Machine learning development to predict the electrical efficiency of photovoltaic-thermal (PVT) collector systems

According to the increasing rate of renewable energy use, especially solar energy, photovoltaic-thermal (PVT) solar panels are getting more attention and they have become significantly important for extracting heat and electricity from solar energy. In this regard, the theoretical equations used to calculate the PVT performance lack accuracy, and many uncertainties and calculation impediments result in deviation from the experimental outputs. Therefore, machine learning (ML) methods can overcome these disadvantages and can be used to predict PVT efficiency more reliably and effectively. In this study, three ML methods, namely, multilayer perceptron (MLP), random forest (RF), and support vector regression (SVR) were implemented to build trained models predicting the electrical efficiency of PVTs. These models are based on more than 380 datasets that were extracted from the literature where all PVT benches use water as their working fluid. The models considered mass flow rate, solar radiation, ambient temperature, wind speed, fluid inlet temperature, PVT surface area, and pipe inner diameter as input variables. The optimized models were attained through rigorous hyperparameters variations through random, coarse and fine grid searches. The results showed that the RF model has a root mean squared error (RMSE) of 0.2233, 0.4638, and 0.671 for training, testing, and validation datasets respectively, and training coefficient of determination (R-square), with a value of 0.9862, providing relatively high prediction accuracy for the electrical efficiency. Next, the MLP model with a testing R-square value of 0.8775 and the SVR model with a testing R-square value of 0.7639 can predict electrical efficiencies. Further, the output results are visualized using explainable artificial intelligence (AI) method such as SHapley Additive exPlanations (SHAP) which declared that mass flow rate, pipe inner diameter, and wind speed are the most effective variables in the RF model. For validation purposes, 46 datasets characterized with at least one out-domain parameter are used to test the performance of our models. For out-of-range input variables, the RF model most accurately predicted the electrical efficiency for cell absorptance and inlet fluid temperature variables, outperforming the MLP and SVR models. Meanwhile, the SVR model showed superior accuracy over both RF and MLP when dealing with datasets featuring solar radiation values beyond the training domain.