High reverse power flow of renewable energy in electricity distribution networks might lead to overloading problems and voltage violations causing huge economic damages as well as 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, and, in this way, predict overloading problems and generate automatic warnings.

In this talk, we present two different stochastic models for the prediction of solar power supply to distribution networks, based on temporal and spatially correlated weather forecasts for a 20x20 km grid covering the territory of Germany. In particular, by analyzing the dependency between solar power generated by solar fields and global radiation forecasts, we build probabilistic prediction models using the representation of multivariate probability distributions by copula functions.

First, for purposes of data harmonization, we interpolate the radiation forecasts at the feed-in points of the considered solar fields by an inverse-distance weighting and normalize the supplied solar power for each of these locations to allow for comparison. Then, for each feed-in point we determine the joint probability distribution of global radiation forecast and supplied solar power at this location, by fitting both marginal distributions and a bivariate Archimedean copula. This allows us to estimate the conditional probability distribution of supplied solar power at each feed-in point, given an interpolated global radiation forecast at this location. Note that this conditional probability distribution is computed regardless of the global radiation forecasts at other locations.

Furthermore, we determine the joint probability distribution of the *n*-dimensional vector of global radiation forecasts at *n *feed-in points, directly connected with a certain network control point, and the solar power supplied at this network node, i.e., the aggregated solar power generated at the *n* feed-in points. This (*n*+1)-dimensional probability distribution is fitted by means of D-vine copulas. Similar to the previously described two-dimensional case, we can then estimate the conditional probability distribution of supplied solar power at each network control point, given the vector of global radiation forecasts at the *n *feed-in points directly connected with this network node.

Thus, we showed that global radiation forecasts can be used to generate probabilistic predictions of solar power supply at network control points.