  There is a growing need for new optimization methods to facilitate the
reliable and cost-effective operation of power systems with intermittent
renewable energy resources. In this paper, we formulate the robust AC optimal
power flow (RAC-OPF) problem as a two-stage robust optimization problem with
recourse. This problem amounts to a nonconvex infinite-dimensional optimization
problem that is computationally intractable, in general. Under the assumption
that there is adjustable generation or load at every bus in the power
transmission network, we develop a technique to approximate RAC-OPF from within
by a finite-dimensional semidefinite program by restricting the space of
recourse policies to be affine in the uncertain problem data. We establish a
sufficient condition under which the semidefinite program returns an affine
recourse policy that is guaranteed to be feasible for the original RAC-OPF
problem. We illustrate the effectiveness of the proposed optimization method on
the WSCC 9-bus and IEEE 14-bus test systems with different levels of renewable
resource penetration and uncertainty.
