## 5 Results and Discussion
### Validation of the Methodology on a 136-Bus Microgrid
This implies that the  
Figure 19: Voltage regulation performance achieved by the PMVO algorithm in a representative weekly scenario for a 136-node system in grid-dependent and self-powered modes. approach can adapt to forecast uncertainties and changing conditions, providing reliable voltage regulation in both grid-supported and islanded microgrid configurations. Figure 20 presents the maximum loadability percentages of the 136-node distribution system for each day of the week under grid-connected and self-powered configurations based on the optimal dispatch of BESS, which is found by the PMVO algorithm. In the grid-dependent mode, the system exhibits relatively stable maximum loadability values of around 47.6% across all days, well below the 100% operational limit, indicating a comfortable margin against line overloads. This consistent performance suggests that the algorithm effectively balances power flows, preventing any single line from reaching critical loading levels. The minor day-to-day variations (less than 0.05%) reflect the system's response to typical daily demand and generation patterns without compromising safety or reliability. Under the self-powered configuration, maximum loadability values are significantly lower, ranging from 11.5% to 12.6%. This reduction is expected since the system operates relying solely on local generation and storage, limiting power transfers over the lines and, thus, reducing line stress. Slightly higher values observed midweek (Wednesday) indicate minor load shifts but remain far from critical levels, showcasing the algorithm's adaptability to different operating modes while preserving network integrity. Overall, the PMVO algorithm maintains line loadings at safe, moderate levels regardless of the operation mode, demonstrating its capability to manage power flows effectively in a large-scale network. The stable and repeatable loadability profile over the week highlights the robustness of the dispatch strategy against demand variability. These results reinforce the scalability of the approach and suggest that it can reliably ensure operational security in complex microgrids under varying configurations. The SoC profiles in Figure 21 demonstrate the coordinated operation of BESS units within safe operating limits (10-90%) under grid-dependent mode over the course of a full week of operation, accounting for the variability of both demand and generation. Analysis reveals three distinct operational strategies: BESS C serves as the primary flexible resource with aggressive cycling (minimum 10% SoC on Day 2); BESS B maintains stable operation (SoC > 35%) for grid stabilization; and BESS A provides intermediate support with adaptive cycling (27.38% discharge on Day 3). All units exhibit synchronized daily patterns with midday solar charging and evening discharge while maintaining complementary weekly operation that balances battery health preservation with grid support requirements. The system achieves optimal performance through this tiered operational approach, where each BESS unit fulfills specific grid support functions according to its cycling characteristics. Figure 20: Maximum loadability performance achieved by the PMVO algorithm in a representative weekly scenario for a 136-node system in grid-connected and self-powered modes. The SoC profiles in Figure 22 reveal distinct operational strategies for BESS units in self-powered mode with the objective of minimizing energy losses, with all systems maintaining safe operating limits (10-90%). BESS A demonstrates moderate cycling with gradual charge-discharge patterns, typically operating between 30-90% SoC, except for a strategic deep discharge to 10% during hours 79-81 to address critical system needs. BESS B shows more aggressive utilization, frequently charging to 90% capacity and undergoing periodic deep discharges (reaching 10% during hours 154-160), suggesting its role as the primary energy buffer.