## 1 Introduction
### State of Art
Studies in this field are advancing by introducing and combining different optimization algorithms and merging various concepts into the problem to be optimized (functions, constraints, objectives, etc.). In the work [25] recently published by [PERSON] et al., an ant colony optimization (ACOA)-based method is introduced, which optimizes both network reconfiguration and the placement and size of different types of DG, improving system stability and significantly reducing active power losses and voltage drops at the buses, all while maintaining the radial structure of the system and improving its reliability. Regarding the approach followed in this work, it is essential to highlight the concept of optimal power flow, known as OPF. This method is a key tool in the operation and planning of electrical systems, as it aims to find the optimal point of control variables that minimize an objective function, generally associated with generation costs, while satisfying all system constraints [26; 27]. The primary objective of OPF is to determine the optimal dispatch of generating units, adjust the voltage levels, and define power flow through the network, all in a way that minimizes the costs associated with operation, such as fuel costs, and maximizes system efficiency. Additionally, in some approaches/algorithms, OPF may also consider minimizing active and reactive power losses, as well as optimizing the voltage profile in the network. However, it is important to note that traditional OPF methods usually assume a fixed network topology, which means that the network structure does not change during the optimization process. This assumption limits the applicability of OPF in systems that may require dynamic reconfiguration, either for operational reasons or in response to contingencies. In this context, research has emerged that integrates network topology reconfiguration with OPF, allowing greater system flexibility and adaptability to changes [28; 29; 30]. This work presents a comprehensive approach that combines network reconfiguration with the implementation of flexible power buses to address challenges arising from increased distributed generation (DG) penetration, microgrid integration, gradual and growing electricity demand, and the stochastic variability of renewable production. The main contributions of this work are as follows:  
* Flexible Power Buses: The concept of flexible power buses is introduced, where each bus can dynamically adjust its active and reactive power within a predefined range in order to satisfy distribution system requirements. This flexibility allows for better adaptation to varying demand and generation conditions, enhancing overall system performance. This concept will be discussed in the next section. * Integration of Flexible Power Buses with System Reconfiguration: The proposed algorithm systematically explores all possible radial configurations derived from the base system, incorporating flexible buses. By assessing each potential configuration, the method ensures that the global optimal solution is identified. This approach enables the distribution system to dynamically adapt to changes in demand and DG, providing a more robust and efficient operational topology. * Optimization Framework: A comprehensive formulation of the optimization problem is presented, defining key decision variables, objective functions, and constraints. The framework integrates load flow analysis, allowing for precise adjustments to active (\(P\)) and reactive (\(Q\)) power flows. The optimization aims to minimize both operational costs and power losses, leading to a more efficient and cost-effective distribution network. The remainder of this paper is organized as follows: Section 2 provides an overview of the approach. Section 3 covers key technical components, including power flow analysis (Section 3.1), the reconfiguration algorithm (Section 3.2), and the optimization problem formulation (Section 3.3).