Hawaii International Conference on System Science, January 2003, Hawaii, © 2003 IEEE Blackout Mitigation Assessment in Power Transmission Systems B. A. Carreras Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA carrerasba@ornl.gov V. E. Lynch Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA lynchve@ornl.gov D. E. Newman Physics Department, University of Alaska, Fairbanks, AK 99775 USA ffden@uaf.edu I. Dobson ECE Department, University of Wisconsin, Madison, WI 53706 USA dobson@engr.wisc.edu Abstract Electric power transmission systems are a key infrastructure and blackouts of these systems have major direct and indirect consequences on the economy and national security. Analysis of North American Electrical Reliability Council blackout data suggests the existence of blackout size distributions with power tails. This is an indication that blackout dynamics behave as a complex dynamical system. Here, we investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power tails. Thus, while the absolute frequency of disruptions of all sizes may be reduced, the underlying forces can still cause the relative frequency of large disruptions to small disruptions to remain the same. Moreover, in some cases, efforts to mitigate small disruptions can even increase the frequency of large disruptions. This occurs because the large and small disruptions are not independent but are strongly coupled by the dynamics. 1. Introduction Electric power transmission systems are an important element of the national and global infrastructure, and blackouts of these systems have major direct and indirect consequences on the economy and national security. Although large cascading blackouts in the power transmission system are relatively rare, their impact is such that understanding the risk of large blackouts is a high priority. In addition to the direct consequences of blackouts, the growing interconnections between different elements of the infrastructure (e.g., communications, economic markets, transportation) can cause a blackout to impact other vital infrastructures. This interconnected nature of the infrastructure begs for an even more integrated (more global) approach than we will be taking here and suggests that the “complex system” approach is likely to be even more important in understanding the entire interconnected system. While it is useful and important to do a detailed analysis of the specific causes of individual blackouts, it is also important to understand the global dynamics of the power transmission network and the frequency distribution of blackouts that they create. There is evidence that global dynamics of complex systems is largely independent of the details of the individual triggers such as shorts, lightning strikes etc. In this paper, we focus on the intrinsic dynamics of blackouts and how complex system dynamics affect both blackout risk assessment and the impact of mitigation techniques on blackout risk. It is found, perhaps counterintuitively, that apparently sensible attempts to mitigate failures in complex systems can have adverse effects and therefore must be approached with care. First, as motivation for our work we consider the properties of a series of blackouts. The North American Electrical Reliability Council (NERC) has a documented list summarizing major blackouts of the North American power transmission system from 1984 to 1998 [1]. If blackouts were largely uncorrelated with each other, one might expect a probability distribution of blackout sizes to fall off exponentially (as, for example, in a Weibull distribution). However, analyses of the NERC data [2], [3], [4], [5] show that the probability distribution of the blackout sizes does not decrease exponentially with the size of the blackout, but rather has a power law tail. The probability distribution function (PDF) is empirically estimated by the frequency of blackout sizes in a short interval divided by the length of the interval and is then normalized so that the total probability is one. As an example, one measure of blackout size is load shed. Figure 1 plots on a log-log scale the empirical probability distribution of load shed in the North American blackouts. The fall-off with blackout size is approximately a power law with an exponent of about -1.1. (An exponent of -1 would imply that doubling the blackout size only halves the probability.) Thus the NERC data suggests that large blackouts are much more likely than might be expected which has implications for risk analysis models. Additionally, power law tails, particularly with an exponent between –1 and –2 are consistent with those found in many “complex systems” models which helps motivate the use of such models to understand the electric power transmission system. The NERC blackout data are the best we have found; however, the statistics have limited resolution because the data are limited to only 15 years. Therefore the NERC data suggest rather than prove the existence of the power tails and are consistent with complex systems models rather then conclusively validating them. However, because of the potential benefits, including risk and mitigation information that cannot be accessed without them, modeling and simulation of the complex system dynamics are clearly indicated. Progress has been made in modeling the overall forces shaping the dynamics of series of blackouts. Simulations of power networks using the Oak Ridge-Pserc-Alaska (OPA) model [6], [7], [8] yield power tails that are remarkably consistent with the NERC data as shown in Figure 1.