Ultra-short-term wind power probabilistic forecasting based on an evolutionary non-crossing multi-output quantile regression deep neural network

Ultra-short-term wind power probabilistic forecasting is of significance for stable power grid operation; however, it is still challenging due to the inherent nonlinearity and uncertainty. Most state-of-the-art methods have focused on achieving quantile prediction using a combination of linear quantile regression and nonlinear complex deep neural networks. Yet, these methods struggle with several dilemmas. Quantile regression deep neural networks require a complete training once for each quantile. The multi-training mode and complex structure of quantile regression deep neural network can lead to extremely high computational complexity. Most of the training of quantile regression deep neural networks are guided by the loss of each quantile, and the weights are adjusted by gradient descent in which the gradient explosion and quantile crossover may be encountered. Therefore, this paper proposes a non-crossing multi-output quantile regression deep neural network optimized by chaotic particle swarm optimization. It designs a multi-output deep neural network to output all quantile estimations simultaneously through one training, effectively solving the structural complexity problem of traditional quantile regression deep neural networks. Since quantile regression produces a non-differentiable loss function which significantly hinders model training, the proposed neural network is trained by chaotic particle swarm optimization. It not only achieves the effect of optimizing all quantile losses simultaneously, but also can significantly alleviate the dilemma of training in traditional neural network weight optimization. In addition, several non-crossing constraints are designed for avoiding quantile crossover. The proposed model is trained and tested on two real-world wind power case studies. The experiment results show that the proposed model shows superiority in performance criteria, training speed, and avoiding quantile crossover.