Parametric Probabilistic Forecasting of Solar Power with Fat-Tailed Distributions and Deep Neural Networks

The need of solar power uncertainty quantification in the power system has inspired probabilistic solar power forecasting. This paper proposes a novel multi-step parametric method for intra-day probabilistic solar power forecasting. First, statistical analysis on solar power distribution is done using four forecasting methods in real-world data. Fat tails are clearly found in solar power distribution, which could not be modelled by the widely-used normal distribution. In light of this discovery, two fat-tailed distributions, i.e., Laplace and two-sided power distributions, along with their generalized variants are then proposed to better model the conditional distribution of solar power output. Second, a recently proposed DeepAR model for time series probabilistic forecasting based on deep recurrent neural network is used to map various predictors into parameters of the fat-tailed distribution. Moreover, a novel loss function based on the continuous ranked probability score is proposed, and its closed-form formula over the proposed fat-tailed distributions is derived for efficient model training. Numerical results on public real-world data show that our method is very effective and the proposed model can provide intra-day probabilistic solar power forecasting with high quality and reliability.