Closed-loop error correction enhanced wind power forecasting via multi-scale decomposition and hybrid modeling

To address the forecasting challenges posed by the strong volatility and nonlinearity of wind power sequences, this study proposes a dynamic hybrid forecasting framework integrating Complementary Ensemble Empirical Mode Decomposition (CEEMD), Permutation Entropy (PE), Improved Harris Hawks Optimization (IHHO), and Autoformer-MLP, enhanced with an error correction mechanism for improved reliability. The framework first decomposes raw power sequences into multi-scale Intrinsic Mode Functions (IMFs) via CEEMD. Leveraging PE’s entropy-quantization properties, IMFs are precisely categorized into high-frequency stochastic fluctuations (modeled by an IHHO-optimized Autoformer capturing temporal features through autocorrelation mechanisms), medium-frequency periodic components (characterized via Autoformer’s periodic dependency modeling), and low-frequency trends (robustly fitted by an MLP with L2 regularization). Second, the framework introduces an IHHO-optimized Autoformer residual correction module to dynamically compensate for errors from the preliminary reconstruction, establishing a closed-loop “decomposition–frequency division–forecasting–correction” system. Validated on 35 042 real-world data points from a Xinjiang wind farm (2023) across four seasons, the model achieves reductions of 26.99% in mean absolute error, 27.97% in root mean square error, and 27.15% in mean absolute percentage error vs conventional models; goodness-of-fit (R2) consistently >0.96; and 12.56%–17.76% error suppression during extreme events (e.g., spring gusts). Furthermore, ablation studies and comparative experiments demonstrate that IHHO outperforms mainstream evolutionary computation algorithms—including genetic algorithms, particle swarm optimization, and differential evolution—in hyperparameter optimization efficiency and convergence stability. Detailed algorithmic configurations are provided to ensure reproducibility. The proposed framework significantly enhances generalization capability and robustness in complex scenarios, providing a novel pathway for high-precision wind power forecasting and renewable energy grid integration.