Optimal Power Flow (OPF) Analysis for AC–DC Active Distribution Networks Utilizing Second-Order Cone Programming (SOCP) Approach

Designing optimal power flow (OPF) models for ac–dc distribution networks poses significant challenges due to their highly nonlinear nature. However, convex relaxations can overcome the complexities. Therefore, this article presents a novel OPF model for ac–dc radial distribution systems using second-order cone programming (SOCP). Along with the optimal power injection reference, the model provides the optimal modulation index for the converters. Due to the computational superiority of convex models, the OPF model is applicable for ac–dc networks with high integration of distributed energy resources (DERs). The developed convex OPF model is tested on multiple distribution feeders with DERs and compared with the nonlinear programming OPF model. As a convex model, SOCP-OPF analysis provides a globally optimal solution that is exact for convex objective functions. The model is analyzed for a range of weighted factors of different objectives and a wide range of penetration levels of DERs.