On the Exact Solution to a Smart Grid Cyber-Security Analysis Problem

TL;DR

This paper demonstrates that an $l_1$ relaxation technique can exactly solve a constrained cardinality minimization problem in smart grid cyber-security analysis, providing a new approach to vulnerability assessment.

Contribution

It introduces a novel proof that $l_1$ relaxation yields exact solutions for a specific security problem, differing from traditional mutual coherence and RIP-based methods.

Findings

Exact $l_1$ solution for cardinality minimization in smart grid security

Application to IEEE 118-bus and 300-bus systems

Polyhedral combinatorics-based proof

Abstract

This paper considers a smart grid cyber-security problem analyzing the vulnerabilities of electric power networks to false data attacks. The analysis problem is related to a constrained cardinality minimization problem. The main result shows that an $l_1$ relaxation technique provides an exact optimal solution to this cardinality minimization problem. The proposed result is based on a polyhedral combinatorics argument. It is different from well-known results based on mutual coherence and restricted isometry property. The results are illustrated on benchmarks including the IEEE 118-bus and 300-bus systems.