Stochastic AC optimal power flow with affine recourse

With the increasing penetration of intermittent renewable energy sources into the electric power grid, there is an emerging need to develop stochastic optimization methods to enable the reliable and efficient operation of power systems having a large fraction of their power supplied form uncertain resources. In this paper, we formulate the stochastic AC optimal power flow (OPF) problem as a two-stage stochastic program with robust constraints. This problem amounts to an infinite-dimensional nonconvex optimization problem. We develop a finite-dimensional inner approximation as a semidefinite program. Its solution yields an affine recourse policy that is guaranteed to be feasible for the stochastic AC OPF problem.