Integrating a softened multi-interval loss function into neural networks for wind power prediction

High-quality wind power interval prediction is an effective means to ensure the economic and stable operation of the electric power system. Comparing with single-interval prediction, multi-interval prediction is conducive to providing more uncertainty information to decision-makers for risk quantification. Existing multi-interval prediction methods require several independent forecasting models to generate prediction intervals (PIs) at different prediction interval nominal confidence (PINC) levels, which would lead to long training time and cross-bound phenomenon. This paper constructs a novel framework to simultaneously generate multiple PIs for wind power by integrating a proposed softened multi-interval loss function into neural networks. Firstly, the effectiveness of the proposed loss function is verified via simulation data, and the suitable training method and softening factor range are found. Then, five widely used neural networks are employed with both single-interval and multi-interval loss functions to carry out multiple interval prediction on two real-world wind power datasets. The results indicate that the proposed loss function can effectively avoid the cross-bound phenomenon and decrease the mean prediction interval width of PIs. In addition, the echo state network (ESN) with the proposed loss function exhibits the best forecasting performance among the investigated models for both point prediction and interval prediction.