EE 394V New Topics in Energy Systems

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EE 394V New Topics in Energy Systems Distributed
Generation Technologies Fall 2008 September
9 and 11, 2008
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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 through 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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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
• ( 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 mass-no charge elementary
  particles).
• This reaction requires extreme temperatures and
  pressures to bring two protons so close (lt
  10-15m) that the repulsion force between them
  disappears.
• Step 2
• where ? represent a photon.
• Step 3.1
• Step 3.2
• where is tritium an hydrogen isotope formed
  by 2 neutrons and a proton

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Photons Journey into Electricity

• Fusion reactions (continue)
• Step 4.1
• Step 4.2
• The overall reaction is
• 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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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
• The Sun closely behaves like a black body at a
  temperature T5800 K (the Suns surface
  temperature)

• Total blackbody radiation rate (area under the
  curve)
• EAsT4
• For the Sun it equals 1.37 kW/m2
• Wavelength for the maximum
• For the Sun it approximately equals 0.5 µm

http//en.wikipedia.org/wiki/ImageEffectiveTemper
ature_300dpi_e.png
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Photons Journey into Electricity

• Finally, the photons reach the Earth.

US Solar Insolation Map NREL
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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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Photons Journey into Electricity

• Direct-beam radiation
• The extraterrestrial solar insolation is given
  by
• This is the solar insolation before entering the
  Earths 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 earths surface.
• where A and k are constants and m is the air mass
  ratio that takes into account that the suns 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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Photons Journey into Electricity

• Suns location terms

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Photons Journey into Electricity

• Magnetic vs. celestial poles
• Magnetic poles
• Created by Earths magnetic field
• Can be located with a compass
• They move along Earths surface!
• Celestial poles
• Created by Earths rotation.
• They are two imaginary stationary
• points in the sky.
• Important for PV system applications.

Geological Survey of Canada
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Photons Journey into Electricity

• Suns position in the sky throughout the day and
  during an entire year.

NOON
Jun
1 PM
3 PM
Sep
Dec
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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 ? is given by

• Then, the direct-beam insolation is

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Photons Journey into Electricity

• Impact of the suns position for the calculation
  of the direct-beam radiation with respect to the
  incidence angle and the air mass ratio

Edge of PV module (for incidence angle
calculation)
Austins Latitude 30o
30o
June 21
Tropic of Cancer Latitude 23.45o
March 21 September 21
23.45o
23.45o
Equator
December 21
Tropic of Capricorn Latitude -23.45o
Earths surface (for air mass ratio calculation)
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Photons Journey into Electricity

• Assuming that the diffuse radiation does not
  depends on the suns position in a clear sky,
  then it is modeled using the following equation\
• 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 ? of the surface in
  front of the PV module
• This is another deterministic value.
• The total radiation rate on a PV module is,
  therefore, given by

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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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Photons Journey into Electricity

• Atoms energy model
• Photons energy is quantized. The energy of a
  photon with a wavelength of ? (or a frequency of
  ?) is
• where h is Plancks constant

Conduction band (partially filled)
Conduction band (Empty at T 0K)
Electron Energy
Electron Energy
Eg
Forbidden band
Eg
Forbidden band
Filled band
Gap
Gap
Filled band
Filled band
Metals
semiconductors
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Photons Journey into Electricity

• if the last equation is plotted we obtain that
• 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

Lost in heat
From the courses recommended book
From the courses recommended book
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Photons Journey into Electricity

• Efficiency limit can be understood by comparing
  the following two figures
• So for an air mass ratio of 1.5 the efficiencies
  are (see next slide)

http//en.wikipedia.org/wiki/ImageEffectiveTemper
ature_300dpi_e.png
From the courses recommended book
Insufficient energy
Excess energy
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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.