Optimal Power Flow for Three-phase Unbalanced Active Distribution Networks with Delta Connections

This paper presents a linear-convex formulation for the optimal power flow (OPF) in three-phase unbalanced power distribution networks considering mixed wye and delta-connected loads. The present approach describes an optimization model based on Taylor's expansion of the power flow equations, using Wirtinger's Calculus; this expansion transforms the non-linear space into an affine set that uses convex optimization techniques, thus, the proposed model guarantees global optimum, uniqueness of the solution, and convergence of the interior point method. The power flow proposal is compared with the successive approximation, which is a generalization of the backward forward sweep (BFS) algorithm, demonstrating the efficiency of the approach, and being applicable for the OPF problem contrary to the BFS. Moreover, numerical results in several IEEE demonstrates that the linear approximation can efficiently solve the optimal power flow for different test systems in generic Medium Voltage grids.