The optimal power flow (OPF) problem for active distribution networks with distributed generation (DG) and a variety of discretely adjustable devices (e.g., on-load tap-changers, OLTCs) is essentially a non-convex, nonlinear, mixedinteger optimization problem. In this paper, the quadratic model of three-phase OLTCs is proposed by adding branch currents as unknown variables, which guarantee a constant Hessian matrix throughout iterations. This paper proposes a three-phase OPF model for active distribution networks, considering a three-phase DG model. The OPF model is solved by an interior point method incorporating a quadratic penalty function as opposed to a Gaussian penalty function. Furthermore, a voltage regulator is also incorporated into the OPF model to form an integrated regulation strategy. The methodology is tested and validated on the IEEE 13-bus three-phase unbalanced test system.
Zhao, F., Zhao, T., Ju, Y., Ma, K., & Zhou, X. (2018). Research on Three-phase Optimal Power Flow for Distribution Networks Based on Constant Hessian Matrix. IET Generation, Transmission and Distribution, 12(1), . https://doi.org/10.1049/iet-gtd.2017.0889