Mathematical Modeling of Battery Energy Storage System Operating Modes using Volterra Integral Equations

Abstract

The integration of powerful photovoltaic systems and wind farms into energy systems significantly affects the operating modes due to frequent power fluctuations, thereby justifying the use of energy storage devices. The improvement of mathematical models describing operating modes of power facilities is a consequence of structure and process complication occurring in energy systems. The article presents a method for modelling the operating parameters of battery energy storage systems, based on the Volterra integral equations. The sequence of the solution is described, as well as its applicability in energy systems research. To determine the operating modes of battery energy storage systems, a non-standard class of Volterra integral equations of the first kind is used in the research. This makes it possible to calculate the operating modes of storage batteries in terms of the inverse problem, when the generation and power imbalance functions are known. To calculate the operating modes of several types of storage devices operating simultaneously within the same power system, the form of such equations can be specified in the form of piecewise constant functions. This method has a number of advantages, since it allows one to take into account nonlinear processes in the kernels of integral equations. Thus, the processes of degradation of energy storage devices that affect the efficiency of their operation are taken into account. The use of regularizing algorithms makes it possible to reduce the error. As an example, an autonomous photovoltaic system with batteries was considered. The obtained results and their visualization show the viability of applying the approach.