A fractional derivative approach to modelling a smart grid-off cluster of houses in an isolated area

Abstract

. This paper presents an operational model of an electrical power supply in order to meet the load of a cluster of houses in a remote mountainous area. In outlying areas, an isolated power network represents the most economical solution. However, the implementation of a cluster of houses in an electrical microgrid requires optimal management of the power supply-demand in order to reach the users’ requirements. Our case study is located in the “Cirque de Mafate” in Reunion Island. To build the model, the different types of individual consumption and the available energy production in situ are described. Energy management is achieved through a large mixed integer linear programming system. The model allows the production to fit the consumption by minimizing losses. Numerical calculations have been performed in order to determine an optimal solution that minimizes the use of the battery energy storage system and also satisfies the comfort of the inhabitants. The use of fractional derivative is introduced in the battery storage model. Simulations show that this emerging technology may lead to a technical solution that meets the above requirements of battery energy use and consumer satisfaction. It is also shown that a most effective and efficient use of energy resources is required in order to achieve sustainable management of electrical energy.