Optimal control of cascading power grid failures

We study algorithms for computing optimal load shedding schedules in the event of a cascading power system failure. The algorithms compute an affine control at the onset of the cascade; the control is applied during the cascade as a function of observed state parameters such as line overloads. In the case of line outages that follow a deterministic rule, we obtain an efficient (polynomial time) algorithm for computing an optimal control. For the case of stochastic line outages we describe a stochastic gradients algorithm. We present computational experiments with a parallel implementation of our algorithms, tested on a snapshot of the U.S. Eastern Interconnect.