A Second-Order Cone Programming (SOCP) Based Optimal Power Flow (OPF) Model With Cyclic Constraints for Power Transmission Systems

For meshed power networks, even though the conic relaxation is shown to be exact, the relaxation of angles may not be exact using the existing Second-Order Cone Programming (SOCP) based optimal power flow (OPF) models. Power transmission networks generally have meshed orientation, and the cyclic angle constraints are not satisfied with the existing SOCP-OPF models. This work proposes a SOCP-OPF model for power transmission networks that satisfies the cyclic angle constraints for any mesh in the network. The novelty of the proposed OPF model is that it defines a convex envelope to represent the relative bus voltage angles that satisfy the cyclic constraint criteria for a meshed network. The proposed SOCP-OPF model is tested on the IEEE 14-bus, 57-bus, 118-bus, 500-bus, and 2736-bus networks. The case studies demonstrate that the proposed model is computationally efficient and scalable for large transmission networks compared to the Nonlinear Programming (NLP) and semi-definite programming (SDP) counterparts.