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An increasing dependence on natural gas has amplified existing vulnerabilities to the power grid, including disruptions to gas transmission networks from natural and man-made disasters. To address the operational challenges arising from these disruptions, we consider the problem of estimating the steady-state operating capacity of a damaged gas pipeline network while ensuring the maximal delivery of load. Specifically, we formulate the mixed-integer nonconvex maximal load delivery (MLD) problem, which proves difficult to solve on large-scale networks. To address this challenge, we present a relaxation of the MLD problem and use it to determine bounds on the transport capacity of a gas pipeline system. A rigorous computational evaluation over network models ranging in size from 11 to 4 , 197 junctions shows that the relaxation-based method is suitable for analyzing the impacts of multi-contingency network disruptions, often converging to the optimal solution of the relaxation in less than ten seconds. • Maximal Load Delivery (MLD) analysis estimates the capacity of a damaged gas system. • Relaxations of gas network physics increase the tractability of an MLD analysis. • Rigorous benchmarking illustrates computational advantages of the relaxations. • MLD analyses can help estimate the effects of natural disasters on gas networks. [ABSTRACT FROM AUTHOR]

This paper studies the restoration of a transmission system after a significant disruption such as a natural disaster. It considers the co-optimization of repairs, load pickups, and generation dispatch to produce a sequencing of the repairs that minimizes the size of the blackout over time. The core of this process is a Restoration Ordering Problem (ROP), a non-convex mixed-integer nonlinear program that is outside the capabilities of existing solver technologies. To address this computational barrier, the paper examines two approximations of the power flow equations: The DC model and the recently proposed LPAC model. Systematic, large-scale testing indicates that the DC model is not sufficiently accurate for solving the ROP. In contrast, the LPAC power flow model, which captures line losses, reactive power, and voltage magnitudes, is sufficiently accurate to obtain restoration plans that can be converted into AC-feasible power flows. An experimental study also suggests that the LPAC model provides a robust and appealing tradeoff between accuracy and computational performance for solving the ROP. [ABSTRACT FROM AUTHOR]