## 4 Use Cases
### Kumamoto System
To delve deeper into this analysis, Figure 8 presents a closer view of the voltage peaks in the different optimized systems. Here, systems that do not meet the voltage constraints are highlighted, clearly showing how the voltage profiles of some systems fall below the lower limit of 0.95 p.u., disqualifying them as viable configurations. This analysis is crucial as it allows for the automatic filtering and discarding of configu  
Figure 6: Data from optimized systems. (**a**) Total losses, (**b**) total costs. Figure 7: Surface of voltage profiles in different buses for every optimized system. the voltage constraints. Although these constraints have been established in the optimizer, it may happen that, among the various reconfigured systems, no combination of active and reactive power values at the flexible buses results in a system with voltage values within the range due to the nature of the topology (buses' organization). A total of 89 reconfigured systems out of the 432 total do not meet the imposed voltage limits. Figure 9 shows the correlation between voltages and power losses, providing a combined view that allows comparing the \"performance\" of each system from both perspectives. It is observed that systems with better voltage profiles, i.e., those with smaller voltage drops throughout their profile, tend to present lower power losses. This suggests that good voltage control is not only necessary to maintain good voltage levels in the system but is also associated with higher efficiency in terms of power losses. In contrast, systems that show greater voltage drops tend to have higher losses. Figure 10 displays the total costs of optimized systems both with (in orange) and without (in blue) the use of flexible power. The objective of this figure is to verify the optimization algorithm's functionality and its ability to reduce total costs through the intelligent use of flexible power. Comparing both sets of data, it is observed that the use of flexible power (represented in orange) is predominant in those systems where its application is profitable. This is clearly evident starting from approximately EUR 80. At this point, systems that use flexible power achieve a significant reduction in total costs compared to those that do not use it (represented in blue). This confirms that the optimizer makes appropriate decisions, applying flexible power in configurations where its economic impact is significant, allowing for a cost reduction when it is most advantageous to do so. Thus, it can be verified that the algorithm not only identifies optimal configurations in terms of power losses but also knows when it is profitable to use flexible power to minimize total costs. In the simulated scenario, there were reconfigurations that did not require the use of flexible power for optimization, as incorporating it would have increased the overall operational costs of the distribution system. However, it is important to note that this may not always be the case. Under different conditions or scenarios, it is possible that all reconfigured systems could exhibit higher operational costs compared to the base case, necessitating the use of flexible power to minimize costs. In such situations, the optimization algorithm becomes crucial, as it intelligently determines when the application of flexible power is economically advantageous, ensuring that the total system costs are reduced whenever possible. This adaptability highlights the importance of the proposed approach, demon  
Figure 8: Visualization of voltage peaks in different optimized systems. starting its capability not only to optimize reconfiguration but also to strategically utilize flexible power to achieve cost-effective solutions under various operational scenarios.