Robustness analysis and optimization of interdependent power and communication networks

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.

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.

With continuous deepening of researches on complex network problems, the cascading failure problem of interdependent networks becomes one of the hot research topics in this field at present. This paper establishes a cascading failure model of interdependent networks based on a load-capacity model. And then we focus on the robustness problem of interdependent networks under random attacks based on four different network combinations. At last, an interdependent coupling network constituted of two networks with the node quantity of ten is taken as the example to verify conclusions obtained in this paper. Research results show that under random attacks, robustness of the asymmetric interdependent networks is similar with the previous research results, namely, robustness of the networks decreases with the increase of removal proportion and increases with the increase of tolerance coefficient. In addition, BA-BA interdependent networks and disassortative link networks perform better than other network combinations and coupling manners.

Blackouts generally stem from cascading failures in power system operation. Their diminution requires very much the development of approaches and algorithms that analyze cascading failure and identify weak links of power system. Different from optimal load shedding model widely used in conventional assessment, this paper considers the impact of cascading failures on power system, and adopts a practical re-dispatch model. A fault chain model is established to better describe the propagation process of cascading failures and to calculate the occurrence probability of cascading failures quantitatively. To better understand how cascading failures propagate and to effectively identify weak links that are crucial for cascading failure propagation, this paper proposes the index called risk participation factor to measure the effect of branches on the reliability level of power system. Besides, Monte Carlo simulation method is applied to assess these indices. The proposed cascading failures model and fault chain model are validated on the IEEE 39-bus system. Results show that the proposed model that considers the propagation of cascading failures can provide more weak links information for power system planning and operation.

Cascading failures take place between networks after initial failures occur in interdependent networks. Most previous studies are limited to undirected networks, while many real-world networks are directed. For interdependent directed networks, earlier studies focused on random initial failures. How the interdependent directed networks respond to targeted attacks has not been addressed. In this work, we develop a general theoretical framework for analyzing the robustness in interdependent directed networks under targeted attack on nodes with high or low degrees (in-degrees or out-degrees). We find that for degree heterogeneous networks, targeted attacks perform more efficiently in breaking down the system than random failures, with the degree-based attacks being the most efficient way. Interestingly, we find that system robustness first increases then decreases as the degree heterogeneity increases, showing a peak, which helps understand system robustness and enables the better design of robust infrastructure systems.

Attack robustness of cascading load model in interdependent networks

Today one of the main challenges in interdependent networks is cascading failure. In infrastructure networks due to the nature of these networks, they usually depend on other infrastructure networks. Researches in this field are mostly focused on methods for evaluating networks and finding vulnerabilities according to the structure of the network. In this research, we pay attention to this problem from another point of view that is to predict before the failure occurs and then use algorithms to retrieve the network as soon as possible. The input data is randomly generated by the standard cascading failure simulation algorithm, the CFS algorithm. We teach our regression model with numbers of CFS reports that show how much of the network disrupts, when attack accrued on each node of the network. In this way we can predict the problem of cascading failure before it occurs in the network. This regression model employs node centralities in the network. This method is able to predict up to 80% of attacks that lead to failures above 10% and to recover the network quickly using the methods available for recovery.

Different from the direct contact in epidemics spread, overload failures propagate through hidden functional dependencies. Many studies focused on the critical conditions and catastrophic consequences of cascading failures. However, to understand the network vulnerability and mitigate the cascading overload failures, the knowledge of how the failures propagate in time and space is essential but still missing. Here we study the spatio-temporal propagation behaviour of cascading overload failures analytically and numerically on spatially embedded networks. The cascading overload failures are found to spread radially from the centre of the initial failure with an approximately constant velocity. The propagation velocity decreases with increasing tolerance, and can be well predicted by our theoretical framework with one single correction for all the tolerance values. This propagation velocity is found similar in various model networks and real network structures. Our findings may help to predict the dynamics of cascading overload failures in realistic systems.

In cyber‐physical power systems, tiny failure occurring in the communication network could propagate to affect the operation of the physical power grid through inter‐links and even cause catastrophic blackouts. The authors propose a partial random coupling systems model to study the vulnerability of nodes and connectivity of systems in a cascading failure. In terms of traffic loads generated in systems, they employ load spill index to analyse dynamic states of nodes in cascading failure. In cascading failure, considering the effect from a communication network, vulnerability matrices are established to study the vulnerability of nodes in the physical power grid. Furthermore, an efficiency index is defined to analyse connectivity of systems. In the numerical simulation, they verify the accuracy of the proposed evaluation approach and test its scalability and universality in different power systems.

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.

With more power electronics deployed in power system, the propagation of cascading failure become more complex and it is necessary to investigate the mechanism of cascading failure in the novel power system. This paper reveals a new cascading failure mode in multi-infeed high voltage direct current (HVDC) systems. Firstly, the mechanism of multi-timescale cascading failure is proposed. Then the simulation results of multi-infeed HVDC systems which is carried out in Power system department-Bonneville power administration (PSD-BPA) indicate that the dominant cascading failure modes in different timescales are different and they are coupling with each other. Finally, several dominant factors of different timescale cascading failure modes are pointed out.

Recent years have witnessed a surge of extensive study upon the robustness of a system consisting of interdependent networks. Both the mechanism of cascading failures and the corresponding recovery strategies, which means to heal malfunction of a system before it runs completely into collapse, are two key issues in the field of robustness analysis of interdependent networks. An essential question that has always been ignored is how to design a fault tolerance scheme to buffer against cascading failures. In order to deeply understand the relationship between the fault-tolerance assignment and the robustness of interdependent networks, we propose a cascading failure model with the consideration of the fault tolerance property of the nodes in interdependent networks, where the node are specified different fault tolerant capacity according to their degree values. By theoretical and numerical studies, it is found that the robustness of a system can be improved significantly if the high-degree nodes are assigned high fault tolerant capacity. However, robustness of a system can be hampered if the high degree nodes are assigned low fault tolerant capacity. Our results prove that the fault tolerance assignment scheme of the nodes has great impacts on the robustness of interdependent networks and provide important thoughts to reinforce reliability of the interdependent systems by the proper allocation of fault tolerant capacity.

Assessing the impact of systemic heterogeneity on failure propagation across interdependent critical infrastructure systems

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

Percolation on interdependent networks with cliques and weak interdependence