## 5 Results and Discussion
### Validation of the Methodology on a 136-Bus Microgrid
Similarly, in the case of CO2 emissions, the PMVO achieved a weekly average reduction of 14.3062 kgCO2 compared to the base scenario, representing an average improvement of 0.0052%. Daily absolute reductions ranged from 1.6691 to 2.2718 kgCO2. With a weekly standard deviation of approximately 1.7562%, these results highlight the robustness and consistency of the PMVO under different operational scenarios. The average computation time required to solve the CO2 emissions minimization problem was approximately 89.1909 s per day (1.49 min), which is consistent with the execution time observed for energy loss minimization. These results confirm the practicality and scalability of the proposed optimization framework for multi-objective operation planning in both real-time and day-ahead contexts. To further evaluate the robustness of the proposed methodology under more restrictive conditions, the PMVO was also applied to the same 136-node microgrid operating in self-powered (islanded) mode. Table 6 presents the results obtained in this scenario, including daily performance for each objective function and the corresponding baseline cases. In terms of energy losses, the PMVO achieved a weekly average reduction of 3.3938 kWh compared to the base case, which corresponds to a technical improvement of approximately 0.3635%. Daily absolute reductions ranged from 26.5283 Wh to 1.1961 kWh. The low standard deviation of approximately 3.3871% across the week indicates that the energy loss reductions were consistently achieved each day, regardless of operational variability. Regarding execution time, the methodology required an average of 389.7953 s per day (approximately 6.49 min) to solve the energy loss minimization problem. Although this represents a higher computational demand compared to the grid-connected case, it remains reasonable for offline planning or short-term scheduling in more constrained systems. For CO2 emissions, the PMVO reported a weekly average reduction of 2.8774 kgCO2, representing an average improvement of 0.0028%. The standard deviation, measured at 2.2336%, suggests stable behavior in emissions reduction throughout the week, with the algorithm adapting effectively to day-to-day variations in system conditions. The corresponding average computation time for solving the emissions minimization problem was 160.3519 s per day (approximately 2.67 min), which is consistent across the week and aligned with the performance observed in the energy loss case. These results confirm that the proposed framework maintains its effectiveness and computational feasibility even in isolated microgrid conditions, reinforcing its applicability for diverse operational contexts. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Objective Function** & **Case** & **Monday** & **Tuesday** & **Wednesday** & **Thursday** & **Friday** & **Saturday** & **Sunday** \\ \hline \multirow{3}{*}{Energy Loss (kWh)} & Base Case & 136.4297 & 133.7218 & 135.2536 & 136.7316 & 136.9853 & 129.0127 & 125.3783 \\  & PMVO & 135.2337 & 133.5115 & 134.86347 & 136.4138 & 136.9544 & 127.7908 & 125.3518 \\  & Time & 380.4747 & 378.2386 & 378.7801 & 385.7859 & 393.8756 & 403.8317 & 407.5802 \\ \hline \multirow{3}{*}{Emissions (TonCO2)} & Base Case & 14.9350 & 14.3373 & 14.6324 & 14.6519 & 14.9657 & 14.2166 & 14.1764 \\  & PMVO & 14.9347 & 14.3372 & 14.6321 & 14.6516 & 14.9656 & 14.2160 & 14.1753 \\ \cline{1-1}  & Time & 164.7517 & 159.9047 & 158.8186 & 160.2062 & 159.5723 & 160.1344 & 159.0750 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance results for the 136-node self-powered test system. Figures 17 and 18 illustrate the weekly performance of the PMVO algorithm in terms of daily energy loss and CO\({}_{2}\) emission reductions for the 136-node system under both grid-dependent and self-powered configurations. In Figure 17, PMVO demonstrates noticeable variability in daily energy loss reductions depending on the operation mode.