Parametric Probabilistic Forecasting of Solar Power With Fat-Tailed Distributions and Deep Neural Networks
Lin Fan, Yao Zhang, Ke Wang, Jianxue Wang, Morun Zhu
Abstract
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.