The Influence Model for Cascading Failures

Professor Bernard Lesieutre, Electrical Engineering and computer Science, Massachusetts Institute of Technology

Motivated by cascading outages observed in the electric power grid, and concern that fundamental changes in the electric power industry may tend to increase the possibility of failures, we are investigating dynamics of large-scale networks. An important long-term goal is to describe how the underlying structure of a network and the characteristics of the network components affect large-scale failure dynamics. Towards this end, we introduce the "Influence Model," a general probabilistic model to describe both the occurrence of initial failure events in networks and the influence of these failures on other parts of the network. In the influence model each node has a status (for instance: normal, or failed) that behaves as a Markov chain, but the transitions of each chain are influenced by the present status of each neighboring node. The overall network could be described as a Markov chain, but with order equal to the product of the orders of the individual node chains. We establish that analysis of a greatly reduced model, of dimension equal to the sum of the individual node orders, suffices to characterize many dynamic and steady-state properties of interest. We also present analyses and simulations of failure dynamics using the influence model for a few interesting cases.