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Solar Cell Filling Factor Evaluation by Lagrangian Method
M. Abdelkrim, J. Ben Amor, M. Fathallah, and J-P. Charles

The maximum output power of a solar cell is given by the relationship: Pmax = IscVocFF, where Isc is the short-circuit current, Voc the open-circuit voltage, and FF the filling factor of the cell. While these three quantities are not totally independent of one another in the present technology they can be varied independently and represent a convenient and meaningful way of treating cell design The knowledge of the filling factor (or shape factor) FF and its dependence on descriptive parameters occurring in the I-V relationship of the solar cell informs us about the cell performance. In this paper we use an original optimization method of calculation, the Lagrange’s multipliers, to determine the filling factor in the most general case of real solar cells modelled as the one diode equivalent circuit. This optimization method allowed us to determine Lagrange’s multiplier and to realize hat it has the dimension of a positive voltage. Theoretical and experimental results are in good agreement. An efficiency of over 5% is determined. The validity limits of the method are discussed.

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