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

Sun characteristics Temperature: 5,780 K Diameter: km Distance: km

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: J.s c: Light velocity m.s -1 k: Boltzmann’s constant: J.K -1 T: Black body temperature K λ: Wave length m

Solar Radiation Visible Infrared

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

Radiation received by the earth Distance effect 150 M km

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

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

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 )

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

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

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

Declination Earth oscillates along its polar axis See:

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

Absorption calculation “A Simplified Clear Sky model for Direct and Diffuse Insulation on Horizontal Surfaces” R.E. Bird, R.L. Hulstrom SERI TR 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 Look for Solrad – Greg Pelletier

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

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

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

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

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

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

Tracker vs Fix Panel Summer

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

Direct and Diffuse Radiation Direct and diffuse radiation

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

Map of solar radiation

California Resources Source: California Solar Resources CEC April 2005

Other sources Energy Plus standard files for California climate zones (DOE) gion=4_north_and_central_america_wmo_region_4/country=2_california_climat e_zones/cname=California%20Climate%20Zones 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) NASA Surface meteorology and Solar Energy

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

Solar Path Finder Source:

Solar Path Finder Results

San Francisco Solar Map

San Francisco Solar Map