Introduction: The integration of photovoltaic (PV) power into the grid is challenged by the inherent uncertainty of PV power. This study aims to develop a probabilistic forecasting model for day-ahead PV power that effectively captures temporal dependencies while ensuring mathematically sound prediction intervals. Methods: This study develops a hybrid model integrating an Auto-Encoder (AE), a Bidirectional Long Short-Term Memory (BiLSTM) network, and Quantile Regression (QR). First, the AE was employed to learn a dense latent representation of input features, which was then concatenated with the original features. Next, the BiLSTM processed these features to capture bidirectional temporal dependencies. Finally, an Incremental Monotonicity Enforcement (IME) mechanism within the QR layer generated non-crossing prediction intervals by predicting a baseline value and nonnegative increments. Results: Experiments on a real-world PV dataset demonstrated that the proposed model outperforms several baseline models in day-ahead probabilistic forecasting. The generated prediction intervals were more reliable, sharper, and mathematically coherent. Discussion: These results suggest that integrating deep feature learning with monotonicity-enforced quantile regression effectively addresses the quantile crossing problem. The improved interval reliability has practical implications for grid scheduling. A limitation is the model's reliance on historical data quality. Conclusion: The proposed AE-BiLSTM-QR model with the IME mechanism provides an effective and reliable solution for day-ahead PV power probabilistic forecasting. It innovatively integrates deep feature learning, bidirectional temporal modeling, and structurally enforced quantile monotonicity, offering a reliable technical approach for the grid integration of solar energy.
Li et al. (Tue,) studied this question.