A Predictive Stacking Framework for Energy Output in Photovoltaic System With Uncertainty Estimates

The integration of grid-connected photovoltaic (PV) systems has transformed the global energy landscape by offering sustainable and efficient alternatives to conventional energy sources. However, the inherent variability and intermittency of solar energy pose significant challenges for grid operators, complicating reliable energy forecasting and management. Consequently, it is imperative to develop a predictive model that not only delivers accurate forecasts but also incorporates uncertainty analysis to enhance the reliability and decision-making processes. To address these issues, this study proposes a new stacking ensemble model with uncertainty analysis to accurately forecast the energy output in grid-connected PV systems. The model leverages an Extreme Learning Machine (ELM) and Convolutional Neural Network (CNN) as base learners, with a Bayesian Ridge regression model serving as a meta-learner to refine and aggregate the predictions. The ELM regressor was enhanced through bootstrapping, whereas the CNN employed a Monte Carlo Dropout to estimate the prediction uncertainty. The model’s incorporation of uncertainty analysis allows for the computation of the standard deviation and 99% confidence intervals for the predictions. Feature engineering using Shapley additive explanation (SHAP) analysis was employed to enhance predictive accuracy. The performance of the model was simulated using real-time meteorological data from Dammam, Saudi Arabia, for Amorphous Silicon (a-Si) modules. The results showed R² values of 0.9999 (train), 0.9997 (test), and 0.9997 (forecast), with corresponding MAE values of 4.29, 7.75, and 6.71 W, respectively, indicating high accuracy for both seen and unseen data. The uncertainty analysis achieved a standard deviation of 7.77 W, PICP of 91%, and PIW of 46.56 W, demonstrating the model’s strong probabilistic reliability, narrow prediction intervals, and effective coverage of the true output values. The proposed model offers a robust and reliable framework for forecasting the energy output of grid-connected PV systems, supporting solar integration, and reducing greenhouse gas emissions.