Wind Power History Advantages & Disadvantages Wind Turbine & Components Power From Wind Mill Swept area Of Wind Mill Rotor Wind Speed Variation with Height Density & Temperature Variation with Height Global Wind Patterns Wind Speed Measurements Wind Speed Distribution Weibull Probability Distributions

1. Wind Power Generation,
Patterns and Distribution
Bhavesh Solanki

2. Wind Power
• First use of wind was to sail ship
• Pump water : 1700s and 1800s
• First wind-mill to generate electricity: 1890 in rural USA
• Design improvement and plant utilization contribute to decline the
cost.
• 35% in 1980 and 5% in 1997

3. Declining cost of wind generated electricity
Figure 1: Declining cost of wind generated electricity [1]

4. Installed wind capacity in selected countries
Table 1: Installed wind capacity in selected countries [1]

5. Advantages
• Using modern technology wind energy can be captured efficiently.
• Does not cause green house gases or other pollutants.
• Remote areas that are not connected to the electricity power grid can
use wind turbines to produce their own supply.
Disadvantages
• At all places wind strength is not enough to support wind turbine.
• The strength of the wind is not constant.
• Wind turbines are noisy.

6. Horizontal axis wind turbine
Figure 2: Horizontal axis wind turbine [2]

7. Vertical axis wind turbine
Figure 3: Vertical axis wind turbine [3]

8. Components in Turbine Hub
Figure 4: Components of wind turbine head [4]

9. Speed and Power relations
• Moving mass ‘m’ (air mass) have
K.E. =
1
2
m 𝑉2
Joules
• The power in moving air is flow rate of K.E. per second
power =
1
2
(mass flow rate per second) 𝑉2
• Volumetric flow = (A*V).
• If air density 𝜌 then mass flow rate = (A*V* 𝜌).
P =
1
2
(A*V* 𝜌) 𝑉2 =
1
2
𝜌 A 𝑉3 watts

10. • Two wind sites are compare in terms of the specific wind power
(Power/rotor swept area)
Specific wind power =
1
2
𝜌 𝑉3
watt per 𝑚2
• It is power in upstream side.
• Linearly varies with ‘𝜌’ and with cube root of ‘V’.
• 100% power not extract.
• At down stream air moves at lower speed.

11. Power extracted from the wind
• The actual power extracted
𝑃𝑜 = Power at upstream- power at down stream
=
1
2
mass flow rate per second [𝑉2 − 𝑉𝑜
2]
• The air velocity is discontinuous from 𝑉 to 𝑉𝑜
• There for mass flow rate from rotor blade is
mass flow rate = 𝜌 A
𝑉+𝑉𝑜
2

12. • Power, which is driving electrical generator
𝑃𝑜 =
1
2
𝜌 𝐴
𝑉+ 𝑉𝑜
2
(𝑉2 − 𝑉𝑜
2)
𝑃𝑜 =
1
2
𝜌 𝐴 𝑉3
𝐶 𝑝
where, 𝐶 𝑝 =
1+
𝑉 𝑜
𝑉
1−
𝑉 𝑜
𝑉
2
2
• 𝐶 𝑝 = Power coefficient of rotor
• 𝐶 𝑝 is maximum when
𝑉𝑜
𝑉
is one- third, maximum value is 0.59.
𝑃𝑜 =
1
2
𝜌 𝐴 𝑉3 (0.59)

13. • 𝐶 𝑝= 0.59 is theoretical, practically
• 0.5 for high speed turbine and 0.2 to 0.4 for multi blade low speed
turbine.
Figure 5: Rotor efficiency vs
𝑉𝑜
𝑉
[1]

14. ROTOR SWEPT AREA
• Power linearly depends on A,
A =
𝜋
4
𝐷2
• For vertical axis machine, involves elliptical integrals.
A =
2
3
(maximum rotor width at center) (Height of rotor)
• Solidity =
𝑆𝑜𝑙𝑖𝑑 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐵𝑙𝑎𝑑𝑒𝑠
𝑆𝑤𝑒𝑝𝑡 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑜𝑡𝑜𝑟
(For 2 and 3 blade Solidity 5 to 10%)
• Tip speed ratio =
𝑇𝑖𝑝 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑙𝑎𝑑𝑒
𝑊𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑

15. Figure 6: rotor power coefficient for different rotor [1]

16. Variation of wind speed with height
1. 𝑉2 = 𝑉1
𝑙𝑛
ℎ2
𝑧0
ln
ℎ1
𝑧0
(logarithmic height formula)
where, 𝑉1 = velocity of wind at elevation ℎ1
𝑉2 = velocity of wind at elevation ℎ2
𝑍0= roughness length
2. 𝑉2 = 𝑉1
ℎ2
ℎ1
𝛼
(Hellman’s approach, 𝛼 = Hellman’s component)
Lake, ocean, smooth hard ground 0.1
Foot high grass on level ground 0.15
Tall crops, shrubs, hedges 0.20
Ground with many trees 0.25
Small city 0.30
City area with tall buildings 0.40

17. Figure 7: Wind speed vs height from ground [1]

18. Variation of density and temperature
• At sea level air P =1 atm, density = 1.225 kg/m3, T = 60 ℉.
• Density variation with altitude (up to 6000meter) is given by
𝜌 = 𝜌0 𝑒
−
0.297 𝐻 𝑚
3048
𝜌 = 𝜌0 (−1.194 ∙ 10−4) 𝐻 𝑚
• Temperature variation with elevation
T = 15.5 -
19.83 𝐻 𝑚
3048
℃

19. GLOBAL WIND PATTERNS
• Atmospheric force that cause wind
- Pressure force
- The Coriolis force caused by the rotation of earth
- Inertia forces due to large – scale circular motion
- Friction forces at earth’s surface
• The global wind pattern are created by uneven heating and
spinning of the earth.

20. Figure 8: Wind pattern on earth [5]

21. Figure 9: Wind pattern cells on earth [6]

22. • Six major wind belts, three in each hemisphere.
• Polar easterlies, the westerlies, and the trade winds.
• Each belt occupies about 30 degrees of latitude.
• Polar Easterlies: 60-90 degrees, the Polar Easterlies blow
irregularly from the east and north.
• Prevailing Westerlies: 30-60 degrees, the Westerlies blow from the
west, tending somewhat toward the north.
• Trade Winds: About 30 degrees latitude. Trade winds blow mostly
from the northeast toward the equator. These were the sailor's
favorite winds.

23. • Polar front: Between the polar easterlies and the westerlies is
the polar front.
• Horse Latitudes: Where the Westerlies meet the trade winds at
about 30 degrees. This is a region of high pressure, dry air, and
variable winds, and is associated with deserts over land.
• Doldrums/ Intertropical Convergence Zone : At about the equator
is doldrums, a region of light and irregular wind broken by
occasional thunderstorms and squalls.
• The width and exact location of the doldrums were hard to predict.
Sailing ships are sometimes becalmed here for many days waiting
for a proper wind.

24. • Southern hemisphere: In the southern hemisphere the belts are
reversed. The southeast trade winds blow from the southeast
toward the equator.
• Hadley cell: Hot air rises at the doldrums. As it rises, it cools
producing thunderstorms. The dry air flows north at a high
altitude and descends at the horse latitudes and flows back to the
equator with the trade winds. This is called the Hadley cell.
• There is also a Ferrel cell over the westerlies and a polar cell over
the pole

25. WIND SPEED MEASUREMENT
• Anemometer: The angular speed of the spinning shaft is calibrated
in terms of the linear speed of wind.
Figure 10.1: Anemometer [7] Figure 10.2: Digital anemometer [8]

26. WIND DIRECTION
• Weather vane: The wind direction is indicated by an arrow
fastened to the spoke, in terms of 360° circulation scale.
Figure 11: Weather vane [9]

27. Optical sensor
• Developed at the ‘Georgia institute of technology’, which may improve
measurement accuracy of speed.
• The mechanical anemometer reading is for single location where it is
actually placed.
• For measurement of average speed in large area such as wind farm then
optical sensor gives accurate result than mechanical anemometer.
• The sensor mounted on large telescope and a helium neon laser about
50mm diameter.
• It projects beam light on to a target about 100meters away.
• Target made of the retroflective material used on road signs.
• The telescope collect laser light reflected from the target and send it
through a unique optical path in the instrument.

28. Figure 12: optical wind speed measurement [1]

29. WIND SPEED DISTRIBUTION
• Power have cubic relation with speed.
• Speed is most critical data needed to estimate the power potential
of a candidate site.
• Wind speed influenced by the weather system, the local land
terrain, and the height above the ground surface.
• The annual mean speed needs to be averaged over 10 or more
years.
• Long term measurement is expensive and project can not wait that
long.

30. • The short term(1 year) data is compared with a near by site
having long term data.
• This is known as “measure, correlate and predict (mcp)”
technique.
• Wind is driven by sun and seasons, the wind pattern generally
repeats over the period of one year.
• The monthly data aggregated over the year for brevity in reporting
the overall ’’windiness ’’ of various site.
• The wind speed variation over the period can be described by a
probability distribution function.

31. Weibull probability distribution
• Two parameter shape parameter ‘k’ and the scale parameter ‘c’.
• The probability of wind speed being v at any time interval is
h(v) =
𝑘
𝑐
𝑣
𝑐
(𝑘−1)
𝑒
−
𝑣
𝑐
𝑘
for 0 < V < ∞
• The probability chart, h is plotted against V over a chosen time period
where
h =
𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡𝑖𝑚𝑒 𝑤𝑖𝑛𝑑 𝑠𝑝𝑒𝑒𝑑 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑣 𝑎𝑛𝑑 (𝑣+∆𝑣)
∆𝑣

32. ‫׬‬0
∞
ℎ 𝑑𝑣 = 1
• For one year, probability function express in terms of hours in the
years,
h =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑜𝑢𝑟𝑠 𝑡ℎ𝑒 𝑤𝑖𝑛𝑑 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑣 𝑎𝑛𝑑 (𝑣+∆𝑣)
∆𝑣
• Unit of ‘h’ is hours per year per meter/second.
• Bellow plot is ‘h’ versus ‘v’ for different value of k.

33. • Scale parameters c = 10 and k = 1,2 and 3.
Figure 13: Weibull’s probability distribution curve [1]

34. • Distribution with k = 1, exponential distribution.
• Middle curve(k = 2) is a typical wind distribution found at most of
sites.
• For k=3, distribution is bell shape.
• Value of k determine the shape of curve hence is called shape
parameter.
• Bellow figure shows the distribution with k = 2 and different values of
c ranging from 8 to 16 mph (1 mph = 0.446 m/s).

35. • Shift the distribution of hours at higher wind speed scale, c is
called ‘scale parameter’.
Figure 14: Effect of scale factor on distribution [1]

36. • Weibull distribution with k = 2, known as the Rayleigh
distribution.
• The actual measurement data taken at site compare with Rayleigh
distribution, as seen in figure.
Figure 15: compare actual values with Rayleigh distribution [1]

37. Weibull distribution
• For k = 1 makes exponential distribution, h = λ 𝑒−λ 𝑉 where λ =
1/c
• For k = 2 makes Rayleigh distribution, h = 2 λ2 𝑉 𝑒− λ 𝑉
2
• For k = 3 makes it approach a normal bell-shape distribution.
• Most of time scale parameter ranging from 10 to 20 mph (5 to
10m/s)
• And shape parameter from 1.5 to 2.5 (rarely 3.0).

38. • For k = 1.5, 2 and 3.
• As ‘c’ increase distribution shift higher speed value.
• As k increase from 1.5 to 3 curve become bell shape from flatter
shape.
Figure 16: Effect of shape and scale factor [1]

39. Mode and Mean Speeds
• Mode speed is speed at which wind blows most of times.
• Mean speed over the period define as the total area under curve h-
V.
• The annual mean speed is,
𝑉𝑚𝑒𝑎𝑛 =
1
8760
‫׬‬0
∞
ℎ 𝑣 𝑑𝑣
• the integral expression can be approximated to the Gamma
function.
𝑉𝑚𝑒𝑎𝑛 = C *gamma(1+ 1/k)

40. • Rayleigh distribution for k = 2, the gamma function can be
approximate to
𝑉𝑚𝑒𝑎𝑛 = 0.90 C
• For Rayleigh distribution scale parameter C = 𝑉𝑚𝑒𝑎𝑛/0.9 and k = 2.
h(v) =
2𝑣
𝑐2 𝑒
−
𝑣
𝑐
2
=
2𝑣
𝑉 𝑚𝑒𝑎𝑛
2 𝑒
−
𝑣
𝑣 𝑚𝑒𝑎𝑛
2

41. Root mean cube speed(rmc)
𝑉𝑟𝑚𝑠 =
3 1
8760
‫׬‬0
∞
ℎ 𝑣3 𝑑𝑣
• rmc speed use for estimation of annual average power
𝑃𝑟𝑚𝑠 =
1
4
𝜌 𝑉𝑟𝑚𝑠
3
watts/m2

42. Energy distribution
• energy distribution function
e =
𝑘𝑊ℎ 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑦𝑒𝑎𝑟 𝑏𝑦 𝑡ℎ𝑒 𝑤𝑖𝑛𝑑 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑣 𝑎𝑛𝑑 (𝑣+∆𝑣)
∆𝑣
Figure 17: Energy distribution [1]

43. References
[1] Wind and Solar power system by Mukund R. Patel, CRC Press (Book)
[2] https://learnforsustainability.wordpress.com/offshore-wind/
[3] http://www.green-mechanic.com/2013/03/vertical-axis-wind-turbine-parts.html
[4]https://en.wikipedia.org/wiki/Wind_turbine#/media/File:EERE_illust_large_turbine.gif
[5] https://en.wikipedia.org/wiki/File:Atmospheric_circulation.svg
[6] http://www.metoffice.gov.uk/learning/learn-about-the-weather/how-weather-
works/global-circulation-patterns
[7] https://en.wikipedia.org/wiki/File:Wea00920.jpg
[8] https://www.jaycar.com.au/hand-held-anemometer-with-separate-sensor/p/QM1646
[9] http://www.ebay.co.uk/gds/How-to-Install-a-Weathervane-
/10000000178630524/g.html

44. Thank You