Stochastic Models for Irradiations and Photovoltaic Yields

The importance of renewable energies in the worldwide electricity generation has increased over the past years. In this context, especially photovoltaic energy plays a significant role. In contrast to conventional energy sources, the output of photovoltaic energy has seasonal fluctuations. Through exogenous weather influences the output is difficult to predict. Apart from models for short-term forecasting of the outputs there is an increasing need of long-term models because of the increasing installed capacity. Long-term models are needed, e. g. for the planning of the grid infrastructure. In addition, companies can take advantage of long-term models to optimize the dimension of a photovoltaic (PV) plant and to evaluate the financial benefit. This thesis’ main focus is the development of probabilistic hourly models for irradiations and PV yields. In the course of this thesis, we develop various model approaches of hourly irradiation that can also be applied for PV yields. Besides models from classical time series analysis we consider univariate copula-based time series models and models based on a truncated Dirichlet distribution. Moreover, we develop seasonal upper and lower bounds of global horizontal irradiation with a quantile regression and methods from extreme value theory. The developed models shall reproduce the characteristics of the process, especially the hourly dependence structure. For this purpose, we evaluate the out-of-sample forecast accuracy of the different models with so-called scoring rules for probabilistic forecasts. In combination with models for other renewables, electricity prices and electricity loads of companies the models that are introduced in this thesis offer a number of possible applications. Some of them are shown at the end of this thesis.