A Phase Transition Approach for Predicting Cascading Failure in Networked Systems

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

As the scale of engineered systems such as electric power grids, communication networks, and the internet expands, and as society's dependence upon reliable operation of these networks increases, it is vital that system engineers seek a better understanding of how small scale failures of individual elements may propagate to produce global system-wide failures. The work proposed here is motivated largely by the electric power systems application, and the challenge in bringing analytic stability techniques to bear on the problem of cascading line and generator tripping. The goal is to capture the role of transient dynamic response following a specified initiating disturbance, and examine subsequent ("cascading") element failures that are induced when operating thresholds for individual elements are exceeded along the state trajectory. This approach will exploit "Hamiltonian-like" structure that appears in power system dynamics and related classes of networked systems, in which the differential equations governing behavior are often closely related to an easily identified storage function. By relating element failure to thresholds of maximally allowable energy storage in network elements the work will seek to develop a tractable, smooth model for element failure that is amenable to Lyapunov type stability analysis. It will be argued that cascading element failure can then be captured as a sequence of transitions between potential basins about (possibly) stable equilibria, with each equilibrium defined by a partially degraded network configuration.