Nonparametric Probabilistic Forecasting for Wind Power Generation Using Quadratic Spline Quantile Function and Autoregressive Recurrent Neural Network

Compared with commonly-used point forecasting, probabilistic forecasting provides quantitative information on the uncertainty associated with wind power output. However, most studies focus on modelling only a fixed set of quantiles or intervals, which cannot provide the entire information of wind power distribution. In this paper, we propose a non-parametric and flexible method for probabilistic wind power forecasting. First, the distribution of wind power output is specified by spline quantile function, which avoids assuming a parametric form and also provides flexible shape for wind power density. Then, autoregressive recurrent neural network is used to build the non-linear mapping from input features to the parameters of quadratic spline quantile function. A novel loss function based on continuous ranked probability score (CRPS) is designed to train the forecasting model. We also derive the closed-form solution of the integral required in computing the CRPS-based loss function in order to improve the computational efficiency in training. The effectiveness of our proposed method has been validated with public real-world data from Global Energy Forecasting Competition 2014. Compared with some advanced benchmarks, our proposed approach outperforms them at least six percent in terms of CRPS, indicating that it can provide probabilistic wind power forecasting with high quality.