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

•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.