Research Article

Small vulnerable sets determine large network cascades in power grids

See allHide authors and affiliations

Science  17 Nov 2017:
Vol. 358, Issue 6365, eaan3184
DOI: 10.1126/science.aan3184

You are currently viewing the abstract.

View Full Text

Log in to view the full text

Log in through your institution

Log in through your institution

The domino effect in power failure

Sometimes a power failure can be fairly local, but other times, a seemingly identical initial failure can cascade to cause a massive and costly breakdown in the system. Yang et al. built a model for the North American power grid network based on samples of data covering the years 2008 to 2013 (see the Perspective by D'Souza). Although the observed cascades were widespread, a small fraction of all network components, particularly the ones that were most cohesive within the network, were vulnerable to cascading failures. Larger cascades were associated with concurrent triggering events that were geographically closer to each other and closer to the set of vulnerable components.

Science, this issue p. eaan3184; see also p. 860

Structured Abstract


Cascading failures in power grids are inherently network processes, in which an initially small perturbation leads to a sequence of failures that spread through the connections between system components. An unresolved problem in preventing major blackouts has been to distinguish disturbances that cause large cascades from seemingly identical ones that have only mild effects. Modeling and analyzing such processes are challenging when the system is large and its operating condition varies widely across different years, seasons, and power demand levels.


Multicondition analysis of cascade vulnerability is needed to answer several key questions: Under what conditions would an initial disturbance remain localized rather than cascade through the network? Which network components are most vulnerable to failures across various conditions? What is the role of the network structure in determining component vulnerability and cascade sizes? To address these questions and differentiate cascading-causing disturbances, we formulated an electrical-circuit network representation of the U.S.–South Canada power grid—a large-scale network with more than 100,000 transmission lines—for a wide range of operating conditions. We simulated cascades in this system by means of a dynamical model that accounts for transmission line failures due to overloads and the resulting power flow reconfigurations.


To quantify cascade vulnerability, we estimated the probability that each transmission line fails in a cascade. Aggregating the results from multiple conditions into a single network representation, we created a systemwide vulnerability map, which exhibits relatively homogeneous geographical distribution of power outages but highly heterogeneous distribution of the underlying overload failures. Topological analysis of the network representation revealed that the transmission lines vulnerable to overload failures tend to occupy the network’s core, characterized by links between highly connected nodes. We found that only a small fraction of the transmission lines in the network (well below 1% on average) are vulnerable under a given condition. When measured in terms of node-to-node distance and geographical distance, individual cascades often propagate far from the triggering failures, but the set of lines vulnerable to these cascades tend to be limited to the region in which the cascades are triggered. Moreover, large cascades are disproportionately more likely to be triggered by initial failures close to the vulnerable set.


Our results imply that the same disturbance in a given power grid can lead to disparate outcomes under different conditions—ranging from no damage to a large-scale cascade. The association between large cascades and the triggering failures’ proximity to the vulnerable set indicates that the topological and geographical properties of the vulnerable set is a major factor determining whether the failures spread widely. Because the vulnerable set is small, failures would often repeat on the same lines in the absence of interventions. Although the power grid represents a complex system in which changes can have unanticipated effects, our analysis suggests failure-based allocation of resources as a strategy in upgrading the system for improved resilience against large cascades.

Cascade-resistant portion of the U.S.–South Canada power grid.

The network is visualized on a cartogram that equalizes the density of nodes. (Top) Power lines that never underwent outage in our simulations under any grid condition are shown in green, whereas all the other lines—whose vulnerability varies widely—are in gray. (Bottom) Spreading of a cascade triggered by three failures at time t = 0 (arrows), which resulted in 254 failures at t = 100 (the end of the cascade in linearly rescaled time).


The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.

View Full Text