On the application of the branch DistFlow using second-order conic programming in microgrids

In recent years, the Second-Order Conic Programming (SOCP) model of Distribution Power Flow (DistFlow) has been widely adopted in operation and planning studies of distribution systems due to its simplicity for various applications compared to other convex models. It provides a relaxed convex formulation of DistFlow equations to ensure the feasibility of solutions. This Paper investigates the performance of the SOCP model in Microgrids (MGs) and Active Distribution Systems (ADSs). It identifies scenarios where the SOCP model results in incorrect solutions, implying that it does not necessarily guarantee solution feasibility. Mathematical proofs are also presented to demonstrate that the SOCP DistFlow is not completely capable of maintaining the security of MGs and ADSs. Due to the high popularity of the SOCP model over other DistFlow models in the literature, an effective algorithm is proposed for the SOCP model to ensure the consistency of solutions in MGs and ADSs, regardless of operational conditions. The convergence of the proposed algorithm to the optimal solution is mathematically proved. The results are verified using OpenDSS software. The results demonstrate that the proposed algorithm enhances convergence speed and accuracy, while maintaining the simplicity needed for practical use in operation and planning studies. • Inconsistency of the second-order conic programming model. • Reserve power flow problem in microgrids and active distribution systems. • Proposing mathematical proof for current manipulation. • Remedial algorithm for the second-order conic programming. • Convex and easy-to-use model in different operation and planning problems.