## 2 Remarks on the Topology of Microgrid
### Microgrid Applications  
Microgrid applications are diverse, with the most common being rural electrification in remote areas, industrial facilities requiring efficient energy management and resilience, military installations seeking energy independence and security, and urban or commercial environments benefiting from increased energy reliability. They can be implemented in various configurations, isolated from or connected to the main power grid, to address each sector's specific needs and challenges [35]. In rural areas, microgrids provide a viable solution for electrification, reducing dependence on fossil fuels and improving the quality of life. Operating in isolated mode is particularly useful in these areas, where the central grid infrastructure may need to be improved or non-existent [11]. In the industrial sector, microgrids enable more efficient energy management and the integration of DER. By reducing operational costs and enhancing the resilience of the facility's energy system, microgrids contribute significantly to overall efficiency [36]. Microgrids also have applications in the military sector, where energy independence and security are priorities. Operating autonomously and ensuring a continuous energy supply in emergencies is crucial. The following are outstanding examples of the practical implementation of optimal microgrid planning, which also present challenges inherent to their specific environments. First, the study in [11] describes using an particle swarm optimization (PSO) algorithm for energy planning of an isolated microgrid in Colombia. This system is designed to supply energy to a remote population of seven houses in a region with difficult access and high resource transportation costs. The optimization strategy focused on taking advantage of local natural resources, mainly due to the limited availability of conventional energy sources and logistical difficulties for regular supply. This application illustrates how geographic  
Figure 4: Schematic of a microgrid with renewable energy integration. and access particularities can condition design decisions in microgrid planning, focusing on sustainability and energy autonomy. On the other hand, the Gorona del Viento project on the island of El Hierro, Spain, implements a hybrid renewable energy system that combines wind energy with pumped hydroelectric storage. This project has enabled the island to operate nearly self-sufficiently, significantly reducing its dependence on traditional diesel generators. The system design takes advantage of the island's topography, using the La Caldera crater as an upper reservoir for water storage, which facilitates the accumulation of energy during periods of high wind production. However, challenges were faced during implementation, mainly due to the limited storage capacity of the reservoir, which resulted in reduced grid stability during periods of low wind speed [37]. This case highlights the importance of adapting system components to the geological and climatic characteristics of the site and how the combination of energy sources and storage strategies can help mitigate the intermittency of renewable sources. These examples highlight how the selection of optimization strategies and microgrid configuration can vary according to the local context and available resources, impacting both costs and carbon emission reductions. Table 2 provides an overview of microgrid applications across different sectors. The topology of microgrids is essential for their efficiency, stability, and sustainability, especially when integrating renewable sources. The choice of operation mode and electrical configuration influences a microgrid's flexibility and technical feasibility and adaptation to various applications, from rural areas to industrial and military environments. The following sections discuss sizing methodologies Moreover, exploring energy management strategies that optimize microgrid operation provides a comprehensive analysis of tools in microgrid energy planning.