Cascading Failure Model Research Articles

Research on Optimization of Robustness for Cascading Failure in Power Grid

When considering the cascading failures or the robust performance of the power network, most of the researches in network science are based on the topology of the power network. However, according to some researches, only using the topology of the power network can not reasonably evaluate the robustness of the power network.Therefore, when considering the cascading failures in the power network, we must combine the electrical characteristics with the network topology to make a better evaluation. From the perspective of network science, the related research on cascading failures has made a lot of progress. In order to optimize the robustness of power network, the optimal topology of power network is designed under the cascading failure model combined with real electrical characteristics.

Quantitative comparison of cascading failure models for risk-based decision making in power systems

The accurate allocation and prediction of risk in power systems is vital for reliable operations of the electrical infrastructure. Several models with varying degrees of accuracy and computational cost are available. Relying on less computationally intensive methods increases the efficiency of risk assessment provided that the output does not impair control actions and decision making. This study focuses on comparing two established cascading failure models for determining their consistency to risk-based decision making. Effects of ambient conditions are captured via temperature-dependent dynamic transmission line ratings. The investigations on the IEEE 24-Bus reliability test system highlight that, when the power grid is subjected to elevated temperature and demand levels, the deviations between Manchester and OPA model can be significant. However, both models show the same general trends, namely, that the demand not served generally increases with increasing temperature and demand. Further similarities are found in terms of the most critical lines and the most heavily loaded generators, providing useful information for power system expansion planning. The OPA model displays a much larger area of elevated risk across the input space that also includes almost the entire area found by the Manchester model, providing conservative estimates in highly stressed power systems.

Controllability Robustness Against Cascading Failure for Complex Logistics Networks Based on Nonlinear Load-Capacity Model

In order to achieve good connectivity after the cascading failure of a logistics network, this paper studies the controllability robustness of complex logistics network based on the nonlinear load-capacity (NLC) model. Firstly, the extended Baraba' si and Albert (BA) network is constructed as a complex logistics network for experiments, based on the power law distribution and the agglomeration and sprawl evolution mechanism. Secondly, the existence of the NLC relationship of the real logistics network is proved, and then the NLC model of complex logistics networks is proposed. Furthermore, a simulation analysis of the controllability robustness and influencing factors of the complex logistics network is carried out under four different cascading failure models. In those models, different scenarios of the NLC and the classical linear load-capacity (LLC) model with initial load (IL)/initial residual capacity (IRC) load-redistribution strategies are combined. The research results show that the main influencing factors of the cascading failure of complex logistics networks for the controllability robustness P' are the tolerance parameters β and γ. Moreover, the effect of γ on the load-capacity relationship under the NLC model is more significant than that of β. Among the four cascading failure models, the one based on the NLC model with IRC strategy is the optimal for controllability robustness. Based on the optimal model, the simulation considering the perspective of the logistics economy shows that the relationship among the network cost e, P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> and γ is as follows: under a fixed cost, the greater is γ, the stronger is P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> . Also, when 2 <; γ ≤ 9, the robustness of the network is controllable. According to the requirements of real logistics networks, both controllability robustness and the logistics cost can be controlled, and a solution that against cascading failure can be obtained by adjusting the minimum residual load.

Dynamic Cascading Failure Analysis in Congested Urban Road Networks With Self-Organization

An efficient freight transportation system is a core part of the modern urban logistics. The transportation system depends on an efficient urban road network. In urban road networks, the failure of some components leads to others failing in succession, triggering cascading failures. This may cause the collapse of the freight transportation system. A cascading failure model is proposed for analyzing the propagation of failures on urban road networks, which can provide guidance for the planning of freight transportation routes in case of emergency. When analyzing the cascading failure process, failed components are commonly deleted permanently. Travelers will avoid failed components, resulting in no increase in traffic flow on the failed components. At the same time, vehicles on these failed components will evacuate slowly to alleviate congestion. Considering this point, this paper proposes a dynamic cascading failure model. This model is established based on a hybrid routing strategy in which traffic flow is distributed according to global and local information. Specifically, the new input traffic demand is assigned along efficient paths in an urban road network (using global information). Efficient paths are determined according to the weights of all edges in urban road networks. Meanwhile, failed edges transfer some traffic flow to their normally working neighbors by self-organization (using local information). The proportion of transferred traffic flow is determined by the residual capacity of the failed edges' normally working neighbors. The feasibility of the proposed model is verified in a partial road network in Changchun, China.

A Probabilistic Cascading Failure Model for Dynamic Operating Conditions

Failure propagation in power systems, and the possibility of becoming a cascading event, depend significantly on power system operating conditions. To make informed operating decisions that aim at preventing cascading failures, it is crucial to know the most probable failures based on operating conditions that are close to real-time conditions. In this paper, this need is addressed by developing a cascading failure model that is adaptive to different operating conditions and can quantify the impact of failed grid components on other components. With a three-step approach, the developed model enables predicting potential sequence of failures in a cascading failure, given system operating conditions. First, the interactions between system components under various operating conditions are quantified using the data collected offline, from a simulation-based failure model. Next, given measured line power flows, the most probable interactions corresponding to the system operating conditions are identified. Finally, these interactions are used to predict potential sequence of failures with a propagation tree model. The performance of the developed model under a specific operating condition is evaluated on both IEEE 30-bus and Illinois 200-bus systems, using various evaluation metrics such as Jaccard coefficient, F 1 score, Precision@K, and Kendall's tau.

Optimization of Water Distribution Network Design for Resisting Cascading Failures

Water distribution networks (WDNs) is crucial to ensure social operations and economic activities. However, WDNs are highly sensitive and vulnerable to disasters. The aim of this study is to mitigate the catastrophic consequences of cascading failures in WDNs. A flow-based WDN cascading failure model is built. The extended multi-objective particle swarm optimization model is developed to resist cascading failures and improve resilience. This model takes pipe diameter as the decision variable to minimize cost and maximize pressure deficit. Water balance, pressure, and standard pipe diameter are the constraints. The classical optimal scenario (COS) and the cascading failure scenario (CFS) are simulated. The model is applied to a small and medium-sized benchmarked WDN. Results show that the extended PSO can find the optimal solution on the benchmarked WDN. The Pareto fronts are obtained. Compare to the Pareto fronts between COS and CFS, the pressure deficit under CFS is significantly reduced, and the cost is reduced while the same pressure deficit increased. Different tolerance parameters are tested. The small network is not sensitive to the tolerance parameter, but the medium-sized network is sensitive. The model evaluates a variety of conflicting goals, which help designers and water managers resist cascading failures in WDNs.

Controllability Robustness Against Cascading Failure for Complex Logistic Network Based on Dynamic Cascading Failure Model

Inspired by the empirical dynamic characteristics of the load of real logistics network, we propose a dynamic cascading failure model against cascading failure, which is more suitable for complex logistics network by adding dynamic factors based on the nonlinear load-capacity model under initial residual capacity load-redistribution strategy. The simulation is executed on the complex logistics network model and the results show that the controllability robustness and economy after cascading failure based on the dynamic cascading failure model is feasible and effective. It can effectively reduce the logistics cost and enhance controllability robustness against cascading failure by adjusting the network cost $e$ and capacity parameter $\gamma $ , so as to balance the controllability robustness and economy for the complex logistics network.

The Robustness of Interdependent Networks With Traffic Loads and Dependency Groups

Existing researches on cascading failures of interdependent networks are mainly based on the percolation theory and do not consider the influence of dynamic load propagation and dependency groups. In this paper, we develop a novel interdependent system model to capture this phenomenon, also known as the hybrid cascading failure model. A degree-based targeted attack strategy on the cascading failure process of interdependent networks is studied. Combining dependency groups, interdependent relations, and traffic loads, small fraction of initial failed nodes may lead to the complete fragmentation of interdependent networks. The influence of two different dependency groups distributions on the robustness of interdependent networks under three coupling preferences is studied respectively. We provide a thorough analysis of the dynamics of cascading failures in interdependent networks initiated with a targeted attack. The system robustness is quantified as the surviving fraction of nodes in the giant connected component at the end of cascading failures. Our results highlight the need to consider loads, group effects and coupling preferences when designing the robust interdependent networks. And it is necessary to take steps in the early stage to reduce the losses caused by the large-scale cascading failures of infrastructure networks.

Dual Hidden Failure Model for Cyber Physical Power System

With the increasingly close coupling between the cyber network and the physical power grid in Cyber Physical Power System (CPPS), the failure of cyber network has become an important cause of blackout. Equipment failure or abnormal operation state will be appeared without alarm in complex cyber network, which brings hidden failures not been diagnosed and dealt with in time. The invisibility and harmfulness of hidden failures pose a significant threat to the safe, reliable, and stable operation of CPPS. The dual hidden cascading failure model for CPPS is proposed to reveal the failure characteristics of CPPS accurately, considering not only the hidden faults in the power grid, but also the hidden failures in the cyber network. With the different coupled relationships between power systems and cyber networks, the cyber network topology with corresponding failure threshold is obtained according to the simulation of the model with different hidden failure rates of cyber network nodes. When the hidden failure rate is lower than the failure threshold, the scale-free topology cyber network coupled mode is adopted between power grids and cyber networks, otherwise the small-world topology cyber network coupled mode is adopted, which can effectively reduce the risk of power system blackouts. The method proposed in this paper is tested by using IEEE-118 power system and its cyber network. The results show that the method is effective.

Cascades in coupled map lattices with heterogeneous distribution of perturbations

As an important aspect of network robustness, cascading failure in complex networks has attracted a tremendous amount of interest in recent years. In the paper, we propose a novel cascading failure model of coupled map lattices by introducing heterogeneous distribution of perturbations, where a number of nodes are perturbed at the initial attack. The performance of four general attacking strategies are explored, which shows that high-betweenness strategy outperforms three other attacking strategies when heterogeneous perturbation mechanism is adopted. The results also indicate that increasing the coupling strength on direct neighbors can make the network more vulnerable and accelerate the propagation speed of cascades. And a more compact network structure will restrain the range and the propagation speed of cascading failures. We verify the influence of the heterogeneous perturbation principle on two real-world networks. In general, the effect on two real networks is in good accordance with that of BA scale-free networks, which means that the model can serve as a powerful tool to study realistic network robustness against cascades. Our work gains insight into the robustness and vulnerability of complex networked systems with respect to cascading failures.

Cascade Failure Model in Multimodal Transport Network Risk Propagation

The cascade failure theory is introduced into the risk propagation problem of the multimodal transport network in order to study the inherent law of risk propagation and provide theoretical support for the safety management of multimodal transport networks. Firstly, this paper analyses the characteristics of the multimodal transport network and concludes that the risk of the multimodal transport network belongs to failure risk. Secondly, the applicability of cascade failure theory is expounded. Based on cascade failure theory, a risk propagation model of the multimodal transport network is established. Through simulation experiments, the risk propagation of the multimodal transport network is analyzed from the differences of node distribution and node type. The process is analyzed, and the results show that different node distributions and different types of risk source nodes will have an impact on the risk propagation process. The influence of four types of node distributions on the risk propagation effect is in the following order: increasing type &gt; concave-convex type ≈ balanced type &gt; decreasing type. The influence of four types of source nodes on the risk propagation effect is in the following order: transportation type &gt; transporting type &gt; storage type &gt; assistant type.

The Impact of a Network Split on Cascading Failure Processes

Cascading failure models are typically used to capture the phenomenon where failures possibly trigger further failures in succession, causing knock-on effects. In many networks, this ultimately leads to a disintegrated network where the failure propagation continues independently across the various components. In order to gain insight into the impact of network splitting on cascading failure processes, we extend a well-established cascading failure model for which the number of failures obeys a power-law distribution. We assume that a single line failure immediately splits the network in two components and examine its effect on the power-law exponent. The results provide valuable qualitative insights that are crucial first steps toward understanding more complex network splitting scenarios.

Robustness analysis of the networks in cascading failures with controllable parameters

Network robustness is a core problem in network researches, it has achieved many good results by now. However, the network robustness against cascading failures under various controllable parameters has not been systematically studied.Therefore, based on load-capacity(LC) cascading failures model, a new definition of node load is proposed. An attenuation coefficient γ and exponential coefficient α are added to LC model, it can be proportional to node degree, but not completely proportional and achieves the greater degree and stronger load capacity, which is different from the existed model in related researches. The LC model which combines with random attacks and intention attacks strategies, called hybrid attacks strategy, is established on networks with cascading failures. By simulation, the results show that, in the cases of random attacks and hybrid attacks, the network robustness against cascading failures increases with the increase of scaling attacks and tolerance parameter, and the later parameter displays greater influence when it increases the robustness of networks shifted obviously to right, but declines significantly with the increase of load parameter; in the situation of intention attacks, network experienced extreme vulnerability under two types of controllable parameters and networks show the worst robustness.

Cascading failure model for improving the robustness from the perspective of traffic planning

In the field of complex networks, construction cost and operational stability are the main topics for traffic networks. Increasing the investment in key edges and reducing the investment in nonkey edges can effectively reduce the cost and improve the network stability. Much empirical evidence shows that an edge with a high load is not always the priority. A new method of unifying the weights is presented. This method can compare the importance of edges in different cascading failure models. By studying a large number of research experiments, a new model for controlling the cascading failure and construction cost is proposed. The performance of three models for the scale-free network and the traffic network has been explored. The reason why the new model shows a more stable performance than the other models has been explained through the computational methods. In conclusion, the new model can control the spreading of a cascading failure in the traffic network well. This paper might be useful for preventing and mitigating cascading failures in other traffic networks.

Elasticity analysis in chemical industry parks

ABSTRACTBased on the social network analysis (SNA) and the cascading failure model, this paper develops a model of elasticity analysis of the Industrial Symbiosis (IS) network and evaluates the Nanjing Chemical Industry Parks (NCIP) by the metrics of network efficiency and survival rate of the nodes. This paper finds that the NCIP is mainly composed of three major industrial chains, involving the circulation flow of the material, by-products, and energy, and show heterogeneous. Under an intentional attack on the consumer nodes, most of the node's failure cause a chain reaction and bring about changes in network efficiency, and the resilience is not identical accordingly. The network efficiency increases with the augment of the elasticity level, it will not change when reached a certain peak, and the survival rate of the node also increases with the increase of the elasticity level. Therefore, the choice of the optimal elasticity level is helpful to the construction and normal operation of the symbiosis network. At the same time, in order to improve the resilience of the symbiotic network, enterprises should communicate periodically. Because of the ability to find and eliminate the adverse factors, periodic checks are critical for symbiosis between nodes. In order to prevent a network collapse, the NCIP management committee should evaluate the resilience of the IS network regularly, and the government should support the construction of the IS network and give tax subsidies or deductions.

Dynamical modeling of cascading failures in the Turkish power grid.

A reliable supply of electricity is critical for our modern society, and any large-scale disturbance of the electrical system causes substantial costs. In 2015, one overloaded transmission line caused a cascading failure in the Turkish power grid, affecting about 75×106 people. Here, we analyze the Turkish power grid and its dynamical and statistical properties. Specifically, we propose, for the first time, a model that incorporates the dynamical properties and the complex network topology of the Turkish power grid to investigate cascading failures. We find that the network damage depends on the load and generation distribution in the network with centralized generation being more susceptible to failures than a decentralized one. Furthermore, economic considerations on transmission line capacity are shown to conflict with stability.

Dynamic evolution algorithm designing and control parameters quantitatively grading for the cascading failures based reliability model of an interdependent public transit network

To promote the engineering application of the cascading failures (CFs) based reliability study framework for interdependent public transit network (PTN), the dynamic evolution algorithm for activating different components of CFs model should be designed, thereby providing the prerequisite for mastering different control capabilities of multiple CFs control parameters. First, through analyzing the internal cohesion and cooperative evolution mechanism of the different components of CFs model, the dynamic evolution algorithm with high operability is designed to realize the efficient simulation of CFs dynamics evolution. Second, taking Jinan’s interdependent PTN as simulation case, the dynamics evolutions under multiple CFs control parameters are analyzed based on the multi-perspective CFs measurement indicator system. Thereby, the obtained dynamics analysis sample is large enough for measuring the reliability of multiple CFs measurement indicators, and provides the general demonstration analysis framework for being widely used in other cities. Third, we propose the classification distinguishing criteria for evaluating the simulation experiment results, thus getting the basic classification results table. Then, through providing experts with this suggested classification results table as well as all corresponding simulation figures and their dynamics simulation analyses, we qualitatively grade the reliability of CFs measurement indicators by combining the expert comments with our observations. Finally, through analyzing relation mechanism between the CFs control parameters and the multi-perspective CFs measurement indicator system, the quantitatively grading method of CFs control parameters considering analytic hierarchy process (AHP) is proposed. The designed dynamic evolution algorithm provides the basic simulation platform for future extended study, and the designed quantitatively grading method of CFs control parameters helps the city traffic manager to clearly know the priority control sequence of CFs control parameters, making the CFs based reliability be able to be optimized from multiple measures.

Dynamic behavior analysis of an internet flow interaction model under cascading failures.

Cascading failures in the internet have attracted recent attention due to their unpredictability and destructive consequences. Exploring the failure behavior patterns is necessary because they can provide effective intervention approaches to prevent huge network disasters. To analyze internet flow behaviors during cascading failures (chain reactions in router and link failures), we characterize the internet as two coupled networks, the router network and the flow network. Here the flow network is an abstract representation of data correlations obtained from the router network. We use this coupled network to build a cascading failure model for studying flow transmission and competition, which is reflected in bandwidth competition given by limited link capacity. We first study the dependency between routers and flows to explore the flow transmission efficiency when a failure event occurs. Moreover, we find that rerouting enables flow competition area (the number of flows with which one flow has a competitive relationship) to initially remain stable during a failure episode, but that it then quickly drops due to poor physical network connectivity. Additionally, in the early stage after the failure event, the degree of flow competition sharply increases because of the growing number of the flows and congestion. Subsequently, the flow competition decreases due to the failure of flow transmission.

Cascading failures on interdependent networks with star dependent links

In this paper, we propose a cascading failure model with star interdependent links. To describe the model theoretically, a generalized percolation theory is developed. Through extensive numerical simulations and theoretical analyses, we study the phase transition of the system on artificial networks. On both ER-ER and SF-SF networks, the system exhibits a continuous (discontinuous) phase transition for small (large) fraction of service nodes. On ER-ER networks, the more service links of a service node, the system is more likely to exhibit a discontinuous phase transition. On SF-SF networks, the service links of a service node cannot alter the phase of the system. Our suggested theory agrees well with the numerical simulations.

Robustness of complex networks: Cascading failure mechanism by considering the characteristics of time delay and recovery strategy

To study the robustness of complex networks while encountering random failures or deliberate attacks, the cascading failure model is constructed by considering failure propagation with probability, which can depict the dynamic failure process. In particular, the characteristics of time delay and repetitive failure are taken into account in our model, and the network comprehensive robustness index (RI) is further designed according to valid survival edges and nodes. Additionally, the probability recovery strategy is proposed as well, and it is implemented in four typical networks, including the BA network, WS network, NC network and ER network. Different parameters in our model, including α, f, R, and β, are applied in simulation experiments to reveal their effects on RI in the cascading failure process. The simulation results show that nodes’ recovery abilities increase with R, which reduce the impacts of cascading failures and produce good network robustness. Meanwhile, the time delay increases with parameter α, and the size of the cascading failure decreases accordingly, which indicates that the larger that the time delay is, the stronger the RI. Additionally, the speed of the cascading failure process and the size of the cascading failure both present an increasing trend when parameter f increases gradually in the cascading failure. This indicates that the failure probability apparently impacts the RI. We also analyze the turning point t for RI(t) during the cascading failure process.