Graph-Theoretic Framework for Unified Analysis of Observability and Data Injection Attacks in the Smart Grid
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In this paper, a novel graph-theoretic framework is proposed to generalize the analysis of a broad set of security attacks, including observability and data injection attacks, that target the smart grid. First, the notion of observability attacks is defined based on a proposed graph-theoretic construct. In this respect, an algorithm is proposed to characterize the critical set of measurements which must be removed along with a certain measurement to make the system unobservable. It is then shown that for the system to be observable these critical sets must be part of a maximum matching over a proposed bipartite graph. In addition, it is shown that stealthy data injection attacks are a special case of these observability attacks. Then, various attack strategies and defense policies for observability and data injection attacks are shown to be amenable to analysis using variations of the formulated maximum-matching problem. The proposed framework is then shown to provide a unified basis for exact analysis of four security problems (among others), pertaining to the characterization of: 1) The sparsest stealthy attack, 2) The sparsest stealthy attack including a certain specific measurement, 3) A set of measurements which must be defended to thwart all potential stealthy attacks, and 4) The set of measurements, which when protected, can thwart any attack whose cardinality is below a certain threshold. A case study using the IEEE 14-bus system containing a set of 17 measurement units is used to corroborate the theoretical findings. In this case analysis, stealthy attacks of lowest cardinality are characterized and shown to have a cardinality equal to 2. In addition, it is shown that defending only 3 out of the 17 measurements is enough to thwart any stealthy attack with cardinality lower than 3, while defending a minimum of 13 measurements is needed to thwart all possible stealthy attacks.
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