  Recent increases in gas-fired power generation have engendered increased
interdependencies between natural gas and power transmission systems. These
interdependencies have amplified existing vulnerabilities to 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 1,191 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.
