1. Wind 1

2. 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

3. 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

4. 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! 4

5. Lots of ideas, only a few good…

6. Vertical Axis Wind Turbines
Darrieus 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 6

7. 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 7

8. 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 8

9. Power in the Wind
Consider 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 9

10. Power in the Wind Combining we get P (Watts) = power in the wind
ρ (kg/m3)= air density (1.225kg/m3 at 15˚C and 1 atm)
A (m2)= the cross-sectional area that wind passes through
v (m/s)= windspeed normal to A (1 m/s = mph) 10

11. Power in the Wind Power 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… 11

12. Wind Power Classification Scheme

13. US Wind Resources 13

14. 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? 14

15. Power Curve for Turbine
Plateau
Generator maxed out
Cut out speed
Park turbine to avoid damage
Cut in speed
Not enough energy to justify O&M costs

16. 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

17. Maximum Rotor Efficiency
Consider wind passing though turbine: as energy extracted, air slows down
ṁ = mass flow rate of air within stream tube
v = upwind undisturbed windspeed
vd = downwind windspeed

18. Mass Flow Rate At 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

19. Power Extracted by the Blades
Then power relationship at the rotor could be
Define new parameter l such that
We can rewrite the power relationship as

20. Power Extracted by the Blades
Power in the wind
Rotor efficiency (CP)

21. Maximum Rotor Efficiency
So what is the windspeed ratio λ which maximizes the rotor efficiency, CP ?
Plug into CP to find the maximum rotor efficiency:
Maximum efficiency of 59.3% when air is slowed to 1/3 of its upstream speed!
“Betz limit”

22. Maximum Rotor Efficiency

23. Number of Rotating Blades
Windmills 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 23

24. Brush wind turbine

27. 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
D = rotor diameter (m)
v = upwind undisturbed windspeed (m/s)
rpm = rotor speed, (revolutions/min)

28. Air moved this far
Airfoil interacted with
this much air, call it Xs

29. Optimal Tip Speed Ratio
If 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

30. Optimal Tip Speed Ratio
Then for a three bladed turbine,
And for a two bladed turbine

31. Tip-Speed Ratio (TSR)
Rotors with fewer blades reach their maximum efficiency at higher tip-speed ratios

32. 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? 32

33. 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
Note this is just an approximation, others exist (ex. von Karman’s log velocity profile) 33

34. Impact of Terrain on Wind Power
Remember wind power goes as third power of wind speed. 34

35. Impact of Terrain on Wind Power
In a town (a≈0.3), windspeed at 100 m is twice that at 10 m
Areas with smoother surfaces have less variation with height 35

36. Rotor Stress
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
65 m
50 m
35 m
Power in the wind at the top of the blades is 45% higher!
Can cause significant stress (failure)
Picture may not be to scale 36

37. As you may expect, turbines interfere with each other…

38. Wind Farms
It 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?

39. Wind Farms
For closely spaced towers, efficiency of array becomes worse as more wind turbines are added

40. 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

41. Average Power in the Wind
How 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

42. 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:

43. Idealized Site Windspeed Data

44. Weibull p.d.f.
k=2 looks reasonable for wind

45. Wind Probability Density Functions
Windspeed probability density function (p.d.f)
Values between 0 and 1
Area under the curve is equal to 1

46. 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 = shape parameter
c = scale parameter

47. Rayleigh p.d.f. (Weibull with k=2)
Higher c implies higher average windspeeds

48. Real Data vs. Rayleigh Statistics
(It is important to gather as much real wind data as possible!)

49. Average Windspeed using p.d.f.
Now that we have a function that approximates wind speed…
And for average v3

50. 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

51. 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!

52. 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

53. Estimates of Wind Turbine Energy
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%
Wind
Rotor
Gearbox & Generator
Power in the Wind
Power Extracted by Turbine
Electric Power

54. 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

55. 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 55

56. 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

57. Renewables Forecasting and the Variability Issue

58. Wind Power: Deviations of Power Production

59. Wind Power Deviations For One Year

60. Number of Occurrences by Magnitude

61. Capital Cost = $200/kW, $350/kWh Cycle Cost = $0.46/kW·h·cycle
Operating Cost = $5/kW·yr Replacement Cost = ∗CapitalCost∗Cycle/2000

62. 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
0.5500
0.2336

63. Energy Storage

64. Environmental Aspects of Wind Energy
US 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 64

65. Issue: Bird/Bat fatalities

66. 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, Summary of Anthropogenic Causes of Bird Mortality 66

67. 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 67

68. 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 68

69. Cape Wind Simulated View, Nantucket Sound, 6.5 miles Distant
Source: 69

70. Environmental: Human Well-Being
Some 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) 70

71. Environmental: Human Well-Being
Variables 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

72. Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass
Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass. Amherst

73. Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass
Anthony L. Rogers, Renewable Energy Research Laboratory, U. Mass. Amherst

74. Anthony L. Rogers
Renewable Energy Research Laboratory, U. Mass. Amherst