# Solar Irradiance as a Function of Wavelength

Solar Irradiance $I(\lambda)$ refers to Solar Energy falling on to the Earth on a unit area. Since this Solar Energy is limited to certain wavelengths (or frequencies) therefore it is usually given as a function of wavelength and the has the units of Watts/m2/wavelength. This is shown in the figure below for a unit area perpendicular to the solar rays and lying outside the Earth's atmosphere. This is referred to as AM0 since there is zero atmosphere, as opposed to AM1.5 which is on the Earth's surface.

So roughly speaking we can say that most of the Solar Energy lies between the 0 to 4 micrometer (NREL gives the AM0 spectrum from 280 to 4000 nanometer). A device that can capture all of this energy would be very useful and this is the aim of all modern Solar Cell manufacturers. The total Solar Power available on a surface of unit area can be easily calculated by integrating the above given Solar Irradiance curve from 0 to infinity and this gives us a magic number of 1367W/m2 (the value of the dotted curve at 4000 nanometer).

But all of this power does not reach the Earth's surface. Some of it is absorbed on the way. The total Solar Power available on the Earth's surface is equal to 1000W/m2 i.e. a reduction of 27% from that outside the Earth's atmosphere. The magic number of 1367W/m2 might be important for satellites using Solar Panels for their energy requirements and orbiting the Earth outside its atmosphere.

The Solar Spectra can also be calculated by using the theory of Black Body Radiation. According to this the Solar Spectra can be well estimated by a Black Body radiating at a temperature of 5960K (blue curve).

Note:

1. The Irradiance of 1000W/m2 is under ideal conditions (bright sunny day, at zero altitude and solar rays perpendicular to the capturing surface) but even this is not available to a Solar Home since the Solar Panels only have 15%-20% efficiency. So a 1m2 Solar Panel might only give you 150W-200W under ideal conditions. But do not get depressed yet as new research findings promise Solar Cells with efficiencies as high as 45%.

# Primary and Secondary Batteries

A battery is a device that is used to store electrical energy in a solar system. The energy stored in a battery also called the charge capacity is given in Ampere Hours (AH). A 10AH battery can give 1A for 10hours or 2A for 5hours or any other combination. The voltage of the battery together with its charge capacity defines the energy stored in Watt Hours (WH) e.g. a 10AH battery operating at 12V can store 120WH of electrical energy. The energy storage capacity of a battery depends upon the type and weight of the material used. An important metric in this regard is the energy storage capacity per kilogram of material (WH/kg).

Batteries are composed of two terminals called anode (negative) and cathode (positive) and an electrolyte. Based upon the materials used in construction of batteries they can be classified into primary or secondary.

## Primary Cells or Batteries

• Not rechargeable
• Electrolyte is contained by absorbent (dry cell)
• Convenient, inexpensive, lightweight
• Used for portable electronics and electric devices, lighting, etc
• Good shelf life
• High energy density
• No or low maintenance
• Usually small scale power

## Secondary Cells or Batteries

• Rechargeable
• Used for energy storage applications (e.g. solar backup, automotive)
• Used as rechargeable primary battery (electronics, electrical car)
• High power density
• High discharge rate
• Usually lower energy density
• Poorer charge retention

# 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 🙂 ).