Publisher: Earthscan, UK Homepage: earthscan.co.uk/?tabid=101808

1. Energy and the New Reality, Volume 2:C-Free Energy SupplyChapter 3: Wind EnergyL. D. Danny Harveyharvey@geog.utoronto.ca Publisher: Earthscan, UKHomepage: www.earthscan.co.uk/?tabid=101808 This material is intended for use in lectures, presentations and as handouts to students, and is provided in Powerpoint format so as to allow customization for the individual needs of course instructors. Permission of the author and publisher is required for any other usage. Please see www.earthscan.co.uk for contact details.

2. Figure 3.1a Annual additions to wind energy capacity

3. Figure 3.1b Growth in total wind energy capacity

4. Figure 3.2a Breakdown of installed capacity at the end of 2009

5. Figure 3.2b Capacity (MW) installed in 2009

6. Figure 3.3 Wind farm at Pincher creek, Alberta Source: Garry Sowerby

7. Table 3.1 Market shares of the world’s leading wind turbine manufacturers. Source: BTM Consult Press Release, March 2007

8. Components of a Wind Turbine • Foundation • Tower • Rotor • Nacelle • Gearbox (usually) • High speed shaft • Generator • Control system, cooling unit, anemometer • Yaw mechanism

9. Turbine characteristics • Rotor diameter – up to 120 m • Hub height – up to 120 m • Peak electrical power output – up to 5 MW now, up to 10 MW foreseen • Cut-in wind speed (typically 3-4 m/s) • Rated wind speed (typically 15 m/s) • Cut-out wind speed (typically 25 m/s)

10. Figure 3.4 Progression of rotor sizes over time

11. Figure 3.5a Rotor diameter vs rated power

12. Figure 3.5b Hub height vs rated power

13. Figure 3.6 Minimum hub height vs rotor diameter

14. Figure 3.7a Power curves for wind turbines with 80-m, 87-m, and 90-m rotors and a 2.0-MW generator

15. Figure 3.7b Power curves for wind turbines with different rotor-generator combinations

16. Wind turbine aerodynamics • Lift, not a pushing force, is what makes the rotor rotate • Thus, the aerodynamics of a wind turbine have much in common with the aerodynamics of an airplane wing

17. Figure 3.8 Airflow Past Wing

18. Figure 3.9 Forces acting on a turbine rotor blade Source: Danish Wind Turbine Manufacturers’ Association

19. Efficiency of a wind turbine: this is the ratio of the electrical power produced (W) to the power of the wind passing through the area swept by the rotor blades. It is the product of three factors: • Aerodynamic efficiency (ratio of mechanical power of the rotor to wind power) • Mechanical efficiency (ratio of mechanical power of the generator axis to the mechanical power of the rotor axis) • Electrical efficiency (ratio of electrical power fed into the grid to the mechanical power of the generator axis)

20. The maximum possible aerodynamic efficiency, as given by Betz’ Law, is 59.3%, and occurs if the turbine slows the wind down to 2/3 of its original speed. The aerodynamic efficiency of a real turbine varies with wind speed, having a typical peak value of 44% and a typical value averaged over all wind speeds of 25% • A typical mechanical efficiency is 96-99% • A typical electrical efficiency is 96-97% • Multiply the efficiencies (expressed as a fraction) to get the overall efficiency

21. Figure 3.10: Variation of power output and efficiency with wind speed for the Nordex N90-2.3 turbine

22. Turbine generators • Synchronous • Asynchronous (induction) • Variable speed

23. Synchronous generators • Common in fossil fuel powerplants, but rare in wind turbines • Rotation speed is synchronized with the grid frequency

24. Recap Volume 1 Figure 3.2 Two Pole Synchronous Generator

25. Recap Volume 1 Figure 3.1 Three Phase AC Current

26. Asynchronous (induction) generators • If the rotor were to rotate at the same frequency as the electric field in the stator, no electricity would be produced • When the rotor of the generator rotates faster than the stator, a strong current is induced in the rotor • The harder one cranks on the rotor, the more power that is transferred as electromagnetic force to the stator, converted to electricity, and fed to the grid • The difference in the rotation speed between no power and peak power is about 1%, but this slip reduces stress on the rotor and smoothes out power variations

27. Variable Speed Generators • Becoming more common • Rotation rate of rotor varies with wind speed from 8 rpm to 16 rpm • Results in less stress on the structure and more uniform variation in power output • Requires more complex electronics and gearbox to always produce electricity at the fixed grid frequency

28. Characteristics of wind • Variation of mean wind speed with height • Variation of turbulence intensity with height • Weibull probability distribution function for wind speed

29. Figure 3.11 Logarithmic velocity profile U plots as a straight line on semi-log paper, with slope u*/ĸ. zo is the height at which U extrapolates to zero

30. Figure 3.12 Effect of surface roughness on velocity profiles Wind speed 100-200 m above the surface is fixed (governed by the large scale pressure patterns) Rougher surface – the air “feels” the surface to a greater height, so wind speeds are slower at all heights within the first 100-200 m.

31. An alternative mathematical representation of the variation of wind speed with height is using a power relationship,Uh/Uref = (H/href)nThe logarithmic relationship is theoretically valid in a neutral atmosphere only.The power relationship has no theoretical basis but provides a good fit to observed atmospheric wind profiles

32. Figure 3.13 Turbulence intensity (wind speed standard deviation divided by mean wind speed) vs height Source: Soker et al (2000, Offshore Wind Energy in the North Sea: Technical Possibilities and Ecological Considerations - A Study for Greenpeace)

33. Power output from a wind turbine • Kinetic energy of a moving mass = ½ mv2 • Power density of wind = ½ ρV3 • The efficiency of a wind turbine is defined as the ratio of power output to the power of the wind in the area swept by the rotating rotor. Thus, • Power output of a wind turbine = efficiency x swept area x power density of wind, or P=1/2 η(πR2) ρ V3

34. Weibull Distribution Function • Gives the probability of a wind speed occurring per unit of wind-speed interval • Thus, the units are 1/(m/s) • The value of the function times the width of the interval gives the probability of the wind speed occurring in that interval • The function is f(u)=k/c(u/c)k-1exp(-(u/c)k) where c is the scale parameter and k is the shape parameter

35. Figure 3.15 Weibull wind speed distribution with c=5 m/s and k=1.6

36. Figure 3.14 Distribution of best-fit Weibull scale factor (c) and shape factor (k) deduced from observed wind velocity variations at various sites

37. Figure 3.16 Weibull wind speed probability distributions

38. Because wind power varies non-linearly with wind speed • The mean (average) wind power for a given mean wind speed depends on the shape of the probability distribution on either side of the mean wind speed • The mean wind power (based on wind power computed at many different wind speeds and then weighted by the probabilities) is about twice the wind power computed once at the mean wind speed

39. Figure 3.17 Mean wind power vs mean wind speed.A smaller k means a more spread out wind speed distribution, so more winds at both very high and very low wind speeds, but the high wind speeds disproportionately contribute to wind power (due to the cubic dependence), so the mean wind power is greater at a given mean wind speed with smaller k

40. Table 3.3. Comparison of wind power computed at the average wind speed with the average wind power computed over a distribution of wind speeds giving the same average wind speed.

41. Mean Efficiency • The power output at any given wind speed is given by the wind power x swept area x efficiency, so the efficiencies matter more when the wind power is larger than when it is smaller • Thus, the appropriate mean efficiency involves the efficiency at each wind speed times the probability of that wind speed interval times the wind power at that wind speed, divided by the mean wind power

42. Figure 3.18a Mean efficiency vs wind speed, computed from the turbine power curve and the Weibull wind speed probability distribution using 3 different shape parameters

43. Figure 3.18b Mean turbine efficiency vs mean wind speed for three turbines with similar generator ratings

44. Capacity Factor This is the mean (average) power output of the turbine divided by the peak (or rated) power output The mean power output is computed as the power output in the centre of each wind speed interval, times the probability of that interval, summed over all intervals and divided by the total probability (which is 1.0)

45. Figure 3.19a Variation of capacity factor with wind speed for 3 different Weibull shape parameters

46. Figure 3.19b Variation of capacity factor with wind speed for three different turbines

47. Table 3.4 Average wind turbine capacity factors in 2001. Source: BTM Consult (2002).

48. Figure 3.20 Mean wind speed over North America at a height of 100 m. Wind speed (m/s) Source for this and other wind maps: Prepared from data file at power.larc.nasa.gov (go to Sustainable Buildings, Global Datasets)

49. Figure 3.21 Mean wind speed over Europe at a height of 100 m. Wind speed (m/s)

50. Figure 3.22 Mean wind speed over China and surrounding regions at a height of 100 m. Wind Speed (m/s)