Abstract
The increasing focus on the active participation of low-voltage (LV) active distribution networks (DNs) in electricity markets requires the real-time optimal control of these DNs. To achieve this goal, a cheap semi-definite programming (SDP)-based optimal power flow (OPF) model for active neutral-equipped DNs, hosting both wye- and delta-connected loads, is proposed in this paper, aiming at overcoming the high computational requirement of the primal SDP-based OPF model. The coupled power injections between conductors are explicitly represented for each conductor by utilizing the network admittance matrix-based approach. Furthermore, three novel propositions (P1, P2 and P3) are proposed for the modelling of the constant current component of ZIP end-users in the context of the proposed OPF model. Moreover, the impact of the voltage-angle deviation on the exactness of the P1- and P2-based models is discussed. Simulations are carried out on several LV active DNs for various parameters of ZIP end-users, and the quality of the proposed OPF model is verified through the %optimality gap, power mismatch, voltage violation and root-mean-square error criteria. It is successfully shown that the proposed OPF model provides an optimal and feasible solution for all load types (wye, delta, mixed wye-delta) under a large range of ZIP load parameters. Furthermore, among the three propositions, the P3-based OPF model appears to be the most accurate in terms of determining an optimal and feasible solution. Finally, the reduced computational time of the cheap conic model allows its real-time implementation for medium- and large-sized DNs for which the primal multi-phase SDP-based model is practically difficulty to realize.
Highlights
The optimal power flow (OPF) problem formulation based on the convex relaxation and approximation techniques has gained significant attention in the past few years due to the fact that these techniques ensure global optimality and problem infeasibility through several sufficient conditions and criteria
CONTRIBUTIONS 1) Extension of a centralized three-phase cheap SDPbased OPF model, which utilizes the branch flow model (BFM)-based power system representation, for distribution networks equipped with neutral conductor(s) (DNNs) containing both wye- and delta-connected ZIP loads 2) Proposal of three novel techniques for the approximate modelling of the constant current component of a ZIP end-user to incorporate it into the proposed OPF model 3) Development of tighter limits for the complex phase-ground voltage variables involved in propositions 1 and 2, and proposal of a novel approach for determining the bounds on neutral conductor voltage variables 4) Demonstration of the impact of the voltage-angledeviation bounds on the exactness of the proposed OPF models
The cheap semi-definite programming (SDP)-based OPF models for DNNs hosting both wye- and delta-connected ZIP loads provide an alternative solution to the primal SDP-based OPF methodology for realizing the real-time optimal control and management of these networks
Summary
The optimal power flow (OPF) problem formulation based on the convex relaxation and approximation techniques has gained significant attention in the past few years due to the fact that these techniques ensure global optimality and problem infeasibility through several sufficient conditions and criteria. For neutral-equipped DNs, a detailed primal SDP-based OPF model was recently introduced by the authors in [27], [28]; this model successfully incorporates both wye- and delta-connected loads and distributed generators (DGs) without reducing the network configuration from four conductors to three phases. A. CONTRIBUTIONS 1) Extension of a centralized three-phase cheap SDPbased OPF model, which utilizes the BFM-based power system representation, for DNNs containing both wye- and delta-connected ZIP loads 2) Proposal of three novel techniques for the approximate modelling of the constant current component of a ZIP end-user to incorporate it into the proposed OPF model 3) Development of tighter limits for the complex phase-ground voltage variables involved in propositions 1 and 2, and proposal of a novel approach for determining the bounds on neutral conductor voltage variables 4) Demonstration of the impact of the voltage-angledeviation bounds on the exactness of the proposed OPF models. Let x and x denote the lower and upper limits of a scalar/vector variable x, respectively, and let x∗ denote the conjugate of a complex variable x
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