  To address computational challenges associated with power flow
nonconvexities, significant research efforts over the last decade have
developed convex relaxations and approximations of optimal power flow (OPF)
problems. However, benefits associated with the convexity of these relaxations
and approximations can have tradeoffs in terms of solution accuracy since they
may yield voltage phasors that are inconsistent with the power injections and
line flows, limiting their usefulness for some applications. Inspired by state
estimation (SE) techniques, this paper proposes a new method for obtaining an
AC power flow feasible point from the solution to a relaxed or approximated
optimal power flow (OPF) problem. By treating the inconsistent voltage phasors,
power injections, and line flows analogously to noisy measurements in a state
estimation algorithm, the proposed method yields power injections and voltage
phasors that are feasible with respect to the AC power flow equations while
incorporating information from many quantities in the solution to a relaxed or
approximated OPF problem. We improve this method by adjusting weighting terms
with an approach inspired by algorithms used to train machine learning models.
We demonstrate the proposed method using several relaxations and
approximations. The results show up to several orders of magnitude improvement
in accuracy over traditional methods.
