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Solar EnergyPart 1: Resource
San Jose State UniversityFX Rongère
January 2009
Sun characteristics
Temperature: 5,780 K Diameter: 1.4 106 km Distance: 150 106 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:
)1(
1
.
..2)(
..
.5
2
,
Tk
chb
e
chi
iλ,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. 108 m.s
-1
k: Boltzmann’s constant: 1.381. 10-23
J.K-1
T: Black body temperature K
λ: Wave length m
c
hh ..
Black Body radiation intensity5780 K
1.0E+00
5.0E+06
1.0E+07
1.5E+07
2.0E+07
2.5E+07
3.0E+07
0 0.5 1 1.5 2 2.5 3
Wavelength (μm)
Rad
iation
Inte
nsi
ty (W
.m-2.μ
m-1.s
r-1)
Solar Radiation
Visible Infrared
Sun Radiation Power
The energy radiated by the sun is calculated by integrating the Planck’s function:
WTRE
ch
kwithTddi
sun
b
2642
23
544
0
,
10.9.3....4
.
..
15
2.)(
σ: Stefan-Boltzmann constant 5.67. 10-8 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:
22
.370,1..4
mW
r
Ee sun
Absorption by the atmosphere
1
2
So
lar
Sp
ectr
al I
rrad
ian
ce (
103 W
.m-2.μ
m-1)
Wavelength (m)
0
22, .1.000,1 mkWmWesea
H2O
H2O & CO2
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
Greenwich
Two coordinates: Declination (angle from the Equator) δs
Hour-angle (angle from the meridian of Greenwich) ωs
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: http://www.powerfromthesun.net/chapter3/Chapter3Word.htm
Position of the sun in the sky
Two coordinates: Azimuth (angle from the North) αs Altitude (angle over the horizon) γs
γCαC
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
Look for Solrad – Greg Pelletier
ExamplesSolar Altitude and Normal Solar Radiation
San J ose J une 21, 2007
0
100
200
300
400
500
600
700
800
900
4:00 8:00 12:00 16:00 20:00 0:00
Time
Nor
mal
Flu
x (W
/m2)
0
10
20
30
40
50
60
70
80
Sola
r Altitude in D
egr
ees
Solar Altitude and Normal Solar Radiation
Seattle J une 21, 2007
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
900.00
4:00 8:00 12:00 16:00 20:00 0:00
Time
Nor
mal
Flu
x (W
/m2)
0.000
10.000
20.000
30.000
40.000
50.000
60.000
70.000
80.000
Sola
r Altitude in D
egr
ees
Energy for the day: 8.6 kWh/m2 Energy for the day: 8.9 kWh/m2
dttPowertEnergyt
.0
Power is in Watt [W]Energy is in Joule [J] or in [kWh]
37.3N – 121.8W 47.6N – 122.3W
Parameter Influence
Each Parameter is valued to min and max:
Aerosols have the most influence followed by water vapor
.05 cm .4 cm 0.01cm 6.5 cm 0.02 0.5 0.1 0.5Value 9,297 9,422 9,201 10,552 9,085 10,767 8,185 10,203 8,540 7,324 14,054% 0% 1% -1% 13% -2% 16% -12% 10% -8% -21% 51% 72%Value 6,507 6,581 6,451 7,360 6,361 7,284 5,869 6,996 6,077 5,328 9,098% 0% 1% -1% 13% -2% 12% -10% 8% -7% -18% 40% 58%Value 5,416 5,473 5,372 6,117 5,295 5,993 4,929 5,781 5,089 4,500 7,385% 0% 1% -1% 13% -2% 11% -9% 7% -6% -17% 36% 53%
ReferenceOzone Water Vapor Aerosol 500 nm Aerosol 380 nm
Min Max
Normal to the beam
HorizontalTilt South 37.3
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-αs
γs
x - South
y - East
z - Zenith
sss
ssss
ssss
z
y
x
sin.
)sin(.cos.
)cos(.cos.
Cartesian coordinates of the opposite of the beam from the sun:
φs
Cartesian Coordinates
cc
ccc
ccc
z
y
x
sin
)sin(.cos
)cos(.cos
π-αs
γs
x - South
y - East
z - ZenithCartesian coordinates of the vector normal to the panel:
γc
π-αc
Scalar product
cc
cscscsscs
Tilt
n
2
sin.sincos.cos.cos..
0. cs nIf
Then the radiation is received by the back of the panel. The net radiation on the panel is null.
cscscsccczss zzyyxxzyxzyx ...,,.,,
Tracker vs Fix Panel
Summer
Reference case - San Jose June 21, 2007
-100
0
100
200
300
400
500
600
700
800
900
0:00 4:00 8:00 12:00 16:00 20:00 0:00
Time of the day
Sola
r Rad
iati
on (
W/m
2)
Normal to the beam Horizontal Tilt 37.3 Tilt 20
Normal to the beam 9,297 W.h 100%Horizontal 6,507 W.h 70%Tilt 37.3 5,416 W.h 58%Tilt 20 6,229 W.h 67%
Energy over the day
Tracker vs Fix Panel
Spring
Reference case - San Jose March 21, 2007
0.00
200.00
400.00
600.00
800.00
1000.00
0:00 4:00 8:00 12:00 16:00 20:00
Time of the day
Sola
r Rad
iati
on (
W/m
2)
Normal to the Beam Horizontal Tilt 37.3 Tilt 20
Normal to the beam 7,551 W.h 100%Horizontal 4,456 W.h 59%Tilt 37.3 5,567 W.h 74%Tilt 20 5,329 W.h 71%
Energy over the day
A fix panel solar will provide about 30% less energy than a tracking system
Direct and Diffuse Radiation
Direct and diffuse radiationTotal Solar Radiation on a panel (Tilt 30)
San J ose J une 21, 2007
0
100
200
300
400
500
600
700
800
900
1000
0:00 6:00 12:00 18:00 0:00
Time
Rad
iation
(W
/m2)
Direct Tilt 30
Diffuse
Total
Capacity Factor:
Example: If Annual average of daily solar
energy equals 6 kWh.m-2/day
Annual average of daily solar energy
8760
0
,,,, ).(.365/1 dttee LatTiltSouthlocLatTiltSouthday
YearPowerMaximal
EnergyAnnualCF
.
%2524..1
..62
2
hmkW
hmkWCF
Map of solar radiation
California Resources
Source: California Solar Resources CEC-300-2005-007 April 2005
Other sources
Energy Plus standard files for California climate zones (DOE) http://www.eere.energy.gov/buildings/energyplus/cfm/
weather_data3.cfm/region=4_north_and_central_america_wmo_region_4/country=2_california_climate_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
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: http://www.solarpathfinder.com/works.html?id=VQjGmAZv
Solar Path Finder Results
http://www.solarpathfinder.com/video?id=TwtmyFfS
San Francisco Solar Map
http://sf.solarmap.org/#
San Francisco Solar Map