Active distribution networks (ADNs) are a typical cyber–physical system (CPS), which consist of two kinds of interdependent sub-networks: power networks (PNs) and communication networks (CNs). The combination of typical characteristics of the ADN includes (1) a large number of distributed generators contained in the PN, (2) load redistribution in both the PN and CN, and (3) strong interdependence between the PN and CN, which makes ADNs vulnerable to cross-domain cascading failures (CCFs). In this paper, we focus on the robustness analysis of the ADN against the CCF. Rather than via the rate of the clusters with size greater than a predefined threshold, we evaluate the robustness of the ADN using the rate of the clusters containing generators after the CCF. Firstly, a synchronous probabilistic model is derived to calculate the proportions of remaining normal operational nodes after the CCF. With this model, the propagation of the CCF in the ADN can be described as recursive equations. Secondly, we analyze the relationship between the proportions of remaining normal operational nodes after the CCF and the distribution of distributed generators, unintentional random initial failure rate, the interdependence between the sub-networks, network topology, and tolerance parameters. Some results are revealed which include (1) the more distributed generators the PN contains, the higher ADN robustness is, (2) the robustness of the ADN is negatively correlated with the unintentional random initial failure rate, (3) the robustness of the ADN can be improved by increasing the average control fan in of each node in the PN and the average power fan in of each node in the CN, (4) the robustness of the ADN with Erdos–Renyi (ER) network topological structure is greater than that with Barabasi–Albert (BA) network topological structure under the same average node degree, and (5) the robustness of the ADN is greater, when the tolerance parameters increase. Lastly, some simulation experiments are conducted and experimental results also demonstrate that the conclusions above are effective to improve the robustness of the ADN against the CCF.
Cyber–Physical Active Distribution Networks Robustness Evaluation against Cross-Domain Cascading Failures