Modelo estatístico para predição de geração de energia solar fotovoltaica

Abstract

Over the past 10 years, there has been a significant increase in energy generation through photovoltaic plants, both residential and large-scale. In regions with abundant solar incidence, such as Brazil, photovoltaic plants are often installed due to financial viability. As a result, more and more photovoltaic plants are being connected to the electrical grid system of cities every day. However, this can cause instability in the grid, creating challenges for energy concessionaires, as they manage the structure of transmission and distribution of electrical energy. A tool to help solve this problem is the development of predictive models capable of informing with high reliability the amount of energy that will be generated and inserted into the electrical system by a plant. In this dissertation, we propose a Bayesian approach to estimate the curve of a function f(·) that models the solar power generated at k moments per day for n days and to forecast the curve for the (n + 1)th day by using the history of recorded values. We assume that f(·) is an unknown function and adopt a Bayesian model with a Gaussian-process prior on the vector of values f(t)=(f(1),...,f(k)). An advantage of this approach is that we may estimate the curves of f(·) and fn+1(·) as “smooth functions” obtained by interpolating between the points generated from a k-variate normal distribution with appropriate mean vector and covariance matrix. Since the joint posterior distribution for the parameters of interest does not have a known mathematical form, we describe how to implement a Gibbs sampling algorithm to obtain estimates for the parameters. The good performance of the proposed approach is illustrated using two simulation studies and an application to a real dataset. As performance measures, we calculate the absolute percentage error, the mean absolute percentage error (MAPE), and the root-mean-square error (RMSE). In all simulated cases and in the application to real-world data, the MAPE and RMSE values were all near 0, indicating the very good performance of the proposed approach. Palavras chave: Photovoltaic solar power forecasting; statistical modeling; Bayesian inference; Gaussian process; MCMC; Gibbs sampling algorithm