Modeling the Dynamics of Cascading Failures in Power Systems

In this paper, we use a circuit-based power flow model to study the cascading failure propagation process, and combine it with a stochastic model to describe the uncertain failure time instants, producing a model that gives a complete dynamic profile of the cascading failure propagation beginning from a dysfunctioned component and developing eventually to a large-scale blackout. The sequence of failures is determined by voltage and current stresses of individual elements, which are governed by deterministic circuit equations, while the time durations between failures are described by stochastic processes. The use of stochastic processes here addresses the uncertainties in individual components' physical failure mechanisms, which may depend on manufacturing quality and environmental factors. The element failure rate is related to the extent of overloading. A network-based stochastic model is developed to study the failure propagation dynamics of the entire power network. Simulation results show that our model generates dynamic profiles of cascading failures that contain all salient features displayed in historical blackout data. The proposed model thus offers predictive information about occurrences of large-scale blackouts. We further plot cumulative distribution of the blackout size to assess the overall system's robustness. We show that heavier loads increase the likelihood of large blackouts and that small-world network structure would make cascading failure propagate more widely and rapidly than a regular network structure.