Reflection of Cyber and Physical Stresses in Smart Grids on their Graph Signals

Graph signal processing has been shown to provide a unique platform and new perspective for representing and analyzing power system measurements. In this paper, the effects of various cyber and physical stresses, as well as their differences on the graph signals of the system and their spectral domain are presented and discussed. Specifically, graph Fourier transform (GFT) and the local smoothness corresponding to the graph signals are presented as tools for the characterization of the effects of stresses. Particularly, various cyber-attacks including denial-of-service, replay attack, ramp attack, and delay attack are considered on the time-series associated with the voltage angle measurements. An analysis of the relation of the degrees of the nodes under cyber-attack with the GFT of the associated graph signal has also been presented. Finally, a comparative analysis of the effects of cyber and physical stresses on the graph spectrum in the context of detecting and locating stresses in the smart grid are presented.