Abstract
With the aim to determine the photo-generated current, diode saturation current, ideality factor, shunt, and series resistances related to the one-diode model for p-i-n planar perovskite solar cells, reference cells with active area of approximately 1 cm2 and efficiencies ranging between 4.6 and 12.2% were fabricated and characterized at standard test conditions. To estimated feasible parameters, the mean square error between the I-V curve data of these cells and the circuital model results were minimized using a Genetic Algorithm combined with the Nelder-Mead method. When considering the optimization process solutions, a numerical sensitivity analysis of the error as a function of the estimated parameters was carried out. Based on the errors behavior that is showed graphically through maps, it was demonstrated that the set of parameters estimated for each cell were reliable, meaningful, and realistic, and being related to errors lower than 9.1 × 10−9. Therefore, these results can be considered as global solutions of the optimization process. Moreover, based on the lower errors obtained from the optimization process, it was possible to affirm that the one-diode model is suitable to model the I-V curve of perovskite solar cells. Finally, the estimated parameters suggested that the average ideality factor is close to 2 when the fill factor of the I-V curves is higher than 0.5. Lower fill factors corresponded to ideality that was higher than 3, linked to lower efficiencies, and high loses effects reflected on lower shunt resistances. Lower ideality factor of 1.4 corresponds to the best performing solar cells.
Highlights
The electrical performance of solar cells and panels is described by the I-V curve
With the aim of obtaining the five parameters according to the one-diode model for a broad range of performance Perovskite solar cells (PSC), the I-V curves of devices fabricated and characterized in Section 2 were fitted to the circuital model
Showing that the problem of estimate the one-diode model parameters from the I-V curve is very sensitive to small differences in the parameters that are involved, and that different parameter combinations lead to the reduction of the mean square error (MSE) even by solutions lacking physical meaning as negative resistances, being these results local minimal solutions defined by feasible, but not realistic, regions
Summary
The electrical performance of solar cells and panels is described by the I-V curve. This curve presents all the possible operative points, including the Short-Circuit Current (0, Isc ), Open CircuitVoltage (Voc , 0) and the Maximum Power Point (Vmpp , Impp ). The electrical performance of solar cells and panels is described by the I-V curve. This curve presents all the possible operative points, including the Short-Circuit Current (0, Isc ), Open Circuit. Several numerical models have been developed to reproduce this curve at different conditions and illumination levels. Some of them are based on electrical circuits [1,2], partial differential equations or semiconductor equations [3,4], artificial intelligent technics [5,6], curve fitting [7,8], among others. Circuital models based on the Kirchhoff’s current law, such as the one-diode model have been widely used to reproduce the I-V curve of different solar technologies [9,10] under different environmental conditions [11,12]. Up to 34 methods were proposed in literature to extract or estimate the five parameters related to the Energies 2018, 11, 1963; doi:10.3390/en11081963 www.mdpi.com/journal/energies
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
