# Integrating the Solar Spectrum

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1 Integrating the Solar Spectrum PHYS 4400, Principles and Varieties of Solar Energy Instructor: Randy J. Ellingson The University of Toledo January 24, 203

2 Pop Quiz Note: quiz does not count toward grade Write down the approximate wavelengths associated with these colors:. Green 2. Blue-green 3. Yellow 4. Red 5. Orange 6. Deep blue 7. Ultraviolet 8. Near-infrared 9. Infrared

3 Focusing sunlight maximum concentration (from Section 2. of text) 2 2 = ~0.534 Maximum concentration of sunlight at earth is approximated by C max = n 2 sin -2 ( ) C max 46,000 How do we calculate this?

4 Air Mass examples (Toledo, Ohio) Today (January 24): From sunposition.info, at pm today, the sun will be at a zenith angle of s = 29 above the horizon. AM cos AM s csc sin s s Therefore, AM = 2.06 (at pm, assuming it s sunny/clear). How about June 2, at noon? In that case, s = 63, so that AM =.2. What about the intensity of the sunlight expected? AM I.xI x0.7 where I 0 = 366 W/m 2 ;,022 W/m 2 on June en.wikipedia.org/wiki/air_mass_(solar_energy)

5 Air Mass (continued) AM cos AM when = 90 AM cos In-class exercises: Calculate the intensity of sunlight in Toledo for January 24 at :00 pm using AM = Calculate I again using the AM as calculated by the equation accounting for Earth s curvature.

6 AM0: the spectrum above Earth s atmosphere The AM0 spectrum applies to satellites and high-flying aircraft, which access the spectrum prior to any influence from Earth s atmosphere. Integrated spectral irradiance = 366 W/m 2.

7 Spectral Irradiance (W m -2 nm - ) AM.5G: reference spectrum including direct and diffuse sunlight AM.5: From the equation provided for Air Mass, one calculates that cos = 0.667, so that = This represents the zenith angle, that it, the angle relative to the direction normal to Earth s surface. From the standard: The receiving surface is defined in the standards as an inclined plane at 37 tilt toward the equator, facing the sun (i.e., the surface normal points to the sun, at an elevation of 4.8 above the horizon). Note that 4.8 is the complement of Toledo latitude: N Integrating the energy within AM.5G yields 000 W m ASTM G73 (AM.5G) Standard spectrum Wavelength (nm)

8 Standard Solar Reference Spectra Where do these spectra come from (where can we get them)? Start here: The spectra most often referenced are the AM.5G (technically referred to as the ASTM G-73) and the AM0 (technically known as the ASTM E-490).

9 Spectral Irradiance (W m -2 nm - ) What s in a square meter area of sunlight? Assuming that the receiving area is normal to the incoming sunlight: Power, which when integrated with respect to time sums up to Energy. For example,,366 W/m 2 of sunlight, integrated for hour, gives (366 W/m 2 )*( hr)*(3600 s/hr)*( J/s per W) = 4.92 x 0 6 J/m 2. Photons. A very large number of photons per second (as we will find). As a look ahead, each photon with energy above a semiconductor s bandgap can be absorbed, boosting an electron from the valence band to the conduction band and contributing an electron to the photocurrent of the PV cell ASTM G73 (AM.5G) Standard spectrum Wavelength (nm)

10 In-class exercises: integration of the solar spectra How can we add up the power contained within the AM0 and AM.5G spectra? Answer: add up the values for the spectral irradiance but we must do so carefully. If we have values for the Spectral Irradiance with each data point corresponding to a nm spectral width (e.g., from 500 nm to 50 nm), the problem is simpler. However, upon examining the data contained in either of these spectra: we find that the wavelength values start at 0.5 nm spacing, then move the nm spacing, and ultimately go to 5 nm or larger spacing between points. To properly integrate the spectrum, we can either break up the data into regions depending on the wavelength increment between data points, or we can interpolate the data to fix it so that it is spaced by nm for all wavelength regions. Let s interpolate, after which we can simply add up the values, effectively multiplying each value by the nm of spectral bandwidth to which it applies The interpolated data for AM0 and AM.5G is provided on the course web site

11 Spectral Irradiance (W m -2 nm - ) In-class exercise: integration of the AM.5G solar spectrum How much power per unit area is contained within the AM.5 spectrum? This is much more easily answered using the interpolated spectra summing from 400 nm to 700 nm yields W m -2. What fraction of the total power of the AM.5G spectrum falls within the visible range ( nm)? Summing the AM.5G over the full range from 280 to 4000 nm gives W m -2, so the fraction of power contained in the visible = 43. %..6.4 AM.5G Standard Solar Spectrum Green region shows visible range, nm Wavelength (nm)

12 Spectral Irradiance (photons s - m -2 nm - ) In-class exercises: integration of the solar spectra Conversion of spectral irradiance from (W m -2 nm - ) to (photons s - m -2 nm - ) is required to calculate photon flux within solar spectra. Accomplished by dividing the (W m -2 nm - ) values by the photon energy, to convert W to photons/second How many photons per second per unit area are incident within the visible portion of the AM.5G spectrum? For 400 nm to 700 nm range, we calculated.9 x 0 2 photons s - m -2. What fraction of the total AM.5G photons (from 280 to 4000 nm) lie in this visible range? We calculate a total irradiance of 4.30 x 0 2 photons s - m -2, so the fraction in the visible is.9/4.30 = 27.7 %. 5x Wavelength (nm)

13 Spectral Irradiance (photons s - m -2 nm - ) Comparing shape of spectra, W vs. photons/s 5x Spectral Irradiance (photons s - m -2 nm - ) Spectral Irradiance (W m -2 nm - ) Spectral Irradiance (W m -2 nm - ) Wavelength (nm) What s going on here?

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