This paper is aimed at first to present a thorough review of published research works for evaluating the photovoltaic module parameters in three categories. In the first category, the parameters were determined successively one-by-one based on several approximations. The second category was an extension to the first category but through one-or two-loops for determining one- or two-parameters. Then, the remaining parameters were obtained one-by-one. In the third category, an iterative procedure was presented for simultaneous solution of the describing equations based on assumed initial values of some parameters. The remaining parameters -if any- were determined in terms of those already obtained by iteration. The present paper proposes a method for determining the parameters based on datasheet values at three key points on the module current-voltage (I-V) curve and solution of describing equations of the module with the same well-defined initial values, which serve solution for single- and double-diode models irrespective of module type and rating by using Matlab "fsolve" routine. To the authors' knowledge, one of the formulated equations includes -for the first time- the value of the module maximum power. This value was never considered before by other approaches reported in the literature for evaluating the module parameters. The obtained results confirmed the superiority of the proposed method in assessing the module parameters with higher accuracy than that of other methods reported in the literature. The root-mean-square-deviation from the describing equations records a value of 0.005 against a range from 0.03 to 2.45 by other methods for the same module.  As a second check, the percentage deviation of the slope of I-V curve at maximum-power-point from its nominal value reached 0.07% for the proposed method against a range from 0.22 to 44.5 % by other methods. As a third check, the accuracy is evaluated at points different from the key points of the datasheet.  The module current value at open-circuit voltage is 0.0029A and closer to zero on using the module parameters predicted by the proposed method when compared with values in a range from -0.23 to + 0.92A obtained by other methods.