Physics-constrained wind power forecasting aligned with probability distributions for noise-resilient deep learning

Wind power plays a critical role in achieving carbon neutrality as one of the key renewable energy sources. However, accurate wind power forecasting is challenged by high-noise forecast wind speed data, compromising forecast accuracy and robustness. To address this issue, we propose theory-guided (physics-constrained) deep-learning wind power forecasting (TgDPF). TgDPF integrates the domain knowledge of wind power curves, which represent the probability distribution of wind power, with the deep learning model Long Short-Term Memory (LSTM). This integration ensures that the model's output aligns with the probability distribution of the wind power, adhering to physical constraints and enhancing noise resistance. Consequently, TgDPF exemplifies a physics-constrained method. While the probability distribution of wind power is crucial for accurate predictions, effectively utilizing this distribution presents significant challenges, including maintaining model differentiability after embedding the distribution and measuring distribution similarity. To overcome these challenges, TgDPF employs kernel density estimation (KDE) to compute the wind power curve, ensuring the model's differentiability. The discrepancy between the LSTM-generated and actual wind power curves, quantified by the Jensen-Shannon (JS) divergence, is incorporated into the LSTM training process. Compared to the MSE loss-trained LSTM model, TgDPF aligns with the pre-calculated wind power curve, enhancing forecasting reliability and robustness. Experiments on 25 different wind turbines show that the performance of TgDPF is obviously better than that of LSTM when adding noise of different proportions to wind speed. Specifically, when unbiased high noise N(0, 0.5), N(0, 0.7) is added, TgDPF outperforms the MSE loss-trained LSTM model by 24.7 % and 35.8 % respectively. Additionally, with biased high noise N(0.5, 0.5), N(0.7, 0.7), TgDPF surpasses the LSTM model by 67.2 % and 73.9 % respectively.