Stochastic Modeling of Photovoltaic Power Generation and Electricity Prices

Abstract

We propose a stochastic model for the maximal production of photovoltaic (PV) power on a daily basis based on data from three transmission system operators in Germany. We apply the sun intensity as a seasonal function and model the deseasonalized data by an autoregressive process with skewed normally distributed noise with seasonal variance to explain the stochastic dynamics. It is further demonstrated that the power spot prices are negatively depending on the PV production. As an application of our results, we discuss virtual power plant derivatives and energy quanto options, as well as continuous time stochastic processes for PV and power spot price dynamics.