A novel nonlinear grey model with parameter estimation optimization and its application in wind power forecasting

Wind power forecasting is crucial for optimizing energy structure and enhancing power system economics, but the nonlinear and non-stationary nature of the data complicates this task. Therefore, this paper proposes a novel nonlinear grey Bernoulli model with an optimized parameter estimation framework. Firstly, new background value expressions are constructed at the geometric level to capture the spatio-temporal dynamics of data. Secondly, a kernel function is employed to construct a prioritized weighting matrix, and combine it with weighted least squares to enhance the impact of new-information. Utilizing the power index to characterize system nonlinear behavior. Furthermore, the Hiking Optimization Algorithm is employed for hyper-parameter tuning. The model was validated using data from China, the United States, and Brazil, and compared with various statistical, machine learning, and grey models. Results demonstrate its superior accuracy, with Mean Absolute Percentage Error on training and test sets ranging from 0.81%–3.36% and 0.31%–7.02%, with average accuracy improvements of 2.40 and 3.25 percentage points, respectively. Monte Carlo simulations and cross-validation confirmed its robustness. Moreover, a long-term forecast has been conducted for the period 2024–2030. The findings provide quantitative decision support for the wind power strategies, infrastructure investment, and grid planning of the three countries.