Optimal Power Flow Under Uncertainty: An Extensive Out -Of-Sample Analysis

The uncertainty induced by high penetration of stochastic generation in power systems requires to be properly taken into account within Optimal Power Flow (OPF) problems to make informed day-ahead decisions that minimize the social cost in view of potential balancing actions. This ends up in a two-stage OPF problem that is usually solved using two-stage stochastic programming or adaptive robust optimization. Another alternative is the use of chance-constrained programming that allows to control the conservativeness of the decisions. In this paper, we aim at defining a fair basis for assessing the performance of these three techniques, using an extensive out-of-sample evaluation. Considering a common wind power database, each technique leads to optimal day-ahead decisions that are a posteriori assessed through the real-time stage on unseen realizations of the uncertainty. Our main conclusion is that undertaking conservative decisions results in lower standard deviations of the cost, but at the expense of higher expected cost.