing energy losses to the best value of 2373.5262 kWh and emissions to 16.0364 TonCO\({}_{2}\). The average performance remained \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Energy Loss (kWh)**} & \multicolumn{2}{c}{**Emissions (TonCO\({}_{2}\))**} & \multicolumn{2}{c}{**Performance Metrics**} \\ \cline{2-7}  & **Best** & **Avg. \(\pm\)\%** & **Best** & **Avg. \(\pm\)\%** & **Avg. Time (s)** & **Rank** \\ \hline
**Base Case** & 2484.5741 & – & 16.0659 & – & – & – \\ CBGA & 2396.5347 & 2408.1874 \(\pm\) 0.2062 & 16.0427 & 16.0454 \(\pm\) 0.0068 & 5.5936 & 3 \\ PVSA & 2374.2757 & 2384.2941 \(\pm\) 0.3722 & 16.0365 & 16.0393 \(\pm\) 0.0149 & 248.7784 & 2 \\ PMVO & **2373.5262** & **2380.1794 \(\pm\) 0.2989** & **16.0364** & **16.0386 \(\pm\) 0.0113** & 155.5360 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance results for the 33-node self-powered test system over a 24 h evaluation horizon. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Energy Loss (kWh)**} & \multicolumn{2}{c}{**Emissions (TonCO\({}_{2}\))**} & \multicolumn{2}{c}{**Performance Metrics**} \\ \cline{2-7}  & **Best** & **Avg. \(\pm\)\%** & **Best** & **Avg. \(\pm\)\%** & **Avg. Time (s)** & **Rank** \\ \hline
**Base Case** & 2484.5741 & – & 9.8874 & – & – & – \\ CBGA & 2383.4955 & 2392.9080 \(\pm\) 0.3253 & 9.8708 & 9.8721 \(\pm\) 0.0085 & 2.7427 & 3 \\ PVSA & 2375.3347 & 2392.9807 \(\pm\) 0.6240 & 9.8694 & 9.8725 \(\pm\) 0.0255 & 38.4663 & 2 \\ PMVO & **2374.8497** & **2391.8690 \(\pm\) 0.3974** & **9.8693** & **9.8719 \(\pm\) 0.0172** & 90.4112 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance results for the 33-node grid-dependent test system over a 24 h evaluation horizon. superior across both metrics with low dispersion. All optimization strategies significantly outperformed the base case regarding both technical and environmental indicators, validating the positive impact of BESS scheduling regardless of the selected method. An important aspect to highlight is the execution time of the algorithms. While PMVO required slightly more computational time compared to CBGA and PVSA, it consistently outperformed them in both operational and environmental objectives. However, this increased execution time is not a drawback in this context. Since the planning problem addressed here is executed offline and not in a real-time environment, the solution time is not a critical constraint.