Shunt Resistance

Significant power losses caused by the presence of a shunt resistance, RSH, are typically due to manufacturing defects, rather than poor solar cell design. Low shunt resistance causes power losses in solar cells by providing an alternate current path for the light-generated current. Such a diversion reduces the amount of current flowing through the solar cell junction and reduces the voltage from the solar cell. The effect of a shunt resistance is particularly severe at low light levels, since there will be less light-generated current. The loss of this current to the shunt therefore has a larger impact. In addition, at lower voltages where the effective resistance of the solar cell is high, the impact of a resistance in parallel is large.

circuit diagram of a solar cell including the shunt resistance

Circuit diagram of a solar cell including the shunt resistance.

The equation for a solar cell in presence of a shunt resistance is:

I= I L I 0 exp[ qV nkT ] V R SH

where: I is the cell output current, IL is the light generated current, V is the voltage across the cell terminals, T is the temperature, q and k are constants, n is the ideality factor, and RSH is the cell shunt resistance.

The effect of a low shunt resistance is shown in the animation below.



The effect of shunt resistance on fill factor in a solar cell. The area of the solar cell is 1 cm2, the cell series resistance is zero, temperature is 300 K, and I0 is 1 x 10-12 A/cm2. Click on the graph for numerical data.

An estimate for the value of the shunt resistance of a solar cell can be determined from the slope of the IV curve near the short-circuit current point.

The impact of the shunt resistance on the fill factor can be calculated in a manner similar to that used to find the impact of series resistance on fill factor. The maximum power may be approximated as the power in the absence of shunt resistance, minus the power lost in the shunt resistance. The equation for the maximum power from a solar cell then becomes;

P MP ' V MP I MP V MP 2 R Sh = V MP I MP ( 1 V MP I MP 1 R SH   )= P MP ( 1 V OC I SC 1 R SH )

$$P_{M P}^{\prime}=P_{M P}\left(1-\frac{R_{C H}}{R_{S}}\right)$$

Defining a normalized shunt resistance as;

$$r_{S H}=\frac{R_{S H}}{R_{C H}}$$

Assuming that the open-circuit voltage and short-circuit current are not affected by the shunt resistance allows the impact of shunt resistance on FF to be determined as;

$$P_{M P}^{\prime}=P_{M P}\left(1-\frac{1}{r_{S H}}\right)$$

$$V_{O C}^{\prime} I_{S C}^{\prime} F F^{\prime}=V_{O C} I_{S C} F F\left(1-\frac{1}{r_{S H}}\right)$$

In the above equation FF, the fill factor which is not affected by shunt resistance is denoted by FF0 and FF' is called FFSH. The equation then becomes;

An empirical equation, which is slightly more accurate for the relationship between FF0 and FFSH is;

which is valid for rsh > 0.4.

The following calculator determines the effect of Rsh on the solar cell fill factor. Typical values for area-normalized shunt resistance are in the MΩcm2 range for laboratory type solar cells, and 1000 Ωcm2 for commercial solar cells.

Shunt Resistance Calculator