Multi-Objective Optimization of Hybrid Renewable Energy Systems (Solar–Wind–Battery) for Microgrids Using an Enhanced NSGA-II with Uncertainty and Carbon Tax Integration

Hybrid Renewable Energy Systems (HRES) integrating solar photovoltaic (PV), wind turbines (WT), and battery energy storage systems (BESS) are critical for sustainable microgrids, addressing energy demands while minimizing environmental impact. This study proposes an enhanced Non-dominated Sorting Genetic Algorithm II (NSGA-II) that incorporates Monte Carlo simulation for meteorological uncertainties and carbon tax penalties in the cost function. The quad-objective framework minimizes total annualized cost (TAC) including carbon tax, loss of power supply probability (LPSP), CO2 emissions, and maximizes renewable fraction (RF). Using real data from Dakhla, Morocco, the Pareto front yields solutions with TAC ranging from $122,100 to $205,800, LPSP below 0.08, emissions under 36 tons/year, and RF exceeding 95% in optimal cases. The enhanced NSGA-II improves convergence by 18% and diversity by 22% compared to standard NSGA-II and Gravitational Search Algorithm (GSA). Sensitivity analysis on carbon tax shows a 15% increase in RF at higher rates, offering policy insights. This novel approach provides a robust tool for engineers and policymakers, aligning with UN Sustainable Development Goals 7 (Affordable and Clean Energy) and 13 (Climate Action).