## 5 Results and Discussion
### Validation of the Methodology on a 136-Bus Microgrid
In the grid-dependent configuration, the reductions fluctuate between 0.344% (Sunday) and 0.602% (Tuesday), whereas, in the self-powered mode, the range is broader, from as low as 0.021% (Sunday) to a peak of 0.947% (Saturday). The weekly average energy loss reduction for the grid-dependent case is approximately 0.5236%, with a standard deviation of 0.0815%, indicating relatively stable but modest performance across the week. In contrast, the self-powered mode yields a higher variability, with a weekly mean of 0.3636% and a standard deviation of 0.3391%, reflecting the influence of local generation dynamics and load profiles on the performance of PMVO. Figure 18 presents the corresponding CO\({}_{2}\) emission reductions. Although the absolute values are lower due to the nature of the metric, the overall trend aligns with the observed pattern in energy losses. In the grid-dependent configuration, reductions range from 0.004% to 0.006%, with a weekly average of 0.0053% and a standard deviation of 0.0009%, indicating stable performance throughout the week. In contrast, the self-powered mode exhibits greater variability, with values spanning from 0.001% to 0.007%, a weekly  
Figure 17: Energy loss reduction: Results for a 136-node system in grid-dependent and self-powered modes over a 1-week evaluation horizon. Figure 18: CO\({}_{2}\) emissions reduction: Results for a 136-node system in grid-dependent and self-powered modes over a 1-week evaluation horizon. average of 0.0029%, and a higher standard deviation of 0.0021%. This increased dispersion reflects the effects of intermittent power flows and the absence of centralized dispatch control. These results highlight that the algorithm's performance, both in terms of energy loss and CO2 emission reductions, is strongly influenced by the specific configuration of the distribution network, particularly the placement of photovoltaic generators and battery systems. It is worth noting that the 136-node test system originally lacked both PV generation and storage units; consequently, these components were assigned to arbitrary locations within the network. While the reported outcomes demonstrate the algorithm's potential, they could likely be enhanced through an optimized siting strategy for DERs, a topic beyond the scope of this study but identified as a direction for future research. Figure 19 displays the hourly voltage regulation of a 136-node distribution network optimized with the PMVO algorithm under both grid-connected and self-powered configurations, using daily operational profiles over a full week to capture typical load and generation fluctuations. In the grid-connected mode, voltage regulation remains within 2.3% to 5.08%, always below the 10% operational limit. The lowest deviations occur in the early morning hours (1-6), with regulation levels near 2.3-2.6% due to lower demand and system stress. Voltage deviations increase gradually during the day, peaking consistently at hour 20 with a maximum of 5.08%, reflecting evening peak demand. Despite day-to-day variability, the algorithm maintains a narrow voltage band with minimal fluctuations between days, demonstrating robustness against variable operating conditions. Under the self-powered scenario, voltage regulation is even more constrained, ranging from 0.57% to 1.21%, with similar daily trends. These lower values stem from a different voltage reference related to slack-less operation. Peak deviations occur, again, near hour 20, with all days converging at around 1.208%, confirming the repeatability of this peak pattern. The results confirm that the PMVO algorithm effectively controls voltage within safe operational limits over a larger, more complex network, achieving a similar regulation quality to that previously demonstrated in a 33-node system. The use of detailed daily profiles covering multiple days illustrates the algorithm's capacity to handle typical variability and suggests its suitability for integration into EMS frameworks with frequent updates.