chemical, biological and environmental engineering wind 1
TRANSCRIPT
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Chemical, Biological and Environmental Engineering
Wind 1
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Advanced Materials and Sustainable Energy LabCBEE
How Lift Based Turbines Extract Energy from Fluid
Bernoulli’s Principle - air pressure on top is lower than air pressure on bottom because it has further to travel, creates lift
Airfoil – could be the wing of an airplane or the blade of a wind turbine
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Advanced Materials and Sustainable Energy LabCBEE
Angle of Attack, Lift, and Drag
Increasing angle of attack increases lift, but it also increases drag
When angle of attack is too great, “stall” occurs where turbulence destroys the lift
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Advanced Materials and Sustainable Energy LabCBEE
Wind Turbines“Windmill”- used to grind grain into flour (or pump
water in Holland)
Can have be horizontal axis wind turbines (HAWT) or vertical axis wind turbines (VAWT)
Groups of wind turbines are located in what is called either a “wind farm” or a “wind park”
Important to note: very fast “energy payback” – it takes a few months for a wind turbine to generate (i.e. convert) as much energy as it took to manufacture it!
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Advanced Materials and Sustainable Energy LabCBEE
Lots of ideas, only a few good…
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Advanced Materials and Sustainable Energy LabCBEE
Vertical Axis Wind TurbinesDarrieus rotor - the only vertical axis machine with any
commercial success
Wind hitting the vertical blades (airfoils) generates lift to create rotation
Advantages• No yaw (rotation about vertical axis)
control needed to keep facing into wind
• Heavy machinery located on the ground
Disadvantage• Blades are closer to ground where
windspeeds are lower
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Advanced Materials and Sustainable Energy LabCBEE
Horizontal Axis Wind Turbines“Downwind” HAWT – a turbine with the blades behind
(downwind from) the tower
No yaw control needed- they naturally orient themselves in line with the wind
Shadowing effect – when a blade swings behind the tower, the wind it encounters is briefly reduced and the blade flexes
-Also causes noise
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Advanced Materials and Sustainable Energy LabCBEE
Horizontal Axis Wind Turbines“Upwind” HAWT – blades are in front of (upwind of)
the tower
Most modern wind turbines are this type
Because blades are “upwind” of the tower• Require active yaw control to keep facing into wind• Operate more smoothly and deliver more power
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Advanced Materials and Sustainable Energy LabCBEE
Power in the WindConsider the kinetic energy of a “packet” of air with
mass m moving at velocity v
Divide by time and get power
The mass flow rate is
21KE
2mv
21 passing though APower through area A
2
mv
t
passing though A= = A
mm v
t
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Advanced Materials and Sustainable Energy LabCBEE
Power in the Wind Combining we get
21Power through are A A
2 a v v
31P A
2v
P (Watts) = power in the windρ (kg/m3)= air density (1.225kg/m3 at 15˚C and 1 atm)A (m2)= the cross-sectional area that wind passes throughv (m/s)= windspeed normal to A (1 m/s = 2.237 mph)
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Advanced Materials and Sustainable Energy LabCBEE
Power in the WindPower increases as (wind
speed)3
Doubling the wind speed increases the power by eight
1h x 20mph wind is same energy as 8h x 10 mph wind…-i.e., most power from a turbine is produced at high wind speed for a short time…
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Advanced Materials and Sustainable Energy LabCBEE
Wind Power Classification Scheme
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Advanced Materials and Sustainable Energy LabCBEE
US Wind Resources
http://www.windpoweringamerica.gov/pdfs/wind_maps/us_windmap.pdf
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Advanced Materials and Sustainable Energy LabCBEE
Power in the Wind (cont.)
Power in the wind is also proportional to A
For a conventional HAWT, A = (π/4)D2, so wind power is proportional to the blade diameter squared
Cost is roughly proportional to blade diameter
How do you think cost of wind power scales with turbine diameter?
31P A
2v
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Advanced Materials and Sustainable Energy LabCBEE
Power Curve for Turbine
Cut in speedNot enough energy to justify O&M costs
Cut out speedPark turbine to avoid damage
PlateauGenerator maxed out
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Advanced Materials and Sustainable Energy LabCBEE
Maximum Rotor Efficiency
At the extremes:• Downwind velocity is zero – turbine extracted all of
the energy (for zero time…) • Downwind velocity is the same as the upwind
velocity – turbine extracted no energy…
Albert Betz 1919
Q: What is the ideal extraction of KE from wind so that the turbine extracts the maximum power
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Advanced Materials and Sustainable Energy LabCBEE
Maximum Rotor Efficiency
Consider wind passing though turbine: as energy extracted, air slows down
2 21
2 dP m v v
ṁ = mass flow rate of air within stream tube
v = upwind undisturbed windspeed
vd = downwind windspeed
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Advanced Materials and Sustainable Energy LabCBEE
Mass Flow RateAt the rotor with area A and, mass flow rate is
If velocity through the rotor vb is the average of upwind velocity v and downwind velocity vd
bm Av
= 2 2
d db
v v v vv m A
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Advanced Materials and Sustainable Energy LabCBEE
Power Extracted by the BladesThen power relationship at the rotor could be
Define new parameter l such that
We can rewrite the power relationship as
2 21
2 2d
b d
v vP A v v
dv
v
2 2 21
2 2b
v vP A v v
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Advanced Materials and Sustainable Energy LabCBEE
Power Extracted by the Blades
Power in the wind
2 2 21
2 2b
v vP A v v
3 2 3 3 3 3
- + - 2 2 2 2
v v v v
3
2 = 1 - 12
v
3
2 = 1 12
v
3 21 11 1
2 2bP Av
Rotor efficiency (CP)
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Advanced Materials and Sustainable Energy LabCBEE
Maximum Rotor EfficiencySo what is the windspeed ratio λ which maximizes the
rotor efficiency, CP ?
2 3
21 11 1 = - + -
2 2 2 2 2PC
20 2 1 3PC
3 1 1 0 1
1
3
Plug into CP to find the maximum rotor efficiency:
2
1 1 1 161 1 = 59.3%
2 3 3 27PC
Maximum efficiency of 59.3% when air is slowed to 1/3 of its upstream speed!“Betz limit”
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Advanced Materials and Sustainable Energy LabCBEE
Maximum Rotor Efficiency
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Advanced Materials and Sustainable Energy LabCBEE
Number of Rotating BladesWindmills have multiple blades– need to provide high starting torque to overcome weight
of the pumping rod– must be able to operate at low windspeeds to provide
nearly continuous water pumping– a larger area of the rotor faces the wind
Turbines with many blades must operate at lower rotational speeds – as speed increases, turbulence caused by one blade impacts other blades
Most modern wind turbines have two or three blades
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Advanced Materials and Sustainable Energy LabCBEE
Brush wind turbine
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Advanced Materials and Sustainable Energy LabCBEE
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Advanced Materials and Sustainable Energy LabCBEE
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Advanced Materials and Sustainable Energy LabCBEE
Tip-Speed Ratio (TSR)Efficiency is a function of how fast the rotor turns
Define “Tip-Speed Ratio” (TSR) as ratio of speed of tip of blade to windspeed
Rotor tip speed rpm DTip-Speed-Ratio (TSR) =
Wind speed 60v
D = rotor diameter (m) v = upwind undisturbed windspeed (m/s) rpm = rotor speed, (revolutions/min)
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Advanced Materials and Sustainable Energy LabCBEE
Air moved this farAirfoil interacted with this much air, call it Xs
At it takes for wind to reestablish itselfsw w
w
Xv t
v
2Also, for an n bladed turbine, it takes for
next blade to get to same position
st n
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Advanced Materials and Sustainable Energy LabCBEE
Optimal Tip Speed RatioIf ts<<tw then wind turbine is interacting with disturbed air → low
efficiency
If ts>>tw then turbine does not get to all useful air… → low efficiency
Optimal is if ts≈tw
4Then opt n
1It has been shown (empirically) that wind reestablishes itself in
2SX
r
22 s ws w opt
opt w s
X vt t
n v nX
2Since and then tip opt
tip optw w s
v r rv r
v v nX
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Advanced Materials and Sustainable Energy LabCBEE
Optimal Tip Speed RatioThen for a three bladed turbine,
And for a two bladed turbine
41.33 4.19
3opt
42 6.28
2opt
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Advanced Materials and Sustainable Energy LabCBEE
Tip-Speed Ratio (TSR)Rotors with fewer blades reach their maximum
efficiency at higher tip-speed ratios
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Advanced Materials and Sustainable Energy LabCBEE
Impact of Terrain on Windspeed
We saw power depends on cube of windspeed: small change of wind speed can have large impact
System design must consider effect of terrain friction on wind speed– Important in first few hundred meters above ground level– Smooth surfaces (like water) are better– Windspeeds are greater at higher elevations – tall towers
are better– Forests and buildings slow the wind down a lot
Can we quantify impact of terrain and height on wind speed?
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Advanced Materials and Sustainable Energy LabCBEE
Wind Speed Losses as Function of Terrain
v = windspeed at height H
v0 = windspeed at height H0 (H0 is usually 10 m)
α = friction coefficient
Open terrain, α ≈ 1/7 (0.147)
City, α = 0.4;
Calm water, α = 0.1
0 0
v H
v H
Note this is just an approximation, others exist (ex. von Karman’s log velocity profile)
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Advanced Materials and Sustainable Energy LabCBEE
Impact of Terrain on Wind PowerRemember wind power goes as third power of wind
speed.
3
0
v
v
3
300
12 12
AvP
P Av
3
0
H
H
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Advanced Materials and Sustainable Energy LabCBEE
Impact of Terrain on Wind Power
In a town (a≈0.3), windspeed at 100 m is twice that at 10 mAreas with smoother surfaces have less variation with height
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Advanced Materials and Sustainable Energy LabCBEE
Let’s calculate ratio of power at highest point to lowest point on wind turbine with hub at 50m, 30m diameter rotor, α = 0.2
Power in the wind at the top of the blades is 45% higher!
Can cause significant stress (failure)
Rotor Stress
3 0.2
0
65 = 1.45
35
P
P
50 m
35 m
65 m
Picture may not be to scale
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Advanced Materials and Sustainable Energy LabCBEE
As you may expect, turbines interfere with each other…
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Advanced Materials and Sustainable Energy LabCBEE
Wind FarmsIt makes sense to install a large number of wind
turbines in a wind farm or a wind park
Benefits – Able to get the most use out of a good wind site– Reduced development costs– Simplified connections to the transmission system– Centralized access for operations and maintenance
How many turbines should be installed at a site?
What is a sufficient distance between wind turbines so that windspeed has recovered enough before it reaches the next turbine?
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Advanced Materials and Sustainable Energy LabCBEE
Wind Farms
For closely spaced towers, efficiency of array becomes worse as more wind turbines are added
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Advanced Materials and Sustainable Energy LabCBEE
Wind Farms• Previous figure considered square arrays
(but square arrays don’t make much sense)– Rectangular arrays with only a few long rows are better– Recommended spacing is 3-5 rotor diameters between
towers in a row and 5-9 diameters between rows– Offsetting or staggering the rows is common
• Sites commonly have a prevailing wind direction
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Advanced Materials and Sustainable Energy LabCBEE
Average Power in the WindHow much energy can we expect from a wind turbine?
Remember, power goes as cube of wind speed
Therefore we need to know the average of the cube of wind speed…
I.e., we can’t use average windspeed to find the average power in the wind
3 31 1
2 2avg avgavg
P Av A v
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Advanced Materials and Sustainable Energy LabCBEE
Windspeed probability density function (pdf)
If we had a function f(v) that gave windspeed we could calculate average power in wind…
People have examined statistics of windspeed over various locations
A reasonable approximations is the Weibull distribution
• # of hours/year that the wind is between two windspeeds:
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Advanced Materials and Sustainable Energy LabCBEE
Idealized Site Windspeed Data
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Advanced Materials and Sustainable Energy LabCBEE
Weibull p.d.f.
k=2 looks reasonable for wind
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Advanced Materials and Sustainable Energy LabCBEE
Wind Probability Density FunctionsWindspeed probability density function (p.d.f)
Values between 0 and 1
Area under the curve is equal to 1
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Advanced Materials and Sustainable Energy LabCBEE
Weibull p.d.f.Weibull with k=2 has shape similar to windspeed distribution
Often used as first guess when little is known about a particular site
Fairly realistic for a wind turbine site: winds are mostly pretty strong, but there are some periods of low wind and high wind
k-1-
( ) e Weibull p.d.f.
kv
ck vf v
c c
k = shape parameter c = scale parameter
2
-
2
2( ) e Rayleigh p.d.f. (Weibull with k=2)
v
cvf v
c
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Advanced Materials and Sustainable Energy LabCBEE
Rayleigh p.d.f. (Weibull with k=2)
Higher c implies higher average windspeeds
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Advanced Materials and Sustainable Energy LabCBEE
Real Data vs. Rayleigh Statistics
(It is important to gather as much real wind data as possible!)
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Advanced Materials and Sustainable Energy LabCBEE
Average Windspeed using p.d.f.Now that we have a function that approximates wind
speed…
And for average v3
0
( ) avgv v f v dv
3 3
0
( ) avg
v v f v dv
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Advanced Materials and Sustainable Energy LabCBEE
Average windspeed from Rayleigh p.d.f.
For a Rayleigh p.d.f., there is a direct relationship between average wind speed v and scale parameter c (not surprising really)
You can, of course, use this to extract a c for your site
0
( ) avgv v v f v dv
-
20
2e
kv
cvv dvc
0.886
2c c
2=1.128 avgc v v
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Advanced Materials and Sustainable Energy LabCBEE
Rayleigh Statistics – Average Power in Wind
Remember, to find average power in the wind, we needed (v3)avg
If we are still assuming wind speed distribution has a Rayleigh distribution
Then we can put (v3)avg in terms of vavg!
3 3
0
( ) avg
v v f v dv
33 = c
4
2
3 42
0
e 2
v
vvv dv
v
3 33 6=1.91avg avgavg
v v v
2
=1.128 avgc v v
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Advanced Materials and Sustainable Energy LabCBEE
Rayleigh Statistics – Average Power in Wind
Using the expression for (v3)avg in terms of vavg (from Rayleigh distribution assumption), average power in wind is
3 31 1
2 2avg avgavg
P Av A v
36 1
2 avgA v
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Advanced Materials and Sustainable Energy LabCBEE
Not all of the power in the wind is retained - the rotor spills high-speed winds and low-speed winds are too slow to overcome losses (see power curve)
Depends on rotor, gearbox, generator, tower, controls, terrain, and the wind
Overall conversion efficiency (Cp·ηg) is around 30%
Estimates of Wind Turbine Energy
WPBP EP
Power in the Wind
Power Extracted by Turbine
Electric Power
Wind PC
RotorGearbox & Generator
g
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Advanced Materials and Sustainable Energy LabCBEE
Time Variation of Wind
Need to consider when wind blows with respect to the electric load– In the Midwest the wind tends to blow the strongest
when the electric load is the lowest…
Wind patterns vary with geography– Wind can change drastically within hours…– Coastal and mountain regions have steadier winds
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Advanced Materials and Sustainable Energy LabCBEE
Wind Power Variability and Integration
Currently wind is a small fraction of generation– Impact of grid operations is small– As wind power grows it will have larger impact– Impacts expected to range from transient stability (seconds) to
steady-state (power flow)
Because wind turbine output varies as cube of wind speed, small changes in wind speed can have large impact– Current perception is that at the 10%-15% penetration level, wind
may cause system instability– BPA balancing region is ca. 10GW, has signed LGIA for 4GW wind
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Advanced Materials and Sustainable Energy LabCBEE
Wind Power Variability and Integration
The key constraint:
Total power system generation must match the total load plus losses
Sudden generation shortfalls dealt with by maintaining sufficient “spinning reserve” to account for the loss of the largest single generator in region
Spinning reserve: generation that is on-line but not fully used and can be brought into production in very short time period
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Advanced Materials and Sustainable Energy LabCBEE
Renewables Forecasting and the Variability Issue
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Advanced Materials and Sustainable Energy LabCBEE
Wind Power: Deviations of Power Production
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Advanced Materials and Sustainable Energy LabCBEE
Wind Power Deviations For One Year
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Advanced Materials and Sustainable Energy LabCBEE
Number of Occurrences by Magnitude
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Advanced Materials and Sustainable Energy LabCBEE
Capital Cost = $200/kW, $350/kWh Cycle Cost = $0.46/kW·h·cycleOperating Cost = $5/kW·yr Replacement Cost =
0.20 CapitalCost Cycle/2000 ∗ ∗
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Advanced Materials and Sustainable Energy LabCBEE
Minimum cost ES size ($ PU)
Power Energy $/Power
1hr 0.1500 0.8000 0.3366
30min 0.1125 0.4500 0.2031
30 min ANN 0.1125 0.5500 0.2336
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Advanced Materials and Sustainable Energy LabCBEE
Energy Storage
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Advanced Materials and Sustainable Energy LabCBEE
Environmental Aspects of Wind EnergyUS National Academies 2007 report:• Wind systems emit no air pollution and no carbon
dioxide; have essentially no water requirements
• Wind serves to displace energy production from mainly fossil fuel burning: net decrease in emissions
• Other impacts of wind energy are on animals (primarily birds and bats) and humans– Large bird (raptor) mortality is about 0.04 bird/MW/year
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Advanced Materials and Sustainable Energy LabCBEE
Issue: Bird/Bat fatalities
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Advanced Materials and Sustainable Energy LabCBEE
Environmental Aspects of Wind: Birds and Bats
Wind turbines kill birds and bats!
But so do lots of other things
Windows kill between 100 and 900 million per year
Estimated Causes of Bird Fatalities, per 10,000
Source: Erickson, et.al, 2002. Summary of Anthropogenic Causes of Bird Mortality
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Advanced Materials and Sustainable Energy LabCBEE
Environmental Issues: Human Aesthetics
Aesthetics is the primary human concern about wind energy projects (beauty is in the eye of the beholder);
Night lighting (aircraft collision warning) can also be an issue
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Advanced Materials and Sustainable Energy LabCBEE
Environmental Issues: Offshore Wind and Aesthetics
Remember, terrain effect is smallest over water…
Capacity factors are much better off-shore
Offshore wind currently needs to be in shallow water; maximum distance from shore depends on the seabed
Image Source: National Renewable Energy Laboratory
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Advanced Materials and Sustainable Energy LabCBEE
Cape Wind Simulated View, Nantucket Sound, 6.5 miles Distant
Source: www.capewind.org
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Advanced Materials and Sustainable Energy LabCBEE
Environmental: Human Well-BeingSome people living near turbines may be affected by noise and
shadow flicker– Noise comes from gearbox/generator
and aerodynamic interaction of the
blades with the wind– Noise impact is moderate:
50-60 dB up close (40m)
35-45 dB at 300m
• Shadow flicker appears to be issue
in high latitude regions
(lower sun casts long shadows)
10,0
,0
P( ) 20log
Pwhere P is threshold of hearing
rms
rms
rms
I db
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Advanced Materials and Sustainable Energy LabCBEE
Environmental: Human Well-BeingVariables related to annoyance by wind turbine noise– Stress related to turbine noise– Daily hassles– Visual intrusion of wind turbines in the landscape– Age of turbine site – The longer system in operation, the less the annoyance
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Advanced Materials and Sustainable Energy LabCBEE
Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass. Amherst
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Advanced Materials and Sustainable Energy LabCBEE
Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass. Amherst
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Advanced Materials and Sustainable Energy LabCBEE
Anthony L. Rogers
Renewable Energy Research Laboratory, U. Mass. Amherst