Effects of Shunt Resistance
Substantial losses of power caused by the existence of RSH -which is the shunt resistance- are usually resulting from manufacturing defects, more than bad solar cell design. Low RSH 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. RSH effect is especially severe at levels of low light, as there would be less light generated current.
The losses in this current to the RSH 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=IL−I0exp[qV / nkT] – V / RSH
I: the cell output current
IL: the light generated current
V: voltage across the cell terminals
q & k: constants
n: ideality factor
RSH: shunt resistance of the solar cell.
Formulas for Shunt Resistance and FF
The effect of the RSH 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 RSH 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 ≈ VMPIMP – V2MP/RSH= VMPIMP ( 1 – ( VMP / IMP) *1/RSH) = PMP (1 –( VOC / ISC) * 1 /RSH )
P’MP = PMP ( 1 – RCH / RS)
While a normalized series resistance is defined as:
rSH = RSH / Rch
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 = PMP ( 1 – 1 / rSH )
V’OCI’SCFF’= VOCISCFF(1– 1 / rSH)
FF’=FF (1– 1 / rSH)
In the equation above the FF that is unaffected by shunt resistance is named FF0 and FF’ is denoted by FFSH. The equation then is:
FFsH=FF0 (1– 1 / rSH )
A slightly more accurate empirical equation, for the relating both FF0 and FFSH is then:
FFSH=FF0 (1– (VOC + 0.7)/ VOC * (FF0 / rSH )
This is valid for rSH greater than 0.4
Normal values for the area normalized shunt resistance are in the range of MΩcm2 for the type of laboratory solar cells, and for commercial solar cells 1000 Ωcm2.