On the Feasibility ofAC and DC Optimal Power Flow Models: Analytics and Comparison

DC optimal power flow (DC OPF) has been a popular model for optimal power flow computation and design. This paper undertakes the study of the feasibility of DC OPF and shows major differences between the feasible region of the DC OPF and AC OPF models, which may play a key role in the development of OPF methods. Several analytical results are developed on the feasibility and geometrical properties of both the AC OPF model and the DC OPF model. In particular, the feasible region of AC OPF and that of DC OPF never intersect or are included. DC OPF feasible solutions are not feasible solutions to AC OPF. In addition, the infeasibility degree (IFD) is proposed and used to measure the feasibility of DC OPF feasible solutions. It is shown that care must be taken to make decisions based on DC OPF solutions. The medium loading and low network loss condition are more suitable for use with DC OPF. The IEEE 5-, 9-, 39- and U8- bus systems are used to illustrate the properties and results.