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• A CPHVA is proposed to evaluate the vulnerability of nodes in islanded MG. • The interruption problem in communicators is solved by path reconstruction. • The interruption problem in sensors is solved by predictive compensation. • A novel secondary control method is proposed to improve the control effect on DERs. Recently, more and more consensus-based hierarchical control methods are proposed in micro-grid. The main components of these methods are primary and secondary controllers. And they are usually used to adjust the output frequency and voltages of distributed energy resources. But the implementation of these methods is highly dependent on the communication network which is consisted by sensors and communicators. Once the data transmit of some sensors or communicators is interrupted, it will directly affect the control effect of hierarchical control. To solve the above problems, a cyber-physical cooperative response strategy is proposed in this paper. The main designs are as follows: (1) To solve the interruption problem among communicators, there are two defense methods proposed in the cyber layer: path planning and path reconstruction. Both methods are combined with cyber-physical hybrid vulnerability assessment and improved genetic algorithm; (2) To solve the interruption problem in the output channels of sensors, a distributed predictive compensation method combined with extreme learning machine and model predictive control is proposed in physical layer; (3) Based on the designs in (1) and (2), a novel secondary controller is proposed in this paper. Finally, the simulation results confirm the effectiveness of the proposed cooperative response strategy. [ABSTRACT FROM AUTHOR]

• Considerable clusters are mutually interdependent to stay alive in cascading failure. • Heterogeneity of nodes in physical power grid, distributed generator and substation. • In physical power grid, the cluster with one distributed generator can stay alive. • The positive correlation between average size of clusters and robustness of systems. • The simulation analysis can guide rational allocation of inter-links in systems. 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. [ABSTRACT FROM AUTHOR]