A Copula-Based Approach to Statistical Modelling of Solar Irradiance

Estimating and predicting surface solar irradiance, particularly its variability, is critical for solar engineering, enhancing solar energy utilisation and photovoltaic power generation. Cloud cover is the most significant contributor to solar irradiance depletion because it limits the total quantity of radiation reaching the earth’s surface. In this chapter, we propose an approach to model the instantaneous solar irradiance by using a multivariate probability distribution, constructed via a copula, to model the clear-sky indices and account for the dependency between the Direct Normal Irradiance and the Direct Horizontal Irradiance indices. The distributions considered for the marginal distributions are a mixture of two re-parameterised beta distributions, the unit inverse Gaussian distribution (UIG) and a mixture distribution of an exponential distribution and the UIG distribution for the clear-sky direct irradiance index and a gamma distribution for the clear-sky diffused irradiance index. We model solar irradiance data from two South African Universities Radiometric Network radiometric stations located at the University of Pretoria in Gauteng, and Stellenbosch University in the Western Cape.