## 5 Conclusions  
This study presents a methodology for optimizing distribution systems through network reconfiguration and the use of flexible buses. With the increasing penetration of  
Figure 11: Total costs of reconfigured systems, in blue without use and in orange with use of flexible power (optimized).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Bus Number**} & \multirow{2}{*}{
\begin{tabular}{c} **Interval over** \\ **Initial Value** \\ **(\%)** \\ \end{tabular} } & \multicolumn{3}{c}{**Active Power (P) (p.u.)**} & \multicolumn{3}{c}{**Reactive Power (Q) (p.u.)**} \\ \cline{2-7}  & & **Minimum** & **Initial Value** & **Maximum** & **Minimum** & **Initial Value** & **Maximum** \\  & & **Value** & **(Base)** & **Value** & **Value** & **(Base)** & **Value** \\ \hline
9 & 35 & 0.00039 & 0.0006 & 0.00081 & 0.00013 & 0.0002 & 0.00027 \\
5 & 50 & 0.0003 & 0.0006 &  
distributed generation, the rise of microgrids, and advancements in power system controllability, the integration of flexible buses becomes essential. These buses represent the sum of several microgrids connected to a point in the system, providing a range of values for active and reactive power adjustments. This approach allows for the dynamic optimization of power flows, enhancing the network's efficiency and adaptability under varying distributed generation and demand scenarios.  
A notable feature of this algorithm is its ability to evaluate all possible radial configurations that can arise from the base system. Unlike conventional optimization techniques, which may only consider a subset of potential configurations, this methodology ensures that all feasible radial systems are evaluated, guaranteeing that the global optimal solution is identified.  
The optimization problem is formulated with clear decision variables and objective functions, enabling the systematic adjustment of power variables at flexible buses. This minimizes the operational costs and power losses, while accommodating the flexibility introduced by new technologies and the integration of distributed energy resources.  
The application of this methodology to the Kumamoto and IEEE-33 system case study shows a 43.9% and 66.6%, respectively, reduction in power losses compared to the initial configuration, with a corresponding decrease in operational costs. This demonstrates the potential of the proposed approach in improving distribution network performance and highlights the significance of flexible buses in modern power systems.  
Conceptualization, J.C.-C. and F.J.R.-R.; methodology, R.S.-H.; software, J.C.-C. and A.C.A.; validation, F.J.R.-R. and R.S.-H.; formal analysis, J.C.-C., F.J.R.-R., R.S.-H. and A.C.A.; investigation, J.C.-C., F.J.R.-R., R.S.-H. and A.C.A.; resources, J.C.-C.; data curation, F.J.R.-R.; writing--original draft preparation, J.C.-C.; writing--review and editing, F.J.R.-R. and A.C.A.; visualization, A.C.A.; supervision, R.S.-H.; project administration, F.J.R.-R. and R.S.-H. All authors have read and agreed to the published version of the manuscript.  
This paper is framed in the project \"Integral control system to optimize the microgrids energy demand\" and was supported by the grant PID2020-117828 RB-I00 funded by MI-CIU/AEI/10.13039/501100011033 and, by Spanish Ministry of Science, Innovation and Universities. In addition, the author [PERSON] is enjoying a INVESTIGO research fellowship funded by the European Union--NextGenerationEU.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.