Modeling cascading failures in the North American power grid

Kinney, Ryan; Crucitti, Paolo; Albert, Réka; Latora, Vito

doi:10.1140/epjb/e2005-00237-9

Cited by 613 publications

(377 citation statements)

References 31 publications

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“…Finding network topologies that enhance the stability of power grids has been an active subfield of network theory. Previous studies have typically focused on the structural vulnerability of power grids against external attacks [1][2][3][4][5][6][7] and the cascading spreading of system failure over power grids [6,[8][9][10]. In addition, researchers have studied the relation between topology and dynamics via network synchronization models.…”

Section: Introductionmentioning

confidence: 99%

Building blocks of the basin stability of power grids

2016

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Given a power grid and a transmission (coupling) strength, basin stability is a measure of synchronization stability for individual nodes. Earlier studies have focused on the basin stability's dependence of the position of the nodes in the network for single values of transmission strength. Basin stability grows from zero to one as transmission strength increases, but often in a complex, nonmonotonous way. In this study, we investigate the entire functional form of the basin stability's dependence on transmission strength. To be able to perform a systematic analysis, we restrict ourselves to small networks. We scan all isomorphically distinct networks with an equal number of power producers and consumers of six nodes or less. We find that the shapes of the basin stability fall into a few, rather well-defined classes, that could be characterized by the number of edges and the betweenness of the nodes, whereas other network positional quantities matter less.

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Section: Introductionmentioning

confidence: 99%

Building blocks of the basin stability of power grids

2016

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“…Previous research has studied the relationship between a network ′ s structure and its topological resilience to incremental node loss [24] and the relationship between average degree and the effect of single node damage [10]. It was shown that the larger the average node degree, the less stable a steady state is against single node damage.…”

Section: Resultsmentioning

confidence: 99%

Compensatory interactions to stabilize multiple steady states or mitigate the effects of multiple deregulations in biological networks

2016

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Complex diseases can be modeled as damage to intra-cellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those corresponding to disease. Previous work designed compensatory interactions to stabilize an attractor of a Boolean network after single node damage. We generalize this method to a multi-node damage scenario and to the simultaneous stabilization of multiple steady state attractors. We classify the emergent situations, with a special focus on combinatorial effects, and characterize each class through simulation. We explore how the structural and functional properties of the network affect its resilience and its possible repair scenarios. We demonstrate the method ′ s applicability to two intra-cellular network models relevant to cancer. This work has implications in designing prevention strategies for complex disease.

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“…The question is then under which conditions this failure leads to a cascade of macroscopic size. Applications of this case include power-grid cascade failures [4,5,10], or failures of server infrastructure [6].…”

Section: Results For the Rie Regimementioning

confidence: 99%

“…A fixed relation between fragility and threshold was first used in [4] to describe cascading processes in power grids and Internet (see also [5,9,10]). It basically reflects the situation of many socio-technical systems in which the capacity of agents is usually ad hoc designed to handle the load, because limited by cost, under normal conditions.…”

Section: /23mentioning

confidence: 99%

How Big Is Too Big? Critical Shocks for Systemic Failure Cascades

et al. 2013

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External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighboring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold θ i determining their capacity to handle a load αθ i with 1 − α being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P (θ), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.

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Modeling cascading failures in the North American power grid

Cited by 613 publications

References 31 publications

Building blocks of the basin stability of power grids

Building blocks of the basin stability of power grids

Compensatory interactions to stabilize multiple steady states or mitigate the effects of multiple deregulations in biological networks

How Big Is Too Big? Critical Shocks for Systemic Failure Cascades

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