In this paper, we are interested in the diode ideality factor study of the double exponential equivalent model, based on the properties of the fixed point method. The optimal choice of this factor will improve the photovoltaic installation profitability. The diode ideality factor is a crucial parameter to describe solar cell behavior. Different methods have been elaborated to determine its value; some of them are analytical as Lambert function and others are direct as the normal method of the coordinates of the parameters. In our case, we applied the fixed point method which is an iterative algorithm to solve non-linear equations. The values obtained by this method are compared with the calculated values achieved by other methods to prove its significance and effects.

The modeling and extraction of solar cell parameters are the crucial steps for simulating and optimizing the photovoltaic systems to meet specific properties. These parameters are directly related to the current-voltage characteristic of the solar cell under illumination, the latter is generally represented, by an equivalent electrical circuit whose parameters (the shunt resistance , the saturation current, the series resistance and the ideality factor of the diode) have been the subject of several researches. This paper describes an iterative algorithm based on fixed point method to calculate the ideality factor of a photovoltaic cell. The procedure uses the electrical and mathematical equations governing the solar cell behavior. The obtained results were compared to the previous works to show its effeteness.