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Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation's effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem's globally optimal solution within ten seconds. [ABSTRACT FROM AUTHOR]

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]