Shunt Resistance

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−I₀exp[qV / nkT] – V / R_SHwhere:I: the cell output current I_L: the light generated current V: voltage across the cell terminalsT: temperatureq & k: constantsn: ideality factor

R_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_MPI_MP – V²_MP/R_SH= V_MPI_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_chUsing 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’_OCI’_SCFF’= V_OCI_SCFF(1– 1 / r_SH)FF’=FF (1– 1 / r_SH)In the equation above the FF that is unaffected by shunt resistance is named FF₀ and FF' is denoted by FF_SH. The equation then is:FFs_H=FF₀ (1– 1 / r_SH )A slightly more accurate empirical equation, for the relating both FF₀ and FF_SH is then:FF_SH=FF₀ (1– (V_OC + 0.7)/ V_OC * (FF₀ / r_SH )This is valid for r_SH  greater than 0.4Normal 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.