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The increasing penetration of renewable energy resources, paired with thefact that load can vary significantly, introduce a high degree of uncertaintyin the behavior of modern power grids. Given that classical dispatch solutionsare "rigid," their performance in such an uncertain environment is in generalfar from optimal. For this reason, in this paper, we consider AC optimal powerflow (AC-OPF) problems in the presence of uncertain loads and (uncertain)renewable energy generators. The goal of AC-OPF design is to guarantee thatcontrollable generation is dispatched at minimum cost, while satisfyingconstraints on generation and transmission for "almost all" realizations of theuncertainty.  We propose an approach based on a randomized technique recently developed,named "scenario with certificates", which allows to tackle the problem withoutassuming any a-priori dependence of the voltages in the network on theuncertain generators/loads. The proposed solution can exploit the usuallyavailable probabilistic description of the uncertainty and variability, andprovides solutions with a-priori probabilistic guarantees on the risk ofviolating the constraints on generation and transmission.

AC optimal power flow in the presence of renewable sources and uncertain loads