1. Chemical, Biological and Environmental Engineering Introduction to Solar Power

2. Advanced Materials and Sustainable Energy Lab CBEE The Solar Resource Before we can talk about solar power, we need to talk about the sun How much sunlight is available? –Relates to what is the resource at a site? Where the sun is at any time? –Relates to chosing effective locations and panel tilts of solar panels

3. Advanced Materials and Sustainable Energy Lab CBEE The Sun and Blackbody Radiation The sun –1.4 million km in diameter –3.8 x 10 20 MW of radiated electromagnetic energy Blackbodies –Both a perfect emitter and a perfect absorber –Perfect emitter – radiates more energy per unit of surface area than a real object of the same temperature –Perfect absorber – absorbs all radiation, none is reflected (Clearly, no such thing exists but is a good approximation)

4. Advanced Materials and Sustainable Energy Lab CBEE Plank’s Law Plank’s law – energy at a given wavelength emitted by a blackbody depends on temperature λ = wavelength (μm) E λ = emissive power per unit area of blackbody (W/m 2 - μm ) T = absolute temperature (K)

5. Advanced Materials and Sustainable Energy Lab CBEE Electromagnetic Spectrum Source: en.wikipedia.org/wiki/Electromagnetic_radiation Visible light has a wavelength of between 0.4 and 0.7 μm, ultraviolet values immediately shorter, infrared longer

6. Advanced Materials and Sustainable Energy Lab CBEE Stefan-Boltzmann Law Total radiant power emitted is given by the Stefan–Boltzman law of radiation E = total blackbody emission rate (W) σ = Stefan-Boltzmann constant = 5.67x10 -8 W/m 2 -K 4 T = absolute temperature (K) A = surface area of blackbody (m 2 )

7. Advanced Materials and Sustainable Energy Lab CBEE Wien’s Displacement Rule The wavelength at which the emissive power per unit area reaches its maximum point T = absolute temperature (K) λ max = wavelength for maximal emissive power (μm) For the sun, T = 5800 K; λ max =0.5 μm For earth (as a blackbody), T = 288 K; λ max = 10.1 μm

8. Advanced Materials and Sustainable Energy Lab CBEE 288 K Blackbody Spectrum The earth as a blackbody Area under curve is the total radiant power emitted

9. Advanced Materials and Sustainable Energy Lab CBEE Extraterrestrial Solar Spectrum Integrate over all wavelengths to get solar constant SC = 1.377 kW/m 2

10. Advanced Materials and Sustainable Energy Lab CBEE Air Mass Ratio h 1 = path length through atmosphere with sun directly overhead h 2 = path length through atmosphere to spot on surface β = altitude angle of the sun As sunlight passes through the atmosphere, less energy arrives at the earth’s surface

11. Advanced Materials and Sustainable Energy Lab CBEE Air Mass Ratio “AM1” (Air mass ratio of 1) means sun is directly overhead AM0 means no atmosphere AM1.5 is assumed average at the earth’s surface

12. Advanced Materials and Sustainable Energy Lab CBEE Solar Spectrum on Surface As sun appears lower in sky air mass (m in figure) increases. Notice large loss towards blue end for higher m (which is why sun appears reddish at sunrise and sunset)

13. Advanced Materials and Sustainable Energy Lab CBEE The Earth’s Orbit One revolution every 365.24 days Distance of the earth from the sun n = day number (Jan. 1 is day 1) d (km) varies from 147x10 6 km on Jan. 2 to 152x10 6 km on July 3 (closer in winter, further in summer!) (I’ll be doing angles in degrees throughout)

14. Advanced Materials and Sustainable Energy Lab CBEE The Earth’s Orbit In one day, the earth rotates 360.99˚ The earth sweeps out what is called the ecliptic plane –Earth’s spin axis currently makes angle of 23.45˚ with ecliptic –Equinox – equal day and night (approx 3/21 and 9/21) –Winter solstice – North Pole is tilted furthest from the sun –Summer solstice – North Pole is tilted closest to the sun

15. Advanced Materials and Sustainable Energy Lab CBEE The Earth’s Orbit For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging

16. Advanced Materials and Sustainable Energy Lab CBEE Direct beam radiation I BC – passes in a straight line through the atmosphere to the receiver Diffuse radiation I DC – scattered by molecules and particulates in the atmosphere Clear Sky Direct-Beam Radiation Reflected radiation I RC – bounced off a surface near the reflector

17. Advanced Materials and Sustainable Energy Lab CBEE Extraterrestrial Solar Insolation I 0 Starting point for clear sky radiation calculations I 0 passes perpendicularly through an imaginary surface outside of the earth’s atmosphere I 0 depends on distance between earth and sun and on intensity of the sun which is fairly predictable Ignoring sunspots, I 0 can be written as SC = solar constant = 1.377 kW/m 2 n = day number

18. Advanced Materials and Sustainable Energy Lab CBEE Extraterrestrial Solar Insolation I 0 In one year, less than half of I 0 reaches earth’s surface as a direct beam On a sunny, clear day, beam radiation may exceed 70% of I 0 Figure 7.19

19. Advanced Materials and Sustainable Energy Lab CBEE Attenuation of Incoming Radiation Treat attenuation as an exponential decay function I B = beam portion of the radiation that reaches the earth’s surface A = apparent extraterrestrial flux k = optical depth m = air mass ratio

20. Advanced Materials and Sustainable Energy Lab CBEE Attenuation of Incoming Radiation A and k can be approximated as

21. Advanced Materials and Sustainable Energy Lab CBEE Solar Insolation on a Collecting Surface Direct-beam radiation is a function of the angle between the sun and the collecting surface In order to optimize this we need to know where the sun is in the sky… Diffuse radiation comes from all directions; typically between 6% and 14% of the direct value Reflected radiation comes from nearby surfaces, –Depends on surface reflectance –0.8 for clean snow to 0.1 for asphalt shingle roof

22. Advanced Materials and Sustainable Energy Lab CBEE Solar Insolation on a Collecting Surface

23. Advanced Materials and Sustainable Energy Lab CBEE Other essential data for your site You need to know: Average cloud cover for site –You can get this from the “National Solar Radiation Data Base” (NSRDB) –Maps for solar resource as affected by weather available –Database available at http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/ http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/ Whether there are obstacles in path of sun –We need to figure out the path of the sun in the sky…

24. Advanced Materials and Sustainable Energy Lab CBEE US Annual Insolation

25. Advanced Materials and Sustainable Energy Lab CBEE Worldwide Annual Insolation In 2007 worldwide PV peak was about 7800 MW, with almost half (3860 MW) in Germany, 1919 MW in Japan, 830 in USA and 655 in Spain

26. Advanced Materials and Sustainable Energy Lab CBEE The Sun’s Position in the Sky Predicts where the sun will be in the sky at any time Allows you to pick the best tilt angles for (PV) panels Rule of thumb for the Northern Hemisphere - a south facing collector tilted at an angle equal to the local latitude Solar declination

27. Advanced Materials and Sustainable Energy Lab CBEE Solar Declination Solar declination δ – the angle formed between the plane of the equator and the line from the center of the sun to the center of the earth δ varies between +/- 23.45˚ Assuming a sinusoidal relationship, a 365 day year, and n=81 is the spring equinox, the approximation of δ for any day n can be found from

28. Advanced Materials and Sustainable Energy Lab CBEE Altitude Angle and Azimuth Angle Azimuth Angle Altitude Angle

29. Advanced Materials and Sustainable Energy Lab CBEE Solar Position at Any Time of Day Described in terms of altitude angle β and azimuth angle of the sun ϕ S –β and ϕ S depend on latitude, day number, and time of day Azimuth angle ( ϕ S ) convention –positive in the morning when sun is in the east –negative in the evening when sun is in the west –reference in the Northern Hemisphere (for us) is true south Hours are referenced to solar noon

30. Advanced Materials and Sustainable Energy Lab CBEE Solar Noon and Collector Tilt Solar noon – sun is directly over the local line of longitude Optimal tilt angle for a collector is when the sun is perpendicular to that surface (therefore = L)

31. Advanced Materials and Sustainable Energy Lab CBEE Altitude Angle β N at Solar Noon Altitude angle at solar noon β N – angle between the sun and the local horizon Zenith – perpendicular axis at a site

32. Advanced Materials and Sustainable Energy Lab CBEE Altitude Angle and Azimuth Angle Hour angle H- the number of degrees the earth must rotate before sun will be over your line of longitude The earth rotates at 15˚/hr, then At 11 AM solar time, H = +15˚ (the earth needs to rotate 1 more hour to get to solar noon…) At 2 PM solar time, H = -30˚

33. Advanced Materials and Sustainable Energy Lab CBEE Altitude Angle and Azimuth Angle H = hour angle L = latitude (degrees) Test to determine if the angle magnitude is less than or greater than 90˚ with respect to true south-

34. Advanced Materials and Sustainable Energy Lab CBEE Solar Time vs. Clock Time Solar equations work in solar time (ST) Solar time is measured relative to solar noon Adjustments – –For a longitudinal adjustment related to time zones –For the uneven movement of the earth around the sun (usually ignored) Clock time has 24 1-hour time zones, each spanning 15˚ of longitude –Solar time differs 4 minutes for 1˚ of longitude

35. Advanced Materials and Sustainable Energy Lab CBEE World Time Zone Map Source: http://aa.usno.navy.mil/graphics/TimeZoneMap0802.pdf

36. Advanced Materials and Sustainable Energy Lab CBEE US Local Time Meridians Time ZoneLocal Time Meridian Eastern75˚ Central90˚ Mountain105˚ Pacific120˚ Eastern Alaska135˚ Alaska and Hawaii150˚

37. Advanced Materials and Sustainable Energy Lab CBEE Solar Time vs. Clock Time The earth’s elliptical orbit causes the length of a solar day to vary throughout the year Difference between a 24-h day and a solar day is given by the Equation of Time E (n is the day number again)

38. Advanced Materials and Sustainable Energy Lab CBEE Solar Time vs. Clock Time Combining longitude correction and the Equation of Time we get the following: CT – clock time ST – solar time LT Meridian – Local Time Meridian During Daylight Savings, add one hour to the local time

39. Advanced Materials and Sustainable Energy Lab CBEE Monthly and Annual Insolation Total annual output of fixed system insensitive to tilt angle Significant variation of month when most energy is generated

40. Advanced Materials and Sustainable Energy Lab CBEE Tracking Systems Most residential solar systems have a fixed mount Sometimes tracking systems are cost effective Tracking systems are either: –single axis (usually with a rotating polar mount [parallel to earth’s axis of rotation) –two axis (horizontal [altitude, up-down] and vertical [azimuth, east-west] Approximate benefits are 20% gain for single axis, 25% to 30% gain for two axis

41. Advanced Materials and Sustainable Energy Lab CBEE Sun Path Diagrams for Shading Analysis We now know how to locate the sun in the sky at any time –This can also help determine what sites will be in the shade at any time Use Sun Path diagram for your location (latitude) –Sketch the azimuth and altitude angles of trees, buildings, and other obstructions –Sections of the sun path diagram that are covered indicate times when the site will be in the shade

42. Advanced Materials and Sustainable Energy Lab CBEE Sun Path Diagram for Shading Analysis Trees to the southeast, small building to the southwest Estimate the amount of energy lost to shading

43. Advanced Materials and Sustainable Energy Lab CBEE Here’s a Sun Path Diagram for CVO You can create one for your site at http://solardat.uoregon.edu/SunChartProgram.htmlhttp://solardat.uoregon.edu/SunChartProgram.html

44. Advanced Materials and Sustainable Energy Lab CBEE California Solar Shade Control Act The shading of solar collectors has been an area of legal and legislative concern (e.g., a neighbor’s tree is blocking a solar panel) California has the Solar Shade Control Act (1979) to address this issue –No new trees and shrubs can be placed on neighboring property that would cast a shadow greater than 10 percent of a collector absorption area between the hours of 10 am and 2 pm. –Exceptions are made if the tree is on designated timberland, or the tree provides passive cooling with net energy savings exceeding that of the shaded collector –First people were convicted in 2008 because of their redwoods

45. Advanced Materials and Sustainable Energy Lab CBEE The Guilty Trees were Subject to Court Ordered Pruning Details: –Trees planted in 1997 –Complainant moved in 1993 –Installed PV in 2001 –No shade from trees in 2001… Source: NYTimes, 4/7/08