Dimensional Analysis-Based Prediction of Photovoltaic Module Electrical Characteristics Under Variable Environmental Conditions

This paper presents a simplified dimensionless model for predicting the electrical performance of photovoltaic (PV) modules under varying irradiance and temperature conditions. Unlike conventional equivalent-circuit models that require detailed parameter extraction, the proposed approach employs dimensional analysis to establish direct relationships between key PV operating points and normalized environmental variables, without assuming a predefined physical model. The model is validated using experimental datasets from Sandia National Laboratories, covering a wide range of irradiance (100–1100 W/m2) and module temperatures (15–75 °C). Model accuracy is evaluated using normalized root mean square error (nRMSE). The results demonstrate strong predictive capability, with average nRMSE values below 2.5% for maximum power point voltage and current, below 1% for maximum power, and low errors for open-circuit voltage and short-circuit current. To the best of the authors’ knowledge, this represents the first application of the Buckingham π theorem to derive dimensionless scaling laws for predicting PV module electrical characteristics under varying irradiance and temperature conditions. The proposed model provides a computationally efficient and accurate alternative to conventional PV models. Moreover, the dimensionless framework offers strong potential for predicting the performance of complex multiphysics energy systems, where conventional equivalent-circuit-based approaches are often difficult to apply or fail to achieve satisfactory accuracy.