Open Circuit Voltage Of Solar Cell Formula + Solved Example

Open circuit voltage (VOC) is the most widely used voltage for solar cells. It specifies the maximum solar cell output voltage in an open circuit; that means that there is no current (0 amps). We can calculate this voltage by using the open circuit voltage formula for solar cells.

We are going to look at this equation. To illustrate how to use the equation, we are going to solve 1 example and calculate the solar cell open circuit voltage for a 5 amps IL cell.

equation for open circuit voltage for a solar panel
Solar panel open circuit voltage is basically a summary of all PV cells Voc voltage (since this they are wired in series).

Let’s start with the formula:

Open Circuit Voltage Formula For Solar Cells

This equation is derived by setting the current in the solar cell efficiency equation to zero (and doing some additional complex derivation). Here is the resulting formula:

VOC = (n × k × T × ln (IL/I0 + 1)) / q

As we can see from this equation, the open circuit voltage of a solar PV cell depends on:

  • n or intrinsic carrier concentration (also known as ideality factor, ranging from 0 to 1). The higher the intrinsic carrier concentration (you can read more about it here), the higher the open circuit voltage.
  • k × T / q is the terminal voltage at a specified temperature (at 300K, that’s 0.02586 volts). k here represents Boltmann’s constant, and q is the basic electric charge (1.602 × 10-19 Coulomb).
  • IL is the Light generated current.
  • I0 is the Dark saturation current.

Let’s solve an example to illustrate how the open circuit voltage works for solar cells.

Let’s say that we have a solar cell with 1 ideality factor. The measured light generated current (IL) is 3 amps, and the dark saturation current (I0) is 5 × 10-9. We want to calculate the open circuit voltage at 77°F (that’s 298.15K). We put all of this into the equation, along with the constants, like this:

VOC = (1 × 1.38 × 10-23 J/K × 298.15K × ln (5 Amps / 5×10-9 Amps + 1)) / 1.602 × 10-19 = 0.532 V

As we can see, this solar cell has an open circuit voltage of 0.532 volts.

Obviously, this equation is quite complex, and getting the correct input is even harder. However, if you can get all the inputs, you can calculate the open circuit voltage for any solar cell.

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