Identifying the Smallest Adversarial Load Perturbation that Renders DC-OPF Infeasible

TL;DR

This paper develops methods to identify the smallest load perturbation that makes the DC-OPF problem infeasible, with applications in grid security and robustness, by formulating a nonconvex optimization problem and providing bounds on attack size.

Contribution

It introduces a novel nonconvex formulation for adversarial load perturbations in DC-OPF and proposes a control policy to efficiently estimate bounds on attack size.

Findings

The proposed methods provide tight bounds on minimal adversarial perturbations.

Benchmarking shows the approach outperforms existing lower bounds from Gurobi's solver.

The approach is effective on small to medium-sized power system test cases.

Abstract

What is the globally smallest load perturbation that renders DC-OPF infeasible? Reliably identifying such "adversarial attack" perturbations has useful applications in a variety of emerging grid-related contexts, including machine learning performance verification, cybersecurity, and operational robustness of power systems dominated by stochastic renewable energy resources. In this paper, we formulate the inherently nonconvex adversarial attack problem by applying a parameterized version of Farkas' lemma to a perturbed set of DC-OPF equations. Since the resulting formulation is very hard to globally optimize, we also propose a parameterized generation control policy which, when applied to the primal DC-OPF problem, provides solvability guarantees. Together, these nonconvex problems provide guaranteed upper and lower bounds on adversarial attack size; by combining them into a single optimization problem, we can efficiently "squeeze" these bounds towards a common global solution. We apply these methods on a range of small- to medium-sized test cases from PGLib, benchmarking our results against the best adversarial attack lower bounds provided by Gurobi 12.0's spatial Branch and Bound solver.