This paper proposes a trilevel mixed-integer formulation to coordinately schedule the electricity-hydrogen distribution network (EHDN) with resilience consideration. The rescue hydrogen distribution system is first studied and modeled based on the roadway transportation and vehicle-to-grid power supply of mobile hydrogen energy resources (MHERs). Various practical constraints on traffic capacity, travel distances and time delaying of hydrogen transportation are incorporated. Then, to improve the economic viability of EHDN to fulfill the load survivability requirement in disastrous situations, we propose a risk-constrained trilevel optimization formulation. In particular, the resilience constraint with a $\min -\max$ mixed-integer program structure is introduced, which ensures the post-event service preservation by co-optimizing the re-routing of MHERs and network reconfiguration under worst-case damage scenario. Then, by making use of its structural properties, this complex formulation is solved by a customized nested column-and-constraint generation (NC&CG) algorithm with effective enhancements. Numerical results on an exemplary EHDN indicate that the proactive deployment and adaptive relocation of MHERs provide an economically feasible solution to achieve grid resiliency target. Also, comparing to the standard NC&CG, our improved customization demonstrates a superior performance that drastically reduces the computation time, and thus enables efficient emergency response and disaster relief with synergistic network operations.

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.

The advanced switching techniques enable the topology reconfiguration of microgrids (MGs) in active distribution network. In this paper, we enhance and generalize the traditional reconfiguration strategy resorting to the concept of “dynamic MGs” (i.e., the reorganization of MGs boundaries), to achieve a higher operational feasibility against the emergency islandings. Also, a risk-averse two-stage mixed integer conic program model is presented to support the networked MGs planning with generalized reconfiguration decisions. The MGs capacity expansion and seasonal reconfiguration decisions are made in the first stage, and validated under stochastic islanding scenarios in the second stage, where the network operations are captured by a second-order conic program (SOCP). Furthermore, a conditional value-at-risk (CVaR) measure is involved to quantitatively control the islanding risks. By theoretically proving the strong duality of the SOCP subproblem, we develop and customize Benders decomposition method with the guaranteed finite convergence to the optimal value. Finally, numerical results on 33- and 56-bus networked MGs validate the effectiveness of proposed reconfiguration strategy as well as planning approach. Our method demonstrates a cost-saving up to 22.56% when comparing to the traditional scheme with fixed MGs boundaries.

In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional, and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage, and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error, and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency, and robustness of dispatch decisions.

Integrated Hydrogen-Electrical (IHE) microgrids are desirable testbeds for the practice of carbon-neutral energy supply. This paper studies the IHE microgrids planning (IHEMP) under a dynamic perspective. To keep track with the fast development of hydrogen industry, we propose a multistage stochastic mixed-integer program (MS-MIP) formulation. It comprehensively considers the siting and sizing decisions of IHE microgrids, the dynamic expansion of distributed energy facilities, and the detailed operational model to derive a robust, flexible and profitable investment policy. Moreover, a scenario-tree based sampling strategy is leveraged to capture both the large-scale strategic uncertainties (e.g., the long-term growth of electric loads and hydrogen refueling demands, as well as the cost changes of system components) and fine-scale operating uncertainties (e.g., random variation of renewable energy outputs and loads) under different time scales. As the resulting formulation could be computationally very challenging, we develop a nested decomposition algorithm based on Stochastic Dual Dynamic Integer Programming (SDDiP). Case studies on exemplary IHE microgrids validate the effectiveness of our dynamic planning approach. Also, the customized SDDiP algorithm shows a superior solution capacity to handle large-scale MS-MIPs than the state-of-the-art solver (i.e., Gurobi) and a popular scenario-oriented decomposition method (i.e., progressive hedging algorithm).

This paper presents a chance constrained stochastic conic program model for networked microgrids planning. Under a two-stage optimization framework, we integrate a multi-site microgrids investment problem and two sets of operational problems that correspond to the grid-connected and islanding modes, respectively. To handle the uncertain nature of renewable energy generation and load variation, as well as the contingent islanding caused by external disruptions, stochastic scenarios are employed to capture randomness and a joint chance constraint is introduced to control the operational risks. A second-order conic program (SOCP) formulation is also utilized to accurately describe the AC optimal power flow (OPF) in operational problems. As the resulting mixed integer SOCP model is computationally difficult, we customize the bilinear Benders decomposition with non-trivial enhancement techniques to deal with practical instances. Numerical results on 5-and 69-bus networked microgrids demonstrate the effectiveness of the proposed planning model and the superior performance of our solution algorithm.