Physics and Astronomy Outreach Program at the University of British Columbia Renewable And Clean Energy Wind Turbines Lecture Notes
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Physics and Astronomy Outreach Program at the University of British Columbia
Renewable
And Clean
Energy
Wind Turbines
Lecture Notes
Wind
Turbines
1) How much energy is available in
wind?
2) How is a useful amount of energy (or
power) extracted using wind turbine
technology?
Physics and Astronomy Outreach Program at the University of British Columbia
Physics and Astronomy Outreach Program at the University of British Columbia
Wind energy:
• Proposed alternative energy source
• Is in the early stages of large scale
development
• Used in Persia as early as 500 AD to
grind grain and pump water
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• The question to ask in this early stage
of large scale development:
Is it possible to extract a useful amount
of raw energy from the wind?
• We will consider constraints of time,
location and machinery.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Is there enough energy in wind?
• First, it is important to make the
distinction between kinetic energy and
power.
Kinetic energy: The energy resulting
from the movement of masses.
Power: The rate of doing useful work.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Wind possesses a lot of kinetic
energy, but the rate at which this
energy can be extracted limits the
amount of useful power available.
• How much power can be harnessed
from wind?
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Wind energy comes from a series of
energy transformations from solar
energy (radiation) to wind energy
(kinetic).
• About 2% of the solar energy
absorbed by the earth goes into wind.
• Solar radiation is absorbed by the
surface of the earth and heats it
unevenly.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Uneven heating:
o Intensity of solar energy varies due to
the angle of the Sun (the equator vs.
the poles).
o Land heats up faster than water does,
but also loses heat faster (inland vs.
coast).
• These differences in air temperature
across the globe can create wind!
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 1. A wind energy map of Canada showing the average power
(in W/m2) that can theoretically be extracted from the wind.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• solar intensity at the top of the earth's
atmosphere = 350 W/m2.
• Given that only 2% is converted to wind
thus ~ 7 W/m2 goes into wind energy.
• 35% of wind energy (2.45 W/m2) is
dissipated in the first kilometre above
Earth's surface and available for
turbines.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Over a period of one year, the wind energy (E)
is approximately...
E = intensity ∙ Earth's SA ∙ seconds per year
= (2.45 W/m2) (5.1 x 1014 m2) (3.2x107 s)
= 4.0 x 1022 J
...which is 200 times larger than our energy
consumption on Earth, estimated to be
2 x 1020 J.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Calculate the power extracted from
wind.
• Calculate kinetic energy, KE = ½mv2 of
air passing through the rotor of the wind
turbine.
• Measure mass of air travelling through
area of circle swept out by rotor blades
in time Δt.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 2. At time t = 0, the mass of air is just about to pass through the hoop, but
Δt later, the mass of air has passed through the hoop. The mass of this piece of air
is the product of its density ρ, area A, and length v ∙ Δt.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
From this you can find the mass...
mass
ρ is the density of the air (1.2 kg/m3 for standard
temperature and pressure)
v is the velocity of the air
Δt is the length of time for a unit of air to pass through
the loop.
A is the area swept by the blades, not the blade area.
Wind
Turbines
density volume
Avt
Physics and Astronomy Outreach Program at the University of British Columbia
Therefore the kinetic energy, K, is found
to be:
while the power of the wind passing
through our hoop is:
Wind
Turbines
K 1
2mv2
1
2Atv 3
P 1
2
Atv 3
t1
2Av 3
Physics and Astronomy Outreach Program at the University of British Columbia
• But turbines can’t extract all of the
kinetic energy of the wind.
Why not?
• If this was the case the air would stop
as soon as it passed through the blades
and no other wind would be able to
pass through.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• But you cannot capture more than
59.3% (2/3) of wind’s energy (Betz,
1919).
• maximum ratio of P/P0 = 2/3 is found at
v2/v1 ≈ 1/3.
• Ideally you want the turbine to slow the
wind down by 2/3 of its original speed.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 3.The plot agrees with Betz’s conclusions that the
maximum power output (of 59.3%) occurs when v2 is 1/3 of v1.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Wind turbines are not 100% efficient:
power = efficiency ∙ max power extracted
where d is the diameter of the circle covered
by the rotor.
Wind
Turbines
23
2
3
3
8
1
22
1
2
1
dv
dv
AvP
Physics and Astronomy Outreach Program at the University of British Columbia
• This expression is true for a single wind
turbine in constant wind conditions.
• In real life, however, wind conditions
change.
What local conditions must be satisfied
in order to make the use of wind
turbines feasible?
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Wind turbines are most efficient when
wind moves uniformly in the same
direction.
• Turbulence is caused by buildings,
trees, and land formations.
• The edge of a continental shelf, high
ground and tundra have low turbulence
and are the best locations to build a
turbine.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Local wind speed is also an important
factor since:
power α (wind speed)3
• The local wind speed should be, on
average, at least 7 m/s at 25 m above
the earth’s surface in order to make
harnessing wind from it worthwhile.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Demand and dependability are
important.
• Wind is not locally predictable in the
short term, and so its use should be
limited to only fulfill 5 – 15% of the total
energy demand of the area.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Setting up turbines in several locations
makes wind energy more reliable.
• The available power is averaged out.
• Globally there is always a relatively
constant amount of wind energy being
harnessed at any one moment.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• The machinery of a wind turbine also
limits how much power can be
extracted from wind.
• Some terminology: foundation, tower,
nacelle and rotor. (See Figure 4 on next
slide)
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 4. A turbine is composed of a foundation, a tower,
a nacelle and a rotorconsisting of 3 blades.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• The wind turns the rotor, which turns
the generator to produce electricity.
• To maximize the power extracted, the
nacelle, which connects the rotor to the
tower and houses the generator, can be
rotated into the direction of the wind.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 5. The dimensions and characteristics of a typical smaller
sized turbine.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• The power produced by a wind turbine
depends on:
• rotor area
• air density
• wind speed
• wind shear.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Wind shear is a difference in wind
speed and direction over a short
distance and is caused by mountains,
coastlines and weather patterns.
• Air density increases with colder
temperatures, decreased altitude, and
decreased humidity.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Wind speed increases the farther you
get away from the ground.
• To maximize the power output of wind
turbines, rotors are tilted slightly
upwards.
Why do you think this is?
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 6. As you get higher off the ground, the air speed increases, corresponding
to a longer arrow. The rotors are tilted slightly upwards so that each part of the
rotor is exposed to the same speed.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Cities and countries need huge wind
farms to satisfy their energy needs.
• To optimize energy production in a wind
farm, turbines are spread 5 – 9 rotor
diametres apart in the prevailing wind
direction and 3 – 5 rotor diameters
apart in the perpendicular direction (Fig.
7).
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
Figure 7. On a wind farm, turbines must be spaced out enough so that they do not
interfere with each other. As the wind passes through the turbine it slows down,
and so there is no point in putting a turbine in the region where the air is
guaranteed to be slow. One common way of spacing them out is ensuring there is
at least 5 rotor diametres between each turbine.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
When the turbines are placed on a square grid,
the power per unit land area is:
where n is the number of turbine diametres
between turbines.
Wind
Turbines
2
23
8
1
nd
dv
arealand
power
Physics and Astronomy Outreach Program at the University of British Columbia
• The average power of a wind turbine
farm is the product of the capacity of
the farm and the fraction of the time
when the wind conditions are near
optimal.
• The capacity factor is usually around
15 – 30%.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Now that it is established that wind is a
possible source of power, the benefits
and drawbacks need to be considered.
Why use wind power in lieu of other
energy sources?
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• Harnessing wind power does not produce
hazardous wastes, use non-renewable
resources or cause significant amounts of
damage to the environment.
• Some CO2 is produced in the
manufacturing of the turbines, but it is
much less than the emissions from
burning an energy-equivalent amount of
coal or natural gas.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
• The use of wind power can reduce
hidden costs such as those related to
pollution and in the longer term, climate
change.
• Since you can farm around them, wind
turbines use less space than traditional
power stations.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
So why, in light of these positive elements,
is there so much resistance against wind
turbines?
•Arguments against include fears of
damages from collapsing turbines, noise, a
less attractive skyline, an unreliable power
source, unnecessarily high bird fatality, and
significantly modifying the Earth’s wind
patterns.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
DISCLAIMERS
• Noise: the noise of a typical turbine is
45 dB at 250 m away. This level is
lower than the background noise at an
office or a home.
• Reliability: the reliability of wind energy
increases depending on location and
how many farms are operating in a
variety of sites within the area.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
DISCLAIMERS
• Birds: in the US less than 40,000 are said
to die from turbine blades while hundreds
of millions are said to die from domestic
cats!
• Earth’s climate: it is plausible that one
would see local climate change
surrounding areas with concentrated wind
farms, but the large-scale climatic effects
will likely be negligible.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
DISCLAIMERS
• Earth’s climate: wind turbines would be
replacing coal-fired power plants, so if
anything, we anticipate a considerable
reduction in CO2 emissions.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
1. Siemens Energy and Automation, Inc. Wind Turbine (online).
http://www2.sea.siemens.com/NR/rdonlyres/1F91AFE0-BB27-4D13-
91F7-153AEA0D6C98/0/WindTurbine.jpg [9 June 2009].
2. Cullum A, Kwan C, Macdonald K. British Columbia Wind Energy
Feasibility Study (online).
http://www.geog.ubc.ca/courses/geog376/students/class05/cskwan/int
ro.html [4 May 2009].
3. Dodge, Darrel. Part 1 - Early History Through 1875: Wind Power's
Beginnings (online). Illustrated History of Wind Power Development.
http://www.telosnet.com/wind/early.html [10 June 2009].
4. Aubrecht GJ. Solar Energy: Wind, Photovoltaics, and Large-Scale
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Education Inc., 2006, chapt. 21, 461-465.
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Circulation System. In: The Earth System (2), edited by Patrick Lynch.
Upper Saddle River, New Jersy, USA: 2004, chapt. 4, pp. 55-82.
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
6. Environment Canada. Canadian Atlas Level 0 (online).
http://collaboration.cmc.ec.gc.ca/science/rpn/modcom/eole/Canadian
Atlas0.html [20 May 2009].
7. Gustavson MR. Limits to Wind Power Utilization. Science 204: 13 –
17, 1979.
8. MacKay DJC. Sustainable Energy – Without the Hot Air (Online). UIT
Cambridge.
http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/253.326.p
df [4 May 2009].
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(online). http://www.windpower.org/en/tour.htm [4 May 2009].
10.Learning (online). Solacity Inc.
http://www.solacity.com/SiteSelection.htm [20 May 2009].
11.D’Emil B, Jacobsen M, Jensen MS, Krohn S, Petersen KC, and
Sandstørm, K. Wind with Miler (online). Danish Wind Industry
Association. http://www.windpower.org/en/kids/index.htm [4 May
2009].
Wind
Turbines
Physics and Astronomy Outreach Program at the University of British Columbia
12.Clarke S. Electricity Generation Using Small Wind Turbines At Your
Home Or Farm (Online). Ontario Ministry of Agriculture, Foods and
Rural Affairs. http://www.omafra.gov.on.ca/english/engineer/facts/03-
047.htm#noise [25 May 2009].
13.Marris E and Fairless D. Wind Farms' Deadly Reputation Hard to
Shift. Nature 447: 126, 2007.
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Calgary. http://www.ucalgary.ca/~keith/WindAndClimateNote.html [20
May 2009].
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Wind
Turbines
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