Cascading Failure Vulnerability Analysis in Interdependent Power Communication Networks

Smart grid is a cyber-physical system with interdependent power grid and communication network. Such interdependence make the smart grid fragile against cascading failures, where an initial failure in communication network may lead to further failures in power grid, and vice versa. We prevent such inter-network cascading failure by stopping an initial failure from propagating. This is achieved by providing a sufficient number of power-disjoint communication routes between power nodes and control center. The number of power-disjoint routes is a robustness metric. We aim to maximize robustness by configuring the interdependence relationship between power grid and communication networks. Such relationship indicates which power node supplies energy to which communication node, and which communication route is used to connect which power node to the control center. Following Menger's Theorem, we transform such configuration problem into a Maxflow problem and solve it using the simplex algorithm. We have evaluated the proposed method through extensive simulations. The results confirm the optimality and computational efficiency of the proposed method. The number of power-disjoint routes increases with an increase in the network size, but can never exceed the number of node-disjoint routes for a same network.

Electrical power communication networks undertake complicated power services. They interact with physical power grids all the time, which will result in a high risk to power grids when their electric power communication network is attacked. Therefore, to improve the reliability of power systems, it is of great significance to identify the key links of communication networks. Existing research studies focus more on the risk of power communication services undertaken by communication links, which ignores the frequent interaction between power grids and communications networks. In this paper, from a multi-layer network perspective, an assessment method of communication equipment is proposed in view of the operation characteristics of nodes in different systems as well as the dynamic fault propagation between homogeneous communication nodes. Firstly, we build a model of cyber-physical power interdependent network. Then, for communication nodes, a dynamic model is adopted for cascading failure among the nodes based on the load-capacity model. Afterward, we define an index to evaluate the node importance considering characteristics of the operation of both communication networks and power grids. Finally, a local power grid is taken as an example for verification by comparing the effects of different indexes. The simulation results demonstrate the validity of the evaluation method proposed.

In smart power grid, power grid and communication network are connected and mutually dependent. The failure in power grid might cause failures in communication network, and vice versa. A tiny failure in either of them could trigger cascade of failures within the entire system. In this paper, we focus on understanding the structure of smart power grid and studying the underlying network model, their interactions, relationships and how cascading failures occur in the system. We propose a practical model for smart power grid as interdependent complex network. The interdependency between two networks is `oneto-multiple': each node in the communication network has only one support link from the power grid, while each node in power grid is connected to multiple communication nodes. We study the effect of cascading failures using percolation theory, and present detailed mathematical analysis of failure propagation in the system. We analyze the robustness of our model caused by random attacks or failures by calculating the size of functioning parts in both networks. Using simulations, we prove that there exists a threshold for the proportion of faulty nodes, beyond which the system collapses. Also we determine the critical values for different system parameters. To the best of our knowledge, this is the first work that models smart grid as interdependent complex networks and studies its fault tolerance.

Epigenetic communication through histone and cytosine modifications is essential for gene regulation and cell identity. Here, we propose a framework that is based on a chromatin communication model to get insight on the function of epigenetic modifications in ESCs. The epigenetic communication network was inferred from genome-wide location data plus extensive manual annotation. Notably, we found that 5-hydroxymethylcytosine (5hmC) is the most-influential hub of this network, connecting DNA demethylation to nucleosome remodeling complexes and to key transcription factors of pluripotency. Moreover, an evolutionary analysis revealed a central role of 5hmC in the co-evolution of chromatin-related proteins. Further analysis of regions where 5hmC co-localizes with specific interactors shows that each interaction points to chromatin remodeling, stemness, differentiation, or metabolism. Our results highlight the importance of cytosine modifications in the epigenetic communication of ESCs.

Optimization and control of cyber–physical power systems under dual-network interactive cascading failure

Influential nodes act as a hub for information transmission in a command and control network. The identification of influential nodes in a network of this nature is a significant and challenging task; however, it is necessary if the invulnerability of the network is to be increased. The existing k-shell method is problematic in that it features a coarse sorting granularity and does not consider the local centrality of nodes. Thus, the degree of accuracy with which the influential nodes can be identified is relatively low. This motivates us to propose a method based on an integral k-shell to identify the influential nodes in a command and control network. This new method takes both the global and local information of nodes into account, introduces the historical k-shell and a 2-order neighboring degree, and refines the k-shell decomposition process in a network. Simulation analysis is carried out from two perspectives: to determine the impact on network performance when influential nodes are removed and to obtain the correlation between the integral k-shell value and its propagation value. The simulation results show that the integral k-shell method, which employs an algorithm of lower complexity, accurately identifies the influence of those nodes with the same k-shell values. Furthermore, the method significantly improves the accuracy with which the influential nodes can be identified.

Most existing studies model interdependent networks as simple network systems consisting of two or more undirected subnets, and the interdependent edges between the networks are undirected. However, many real-world interdependent networks are coupled by a directed subnet and an undirected subnet, such as supply chain networks coupled with cyber networks, and cyber manufacturing networks coupled with service networks. Therefore, in this work, we focus on a ubiquitous type of interdependent network-the directed-undirected interdependent network-and research the cascading failures of directed-undirected interdependent networks with different coupling patterns. Owing to the diversity of coupling patterns to realistic interdependent network systems, we introduce two types of interdependent edges (i.e., directed-to-undirected and undirected-to-directed interdependent edges). On this basis, we generated different types of directed-undirected interdependent networks with varying coupling patterns (i.e., one-to-one, one-to-many, and many-to-one) and investigated the cascading failure robustness of these types of networks. Finally, we explored the cascading robustness of directed-undirected interdependent networks under two different attack strategies (single-node attack and multi-node attack). Through extensive experiments, we have obtained some meaningful findings: (1) the cascading robustness of directed-undirected interdependent networks is positively related to the overload tolerance coefficient and load exponential coefficient; (2) high-degree nodes and high-in-degree nodes should be protected to improve the cascading robustness of directed-undirected interdependent networks; (3) the cascading robustness of one-to-many interdependent networks can be improved by adding directed-to-undirected interdependent edges; and the cascading robustness of many-to-one interdependent networks can be improved by adding undirected-to-directed interdependent edges.

Critical infrastructures, including those that concern the nation's economy and security such as electrical power systems, water distribution systems and transportation systems, are becoming more and more interdependent with each other. Although they bring unprecedented improvements on efficiency and flexibility, the interdependent relations enable failures in one network to propagate and impact the performance of other coupled networks. Cascading failures is one such phenomenon that creates dramatic damages to critical infrastructures, where a small initial shock can get escalated due to the intricate dependencies and result in system-wide collapses. This dissertation aims to understand and mitigate the root cause of the seemingly unexpected large-scale cascading failures by characterizing and modeling the inherent dependencies between and within different networks. A main finding is that allocating the available redundancies uniformly across the system maximizes the robustness against random failures. We support this thesis statement with different networks and attack types: flow-carrying networks under random and targeted attack, interdependent flow-carrying networks under random attacks, and interdependent cyber-physical networks under random attacks. In the flow redistribution network, we propose a global and equal flow redistribution model to capture the cascading failure dynamics. In the case of random attacks, we derive the final system size and critical attack size, and prove that the optimal robustness is reached when system redundancy is allocated uniformly. For targeted attacks, we propose the optimization problem of finding the best k lines to attack so as to minimize the number of alive lines at the steady-state, to reveal the worst-case attack vulnerability of the system. In interdependent flow-carrying networks, we study a model where the flow of a failed line is redistributed partially within the network that the failed line belongs to, with the rest being shed to other coupled networks. Analyzing the cascading failures in this model, we show that interdependence has a multi-faceted impact on system robustness in that as the level of coupling increases, the chance for both networks to survive or collapse concurrently increases, whereas it becomes more difficult for each component network to survive on its own. To understand the robustness of integrated cyber-physical systems (CPSs), we develop a novel interdependent system model to capture the inherently different failure cascade characteristics of each component network; i.e., the cyber and the physical networks are governed by different cascade rules to be able to function. We demonstrate the ability of our model to capture the unexpected nature of large-scale cascading failures in CPSs, and provide insights on improving system robustness by proposing optimal redundancy allocation schemes.

Performance and reliability of electrical power grids under cascading failures

Influence maximization refers to selecting a small number of influential nodes in a given network to maximize the influence affected by the subset. In social network analysis and viral marketing, influence maximization is greatly significant. The greedy-based algorithm is time-consuming in estimating the expected influence diffusion of a given node set, which is unsuitable for large-scale network. The traditional heuristics often have the problem of low accuracy. In this study, in order to solve the influence maximization problem more effectively, a meta-heuristic discrete crow search algorithm (DCSA) using the intelligence of crow population is proposed. In DCSA, a new coding mechanism and discrete evolution rules are constructed. The degree-based initialization method and the random walk strategy are adopted to enhance the search ability. Moreover, according to the network topology, influential nodes Candidates are generated to avoid blindness in the process of crow search. Extensive experiments are conducted on six real-world social networks under independent cascade (IC) model, the results show that DCSA outperforms other state-of-the-art algorithms and obtains comparable influence diffusion results to CELF but with lower time complexity.

The smart grid has evolved into cyber-physical power system (CPPS) with the integration of information and communication technologies (ICTs). CPPS can be treated as a typical hierarchical control system (HCS) which can be divided into two parts: power grid and communication network, and four layers: physical layer, secondary device layer, zone control layer and control layer. Compared with traditional power systems, CPPS will face new contingencies, especially from communication networks which can cause cascading consequences. To address this challenge, a vulnerability assessment using double power flow method is proposed in this paper. In addition, a whole CPPS model including four layers is presented. The model is based on the IEEE 39-bus network using MATLAB and MATPOWER toolbox. The model contains double power flows, one is to simulate the virtual power flow driven by the decision from the control centre and second one is to simulate the actual power flow. During a cyber-attack, the results from the double power flow method demonstrate a difference which serves as an indicator that a cyber-attack has occurred. The proposed novel vulnerability assessment index considers cyber latency, voltage variation and node centrality as three key parameters in comparing the importance of different nodes. The results can quantify the vulnerabilities in cyber nodes and assess the impact for cyber security strategy.

To study the underlying organizing principles of various complex systems, designing an efficient graph-based model for data representation, is a fundamental aspect. As the topological structure of the network changes over time, it is a challenging task to design a communication system having ability to respond to randomly changing traffic. We are interested to find out the suitable and fair traffic flow rates to each system for getting optimal system utility using dynamic complex network model. In this context, we design and simulate a growth model of the data communication network based on the dynamics of in-flowing links which is motivated by the concept that newly added node will connect to the most influential nodes already present in the system. The connectivity distribution of the evolved communication networks follows power law form, free from network scale. We analyze Kelly’s optimization framework for a rate allocation problem in communication networks at different time instants, and optimal rates are obtained with the consideration of arbitrary communication delays.

Electric power has become an essential part of daily life: we plug our electronic devices in, switch our lights on, and expect to have power. As the availability of power is usually taken for granted in modern societies, we mostly feel annoyed at its absence and perceive the importance of power during outages which have severe effects on the public order. Blackouts have had disastrous consequences for many countries and they continue to occur frequently. Such examples demonstrate the necessity for careful analysis and planning of power grids, to ultimately increase the reliability of power grids. The power grids have evolved due to economic, environmental and human-caused factors. In addition to the contingency analysis, nowadays, the operation and planning of power grids are facing many other challenges (such as demand growth, targeted attacks, cascading failures, and renewable energy integration). Thus, many questions arise, including: which buses (nodes) to connect with a new line (link)? What are the impacts of malicious attacks on power grids? How may an initial failure result in a cascade of failures? How to prepare for the integration of renewable energy? Answering such questions requires developing new concepts and tools for analysing and planning of power grids. Power grids are one of the largest and the most complex man-made systems on earth. The complex nature of power grids and its underlying structure make it possible to analyse power grids relying on network science. The applications of network science on power grids have shown the promising potential to capture the interdependencies between components and to understand the collective emergent behaviour of complex power grids. This thesis is motivated by the increasing need of reliable power grids and the merits of network science on the investigation of power grids. In this context, relying on network science, we model and analyse the power grid and its near-future challenges in terms of line removals/additions, malicious attacks, cascading failures, and renewable integration.

Cascading failures has seen as deadly on the network that causing sudden great damage in a different area. In the everyday life, different traffic loads can be carried by different networks those traffic loads whose values are changing from the load forwarding in the equivalent network and interruption provoked by interdependent network. Amount of opposed types of interdependencies demonstrate that higher interdependency drives to a smaller possibility of a wide blackout, inter- dependencies between networks are modeled and process of cascade failure is learned regarding their effects on the propagation failure. For then, reinstallation effects count on the activation timing, reinstallation possibility and primacy of the reinstallation actions along with the additional interruption. In this work, interdependencies between networks are modeled and the cascade failure process is learned desiring their effects on failure propagation. Our results demonstrate the necessity of reducing the high cascading failure by designing and controlling interdependent network sufficiently. Besides, when the transmission inability is below the maximum values some of power system can be useful.

Past events have revealed that widespread blackouts are mostly a result of cascading failures in the power grid. Understanding the underlining mechanisms of cascading failures can help in developing strategies to minimize the risk of such events. Moreover, a real-time detection of precursors to cascading failures will help operators take measures to prevent their propagation. Currently, the well-established probabilistic and physics-based models of cascading failures offer low computational efficiency, hindering them to be used only as offline tools. In this work, we develop a data-driven methodology for online estimation of the risk of cascading failures. We utilize a physics-based cascading failure model to generate a cascading failure dataset considering different operating conditions and failure scenarios, thus obtaining a sample space covering a large set of power grid states that are labeled as safe or unsafe. We use the synthetic data to train deep learning architectures, namely Feed-forward Neural Networks (FNN) and Graph Neural Networks (GNN). With the development of GNNs, improved performance is achieved with graph-structured data, and GNNs can generalize to graphs of diverse sizes. A comparison between FNN and GNN is made and the GNNs inductive capability is demonstrated via test grids. Furthermore, we apply transfer learning to improve the performance of a pre-trained GNN model on power grids not seen in the training process. The GNN model shows accuracy and balanced accuracy above 96% on selected test datasets not used in the training. Conversely, the FNN shows accuracy above 85% and balanced accuracy above 81% on test datasets unseen during training. Overall, the GNN model is successful in determining, if one or several simultaneous outages result in a critical grid state, under specific grid operating conditions.