## 1 Introduction  
### Problem Description  
In recent years, the global shift towards renewable energy sources and distributed generation technologies has significantly accelerated the transformation of electrical systems, driving improvements in sustainability, efficiency, and resilience [1]. In this evolving landscape, microgrids (MGs) have emerged as a key solution, given their ability to integrate a wide variety of distributed energy resources and operate flexibly in both grid-connected and islanded modes. This flexibility entails more efficient energy management, balances local generation and demand, improves system reliability, and contributes to reducing environmental impacts [2; 3]. Moreover, the growing global energy demand, in addition to the technical, economic, and environmental constraints of conventional power systems, further highlights the need for innovative and decentralized paradigms (e.g., MGs) to address the challenges of operating modern power systems [4; 5].  
MGs are small- to medium-scale systems that coordinate multiple distributed generators (DGs) to optimize the use of locally available energy resources [5]. Depending on system configuration and operational criteria, MGs can seamlessly transition between grid-connected [6] and islanded [7] operations. Among the renewable technologies integrated into MGs, wind turbines (WTs) play a prominent role due to their widespread availability, their ability to generate power around the clock, their low maintenance costs, and their lack of greenhouse gas emissions [8; 9]. These attributes align closely with global sustainability goals, particularly with those aimed at reducing dependence on fossil fuels and mitigating environmental degradation.  
The intelligent operation of renewable energy sources has been widely studied in recent years, with a particular emphasis on photovoltaic systems (PVs). Numerous optimization strategies have been proposed in this regard, often yielding high-quality solutions with low computational effort [10; 11; 12]. However, most of these studies lack a rigorous statistical evaluation of performance and repeatability, which is essential for ensuring operational reliability in real-world applications. Optimization strategies applied to MGs must guarantee the best possible performance in every execution while maintaining short processing times in order to effectively respond to the inherent variability of both generation and demand. Ultimately, these strategies should aim to enhance the economic, technical, and environmental performance of power systems.  
In contrast, wind generation has received less attention in the development of intelligent operation strategies despite its high potential to address emerging challenges, particularly the curtailment of renewable energy in countries with high levels of penetration [13]. Unlike PVs, WTs can operate continuously throughout the day, and when active power injection is not possible, their power converters can be leveraged to supply reactive power, thereby enhancing voltage support and improving system stability [14]. Nowadays, this characteristic is especially valuable in the global energy context, where the need to maximize the utilization of renewable resources is more urgent than ever. In this vein, the efficient operation of WTs within electrical networks, particularly in MGs, has become a critical research focus necessary for progressing toward more flexible, resilient, and sustainable power systems.