  We propose a fully probabilistic prediction model for spatially aggregated
solar photovoltaic (PV) power production at an hourly time scale with lead
times up to several days using weather forecasts from numerical weather
prediction systems as covariates. After an appropriate logarithmic
transformation of the power production, we develop a multivariate Gaussian
prediction model under a Bayesian inference framework. The model incorporates
the temporal error correlation yielding physically consistent forecast
trajectories. Several formulations of the correlation structure are proposed
and investigated. Our method is one of a few approaches that issue full
predictive distributions for PV power production. In a case study of PV power
production in Germany, the method gives calibrated and skillful forecasts.
