Probabilistic prediction of solar power supply to distribution networks , using forecasts of global radiation

Renewable energy sources are continuously gaining in importance as reserves of fossil energy decline and concerns about global warming increase. Consequently, the number of installed solar plants is steadily rising. The resulting high reverse power flow in distribution networks leads to challenges for network operators, since overloading problems and voltage violations can occur causing great economic damages and endangering secure network operation. In response to these problems new computer-based tools are developed, which aim to analyze the dependency between solar power supply and related weather phenomena, predict overloading problems and generate automatic warnings. This paper presents a mathematical model for the prediction of the probabilities of reverse power flow exceeding predefined critical thresholds at feed-in points of a distribution network. The parametric prediction model is based on hourly forecasts of global radiation and uses copulas, a probabilistic tool for modeling the joint probability distribution of two or more strongly correlated random variables with non-Gaussian (marginal) distributions. The model is used for determining the joint distribution of forecasts of global radiation and measured solar power supply at given feed-in points, where respective sample datasets were provided by Deutscher Wetterdienst and the Main-Donau Netzgesellschaft. It is shown that the fitted model replicates important characteristics of the data such as the corresponding marginal densities. The validation results highlight strong performances of the proposed model. The copula-based model enables to predict the solar power supply conditioned on the forecasts of global radiation, thus anticipating great fluctuations in the distribution network.