Flexible Polynomial Mathematical Model of a Photovoltaic Power Plant

Abstract

Solar energy is an important source of clean energy. The purpose of this work is to argue and develop adequate mathematical models that take into account most factors influencing the efficiency of the conversion of the solar energy by photovoltaic power plants. The research methodology is based on a comprehensive analysis of mathematical models of exponential and polynomial form used to describe the current-voltage and volt-watt characteristics characteristics of photovoltaic cells, modules and platforms with PV panels in the mode of electric energy generation. An equation of exponential form is accepted as the basic equation for describing the current – voltage characteristics. A concept and algorithm for formalizing the construction of a mathematical model of a flexible mathematical polynomial model and determining its constant coefficients are proposed. As an approximating function for constructing a polynomial model, the Bernstein polynomial (Bezier function) of the 5th degree is used, using six nodal points. A method for correcting an approximating polynomial has been developed, which consists in changing the coordinates of the selected reference points of the current-voltage curve approximation function when the temperature, insolation and shading of the surfaces of photovoltaics elements change. The accuracy of the approximation of the exponential function by a polynom is estimated. The maximum approximation error does not exceed 1.47%. The feasibility and efficiency of using the polynomial model in calculating the production of electric energy by photovoltaic plants in a given time interval (day, month, year) is shown.