1. the physics of wind turbines
Harvesting the Wind
the physics of wind turbines
Kira Grogg
Carleton College
February 23, 2005

2. Why Wind-power?
Wind-power is clean – wind turbines emits no pollutants and create no other types of waste
Wind is renewable – the fuel replenishes itself at a rate comparable to the extracted rate
Modern wind turbines can run as efficiently as conventional power plants (~30-40%)

3. What is a wind turbine?

4. Outline History Origins of wind Power from the wind
Aerodynamics of the blades
Loads, stress, and fatigue
Generators and Electricity
Current issues
Future developments

5. History First windmills about 1000 B.C.E.
12th century – horizontal wind mills appear in Europe
Water pumping windmills in America
1888 – first experiments with electricity generating wind turbines
– Poul La Cour builds over 100 small wind turbines
Increase in production in 1970s due to oil difficulties

6. The Wind Earth receives 1.74 x 1017 watts from the sun
Each year this is 160 times the total energy in the world’s reserves of fossil fuels.
30% radiated out, 47% warming, 23% absorbed by evaporation of water, the remaining goes to plants, wind, and waves
1-2% of the sun’s energy becomes wind energy—100 times the energy in biomass

7. Forming the Wind
Wind begins as the sun heats the air in the atmosphere
Uneven heating combined with the Coriolis force lead to geostrophic winds
Latitude
90-60°N
60-30°N
30-0°N
0-30°S
30-60°S
60-90°S
Direction NE SW SE NW

8. Finding a Site Landscape Roughness Height vs. wind speed: Sea breezes
10-4 over water to 1 m in cities
Height vs. wind speed:
Sea breezes
Mountains
desired height
roughness length
known velocity at height zref
reference height

9. Wind Speed Distribution

10. Power in the Wind
The power is proportional to the cube of the wind speed:
Wind speed data can be misleading :
Average wind speed data is too:
< U>3 ≠ <U3>

11. Extracting Power from the Wind
Not all of the power in the wind can be turned into useable energy
The upper limit on power extracted for a HAWT is ~ 59%
(Betz’ Law)
Cp = power to rotor / power in wind

12. Power Curves
No system that converts between types of energy can be 100% efficient
Actual power output (of electricity) is about 30% of the power in the wind

13. Wake Rotation Energy and momentum must be conserved
Angular velocity added from the turning of the blades, Ω, implies a compensating angular velocity in the wake of the turbine, ω

14. Tip Speed Ratio λ λ = ratio of rotor speed to wind speed
The tip speed ratio can range from 5 to about 10 for electricity generating applications
Equating the thrust equations:
Tip speed ratio: λ = ΩR/U
where R is the length of the blade

15. Torque and Power Cp
Manwell, et. al (2002)

16. Induction Factors
Tip speed ratio λ= 7.5
Manwell, et. al (2002)

17. The Blades Lift vs. Drag Lift Thrust Drag Weight
Early Persian drag windmill
Manwell, et. al (2002)

18. Airfoils
Types of airfoils:
Airfoil geometry:
Manwell, et. al (2002)

19. Angles and Relative Winds
Angle of attack, α, is usually between degrees during normal operation
The angle of the relative wind is the sum of the angle of attack and the section pitch angle:
Hansen (2000)

20. Manwell, et. al (2002)

21. Lift and Drag Lift and drag coefficients:
Wind tunnel tests of airfoils for lift and drag data
Manwell, et. al (2002)

22. Blade Element Momentum Theory (BEM)
BEM uses conservation of momentum and forces on individual elements

23. Maximizing Power
Computational algorithms are employed to determine the most effective blade shape, in terms of chord length and twist (λ = 7, R = 5, Cl =1, α = 70, B =3)
A new power coefficient with lift and drag:

24. Cp -λ Curve
Manwell, et. al (2002)

25. Blade Control Stall Control Pitch Control Active Stall
Manwell, et. al (2002)

26. Yaw Control Wind Rose data No yaw – only VAWTs
Tail – water pumping windmills
Free/Damped yaw – only downwind HAWTs
Active yaw – upwind HAWTs
Red section is the power x frequency,
Middle section is the wind speed x frequency
Outer section is the wind frequency distribution

27. Loads, Stress, and Fatigue
Types of loads: static, steady, cyclic, transient, impulsive, stochastic, and resonance induced
Certain loads will occur over 109 times during a 20 year lifetime
Testing for fatigue – dynamic and static

28. Some Loads Bending Moments: Coning to reduce flapwise bending:
Edgewise
Coning to reduce flapwise bending:
Hansen (2000)

29. Blade Construction Metal does not work, composites do
Glass reinforced plastic (GRP)
Carbon fibers
Wooded frames
Measuring strains

30. The rotor is about 80m across:
This is what excessive loads can do to a WT
Hansen (2000)

31. Inside the Nacelle

32. Gearbox
As the speed increases, torque decreases, so power remains constant
The ratio of the speeds is equal to the inverse ratio of the number of teeth
The gear ratio of Carleton’s 1.65 MW wind turbine is 1:84.3, so that when the rotor is operating at its rated speed of 14.4 rpm, the generator shaft is turning at about 1214 rpm

33. Gears vs. Direct Connection
Advantages of gearless connection:
Cheaper
Quieter
Fewer losses
Disadvantages:
Special low-speed generator is costly

34. Converting Energy
Electrical to kinetic conversion in an electrical motor is about 90% efficient,
Heat to kinetic conversion of an internal combustion engine is about 10-20% efficient
Coal fired power station—chemical to electrical—is about 35-40% efficient
Newer wind turbines are 30-40% efficient

35. Creating Electricity
Wind turbines use generators to create electricity
Synchronous generators
Asynchronous (induction) generators
Permanent magnet
Compatibility with The Grid

36. Faraday’s Law of Induction
Use a moving part and a magnetic field to create a current
Magnetic flux through a loop of wire in a magnetic field:
Induced emf:
Magnetic field
Angle between A and B
Area of loop
Rotational velocity of loop
ω = θt

37. Magnetic fields and currents
Three phase current
Coil connections
Number of poles N
Manwell, et. al (2002) S S N N S

38. Asynchronous/Induction Generators
Usually 4-pole
Rotor uses converted DC from grid to generate a magnetic field
Stator consists of six coils creating 3-phase current
Slip—ratio of the rotating magnetic field speed to the rotor speed

39. The Parts of the Generator
Cage wound rotor
Layered stator

40. Generator
Manwell, et. al (2002)

41. Electronics
Every part of the turbine has a sensor monitoring and/or controlling it
Every sensor has a duplicate to make sure they are working correctly

42. Power Quality and Grid Connection
Power quality is checked 7680 times per second
The current must be in phase with the grid current before connection
Thyristors (semi-conducting transistor type controlling devices) allow a ‘soft’ start of a wind turbine

43. Current Issues Bird and bat deaths Electromagnetic interference Noise
Visual appearance

44. Off-shore Wind Farms Off shore winds are stronger and less turbulent
Larger turbines, ~4 MW, are feasible
Foundations and transmission are the major obstacles

45. What Now? Optimization of More testing More wind turbines Blade shape
Gearbox
Generator
Tower height
Siting
More testing
More wind turbines

46. Acknowledgements To: my advisor, Steve Parker
the Carleton physics faculty
my fellow physics majors
my friends and family
the audience