The Optimal Power Flow (OPF) model for low voltage active Distribution Networks (DNs), which are equipped with neutral conductors, requires an explicit representation of both phases and neutral conductors in its formulation to obtain complete information about the state variables related to these conductors. In this regard, a centralized OPF relaxation based on semi-definite programming is presented in this paper for neutral-equipped DNs hosting ZIP loads and neutral-ground impedance, and contain a significant level of unbalance. The major restriction in the development of an OPF model for these networks is the coupled power injection across the conductors which is successfully handled by deriving the explicit active and reactive power injections for each conductor through a network admittance matrix-based approach. The shortcomings of existing voltage magnitude-based technique for the modelling of ZIP loads are comprehensively reported and a novel complex voltage variable-based approach is proposed which successfully incorporates ZIP loads in the developed multi-phase OPF relaxation. For the handling of constant current load, a modelling approach based on the first-order-Taylor series is introduced as well. Furthermore, the impact of the application of Kron reduction approach on the global optimal solution of single- and multiple-point grounded DNs is discussed in detail. Three metrics, eigenvalue ratio, power mismatch and cumulative normalized constraint violation, are utilized to evaluate the exactness of proposed relaxation. Simulations, carried out on several medium and low voltage DNs, show that the proposed relaxation is numerically exact under several combinations of ZIP load parameters and a reasonable range of grounding impedance value for both time-varying and extreme system loading scenarios irrespective of the degree of unbalance in a network.

The diffusion of distributed energy resources in distribution networks requires new approaches to exploit the users’ capabilities of providing ancillary services. Of particular interest will be the coordination of microgrids operating as an aggregate of demand and supply units. This work reports a model predictive control (MPC) application in microgrids for the efficient energy management of energy storage systems and photovoltaic units. The MPC minimizes the economic cost of aggregate prosumers into a prediction horizon by forecasting generation and absorption profiles. The MPC is compared in realistic conditions with a heuristic strategy that acts in a instant manner, without taking into account signals prediction. The work aims at investigating the effect that different types of energy tariffs have in enhancing the end-users’ flexibility, based on three examples of currently applied tariffs, comparing the two storage control modes. The MPC always achieves a better solution than the heuristic approach in all considered scenarios from the cost minimization point of view, with an improvement that is amplified by increasing the energy price variations between peak and off-peak periods. Furthermore, the MPC approach provides a cost saving when compared to the case considering a microgrid endowed with only photovoltaic units, in which no storage is installed. Findings in this work confirm that storage units better perform when some knowledge of future demand and supply trends is provided, ensuring an economic cost saving and an important service for the overall community.

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.

The aim of this article is to develop a simplified equivalent dynamic model capable to capture the transient behavior of a gas-fueled co-generator. To comply with this exigency, an online identification methodology based on the sensitivity theory in conjunction with the Lyapunov function is adopted. By this methodology, stable solutions can be achieved in the online environment, renewing the parameters of the model at every change occurring on the physical system. In order to investigate the effectiveness of the proposed methodology in deriving a simplified dynamic model, several simulations and experimental tests were performed on the Prince Lab microgrid located at the Polytechnic University of Bari.