Fast and Physically Constrained Modelling of Solar PV Power Output Using an Optimized Ordinary Differential Equation (ODE) Framework

Abstract

This study develops and validates a physically informed ordinary differential equation (ODE) model for predicting photovoltaic (PV) power output under varying environmental conditions. The proposed framework couples panel thermal dynamics with temperature-dependent electrical efficiency while incorporating multiple environmental forcing variables, including solar irradiance, ambient temperature, wind speed, humidity, and atmospheric pressure. Unknown physical parameters are estimated through bounded optimization using the L-BFGS-B algorithm, ensuring thermodynamic consistency and physically realistic parameter values. The model is validated using real-world hourly operational data from a grid-connected PV system. Results demonstrate strong predictive performance with R² = 0.9824, RMSE = 20.98 W, and MAE = 11.32 W, indicating that the model captures more than 98% of the variance in observed power output. Monte Carlo simulations confirm model robustness under typical sensor noise conditions, producing narrow uncertainty bounds around predicted trajectories. The proposed framework provides a computationally efficient and physically interpretable alternative to purely data-driven forecasting approaches, making it suitable for real-time PV monitoring, forecasting, and grid integration applications.