Photovoltaics: The Role of the Sun Part 2

Let's continue our discussion of solar radiation. The spectral power emission, or spectral radiance, is defined as the radiated power per unit wavelength. 

A body with a temperature above absolute zero, which is zero degrees Kelvin, emits  electromagnetic radiation. The spectral radiance of such a body is described by Planck’s law. Planck’s law assumes that the body is a blackbody. A blackbody  absorbs all the radiation that is incident on it. A perfect blackbody does not exist in nature,  but planets and stars are close enough for Plank’s law to give a very good approximation of  the spectral radiance.

The spectral radiance of a blackbody is a function of only its temperature T. It is remarkable to see that Planck’s law contains three fundamental constants, Planck’s constant, Boltzmann’s constant and the speed of light in vacuo, which are among the most important constants in physics.

Imagine the spectral radiance of three different black bodies as a function of their wavelength. The bodies have a temperature of 6000, 5000 and 4000 Kelvin, respectively. We can see that the total emitted power increases strongly with increasing temperature. Furthermore, the peak of the highest power density shifts towards to lower wavelength region with increasing temperature.

The surface of the sun has a temperature of roughly 6000 Kelvin, so the spectral radiance of our sun follows the yellow line. To calculate the irradiance a blackbody with the size and position of the sun would have on earth, we have to multiply the spectral radiance with the solid angle of the sun as seen from earth. This is described by the appropriate equation, where ‘i’ is the irradiance and omega-sun is the solid sun angle.

The solid sun angle is described by the following equation, where R-sun is the radius of the sun, R-earth is the radius of the earth and ‘AU’ is roughly the distance from earth to the sun, known as an astronomical unit. The solid sun angle is therefore equal to about 68.5 microsteradian. The spectral irradiance of the sun on earth, as described by Planck’s law. Imagine dashed lines that indicate the boundaries of the ultraviolet, visible and infrared part of the spectrum. If we now introduce the empirical data of the spectral solar irradiance, we can see that Planck’s law gives a very good approximation. Only in the visible part of the spectrum is the irradiance underestimated. The red curve shows the spectral irradiance outside of earth’s atmosphere.

This spectrum is known as the AM-0 spectrum. If we look at the spectral irradiance on the surface of the earth, we can see that the irradiance is significantly lower. Such spectrum is known as the AM 1.5 spectrum. It includes absorption of light by particles in earth’s atmosphere. Let’s look at this absorption in some more detail. 

 
A large fraction of the visible and ultraviolet light is absorbed, while in the infrared part of the spectrum the absorption is more concentrated. These absorption bands are caused by specific molecules in earth’s atmosphere. Most bands are caused due to the light absorption by water molecules. But absorption is also caused by carbon dioxide, oxygen and ozone. The absorption in the atmosphere causes the total irradiance to decrease from 1361 watts per square meter in the AM-0 spectrum, to approximately 1000 watts per square meter in the AM 1.5 spectrum. The latter is known as 1 sun illumination. As we have just discussed, solar radiation passing through earth’s atmosphere is attenuated.

The most important parameter that determines the solar irradiance, under clear sky conditions, is the distance that the sunlight has to travel through the atmosphere. This distance is shortest when the sun is at the zenith, so directly overhead. The ratio of an actual path length of the sunlight to this minimal distance is known as the optical air mass. Imagine a figure that shows the sun at its zenith position. As it illuminates earth, light travels through the four main layers of earth’s atmosphere. Excluding the exosphere, these layers are the troposphere, stratosphere, mesosphere and thermosphere.

With the sun at its zenith position the optical air mass is unity, and the spectrum is called AM-1. In space, no atmosphere is traversed, so the spectrum is known as AM-0. When the sun is at an angle theta with the zenith, the air mass is given by one over cosine theta. When the sun is, for example, at an angle of 60 degrees with the zenith, we receive an AM-2 spectrum. The AM-1.5 spectrum we showed earlier is obtained for an angle of 48.2 degrees. How much power is actually incident on a specific surface various with the time of day, with the seasons and the position on earth?

Imagine a figure that shows the average global horizontal irradiance, which is the power incident on a
horizontal surface averaged over the entire year, in kilowatt-hour per square meter per day. While on average, a solar panel in northern Europe may only receive 3 kilowatt-hours per square meter per day, around the equator this number can go up to 6 or 7.

A more convenient way to express the irradiance per day are the daily equivalent sun hours, or ESH. An equivalent sun hours is defined as the number of hours of 1 sun illumination per day. Since 1 sun illumination is equal to 1 kilowatt per square meter, 1 daily equivalent sun hour is equal to 1 kilowatt-hour per square meter per day.

If we look for instance at this map of the Netherlands, which shows the yearly sum of irradiation for panels with an optimal tilt angle. Judging from the colour-distribution we can assume an average yearly irradiation of about 1250 in kilowatt-hour per square meter per year. Dividing this amount by the number of days in a year, we find that the Netherlands receive on average about 3.4 kilowatt-hours per square meter per day for optimal tilted panels, which means that it’s about equivalent to 3.4 sun hours.

In order to compare the performance of different types of solar cells, in different locations, the cell temperature and irradiance have to be controlled. To that end the standard test conditions are defined. These conditions are characterized by a total irradiance of 1000 watts per square meter, the AM-1.5 spectrum, and a cell temperature of 25 degrees Celsius. To measure a solar cell under a controlled AM-1.5 spectrum, solar simulators are used. A solar simulator uses a special lamp, or set of lamps, to
mimic the AM-1.5 spectrum as closely as possible.

Remember the spectral irradiance received from such as solar simulator. The blue area depicts the emitted irradiance, while the red area depicts the part of the spectrum used by an amorphous silicon solar cell. If we overlay the AM-1.5 spectrum in this spectral range, we find that the solar simulator provides a very good approximation of the AM1.5 spectrum in the range used by the solar cell.

In summary, we described how sunlight can be described as a flow of photons, or as a wave. We saw how wavelength and frequency are important properties that define different ranges in the spectrum of electromagnetic radiation. We discussed Planck’s law for blackbody radiation and compared it to the spectral radiance outside the atmosphere and on the surface of the earth. We discussed the concept of air mass and finally, we defined the standard test conditions and solar simulators.

In the next post we will discuss the photovoltaic effect.