Extremal Dependence Modelling of Global Horizontal Irradiance with Temperature and Humidity: An Application Using South African Data

Abstract

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.

Keywords

• archimedean copulas
• bivariate threshold excess model
• conditional multivariate extreme value
• extreme value mixture model
• global horizontal irradiance
• laplace margins