In this paper, a three-dimensional study on a polycrystalline silicon solar cell under polychromatic illumination in an instational regime. The influence of grain size, recombination velocity at the grain boundaries on the density of the minority carriers of a silicon solar cell, is presented. Based on the continuity equation of the minority carriers in the solar cell base, the expressions of the photocurrent density and the photovoltage in function of the grain size, the recombination velocity, are deduced. The continuity equation of the carriers has been solved by a numerical method with boundary conditions and physical constants fixed in relation to our reference model. The influence of time t on the density of the carriers and on the electric power was presented in this work also. The electrical voltage and current were studied according to the recombination velocity. The conversion efficiency according to the grain size and also presented an assessment of the performance of our model of study. The expressions of the output power and the energy conversion of the solar cell, are determined in order to optimize its functional state. We recall that, the objective is to make a numerical resolution, making fewer simplifying hypotheses so that the study is closer to reality compared to other methods of resolution.

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