Quantile regression-based statistical modelling and forecasting of solar irradiance in Southern Africa

Abstract

Solar energy has increased interest because of its enormous and infinite potential to supply the global energy demand. The common and already existing photovoltaic (PV) solar power generation is directly and heavily dependent on so lar irradiance (SI). The rapid fluctuating uncertainty characteristics of SI make PV power generation have intermittent and uncontrollable characteristics that greatly impact the stability of solar power systems. One of the solutions is to improve the prediction accuracy of SI. This thesis contributes to this solution by presenting a guideline for developing an SI forecasting framework based on quantile functions (QFs) and quantile regression (QR). Data exploration was identified as the first and paramount stage in developing a modelling frame work. The thesis presented quantile distributional function modelling (QDFM) to overcome limitations in the currently used deterministic models to explore SI. Deterministic and stochastic elements in the data are combined and analysed simultaneously when fitting the QDFMs. The fitted QDFMs were then used to find population means as explorative parameters that consist of the data’s deterministic and stochastic properties. The thesis demonstrated that applying QFs when exploring data is a practical tool that gives more information than approaches that focus separately on measures of central tendency only or empirical distributions. In this thesis, the curse of dimensionality was identified as a problem affecting predictive models’ accuracy. The study suggested solving the problem as a second and paramount stage of developing a forecasting framework. With so many existing variable selection methods, the study sought to identify the best variable-embedded selection method for ii different location and time horizon combinations from Southern Africa solar irradiance data. Penalised quantile regression, regularised random forests, and quantile regression forest were introduced as new variable selection methods when forecasting SI data. Stability analysis, performance and accuracy metric evaluations were presented to determine the best algorithms in the different data situations and conditions. Identification of predictive models was addressed as the third and most common stage when predicting SI. This thesis contributed to renewable energy studies by conducting a comparative investigation of the quantile generalised model and quantile regression random forest as new non-parametric QR-based models to forecast SI. The thesis presented two chapters on the comparative investigation: one on additive models and the other on decision tree-based models. All non-parametric QR-based models presented were valid and stable to forecast SI from the Southern African region. They had similar behaviours regarding the prediction accuracy of the forecast distribution. However, additive models had better forecasting performances than decision tree-based models. Among the additive models, the QGAM had the near-best forecasting performance. Among the major contributions of this thesis is a suggested guideline for developing a solar irradiance modelling and forecasting framework.