A novel interval estimation framework for wind power forecasting using multi-objective gradient descent optimization

Effective wind power forecasting enables reliable integration of renewable energy into the electric grid and enhances wind farm management and power system dispatch. To mitigate uncertainty in wind power forecasting, interval prediction is commonly used to provide information on confidence levels. The lower upper bound estimation (LUBE) method is a quality-driven solution that constructs prediction intervals (PIs) based on an ensemble loss function comprising two PI quality metrics without assuming any specific distribution function. However, the conventional LUBE method suffers from three major drawbacks: 1) it is incompatible with gradient descent (GD) due to its non-differentiable objective function; 2) its objective function is formulated based on qualitative assessment rather than on a statistical basis; and 3) the ensemble loss function cannot fully represent the PI quality information measured by two conflicting metrics, leading to potential performance loss. In this study, we propose a novel multi-objective gradient descent (MOGD)-based LUBE model to address these drawbacks. The loss function is derived based on the maximum likelihood estimation and is approximated by a sigmoid function to ensure its statistical basis and differentiable form. In the training process, MOGD is applied to search for the direction of GD subject to both PI metrics. The proposed model is compared with several benchmarks using four wind power datasets from different spatial locations. The numerical results indicate the superiority of the proposed MOGD-LUBE model over its counterparts in terms of the reliability and sharpness for efficient wind power forecasting.