Lecture Wind Power Department of Energy Systems Engineering

1. Lecture Wind Power Department of Energy Systems Engineering

2. Wind Power Systems Photos taken (by Kate) near Moraine View State Park, IL

3. Historical Development of Wind Power The first known wind turbine for producing electricity was by Charles F. Brush turbine, in Cleveland, Ohio in 1888 • 12 kW • Used electricity to charge batteries in the cellar of the owner’s mansion Note the person http://www.windpower.org/en/pictures/brush.htm

4. Historical Development of Wind Power First wind turbine outside of the US to generate electricity was built by Poul la Cour in 1891 in Denmark • Used electricity from his wind turbines to electrolyze water to make hydrogen for the gas lights at the schoolhouse http://www.windpower.org/en/pictures/lacour.htm

5. Historical Development of Wind Power In the US - first wind-electric systems built in the late 1890’s By 1930s and 1940s, hundreds of thousands were in use in rural areas not yet served by the grid Interest in wind power declined as the utility grid expanded and as reliable, inexpensive electricity could be purchased Oil crisis in 1970s created a renewed interest in wind until US government stopped giving tax credits Renewed interest again since the 1990s

6. Global Installed Wind Capacity Source: Global Wind Energy Council

7. Annual Installed Wind Capacity Source: Global Wind Energy Council

8. Growth in US Wind Power Capacity Source: AWEA Wind Power Outlook 2nd Qtr, 2010

9. Historical Change in Wind Economics, Constant 2005 Dollars Source: National RenewableEnergy Lab (NREL), Energy Analysis Office

10. Top 10 Countries - Installed Wind Capacity (as of the end of 2009) Total Capacity 2009 Growth Source: Global Wind Energy Council

11. In the News: Cape Wind • For about 10 years Cape Wind Associates has been attempting to build an off-shore 170 MW wind farm in Nantucket Sound, Massachusetts. Because the closest turbine would be more than three miles from shore (4.8 miles) it is subject to federal, as opposed to state, jurisdiction. • Federal approval was given on May 17, 2010 • Cape Wind would be the first US off-shore wind farm • There has been significant opposition to this project, mostly out of concern that the wind farm would ruin the views from private property, decreasing property values.

12. Cape Wind Simulated View, Nantucket Sound, 6.5 miles Distant Source: www.capewind.org

13. State Wind Capacities (7/20/2010) http://www.awea.org/projects/

14. Worldwide Wind Resource Map Source: www.ceoe.udel.edu/WindPower/ResourceMap/index-world.html

15. Types of Wind Turbines “Windmill”- used to grind grain into flour Many different names - “wind-driven generator”, “wind generator”, “wind turbine”, “wind-turbine generator (WTG)”, “wind energy conversion system (WECS)” 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”

16. Vertical Axis Wind Turbines Darrieus rotor - the only vertical axis machine with any commercial success Wind hitting the vertical blades, called aerofoils, generates lift to create rotation • No yaw (rotation about vertical axis) control needed to keep them facing into the wind • Heavy machinery in the nacelle is located on the ground • Blades are closer to ground where windspeeds are lower http://www.reuk.co.uk/Darrieus-Wind-Turbines.htm http://www.absoluteastronomy.com/topics/Darrieus_wind_turbine

17. 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

18. Horizontal Axis Wind Turbines “Upwind” HAWT – blades are in front of (upwind of) the tower Most modern wind turbines are this type Blades are “upwind” of the tower Require somewhat complex yaw control to keep them facing into the wind Operate more smoothly and deliver more power

19. 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 operate at much lower rotational speeds - as the speed increases, the turbulence caused by one blade impacts the other blades Most modern wind turbines have two or three blades

20. 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 (r is air density)

21. Power in the Wind Combining (6.2) and (6.3), Power in the wind PW (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 = 2.237 mph)

22. Power in the Wind (for reference solar is about 600 w/m^2 in summer) Power increases like the cube of wind speed Doubling the wind speed increases the power by eight Energy in 1 hour of 20 mph winds is the same as energy in 8 hours of 10 mph winds Nonlinear, so we cannot use average wind speed Figure 6.5

23. Power in the Wind 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 This explains why larger wind turbines are more cost effective

24. Example 6.1 – Energy in 1 m2 of Wind 100 hours of 6 m/s winds 50 hours of 3 m/s winds and 50 hours of 9 m/s winds - *the average windspeed is 6 m/s Don’t use average windspeed!

25. Air Density for Different Temperatures and Pressures P = absolute pressure (atm) M.W. = molecular weight of air (g/mol) = 28.97 g/mol T = absolute temperature (K) R = ideal gas constant = 8.2056·10-5·m3·atm·K-1·mol-1 Air density is greater at lower temperatures

26. Air Density Altitude Correction Figure 6.7 Using 6.7, we get a differential equation in terms of pressure: where H is in meters

27. Air Density Correction Factors Can correct air density for temperature and altitude using scale factors Temperature correction factors KT and altitude correction factors KA are in Tables 6.1 and 6.2 respectively KT = 1.12 at -15C and 0.92 at 40C; KA = 1 at sea level and 0.827 at 1600m (5249 ft)

28. Impact of Elevation and Earth’s Roughness on Windspeed Since power increases like the cube of windspeed, we can expect a significant economic impact from even a moderate increase in windspeed There is a lot of friction in the first few hundred meters above ground – 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 characterize the impact of rough surfaces and height on wind speed

29. Impact of Elevation and Earth’s Roughness on Windspeed α = friction coefficient – given in Table 6.3 v = windspeed at height H v0 = windspeed at height H0 (H0 is usually 10 m) Typical value of α in open terrain is 1/7 For a large city, α= 0.4; for calm water, α= 0.1

30. Impact of Elevation and Earth’s Roughness on Windspeed Alternative formulation (used in Europe) z is the “roughness length” – given in Table 6.4 Note that both equations are just approximations of the variation in windspeed due to elevation and roughness– the best thing is to have actual measurements

31. Impact of Elevation and Earth’s Roughness on Power in the Wind Combining (6.4) and (6.15), The other constants in the power in the wind equation (6.4) are the same, so they just cancel:

32. Impact of Elevation and Earth’s Roughness on Windspeed Figure 6.8 For a small town, windspeed at 100 m is twice that at 10 m Areas with smoother surfaces have less variation with height

33. Illinois Wind Data • Measurements of wind speed are important to ultimately estimating how much electricity can be generated from wind • Illinois wind resource www.illinoiswind.org • Wind Monitoring Program • Wind measurement data across Illinois • Wind resource maps for Illinois • Many more links and information http://www.illinoiswind.org/winddata/maps.asp

34. Illinois Resource Data Maps http://www.illinoiswind.org/resources/pdf/Transmission.pdf http://www.illinoiswind.org/resources/pdf/WindFarmStatus.pdf

35. Ex. 6.6 Rotor Stress Wind turbine with hub at 50-m and a 30-m diameter rotor, α = 0.2 65 m • Find the ratio of power in the wind at highest point to lowest point • Power in the wind at the top of the blades is 45% higher! 50 m 35 m Picture may not be to scale

36. Maximum Rotor Efficiency Two extreme cases, and neither makes sense- Downwind velocity is zero – turbine extracted all of the power Downwind velocity is the same as the upwind velocity – turbine extracted no power Albert Betz 1919 - There must be some ideal slowing of the wind so that the turbine extracts the maximum power

37. Maximum Rotor Efficiency Constraint on the ability of a wind turbine to convert kinetic energy in the wind into mechanical power Think about wind passing though a turbine- it slows down and the pressure is reduced so it expands Figure 6.9

38. Power Extracted by The Blades ṁ = mass flow rate of air within stream tube v = upwind undisturbed windspeed vd = downwind windspeed From the difference in kinetic energy between upwind and downwind air flows and (6.2)

39. Determining Mass Flow Rate Easiest to determine at the plane of the rotor because we know the cross sectional area A Then, the mass flow rate from (6.3) is Assume the velocity through the rotor vb is the average of upwind velocity v and downwind velocity vd:

40. Power Extracted by the Blades Then (6.18) becomes Define Rewrite (6.20) as

41. Power Extracted by the Blades PW = Power in the wind CP = Rotor efficiency

42. Maximum Rotor Efficiency Find the speed windspeed ratio λ which maximizes the rotor efficiency, CP From the previous slide Set the derivative of rotor efficiency to zero and solve for λ: maximizes rotor efficiency

43. Maximum Rotor Efficiency Plug the optimal value for λ back into CP to find the maximum rotor efficiency: • The maximum efficiency of 59.3% occurs when air is slowed to 1/3 of its upstream rate • Called the “Betz efficiency” or “Betz’ law”