Second-Order Cone Programming (SOCP) Model for Three Phase Optimal Power Flow (OPF) in Active Distribution Networks

With the high penetration of distributed generations (DGs), modern distribution systems require novel and efficient optimal power flow (OPF) models. This paper proposes a second-order cone programming (SOCP) based AC-OPF model for three-phase radial power distribution networks. Mutual coupling effects are generally ignored in the existing multi-phase SOCP AC-OPF models. To overcome this critical issue, the proposed SOCP-OPF model introduces a coupling coefficient for the mutual coupling effects on the three-phase unbalanced lines. The derivation of the coupling coefficients has been illustrated with the required proof that the relaxation is tight and the solution from the proposed OPF model is optimal for an unbalanced multi-phase distribution network. The SOCP-OPF model is evaluated on several IEEE standard distribution networks without and with high penetration of Distributed Energy Resources (DERs). It has been shown that the proposed OPF model provides an optimal global solution for convex objective functions. Also, this OPF model is scalable and computationally efficient compared to Nonlinear Programming (NLP) and other convex OPF models.