2010 Articles

Optimal adaptive control of cascading power grid failures

Bienstock, Daniel

Power grids have long been a source of interesting optimization problems. Perhaps best known among the optimization community are the unit commitment problems and related generator dispatching tasks. However, recent blackout events have renewed interest on problems related to grid vulnerabilities. A difficult problem that has been widely studied, the N-K problem, concerns the detection of small cardinality sets of lines or buses whose simultaneous outage could develop into a significant failure event. This is a hard combinatorial problem which, unlike the typical formulations for the unit commitment problem, includes a detailed model of flows in the grid. A different set of algorithmic questions concern how to react to protect a grid when a significant event has taken place. This is the outlook that we take in this paper. In this context, the central modeling ingredient is that power grids display cascading behavior. In this paper, building on prior models for cascades, we consider an affine, adaptive, distributive control algorithm that is computed at the start of the cascade and deployed during the cascade. The control sheds demand as a function of observations of the state of the grid, with the objective of terminating the cascade with a minimum amount of demand lost. The optimization problem handled at the start of the cascade computes the coefficients in the affine control (one set of coefficients per demand bus). We present numerical experiments with parallel implementations of our algorithms, using as data a snapshot of the U.S. Eastern Interconnect, with approximately 15000 buses and 23000 lines.