Long-Term Wind Power Forecasting via a Hybrid Statistical–Stochastic–Machine Learning Approach

Accurate long-term wind-power forecasting benefits from probabilistic scenario generation that reflects both the temporal dependence of wind conditions and the uncertainty associated with distributional parameters. This study develops a hybrid Statistical–Stochastic–Machine Learning framework for month-ahead wind-power scenario generation. Monthly wind-speed observations are represented using Weibull distributions, whose shape and scale parameters are estimated from historical data and modelled through a bivariate vector autoregressive process defined on the original parameter scale. A heteroskedastic Kalman filter provides the predictive distribution of the next-month Weibull parameters, and this parameter uncertainty is propagated to stochastic wind-speed trajectories using three positive stochastic differential equation (SDE) formulations. Joint parameter samples are drawn from the Kalman predictive distribution using Cholesky-based Gaussian sampling with a simple admissibility constraint, allowing the covariance structure between the forecasted parameters to be retained. The simulated wind-speed trajectories are subsequently mapped to electrical power using an XGBoost-based power curve. The framework is evaluated using observations from multiple wind farms, turbine types, and operating periods, including Kelmarsh, Penmanshiel, and Dundalk. Additional ablation experiments and benchmark comparisons are conducted against time-of-day climatology, persistence-based scenarios, an autoregressive wind-speed model, an independent Weibull sampler, and quantile gradient boosting. The results indicate that the proposed approach produces plausible probabilistic forecasts while maintaining temporal structure in the generated scenarios. The three SDE formulations yield broadly similar probabilistic scores, with the diffusion-first formulation offering a noticeable reduction in computational cost. The overall findings suggest that the proposed method can be applied across different sites and turbine configurations, while broader multi-site and multi-season evaluation would help further assess general applicability.