  Chance constrained optimal power flow (OPF) has been recognized as a
promising framework to manage the risk from variable renewable energy (VRE). In
presence of VRE uncertainties, this paper discusses a distributionally robust
chance constrained approximate AC-OPF. The power flow model employed in the
proposed OPF formulation combines an exact AC power flow model at the nominal
operation point and an approximate linear power flow model to reflect the
system response under uncertainties. The ambiguity set employed in the
distributionally robust formulation is the Wasserstein ball centered at the
empirical distribution. The proposed OPF model minimizes the expectation of the
quadratic cost function w.r.t. the worst-case probability distribution and
guarantees the chance constraints satisfied for any distribution in the
ambiguity set. The whole method is data-driven in the sense that the ambiguity
set is constructed from historical data without any presumption on the type of
the probability distribution, and more data leads to smaller ambiguity set and
less conservative strategy. Moreover, special problem structures of the
proposed problem formulation are exploited to develop an efficient and scalable
solution approach. Case studies are carried out on IEEE 14 and 118 bus systems
to show the accuracy and necessity of the approximate AC model and the
attractive features of the distributionally robust optimization approach
compared with other methods to deal with uncertainties.
