Stochastic Multi-Objective Scheduling of a Hybrid System in a Distribution Network Using a Mathematical Optimization Algorithm Considering Generation and Demand Uncertainties

In this paper, stochastic scheduling of a hybrid system (HS) composed of a photovoltaic (PV) array and wind turbines incorporated with a battery storage (HPV/WT/Batt) system in the distribution network was proposed to minimize energy losses, the voltage profile, and the HS cost, and to improve reliability in shape of the energy-not-supplied (ENS) index, considering energy-source generation and network demand uncertainties through the unscented transformation (UT). An improved escaping-bird search algorithm (IEBSA), based on the escape operator from the local optimal, was employed to identify the optimal location of the HS in the network in addition to the optimal quantity of PV panels, wind turbines, and batteries. The deterministic results for three configurations of HPV/WT/Batt, PV/Batt, and WT/Batt were presented, and the results indicate that the HPV/WT/Batt system is the optimal configuration with lower energy losses, voltage deviation, energy not supplied, and a lower HS energy cost than the other configurations. Deterministic scheduling according to the optimal configuration reduced energy losses, ENS, and voltage fluctuation by 33.09%, 53.56%, and 63.02%, respectively, compared to the base network. In addition, the results demonstrated that the integration of battery storage into the HPV/WT enhanced the various objectives. In addition, the superiority of IEBSA over several well-known algorithms was proved in terms of obtaining a faster convergence, better objective value, and lower HS costs. In addition, the stochastic scheduling results based on the UT revealed that the uncertainties increase the power losses, voltage deviations, ENS, and HPV/WT/Batt cost by 2.23%, 5.03%, 2.20%, and 1.91%, respectively, when compared to the deterministic scheduling.