Relaxations of AC Maximal Load Delivery for Severe Contingency Analysis

TL;DR

This paper introduces convex relaxation techniques to efficiently approximate the maximum load delivery in severely damaged transmission networks, providing scalable solutions with high accuracy for large-scale systems.

Contribution

It demonstrates that convex relaxations can reliably and quickly solve the AC Maximal Load Delivery problem on large transmission networks, outperforming traditional methods.

Findings

Convex relaxations provide high-quality bounds for AC-MLD.

The proposed methods solve large-scale problems in under 20 seconds.

Effective on diverse network sizes from 70 to 6000 buses.

Abstract

This work considers the task of finding an AC-feasible operating point of a severely damaged transmission network while ensuring that a maximal amount of active power loads can be delivered. This AC Maximal Load Delivery (AC-MLD) task is a nonconvex nonlinear optimization problem that is incredibly challenging to solve on large-scale transmission system datasets. This work demonstrates that convex relaxations of the AC-MLD problem provide a reliable and scalable method for finding high-quality bounds on the amount of active power that can be delivered in the AC-MLD problem. To demonstrate their effectiveness, the solution methods proposed in this work are rigorously evaluated on 1000 N-k scenarios on seven power networks ranging in size from 70 to 6000 buses. The most effective relaxation of the AC-MLD problem converges in less than 20 seconds on commodity computing hardware for all 7000 of the scenarios considered.