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

arXiv: https://arxiv.org/abs/2507.07850 · HTML: https://mlsanity.com/paper/2507.07850/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2025.

## Built on by (most cited first, 2 of 2)

- [Generating adversarial inputs for a graph neural network model of AC power flow](https://mlsanity.com/paper/2602.17975/) (2026)
- [Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment](https://mlsanity.com/paper/2608.30201/) (2026)

## Abstract (arXiv)

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.