Mathematically-guided ultra-short-term wind power forecasting based on adaptive mixture of experts

• Proposes a mathematically guided Mixture of Experts (MoE) ensemble that dynamically adapts to rapid wind fluctuations, improving forecast reliability for real-time power system operation. • Introduces a lightweight mathematical module that cooperates with a soft MoE gating network, enhancing expert weighting stability through point estimation, volatility, trend, and prediction boundary information. • Combines wavelet-based time–frequency decomposition with cyclical time encoding to effectively capture both ultra-short-term variability and underlying periodic patterns in wind power data. • Integrates heterogeneous deep learning models with complementary spatiotemporal strengths, enabling improved generalization across varying meteorological and operating conditions. • Extensive experiments show significant accuracy gains over benchmark models and ensemble methods, supporting more secure scheduling, reduced reserve requirements, and enhanced stability in renewable-rich power systems. Accurate and reliable ultra-short-term wind power forecasting remains a critical challenge for secure and efficient renewable energy integration into modern power grids. However, existing approaches face key limitations: single models lack robustness across diverse meteorological conditions, fixed-weight ensemble methods fail to adapt to rapidly changing wind dynamics, and purely data-driven gating mechanisms are sensitive to transient noise due to the absence of explicit statistical guidance. To address these limitations, this paper proposes a dynamic ensemble framework based on a Mixture of Experts (MoE) architecture that adaptively combines multiple forecasting models. Five forecasting models serve as expert predictors, each trained independently with wind data and hybrid temporal features, enhancing each expert's ability to learn both ultra-short-term fluctuations and long-term seasonal dynamics, overcoming the robustness limitations of single models. A context-aware gating network dynamically assigns weights to experts based on recent performance, enabling real-time adaptation to rapidly changing wind dynamics, while a lightweight mathematical module further guides this process by incorporating point and boundary estimation, recent volatility, and trend information, providing explicit statistical guidance. The proposed model is evaluated against eight benchmark models and various ensemble methods using four accuracy metrics. Experimental results demonstrate that the proposed framework achieves improvements of 38.23-42.84% for 10-minute and 33.14-42.76% for 15-minute horizons over the best benchmark model, and 13.43-37.50% over the best benchmark ensemble. The proposed MoE ensemble dynamically selects and emphasizes the most accurate experts at each interval, improving forecast robustness and precision.