# Dye Sensitized Solar Cell model in Mathematical Equations

*Dye Sensitized Solar Cel*l much scrutinized because the cost of a cheap fabrikasinya and continuous performance increases (becomes more efficient). Research conducted by the inventor of the DSSC i.e. Prof. Michael Gratzel DSSC efficiency States that can reach 15% (Tetsuo, 2013). Comparison of commercial solar cells (silicon-based solar cells) that are sold, marketed, DSSC efficiency has exceeded 15% commercial solar cell that is only 10%. In addition, dye DSSC is also capable of absorbing light of fluorescent bulbs, the weather was overcast, and the environment with a low light intensity, and can be printed in a flexible medium such as a plastic and can be transparent. Due to the large number of DSSC excellence, then this article will be elaborated concerning the mathematical modeling of DSSC.

The making of mathematical model of DSSC is very important for the operation of looking for optimization. This can be done by showing a series of equivalent DSSC where parameters calculated based on measurement data (based on experiments) test current and voltage. Differences in modeling are usually located on a number of diode (one diode, diode, two or more), the resistance series and Parallels are limited or unlimited, idealitas diode, which is worth 1, 2 or more. This model is different from each other in terms of his mathematical resolution procedure and the number of parameters required is involved in the calculation of voltage and current. Here is the mathematical modeling of the DSSC is usually used,

1. Models with 1 diode

A series of equivalent standard to model solar cells or DSSC is a model series with 1 diode (m. Belarbi, 2014), which consists of 1 diode, constant source for photo-generated current (Io), series_{ }resistance (Rs) an_{d} a parallel resistance (R_{sh}). Here is a picture of ekuivalenya with its mathematical equations

The current that is produced by the cells of the above mathematical equation satisfies the following:

Description:

I → Flow to look for its value as a result of modeling, so that its value is positive then don't forget multiplied by the – (minus[Ampere]).

V → Voltage of DSSC whose value of 0 V-Voc (_{op}en circuit Volts or volts when there are no barriers[Voltage].

I_{L} → value is equal to the Isc, is obtained from the measurement of the arusnya when there are no barrier[Ampere]s.

I_{O} → saturated Current of th[Ampere]e diode, calculated when the value of I in the equation above is worth 0, and V on the Voc-value equation, so Io can be calculated with the equation to be compiled:

R_{S} → Resistance series, usually assumed to be very small so it is ignored[Ohm].

_{Rs}h → Shunt Resistance (or parallel), usually assumed to be so great that ignored[Ohm].

q → Electron Charge = 1 Coulomb^{ 60}2.10, -19.

k → Boltzman Constant = 1.38. 10^{-23} J/K

A → Factor idealitas diode, value 1 when the electron transport process is diffusion, whereas the value 2 while the process is recombination on the depletion)

T → effective Temperature 300 K[Kelvin].

2. Models with two diodes

Models with two diodes are used in case of minority carriers recombination, both on the surface and volume of the material. Equivalent diagram for the model 2 diodes is shown by the following image:

Equivalent circuit of dye sensitized solar cells

Due to the normally used was model 1, we discussed more diodes in the mathematical modeling of DSSC with 1 diode.

With the increasing value of the voltage, the current begins to decrease exponentially to zero value where at the time of the current value of 0 then a large voltage is the voltage open circuit (_{Vo}c). On the range of values of voltage and current, there is a maximum point that generates maximum power, which was called by the I_{MPP} (the current maximum power point) and_{ the} VMPP (maximum power point Voltage). The valu_{e of} the IM_{PP VMPP} and that is what is used to calculate the efficiency of the DSSC.

The result of the application of mathematical modeling is as follows.

It can be seen from the two graphs above that the results of the modeling of yield curves are ideal, such as using solar simulator.

##### Source:

- Tetsuo Nozawa. 2013. http://techon.nikkeibp.co.jp/english/NEWS_EN/20130716/292380/. Nikkei Electronics. Accessed at 11.57 BST 4/18/2015.
- M. Belarbi, et al. 2013. Study of the Equivalent Circuit of A Dye Sensitized Solar Cells. Advanced Energy: An International Journal (AEIJ), vol. 1, no. 2, April 2014.

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