Abstract
Based on quantile regression (QR) and kernel density estimation (KDE), a framework for probability density forecasting of short-term wind speed is proposed in this study. The empirical mode decomposition (EMD) technique is implemented to reduce the noise of raw wind speed series. Both linear QR (LQR) and nonlinear QR (NQR, including quantile regression neural network (QRNN), quantile regression random forest (QRRF), and quantile regression support vector machine (QRSVM)) models are, respectively, utilized to study the de-noised wind speed series. An ensemble of conditional quantiles is obtained and then used for point and interval predictions of wind speed accordingly. After various experiments and comparisons on the real wind speed data at four wind observation stations of China, it is found that the EMD-LQR-KDE and EMD-QRNN-KDE generally have the best performance and robustness in both point and interval predictions. By taking conditional quantiles obtained by the EMD-QRNN-KDE model as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method, whose bandwidth is optimally determined according to the normal reference criterion. It is found that most actual wind speeds lie near the peak of predicted PDF curves, indicating that the probabilistic density prediction by EMD-QRNN-KDE is believable. Compared with the PDF curves of the 90% confidence level, the PDF curves of the 80% confidence level usually have narrower wind speed ranges and higher peak values. The PDF curves also vary with time. At some times, they might be biased, bimodal, or even multi-modal distributions. Based on the EMD-QRNN-KDE model, one can not only obtain the specific PDF curves of future wind speeds, but also understand the dynamic variation of density distributions with time. Compared with the traditional point and interval prediction models, the proposed QR-KDE models could acquire more information about the randomness and uncertainty of the actual wind speed, and thus provide more powerful support for the decision-making work.
Highlights
Because of the independence from fossil energy and low environmental costs, wind energy has become an important part of sustainable development strategies in many countries [1]
The novelty and contributions of this study can be summarized as follows: A framework for probability density forecasting of wind speed based on quantile regression (QR) and kernel density estimation (KDE) is proposed
Taking the conditional quantiles obtained by the QR-KDE model with the best performance as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method and verified by comparing with the actual wind speed values
Summary
Because of the independence from fossil energy and low environmental costs, wind energy has become an important part of sustainable development strategies in many countries [1]. Energies 2020, 13, 6125 wind power on the grid system becomes more and more obvious. Much attention has been paid to developing accurate wind speed forecasting models, which are mainly designed for point predictions. According to the implementation mechanism, current point forecasting models mainly include two categories: one is called the physical model, which is based on numerical weather prediction. The other is based on historical data to construct statistical models to predict future wind speed. Artificial intelligence and machine learning (AI/ML) models, such as artificial neural networks (ANN) [9], support vector machine (SVM) [10], extreme learning machines (ELM) [11], and deep learning networks (DLN) [12], have been widely used in point prediction of short-term wind speed. In order to improve the prediction accuracy and robustness, hybrid or combined models [13] integrating the advantages of single models are attracting more and more attention
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call