The interaction between global horizontal irradiance (GHI) and temperature helps determine the maximum amount of solar power generated. As temperature increases, GHI increases up to the point that it increases at a decreasing rate and then decreases. Therefore, system operators need to know the maximum possible solar power which can be generated. Using the multivariate adaptive regression splines, extreme value theory and copula models, the present paper seeks to determine the maximum temperature that will result in the generation of the maximum GHI ceteris paribus. The paper also discusses extremal dependence modelling of GHI with temperature and relative humidity (RH) at one radiometric station using South African data from 16 November 2015 to 16 November 2021. Empirical results show that the marginal increases of GHI converge to 0.12 W/m2 when temperature converges to 44.26 ∘C and the marginal increases of GHI converge to −0.1 W/m2 when RH converges to 103.26%. Conditioning on GHI, the study found that temperature and RH variables have a negative extremal dependence on large values of GHI. Due to the nonlinearity and different structure of the dependence on GHI against temperature and RH, unlike previous literature, we use three Archimedean copula functions: Clayton, Frank and Gumbel, to model the dependence structure. The modelling approach discussed in this paper could be useful to system operators in power utilities who must optimally integrate highly intermittent renewable energies on the grid.
Challenges in utilising fossil fuels for generating energy call for the adoption of renewable energy sources. This study focuses on modelling and nowcasting optimal tilt angle(s) of solar energy harnessing using historical time series data collected from one of South Africa’s radiometric stations, USAid Venda station in Limpopo Province. In the study, we compared random forest (RF), K-nearest neighbours (KNN), and long short-term memory (LSTM) in nowcasting of optimum tilt angle. Gradient boosting (GB) is used as the benchmark model to compare the model’s predictive accuracy. The performance measures of mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE) and R2 were used, and the results showed LSTM to have the best performance in nowcasting optimum tilt angle compared to other models, followed by the RF and GB, whereas KNN was the worst-performing model.
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