1. Microgrid Concepts and Distributed Generation Technologies
ECE 2795
Microgrid Concepts and Distributed Generation Technologies
Spring 2017
Week #4
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2. 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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3. 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 (< 10-15m) that the repulsion force between them disappears.
Step 2:
where γ 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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4. 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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5. 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 T=5800 K (the Sun’s surface temperature)
Total blackbody radiation rate (area under the curve):
E=AσT4
For the Sun it equals 1.37 kW/m2
Wavelength for the maximum:
For the Sun it approximately equals 0.5 μm
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6. Photons’ Journey into Electricity
Finally, the photons reach the Earth.
US Solar Insolation Map: NREL
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7. 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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8. Photons’ Journey into Electricity
Direct-beam radiation:
The extraterrestrial solar insolation is given by
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.
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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9. Photons’ Journey into Electricity
Sun’s location terms
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10. Photons’ Journey into Electricity
Magnetic vs. celestial poles:
Magnetic poles:
Caused by Earth’s magnetic field
Can be located with a compass
They move along Earth’s surface!
Celestial poles:
Caused 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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11. Photons’ Journey into Electricity
Sun’s position in the sky throughout the day and during an entire year.
Jun
NOON
1 PM
3 PM
Sep
Dec
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12. 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
Then, the direct-beam insolation is
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13. 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
Edge of
PV module
(for incidence angle calculation)
Austin’s Latitude: 30o
30o
June 21
Tropic of Cancer
Latitude 23.45o
23.45o
March 21
September 21
23.45o
Equator
December 21
Tropic of Capricorn
Latitude o
Earth’s surface
(for air mass ratio calculation)
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14. 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:\
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:
This is another deterministic value.
The total radiation rate on a PV module is, therefore, given by
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15. 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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16. Photons’ Journey into Electricity
Atom’s energy model:
Photons energy is quantized. The energy of a photon with a wavelength of λ (or a frequency of υ) is
where h is Planck’s 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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17. 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 course’s recommended book
From the course’s recommended book
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18. 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)
From the course’s recommended book
Excess energy
Insufficient energy
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19. 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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20. PV Cells Technologies Characterization criterion: Thickness:
Conventional – thick cells ( 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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21. Uni-Solar Laminate PVL-136 Amorphous
PV Cells Technologies
Uni-Solar solar shingle
BP SX170B Polycrystalline
BP SX170B Monocrystalline
Uni-Solar Laminate PVL-136 Amorphous
Mitsubishi PV-TD 190MF5 Multicrystalline
Various types of
PV Modules
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22. 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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23. PV Applications
More conventional applications (not all necessarily for microgrids)
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24. PV Applications
Less conventional applications (not all necessarily for microgrids)
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25. The p-n junction diode n-type substrate Bias voltage p-type substrateId
Vd is the diode voltage
I0 is the reverse saturation current caused by thermally generated carriers
At 25 C:
Ideal diode
Real diode I0
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26. Reverse v-i curve for the diode
PV Cells physics
The current source shifts the reversed diode curve upwards
ISC
VOC
Same curve
The bias source (voltage source) is replaced by a current source powered by the photons
p-n junction is equivalent to a diode
ISC
Reverse v-i curve for the diode
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27. PV Cell steady state characteristic
From Kirchoff’s current law:
The open circuit voltage is
Maximum power point
Power
Pmax  0.7 • Voc • Isc
Current
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28. PV Cell steady state characteristic
Dependence on temperature and insolation:
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29. PV Cell steady state characteristic
More on the dependence on temperature and insolation:
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30. More complex steady-state models
For a more realistic representation we can consider the following (equivalent to a diode’s model):
1) Effect current leakage
2) Effect of internal ohmic resistance
ISC Rp + + RS Vd V
ISC
where
Vd = V+IRS
This is a transcendental equation - -
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31. PV more complex steady-state model
Both effects can be combined to obtain the more realistic (and complex) steady state model: + + RS
ISC Rp Vd V - -
where
Vd = V+IRS
This is a transcendental equation
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32. Dynamic effects
Capacitive effect
As with any diode, there is an associated capacitance. However, this capacitance is relatively small, so the effects on the output can often be neglected. Therefore, PV modules can follow a rapidly changing load very well.
One undesirable effect of the capacitance is that it makes PV cells more susceptible to indirect atmospheric discharges.
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33. More modules (or cells) in series
Modules combination
PV cells are combined to form modules (panels). Modules may be combined to form arrays.
More modules (or cells) in series
More modules (or cells) in parallel
When modules are connected in parallel, the array voltage is that of the module with the lowest voltage.
When several modules are connected in series to achieve a higher array voltage, the array’s current equals that of the module delivering the lowest current.
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34. Shading A shadowed module degrades the performance of the entire array-
A shadowed module degrades the performance of the entire array
(Rp+Rs)(n-1)Imodule + +
One module with 50% shadow
One module with 100% shadow
(n-1)Vmodule
Two modules with 100% shadow -
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35. Bypass diode
Bypass diodes can mitigate the effects of shadows but they don’t solve the issue completely.
A better solution will be presented when discussing power electronics interfaces.
No shade
Shaded without bypass diode
Shaded with bypass diode
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36. Low-power wind generation
For microgrids, power output of each generation unit in the order of a few kW. However, there are cases in which wind turbines with a capacity of hundreds of kW have been used for microgrids.
Power profile is predominately stochastic.
Originally they were used for nautical and rural applications with dc generators. Cost is relatively low.
More modern systems use permanent-magnet generators.
SW Windpower
Whisper 200
1 kW
Rotor diameter: 2.7 m
Air-X 400
400 W
Rotor diameter: 1.15 m
LNP
5 kW
Rotor diameter: 6.4 m
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37. Low-power wind generation
Bergey Excel
7.5 kW
Rotor diameter: 6.4 m
SW Windpower
Whisper 500
3 kW
Rotor diameter: 4.5 m
Solerner
3 kW
YM-CZ3kW
3 kW
Wind generators
In Tokyo
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38. Average wind power in the US
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39. Average wind power in Europe
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40. Generators: Synchronous machine
Output: ac. Electric frequency depends on the rotor angular speed.
Requires a dc input.
Ideally Pmec,in = Pelect,out
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41. Generators: Dynamos (Brushed dc generator)
Output: ac + dc. AC component electric frequency depends on the rotor angular speed.
Important maintenance and reliability issues caused by the brushes
Ideally Pmec,in = Pelect,out
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42. Brushless/Permanent magnet generators
Output: ac. Electric frequency depends on the rotor angular speed.
No issues with brushes
Ideally Pmec,in = Pelect,out
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43. Wind generators model
The output in all types of generators have an ac component.
The frequency of the ac component depends on the angular speed of the wind turbine, which does not necessarily matches the required speed to obtain an output electric frequency equal to that of the grid.
For this reason, the output of the generator is always rectified.
The rectification stage can also be used to regulate the output voltage.
If ac power at a given frequency is needed, an inverter must be also added.
There are 2 dynamic effects in the model: the generator dynamics and the wind dynamics.
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44. Wind power
Consider a mass m of air moving at a speed v. The kinetic energy is
Then power is
The last expression assumes an static wind behavior (i.e. v is constant)
The mass flow rate dm/dt is
Thus,
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45. Typical Power-speed characteristics
SW Windpower
Whisper 200
1 kW
Rotor diameter: 2.7 m
SW Windpower
Whisper 500
3 kW
Rotor diameter: 4.5 m
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46. Conversion efficiency
In the previous slide, power does not varies with the cube of the wind speed. Why?
Because not all the wind power is transmitted through the blades into the generator.
Consider the next figure: vb
Downwind vd
Upwind
Rotor area A vu
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47. Conversion efficiency
The wind energy “absorbed” by the wind turbine rotor equals the kinetic energy lost by the wind as it pass through the blades. Hence, the energy transmitted by the wind to the rotor blades is the difference between the upwind and the downwind kinetic energies:
In the last equation it is assumed that there is no turbulence and the air passes through the rotor as a steady rate.
If it is assumed that vb is the average between vu and vd, then the mass flow rate is
If we define the ratio
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48. Conversion efficiency
Then
The rotor efficiency is maximum when λ is 1/3. For this value, Cp is
Still, we still need to know how much of the “absorbed” power by the blades is transmitted to the generator. This conversion stage is characterized based on the tip-speed ration (TSR):
Power in the wind
Fraction extracted
Rotor efficiency Cp
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49. Conversion efficiency
From the course’s recommended book
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50. Variable rotor speeds
The maximum power point changes as the rotor speed changes.
From the course’s recommended book
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51. Wind stochastic nature
Wind speed probability (then generated power, too) is an stochastic function.
Wind speed probability can be represented using a Rayleigh distribution, which is a special case of a Weibull distribution.
The Rayleigh distribution appears when a 2-dimentional vector has characteristics that:
are normally distributed
are uncorrelated
have equal variance.
A typical probability density distribution
for wind speed is shown next. Rayleigh
distributions approximates these curves.
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52. Wind stochastic nature
The Rayleigh probability density function is given by
where c is a parameter.
The average value of the random variable (wind speed v) is
The average power is If
Then
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