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. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1505810͔ From the analysis of a 15-year time series of North American electric power transmission system blackouts, we have found that the frequency distribution of the blackout sizes does not decrease exponentially with the size of the blackout, but rather has a power law tail. The existence of a power tail suggests that the North American power system has been operated near a critical point. To see if this is possible, here we explore the critical points of a simple blackout model that incorporates circuit equations and a process through which outages of lines may happen. In spite of the simplifications, this is a complex problem. Understanding the different transition points and the characteristic properties of the distribution function of the blackouts near these points offers a first step in devising a dynamical model for the power transmission systems.
An example of a cascading failures model for a power transmission system is discussed in REF .
Critical points and transitions in an electric power transmission model for cascading failure blackouts
Chaos
Chaos
Medicine Mathematics