Use of Regression Models for Estimation of Electric Power Generation by Photovoltaic Power Plants

Abstract

The choice of an approach for accurate forecasting of photovoltaic power plants and modeling of power systems with renewable energy sources depends on the availability of input data, time horizon, installation location, and weather variables. Our goal is to improve mathematical models and find new solutions to improve the performance of predicting the operation of photovoltaic power plants in energy systems using regression models. There is a problem of predicting the amount of electricity generated by photovoltaic plants in Ukraine. The data for 3 years of daily electricity production is used. The problem is solved by the application of the least squares’ method to estimate unknown parameters of the suggested dependence between the length of daylight and daily solar power generation. The main assumption is the following: daily solar power generation can be given as a linear combination of some exponential polynomials with the independent variable as the duration of the sunny day. The regression model is reduced to a system of significantly non-linear equations, which is solved numerically by the iteration method. Regression models were built using R software for big data analysis. Another novelty moment concerns grouping of the data according to the same length of daylight, and then three values were found for each such group: maximum, minimum, and average value. The proposed moving average regression models with the usage of exponential polynomials as approximating functions admit a small standard residual error between the exact values and the predicted values of solar power generation (0.3022 kWh). The forecasting horizon is one year. The significance of the created mathematical forecasting models demonstrates a possibility of using the daylight duration as a parameter in forecasting tasks, as well as evaluating the prospects to consider the parameters that affect the performance of photovoltaic power plants.