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 3.1b Growth in total wind energy capacity, 2000-2016 By comparison, the total global electricity generation capacity is about 5500 GW

3. Figure 3.1a Annual additions to wind energy capacity, 2000-2016 By comparison, the total existing nuclear + hydro + natural gas electricity generating capacity in Ontario is just under 30 GW (with another 10 GW of wind capacity and 2 GW of solar)

4. Note that about half of all the wind turbines installed in the world in 2016 were installed in China. However, China seems to be building up wind energy too fast – there are major problems getting the turbines connected to the grid or being able to transmit the generated electricity. As a result, wind farm output frequently has to be “curtailed”. Curtailment rates are 15-20% in various Chinese provinces, compared to about 2% in the US. Some wind farms are not yet connected to the grid. Between unconnected wind farms and curtailed output, wind electricity production in China in 2012 was only about 65% that expected (Lam et al., 2016, ERL).As well, many of the Chinese wind manufacturers are state-owned and have been willing to sell wind turbines at a loss in order to gain market share or to meet government targets.

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

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

7. Market share of global wind turbine sales in 2016 Source: Renewables 2017, Global Status Report Global employment in the wind energy sector: 1.1 million (REW Jan-Feb 2017, p 20)

8. Components of a Wind Turbine • Foundation • Tower • Rotor • Nacelle • Gearbox (in older units) • 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 6 MW now, up to 15 MW foreseen (offshore) • 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. Turbine size (power capacity) • Onshore – typically 2 MW, some up to 4 MW, but restricted due to the logistical difficulties of transporting blades by road • Offshore – many 6-7 MW turbines are available, the largest currently available is the 9.5 MW Vestas V-164, and 15 MW turbines are currently envisaged • Building larger turbines for offshore is regarded as one of the keys to reducing the still high unit cost of offshore wind energy

11. Figure 3.4 Progression of rotor sizes over time

12. Source: Renewable Energy World, Jan-Feb 2017

13. Note: falling specific power means that rotor area is increasing faster than generator capacity, but this makes it possible to generate more electricity at a given wind speed and to reach full power at a lower wind speed. Source: Renewable Energy World, Jan-Feb 2017

14. The preceding slide shows wind turbines for offshore applications growing in maximum size from 4.1 MW in 2015 to 11 MW by 2030, but there have been discussions of offshore turbines reaching 15 MW and even 50 MW capacity! Bigger turbines require development of ultra-light components (using C fibres, for example)

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

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 generatorsElectricity (the flow of electrons) is produced by a changing magnetic field. An electrical generator consists of 3 stationary magnets as part of a stator, which is a circular ring within which a rotor with further magnets rotates. Wire is wound around each stator magnet. The rotating rotor magnet induces fluctuating voltage in each of the stator windings, and since each stator magnet is offset by 1/3 of the circumference, the current produced in each wire is offset by 1/3 of a cycle from the adjacent wire. The produces what is called 3-phase AC.

23. Recap Volume 1 Figure 3.2 Two Pole Synchronous Generator

24. Three Phase AC Current

25. The frequency of the electricity (cycles per second) produced by the generator rotor with one magnet would equal the rotor frequency, that from a rotor with 2 magnets would be twice the rotor frequency (since the rotor would need to rotate only half a circle to go from one north pole to the next), and so on. Electricity in North America has a frequency of 60 Hz (60 cycles per second), but the wind turbine rotor might rotate at only 10 cycles per minute – so (in most wind turbines), a system of gears is needed to step up from the turbine rotor speed to the required generator rotor speed, and then electronics is used to get an exact match in both the frequency and phase between the turbine electricity output and those of the grid to which it is connected.

26. There are two basic variants of the generator: • An asynchronous or induction generator, in which the magnets in the stator are induced by an electrical current supplied from the grid to which the turbine is connected, and • A synchronous generator, which may or may not have permanent magnets (not requiring any electrical current for magnetization) in the stator • Asynchronous generators can be further divided into the squirrel cage induction generator (SCIG) and the wound rotor induction generator (WRIG), which differ in how the rotor is constructed. They are illustrated in the next slide.

27. Schematic diagram of a squirrel cage induction generator (SCIG)

28. Squirrel cage and wound rotor induction generators

29. The choice of generator strongly affects how the wind turbine rotor rotation rate varies with wind speed, which in turns affects wear and tear, efficiency, and noise

30. Asynchronous SCIGs or WRIGs • If the generator 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 • 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 between the rotor and the stator frequencies is called the slip, and at peak power it is only a few % (i.e., the rotation rate of the turbine rotor varies by only a few % between zero and maximum power output)

31. To allow some variation in rotor speed (from -30% to +40% from the synchronized speed), the doubly-fed induction generator (DFIG) was developed. • “Doubly-fed” means both the stator and the rotor (of the WRIG type) are connected to the grid, the stator as usual with a current that induces magnetization • The rotor directly feds about 30% of the power output through a partial-scale frequency convertor that produces AC current such that when it is blended with the stator output, the resulting current exactly matches the frequency of the grid even as the rotor rotation rate varies.

32. Schematic diagram of a doubly-fed induction generator (DFIG) Source: Wikipedia

33. The latest step in the evolution of turbine generators is the permanent magnet synchronous generator. It is • More expensive and mechanically more complicated than an induction generator • The permanent magnet requires (at present) rare earth elements neodymium (Nd) and dysprosium (Dy) that could be in short supply in the future • However, such turbines are more efficient, allow a wide variation in turbine rotor rotation rate, and lend themselves to elimination of the gear box altogether • Presently, about 10% (by capacity) of wind turbines being sold use permanent magnets, but this fraction will likely grow

34. Aside: the production of Nd and Dy for permanent magnet synchronous wind turbine generators is anything but “clean”, as illustrated by the toxic waste dump next to a processing plant in China shown below Source: Zhang (2013, Peak Nd, MSc thesis)

35. Note, from below, that the AC output of the wind turbine (of varying frequency) is converted to DC, then converted back to AC of the exact frequency and phase needed to match the grid. However, if we were to transmit the electricity as DC (as discussed later), we could skip the DC-AC conversion at this point.

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

37. 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

38. 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 (neither stable nor unstable) atmosphere only.The power relationship has no theoretical basis but provides a good fit to observed atmospheric wind profiles

39. Power output from a wind turbine • Kinetic energy of a moving mass = ½ mv2 • Power density of wind (rate of flow of energy (watts) across a plane perpendicular to the wind, per m2 of plane area) = 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

40. 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

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

42. Comparison Weibull probability function and the corresponding cumulative probability for c=5 m/s and k=1.6

43. Note • The mode is the wind speed where the peak in the probability curve occurs. It can be read off the graph, or computed by setting the derivative of the Weibull distribution function to zero and solving for u • The median is the wind speed such that wind speeds greater or lessor than that wind speed occur 50% of the time – so it is the wind speed such that the cumulative probability = 0.5. It can be found by setting F(u)=0.5, where F(u) is the cumulative distribution function, and solving for u.

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

45. Figure 3.16 Two Weibull wind speed probability distributions with almost the same mean wind speed – but very different mean wind power!

46. 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

47. 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

48. 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.

49. 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

50. 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