Multi-objective optimization of a renewable-powered H2 microgrid using fractional-order control

Renewable-powered hydrogen microgrids require coordinated control of electrolyzer operation, battery state-of-charge (SoC), and power balance under intermittent solar/wind generation and time-varying demand. This paper presents a reproducible multi-objective optimization framework that integrates fractional-order proportional–integral–derivative (FO-PID) control with genetic algorithms (GAs) and reinforcement learning (RL) to improve hydrogen production efficiency while reducing operational losses and preserving battery-friendly SoC behavior. The proposed approach is evaluated on a renewable-powered H2 microgrid model using five strategies: rule-based control, conventional order proportional–integral–derivative (PID), FO-PID, FO-PID tuned by GA (FO-PID + GA), and FO-PID with RL-based decision support (FO-PID + RL). Performance is assessed using hydrogen utilization, power-loss ratio, and a SoC stability index (SSI), where deviations outside the recommended 20%–90% operating window are penalized to discourage deep cycling and boundary stress. Results demonstrate that FO-PID + RL achieves the best overall trade-off among the objectives. Compared with the proportional–integral–derivative (PID) baseline, FO-PID + RL increases hydrogen utilization from 2.8 to 4.5 kg/h (≈60.7%) and reduces the power-loss ratio from 12.4% to 5.9% (≈52.4%), while improving SSI from 0.72 to 0.91, indicating smoother SoC trajectories and reduced stress. These outcomes confirm that combining fractional-order control with Pareto-based optimization and learning-based scheduling can enhance both efficiency and operational reliability in renewable-powered hydrogen microgrids.