Characteristic Resistance

The characteristic resistance of a solar cell is the cell's output resistance at its maximum power point. If the resistance of the load is equal to the characteristic resistance of the solar cell, then the maximum power is transferred to the load, and the solar cell operates at its maximum power point. It is a useful parameter in solar cell analysis, particularly when examining the impact of parasitic loss mechanisms. The characteristic resistance is shown in the figure below.

The characteristic resistance of a solar cell is the inverse of the slope of the line, shown in the figure above as V_MP divided by I_MP ^[Green1982]. For most cells, R_CH can be approximated by V_OC divided by I_SC:

$R_{C H} = \frac{V_{M P}}{I_{M P}} \approx \frac{V_{O C}}{I_{S C}}$

R_CH is in Ω (ohms) when using I_MP or I_SC as is typical in a module or full cell area. When using the current density (J_MP or J_SC) then the units of R_CH are Ωcm² (ohm cm²)

The characteristic resistance is useful because it puts series and shunt resistance in context. For example, commercial silicon solar cells are very high current and low voltage devices. A 156 mm (6 inch) square solar cell has a current of 9 or 10 amps and a maximum power point voltage of 0.6 volts giving a characteristic resistance, R_CH, of 0.067 Ω. A 72 cell module from the same cells has R_CH = 4 to 5 ohm. A lead resistance of 30 milliohms has a negligible effect on a full module but has a catastrophic effect on a single cell coupon.

Series Resistance and Power Loss

As long as the power loss is reasonable (< 20%), the characteristic resistance also allows for a conversion between the fractional power loss and series resistance in Ω or Ω cm².

$R_{s e r i e s} = f \times R_{C H}$

$f = \frac{R_{s e r i e s}}{R_{C H}}$

Where f is the fraction power loss from 0 to 1. R_series is in the same units as R_CH, either or Ω or Ω cm².

E.g. a typical solar cell has R_series = 1 Ω cm², V_MP = 0.650 V and J_MP = 36 A/cm². The resulting RCH = 18 Ω cm² and the fractional power loss is 1/18 = 5.5%.

Shunt Resistance and Power Loss

Similarly, the shunt resistance is related to the power loss by:

$R_{s h u n t} = f \times R_{C H}$

$f = \frac{R_{C H}}{R_{s h u n t}}$

Where f is the fraction power loss from 0 to 1. R_shunt is in the same units as R_CH, either or Ω or Ω cm².

E.g. a typical solar cell has R_shunt = 10000 Ω cm², V_MP = 0.650 V and J_MP = 36 mA/cm². The resulting RCH = 18 Ω cm² and the fractional power loss is 18/10000 = 0.18%.

References

M. Green, “Accuracy of Analytical Expressions for Solar Cell Fill Factors,” Solar Cells, vol. 7, pp. 337-340, 1982.