Structural detectability analysis of cyber attacks for power grids via graph theory

Cyber-physical systems are pervasive in every walk of life. The safety performances of these systems are threatened by external malicious attacks and unforeseen failures. In terms of grid structural characteristics and graph theory, this study proposes a new framework to solve the problem of structural vulnerability which is caused by undetectable attacks in power grids. Based on the linear continuous-time descriptor system model, the digraph associated with structural matrix model for power grid is introduced in detail. To analyse the attack detectability in digraph, a series of basic properties are proposed about digraphs of structural power grids. Then an algorithm is proposed for obtaining the positions of the detection outputs to ensure left-invertible and observability for grid systems. In addition, an algorithm for judging whether there exists a structural vulnerability for the arrangement of the attack inputs and outputs of power grids is proposed, by which one can find disjoint paths if there exists structural vulnerability. Finally, some examples are shown to verify the effectiveness of the proposed algorithms