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.

Cascading failures in large-scale electric power transmission systems are an important cause of blackouts. Analysis of North American blackout data has revealed power law (algebraic) tails in the blackout size probability distribution which suggests a dynamical origin. With this observation as motivation, we examine cascading failure in a simplified transmission system model as load power demand is increased. The model represents generators, loads, the transmission line network, and the operating limits on these components. Two types of critical points are identified and are characterized by transmission line flow limits and generator capability limits, respectively. Results are obtained for tree networks of a regular form and a more realistic 118-node network. It is found that operation near critical points can produce power law tails in the blackout size probability distribution similar to those observed. The complex nature of the solution space due to the interaction of the two critical points is examined.

Cascading outages can cause large blackouts, and a variety of methods are emerging to study this challenging topic. The Task Force on Understanding, Prediction, Mitigation, and Restoration of Cascading Failures, under the IEEE PES Computer Analytical Methods Subcommittee (CAMS), seeks to consolidate and review the progress of the field towards methods and tools of assessing the risk of cascading failure. This paper discusses the challenges of cascading failure and summarizes a variety of state-of-the-art analysis and simulation methods, including analyzing observed data, and simulations relying on various probabilistic, deterministic, approximate, and heuristic approaches. Limitations to the interpretation and application of analytical results are highlighted, and directions and challenges for future developments are discussed.

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of self-organized criticality (SOC). The probability distribution functions of various measures of blackout size have a power tail and rescaled range analysis of the time series shows moderate long-time correlations. Moreover, the same analysis applied to a time series from a sandpile model known to be self-organized critical gives results of the same form. Thus, the blackout data seem consistent with SOC. A qualitative explanation of the complex dynamics observed in electric power system blackouts is suggested.