Twenty-Four-Hour Ahead Probabilistic Global Horizontal Irradiance Forecasting Using Gaussian Process Regression

Abstract

Probabilistic solar power forecasting has been critical in Southern Africa because of major shortages of power due to climatic changes and other factors over the past decade. This paper discusses Gaussian process regression (GPR) coupled with core vector regression for short-term hourly global horizontal irradiance (GHI) forecasting. GPR is a powerful Bayesian non-parametric regression method that works well for small data sets and quantifies the uncertainty in the predictions. The choice of a kernel that characterises the covariance function is a crucial issue in Gaussian process regression. In this study, we adopt the minimum enclosing ball (MEB) technique. The MEB improves the forecasting power of GPR because the smaller the ball is, the shorter the training time, hence performance is robust. Forecasting of real-time data was done on two South African radiometric stations, Stellenbosch University (SUN) in a coastal area of the Western Cape Province, and the University of Venda (UNV) station in the Limpopo Province. Variables were selected using the least absolute shrinkage and selection operator via hierarchical interactions. The Bayesian approach using informative priors was used for parameter estimation. Based on the root mean square error, mean absolute error and percentage bias the results showed that the GPR model gives the most accurate predictions compared to those from gradient boosting and support vector regression models, making this study a useful tool for decision-makers and system operators in power utility companies. The main contribution of this paper is in the use of a GPR model coupled with the core vector methodology which is used in forecasting GHI using South African data. This is the first application of GPR coupled with core vector regression in which the minimum enclosing ball is applied on GHI data, to the best of our knowledge.

Non-parametric quantile regression-based modelling of additive effects to solar irradiation in Southern Africa

“…We concur with the authors on the idea of including pairwise interaction effects because, in our yet-to-be-published paper, we discovered that a significant number of SI data sets from Southern Africa had covariates with significant multicollinearity. Although 2 did not apply QR in their study, their results also confirm that modelling SI with pairwise interactions included significantly improved forecasting model performances. Forecasts were further improved by extending the application of QR to combine forecasts through quantile regression averaging.…”

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

“…The spatio-temporal GP outperformed the other two models, proving to be the most appropriate model for predicting GHI in South Africa. Most authors (see, for example, [20,31]) applied models based on single-site data sets for predicting solar power irradiation. Accurate forecasts of solar power from multi-sites are important to the system operator, as they facilitate large-scale integration of solar power onto the power grid.…”

“…We predicted solar irradiation using spatial regression coupled with Gaussian process modeling using Bayesian inference. GP regression has proved to be a very powerful tool for modeling the variability and uncertainty of solar irradiation [20], though it is very computationally expensive. The spatial analysis then improves the predictive accuracy since it reduces the computational burden in regression analysis.…”

“…The RMSE given in Equation ( 18) is used in this study to determine the forecast skill (S k ), which helps in benchmarking the forecast quality of the models to the naive model (the model based on unstandardized forecasts). The forecasting skill is given in Equation (20).…”

Bootstrapping Time-Varying Uncertainty Intervals for Extreme Daily Return Periods

“…Hence, it is critical to focus on coming up with a more accurate model. A study by Chandiwana et al (2021) used a Gaussian process regression coupled with core vector regression for short-term hourly global horizontal irradiance forecasting with uncertainty. On the other hand, Rigotti and Shannon (2005) considered a general equilibrium model in which the distinction between uncertainty and risk is formalized by assuming that agents have incomplete preferences over state-contingent consumption.…”