  The optimal power flow problem plays an important role in the market clearing
and operation of electric power systems. However, with increasing uncertainty
from renewable energy operation, the optimal operating point of the system
changes more significantly in real-time. In this paper, we aim at developing
control policies that are able to track the optimal set-point with high
probability. The approach is based on the observation that the OPF solution
corresponding to a certain uncertainty realization is a basic feasible
solution, which provides an affine control policy. The optimality of this basis
policy is restricted to uncertainty realizations that share the same set of
active constraints. We propose an ensemble control policy that combines several
basis policies to improve performance. Although the number of possible bases is
exponential in the size of the system, we show that only a few of them are
relevant to system operation. We adopt a statistical learning approach to learn
these important bases, and provide theoretical results that validate our
observations. For most systems, we observe that efficient ensemble policies
constructed using as few as ten bases, are able to obtain optimal solutions
with high probability.
