Complex systems analysis of series of blackouts: Cascading failure, critical points, and self-organization

Abstract

We give an overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics and dynamics of series of blackouts with approximate global models. Blackout data from several countries suggest that the frequency of large blackouts is governed by a power law. The power law makes the risk of large blackouts consequential and is consistent with the power system being a complex system designed and operated near a critical point. Power system overall loading or stress relative to operating limits is a key factor affecting the risk of cascading failure. Power system blackout models and abstract models of cascading failure show critical points with power law behavior as load is increased. To explain why the power system is operated near these critical points and inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near a critical point and confirm this idea using a power system model. The slow evolution of the power system is driven by a steady increase in electric loading, economic pressures to maximize the use of the grid, and the engineering responses to blackouts that upgrade the system. Mitigation of blackout risk should account for dynamical effects in complex self-organized critical systems. For example, some methods of suppressing small blackouts could ultimately increase the risk of large blackouts.

Suppressing cascades of load in interdependent networks

“…S7. Other models of cascades in power grids conclude that upgrading and repairing the system to mitigate the smallest blackouts may increase the risk of the largest blackouts (15). Similarly, extinguishing small forest fires, a common policy in the 20th century, increases forest vegetation and thus the risk of large forest fires-a phenomenon known as the "Yellowstone effect" (32).…”

“…We study Bak-TangWiesenfeld sandpile dynamics (23,24) on networks derived from real, interdependent power grids and on sparsely coupled, random regular graphs that approximate the real topologies. Sandpile dynamics are paradigms for the cascades of load, self-organized criticality, and power law distributions of event sizes that pervade disciplines, from neuronal avalanches (25)(26)(27) to cascades among banks (28) to earthquakes (29), landslides (30), forest fires (31,32), solar flares (33,34), and electrical blackouts (15). Sandpile cascades have been extensively studied on isolated networks (35)(36)(37)(38)(39)(40)(41).…”

“…The first models of interdependent grids use simplified topologies and global coupling to find that interconnections affect critical points of cascades (19), which suggests that they may affect the power law distributions of blackout size (12,15). Models with interconnections among distinct infrastructure have focused on the spread of topological failures, in which nodes are recursively removed (20)(21)(22), and not on the dynamical processes occurring on these networks.…”

“…Researchers have begun to model cascades of load and failure within individual power grids using probabilistic models (15), linearized electric power dynamics (16,17), and game theory (18).…”

Building blocks of the basin stability of power grids

“…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.…”