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Recent increases in gas-fired power generation have engendered increasedinterdependencies between natural gas and power transmission systems. Theseinterdependencies have amplified existing vulnerabilities to gas and powergrids, where disruptions can require the curtailment of load in one or bothsystems. Although typically operated independently, coordination of thesesystems during severe disruptions can allow for targeted delivery to lifelineservices, including gas delivery for residential heating and power delivery forcritical facilities. To address the challenge of estimating maximum jointnetwork capacities under such disruptions, we consider the task of determiningfeasible steady-state operating points for severely damaged systems whileensuring 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 convexrelaxation of the MLD problem. Then, to demonstrate the relaxation'seffectiveness in determining bounds on network capacities, exact and relaxedMLD formulations are compared across various multi-contingency scenarios onnine joint networks ranging in size from 25 to 1,191 nodes. Therelaxation-based methodology is observed to accurately and efficiently estimatethe impacts of severe joint network disruptions, often converging to therelaxed MLD problem's globally optimal solution within ten seconds.

Convex Relaxations of Maximal Load Delivery for Multi-contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks