Convex Relaxation of Optimal Power Flow for Hybrid LCC-HVDC and AC Power Grids
Line-commutated converter (LCC)-based high-voltage DC (HVDC) systems have been integrated with bulk AC power grids for the interregional transmission of renewable power generation. The nonlinear HVDC model brings additional nonconvexity to the optimal power flow (OPF) of hybrid AC-DC power grids. The convex relaxation of such an OPF model could be a remedy, which has been discussed by little work. In this paper, a convexification method for the OPF of LCC-based AC-DC power grids is proposed using second-order cone programing relaxation. A sufficient condition for the exactness of the proposed convex relaxation is proposed and proven. The properties, exactness and efficiency of the proposed model are verified in three numerical simulations. The simulation results demonstrate that a globally optimal solution of the original OPF can be obtained from the proposed relaxed model with high computational efficiency.