In recent years several numerical methods have been proposed to identify the one-diode model for photovoltaic modules by introducing simplifications/approximations techniques or by using suitable data interpolations from the panel characteristic curves. In this paper a complete theoretical and practical analysis on the extraction of the five parameters identifying the one-diode model for photovoltaic modules from data available on PV panel datasheets is proposed. The present theoretical analysis is utilized, from a hand, to gain insight into this model and, at the same time, to develop few practical rules to strongly improve both the accuracy of the solutions and the computational costs with respect the performances present in literature. In particular, we prove how it is possible to separate the independent variables from the dependent ones within the system by using suitable algebraic manipulations of the commonly used equations. This splitting of the parameters allows a new paradigm in the writing of the open circuit, short circuit and maximum power point constraints, giving the possibility both to exactly verify these conditions and to reduce the dimensions of the search space. Moreover, thanks to this paradigm we have the possibility to address the issues regarding the existence, the uniqueness and the meaningless of the solutions of the identification problem under specific conditions. In this way, the feasible domain of solutions and the conditions for the existence of a unique solution as well as the unphysical solutions will be proven and justified. Lastly some critical issues of the approaches currently used in literature for this problem are discussed and an adequate solution of the identification of the one-diode model is provided for PV designers. All the analytical dissertations presented in this work, as well as the obtained results, have been validated on hundreds of PV panels belonging to the California Energy Commission database. (C) 2014 Elsevier Ltd. All rights reserved.