Title: A time series model for global horizontal irradiation based on extreme value theory and copulas
Authors: Alfred Mueller - University of Siegen (Germany) [presenting]
Matthias Reuber - University of Siegen (Germany)
Abstract: The importance of renewable energies, especially photovoltaics, in the worldwide electricity generation has increased over the past years. Thus, there is an increasing demand for probabilistic hourly models for local and global PV yields. We use an indirect modeling approach of local PV yields with irradiation data provided by the Copernicus Atmosphere Monitoring Service. We propose a statistical estimation for lower and upper bounds of global horizontal irradiations based on extreme value theory. Moreover, we introduce copula based time series models for the hourly and daily dependence structure. Time dependent parameters of the beta distributed marginals are obtained through a beta regression. We use simple vine copula models in the form of Markov trees to describe the dependence structure. There is empirical evidence for different degrees of upper and lower tail dependence in the data. Therefore we compare different approaches using Gaussian, Gumbel, BB1- and BB7-copulas. Evaluation methods like the continuous ranked probability score (CRPS) and the variogram score (VS) are used to compare the predictive power of the various model approaches.