Physics-constrained and peak-aware hybrid deep learning for ultra-short-term photovoltaic power forecasting

Accurate prediction of ultra-short-term photovoltaic (PV) power is crucial for ensuring the safe and stable operation of the power grid and promoting the efficient integration and utilization of renewable energy. Existing data-driven models have significant limitations in handling multi-scale non-stationary fluctuations in PV power, often resulting in physically inconsistent predictions and systematic underestimation of peak power. To address these challenges, this paper proposes PC-PBT, a parallel BiLSTM-Transformer hybrid forecasting framework integrating physical constraints and peak-aware optimization. First, an improved Chaotic Nutcracker Optimization Algorithm (CNOA) is employed to collaboratively optimize the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and network hyperparameters within a unified decision space, achieving adaptive multi-scale stationary decomposition of the raw PV power sequence. Second, the decomposed components are fed into a parallel BiLSTM-Transformer architecture to extract global long-range dependencies and local transient features of the power sequence. Subsequently, PIEM incorporates a physical-consistency loss into model training and applies a dynamic projection during both training and inference to ensure physical feasibility. Finally, a peak-aware loss function is constructed, using nonlinear exponential weighting to intensify gradient penalties in the high-power region and suppress peak-clipping bias. Validation at two sites with significantly contrasting climatic characteristics—Xinjiang, China and Yulara, Australia—demonstrates that the proposed framework outperforms 14 benchmark models across all evaluation metrics. Specifically, the Xinjiang site achieves a coefficient of determination (R 2 ) of 0.8947, a root mean square error (RMSE) of 0.9516, and a 24.36 % reduction in Peak Mean Absolute Error (Peak MAE); while the Australian site achieves an R 2 of 0.8846, an RMSE of 0.6718, and a 26.06 % reduction in Peak MAE. This framework achieves a deep integration of multi-scale decomposition, parallel feature learning, physical constraint enforcement, and peak-value optimization, providing an effective technical solution for high-accuracy ultra-short-term PV power forecasting.