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Title: 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 themore » 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.« less

Authors:
 [1];  [2];  [2];  [3]
  1. University of Wisconsin, Madison
  2. ORNL
  3. University of Alaska
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
Work for Others (WFO)
OSTI Identifier:
931128
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos; Journal Volume: 17; Journal Issue: 2
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; CRITICALITY; ECONOMICS; ELECTRIC POWER; MITIGATION; OUTAGES; POWER SYSTEMS; STATISTICS; SYSTEMS ANALYSIS

Citation Formats

Dobson, Ian, Carreras, Benjamin A, Lynch, Vickie E, and Newman, David E. Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization. United States: N. p., 2007. Web. doi:10.1063/1.2737822.
Dobson, Ian, Carreras, Benjamin A, Lynch, Vickie E, & Newman, David E. Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization. United States. doi:10.1063/1.2737822.
Dobson, Ian, Carreras, Benjamin A, Lynch, Vickie E, and Newman, David E. Mon . "Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization". United States. doi:10.1063/1.2737822.
@article{osti_931128,
title = {Complex systems analysis of series of blackouts: cascading failure, critical points, and self-organization},
author = {Dobson, Ian and Carreras, Benjamin A and Lynch, Vickie E and Newman, David E},
abstractNote = {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.},
doi = {10.1063/1.2737822},
journal = {Chaos},
number = 2,
volume = 17,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • We compare and test statistical estimates of failure propagation in data from versions of a probabilistic model of loading-dependent cascading failure and a power systems blackout model of cascading transmission line overloads. The comparisons suggest mechanisms affecting failure propagation and are an initial step towards monitoring failure propagation from practical system data. Approximations to the probabilistic model describe the forms of probability distributions of cascade sizes.
  • The critical dynamics of a two-threshold system with the law of conservation of the basic quantity z and in the absence of sink on a scale-free network has been studied. It has been shown that the critical state that is a set of metastable states appears in such a system. The structure of the metastable states is a set of stable clusters of nodes at which the z values are close to the positive and negative threshold values. Avalanches transforming the system from one metastable state to another state appear in the system. The absence of sink is effectively replacedmore » by the annihilation process. The statistics of avalanches in such a system has been analyzed. It has been shown that the self-organized critical state can appear in the system.« less
  • A two-dimensional exactly solvable model of a conformal quantum field theory is developed which is self-dual and has Z/sub N/ symmetry. The operator algebra, the correlation functions, and the anomalous dimensions of all fields are calculated for this model, which describes self-dual critical points in Z/sub N/-symmetric statistical systems.
  • Promptly following any blackout, an investigation is conducted to determine the who, what, where, when, why, and how. For system operators, it is important to quickly grasp the scale and magnitude of the event and rapidly restore service. Then a broader set of stakeholders get involved to assess system performance, determine root causes, compile lessons learned, and develop recommendations. At the heart of the post-mortem investigation is the detailed sequence of events. As accurately as possible, investigators need to know what happened and when. Especially during a cascading failure where events occur rapidly, accurate timing is crucial to understanding howmore » the event unfolded so that the root causes can be determined. The sequence of events is based on vast amounts of data collected from multiple points in the system from a myriad of data collection instruments, some devoted to the purpose of supporting system disturbance post mortem analysis, others providing useful additional context or filling in missing gaps. The more that the investigators know about their available sources of data, and the inherent limitations of each, the better (and quicker) will be the analysis. This is especially important when a large blackout has occurred; there is pressure to find answers quickly, but due to the size and complexity of the event, a deliberate and methodical investigation is necessary. This article discusses the role that system monitoring plays in supporting the investigation of large-scale system disruptions and blackouts.« less