Statistical Method for Single-Diode Model Parameters Extraction of a Photovoltaic Module

Abstract

In this work a modeling method for photovoltaic (PV) modules based on statistical analysis is presented. In this sense, the work deals with the determination of the parameters of the non-linear I-V equation, represented by the single-diode model. The parameters estimation of the PV model starts with experimental tests on PV panels under different irradiance and temperature conditions. A database is built with the parameters extracted from the family of experimental curves, where mathematical expressions, through linear regression analysis, are obtained to determine electrical variables of interest, such as: $I_{sc},\ V_{oc},\ I_{m},\ V_{m}$ and $P_{m}$ which are dependent of irradiance $\text{and}/\text{or}$ operating temperature. The parameters of the non-linear I-V equation given by the resistances $R_{sh},\ R_{s}$ and the ideality factor $n$, the analysis demonstrate that average values are representative; while the light-generated and diode-saturation currents depend on the incident irradiance. The capacity of the models was validated through the analysis of different statistical criteria, such as: the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and the coefficient of determination ($R^{2}$). The results were accepted for applications where a high precision is not necessary, or for modeling and/or forecasting purposes.