Cascading failures of loads in interconnected networks under intentional attack

RETRACTED: Vulnerability analysis of road network for dangerous goods transportation considering intentional attack: Based on Cellular Automata

Cascading failures in interconnected networks with dynamical redistribution of loads

Research on cascading failure in multilayer network with different coupling preference

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.

There have been many researches on border gateway protocol (BGP) security, most of which mainly focused on how to enhance the security of the BGP protocol or the interdomain routing system. However, few works studied the vulnerabilities especially the production mechanism of security events in the interdomain routing system. It takes many obstacles to understand and improve the security of the interdomain routing system. This paper explores the cascading failure phenomenon of the interdomain routing system. First, we devise a state machine to describe the state transition of BGP nodes and then give a detailed analysis of the BGP failure. Second, on the basis of the preferential attachment characteristic, we propose a cascading failure model for the interdomain routing system, which depicts the production mechanism of cascading failure, and introduce two evaluating indicators, the proportion of failed nodes and the proportion of failed links, to assess the scale of cascading failure. Furthermore, we apply the cascading failure model to display two different cascading failure scenes. The experimental results show that random failure has less influence on the interdomain routing system, while its robustness against hostile attack is weak. Copyright ©2011 John Wiley & Sons, Ltd.

The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in LW network models with different LW sizes were investigated using the cascading failures load model. We found that the LW size has a significant impact on the network’s robustness against deliberate attacks. It is much easier to trigger cascading failures in LW evolving networks with a larger LW size. Therefore, to avoid cascading failures in real networks with local preferential attachment such as the Internet, the World Trade Web and the multi-agent system, the LW size should be as small as possible.

The massive power flow transferring triggers the node overload cascade, which further activates the protection system hidden failures. In this study, we propose a cascading failure model based on complex network theory by combining the node overload failures and hidden failures of transmission lines in blackouts together. The model concerns the electrical characteristics, which has not been involved in the existed cascading failure model when modelling node loads. The cascading failure simulations on the 500 kV Center China power grid and the IEEE‐300‐bus test system demonstrate that the proposed cascading failure model with node load built on electrical characteristics can bring better network invulnerability than the model with that constructed on pure structure topology. Meanwhile, the proposed model can better exhibit the negative aspects of hidden failures in the blackouts. The deliberate attacks based on high‐risk nodes can decrease the invulnerability of power grids more seriously compared with those based on high‐degree and high‐load nodes. The results provide a new way to analyse the power grid cascading failure mechanism based on the complex network theory.

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.

The interdependent network is particularly vulnerable to attacks on high degree nodes; therefore, the improvement of its robustness under intentional attacks has become an important topic. In this paper, we put forward a new metric to quantify the robustness of interdependent networks against intentional attacks and develop an improved simulated annealing algorithm (ISAA) to maximize this metric by optimizing the allocation of intra-links in subnetworks. Based on the comparison between the ISAA and existing algorithms, it is found that the algorithm presented in this paper is more effective to enhance the robustness of an interdependent scale-free network (ISFN). By applying the ISAA to ISFNs with different coupling preferences, there is a key finding that the robustness of the optimized ISFN is significantly stronger than that of the original ISFN. In particular, for cases of disassortative and random couplings, no sudden collapse occurs in optimized ISFNs. According to the analysis of the degree and the clustering coefficient, we find that the subnetwork of the optimized ISFN exhibits an onion-like structure. In addition, the ISFN whose robustness is enhanced to resist the attacks on high degree nodes is still robust to the intentional attacks concerning the betweenness and PageRank.

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

Climate change is one of the most pressing issues of our time and mitigating it requires a reduction of CO2 emissions. A big step towards achieving this goal is increasing the share of renewable energy sources, as the energy sector currently contributes 35% to all greenhouse gas emissions. However, integrating these renewable energy sources challenges the current power system in two major ways. Firstly, renewable generation consists of more spatially distributed and smaller power plants than conventional generation by nuclear or coal plants, questioning the established hierarchical structures and demanding a new grid design. Restructuring becomes necessary because wind and solar plants have to be placed at favorable sites, e.g., close to coasts in the case of wind. Secondly, renewables do not provide a deterministic and controllable power output but introduce power fluctuations that have to be controlled adequately. Many solutions to these challenges are build on the concept of smart grids, which require an extensive information technology (IT) infrastructure communicating between consumers and generators to coordinate efficient actions. However, an intertwined power and IT system raises great privacy and security concerns. Is it possible to forgo a large IT infrastructure in future power grids and instead operate them purely based on local information? How would such a decentrally organized system work? What is the impact of fluctuation on short time scales on the dynamical stability? Which grid topologies are robust against random failures or targeted attacks? This thesis aims to establish a framework of such a self-organized dynamics of a power grid, analyzing its benefits and limitations with respect to fluctuations and discrete events. Instead of a centrally monitored and controlled smart grid, we propose the concept of Decentral Smart Grid Control, translating local power grid frequency information into actions to stabilize the grid. This is not limited to power generators but applies equally to consumers, naturally introducing a demand response. We analyze the dynamical stability properties of this framework using linear stability methods as well as applying numerical simulations to determine the size of the basin of attraction. To do so, we investigate general stability effects and sample network motifs to find that this self-organized grid dynamics is stable for large parameter regimes. However, when the actors of the power grid react to a frequency signal, this reaction has to be sufficiently fast since reaction delays are shown to destabilize the grid. We derive expressions for a maximum delay, which always desynchronizes the system based on a rebound effect, and for destabilizing delays based on resonance effects. These resonance instabilities are cured when the frequency signal is averaged over a few seconds (low-pass filter). Overall, we propose an alternative smart grid model without any IT infrastructure and analyze its stable operating space. Furthermore, we analyze the impact of fluctuations on the power grid. First, we determine the escape time of the grid, i.e., the time until the grid desynchronizes when subject to stochastic perturbations. We simulate these events and derive an analytical expression using Kramer's method, obtaining the scaling of the escape time as a function of the grid inertia, transmitted power, damping etc. Thereby, we identify weak links in networks, which have to be enhanced to guarantee a stable operation. Second, we collect power grid frequency measurements from different regions across the world and evaluate their statistical properties. Distributions are found to be heavy-tailed so that large disturbances are more common than predicted by Gaussian statistics. We model the grid dynamics using a stochastic differential equation to derive the scaling of the fluctuations based on power grid parameters, identifying effective damping as essential in reducing fluctuation risks. This damping may be provided by increased demand control as proposed by Decentral Smart Grid Control. Finally, we investigate discrete events, in particular the failure of a single transmission line, as a complementary form of disturbances. An initial failure of a transmission line leads to additional load on other lines, potentially overloading them and thereby causing secondary outages. Hence, a cascade of failures is induced that propagated through the network, resulting in a large-scale blackout. We investigate these cascades in a combined dynamical and event-driven framework, which includes transient dynamics, in contrast to the often used steady state analysis that only solves static flows in the grid while neglecting any dynamics. Concluding, we identify critical lines, prone to cause cascades when failing, and observe a nearly constant speed of the propagation of the cascade in an appropriate metric. Overall, we investigate the self-organized dynamics of power grids, demonstrating its benefits and limitations. We provide tools to improve current grid operation and outline a smart grid solution that is not reliant on IT. Thereby, we support establishing a 100% renewable energy system.

The increasing penetration of renewable energy generation (REG) introduces an amount of uncertainty and power electronics devices into power grid that severely affects the physical responses in the evolution of cascading failure. However, existing cascading failure models cannot accurately describe the physical responses affected by the features of REG and their interaction in the propagation of cascading failure. In this paper, a cascading failure model integrating the multiply physical responses is proposed. In this model, the physical responses affected by REG are described, including relay protection, frequency regulation and dispatching strategy. In the experiment, our model is compared with the model in traditional power grid. The experimental results show that the penetration of REG will change the evolution path of failure, and the probability of blackouts will increase with the increasing penetration level of REG.

Robustness of multipartite networks in face of random node failure

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.

Container shipping networks are vulnerable to cascading failures due to seaport disruptions, underscoring the need for resilient multimodal transport systems. This study proposes a cascading failure model for the seaport–dry-port network in container transport, incorporating a multi-stage load redistribution strategy (CM-SDNCT-MLRS) to enhance network resilience. Extending the Motter–Lai framework, the model introduces multiple port state transitions and accounts for uncertainties in load redistribution, tailoring it to the cascading failure dynamics of SDNCT. Using empirical data from China’s coastal port system, the proposed MLRS dynamically reallocates loads through dry-port buffering, neighboring seaport sharing, and port skipping. This strategy effectively contains cascading failures, mitigates network efficiency losses, and protects major seaports while reducing mutual disruptions. Resilience analysis demonstrates that the network exhibits scale-free properties, with its resilience being highly sensitive to random port failures and critical port vulnerabilities. The experimental results highlight the pivotal role of dry ports, where operational numbers influence resilience more significantly than capacity. In addition, the study identifies the optimal port-skipping probability that mitigates cascading disruptions. These findings provide valuable insights for port management and logistics planning, contributing to the development of more resilient container transport networks.