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

Solutions of DC OPF are Never AC Feasible