Optimal sizing of isolated photovoltaic-hydrogen microgrids using covariance matrix adaptation evolution strategy considering real-gas modeling of hydrogen

This paper investigates the application of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to the optimal sizing of isolated photovoltaic-hydrogen microgrids. Accurate sizing of system components—particularly photovoltaic (PV) panels and hydrogen energy storage systems (HESS)—is critical to ensuring cost-effectiveness, energy autonomy, and operational reliability. This study introduces an advanced HESS model based on real gas behavior, offering improved physical realism over conventional ideal-gas approximations. While metaheuristic optimization methods such as genetic algorithms (GA) and particle swarm optimization (PSO) are widely used in microgrid design, Evolution Strategies (ES) remain significantly underutilized, despite their strong performance on complex, high-dimensional problems. CMA-ES, in particular, requires minimal parameter tuning and adapts effectively to non-convex, multimodal landscapes. A comparative evaluation of five evolutionary algorithms including 4 ES variants shows that CMA-ES avoids premature convergence, unlike GA, and achieves a 26 % improvement in final fitness value, demonstrating superior robustness to difficult problems and solution quality. While the No Free Lunch Theorem reminds us that no algorithm is universally optimal, this work highlights CMA-ES as a highly usable, plug-and-play tool with excellent performance across a wide range of problem types—making it especially suitable for real-world microgrid design applications.