Solutions of DC OPF are Never AC Feasible

TL;DR

This paper proves that solutions from the standard DC optimal power flow problem cannot satisfy AC power flow constraints, highlighting fundamental limitations in using DC solutions for AC feasibility.

Contribution

It establishes that, under mild assumptions, the feasible sets of DC and AC OPF problems do not intersect, and DC solutions are inherently not AC feasible even with generation adjustments.

Findings

DC OPF solutions are never AC feasible.

The intersection of feasible sets for DC and AC OPF is empty.

Generation adjustments in DC OPF do not ensure AC feasibility.

Abstract

In this paper, we analyze the relationship between generation dispatch solutions produced by the DC optimal power flow (DC OPF) problem by the AC optimal power flow (AC OPF) problem. While there has been much previous work in analyzing the approximation error of the DC assumption, the AC feasibility has not been fully explored, although difficulty achieving AC feasibility is known in practice. Here, we consider the set of feasible points in a standard DC OPF problem and the set of feasible points in a standard AC OPF problem. Under some very light assumptions, we show that the intersection of these sets is the empty set; i.e., that no solution to the DC OPF problem will satisfy the AC power flow constraints. Then, it is demonstrated that even with generation adjustments in DC OPF to account for losses, DC OPF solutions are still not AC feasible.