Robustness of cyber-physical power systems in cascading failure: Survival of interdependent clusters

In cyber-physical power systems, tiny failure generating in unilateral network may cause cascading failure iterative between physical power grid and communication network, and finally makes systems break into considerable clusters. In this paper, we find that considerable clusters respectively in physical power grid and communication network are mutually interdependent to survive in cascading failure. Taking account of survival clusters, we study robustness of cyber-physical power systems in various attack scenes. We employ IEEE Standard Bus test case and random network to model cyber-physical power systems. The numerical simulation illustrates that targeted attack disintegrates systems into more clusters than random attack, but with less nodes remained than random attack, which validates the positive correlation between average size of clusters and robustness of systems. Further, the simulation has proved the negative correlation between number of clusters and defined threshold of cluster size. Moreover, the simulation analysis on coupling interdependency and correspondence relation can guide rational allocation of inter-links in systems.