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Introduction to Solar Power

Introduction to Solar Power. 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.

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Introduction to Solar Power

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  1. Introduction to Solar Power

  2. 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. The Sun and Blackbody Radiation The sun • 1.4 million km in diameter • 3.8 x 1020 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. Plank’s Law • Plank’s law – energy at a given wavelength emitted by a blackbody depends on temperature • λ= wavelength (μm) • Eλ = emissive power per unit area of blackbody (W/m2-μm) • T = absolute temperature (K)

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

  6. Stefan-Boltzmann Law • Total radiant power emitted is given by the Stefan–Boltzmanlaw of radiation • E = total blackbody emission rate (W) • σ= Stefan-Boltzmann constant = 5.67x10-8 W/m2-K4 • T = absolute temperature (K) • A = surface area of blackbody (m2)

  7. Wien’s Displacement Rule • The wavelength at which the emissive power per unit area reaches its maximum point • T = absolute temperature (K) • λmax = wavelength for maximal emissive power (μm) • For the sun , T = 5800 K; λmax =0.5 μm • For earth (as a blackbody), T = 288 K; λmax = 10.1 μm

  8. 288 K Blackbody Spectrum The earth as a blackbody Area under curve is the total radiant power emitted

  9. Extraterrestrial Solar Spectrum Integrate over all wavelengths to get solar constant SC = 1.377 kW/m2

  10. Air Mass Ratio As sunlight passes through the atmosphere, less energy arrives at the earth’s surface h1 = path length through atmosphere with sun directly overhead h2 = path length through atmosphere to spot on surface β= altitude angle of the sun

  11. 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. 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. 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 147x106 km on Jan. 2 to 152x106 km on July 3 (closer in winter, further in summer!) (I’ll be doing angles in degrees throughout)

  14. 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. The Earth’s Orbit For solar energy applications, we’ll consider the characteristics of the earth’s orbit to be unchanging

  16. Clear Sky Direct-Beam Radiation Direct beam radiation IBC – passes in a straight line through the atmosphere to the receiver Diffuse radiation IDC – scattered by molecules and particulates in the atmosphere Reflected radiation IRC – bounced off a surface near the reflector

  17. Extraterrestrial Solar Insolation I0 Starting point for clear sky radiation calculations I0 passes perpendicularly through an imaginary surface outside of the earth’s atmosphere I0 depends on distance between earth and sun and on intensity of the sun which is fairly predictable Ignoring sunspots, I0 can be written as SC = solar constant = 1.377 kW/m2 n = day number

  18. Extraterrestrial Solar Insolation I0 In one year, less than half of I0 reaches earth’s surface as a direct beam On a sunny, clear day, beam radiation may exceed 70% of I0 Figure 7.19

  19. Attenuation of Incoming Radiation Treat attenuation as an exponential decay function IB = beam portion of the radiation that reaches the earth’s surface A = apparent extraterrestrial flux k = optical depth m = air mass ratio

  20. Attenuation of Incoming Radiation A and k can be approximated as

  21. 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. Solar Insolation on a Collecting Surface

  23. 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/ • Whether there are obstacles in path of sun • We need to figure out the path of the sun in the sky…

  24. US Annual Insolation

  25. 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. 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. 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. Altitude Angle and Azimuth Angle Altitude Angle Azimuth Angle

  29. Solar Position at Any Time of Day Described in terms of altitude angle βand azimuth angle of the sun ϕS • β and ϕS depend on latitude, day number, and time of day Azimuth angle (ϕS ) 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. 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. Altitude Angle βN at Solar Noon Altitude angle at solar noon βN – angle between the sun and the local horizon Zenith – perpendicular axis at a site

  32. 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. 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. 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. World Time Zone Map Source: http://aa.usno.navy.mil/graphics/TimeZoneMap0802.pdf

  36. US Local Time Meridians

  37. 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. 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. Monthly and Annual Insolation Total annual output of fixed system insensitive to tilt angle Significant variation of month when most energy is generated

  40. 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. 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. Sun Path Diagram for Shading Analysis Trees to the southeast, small building to the southwest Estimate the amount of energy lost to shading

  43. Here’s a Sun Path Diagram for CVO You can create one for your site at http://solardat.uoregon.edu/SunChartProgram.html

  44. 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. 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

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