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Graph signal processing (GSP) has emerged as a powerful tool for practicalnetwork applications, including power system monitoring. Recent research hasfocused on developing GSP-based methods for state estimation, attack detection,and topology identification using the representation of the power systemvoltages as smooth graph signals. Within this framework, efficient methods havebeen developed for detecting false data injection (FDI) attacks, which untilnow were perceived as non-smooth with respect to the graph Laplacian matrix.Consequently, these methods may not be effective against smooth FDI attacks. Inthis paper, we propose a graph FDI (GFDI) attack that minimizes theLaplacian-based graph total variation (TV) under practical constraints. Wepresent the GFDI attack as the solution for a non-convex constrainedoptimization problem. The solution to the GFDI attack problem is obtainedthrough approximating it using $\ell_1$ relaxation. A series of quadraticprogramming problems that are classified as convex optimization problems aresolved to obtain the final solution. We then propose a protection scheme thatidentifies the minimal set of measurements necessary to constrain the GFDIoutput to a high graph TV, thereby enabling its detection by existing GSP-baseddetectors. Our numerical simulations on the IEEE-57 and IEEE-118 bus test casesreveal the potential threat posed by well-designed GSP-based FDI attacks.Moreover, we demonstrate that integrating the proposed protection design withGSP-based detection can lead to significant hardware cost savings compared toprevious designs of protection methods against FDI attacks.

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