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

TLDR

Cascading failures in power grids are driven by system loading, with models showing critical points that exhibit power‑law behavior as load increases. The study reviews a complex‑systems view of large blackouts, proposes that operating margins drift slowly toward critical points due to load growth and economic pressures, and argues that mitigation must account for these dynamic effects. Using approximate global models, the authors analyze the statistics and dynamics of blackout series, modeling the slow evolution of operating margins driven by increasing load, economic incentives, and post‑blackout upgrades. Data from multiple countries reveal that large blackout frequency follows a power law, indicating high risk and consistency with critical‑point operation, and that suppressing small blackouts can paradoxically raise the risk of large ones.

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.