A New Convex Relaxation Method to Solve AC Optimal Power Flow in Transmission Networks

The optimal power flow (OPF) is a basic optimization problem in the field of power system. The current mainstream convex relaxation methods, including semidefinite programming (SDP), quadratic convex relaxation (QC relaxation) and second-order cone programming (SOCP), have been well applied in the distribution network. However, when the network has a circle, the SOCP method does not support the solution because of the additional relaxation of the phase angle cycle condition, while the SDP and QC methods are less efficient for solving the transmission network. Based on this situation, an AC OPF convex relaxation and solution method suitable for the transmission network were proposed in this paper. The second-order cone relaxation is performed on the voltage expression in the rectangular form of the OPF problem, and the arctangent envelope method is proposed to relax the phase angle cycle constraint. Finally, the feasibility and effectiveness of the proposed method are verified in the simulation results, and the computational speed of the proposed solution is proved to be high.