## 3 Solution Methodology
### Algorithms Used for Comparison  
To evaluate the effectiveness of the proposed approach, five widely used metaheuristic algorithms (MC, PSO, JAYA, GNDO, and MVO) were employed to solve the same optimization problem. These methods were selected for their previous use in the optimal operation of WTs within MGs. However, none had been applied to the specific challenge addressed in this study: the coordinated control of active and reactive power in WTs to improve economic, technical, and environmental performance indicators. All algorithms were implemented in their standard form--as commonly reported in the literature--and carefully tuned through a dedicated parameter optimization process to ensure optimal performance under identical conditions. This ensured a fair and consistent comparison framework. The main characteristics of each of the methods used for comparison are summarized below and detailed in the cited references.  
* The MC algorithm operates by generating a list of elite solutions obtained by evaluating random populations that are independently generated in each iteration. In the context of this research, each individual proposed by MC corresponds to a solution for the operation of WTs within the analyzed MG. In each iteration, MC generates a population, evaluates the fitness function of each solution, and stores the best one in an elite list. Finally, the best solution from the elite list is selected as the solution to the analyzed problem [43].
* The PSO is a bio-inspired optimization method based on the behavior of swarms or herds [44]. This algorithm considers both the individual behavior of each particle and that of the leader, i.e., the particle currently holding the best position in the solution space. By employing random values in each step of the particle swarm's evolution, the algorithm avoids local optima. Once the convergence criterion (typically defined by a maximum number of iterations) is met, all particles converge to the same location, which corresponds to the best solution. This behavior mirrors natural swarming, where the group converges to the most abundant food source in the environment.
* JAYA, named after the Sanskrit translation for _victory_[45], is a metaheuristic algorithm that combines features of evolutionary algorithms and swarm intelligence. This algorithm seeks the global best solutions within the populations it generates and discards the worst individuals. Its main difference from other population-based algorithms is that it does not rely on manually set parameters, which could potentially affect its efficiency.
* The GNDO, belonging to the family of mathematics-inspired techniques, operates based on a Gaussian distribution, and it features both local and global exploration phases [46]. In the former, the search for a new solution involves analyzing the mean and standard deviation of the population, while in the latter, a variety of random variables is used to explore a wider search space in pursuit of the optimal solution.
* The MVO is based on multiverse theory and emulates the presence of black and white holes for the exchange of information between multiple universes. Additionally, wormholes are employed to move the solution space from one universe to a location closer to the best universe [47].  
Each of these methods is applied following the same approach as the PGA; specifically, they are used to determine the active and reactive power dispatch scheme for the WTs installed within the MG. The same hourly power flow analysis based on successive approximations is employed to evaluate the objective functions related to operating costs, energy losses, and \(CO_{2}\) emissions, as well as the problem constraints. These elements are integrated through the proposed fitness function, which returns the impact of each individual generated during the iterative process of the optimization methodologies.