Cheap Conic OPF Models for Low-Voltage Active Distribution Networks

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.