Blackouts, risk, and fat-tailed distributions

IEEE Transactions on Circuits and Systems I: Regular Papers, 2004

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of selforganized 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.

2002

As power system loading increases, larger blackouts due to cascading outages become more likely. We investigate a critical loading at which the average size of blackouts increases sharply to examine whether the probability distribution of blackout sizes shows the power tails observed in real blackout data. Three different models are used, including two simulations of cascading outages in electric power transmission systems. We also derive and use a new, analytically solvable model of probabilistic cascading failure which represents the progressive system weakening as the cascade proceeds.

2000

We examine correlations in a time series of electric power system blackout sizes using scaled window variance analysis and R/S statistics. The data shows some evidence of long time correlations and has Hurst exponent near 0.7. Large blackouts tend to correlate with further large blackouts after a long time interval. Similar effects are also observed in many other complex systems exhibiting self-organized criticality. We discuss this initial evidence and possible explanations for selforganized criticality in power systems blackouts. Selforganized criticality, if fully confirmed in power systems, would suggest new approaches to understanding and possibly controlling blackouts.

2002

A model has been developed to study the global complex dynamics of a series of blackouts in power transmission systems . This model has included a simple level of self-organization by incorporating the growth of power demand and the engineering response to system failures. Two types of blackouts have been identified with different dynamical properties. One type of blackout involves loss of load due to lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackouts versus the other depends on operational conditions and the proximity of the system to one of its two critical points. The first critical point is characterized by operation with lines close to their line limits. The second critical point is characterized by the maximum in the fluctuations of the load demand being near the generator margin capability. The identification of this second critical point is an indication that the increase of the generator capability as a response to the increase of the load demand must be included in the dynamical model to achieve a higher degree of self-organization. When this is done, the model shows a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.

arXiv (Cornell University), 2023

The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has been done by various threshold models, which are self-tuned at their critical points, but as many papers pointed out, explanations are intuitive, and more empirical data is needed to support hypotheses. In this paper, the authors analyze outage data collected from various public sources to calculate the outage energy and outage duration exponents of possible power-law fits. Temporal thresholds are applied to identify crossovers from initial shorttime behavior to power-law tails. We revisit and add to the possible explanations of the uniformness of these exponents. By performing power spectral analyses on the outage event time series and the outage duration time series, it is found that, on the one hand, while being overwhelmed by white noise, outage events show traits of self-organized criticality (SOC), which may be modeled by a crossover from random percolation to directed percolation branching process with dissipation, coupled to a conserved density. On the other hand, in responses to outages, the heavy tails in outage duration distributions could be a consequence of the highly optimized tolerance (HOT) mechanism, based on the optimized allocation of maintenance resources.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004

In order to study the complex global dynamics of a series of blackouts in power transmission systems a dynamical model of such a system has been developed. This model includes a simple representation of the dynamical evolution by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of generator capacity. Two types of blackouts have been identified, each having different dynamical properties. One type of blackout involves the loss of load due to transmission lines reaching their load limits but no line outages. The second type of blackout is associated with multiple line outages. The dominance of one type of blackout over the other depends on operational conditions and the proximity of the system to one of its two critical points. The model displays characteristics such as a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.

2002

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007

We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is governed by a power law. This result is consistent with the power system being a complex system designed and operated near criticality. The power law makes the risk of large blackouts consequential and implies the need for nonstandard risk analysis.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2002

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 ͑algebraic͒ 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.

2000

We give a comprehensive account of a complex systems ap- proach to large blackouts caused by cascading failure. In- stead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is gov- erned by a power