EE 394J-10
Distributed Generation Technologies
Fall 2012
Photovoltaic modules
• Photovoltaic (PV) modules are made by connecting several PV cells. PV
arrays are made by connecting several PV modules.
• Although the sun will eventually die as a white dwarf star in about 4.5 Billion
years, solar power can be considered a renewable source of energy because
we can expect that for the next couple of billion years the sun will still radiate
power without making the Earth inhabitable.
• Solar power is radiated through space.
• Solar power is generated by nuclear fusion.
• Light propagation can be represented through waves or through particles
(dual representation).
• To represent electricity production in PV cells, the particle (photon)
representation is used
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Photons are created at the center or the Sun. It takes an average of 10 million
years for the photons to emerge (they collide many times in the Sun interior).
Then it takes 8 minutes for a photon to reach the Earth.
• Fusion reactions:
• Step 1: 11H  11H  12 D  p   n 0
( 12 D represents an atom of deuterium = an hydrogen isotope
formed by a proton and a neutron, a positron (p+) or antielectron is
an electron with a positive charge, a neutrino n0 are very low massno charge elementary particles).
This reaction requires extreme temperatures and pressures to bring
two protons so close (< 10-15m) that the repulsion force between
them disappears.
• Step 2: p   e    
where γ represent a photon.
2
1
3
• Step 3.1: 1 D  1 H  2 He  
2
2
3

3
0
• Step 3.2: 1 D  1 D  1T  p or 2 He  n
where 13T is tritium an hydrogen isotope formed by 2 neutrons and
a proton
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Fusion reactions (continue):
3
3
4
1
1
• Step 4.1: 2 He  2 He  2 He  1 H  1 H
3
3
4
0
• Step 4.2: 1T  1T  2 He  2n
1

4
1
0
• The overall reaction is: 6 1 H  2e 2 He  2 1 H  2n  6
•This reaction releases 26 MeV
• All photons are created equal. So why photons leaving the sun have different
energy (as indicated by their different frequency in the dual wave model)?
• The emitted photons have high energy. This energy is mostly lost in collisions
with atoms as the photons leave the sun.
•This reaction can only occur due to the high pressure generated by the mass
contraction at the Sun’ s center.
• The Sun is mostly composed of hydrogen (73 %) and Helium (25 %). These
proportions are changing. Eventually the sun will start the fusion process of
heavier elements.
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Ideal radiation of energy is described by the black body radiation.
• Black bodies radiate energy at different wavelengths as indicated by
3.74  108
E 
14400


5
T
 e
 1


• The Sun closely behaves like a black body at a temperature T=5800 K (the
Sun’s surface temperature)
• Total blackbody radiation rate
(area under the curve):
4
E  A T
E=AσT4
For the Sun it equals 1.37 kW/m2
http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png
5
• Wavelength for the maximum:
2898
max (  m) 
T
For the Sun it approximately
equals 0.5 μm
© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Finally, the photons reach the Earth.
US Solar Insolation Map: NREL
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• The incident power has 3 components depending on the final photons path.
Diffuse radiation
Direct-beam radiation
Reflected radiation
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Direct-beam radiation:
• The extraterrestrial solar insolation is given by

 360n  
I 0  (SC) 1  0.034cos 

 365  

(W/m 2 )
This is the solar insolation before entering the Earth’s atmosphere. In
the equation, SC is the solar constant an equals 1.37 kW/m2 and n is
the day number (January 1 is day #1). The day number takes into
consideration that the Earth-Sun distance changes through the year.
• The solar insolation is attenuated as it passes through the atmosphere.
The portion that reaches the earth’s surface.
I B  Ae  km
where A and k are constants and m is the air mass ratio that takes into
account that the sun’s beam path length through the atmosphere changes
with the sun relative position with respect to the earth surface at the
location where the analysis is made.
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Sun’s location terms
Up (−z axis)
zenith
 sun
Line perpendicular to
horizontal plane
Horizontal plane
East
(y axis)
azimuth
 sun
North
(x axis)
West
Note – because of magnetic declination,
a compass in Austin points
approximately 6º east of north.
Figure 4. Sun Zenith and Azimuth Angles
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Magnetic vs. celestial poles:
• Magnetic poles:
• Created by Earth’s magnetic field
• Can be located with a compass
• They move along Earth’s surface!
Celestial poles:
• Created by Earth’s rotation.
• They are two imaginary stationary
points in the sky.
• Important for PV system applications.
Geological Survey of Canada
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Sun’s position in the sky throughout the day and during an entire year.
Solar Zenith versus Azimuth at Austin
22nd Day of Jun, Jly, Aug, Sep, Oct, Nov, Dec
(Sun hrs/day. Jun=13.9,Jly=13.6,Aug=12.8,Sep=12.0,Oct=11.0,Nov=10.3,Dec=10.0)
Azimuth (South = 180)
0
30
60
90
120
150
0
Zenith (Degrees from Vertical)
10
180
NOON
Jun
210
240
300
1 PM
20
3 PM
30
40
Sep
50
60
70
Dec
80
90
11
270
© Alexis Kwasinski, 2012
330
360
Photons’ Journey into Electricity
• The direct-beam insolation IBC depends on the PV module orientation with
respect to the sun. If the PV module is fixed, this insolation will change in a
deterministic way throughout the day and the year:
if the incident angle θ is given by
cos  cos  cos( S  C )sin   sin  cos 
• Then, the direct-beam
insolation is
I BC  I B cos
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Impact of the sun’s position for the calculation of the direct-beam radiation
with respect to the incidence angle and the air mass ratio
Austin’s Latitude: 30o
Tropic of Cancer
Latitude 23.45o
30o
Edge of
PV module
(for incidence
angle
calculation)
23.45o
23.45o
June 21
March 21
September 21
Equator
Tropic of Capricorn
Latitude -23.45o
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December 21
Earth’s surface
(for air mass ratio
calculation)
© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Assuming that the diffuse radiation does not depends on the sun’s position in
a clear sky, then it is modeled using the following equation:\
 1  cos  
I DC  CI B 

2


where C is the sky diffuse factor which can be obtained from ASHRAE. This is
another deterministic value.
• The reflected radiation can be calculated by considering the reflectance ρ of
the surface in front of the PV module:
I RC
 1  cos  
  I B (sin   C ) 

2


This is another deterministic value.
• The total radiation rate on a PV module is, therefore, given by
IC  I BC  I DC  I RC
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• After a long journey, photons are converted into electricity in semiconductors:
• Whenever a photon with enough energy hits an atom, an electron may jump
the energy gap into the conduction band. Once in the conduction band the
electron is free to move in an electric circuit.
• If the circuit is open or if the load requires less current (charge per time) than
the one being produced, the free electrons will eventually decay again.
• Since it is assumed a continuous slow varying incident solar energy, electrons
are freed at a constant rate. Hence, a constant voltage is produced.
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Atom’s energy model:
Eg
Forbidden band
Filled band
Gap
Filled band
Metals
Conduction band
(Empty at T = 0K)
Electron Energy
Electron Energy
Conduction band
(partially filled)
Eg
Forbidden band
Gap
Filled band
semiconductors
• Photons energy is quantized. The energy of a photon with a wavelength of λ
(or a frequency of υ) is
E  h 
hc

•where h is Planck’s constant
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• if the last equation is plotted we obtain that
Lost in heat
From the course’s recommended book
• Hence, there is a theoretical limit to a PV cell power output which depends on
the semiconductor material being used. For different semiconductors we have
that:
From the course’s recommended book
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© Alexis Kwasinski, 2012
Photons’ Journey into Electricity
• Efficiency limit can be understood by comparing the following two figures:
http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png
From the course’s recommended book
Excess
energy
• So for an air mass ratio of 1.5 the efficiencies are (see next slide)
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© Alexis Kwasinski, 2012
Insufficient
energy
Photons’ Journey into Electricity
• For silicon and an air mass of 1.5 the maximum efficiency is about 50%
• As the band gap energy decreases the efficiency improves somewhat.
However, the cost increases significantly.
• Next class: PV cells electrical characteristics and technologies.
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© Alexis Kwasinski, 2012
PV Cells Technologies
• Characterization criterion:
• Thickness:
• Conventional – thick cells (200 - 500 μm)
• Thin film (1 – 10 μm). Tend to be less costly than conventional
(think) cells but they also tend to be less reliable and efficient.
• Crystalline configuration:
• Single crystal
• Multicrystalline: cell formed by 1mm to 10cm single crystal areas.
• Polycrystalline: cell formed by 1μm to 1mm single crystal areas.
• Microcrystalline: cell formed by areas of less than 1μm across.
• Amorphous: No single crystal areas.
• p and n region materials:
• Same material: homojunction (Si)
• Different material: heterojunction (CdS and CuInSe2)
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© Alexis Kwasinski, 2012
PV Cells Technologies
Uni-Solar solar shingle
BP SX170B Polycrystalline
BP SX170B Monocrystalline
Uni-Solar Laminate PVL-136
Amorphous
Mitsubishi PV-TD 190MF5
Polycrystalline
PV Modules at ENS
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© Alexis Kwasinski, 2012
PV Cells Technologies
• Thick film fabrication techniques:
• Czochraski’s (CZ): for single-crystal silicon. Costly.
• Float zone process (FZ): also for single-crystal silicon. Costly
• Ribbon silicon
• Cast silicon: for multicrystalline cells. Less costly.
• Thin film
• Can be used embedded in semitransparent windows.
• Techniques:
• Amorphous Silicon: can achieve higher efficiencies (in the order of 42%
thanks to the multijunction (different multiple layers) in which each layer absorb
photons with different energy.
• Gallium Arsenide (GaAs): relatively high theoretical efficiency (29 %) which is
not significantly affected by temperature. Less sensitive to radiation. Gallium
makes this solution relatively expensive.
• Gallium Indium Phosphide (GaInP): similar to GaAs.
• Cadmium Telluride (CdTe): Issue: Cd is a health hazard (it is very toxic).
• Copper Indium Diselenide (CIS or CuInSe2): relatively good efficiency)
• Silicon Nitrade (N4Si3)
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© Alexis Kwasinski, 2012