First year progress report: Complex systems approach to cascading failures

A model has been developed to study the global complex dynamics of a series of blackouts in power transmission systems [1, 2]. 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. Examining Criticality of Blackouts in Power System Models with Cascading Events, I. Dobson, J. Chen, J.S. Thorp, B.A. Carreras, and D.E. Newman, to appear at 35th Hawaii International Conference on System Sciences, Hawaii, January 2002. [see section 6.2] Abstract: 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. 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. The following five presentations were given: Evidence for self-organized criticality in electric power blackouts, B. A. Carreras, D. E. Newman, I. Dobson, and A. B. Poole, 34rd Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. Modeling blackout dynamics in power transmission networks with simple structure, B.A. Carreras, V.E. Lynch, M. L. Sachtjen, I. Dobson, D. E. Newman, 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. An initial model for complex dynamics in electric power system blackouts, I. Dobson, B. A. Carreras, V.E. Lynch, D. E. Newman, 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. Analysis of electric power system disturbance data, J. Chen, J.S. Thorp, M. Parashar, 34th Hawaii International Conference on System Sciences, Maui, Hawaii, January 2001. Cascading failure and self-organized criticality in electric power system blackouts, I. Dobson, D.E. Newman, B.A. Carreras, and Vicki Lynch, NSF Workshop on Engineering the transport industries, Georgetown, Washington DC, August 13-14, 2001. The following journal paper was submitted to the IEEE Transactions on power systems: Evidence for self-organized criticality in a time series of electric power system blackouts, B. A. Carreras, D. E. Newman, I. Dobson, and A. B. Poole, preprint, submitted to IEEE Transactions on Power Systems, December 2001. [see section 6.4] Abstract: 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 is consistent with self-organized criticality. A qualitative explanation of complex dynamics observed in electric power system blackouts is suggested. 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 is consistent with self-organized criticality. A qualitative explanation of complex dynamics observed in electric power system blackouts is suggested. 4 PLAN FOR SECOND YEAR WORK The first year of the project concentrated on improving, implementing and understanding models capturing the complex dynamics of series of blackouts. These first year activities will be continued in the second year but emphasis will shift towards improving the realism of the models and data, trying to reproduce qualitative features of historical NERC data on blackouts, and assessing the prospects for controlling the complex model dynamics to mitigate or avoid large blackouts. 4.1 SECOND YEAR TASKS The second year of project work builds on the first year tasks. The planned second year project tasks are shown below. There will be a project meeting of all the investigators at the HICSS meeting in January 2002 to revise the second year tasks if this is necessary in the light of the most recent progress and make more detailed plans and assignments. The revised plans will be documented in late January after the HICSS meeting. Task 6: Apply improved global models to more realistic test networks and analyze and interpret results (a) Studies using OPA model (Carreras) (b) Studies using Hidden Failure model (Thorp) Task 7: Refine data, modeling, algorithms, analysis and software to improve the results from task 6. The main objective of task 7 is to reproduce and explain qualitative features of the historical NERC data on blackouts using the models developed by the project. Coordination between Wisconsin, ORNL and Cornell will be needed. The following task 7 subtasks will be revised in the light of the progress in the first year tasks. (a) Implement model upgrades to efficiently compute larger networks (b) Develop models, data sets, and analysis techniques as needed. (c) Develop heuristics and theory that can lead to better understanding Task 8: Report on any implications or insights for power system operation. Assess the prospects for controlling the complex model dynamics to mitigate or avoid large blackouts. This task will require advice from David Newman of the University of Alaska-Fairbanks about general methods of control of complex systems near criticality. Task 9: Draft final report in November 2002; final report finished January 2003 The draft final report will be circulated for comments to be included in the final version. The working title of the final report is "Complex systems approach to cascading failures." The final report will be produced in pdf format suitable for posting on a website.