**Effects of Shunt Resistance**

Substantial losses of power caused by the existence of R_{SH }-which is the shunt resistance- are usually resulting from **manufacturing defects**, more than bad solar cell design. Low R_{SH} results in solar cells power losses by making an alternate current path for the light generated current. This kind of diversion causes a reduction in the amount of current that flows through the solar cell junction and reduction in the voltage from the solar cell. R_{SH} effect is especially severe at levels of **low light**, as there would be less light generated current.

The losses in this current to the R_{SH} as a result, has a bigger impact. Also, at lower voltages when the effective resistance of a solar cell is **high**, the effect of a parallel resistance is **high**.

The equation for the solar cell in existence of shunt resistance is defined below:

**I=I _{L}−I_{0}exp[qV / nkT] – V / R_{SH}**

where:

**I: the cell output current**

** I _{L:} the light generated current**

** V: voltage across the cell terminals**

**T: temperature**

**q & k: constants**

**n: ideality factor**

**R**_{SH}: shunt resistance of the solar cell.

_{SH}: shunt resistance of the solar cell.

An estimation for the value of the shunt resistance of a solar cell can be derived from the slope of the **IV curve** near the point of short circuit current.

**Formulas for Shunt Resistance and FF**

The effect of the R_{SH} on the fill factor can be calculated in a similar way to the method used in finding the effect of series resistance on the fill factor. The maximum power can be approximated as power in the R_{SH} absence, minus the power which is lost in the shunt resistance. The equation for the maximum power from a solar cell then can be defined as the following:

**P’ _{MP }≈ V_{MP}I_{MP }– V^{2}_{MP}/R_{SH}= V_{MP}I_{MP }( 1 – ( V_{MP} / I_{MP}) *1/R_{SH}) = P_{MP} (1 –( V_{OC} / I_{SC}) * 1 /R_{SH} )**

**P’ _{MP = }P_{MP} ( 1 – R_{CH }/ R_{S})**

While a normalized series resistance is defined as:

**r _{SH} = R_{SH} / R_{ch}**

Using the assumption that open circuit voltage and short circuit current are both unaffected by shunt resistance, allows the shunt resistance impact on FF to be defined:

**P’ _{MP} = P_{MP} ( 1 – 1 / r_{SH })**

**V’ _{OC}I’_{SC}FF’= V_{OC}I_{SC}FF(1– 1 / r_{SH})**

**FF’=FF (1– 1 / r _{SH})**

In the equation above the FF that is unaffected by shunt resistance is named **FF _{0} **and

**FF’**is denoted by

**FF**. The equation then is:

_{SH}**FFs _{H}=FF_{0} (1– 1 / r_{SH })**

A slightly more accurate empirical equation, for the relating both FF_{0} and FF_{SH} is then:

**FF _{SH}=FF_{0} (1– (V_{OC} + 0.7)/ V_{OC }* (FF_{0} / r_{SH} )**

This is valid for r_{SH} greater than 0.4

Normal values for the area normalized shunt resistance are in the range of **MΩcm ^{2} **for the type of laboratory solar cells, and for commercial solar cells

**1000 Ωcm**

^{2}.

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