Graph signal processing (GSP) has emerged as a powerful tool for practical
network applications, including power system monitoring. By representing power
system voltages as smooth graph signals, recent research has focused on
developing GSP-based methods for state estimation, attack detection, and
topology identification. Included, efficient methods have been developed for
detecting false data injection (FDI) attacks, which until now were perceived as
non-smooth with respect to the graph Laplacian matrix. Consequently, these
methods may not be effective against smooth FDI attacks. In this paper, we
propose a graph FDI (GFDI) attack that minimizes the Laplacian-based graph
total variation (TV) under practical constraints. In addition, we develop a
low-complexity algorithm that solves the non-convex GDFI attack optimization
problem using ell_1-norm relaxation, the projected gradient descent (PGD)
algorithm, and the alternating direction method of multipliers (ADMM). We then
propose a protection scheme that identifies the minimal set of measurements
necessary to constrain the GFDI output to high graph TV, thereby enabling its
detection by existing GSP-based detectors. Our numerical simulations on the
IEEE-57 bus test case 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.Comment: This work has been submitted to the IEEE for possible publication.
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