Solar Energy Part 1: Resource

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