Probabilistically robust AC optimal power flow

The increasing penetration of renewable energy resources, paired with the fact that load can vary significantly, introduce a high degree of uncertainty in the behavior of modern power grids. Given that classical dispatch solutions are 'rigid,' their performance in such an uncertain environment is in general far from optimal. For this reason, in this paper, we consider ac optimal power flow (AC-OPF) problems in the presence of uncertain loads and (uncertain) renewable energy generators. The goal of the AC-OPF design is to guarantee that controllable generation is dispatched at minimum cost, while satisfying constraints on generation and transmission for almost all realizations of the uncertainty. We propose an approach based on a randomized technique recently developed, named scenario with certificates, which allows us to tackle the problem without the conservative parameterizations on the uncertainty used in currently available approaches. The proposed solution can exploit the usually available probabilistic description of the uncertainty and variability, and provides solutions with a priori probabilistic guarantees on the risk of violating the constraints on generation and transmission.