# Do Numbers Make Sense

Press Release

"The Fraunhofer Institute for Solar Energy Systems ISE, Soitec, CEA-Leti and the Helmholtz Center Berlin have jointly announced that they have achieved a new world record for the conversion of sunlight into electricity using a new solar cell structure with four solar subcells. Surpassing competition after only over three years of research, and entering the roadmap at world class level, a new record efficiency of 44.7% was measured at a concentration of 297 suns. This indicates that 44.7% of the solar spectrum's energy, from ultraviolet through to the infrared, is converted into electrical energy. This is a major step towards reducing further the costs of solar electricity and continues to pave the way to the 50% efficiency roadmap".

"These solar cells are used in concentrator photovoltaics (CPV), a technology which achieves more than twice the efficiency of conventional PV power plants in sun-rich locations. The terrestrial use of so-called III-V multi-junction solar cells, which originally came from space technology, has prevailed to realize highest efficiencies for the conversion of sunlight to electricity. In this multi-junction solar cell, several cells made out of different III-V semiconductor materials are stacked on top of each other. The single subcells absorb different wavelength ranges of the solar spectrum".

## A Closer Look at the Numebrs

Let us now try to validate the numbers given above.

Power is the product of voltage and current.

Pideal=Voc Isc=(4.165)(0.1921)=0.8001Watts

Pmax=Pideal*FF=(0.8001)(0.8650)=0.6921Watts

This is the power produced by 5.20mm2 of solar cell.

1mm2 of solar cell would produce 0.1331Watts.

1m2 of solar cell would produce 133.1kW of solar energy.

This is the power generated due to 297.3 suns.

A single sun would produce 133.1kW/297.3=447.67Watts of power.

This gives us an efficiency of 447.67/1000=0.4477=44.77%.

# 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%.