1,748 research outputs found

    A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids

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    Cascading failures are one of the main reasons for blackouts in electric power transmission grids. The economic cost of such failures is in the order of tens of billion dollars annually. The loading level of power system is a key aspect to determine the amount of the damage caused by cascading failures. Existing studies show that the blackout size exhibits phase transitions as the loading level increases. This paper investigates the impact of the topology of a power grid on phase transitions in its robustness. Three spectral graph metrics are considered: spectral radius, effective graph resistance and algebraic connectivity. Experimental results from a model of cascading failures in power grids on the IEEE power systems demonstrate the applicability of these metrics to design/optimize a power grid topology for an enhanced phase transition behavior of the system

    A model for cascading failures in complex networks

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    Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.Comment: 4 pages, 4 figure

    Nonlocal failures in complex supply networks by single link additions

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    How do local topological changes affect the global operation and stability of complex supply networks? Studying supply networks on various levels of abstraction, we demonstrate that and how adding new links may not only promote but also degrade stable operation of a network. Intriguingly, the resulting overloads may emerge remotely from where such a link is added, thus resulting in nonlocal failure. We link this counter-intuitive phenomenon to Braess' paradox originally discovered in traffic networks. We use elementary network topologies to explain its underlying mechanism for different types of supply networks and find that it generically occurs across these systems. As an important consequence, upgrading supply networks such as communication networks, biological supply networks or power grids requires particular care because even adding only single connections may destabilize normal network operation and induce disturbances remotely from the location of structural change and even global cascades of failures.Comment: 12 pages, 10 figure

    Robustness of scale-free networks to cascading failures induced by fluctuating loads

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    Taking into account the fact that overload failures in real-world functional networks are usually caused by extreme values of temporally fluctuating loads that exceed the allowable range, we study the robustness of scale-free networks against cascading overload failures induced by fluctuating loads. In our model, loads are described by random walkers moving on a network and a node fails when the number of walkers on the node is beyond the node capacity. Our results obtained by using the generating function method shows that scale-free networks are more robust against cascading overload failures than Erd\H{o}s-R\'enyi random graphs with homogeneous degree distributions. This conclusion is contrary to that predicted by previous works which neglect the effect of fluctuations of loads.Comment: 9 pages, 6 figure

    Systemic Risk in a Unifying Framework for Cascading Processes on Networks

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    We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, XX^\ast, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of XX^\ast as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure
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