## 1 Introduction
The study formulates a multi-objective nonlinear optimization problem to minimize active power losses and improve voltage deviations, considering operational constraints such as line capacity, voltage limits, generator capacities, and transformer tap settings. The approach is tested on 30- and 118-bus systems, showing better solution quality compared to GA and PSO. Although statistical analysis is provided, convergence times are not discussed, limiting insights into the computational load. In line with this perspective, recent studies have developed EMS strategies for the optimal operation of BESSs in AC MGs, with an increasing focus on reducing energy losses and CO\({}_{2}\) emissions [17]. These works apply diverse methodologies--such as convex optimization, metaheuristics, and linear programming--to enhance the environmental performance of MGs [18; 19; 20]. Metaheuristic techniques, in particular, have been recognized for their simplicity, robustness, and effectiveness, enabling practical EMS implementations with lower system complexity. Building on these advantages, this study adopts metaheuristic optimization as the core approach to maximize the contribution of BESSs while minimizing technical losses and environmental impact. The work reported in [21] provides a performance comparison between the proposed adapted version of the PSO method and classical optimization techniques, such as GA. Itreports key indicators such as the best result, average performance, and computation time, offering a solid foundation for evaluating optimization quality and efficiency. However, the analysis does not include the standard deviation of the results, which is a critical metric to assess the variability and repeatability of the solutions. Including this statistical measure would enhance the reliability of the findings and support broader validation of the algorithm's consistency across multiple runs. In [22], a comprehensive and well-structured methodology for the optimal integration and operation of BESSs in grid-connected AC distribution networks was presented, demonstrating strong performance in reducing both energy losses and CO\({}_{2}\) emissions. The authors correctly include statistical metrics such as the best, average, and standard deviation of the results, ensuring transparency and repeatability in the evaluation. The operation of batteries is effectively optimized through a PSO-based strategy that responds to hourly variations in load and PV generation. However, the main limitation of the study lies in its exclusive focus on the grid-connected (On-Grid) mode. The methodology does not analyze the behavior of the microgrid under isolated (Off-Grid) conditions, which is essential for realistic energy management in microgrids that frequently switch between operational states. As a result, the proposed approach, while solid, is only applicable to active distribution networks and does not fully capture the operational versatility required in modern microgrids. In [23], the authors propose a two-stage energy management system (EMS) for a grid-connected photovoltaic (PV) charging station integrated with a battery energy storage system (BESS). The first stage performs a day-ahead optimization to minimize CO\({}_{2}\) emissions and electricity costs, while the second stage uses model predictive control (MPC) to manage real-time uncertainties in PV generation and electric vehicle (EV) connections. The proposed method demonstrates clear benefits, including a 36% reduction in emissions and a 33% decrease in energy costs compared to a conventional EMS. However, the study presents several limitations. First, it lacks a statistical analysis of solution variability, such as standard deviation, which is crucial for validating the repeatability of the proposed approach. Second, the evaluation is limited to a simplified mononodal network, whereas real-world distribution systems are multi-nodal and subject to power flow constraints.