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Solar Energy Part 1: Resource: 

Solar Energy Part 1: Resource San Jose State University FX Rongère Septembre 2007

Sun characteristics: 

Sun characteristics Temperature: 5,780 K Diameter: 1.4 106 km Distance: 150 106 km

Black Body radiation intensity: 

Black Body radiation intensity Sun emission is close to the back body spectrum: Planck’s spectral distribution of emissive power of a black body in a vacuum: iλ,b: Radiation intensity of the black body in function of the wave length (W.m-2.μ h: Planck’s constant: 6.626.10-34 J.s c: Light velocity 3. 108 m.s-1 k: Boltzmann’s constant: 1.381. 10-23 J.K-1 T: Black body temperature K λ: Wave length m

Sun Radiation Power: 

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

Radiation received by the earth: 

Radiation received by the earth Distance effect 150 M km

Radiation received by the earth: 

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

Absorption by the atmosphere: 

Absorption by the atmosphere 1 2 Solar Spectral Irradiance (103 W.m-2.μm) Wavelength (m) 0

Computation of the flux received by a cell : 

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 (δs) Hour-angle (ωs) Universal Time (UT) Altitude (γs) Azimuth (αs) Local Time (LT) Latitude (φ) Longitude (λ) Normal angle (θs) Local Time (LT) Latitude (φ) Longitude (λ) Cell orientation (γc,αc)

Sun position in earth coordinates: 

Sun position in earth coordinates Two coordinates: Declination (angle from the Equator) δs Hour-angle (angle from the meridian of Greenwich) ωs

Equation of time: 

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

Equation of time: 

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: 

Position of the sun in the sky Two coordinates: Azimuth (angle from the North) αs Altitude (angle over the horizon) γs

Absorption calculation: 

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 Look for Solrad – Greg Pelletier


Examples Energy for the day: 8.6 kWh/m2 Energy for the day: 8.9 kWh/m2

Annual average of daily solar energy: 

Capacity Factor: Example: If Annual average of daily solar energy equals 6 kWh/year Annual average of daily solar energy

Map of solar radiation: 

Map of solar radiation

California Resources: 

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

Other sources: 

Other sources Energy Plus standard files for California climate zones (DOE) Solar Radiation Data Manual for Flat-Plate and Concentrating Collectors (NREL) NASA Surface meteorology and Solar Energy

Shading effect: 

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

Solar Path Finder: 

Solar Path Finder Source:

Solar Path Finder Results: 

Solar Path Finder Results

Homework Assignment #1: 

Homework Assignment #1 Solar radiation calculations using Solrad Due date September 5th, 2007 Results:

Radiation received by a panel: 

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: 

Cartesian Coordinates π-αs γs x - South y - East z - Zenith Cartesian coordinates of the opposite of the beam from the sun: φs

Cartesian Coordinates: 

Cartesian Coordinates π-αs γs x - South y - East z - Zenith Cartesian coordinates of the vector normal to the panel: γc Here:

Scalar product: 

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

Homework Assignment #1: 

Homework Assignment #1 Results: Received radiation W.h/m2