  This paper presents a novel optimization framework of formulating the
three-phase optimal power flow that involves uncertainty. The proposed
uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework
that is less complex than the existing optimization frameworks involving
uncertainty, and 2) convex such that it admits polynomial-time algorithms and
mature distributed optimization methods. To construct this UaO framework, a
methodology of learning-aided uncertainty-aware modeling, with prediction
errors of stochastic variables as the measurement of uncertainty, and a theory
of data-driven convexification are proposed. Theoretically, the UaO framework
is applicable for modeling general optimization problems under uncertainty.
