Impact of Both Series and Shunt Resistance

In the presence of both series and shunt resistances, the IV curve of the solar cell is given by;

$I=I_L-I_0\exp \left[{\displaystyle \frac{q(V+I{R}_S)}{nkT}}\right]-{\displaystyle \frac{V+I{R}_S}{R_{SH}}}$

and the circuit diagram of the solar cell is given as;

Parasitic series and shunt resistances in a solar cell circuit.

To combine the effect of both series and shunt resistances, the expression for FF_sh, derived above, can be used, with FF₀ replaced by FF_s ^[Green1992]. The overall equation then becomes;

$F{F}_{SH}=F{F}_S(1-{\displaystyle \frac{V_{OC}+0.7}{V_{OC}}}{\displaystyle \frac{F{F}_S}{r_{SH}}})$

where FF_s is given by;

$F{F}_S=F{F}_0(1-1.1r_S)+{\displaystyle \frac{r_S^2}{5.4}}$

and by combining the above equations, the net equation for FF becomes;

$FF=F{F}_0\{(1-1.1r_S)+{\displaystyle \frac{r_S^2}{5.4}}\}\{1-{\displaystyle \frac{V_{OC}+0.7}{V_{OC}}}{\displaystyle \frac{F{F}_0}{r_{SH}}}[(1-1.1r_S)+{\displaystyle \frac{r_S^2}{5.4}}]\}$

X

015

X

1001e6

The following calculator determines the effect of R_s and R_sh on the cell fill factor using the same variable definitions as above.

Effect of Both Resistances Calculator

Input Parameters

V_OC (V) I_SC (A) n = T (K) FF₀ =
R_S (Ohms) R_SH = Ohms

Results

R_CH (Ohms) v_oc = r_s (Ohms) r_sh (Ohms) Approximate fill factor taking into account R_s and R_sh
FF_approx = A more accurate estimation of FF
valid for r_s < 0.4 and v_oc > 10
FF_s = Estimation of FF from R_shuntvalid for r_sh > 0.4
FF_sh = More accurate estimation of FF taking into account R_s & R_sh
FF =

 

References

1. M. Green, “Solar Cells - Operating Principles, Technology and System Application,” University of NSW, 1992.