1,748 research outputs found
A Topological Investigation of Phase Transitions of Cascading Failures in Power Grids
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
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
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
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
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, , and for each of
the three classes we derive a recursive equation to compute its value. The
phase diagram of 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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