Resilient planning and operational management of renewable-integrated hydrogen refueling stations with multiple storage units under delivery delays

The large-scale deployment of hydrogen-powered transportation requires economically viable and operationally resilient control strategies for hydrogen refueling stations (HRSs) operating under renewable variability, dynamic hydrogen demand, and logistics-induced delivery delays associated with fueling hydrogen mobility. To address this, this study develops a relaxation-based model predictive control (RMPC) framework for a renewable-integrated HRS equipped with heterogeneous hydrogen storage units, battery energy storage systems (BESS), and dual participation in hydrogen and electricity markets. The system architecture incorporates high-pressure tanks dedicated to distinct fuel cell electric vehicle (FCEV) classes, along with auxiliary buffer and backup tanks that enable inter-storage routing and enhance flexibility in meeting demand. Hydrogen procurement from external markets is scheduled through the backup tank, providing temporal decoupling between uncertain deliveries and refueling requirements. Based on time-dependent concave delay functions, a logistics-aware delivery delay model is introduced to capture time-varying lead times arising from routing constraints, fleet availability, and congestion. This battery-hydrogen co-optimization strategy enhances operational flexibility and resilience, effectively decoupling on-site hydrogen supply from short-term market volatility and demand fluctuations. A convex relaxation approach addresses the complexity of binary tank-switching decisions, nonlinear dynamics, and inter-market coordination, while maintaining real-time scheduling capability. The proposed RMPC is assessed under idealized and delay-affected market conditions to establish bounds on service continuity and operating cost. In particular, coupling BESSs with hydrogen storage improves station resilience and economic feasibility. The proposed approach yields a significant economic advantage over conventional controllers, with simulations indicating up to a 57% increase in profit when using multi-day predictive optimization, while the HRS achieves >98% refueling availability and reduces energy costs by approximately 15% relative to baseline operation. These results demonstrate the potential of the proposed framework to enable robust, cost-effective, and scalable operation of next-generation hydrogen refueling infrastructure.