Mathematical Formulation of Intelligent Management Algorithms for Isolated Microgrids: A Pareto-Based Critical Approach

This study proposes a simplified mathematical formulation for optimizing isolated microgrids, enhancing computational efficiency while preserving solution quality. The research focuses on the influence of Operation and Maintenance (O&M) costs for Non-Dispatchable Generators (NDGs) and the relationship between costs and pollutant emissions. The proposed simplification reduces computational requirements, improves result interpretability, and increases the scalability of optimization techniques. The O&M costs of photovoltaic and wind systems were excluded from the initial optimization and calculated afterward. A Student's t-test yielded a p-value of 87.3%, confirming no significant difference between the tested scenarios, ensuring that the simplification does not impact solution quality while reducing computational complexity. For emission-related costs, scenarios with single and multiple pollutant generators were analyzed. When only one generator type is present, modifications are needed to enable effective multi-objective optimization. To address this, two alternative mathematical formulations were tested, offering more suitable approaches for the problem. However, when multiple pollutant sources exist, cost and emission differences naturally define the problem as multi-objective without requiring adjustments. Future work will explore grid-connected microgrids and additional optimization objectives, such as loss minimization, voltage control, and device lifespan extension.