Semi-Definite Programming Based Scalable and Accurate Optimal Power Flow Models for Radial Distribution Networks

With high integration of distributed energy resources (DERs), modern distribution networks are subject to optimal power flow (OPF) analysis. Conventional non-linear and linear OPF models suffer from either infeasibility or inaccuracy for large networks, and global optimality is not guaranteed. Addressing computational infeasibility and non-convexity for DERs integrated distribution networks, this article presents a novel approach for OPF analysis employing semi-definite programming (SDP). For the proposed SDP-OPF model, network power flow relations utilize a bus injection model (BIM) for single-phase networks and a branch flow model (BFM) for multi-phased unbalanced power distribution networks. The exactness and the global optimality of the proposed SDP-OPF model are illustrated in this article. The proposed models' performance is evaluated in multiple standard power distribution test cases with a wide range of DER integration. The simulation results are compared with a nonlinear programming (NLP) based and a second order cone programming (SOCP) based OPF models. The comparison and the result analysis demonstrate that the proposed approach yields a more robust solution with improved convergence and accuracy.