1. Solar Energy Part 1: Resource San Jose State University FX Rongère January 2009

2. Sun characteristics Temperature: 5,780 K Diameter: 1.4 10 6 km Distance: 150 10 6 km

3. Black Body radiation intensity Sun emission is close to the back body spectrum: Photon energy: Planck’s spectral distribution of emissive power of a black body in a vacuum: i λ,b : Radiation intensity of the black body in function of the wave length (W.m -2.μm -1.sr -1 ) h: Planck’s constant: 6.626.10 -34 J.s c: Light velocity 3. 10 8 m.s -1 k: Boltzmann’s constant: 1.381. 10 -23 J.K -1 T: Black body temperature K λ: Wave length m

4. Solar Radiation Visible Infrared

5. Sun Radiation Power The energy radiated by the sun is calculated by integrating the Planck’s function: σ: Stefan-Boltzmann constant 5.67. 10 -8 W.m -2.K -4

6. Radiation received by the earth Distance effect 150 M km

7. Radiation received by the earth The flux received by square meter out of the atmosphere is:

8. Absorption by the atmosphere 1 2 Solar Spectral Irradiance (10 3 W.m -2.μm -1 ) Wavelength (m) 0 H2OH2O H 2 O & CO 2

9. Computation of the flux received by a cell The flux received by a cell depends on: the angle of the sun rays with the cell the absorption by the atmosphere Angle calculations: Sun position in the earth coordinates Sun position in local coordinates Sun position in the cell coordinates Declination (δ s ) Hour-angle (ω s ) Universal Time (UT) Altitude ( γ s ) Azimuth ( α s ) Local Time (LT) Latitude (φ) Longitude (λ) Normal angle ( θ s ) Local Time (LT) Latitude (φ) Longitude (λ) Cell orientation (γ c,α c )

10. Sun position in earth coordinates Greenwich Two coordinates: Declination (angle from the Equator) δ s Hour-angle (angle from the meridian of Greenwich) ω s

11. Equation of time Correction to the Hour-angle (ωs) due to the elliptical orbit of the earth around the sun

12. Equation of time Difference between local solar time and local mean solar time Woolf approximation

13. Declination Earth oscillates along its polar axis See: http://www.powerfromthesun.net/chapter3/Chapter3Word.htm

14. Position of the sun in the sky Two coordinates: Azimuth (angle from the North) α s Altitude (angle over the horizon) γ s γCγC αCαC

15. Absorption calculation “A Simplified Clear Sky model for Direct and Diffuse Insulation on Horizontal Surfaces” R.E. Bird, R.L. Hulstrom SERI TR-642-761 February 1981 Altitude Barometric pressure (mb, sea level = 1013) Ozone thickness of atmosphere (cm, typical 0.05 to 0.4 cm) Water vapor thickness of atmosphere (cm, typical 0.01 to 6.5 cm) Aerosol optical depth at 500 nm (typical 0.02 to 0.5) Aerosol optical depth at 380 nm (typical 0.1 to 0.5) Forward scattering of incoming radiation (typical 0.85) Surface albedo (typical 0.2 for land, 0.25 for vegetation, 0.9 for snow) Excel model to download at http://www.ecy.wa.gov/programs/eap/models.html http://www.ecy.wa.gov/programs/eap/models.html Look for Solrad – Greg Pelletier

16. Examples Energy for the day: 8.6 kWh/m 2 Energy for the day: 8.9 kWh /m 2 Power is in Watt [W] Energy is in Joule [J] or in [kWh] 37.3N – 121.8W47.6N – 122.3W

17. Parameter Influence Each Parameter is valued to min and max: Aerosols have the most influence followed by water vapor

18. Radiation received by a panel Radiation is equal to the radiation received by the projection of the panel to normal to the beam θ

19. Cartesian Coordinates π-αsπ-αs γsγs x - South y - East z - Zenith Cartesian coordinates of the opposite of the beam from the sun: φsφs

20. Cartesian Coordinates π-αsπ-αs γsγs x - South y - East z - Zenith Cartesian coordinates of the vector normal to the panel: γcγc π-αcπ-αc

21. Scalar product If Then the radiation is received by the back of the panel. The net radiation on the panel is null.

22. Tracker vs Fix Panel Summer

23. Tracker vs Fix Panel Spring A fix panel solar will provide about 30% less energy than a tracking system

24. Direct and Diffuse Radiation Direct and diffuse radiation

25. Capacity Factor: Example: If Annual average of daily solar energy equals 6 kWh.m -2 /day Annual average of daily solar energy

26. Map of solar radiation

27. California Resources Source: California Solar Resources CEC-300-2005-007 April 2005

28. Other sources Energy Plus standard files for California climate zones (DOE) http://www.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/re gion=4_north_and_central_america_wmo_region_4/country=2_california_climat e_zones/cname=California%20Climate%20Zones http://www.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/re gion=4_north_and_central_america_wmo_region_4/country=2_california_climat e_zones/cname=California%20Climate%20Zones Solar Radiation Data Manual for Flat-Plate and Concentrating Collectors (NREL) http://rredc.nrel.gov/solar/pubs/redbook/ NASA Surface meteorology and Solar Energy http://eosweb.larc.nasa.gov/cgi-bin/sse/register.cgi

29. Shading effect Shading suppress direct flux Diffuse flux is less than 20% of direct flux In addition, energy level of most photons in diffuse radiation is too low to activate conductance for silicon output of shaded cells is almost zero Cells of a solar panel are in series shade on few cells leads to almost null output

30. Solar Path Finder Source: http://www.solarpathfinder.com/works.html?id=VQjGmAZv

31. Solar Path Finder Results http://www.solarpathfinder.com/video?id=TwtmyFfS

32. San Francisco Solar Map http://sf.solarmap.org/#

33. San Francisco Solar Map