Protection Against Graph-Based False Data Injection Attacks on Power Systems

Graph signal processing (GSP) has emerged as a powerful tool for practical network applications, including power system monitoring. Recent research works focused on developing GSP-based methods for state estimation, attack detection, and topology identification using the representation of the power system voltages as smooth graph signals. Within this framework, efficient methods have been developed for detecting false data injection (FDI) attacks, which until now were perceived as nonsmooth with respect to the graph Laplacian matrix. Consequently, these methods may not be effective against smooth FDI attacks. In this article, we propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph total variation under practical constraints. We present the GFDI attack as the solution for a nonconvex constrained optimization problem. The solution to the GFDI attack problem is obtained through approximating it using ℓ₁ relaxation. A series of quadratic programming problems that are classified as convex optimization problems are solved to obtain the final solution. We then propose a protection scheme that identifies the minimal set of measurements necessary to constrain the GFDI output to a high graph TV, thereby enabling its detection by existing GSP-based detectors. Our numerical simulations on the IEEE-57 and IEEE-118 bus test cases reveal the potential threat posed by well-designed GSP-based FDI attacks. Moreover, we demonstrate that integrating the proposed protection design with GSP-based detection can lead to significant hardware cost savings compared to previous designs of protection methods against FDI attacks.