Hydrogen-Based Networked Microgrids Planning Through Two-Stage Stochastic Programming With Mixed-Integer Conic Recourse

Networked microgrids that integrate the hydrogen fueling stations (HFSs) with the on-site renewable energy sources (RES), power-to-hydrogen (P2H) facilities, and hydrogen storage could help decarbonize the energy and transportation sectors. In this paper, to support the hydrogen-based networked microgrids planning subject to multiple uncertainties (e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles), we propose a two-stage stochastic formulation with mixed integer conic program (MICP) recourse decisions. Our formulation involves the holistic investment and operation modeling to optimally site and configure the microgrids with HFSs. The MICP problems appearing in the second-stage capture the nonlinear power flow of networked microgrids system with binary decisions on storage charging/discharging status and energy transactions (including the trading of electricity, hydrogen, and carbon credits to recover the capital expenditures). To handle the computational challenges associated with the stochastic program with MICP recourse, an augmented Benders decomposition algorithm (ABD) is developed. Numerical studies on 33- and 47-bus exemplary networks demonstrate the economics viability of electricity-hydrogen coordination on microgrids level, as well as the benefits of stochastic modeling. Also, our augmented algorithm significantly outperforms existing methods, e.g., the progressive hedging algorithm (PHA) and the direct use of a professional MIP solver, which has largely improved the solution quality and reduced the computation time by orders of magnitude. Note to Practitioners - This paper proposes an optimal planning model for electricity-hydrogen microgrids with the renewable hydrogen production, storage, and refueling infrastructures. Our planning model is extended under a two-stage stochastic framework to address the multi-energy-sector uncertainties, e.g., RES generation, electric loads, and the refueling demands of hydrogen vehicles. The first-stage problem is to optimize the siting and sizing plan of microgrids. Then, in the second-stage problem, the coordinated scheduling of electricity and hydrogen supply systems is modeled as second-order conic programs (SOCPs) to accurately capture the power flow representation under stochastic scenarios. Also, the logical constraints with binary variables are introduced to describe the energy transactions and storage operations, which results in an MICP recourse structure. Note that the stochastic MICP formulation could be very challenging to compute even with a moderate number of scenarios. One challenge certainly comes from integer variables that cause the problem nonconvex. Another challenge follows from the fact that the strong duality of SOCPs might not hold in general. To mitigate those two challenges, we prove that the continuous relaxation of our recourse problem has strong duality, and make use of that continuous relaxation and other enhancements to design an augmented decomposition algorithm. As revealed by our numerical tests, the proposed decomposition method outperforms PHA in both the solution quality and computational efficiency. Comparing to the PHA, our ABD method often achieves tighter bounds with trivial optimality gaps. Also, it could reduce the computation time by orders of magnitude. With the help of advanced analytical tool, the proposed planning framework can be readily implemented in real-world applications.