# Fill Factor and Efficiency

The Efficiency of a solar cell is an important metric that determines how much of the incident solar energy is converted to useful electrical energy e.g. a 1m2 solar panel with 15% Efficiency would convert a radiant energy of 1000W/m2 into 150W of useful electrical energy.

The Efficiency of a solar cell is sometimes defined in terms of the Fill Factor (FF) which is defined as.

$FF = \genfrac{}{}{1}{0}{J_{max} V_{max}}{J_{sc} V_{oc}}$

Simply put its the ratio of area defined by (Vmax, Imax) to the area defined by (Voc, Isc) on the IV curve. And the Efficiency in terms of the Fill Factor is defined as.

$\eta = \genfrac{}{}{1}{0}{J_{sc} V_{oc} FF}{P_{s}}$

The expression for Efficiency can be simplified by substituting FF in the above equation.

$\eta = \genfrac{}{}{1}{0}{J_{sc} V_{oc}}{P_{s}} \genfrac{}{}{1}{0}{J_{max} V_{max}}{J_{sc} V_{oc}}$

or

$\eta = \genfrac{}{}{1}{0}{J_{max} V_{max}}{P_{s}}$

Let us now look at some practical values for Efficiency and Fill Factor.

$\eta = \genfrac{}{}{1}{0}{J_{sc} V_{oc} FF}{P_{s}}$

$\eta = \genfrac{}{}{1}{0}{(400) (0.70) (0.84)} {1000}$

$\eta = 0.2352$

This is the Efficiency ignoring certain practical issues of solar cells. Thus the typical Efficiency of mono-crystalline solar cells would be somewhat lower (15%-20%).

Note:
1. Vmax, Imax is the Voltage and Current respectively at the Maximum Power Point on the IV curve. Remember that Power is just the product of Voltage and Current.

2. From basic circuit theory, the power delivered from or to a device is optimized where the derivative (graphically, the slope) dI/dV of the I-V curve is equal and opposite the I/V ratio (where dP/dV=0). This is known as the Maximum Power Point (MPP) and corresponds to the "knee" of the curve.

3. A solar charge controller is used to charge the batteries from the solar panel operating at its Maximum Power Point.

4. The more rapid the drop in Current as the Voltage approaches the Open Circuit Voltage the closer will be the Fill Factor to the ideal value of 100%.