Stochastic Modeling of Consumption and Solar Radiation Variation and its Application to the Optimal Control of an Autonomous Microgrid of a Cluster of Houses

Abstract

In non-interconnected areas, the efficient use of renewable energies requires an optimal management of power consumption. We study the case of the "Cirque de Mafate" on Reunion Island. A model based on mixed integer linear programming has been developed as optimization tool. In order to minimize energy losses by maximizing the use of electrical appliances or the use of solar energy and the energy stored in the battery during the day, this paper aims to find the optimal balance between the production system and the consumption of the microgrid by considering uncertainties of demand as well as the production resources. The loads are the electrical appliances of a group of three houses. It consists to model, optimize and simulate the stochastic operation of an autonomous microgrid by mutualizing production and storage resources. The uncertainty propagation method is developed to take into account uncertainty of solar radiation as well as electrical consumption of the users in the optimization model. Indeed, to estimate the probability density function of the electricity consumption, non- parametric methods for the estimation of probability density functions are applied. These same methods were used to estimate the probability density functions of solar radiation for the solar resource forecast. Indeed, the prediction of the intermittent resource and the combination of generation sources taking into account the uncertainty of the users' demand is the key for the proper operation of a microgrid in autonomous mode. The results show the performance of the system to achieve self-consumption for three days if the solar forecast is pessimistic and allow us to evaluate the performance of the system under random constraints. Indeed, they allow us to make decisions in order to advise users on the use of electrical appliances by taking into account their behavior and the last minute modification of their time slots of use of electrical appliances.