Cascading Failure Propagation Research Articles

Cascading failures with coupled map lattices on Watts–Strogatz networks

In this paper, we present a cascading failure model based on coupled map lattices, in which a given number of crucial nodes are perturbed at the same time. By comparing the effect of five attacking strategies: random strategy, high-degree strategy, high-clustering coefficient strategy, high-betweenness strategy and high-closeness strategy (HCS) on Watts–Strogatz (WS) small-world networks, we found that HCS outperforms the other attacking strategies with different number of perturbed nodes. The efficiency of HCS on WS small-world networks is explored extensively. The results show that increasing the rewiring probability can reduce the range of cascading failures, but it will enhance the propagation speed of cascades. Furthermore, a more compact network structure will lead to a faster cascading failure propagation speed, and the propagation speed of cascades is inversely proportional to the characteristic path length of WS small-world networks. Our work will highlight a better understanding of cascading failures on complex networks.

Fast Screening of Vulnerable Transmission Lines in Power Grids: A PageRank-Based Approach

In power system operation, there are usually a few vulnerable lines (VLs) which are prone to exacerbate the propagation of cascading failures and lead to severe blackouts with high probability. To facilitate preventing the power grid from cascading blackouts, in this paper, a PageRank-based fast screening method is derived to identify VLs. To this end, we extend the concept of interaction graph to model cascading outages as a directed weighted graph, where impacts of hidden failures are first taken into account. Based on the graph, we modify the celebrated PageRank algorithm to derive an ultra-fast VLs screening algorithm for large-scale power grids. Simulations carried out on the IEEE 118-bus system show that the proposed method can achieve high-accuracy VLs screening while the speed can be enhanced for several orders of magnitude compared with cascading failure simulation methods. Tests on a 1122-bus real power grid in China demonstrate that it can discriminate the most VLs in a practical power grid within only several minutes, showing its great potential for on-line application.

A Stochastic Model of Cascading Failure Dynamics in Communication Networks

In this brief, we propose a stochastic model based on state transition theory to investigate the dynamics of cascading failures in communication networks. We describe the failure events of the nodes in the network as node state transitions. Taking a probabilistic perspective, we focus on two uncertain conditions in the failure propagation process: which node in the network will fail next and how long it will last before the next node state transition takes place. The stochastic model gives each overloaded element a probability of failing, and the failure rate is relevant to the degree of overloading. Moreover, the time dimension is considered in the stochastic process, by removing a node after a time delay when its traffic load exceeds its capacity. We employ this proposed model to study the dynamics of cascading failure evolution in a Barabasi–Albert scale-free network and an Internet AS-level network. Simulation results reveal the effects of the initial failure pattern, community structure and network design parameters on the dynamic propagation of cascading failures.

Optimization of cascading failure on complex network based on NNIA

Recently, the robustness of networks under cascading failure has attracted extensive attention. Different from previous studies, we concentrate on how to improve the robustness of the networks from the perspective of intelligent optimization. We establish two multi-objective optimization models that comprehensively consider the operational cost of the edges in the networks and the robustness of the networks. The NNIA (Non-dominated Neighbor Immune Algorithm) is applied to solve the optimization models. We finished simulations of the Barabási–Albert (BA) network and Erdös–Rényi (ER) network. In the solutions, we find the edges that can facilitate the propagation of cascading failure and the edges that can suppress the propagation of cascading failure. From the conclusions, we take optimal protection measures to weaken the damage caused by cascading failures. We also consider actual situations of operational cost feasibility of the edges. People can make a more practical choice based on the operational cost. Our work will be helpful in the design of highly robust networks or improvement of the robustness of networks in the future.

Machine Learning Based on Bayes Networks to Predict the Cascading Failure Propagation

Considering the engineering characteristics of power systems and the concept of machine learning, a model named “ITEPV” was proposed in this paper to investigate the mechanism of cascading failures in power systems. This model tries to simulate a large number of possible cascading failure chains as “experience”, and then to predict the cascading failure propagation with the highest possibility obtained from the “experience”. In order to get the prediction result, the uncertainty of loads and generations is considered to generate numerous random operating conditions, and then implementing “ $N-1$ ” for each operating condition to obtain the “experience”. Based on the “experience”, a Bayes network can be established to predict the cascading failure propagation. The “ITEPV” model was tested on the IEEE Reliability Test System-1996 (RTS-96), and the results were validated by employing different sample sizes of random operating conditions. From this paper, it can be concluded that employing machine learning into electrical engineering not only simplifies the complicated issue but also makes the results more accurate.

Improving robustness of interdependent networks by a new coupling strategy

There are two kinds of methods to improve the robustness of interdependent networks by changing the edge connection. One is to change the connectivity link, and the other is to change the inter-links. In this paper, we focus on the factors that affect the propagation of cascading failures. And based on the study of the propagation process of failures, the two factors affecting the propagation of cascading failures are found. Finally, a coupling strategy of local optimization NPC (Neighbor node priority connection) is proposed. By applying this strategy to two kinds of interdependent networks ER-ER and SF-SF, we find that the robustness of the interdependent networks coupled by NPC is better than that of the three classical strategies.

Modeling the Dynamics of Cascading Failures in Power Systems

In this paper, we use a circuit-based power flow model to study the cascading failure propagation process, and combine it with a stochastic model to describe the uncertain failure time instants, producing a model that gives a complete dynamic profile of the cascading failure propagation beginning from a dysfunctioned component and developing eventually to a large-scale blackout. The sequence of failures is determined by voltage and current stresses of individual elements, which are governed by deterministic circuit equations, while the time durations between failures are described by stochastic processes. The use of stochastic processes here addresses the uncertainties in individual components’ physical failure mechanisms, which may depend on manufacturing quality and environmental factors. The element failure rate is related to the extent of overloading. A network-based stochastic model is developed to study the failure propagation dynamics of the entire power network. Simulation results show that our model generates dynamic profiles of cascading failures that contain all salient features displayed in historical blackout data. The proposed model thus offers predictive information about occurrences of large-scale blackouts. We further plot cumulative distribution of the blackout size to assess the overall system’s robustness. We show that heavier loads increase the likelihood of large blackouts and that small-world network structure would make cascading failure propagate more widely and rapidly than a regular network structure.

Real‐time monitoring of zone 3 vulnerable distance relays to prevent maloperation under load encroachment condition

Undesired trip operation of zone 3 units of distance relays in power transmission network, during static and dynamic load encroachment can lead to cascading failures and even catastrophic power system blackouts. Stressed conditions such as power flow redistribution and power swing can cause maloperation of the third zone of distance relays. Fast and dependable detection of the symmetrical faults, occurring during these conditions poses an additional challenge. One of the effective methods to avoid the zone 3 contribution in cascading failure propagation is the detection and monitoring of vulnerable relays which are exposed to maloperation in power system stressed conditions. In this study, a new relay ranking index is proposed for real-time identifying the zone 3 of distance relays, most vulnerable to incorrect operation due to load encroachment. A novel synchrophasor data-based monitoring index is also presented for supervision of critical distance relays operation. This index is extracted based on positive-sequence fault component phasors of the current and voltage signals obtained by modern PMUs or GPS based digital relays which have been reconfigured for this application. The proposed monitoring scheme is able to quickly distinguish the fault from load encroachment condition. The performance of the proposed supervisory scheme is evaluated and approved on a nine-bus WSCC system.

An efficient local cascade defense method in complex networks

Cascading failures in networked systems often lead to catastrophic consequence. Defending cascading failure propagation by employing local load redistribution method is an efficient way. Given initial load of every node, the key of improving network robustness against cascading failures is to maximally defend cascade propagation with minimum total extra capacity of all nodes. With finite total extra capacity of all nodes, we first discuss three general extra capacity distributions including degree-based distribution (DD), average distribution (AD) and random distribution (RD). To sufficiently use the total spare capacity (SC) of all neighboring nodes of a failed node, then we propose a novel SC-based local load redistribution mechanism to improve the cascade defense ability of network. We investigate the network robustness against cascading failures induced by a single node failure under the three extra capacity distributions in both scale-free networks and random networks. Compared with the degree-based (DB) local load redistribution method, our SC method achieves higher robustness under all of the three extra capacity distributions. The extensive simulation results can well confirm the effectiveness of the SC local load redistribution method.

An enhanced cascading failure model integrating data mining technique

An enhanced cascading failure model integrating data mining technique is proposed in this paper. In order to better simulate the process of cascading failure propagation and further analyze the relationship between failure chains, in view of a basic framework of cascading failure described in this paper, some significant improvements in emerging prevention and control measures, the subsequent failure search strategy as well as the statistical analysis for the failure chains are made elaborately. Especially, a sequential pattern mining model is employed to find out the association pertinent to the obtained failure chains. In addition, a cluster analysis model is applied to evaluate the relationship between the intermediate data and the consequence of obtained failure chain, which can provide the prediction in potential propagation path of cascading failure to reduce the risk of catastrophic events. Finally, the case studies are conducted on the IEEE 10-machine-39-bus test system as benchmark to demonstrate the validity and effectiveness of the proposed enhanced cascading failure model. Some preliminary concluding remarks and comments are drawn.

Modeling and Vulnerability Analysis of Cyber-Physical Power Systems Considering Network Topology and Power Flow Properties

Conventional power systems are developing into cyber-physical power systems (CPPS) with wide applications of communication, computer and control technologies. However, multiple practical cases show that the failure of cyber layers is a major factor leading to blackouts. Therefore, it is necessary to discuss the cascading failure process considering cyber layer failures and analyze the vulnerability of CPPS. In this paper, a CPPS model, which consists of cyber layer, physical layer and cyber-physical interface, is presented using complex network theory. Considering power flow properties, the impacts of cyber node failures on the cascading failure propagation process are studied. Moreover, two vulnerability indices are established from the perspective of both network structure and power flow properties. A vulnerability analysis method is proposed, and the CPPS performance before and after cascading failures is analyzed by the proposed method to calculate vulnerability indices. In the case study, three typical scenarios are analyzed to illustrate the method, and vulnerabilities under different interface strategies and attack strategies are compared. Two thresholds are proposed to value the CPPS vulnerability roughly. The results show that CPPS is more vulnerable under malicious attacks and cyber nodes with high indices are vulnerable points which should be reinforced.

System Reliability Under Cascading Failure Models

Cascading failure models have been studied more recently as for electric power systems, epidemics, and interdependent networks. The current paper presents three cascading failure models in the point-view of system reliability based on the normalized CASCADE model. The corresponding system reliability indices are developed including system reliability, expectation lifetimes of systems, distributions of total number of failures, distributions of cascading failure propagation generations, and other related probabilities. Two numerical examples are discussed, and the conclusions are summarized.

Spatio-temporal propagation of cascading overload failures in spatially embedded networks.

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.

Nonlocal effects and countermeasures in cascading failures.

We study the propagation of cascading failures in complex supply networks with a focus on nonlocal effects occurring far away from the initial failure. It is shown that a high clustering and a small average path length of a network generally suppress nonlocal overloads. These properties are typical for many real-world networks, often called small-world networks, such that cascades propagate mostly locally in these networks. Furthermore, we analyze the spatial aspects of countermeasures based on the intentional removal of additional edges. Nonlocal actions are generally required in networks that have a low redundancy and are thus especially vulnerable to cascades.

A new approach for mitigating blackout risk by blocking minimum critical distance relays

Abstract Electric power systems are complex and commonly run near their operational limits. Power systems are basically designed based on the ( N − 1) criterion. In these systems, total or partial blackouts are unavoidable. Cascading failures following an initial event is recognized as the main mechanism for power system blackouts. Undesirable activation of zone 3 of distance relays due to their local function has been identified as one of the major causes for propagation of cascading failures. In this paper, in order to mitigate the risk of power system blackouts, a novel approach is proposed for recognizing the critical line outages with the highest contribution in cascading failure and preventing their undesirable outage by blocking zone 3 of their distance relay. In this paper, based on the statistical activation of distance relays, a deterministic–probabilistic approach is developed for identifying the critical lines with the highest contribution in blackouts due to activation of zone 3 of their distance relays. In order to avoid interference of relay blocking with the main protection duty of distance relays, the proposed approach recognizes the minimum critical lines with the highest contribution in cascading failure for blocking zone 3 of their distance relays. The proposed approach is demonstrated on the New England 39-bus system and detailed simulation studies carried out to examine the validity and effectiveness of the proposed approach.

Improving measures of topological robustness in networks of networks and suggestion of a novel way to counter both failure propagation and isolation

The study of interdependent complex networks in the last decade has shown how cascading failure can result in the recursive and complete fragmentation of all connected systems from the destruction of a comparatively small number of nodes. Existing “network of networks” approaches are still in infancy and have shown limits when trying to model the robustness of real-world systems, due to simplifying assumptions regarding network interdependencies and post-attack viability. In order to increase the realism of such models, we challenge such assumptions by validating the following four hypotheses trough experimental results obtained from computer based simulations. Firstly, we suggest that, in the case of network topologies vulnerable to fragmentation, replacing the standard measure of robustness based on the size of the one largest remaining connected component by a new measure allowing secondary components to remain viable when measuring post-attack viability can make a significant improvement to the model. Secondly, we show that it is possible to influence the way failure propagation is balanced between coupled networks while keeping the same overall robustness score by allowing nodes in a given network to have multiple counter parts in another network. Thirdly, we challenge the generalised assumption that partitioning between networks is a good way to increase robustness and find that isolation is a force as equally destructive as the iterative propagation of cascading failure. This result significantly alters where the optimum robustness lies in the balance between isolation and inter-network coupling in such interconnected systems. Finally, we propose a solution to the consequent problem of seemingly ever increasing vulnerability of interdependent networks to both cascading failure and isolation: the use of permutable nodes that would give such systems rewiring capabilities. This last concept could have wide implications when trying to improve the topological resilience of natural or engineered interdependent networks.

Analysis of Road Traffic Network Cascade Failures with Coupled Map Lattice Method

In recent years, there is growing literature concerning the cascading failure of network characteristics. The object of this paper is to investigate the cascade failures on road traffic network, considering the aeolotropism of road traffic network topology and road congestion dissipation in traffic flow. An improved coupled map lattice (CML) model is proposed. Furthermore, in order to match the congestion dissipation, a recovery mechanism is put forward in this paper. With a real urban road traffic network in Beijing, the cascading failures are tested using different attack strategies, coupling strengths, external perturbations, and attacked road segment numbers. The impacts of different aspects on road traffic network are evaluated based on the simulation results. The findings confirmed the important roles that these characteristics played in the cascading failure propagation and dissipation on road traffic network. We hope these findings are helpful to find out the optimal road network topology and avoid cascading failure on road network.

A methodology for criticality analysis in integrated energy systems

Integrated energy systems (IES) such as polygeneration plants and bioenergy-based industrial symbiosis (BBIS) networks offer the prospect of increased efficiency and reduced carbon emissions. However, these highly-integrated systems are also characterized by the strong interdependence among component units. This interdependency results in the risk of propagation of cascading failures within such networks, where disturbances in the operation of one component results in ripple effects that affect the other units in the system. In this work, a novel criticality index is proposed to quantify the effects of a component unit’s failure to run at full capacity within an IES. This index is defined as the ratio of the fractional change in the net output to the fractional change in capacity of the component causing the failure. The component units in the entire system can then be ranked based on this index. Such risk-based information can thus be used as an important input for developing risk mitigation measures and policies. Without this information, risk management based only on network topology could result to counterintuitive results. A simple polygeneration plant and two BBIS case studies are presented to demonstrate the computation of the criticality index.

An Interaction Model for Simulation and Mitigation of Cascading Failures

In this paper the interactions between component failures are quantified and the interaction matrix and interaction network are obtained. The quantified interactions can capture the general propagation patterns of the cascades from utilities or simulation, thus helping to better understand how cascading failures propagate and to identify key links and key components that are crucial for cascading failure propagation. By utilizing these interactions a high-level probabilistic model called interaction model is proposed to study the influence of interactions on cascading failure risk and to support online decision-making. It is much more time efficient to first quantify the interactions between component failures with fewer original cascades from a more detailed cascading failure model and then perform the interaction model simulation than it is to directly simulate a large number of cascades with a more detailed model. Interaction-based mitigation measures are suggested to mitigate cascading failure risk by weakening key links, which can be achieved in real systems by wide area protection such as blocking of some specific protective relays. The proposed interaction quantifying method and interaction model are validated with line outage data generated by the AC OPA cascading simulations on the IEEE 118-bus system.

Assessing the Impact of Cascading Failures on the Interdomain Routing System of the Internet

The Internet is a typical complex network, whose traffic load is controlled by the inter-domain routing system. Due to the co-location of data plane and control plane of Border Gateway Protocol, the survivability of inter-domain routing system is sensitive to severe congestion. Therefore, an initial outage may lead to a cascade of failures in the Internet. But the cascading failures on links are able to be automatically restored when the congestion is mitigated. In this paper, we propose a model - CAFEIN for characterizing this special process. Based on CAFEIN, we assess the difference of impact under intentional attacks and random breakdowns; identify the worst affected part of the Internet; and study the propagation of cascading failures. Through simulations, we find that the cascading failures bring a great deal of added burden to the routing system. However, the cascading effect is amplified globally when the relative capacity of links is very low. Moreover, the difference of impact between intentional attack and random breakdown is not as prominent as previous research due to the unique automatic-restoration process.