  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.
