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In this paper, a novel graph-theoretic framework is proposed to generalizethe analysis of a broad set of security attacks, including observability anddata injection attacks, that target the state estimator of a smart grid. First,the notion of observability attacks is defined based on a proposedgraph-theoretic construct. In this respect, a structured approach is proposedto characterize critical sets, whose removal renders the system unobservable.It is then shown that, for the system to be observable, these critical setsmust be part of a maximum matching over a proposed bipartite graph. Inaddition, it is shown that stealthy data injection attacks (SDIAs) constitute aspecial case of these observability attacks. Then, various attack strategiesand defense policies, for observability and data injection attacks, are shownto be amenable to analysis using the introduced graph-theoretic framework. Theproposed framework is then shown to provide a unified basis for analysis offour key security problems (among others), pertaining to the characterizationof: 1) The sparsest SDIA; 2) the sparsest SDIA including a certain measurement;3) a set of measurements which must be defended to thwart all potential SDIAs;and 4) the set of measurements, which when protected, can thwart any SDIA whosecardinality is below a certain threshold. A case study using the IEEE 14-bussystem with a set of 17 measurements is used to support the theoreticalfindings.

Graph-Theoretic Framework for Unified Analysis of Observability and Data Injection Attacks in the Smart Grid