Three-phase Optimal Load Flow Model and Algorithm for Active Distribution Networks

Three-phase distribution network optimal load flow (T-OLF) cannot be exactly linearized to mixed integer second order cone programming(Ml-SOCP) like single-phase branch flow based OLF. Hence, interior point based OLF (IP-OLF) and mixed integer nonlinear programming based OLF (MINLP-OLF) are both tried out to cope with T-OLF in this paper. For IP-OLF, a quadratic three-phase transformer model is proposed to guarantee IP-OLF applying constant Hessian matrix during iterative process. For MINLP-OLF, to gain better optimization results, a Mixed-Integer Quadratically-Constrained Quadratic Program model (MIQCQP) of T-OLF is formulated via binary scheme and big-M method. Numerical tests implemented on simple 4-bus system, IEEE 13-bus and IEEE 34-bus distribution test feeders verify the validity of proposed models and algorithms.