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

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Abstract Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to solar irradiation. To help develop the frameworks, this current study modelled solar irradiation using non-parametric quantile regression (QR). The approach applies quantile splines when finding the best relationships between covariates and the response variable. As a result, the method was very suitable because relationship structures between covariates and solar irradiation are unknown. However, some additive effects are perceived as linear. Thus, the study included the partially linear additive quantile regression model (PLAQR) in our quest to find how best the additive effects can be modelled. The PLAQR model compared very well on reliability analysis, but it was outperformed by the new quantile generalised additive model (QGAM) we proposed, on all other metrics. Modelling of solar irradiation using QGAM is new to renewable energy studies. The Winkler score is another metric where QGAM was inferior, however, an additive quantile regression model was the best. Even though the models had also approximately the same continuous rank probability score in all cases, the QGAM was the best in most metric evaluations. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

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