Transmission-Capacity Expansion for Minimizing Blackout Probabilities

The objective of this paper is to determine an optimal plan for expanding the capacity of a power grid in order to minimize the likelihood of a large cascading blackout. Capacity-expansion decisions considered in this paper include the addition of new transmission lines and the addition of capacity to existing lines. We embody these interacting considerations in a simulation optimization model, where the objective is to minimize the probability of a large blackout subject to a budget constraint. The probability of a large-scale blackout is estimated via Monte Carlo simulation of a probabilistic cascading blackout model. Because the events of interest are rare, standard simulation is often intractable from a computational perspective. We apply a variance-reduction technique within the simulation to provide results in a reasonable time frame. Numerical results are given for some small test networks including an IEEE 14-bus test network. A key conclusion is that the different expansion strategies lead to different shapes of the tails of the blackout distributions. In other words, there is a tradeoff between reducing the frequency of small-scale blackouts versus reducing the frequency of large-scale blackouts.