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

TL;DR

This paper introduces a convex relaxation approach to estimate maximum load delivery in interconnected gas and power networks during severe disruptions, enabling fast and accurate capacity assessments for critical infrastructure resilience.

Contribution

It presents a novel mixed-integer convex relaxation of the joint Maximal Load Delivery problem, improving tractability and solution speed for multi-contingency scenarios.

Findings

Relaxation accurately bounds network capacities during severe disruptions.

Method converges to global optimum within ten seconds in tested scenarios.

Effective across networks from 25 to 1,191 nodes.

Abstract

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.