Risk analysis of critical loading and blackouts with cascading events

We analyze a 15-year time series of North American electric power transmission system blackouts for evidence of self-organized criticality. The probability distribution functions of various measures of blackout size have a power tail and R/S 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 self-organized criticality. A qualitative explanation of the complex dynamics observed in electric power system blackouts is suggested. Complex dynamics of blackouts in power transmission systems B.A. Carreras, V.E. Lynch, I. Dobson, D.E. Newman Chaos: An Interdisciplinary Journal of Nonlinear Science volume 14, no 3, September 2004, pp 643-652 (reprinted in section 6.12) Abstract: A model has been developed to study the global complex dynamics of a series of blackouts in power transmission systems. This model includes a simple level of self-organization by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of the generator capacity. Two types of blackouts have been identified with different dynamical properties. One type of blackout involves 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 blackouts versus the other depends on operational conditions and the proximity of the system to one of its two critical points. The model shows a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America. A model has been developed to study the global complex dynamics of a series of blackouts in power transmission systems. This model includes a simple level of self-organization by incorporating the growth of power demand, the engineering response to system failures, and the upgrade of the generator capacity. Two types of blackouts have been identified with different dynamical properties. One type of blackout involves 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 blackouts versus the other depends on operational conditions and the proximity of the system to one of its two critical points. The model shows a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America. Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model J. Chen, J.S. Thorp, I. Dobson to appear in International Journal of Electrical Power and Energy Systems in 2005. preprint available at http://eceserv0.ece.wisc.edu/~dobson/home.html Abstract: A hidden failure embedded DC model of power transmission systems has been developed to study the observed power tails of North American blackout data. We investigate the impacts of several model parameters on the global dynamics and evaluate possible mitigation measures. The main parameters include system loading level, hidden failure probability, spinning reserve capacity and control strategy. The sensitivity of power-law behavior with respect to each of these parameters and the possible blackout mitigation are discussed and illustrated using simulation results from the WSCC 179-bus equivalent system and IEEE 118-bus test system. It is our intention that the study can provide guidance on when and how the suggested mitigation methods might be effective. A hidden failure embedded DC model of power transmission systems has been developed to study the observed power tails of North American blackout data. We investigate the impacts of several model parameters on the global dynamics and evaluate possible mitigation measures. The main parameters include system loading level, hidden failure probability, spinning reserve capacity and control strategy. The sensitivity of power-law behavior with respect to each of these parameters and the possible blackout mitigation are discussed and illustrated using simulation results from the WSCC 179-bus equivalent system and IEEE 118-bus test system. It is our intention that the study can provide guidance on when and how the suggested mitigation methods might be effective. A loading-dependent model of probabilistic cascading failure I. Dobson, B.A. Carreras, D.E. Newman to appear in Probability in the Engineering and Informational Sciences vol. 19, no. 1, Jan 2005, pp. 15-32 preprint available at http://eceserv0.ece.wisc.edu/~dobson/home.html Abstract: We propose an analytically tractable model of loading-dependent cascading failure that captures some of the salient features of large blackouts of electric power transmission systems. This leads to a new application and derivation of the quasibinomial distribution and its generalization to a saturating form with an extended parameter range. The saturating quasibinomial distribution of the number of failed components has a power law region at a critical loading and a significant probability of total failure at higher loadings. We propose an analytically tractable model of loading-dependent cascading failure that captures some of the salient features of large blackouts of electric power transmission systems. This leads to a new application and derivation of the quasibinomial distribution and its generalization to a saturating form with an extended parameter range. The saturating quasibinomial distribution of the number of failed components has a power law region at a critical loading and a significant probability of total failure at higher loadings. The following conference papers were produced. A branching process approximation to cascading load-dependent system failure I. Dobson, B.A. Carreras, D.E. Newman Thirty-seventh Hawaii International Conference on System Sciences, Hawaii, January 2004 (reprinted in section 6.1) Abstract: Networked infrastructures operated under highly loaded conditions are vulnerable to catastrophic cascading failures. For example, electric power transmission systems must be designed and operated to reduce the risk of widespread blackouts caused by cascading failure. There is a need for analytically tractable models to understand and quantify the risks of cascading Networked infrastructures operated under highly loaded conditions are vulnerable to catastrophic cascading failures. For example, electric power transmission systems must be designed and operated to reduce the risk of widespread blackouts caused by cascading failure. There is a need for analytically tractable models to understand and quantify the risks of cascading failure. We study a probabilistic model of loading dependent cascading failure by approximating the propagation of failures as a Poisson branching process. This leads to a criticality condition for the failure propagation. At criticality there are power tails in the probability distribution of cascade sizes and consequently considerable risks of widespread catastrophic failure. Avoiding criticality or supercriticality is a key approach to reduce this risk. This approach of minimizing the propagation of failure after the cascade has started is complementary to the usual approach of minimizing the risk of the first few cascading failures. The analysis introduces a saturating form of the generalized Poisson distribution so that supercritical systems with a high probability of total failure can be considered. Dynamical and probabilistic approaches to the study of blackout vulnerability of the power transmission grid B.A. Carreras, V.E. Lynch, D.E. Newman, I. Dobson Thirty-seventh Hawaii International Conference on System Sciences, Hawaii, January 2004 (reprinted in section 6.2) Abstract: The CASCADE probabilistic model for cascading failures gives a simple characterization of the transition from an isolated failure to a system-wide collapse as system loading increases. Using the basic ideas of this model, the parameters that lead to a similar characterization for power transmission system blackouts are identified in the OPA dynamical model of series of blackouts. The comparison between the CASCADE and OPA models yields parameters that can be computed from the OPA model that indicate a threshold for cascading failure blackouts. This is a first step towards computing similar parameters for real power transmission systems. The CASCADE probabilistic model for cascading failures gives a simple characterization of the transition from an isolated failure to a system-wide collapse as system loading increases. Using the basic ideas of this model, the parameters that lead to a similar characterization for power transmission system blackouts are identified in the OPA dynamical model of series of blackouts. The comparison between the CASCADE and OPA models yields parameters that can be computed from the OPA model that indicate a threshold for cascading failure blackouts. This is a first step towards computing similar parameters for real power transmission systems. Probabilistic load-dependent cascading failure with limited component interactions I. Dobson, B.A. Carreras, D.E. Newman, IEEE International Conference on Circuits & Systems, Vancouver, Canada, May 2004 (reprinted in section 6.3) Abstract: We generalize an analytically solvable probabilistic model of cascading failure in which failing components interact with other components by increasing their load and hence their chance of failure. In the generalized model, instead of a failing component increasing the load of all components, it increases the load of a random sample of the components. The size of the sample describes the extent of component interactions within the system. The generalized model is approximated by a saturating branching process, and this leads to a criticality condition for cascading failure propagation that depends on the size of the sample. The criticality condition shows how the extent of component interactions controls the proximity to catastrophic cascading failure. Implications for the complexity of power transmission system design to avoid cascading blackouts are briefly discussed. We generalize an analytically solvable probabilistic model of cascading failure in which failing components interact with other components by increasing their load and hence their chance of failure. In the generalized model, instead of a failing component increasing the load of all components, it increases the load of a random sample of the components. The size of the sample describes the extent of component interactions within the system. The generalized model is approximated by a saturating branching process, and this leads to a criticality condition for cascading failure propagation that depends on the size of the sample. The criticality condition shows how the extent of component interactions controls the proximity to catastrophic cascading failure. Implications for the complexity of power transmission system design to avoid cascading blackouts are briefly discussed. Complex systems analysis of series of blackouts: cascading failure, criticality, and self-organization I. Dobson, B.A. Carreras, V.E. Lynch, D.E. Newman IREP conference: Bulk Power System Dynamics and Control VI, Cortina d'Ampezzo, Italy, August 2004 (reprinted in section 6.4) Abstract: 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. Power system overall load relative to operating limits is a key factor affecting the risk of cascading failure. Blackout models and an abstract model of cascading failure show that there are critical transitions as load is increased. Power law behavior can be observed at these transitions. The critical loads at which blackout risk sharply increase are identifiable thresholds for cascading failure and we discuss approaches to computing the proximity to cascading failure using these thresholds. Approximating cascading failure as a branching process suggests ways to compute and monitor criticality by quantifying how much failures propagate. Inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near criticality and confirm this idea using a blackout model. Mitigation of blackout risk should take care to account for counter-intuitive effects in complex self-organized critical systems. For example, suppressing small blackouts could lead the system to be operated closer to the edge and ultimately increase the risk of large blackouts. Estimating failure propagation in models of cascading blackouts I. Dobson, B.A. Carreras, V.E. Lynch, B. Nkei, D.E. Newman Eighth International Conference on Probability Methods Applied to Power Systems, Ames Iowa, September 2004 (reprinted in section 6.5) Abstract: 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 in practical system data. Approximations to the probabilistic model describe the forms of probability distributions of cascade sizes. 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 in practical system data. Approximations to the probabilistic model describe the forms of probability distributions of cascade sizes. A criticality approach to monitoring cascading failure risk and failure propagation in transmission systems I. Dobson, B. A. Carreras, D. E. Newman Electricity Transmission in Deregulated Markets, conference at Carnegie Mellon University, Pittsburgh PA USA, December 2004 (reprinted in section 6.6) Abstract: We consider the risk of cascading failure of electric power transmission systems as overall loading is increased. There is evidence from both abstract and power systems models of cascading failure that there is a critical loading at which the risk of cascading failure sharply increases. Moreover, as expected in a phase transition, at the critical loading there is a power tail in the probability distribution of blackout size. (This power tail is consistent with the empirical distribution of North American blackout sizes.) The importance of the critical loading is that it gives a reference point for determining the risk of cascading failure. Indeed the risk of cascading failure can be quantified and monitored by finding the closeness to the critical loading. This paper suggests and outlines ways of detecting the closeness to criticality from data produced from a generic blackout model. The increasing expected blackout size at criticality can be detected by computing expected blackout size at various loadings. Another approach uses branching process models of cascading failure to interpret the closeness to the critical loading in terms of a failure propagation parameter λ. We suggest a statistic for λ that could be applied before saturation occurs. The paper concludes with suggestions for a wider research agenda for measuring the closeness to criticality of a fixed power transmission network and for studying the complex dynamics governing the slow evolution of a transmission network. We consider the risk of cascading failure of electric power transmission systems as overall loading is increased. There is evidence from both abstract and power systems models of cascading failure that there is a critical loading at which the risk of cascading failure sharply increases. Moreover, as expected in a phase transition, at the critical loading there is a power tail in the probability distribution of blackout size. (This power tail is consistent with the empirical distribution of North American blackout sizes.) The importance of the critical loading is that it gives a reference point for determining the risk of cascading failure. Indeed the risk of cascading failure can be quantified and monitored by finding the closeness to the critical loading. This paper suggests and outlines ways of detecting the closeness to criticality from data produced from a generic blackout model. The increasing expected blackout size at criticality can be detected by computing expected blackout size at various loadings. Another approach uses branching process models of cascading failure to interpret the closeness to the critical loading in terms of a failure propagation parameter λ. We suggest a statistic for λ that could be applied before saturation occurs. The paper concludes with suggestions for a wider research agenda for measuring the closeness to criticality of a fixed power transmission network and for studying the complex dynamics governing the slow evolution of a transmission network. The Impact of Various Upgrade Strategies on the Long-Term Dynamics and Robustness of the Transmission Grid D. E. Newman, B. A. Carreras, V. E. Lynch, I. Dobson Electricity Transmission in Deregulated Markets, conference at Carnegie Mellon University, Pittsburgh PA USA, December 2004 (reprinted in section 6.7) Abstract: We use the OPA global complex systems model of the power transmission system to investigate the effect of a series of different network upgrade scenarios on the long time dynamics and the probability of large cascading failures. The OPA model represents the power grid at the level of DC load flow and LP generation dispatch and represents blackouts caused by randomly triggered cascading line outages and overloads. This model represents the long-term, slow evolution of the transmission grid by incorporating the effects of increasing demand and engineering responses to blackouts such as upgrading transmission lines and generators. We examine the effect of increased component reliability on the long-term risks, the effect of changing operational margins and the effect of redundancy on those same long-term risks. The general result is that while increased reliability of the components decreases the probability of small blackouts, depending on the implementation, it actually can increase the probability of large blackouts. When we instead increase some types of redundancy of the system there is an overall decrease in the large blackouts with a concomitant increase of the smallest blackouts. As some of these results are counter intuitive these studies suggest that care must be taken when making what seem to be logical upgrade decisions. We use the OPA global complex systems model of the power transmission system to investigate the effect of a series of different network upgrade scenarios on the long time dynamics and the probability of large cascading failures. The OPA model represents the power grid at the level of DC load flow and LP generation dispatch and represents blackouts caused by randomly triggered cascading line outages and overloads. This model represents the long-term, slow evolution of the transmission grid by incorporating the effects of increasing demand and engineering responses to blackouts such as upgrading transmission lines and generators. We examine the effect of increased component reliability on the long-term risks, the effect of changing operational margins and the effect of redundancy on those same long-term risks. The general result is that while increased reliability of the components decreases the probability of small blackouts, depending on the implementation, it actually can increase the probability of large blackouts. When we instead increase some types of redundancy of the system there is an overall decrease in the large blackouts with a concomitant increase of the smallest blackouts. As some of these results are counter intuitive these studies suggest that care must be taken when making what seem to be logical upgrade decisions. Risk assessment in complex interacting infrastructure systems D. E. Newman, B. Nkei, B. A. Carreras, I. Dobson, V. E. Lynch, P. Gradney Thirty-eighth Hawaii International Conference on System Sciences, Hawaii, January 2005 (reprinted in section 6.8) Abstract: Critical infrastructures have some of the characteristic properties of complex systems. They exhibit infrequent large failures events. These events, though infrequent, often obey a power law distribution in their probability versus size. This power law behavior suggests that ordinary risk analysis might not apply to these systems. It is thought that some of this behavior comes from different parts of the systems interacting with each other both in space and time. While these complex infrastructure systems can exhibit these characteristics on their own, in reality these individual infrastructure systems interact with each other in even more complex ways. This interaction can lead to increased or decreased risk of failure in the individual systems. To investigate this and to formulate appropriate risk assessment tools for such systems, a set of models are used to study to impact of coupling complex systems. A probabilistic model and a dynamical model that have been used to study blackout dynamics in the power transmission grid are used as paradigms. In this paper, we investigate changes in Critical infrastructures have some of the characteristic properties of complex systems. They exhibit infrequent large failures events. These events, though infrequent, often obey a power law distribution in their probability versus size. This power law behavior suggests that ordinary risk analysis might not apply to these systems. It is thought that some of this behavior comes from different parts of the systems interacting with each other both in space and time. While these complex infrastructure systems can exhibit these characteristics on their own, in reality these individual infrastructure systems interact with each other in even more complex ways. This interaction can lead to increased or decreased risk of failure in the individual systems. To investigate this and to formulate appropriate risk assessment tools for such systems, a set of models are used to study to impact of coupling complex systems. A probabilistic model and a dynamical model that have been used to study blackout dynamics in the power transmission grid are used as paradigms. In this paper, we investigate changes in the risk models based on the power law event probability distributions, when complex systems are coupled. Understanding the effect of risk aversion on risk U. Bhatt, D.E. Newman, B.A. Carreras, I. Dobson Thirty-eighth Hawaii International Conference on System Sciences, Hawaii, January 2005 (reprinted in section 6.9) Abstract: As we progress, society must intelligently address the following question: How much risk is acceptable? How we answer this question could have important consequences for the future state of our nation and the dynamics of its social structure. In this work, we will elucidate and demonstrate using a physically based model that the attempt to eliminate all thinkable risks in our society may be setting us up for even larger risks. The simplest example to illustrate this point is something with which we are all familiar and have known from the time we were very young. When children burn their finger on a hot item they learn the consequences of touching fire. This small risk has taught the child to avoid larger risks. In trying to avoid these small risks as well as larger risks, one runs the dual danger of not learning from the small ones and of having difficulty in differentiating between large and small risks. We will illustrate this problem with a series of social dynamics examples from the operation of NASA to network operation and then make an analogy to a complex system model for this type of dynamics. From these results, recommendations will be made for the types of risk responses that improve the situation versus those that worsen the situation. In order to progress, society has to recognize that accidents are unavoidable and therefore an intelligent risk management program must be implemented aimed toward avoiding or reducing major accidents. It is not possible to avoid all risk but it is better to avoid the greater risk situations for society. As we progress, society must intelligently address the following question: How much risk is acceptable? How we answer this question could have important consequences for the future state of our nation and the dynamics of its social structure. In this work, we will elucidate and demonstrate using a physically based model that the attempt to eliminate all thinkable risks in our society may be setting us up for even larger risks. The simplest example to illustrate this point is something with which we are all familiar and have known from the time we were very young. When children burn their finger on a hot item they learn the consequences of touching fire. This small risk has taught the child to avoid larger risks. In trying to avoid these small risks as well as larger risks, one runs the dual danger of not learning from the small ones and of having difficulty in differentiating between large and small risks. We will illustrate this problem with a series of social dynamics examples from the operation of NASA to network operation and then make an analogy to a complex system model for this type of dynamics. From these results, recommendations will be made for the types of risk responses that improve the situation versus those that worsen the situation. In order to progress, society has to recognize that accidents are unavoidable and therefore an intelligent risk management program must be implemented aimed toward avoiding or reducing major accidents. It is not possible to avoid all risk but it is better to avoid the greater risk situations for society. Branching process models for the exponentially increasing portions of cascading failure blackouts I. Dobson, B.A. Carreras, D.E. Newman Thirty-eighth Hawaii International Conference on System Sciences, Hawaii, January 2005 (reprinted in section 6.10) Abstract: We introduce branching process models in discrete and continuous time for the exponentially increasing phase of cascading blackouts. Cumulative line trips from real blackout data have portions consistent with these branching process models. Some initial calculations identifying parameters and using a branching process model to estimate blackout probabilities during and after the blackout are illustrated. We introduce branching process models in discrete and continuous time for the exponentially increasing phase of cascading blackouts. Cumulative line trips from real blackout data have portions consistent with these branching process models. Some initial calculations identifying parameters and using a branching process model to estimate blackout probabilities during and after the blackout are illustrated. In addition to the conference papers listed above, which were all presented, the following presentations were made: Blackout mitigation assessment in power transmission systems B.A. Carreras, V.E. Lynch, D.E. Newman, I. Dobson 36th Hawaii International Conference on System Sciences, Hawaii, January 2003. A probabilistic loading-dependent model of cascading failure and possible implications for blackouts I. Dobson, B.A. Carreras, D.E. Newman 36th Hawaii International Conference on System Sciences, Hawaii, January 2003. Cascading failure, I. Dobson, B.A. Carreras, D.E. Newman Talk at the University of Liege, Belgium March 2003 Cascading failure, I. Dobson, B.A. Carreras, D.E. Newman Talk at Imperial College, London England March 2003 Cascading failure, I. Dobson Brief presentation at press conference organized by Wisconsin Public Utility Institute, Madison WI, August 2003 Cascading failure and the risk of large blackouts, I. Dobson, B.A. Carreras, D.E. Newman Talk at UMIST, University of Manchester Institute for Science and Technology, Manchester, England, September 2003 Cascading failure and catastrophic risk in complex systems, I. Dobson, B.A. Carreras, D.E. Newman Invited talk at Institute for Asset Management Workshop, Birmingham, England, September 2003 Cascading failure and the risk of large blackouts, I. Dobson, B.A. Carreras, D.E. Newman, Talk to Wisconsin Public Service Commission, Madison WI, September 2003 Cascading failure and the risk of large blackouts, I. Dobson, B.A. Carreras, D.E. Newman, Talk to Graduate student seminar course, Electrical and Computer Engineering Department, University of Wisconsin, Madison WI, October 2003 Cascading failure, the risk of large blackouts, criticality and self-organization I. Dobson, B.A. Carreras, D.E. Newman, Talk to Plasma Physics seminar, University of Wisconsin, Madison WI, October 2003 Cascading failure, criticality and the risk of large blackouts, I. Dobson, B.A. Carreras, D.E. Newman, Talk to Systems group seminar, Electrical and Computer Engineering Department, University of Wisconsin, Madison WI, October 2003 Cascading failure, the risk of large blackouts, criticality and self-organization I. Dobson, B.A. Carreras, D.E. Newman, Talk to Chaos and Complex Systems seminar, University of Wisconsin, Madison WI, October 2003 Criticality and risk of large cascading blackouts I. Dobson, B.A. Carreras, Presentation at CERTS review meeting, Washington DC January 2004 Cascading failure analysis I. Dobson, B.A. Carreras, D.E. Newman, Presentation to L.R. Christensen Associates, Madison WI April 2004 Cascading failure analysis I. Dobson, B.A. Carreras, D.E. Newman, Presentation to Alliant Energy, Madison WI April 2004 Cascading failure analysis and criticality R. Camfield, I. Dobson Presentation to a major utility, May 2004. Cascading failure propagation and branching processes I. Dobson, B.A. Carreras, D.E. Newman, Presentation to Silicon Graphics Inc and Hydro-Quebec TransEnergie, Madison WI June 2004 Cascading failure analysis I. Dobson, B.A. Carreras, D.E. Newman, Lecture at EEI Market Design & Transmission Pricing School Madison, Wisconsin, July 2004 A preliminary coupled model of electricity markets and cascading line failures in power transmission systems D. Berry, Student Undergraduate Laboratory Internship poster session Oak Ridge, Tennessee, August 2004 Criticality and risk of large cascading blackouts I. Dobson, B.A. Carreras, D.E. Newman, Presentation at PSerc Industry Advisory Board meeting, August 2004 The study of cascading failure in complex systems B. Nkei, B.A. Carreras, V.E. Lynch, 2004 Virginia Tech Symposium for Undergraduate Research in Engineering Blacksburg, Virginia, October 2004 Cascading failures in coupled systems B. Nkei, V. E. Lynch, B. A. Carreras, 71st Annual Meeting of Southeastern Section of the American Physical Society, Oak Ridge, Tennessee, November 2004 Blackouts I. Dobson. 8 lectures (last quarter of the course) in Fall 2004 graduate course at University of Wisconsin: ECE 905 Special topics in Electric power system: operation, markets, reliability, and blackouts; applications of optimization, markets, reliability and self-organized criticality to electric power transmission networks. Students from electrical engineering and policy attended. http://eceserv0.ece.wisc.edu/~dobson/ece905.html I. Dobson was the organizer and chair of a Special session on Probabilistic assessment of cascading events and blackouts at the Eighth International Conference on Probability Methods Applied to Power Systems, Ames Iowa, Sept. 2004. This session brought together most of the international researchers in this emerging area. 3.5 NEWSPAPER AND MEDIA There was considerable interest from the media in this project immediately following the August blackout. Considerable time was spent talking to the media, providing explanations, background and quotes. While some of the articles reflected general information, other articles (title in bold face) cited research results from the project. The articles and radio and TV contacts are listed below; most are available at http://eceserv0.ece.wisc.edu/~dobson/complexsystemsresearch.html. Why the lights went out Jonathan Kay, National Post, August 16 2003 “Last December, four U.S. scientists published a paper in the Journal Chaos entitled Critical points and transitions in an electric power transmission model for cascading failure blackouts. "Detailed analysis of large blackouts has shown that they involve cascading events in which a triggering failure produces a sequence of secondary failures that lead to blackout of a large area of the grid," the authors found. They presciently concluded that "large blackouts are much more likely than might be expected from [conventional statistical analysis]" and are "suggestive of a complex system operating close to a critical point." At 4:10pm on Thursday, Ontario and seven states hit that "critical point." Within seconds, workers in New York City, Toronto and thousands of other communities found themselves staring at blank computer screens. Many were forced to walk home in sticky weather -generally to dark, uncomfortably hot homes. Some are still without power as of Saturday morning. Their only consolation is that the biggest power outage in North American history evidently had nothing to do with terrorism.” ... How a butterfly's wing can bring down Goliath. Chaos theories calculate the vulnerability of megasystems Keay Davidson, San Francisco Chronicle, August 15 2003 This was a first world blackout Chris Suellentrop, Slate magazine, August 15 2003 Wisconsin company believes blackout originated in Lansing, Mich. Associated Press, Star Tribune, August 15 2003 David Newman appeared on NPR radio KUAC FM, August 27 2003 Ian Dobson appeared on ABC Nightline, August 18 2003 Energy scientist studies blackout triggers Pat Daukantas, Government Computer News, August 22 2003 Blackout was no surprise to UAF professor Ned Rozell, Anchorage Daily News, September 7 2003 The chaos behind the wall socket Ned Rozell, Fairbanks Daily News-Miner, September 7 2003 Getting a grip on nation's grid grind R. Cathey Daniels, Oak Ridger, September 16, 2003 Californians work to predict grid-crashing Ian Hoffman, Oakland Tribune, August 25 2003 Set of rules too complex to be followed properly James Glanz and Andrew Refkin, New York Times, August 19 2003 Elusive force may lie at root of blackout Richard Perez-Pena and Eric Lipton, New York Times, September 23 2003 What’s Wrong with the Electric Grid? Eric Lerner, Industrial Physicist, November 3 2003 Quick response is key in emergencies Tom McGinty, NewsDay, November 9 2003 L'energia ha un punto critico Donata Allegri, Ecplanet The power grid: Fertile ground for math research Sara Robinson, SIAM News, Volume 36, Number 8, October 2003 Black-out: cause e mezzi per prevenirli Carlo Alberto Nucci e Alberto Borghetti, Rivista ENERGIA, n. 3, pp. 20-29, 2003 The power grid as complex system, Sara Robinson, SIAM News, Volume 36, Number 10, December 2003 The unruly power grid, Peter Fairley, IEEE Spectrum August 2004 Remember last year's big blackout? Get ready for another one Stephen Strauss, The Globe and Mail, August 14, 2004 3.6 PLAN OF FUTURE WORK This section presents a longer term plan of work that explains how the project is directed towards monitoring tools to be applied to the real power system.