A graph-theoretical characterization of power network vulnerabilities

This work is concerned with the security of a power network against components failure and external attacks. We model a power plant as a linear continuous-time descriptor system. We adopt the framework of structural control theory, and we associate a digraph with the power plant. We provide a necessary and sufficient graph theoretic condition for the existence of vulnerabilities that are inherent to the power network interconnection structure. From a system theoretic perspective, we generalize a known result on the structural rank of the transfer matrix of a state space system to take into account a set of algebraic constraints.