Modelling energy storage systems using Fourier analysis: An application for smart grids optimal management

• We propose a new representation of the optimization dispatch variables.
• The handled variable are subject to zero-integral constraints in a given time interval.
• The basic idea comes from Fourier analysis.
• Fourier decomposition is used to design parametric courses showing zero integral.
• Advantages are for new optimization problems formulation with parametric functions.

In this paper, a new and efficient model for variables representation, named F-coding, in optimal power dispatch problems for smart electrical distribution grids is proposed. In particular, an application devoted to optimal energy dispatch of Distributed Energy Resources including ideal storage devices is here considered. Electrical energy storage systems, such as any other component that must meet an integral capacity constraint in optimal dispatch problems, have to show the same energy level at the beginning and at the end of the considered timeframe for operation. The use of zero-integral functions, such as sinusoidal functions, for the synthesis of the charge and discharge course of batteries is thus consequential. The issue is common to many other engineering problems, such as any dispatch problem where resources must be allocated within a given amount in a considered timeframe. Many authors have proposed different methods to deal with such integral constraints in the literature on smart grids management, but all of them do not seem very efficient. The paper is organized as follows. First, the state of the art on the optimal management problem is outlined with special attention to treatment of integral constraints, then the proposed new model for variables representation is described. Finally, the multiobjective optimization method and its application to the optimal dispatch problem considering different variables representations are considered.

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