A copula-based time series model for global horizontal irradiation

Abstract

The increasing importance of solar power for electricity generation leads to an increasing demand for probabilistic forecasting of local and aggregated PV yields. In this paper we use an indirect modeling approach for hourly medium to long term local PV yields based on publicly available irradiation data. We suggest a time series model for global horizontal irradiation for which it is easy to generate an arbitrary number of scenarios and thus allows for multivariate probabilistic forecasts for arbitrary time horizons. In contrast to many simplified models that have been considered in the literature so far it features several important stylized facts. Sharp time dependent lower and upper bounds of global horizontal irradiations are estimated that improve the often used physical bounds. The parameters of the beta distributed marginals of the transformed data are allowed to be time dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on a simple graphical structure known from the theory of vine copulas. Non-Gaussian copulas like Gumbel and BB1 copulas are used that allow for the important feature of so-called tail dependence. Evaluation methods like the continuous ranked probability score (CRPS), the energy score (ES) and the variogram score (VS) are used to compare the power of the model for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.

Large Scale Probabilistic Simulation of Renewables Production

“…This choice is driven by (i) the strong seasonality at multiple levels; (ii) the non-constant dimension for the simulations, namely the varying number of active periods for solar generation both across days and potentially across different assets due to latitude effects. We refer to [MR20] for a related discussion of calibration in the context of modeling GHI.…”

“…Existing approaches include copulas [MWH17, PZH + 20, TWX + 18]; kriging or Gaussian processes [AYZW15, vdMSS + 18, YLLQ18, WK13] and downscaling of weather forecasting ensembles [BRM + 21]. Among copula approaches, one may distinguish the application of vine copulas [WWL + 17], tail copulas [MR20] and Bayesian copulas [PZH + 20].…”