## 5 Results and Discussion
### Validation of the Methodology on a 136-Bus Microgrid  
To further validate the proposed PMVO approach, it was applied to a 136-bus microgrid [53] over a full week, encompassing both grid-connected and islanded modes. This larger, more complex system tests the algorithm's robustness and flexibility across different microgrid sizes. Figure 14 shows the 136-bus microgrid layout, where node 1 serves as the slack bus, connected either to the main grid or a 4000 kW diesel generator operating between 40% and 80% capacity, following the same constraints as the 33-bus system. Three PV units rated 1125, 1320, and 999 kW are located at nodes 106, 88, and 47. The base values are 13.8 kV and 100 kVA, with environmental parameters consistent with Section 4.1. The system includes three lithium-ion BESS units with the same characteristics as those described in Section 4.1, located at buses 89, 75, and 35, respectively. The selection of these nodes was based on their higher power demand levels, which makes them critical points in the network. By placing storage systems at these locations, the BESS can effectively support the local load and alleviate stress on the distribution network, particularly during peak demand or islanded operation. The technical parameters of the 136-node microgrid (MG) employed in this study are presented in Table 1, located in Appendix A. The description of these parameters follows the same criteria as those detailed in Table 1. For this MG, the maximum allowable voltage deviation is \(\pm 10\%\) of the nominal voltage. The load profile used in this study was sourced from a Colombian distribution company, while the PV generation profile was produced through an artificial neural network (ANN) trained with climatic data from a specific region in Colombia [27]. This ANN was developed by incorporating real meteorological variables, including time, temperature, solar radiation, humidity, and atmospheric pressure, and was employed to simulate hourly PV generation and power demand profiles over a representative 7-day period. Figure 15 shows the weekly load variation, where the \"regular\" curve represents the typical demand pattern observed on Monday, Tuesday, Thursday, and Friday. The remaining curves illustrate the distinctive behavior of the other days of the week. Figure 14: Topological schematic of the 136-node AC microgrid test system in dual-operation modes: Grid-dependent (M\({}_{1}\)) and self-powered (M\({}_{2}\)). Meanwhile, Figure 16 presents the corresponding photovoltaic generation profiles for each day. Table 5 summarizes the results obtained by applying the PMVO to the 136-node microgrid under grid-connected operation. The table reports the values of the different objective functions considered in this work, including the baseline cases for each day of the week and the corresponding outcomes achieved by the PMVO. In terms of energy losses, the PMVO achieved an average weekly reduction of 87.5718 kWh, representing a technical improvement of 0.5261% compared to the base case. Daily absolute reductions ranged from 7.6175 kWh to 14.4985 kWh. The standard  
Figure 16: Daily PV generation profiles for a typical operational week. Figure 15: Representative daily load curves for a typical operational week. \begin{table}
\begin{tabular}{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 & 2458.3857 & 2407.2377 & 2355.2850 & 2444.1375 & 2463.2519 & 2304.2519 & 2213.9967 \\  & PMVO & 2444.6646 & 2392  
deviation over the week was approximately 2.8377%, reflecting the stable and consistent performance of PMVO under varying operating conditions. In addition, the proposed methodology required an average execution time of 91.1643 s per day to solve the energy loss minimization problem, i.e., approximately 1.52 min. This result highlights the practicality of the approach for day-ahead or short-term operational planning.