Critical points and transitions in an electric power transmission model for cascading failure blackouts

TLDR

Cascading failures in large‑scale power transmission systems cause blackouts, and the study identifies two critical points—line‑flow limits and generator‑capability limits—that characterize system vulnerability. The authors investigate how increasing load power demand in a simplified transmission model triggers cascading failures. They model generators, loads, and the transmission network with operating limits, analyze tree and 118‑node networks, and examine how the interaction of the two critical points creates a complex solution space. Analysis of North American blackout data and simulations show that operating near the critical points produces power‑law tails in the blackout‑size distribution, matching observed data.

Abstract

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 (algebraic) 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.