Tightening SOCP relaxation of AC Optimal Power Flow with Linearized Arc-tangent Constraints

Due to the absence of arc-tangent constraints, Second-Order Cone Programming (SOCP) relaxation of AC Optimal Power Flow (ACOPF) does not provide a tighter solution as compared to Semi-definite Programming (SDP) relaxation for meshed networks. In order to tighten the SOCP relaxation of ACOPF, this paper presents a SOCP-based convex formulation of ACOPF with linearized arc-tangent constraints, which provides a feasible solution and a tight bound on the objective of the exact ACOPF formulation. Also, the proposed model is scalable to large transmission networks and is computationally efficient. Numeric results on various NESTA test cases (up to 2869peagase system) demonstrate the proposed formulation’s tightness, computational efficiency, and scalability to large meshed transmission networks.