Small vulnerable sets determine large network cascades in power grids

INTRODUCTION 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. RATIONALE 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. RESULTS 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. CONCLUSION 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.