  Higher levels of renewable electricity generation increase uncertainty in
power system operation. To ensure secure system operation, new tools that
account for this uncertainty are required. In this paper, we formulate a
chance-constrained AC optimal power flow problem, which guarantees that
generation, power flows and voltages remain within their bounds with a
pre-defined probability. We then propose an accurate, yet tractable analytical
reformulation of the chance constraints. The reformulation maintains the full,
non-linear AC power flow equations for the forecasted operating point, and
models the impact of uncertainty through a linearization around this point. We
discuss different solution algorithms, including one-shot optimization with and
without recourse, and an iterative algorithm which enables scalable
implementations. We further discuss how more general chance constraint
reformulations can be incorporated within the iterative solution algorithm. In
a case study based on four different IEEE systems, we compare the performance
of the solution algorithms, and demonstrate scalability of the iterative
scheme. We further show that the analytical reformulation accurately and
efficiently enforces chance constraints in both in- and out-of-sample tests,
and that the analytical approach outperforms two alternative, sample based
chance constraint reformulations.
