# Solar Panels from Used Batteries

Researchers at Massachusetts Institute of Technology (MIT) have demonstrated a procedure to convert used lead acid batteries from automobiles into solar panels. A single battery can be used to produce solar panels for as many as 30 homes. It must be noted that with the advancement in battery technology it is expected that 200 million lead acid batteries would be retired soon from USA alone. This development shows us a way forward to reusing a huge resource of lead that would be otherwise go to dumping sites.

A material that is making this possible is organolead halide perovskite. A layer of perovskite only 1/2 a micrometer thick is enough to produce a solar panel and does not require a very high manufacturing process like for other silicon based solar panels. One might think that this is another experimental material that achieves an efficiency in single digits. But this is hardly the case. In just a few years of research perovskite based solar cells have achieved efficiency of more than 19%. It is expected by the end of 2014 the efficiency would cross the psychological barrier of 20%.

1 Battery Provides Solar Panels for 30 Homes

Perovskite (source: Wikipedia)  is a calcium titanium oxide mineral species composed of calcium titanate, with the chemical formula CaTiO3. The mineral was discovered in the Ural Mountains of Russia by Gustav Rose in 1839 and is named after Russian mineralogist Lev Perovski (1792–1856).

It lends its name to the class of compounds which have the same type of crystal structure as CaTiO3 known as the perovskite structure. The perovskite crystal structure was first described by Victor Goldschmidt in 1926, in his work on tolerance factors. The crystal structure was later published in 1945 from X-ray diffraction data on barium titanate by Helen Dick Megaw.

Efficiency of a solar panel is the ratio of the electrical energy produced to the incident solar radiation e.g. a 20% efficient solar panel of 1 m2 area would produce 200 W when the incident solar radiation reaches a level of 1000 W/m2.

# First Solar Sets New CdTe Solar Cell Efficiency Record

First Solar Inc. an American manufacturer of thin film Photovoltaic (PV) modules announced that it has achieved a record efficiency of 21% for its CdTe Solar Cells. The previous best achieved by the company was 20.4% in Feb of 2014. The record has been accepted by US Department of Energy's National Renewable Energy Laboratory (NREL) and included in "Best Research Cell Efficiency" reference chart. First solar aims to achieve an efficiency of 22% by 2015.

Thin Film Solar Panels

Note: Efficiency of a Solar Cell is the ratio of the Electrical Energy produced to the incident Solar Energy e.g. if the incident Solar Radiation is 1000 W/m2 the Electrical Energy produced by a 21% efficient Solar Panel of 1 m2 area is 210 W (neglecting the various losses that might be encountered).

# 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%.

# Solar Cell Temperature and Efficiency

It is a common misconception that higher the temperature higher is the output of the solar cell. This is not true as the efficiency of a solar cell decreases with increase in temperature and lower efficiency results in lower output power. So in fact a bright sunny day, with sun rays perpendicular to the solar panel and a cool weather is the ideal combination for higher performance of a solar panel.

Let us now look at this in a bit more detail. There are two basic reasons for decrease in efficiency due to increase in temperature.  One is the decrease in the band gap energy (Eg) and the other is the decrease in open circuit voltage (Voc) with increase in temperature. The relationship between band gap energy and and temperature is quite straightforward and is given as.

$E_{g} = E_{g}(0)+\genfrac{}{}{1}{0}{\alpha T^2}{T+\beta}$

One might argue that the decrease in band gap would allow for more carriers to be transferred to the conduction band and yield a higher output power. However this is not true as the output power is the product of current and voltage and a lower voltage would reduce the power. In fact there is an ideal range of band gap which produces the maximum energy. Going too high or too low would not yield the optimum results.

Next we turn out attention to the open circuit voltage Voc. The relationship between temperature and open circuit voltage is not that straightforward. At first it might seem the open circuit voltage increases with increase in temperature as shown in the expression below.

$V_{oc} = \genfrac{}{}{1}{0}{k_{B} T}{e} ln \biggl[1+\genfrac{}{}{1}{0}{J_{L}}{J_{s}}\biggr]$

But in reality this is not the case. Increase in temperature results in increase in intrinsic carrier concentration n which in turn results in higher reverse bias saturation current Js. There is a squared relationship here so increase in intrinsic carrier concentration would cause a very large increase in reverse bias saturation current. And as is evident from the above formula this causes a decrease in open circuit voltage. This is also shown in the figure below.

So to conclude a bright sunny morning in winter might not be the worst time to produce some solar energy (provided you have got your solar panel tilt right 🙂 ).

# 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%.