The paper presents an analytical procedure to calculate the seven parameters of the two-diode model of photovoltaic (PV) panels for any value of the solar irradiance and cell temperature. Six parameters (the photocurrent, the diode reverse saturation currents, the quality factor of the first diode and the series and shunt resistances), are evaluated by solving the equations related to the properties of the main points of the current-voltage (I-V) characteristics. The further information, necessary to calculate the entire set of seven truly independent parameters, is based on two conditions that have to be simultaneously satisfied: 1) the exclusion of negative values of the model parameters; 2) the minimization of the difference between the diode quality factors, which permits to obtain more precise I-V curves of the PV modules. A method to extend the application of the two-diode model to conditions that are different from the standard rating conditions (SRC) is presented. The comparison with alternative two-diode models showed that accurate representations of the I-V characteristics can be achieved using the proposed procedure regardless of the typology of the PV devices (monocrystalline, polycrystalline, HIT, amorphous silicon, CIS, CIGS, tandem). (C) 2019 Elsevier Ltd. All rights reserved.