Bus injection relaxation based OPF in multi-phase neutral equipped distribution networks embedding wye- and delta-connected loads and generators

Abstract

A novel Optimal Power Flow (OPF) model, based on Semi-Definite Programming approach, for multi-phase active Distribution Networks (DNs) equipped with neutral conductor(s) and both wye- and delta-connected loads/Distributed Generators (DGs) is proposed in this paper. The coupled power injection across phase-neutral and phase-phase conductors is decoupled by modelling of a shunt load/DG through a correction current injection approach and, consequently, explicit power injections are obtained for each conductor of a node. Furthermore, the complete ZIP load representation is considered in the OPF model and two approximations, based on the first-order Taylor series and approximation of the first-order Taylor series, are introduced for the modelling of constant current component of a ZIP load in terms of an optimization variable. Simulations are carried out on several medium and low voltage active DNs under various parameters of the ZIP models for the minimization of either slack-bus power or network losses objective functions. It is successfully demonstrated that the proposed relaxation recovers the global optimal solution of the original OPF problem for both load types (wye and delta) under various combinations of ZIP parameters in the case of lightly or moderately unbalanced DNs, whereas in the case of highly unbalanced DNs, a rank-2 solution is obtained when constant current component dominates the other load components. Furthermore, the impact of unrealistic assumption of Kron reduction approach on the quality of the proposed relaxation for a single or multiple point grounded DNs is also discussed. From a computational point of view, the proposed methodology can be realized on a real-time basis for small DNs. However, for medium and large DNs, the incorporation of additional sparsity exploitation or distributed algorithm techniques are required for its real-time implementation.