## 1 Introduction
### Proposed Optimization Methodology and Performance Validation  
In light of the research opportunities identified in the literature, this study addresses current challenges by proposing a novel optimization framework for WT-based MGs that is capable of managing the active and reactive power outputs from WTs while considering their operation in both grid-connected and islanded modes. The optimization objectives include the minimization of operating costs, energy losses, and \(CO_{2}\) emissions (critical performance indices in AC MG operation) while considering key technical constraints such as power balance, generator capacity limits, current thresholds, and voltage bounds, all of which reflect the real operational behavior of AC MGs. Due to the nonlinear and high-dimensional nature of the problem, metaheuristic algorithms are employed, given their proven ability to efficiently solve large-scale and complex tasks involving power systems optimization. To solve the proposed mathematical model, a two-stage optimization methodology is implemented. In the first stage, the PGA is used to determine the optimal dispatch of active and reactive power from WTs over a 24-hour horizon. In the second stage, the successive approximations (SA) method is applied to perform hourly power flow analyses, assessing the feasibility and quality of candidate solutions through a fitness function that aims to fulfill the established objectives while observing the problem's constraints. The choice of the PGA as the core optimization strategy is driven by its robust global search capability, resilience to premature convergence, and adaptability to highly constrained, nonlinear problems [32]. Its population-based approach enables a broad exploration of the solution space, which is particularly advantageous for high-dimensional tasks such as the joint control of active and reactive power in WTs. Moreover, although the PGA has been successfully applied in related contexts involving PVs and battery storage, its use in wind-based MG scenarios remains largely unexplored [31, 33, 34], which makes it a promising and technically justified candidate for addressing the multi-criteria energy management problem under study. In grid-connected mode, the MG assumes the presence of a main grid at the slack node, which is capable of supplying or absorbing power as required. In islanded mode, the slack node is replaced by a diesel generator, introducing generation constraints that must be observed to ensure long-term system reliability. The reverse power flow at the slack node is also restricted in this mode. To ensure a fair and thorough evaluation, several well-established metaheuristic algorithms were selected, adapted, and tuned as comparison methodologies, including PSO, MC simulation, the GA, the JAYA, the GNDO, and MVO. As summarized in Table 1, most of these algorithms have primarily focused on active power control, and only a few (notably PSO and MC) have been used to address active and reactive power regulation. Moreover, current studies tend to optimize economic and technical objectives, such as operating costs and energy losses, while often neglecting environmental impact as a key optimization criterion. For our comparison, the parameter types reported by the original authors (e.g., population size, number of iterations, learning rates) were preserved to ensure methodological consistency. These parameters were then tuned within literature-supported ranges to maximize the performance of each algorithm for the studied problem. Furthermore, all optimization methods employed the same SA load flow model to evaluate the feasibility and system-level impact of the proposed solutions. This ensured that the comparison was carried out under homogeneous technical conditions, making the benchmarking process both fair and technically sound. To validate the proposed approach, a literature-reported 33-node MG model was adapted and tested in both operating modes. The system incorporated variable generation and demand profiles based on the typical conditions of Colombia.