Optimal Power Flow Solution for Distribution Networks using Quadratically Constrained Programming and McCormick Relaxation Technique

This paper presents a quadratically constrained programming (QCP) model to tackle the optimal power flow (OPF) problem in distribution networks. The proposed model is fast, reliable, and precise enough to be embedded into the multi-emporal power system analysis. The proposed model benefits from a standard QCP to solve the branch active and reactive power flows. The second-order conic programming (SOCP) approach has been applied to address the quadratic constraints. The nonconvex feature of the OPF problem has been relaxed utilizing the McCormick envelopes. To find the minimum current of each branch, the lossless power flow model has been first solved and the obtained results have been considered for solving the OPF problem. The IEEE 33-bus test system has been selected as the benchmark to verify the efficient performance of the proposed OPF model. The simulation study confirms that the McCormick envelopes used in the QCP approach lead to precise results with a very fast convergence time. Overall, the presented model for the OPF can be extended for both planning and operation purposes in distribution system studies.