Minimum Sparsity of Unobservable Power Network Attacks

TL;DR

This paper characterizes the minimum sparsity of unobservable power injection attacks in power networks, providing a polynomial-time method to identify such attacks and analyzing how PMU deployment affects their impact.

Contribution

It introduces a simple formula for the sparsest unobservable attacks based on vertex connectivity and offers a polynomial-time algorithm to find all such attacks.

Findings

The sparsest unobservable attack size is $ K(G^M)+1$ with probability one.

Adding more PMUs reduces the maximum potential impact of unobservable attacks.

The method is validated on standard power system models, showing practical applicability.

Abstract

Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $\kappa(G^M) + 1$, where $\kappa(G^M)$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact as functions of the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.