A flow direction enforcing approach for economic dispatch with adjustable line impedance

The adoption of power flow control devices such as FACTS (Flexible AC Transmission Systems) devices has improved the reliability and efficiency of power transmission systems by enabling the adjustment of transmission line impedance. The DC optimal power flow (DC-OPF) problem with adjustable line impedance can be formulated as a mixed integer quadratic program (MIQP) with binary variables presenting the directions of power flows on transmission lines with adjustable impedance. MIQPs are in general NP-hard to solve. In this paper, we explore effective approaches to solve the formulated MIQP. When there is only one transmission line with adjustable impedance, we prove the optimality of a two-step optimization approach (originally proposed in [12]) that determines the binary variables by solving a conventional DC-OPF with (arbitrarily) fixed line impedance. We propose a new approach that enforces the power flow directions with the DC-OPF's corresponding problem with traffic network constraints. Numerical results (on a modified IEEE 118-bus test system) show that when there are many lines with adjustable impedance (e.g., 40 lines with adjustable impedance in a 118-bus system), the proposed approach achieves close-to-optimal performance and can result in significant cost savings compared to the two-step optimization approach.