The current-voltage output of concentrator photovoltaic (CPV) modules shows a complex behaviour under irradiance variations due to the use of multi-junction solar cells and optical elements. The single exponential model (SEM) relates the I-V curve of a PV device and its five characteristic parameters. Hence, it is fundamental to understand the dependence of the SEM model and I-V parameters of CPV modules with irradiance. In this paper, two samples of concentrator modules were characterized under fully controlled conditions by using a CPV solar simulator for light intensities within 700-1000 W/m(2). Results show that the photo-generated current increases linearly with irradiance, the diode ideality factor and saturation current present a stable behaviour under irradiance variations while the parasitic resistances, i.e. series and shunt, trend to decrease as the intensity increases. In addition, different approximations are carried out in the SEM model equation to explain the dependence of the performance of the concentrators with light intensity. Finally, the prediction of the I-V curves and key electrical parameters from reference values is discussed. Results show a good fitting of the I-V curves until 750 W/m(2) and a high accuracy in the estimations of the electrical parameters with a MAPE lower than 1.2%, a MRE within 1% and a R-2 equal of higher than 0.9. (C) 2017 Elsevier Ltd. All rights reserved.