Transcript Class notes (physical)

1
Cyber Physical Power Systems
Fall 2015
Microgrids and Smart Grids
© A. Kwasinski, 2015
Distributed Generation: Concept (a first approach) 2
• Microgrids are independently controlled
(small) electric networks, powered by local
units (distributed generation).
© A. Kwasinski, 2015
Distributed Generation: Concept (newest DOE def.)3
• What is a microgrid?
• Microgrids are considered to be locally confined and independently
controlled electric power grids in which a distribution architecture integrates
loads and distributed energy resources—i.e. local distributed generators
and energy storage devices—which allows the microgrid to operate
connected or isolated to a main grid
© A. Kwasinski, 2015
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4
Microgrids
• Distributed Generation: Advantages
With respect to the traditional grid, well designed microgrids are:
• Higher availability (with diverse power inputs).
• More efficient
• More environmentally friendly
• More flexible
• Less vulnerable
• More modular
• Easier to control
• Immune to issues occurring elsewhere
• Capital investment can be scaled over time
• Microgrids can be integrated into existing systems without having to interrupt
the load.
• Microgrids allow for combined heat and power (CHP) generation.
© A. Kwasinski, 2015
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Microgrids
5
• Distributed Generation: Issues
• Load following
• Power vs Energy profile in energy storage
• Stability
• Cost
• Architecture / design
• Optimization
• Autonomous control
• Fault detection and mitigation
• Cost
• Grid interconnection
© A. Kwasinski, 2015
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Distributed Generation: System Components
Generation units = microsources ( aprox. less than 100 kW)
• PV Modules.
• Small wind generators
• Fuel Cells
• Microturbines
Energy Storage (power profile)
• Batteries
• Ultracapacitors
• Flywheels
Loads
• Electronic loads.
• Plug-in hybrids.
• The main grid.
Power electronics interfaces
• dc-dc converters
• inverters
• Rectifiers
© A. Kwasinski, 2015
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Microgrids
• Application range:
• From a few kW to MW
© A. Kwasinski, 2015
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Microgrids
8
• What is not a microgrid?
• Residential conventional PV systems (grid-tied) are not
microgrids but they are distributed generation systems.
• Why are they not microgrids? Because they cannot operate
isolated from the grid. If the grid experience a power outage the
load cannot be powered even when the sun is shinning bright
on the sky.
© A. Kwasinski, 2015
Distributed Generation and Smart Grids
• European concept of smart grids based on electric networks needs
[http://www.smartgrids.eu/documents/vision.pdf]:
• Flexible: fulfilling customers’ needs whilst responding to the changes and
challenges ahead;
• Accessible: granting connection access to all network users, particularly
for renewable power sources and high efficiency local generation with zero
or low carbon emissions;
•Reliable: assuring and improving security and quality of supply, consistent
with the demands of the digital age with resilience to hazards and
uncertainties;
• Economic: providing best value through innovation, efficient energy
management and ‘level playing field’ competition and regulation
• The US concepts rely more on advanced interactive communications and
controls by overlaying a complex cyberinfrastructure over the existing grid. DG
is one related concept but not necessarily part of the US Smart Grid concept.
© A. Kwasinski, 2015
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Smart grids
Smart grids definition:
• Besides being the new buzz word is not a concept but rather many
technologies.
Smart grid focus:
• Reliability.
• Integration of environmentally friendly generation and loads.
Concept evolution:
• “Smart grid 1.0”: Smart meters, limited advanced communications, limited
intelligent loads and operation (e.g. demand response).
• “Smart grid 2.0” or “Energy Internet”: Distributed generation and storage,
intelligent loads, advanced controls and monitoring.
• Future smart grid: integration among infrastructures in smart cities.
Examples:
• Water, natural gas, transportation and electricity,
• Internet of Things
© A. Kwasinski, 2015
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Smart Grids
11
• A customer-centric view of a power grid includes microgrids as one of
smart grids technologies.
© A. Kwasinski, 2015
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Microgrids
Power Generation Technologies
© A. Kwasinski, 2015
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Microsources
• Most common microsources:
Small wind turbine (<10
kW/turbine)
Microturbine (<100 kW/unit)
Reciprocating Engine – e.g.
diesel generator (<100
kVA/unit)
Fuel Cell (<400 kW/unit)
PV Module (<250 W/module)
© A. Kwasinski, 2015
Real microsources
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Wind turbines +
PV modules
PAFC
Microturbines
MCFC
© A. Kwasinski, 2015
Ideal sources
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Characteristics:
• For a voltage (current) source, the internal impedance is zero (infinity):
• No internal losses.
• Instantaneous dynamic response.
• For an ideal voltage source, current has no effect on the voltage output:
• The output voltage value and waveform are always the same regardless
of the load.
• For current sources replace current by voltage in the last statement.
• An ideal capacitor with an infinite capacitance behaves as a dc voltage
source.
dv
q
C
v
i C
dt
• An ideal inductor with an infinite inductance behaves as a dc current source.
L

i
vL
© A. Kwasinski, 2015
di
dt
Fuel Cells Basics
16
• Fuel cells convert chemical energy directly into electrical energy.
• Difference with batteries: fuel cells require a fuel to flow in order to produce
electricity.
• Heat is produced from chemical reaction and not from combustion.
• Types of fuel cells:
• Proton exchange membrane (PEMFC)
• Direct Methanol fuel cell (DMFC)
• Alkaline fuel cell (AFC)
• Phosphoric acid fuel cell (PAFC) (*)
• Molten-carbonate fuel cell (MCFC) (*)
• Solid-oxide fuel cell (SOFC) (*)
(*) Best suited for microgrids.
© A. Kwasinski, 2015
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Fuel cells operation
• Example: PEMFC
• The hydrogen atom’s electron and proton are separated at the anode.
• Only the protons can go through the membrane (thus, the name
proton exchange membrane fuel cell).
dc current
Heat
Oxygen
Hydrogen
Water
Catalyst (Pt)
Anode (-)
Membrane
(Nafion)
Catalyst (Pt)
Cathode (+)
H 2  2 H   2e 
1/ 2O2  2 H   2e   1H 2O
O2  2H 2  2H 2O
© A. Kwasinski, 2015
(Er  1.23 V )
PEMFC output: Tafel equation
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• The Tafel equation yields the cell’s output voltage Ec considering additional
loosing mechanisms:
Ec  Er  b log(i / i0 )  ir
• The first term is the reversible cell voltage (1.23V in PEMFCs)
• The last term represents the ohmic losses, where i is the cell’s current density,
and r is the area specific ohmic resistance.
• The second term represent the losses associated with the chemical kinetic
performance of the anode reaction (activation losses). This term is obtained
from the Butler-Volmer equation and its derivation is out of the scope of this
course.
• In the second term, i0 is the exchange current density for oxygen reaction and
b is the Tafel slope:
RT
b
n  log( e)
© A. Kwasinski, 2015
PEMFC output: Tafel equation
19
• In the last equation R is the universal gas constant (8.314 Jmol-1K-1), F is the
Faraday constant, T is the temperature in Kelvins, n is the number of electrons
per mole (2 for PEMFC), and β is the transfer coefficient (usually around 0.5).
Hence, b is usually between 40 mV and 80 mV.
• The Tafel equation assumes that the reversible voltage at the cathode is 0 V,
which is only true when using pure hydrogen and no additional limitations, such
as poisoning, occur.
• The Tafel equation do not include additional loosing mechanisms that are
more evident when the current density increases. These additional mechanisms
are:
• Fuel crossover: fuel passing through the electrolyte without reacting
• Mass transport: hydrogen and oxygen molecules have troubles reaching
the electrodes.
• Tafel equation also assumes that the reaction occurs at a continuous rate.
© A. Kwasinski, 2015
PEMFC electrical characteristics
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Er = 1.23 V
Maximum power
operating point
Er =1.23V
b=60mV,
i0=10-6.7Acm-2
r=0.2Ωcm2
Activation loss
region
Ohmic loss region
(linear voltage to current
relationship)
Actual PEMFCs efficiency vary between 35% and 60%
© A. Kwasinski, 2015
Mass transport loss region
PEMFC electrical characteristics
• A very good dynamic model of a PEMFC is discussed in: Wang, Nehrir, and
Shaw, “Dynamic Models and Model Validation for PEM Fuel Cells Using
Electrical Circuits.” IEEE Transactions on Energy Conversion, vol 20, no. 2,
June 2005.
• Some highlight for this model:
Basic circuit
• Rohm: represents ohmic losses
• Ract: represents the activation losses (related with 2nd term in Tafel equation)
• Rconc: losses related with mass transport.
• C: capacitance related with the fact that there are opposing charges buildup
between the cathode and the membrane.
© A. Kwasinski, 2015
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PEMFC electrical characteristics
22
• Model for the internal fuel cell voltage E
Equal to Er


N cell RT
where, f1 ( I , T )  
ln pH* 2 pO* 2  N cell k E (T  298)
2F
f 2 ( I )  N cell Ed ,cell
• Comments:
• The voltage drop related with fuel and oxidant delay is represented by
Ed,cell.
•The fuel cell output voltage depends on hydrogen’s and oxygen’s pressure
• The fuel cell output voltage also depends on the temperature.
• The time constants for these chemical, mechanical, and thermodynamic
effects are much larger than electrical time constants.
© A. Kwasinski, 2015
PEMFC electrical characteristics
23
• Ed,cell can be calculated from the following dynamic equation:
 es
dEd ,cell (t ) 1
di (t )
Ed ,cell ( s)  e I( s)


 Ed ,cell (t )  e
 es  1
dt
e
dt
where τe is the overall flow delay.
• In steady state, both derivatives are zero, so Ed,cell = 0. But when the load
changes, di(t)/dt is not zero, so Ed,cell will be a non-trivial function of time that will
affect the fuel cell internal output voltage.
•When considering fuel cells dynamic behavior, they all tend to have a slow
response caused by the capacitance effect in slide 21, the flow delays, the
mechanical characteristics of the pumps, and the thermodynamic
characteristics.
• Influence of temperature dynamics on fuel cell output is an important cause for
fuel cells slow response.
© A. Kwasinski, 2015
PEMFC Technology and issues
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• Expected life of PEMFC is very short (5,000 to 10,000 hours) and not suitable
for DG.
• The most commonly used catalyst (Pt) is very expensive.
• The most commonly used membrane (Nafion – a sulfonated tetrafluorethylene
copolymer is also very expensive).
• PEMFCs are very expensive.
• CO poisoning diminishes the efficiency. Carbon monoxide (CO) tends to bind
to Pt. Thus, if CO is mixed with hydrogen, then the CO will take out catalyst
space for the hydrogen.
• Hydrogen generation and storage is a significant problem.
• Additional issues to be discussed when comparing other technologies:
dynamic response and heat production.
© A. Kwasinski, 2015
Direct Methanol Fuel Cells (DMFC)
• The main advantage is that they use a liquid fuel.
• Reactions:
• Anode CH 3OH  H 2O  CO2  6 H   6e 
• Cathode 1/ 2O2  2 H   2e   H 2O
• Voltages: 0.046 V at anode, 1.23 V at cathode, 1.18 V overall.
• Methanol has high energy density so DMFC are good for small portable
applications.
• Issues:
• Cost
• Excessive fuel crossover (methanol crossing the membrane)
• Low efficiency caused by methanol crossover
• CO poisoning
• Low temperature production
• Considerable slow dynamic response
© A. Kwasinski, 2015
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Phosphoric Acid Fuel Cells (PAFCs)
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• One of their main advantages is their long life in the order of 40,000 hours.
•The phosphoric acid serves as the electrolyte.
• The reactions are the same than in a PEMFC. Hence, the reversible voltage is
1.23 V
• The most commercially successful FC: 200 kW units manufactured by UTC
• They produce a reasonable amount of heat
• They support CO poisoning better than PEMFC
• They have a relatively slow dynamic response
• Relative high cost is an important issue
© A. Kwasinski, 2015
Alkaline Fuel Cells (AFCs)
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• The main advantage is that their cost is relatively low (when considering the
fuel cell stack only without “accessories”.
• Reactions:
• Anode
H 2  2OH   2 H 2O  2e 
• Cathode 1/ 2O2  2 H 2O  2e   2OH 
• Developed for the Apollo program.
• Very sensitive to CO2 poisoning. So these FCs can use impure hydrogen but
they require purifying air to utilize the oxygen.
• Issues:
• Cost (with purifier)
• Short life (8000 hours)
• Relatively low heat production
© A. Kwasinski, 2015
Molten Carbonate Fuel Cells (MCFCs)
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• One of the main advantages is the variety of fuels and catalyst than can be
used.
• Reactions:
2

• Anode H 2  CO3  H 2O  CO2  2e

2
• Cathode 1/ 2O2  CO2  2e  CO3
• They operate at high temperature. On the plus side, this high temperature
implies a high quality heat production. On the minus side, the high temperature
creates reliability issues.
• They are not sensitive to CO poisoning.
• They have a relatively low cost.
• Issues:
• Extremely slow startup
• Very slow dynamic response
© A. Kwasinski, 2015
Solid Oxide Fuel Cells (SOFCs)
• One of the main advantages is the variety of fuels and catalyst than can be
used.
• Reactions:
H 2  O 2   H 2O  2 e 
• Anode

2
• Cathode 1/ 2O2  2e  O
• They operate at high temperature with the same plus and minus than in
MCFCs.
• They are not sensitive to CO poisoning.
• They have a relatively low cost.
• They have a relatively high efficiency.
• They have a fast startup
• The electrolyte has a relatively high resistance.
© A. Kwasinski, 2015
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Microturbines
• Microturbines are essentially low-power versions of traditional gas turbines
used in large power plants.
• Typical power outputs of microturbines range from a few tens of kW to a few
hundred of kW.
• Natural gas is the most common fuel, but other hydrocarbons, such as
kerosene, or bio-fuels can be used, too.
Exhaust
Recuperator
Natural Gas
Air
Combustion
Chamber
Generator
Compressor
Turbine
© A. Kwasinski, 2015
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Microturbines
Capstone
30 kW and 60 kW units
Ingersoll
70 kW Induction microturbine
250 kW synchronous microturbine
Wilson TurboPower
300 kW
Mariah Energy
30 kW and 60 kW units
© A. Kwasinski, 2015
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Microturbines
32
• Moderate cost and efficiency
• High-frequency output is rectified (and inverted again in ac microgrids).
Generator output frequency is in the order of a few kHz (e.g. 1600 Hz for
Capstone’s 30 kW microturbine).
• Power shaft rotates at high speeds, usually on the order of 50 000 to 120 000
rpm
• Very reliable technology (Essentially microturbines are aircraft’s APU’s).
Critical parts: bearings and generator.
• Generator technologies: Synchronous and permanent magnet
• Moderately fast dynamic response
© A. Kwasinski, 2015
Microturbines
http://www.energy.ca.gov/distgen/equipment/microturbines/microturbines.html
Oak Ridge National Laboratory; ORNL/TM-2003/74
© A. Kwasinski, 2015
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34
Brayton Cycle
• Gas turbines operation follow a Brayton cycle
4
1
2
© A. Kwasinski, 2015
3
Brayton Cycle
• From the previous slide:
P4 P1

P3 P2
•Also, from the previous slide
P 1T   constant
• Thus,
T4 T1

T3 T2
© A. Kwasinski, 2015
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Brayton Cycle
• It can be shown that
36
P4 P1

P3 P2
P 1T   constant
T4 T1

T3 T2
• Then, the simplified expression for the efficiency is
  1
T1
T2
• Usually, the efficiency is expressed in terms of the temperature ratio (TR) or
the pressure ratio (PR)
1
1
  1
 1
(TR)
( PR)( 1) / 
where (TR) 
T2
P
and ( PR)  2
T1
P1
© A. Kwasinski, 2015
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Microturbine characteristics
• The efficiency is improved if T2 is increased. The recuperator is used for that
purpose. Other ways of preheating the air before the combustion stage could
be to use heat from a fuel cell.
• The efficiency decreases as the input temperature increases:
Capstone C30 datasheet
Ingersoll 70L datasheet
© A. Kwasinski, 2015
Reciprocating engines
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• This is likely the most common DG technology.
• Some types of reciprocating engines are the internal combustion engines and
the Stirling engines.
• Types of internal combustion engines:
• Spark ignition (fuel: natural gas)
• Compression ignition (fuel: diesel)
• The engines are used to drive synchronous or permanent magnet generators.
http://www.energy.ca.gov/distgen/equipment/reciprocating_engines/reciprocating_engines.html
© A. Kwasinski, 2015
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Spark Ignition engines
• Natural gas is the most commonly used fuel.
• Thermodynamically they follow an Otto cycle with 4 strokes:
• 1. intake (induction) stroke
• 2. compression stroke
• 3. power stroke: combustion/expansion
• 4. exhaust stroke
• Efficiency:   1 
1
r  1
r is the compression ratio V1/V2
http://en.wikipedia.org/wiki/Imag
e:4-Stroke-Engine.gif#file
© A. Kwasinski, 2015
Compression Ignition engines
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• Diesel is the most commonly used fuel.
• Thermodynamically they follow a Diesel cycle
• 1. intake (induction) stroke
• 2. compression stroke
• 3. power stroke
• 4. expansion stroke


1

1 
• Efficiency:   1 


r  1   (  1) 
r is the compression ratio V1/V2 and α is the ratio V3/V2
http://library.thinkquest.org/C006
011/english/sites/diesel.php3?v=2
More animated engines:
http://library.thinkquest.org/C006
011/english/sites/animations.php3
?v=2
© A. Kwasinski, 2015
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
© A. Kwasinski, 2015
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Photons’ Journey into Electricity
42
• 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.
•The most common Hydrogen fusion 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 and will die as a white dwarf.
© A. Kwasinski, 2015
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
• Wavelength for the maximum:
2898
max (  m) 
T
For the Sun it approximately
equals 0.5 μm
© A. Kwasinski, 2015
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Photons’ Journey into Electricity
• Photons reach Earth in an uneven distribution.
US Solar Insolation Map: NREL
© A. Kwasinski, 2015
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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
© A. Kwasinski, 2015
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Photons’ Journey into Electricity
46
• 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.
© A. Kwasinski, 2015
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
© A. Kwasinski, 2015
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Photons’ Journey into Electricity
48
• 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
I C  I BC  I DC  I RC
© A. Kwasinski, 2015
Photons’ Journey into Electricity
49
• 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.
© A. Kwasinski, 2015
Photons’ Journey into Electricity
• Atom’s energy model:
Eg
Forbidden band
Filled band
Gap
Filled band
Conduction band
(Empty at T = 0K)
Electron Energy
Electron Energy
Conduction band
(partially filled)
Metals
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
© A. Kwasinski, 2015
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Photons’ Journey into Electricity
51
• if the last equation is plotted we obtain that
Lost in heat
From Master’s book on alternative energy
• 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 Master’s book on alternative energy
© A. Kwasinski, 2015
Photons’ Journey into Electricity
52
• Efficiency limit can be understood by comparing the following two figures:
http://en.wikipedia.org/wiki/Image:EffectiveTemperature_300dpi_e.png
From Master’s book on alternative energy
Excess
energy
• So for an air mass ratio of 1.5 the efficiencies are (see next slide)
© A. Kwasinski, 2015
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.
© A. Kwasinski, 2015
53
PV Cells Technologies
54
• 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)
© A. Kwasinski, 2015
55
PV Cells Technologies
Uni-Solar solar shingle
BP SX170B Polycrystalline
BP SX170B Monocrystalline
Uni-Solar Laminate PVL-136
Amorphous
Mitsubishi PV-TD 190MF5
Multicrystalline
PV Modules at ENS
© A. Kwasinski, 2015
PV Cells Technologies
56
• 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)
© A. Kwasinski, 2015
The p-n junction diode
n-type substrate
Bias voltage
p-type substrate
Id
• Vd is the diode voltage
• I0 is the reverse saturation current caused by
thermally generated carriers
• At 25 C:
Vd
 0.026

Id  I0  e
 1


Ideal diode
Real diode
I0
© A. Kwasinski, 2015
57
d
 qV

kT
I d  I 0  e  1


PV Cells physics
58
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
ISC
p-n junction is
equivalent to
a diode
© A. Kwasinski, 2015
Reverse v-i
curve for the
diode
PV Cell steady state characteristic
• From Kirchoff’s current law:
I PV  I SC  I d  I SC
 qVkTd

 I 0  e  1


• The open circuit voltage is
VOC  V ( I PV

kT  I SC
 0) 
ln 
 1
q  I0

Maximum power point
Power
P  I PVVPV
Pmax  0.7 • Voc • Isc
Current
© A. Kwasinski, 2015
59
PV Cell steady state characteristic
• Dependence on temperature and insolation:
© A. Kwasinski, 2015
60
PV more complex steady-state model
• More realistic (and complex) steady state model:
+
ISC
Rp
RS
Vd
-
+
V
Ideal
I PV  I SC
 qVkTd
 Vd
 I 0  e  1 

 Rp
More realistic
where
Vd = V+IRS
This is a transcendental
equation
© A. Kwasinski, 2015
61
Dynamic effects
62
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.
© A. Kwasinski, 2015
63
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.
© A. Kwasinski, 2015
64
Shading
(Rp+Rs)(n-1)Imodule
• A shadowed module
degrades the performance of
the entire array
+
+
One module with 50%
shadow
One module with 100%
shadow
(n-1)Vmodule
Two modules with 100%
shadow
© A. Kwasinski, 2015
Low-power wind generation
65
• Power output of each generation unit in the order of a few kW. 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
© A. Kwasinski, 2015
LNP 6.4-5000
5 kW
Rotor diameter: 6.4 m
66
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
YM-CZ3kW
3 kW
Solerner
3 kW
Wind generators
In Tokyo
© A. Kwasinski, 2015
Average wind power in the US
http://rredc.nrel.gov/wind/pubs/atlas/maps.html
© A. Kwasinski, 2015
67
Average wind power in Europe
http://www.geni.org/globalenergy/library/renewable-energyresources/europe/Wind/Wind%20Map%20of%20Western%20Europe_files/euromap.gif
© A. Kwasinski, 2015
68
Generators: Synchronous machine
• Output: ac. Electric frequency depends on the rotor angular speed.
• Requires a dc input.
• Ideally Pmec,in = Pelect,out
© A. Kwasinski, 2015
69
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
© A. Kwasinski, 2015
70
Brushless/Permanent magnet generators
• Output: ac. Electric frequency depends on the rotor angular speed.
•No issues with brushes
• Ideally Pmec,in = Pelect,out
© A. Kwasinski, 2015
71
Wind generators model
72
• 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.
© A. Kwasinski, 2015
Wind power
• Consider a mass m of air moving at a speed v. The kinetic energy is
1
WK  mv 2
2
• Then power is
P
dWK 1 dm 2

v
dt
2 dt
The last expression assumes an static wind behavior (i.e. v is constant)
•The mass flow rate dm/dt is
dm
  Av
dt
• Thus,
P
1
 Av3
2
© A. Kwasinski, 2015
73
Typical Power-speed characteristics
74
SW Windpower
Whisper 200
1 kW
Rotor diameter: 2.7 m
SW Windpower
Whisper 500
3 kW
Rotor diameter: 4.5 m
© A. Kwasinski, 2015
75
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
Upwind
vu
© A. Kwasinski, 2015
Downwind
vd
Rotor area
A
Conversion efficiency
76
• 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:
Pb 
d ( Eu  Ed ) 1 dm 2 2

(vu  vd )
dt
2 dt
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
v v
dm
 A u d
dt
2
• If we define the ratio
vd

vu
© A. Kwasinski, 2015
Conversion efficiency
77
• Then
1
 vu   vu
Pb   A 
2
2

1
 2
2 2
3 1
2 
(
v


v
)


Av
(1


)(1


)
d
u 
 u
2
2



Power in
the wind
Fraction
extracted
Rotor efficiency
Cp
• The rotor efficiency is maximum when λ is 1/3. For this value, Cp is 0.593.
• 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):
rotor tip speed rpm    D
(TSR) 

wind speed
60vb
© A. Kwasinski, 2015
Conversion efficiency
© A. Kwasinski, 2015
78
Variable rotor speeds
From Master’s book on alternative energy
• The maximum power point changes as the rotor speed changes.
© A. Kwasinski, 2015
79
Wind stochastic nature
80
• 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.
© A. Kwasinski, 2015
81
Wind stochastic nature
• The Rayleigh probability density function is given by
2v
f (v )  2 e
c
v
 
c
2
where c is a parameter.
• The average value of the random variable (wind speed v) is


0
2
v   v. f (v)dv 
c
• The average power is
Pavg
• If
1
  A(v3 )avg
2

3
6
(v ) avg   v3 f (v)dv  c3   v 3
0
4

3
• Then
Pavg 
61
 Av 3
2
© A. Kwasinski, 2015
Emissions comparison
http://www.raponline.org/ProjDocs/DREmsRul/Collfile/DGEmissionsMay2001.pdf
© A. Kwasinski, 2015
82
DG technologies comparison
Resource Dynamics Corporation, “Assessment of Distributed Generation Technology Applications”, Feb. 2001
© A. Kwasinski, 2015
83