Wind Energy

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2.1. Introduction

• Unit cost of Electricity - Capital Investment &

Operating costs
• It contains many components of
horizontal axis turbine are the rotor
gear box
generator
enclosure and various sensors
controls, couplings, a brake and lightening protection
land and access area etc.
The cost/kW of maximum power output varies with the
size of wind turbine.

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World Energy Resources

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Wind Resources in India

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To help protect y our priv acy , PowerPoint has block ed automatic download of this picture.

Total 28,082.95 MW (October 2016)

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Wind Basics

Wind is simple air in motion.

It is caused by the uneven heating of the earth’s surface by the sun.

During the day, the air above the land heats up more quickly than the air over
water. The warm air over the land expands and rises, and the heavier, cooler air
rushes in to take its place, creating winds.

At night, the winds are reversed because the air cools more rapidly over land
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than over water.

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 Wind Turbine

Kinetic Mechanical Electrical

Energy of Energy on Energy on
Wind the rotor the Grid

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2.1.1.Power Extracted From the Wind

The ability of a wind turbine to extract power from wind is a

function of three main factors:

• Wind power availability

• Power curve of the machine

• Ability of the machine to respond to wind perturbations

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Power in the Wind

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Power Density

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 Power in the Wind

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Wind Speed Vs Power Output

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• Cut-in Speed: Minimum speed when blades turn and
generate usable power (2.5 m/s to 5m/s).

• Rated Speed: Speed at which the turbine would

generate at its rated capacity.

• Cut-out Speed: speed turbine cease power generation to

avoid damage. It is also called Furling Speed (25 m/s to
40 m/s).

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Lift Mechanism of Wind Turbine Blade

• The movement of wind turbine blades can be explained by the

use of Bernoulli’s Theorem.

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Albert Betz’s Formulation

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 Rotor Efficiency

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Maximum Rotor Efficiency

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 Betz’s Law

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Tip Speed Ratio

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Effect of Tip Speed Ratio:

Tip speed ratio increases as solidity decreases

Maximum power increases as tip speed ratio increases

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A Typical 1 MW Wind Energy

Conversion System
Details
1. Rotor diameter 61 m
2. Blade length 30 m
3. Rotor speeds 13 RPM / 22 RPM
4. Tower height 60 m
5. Wind speed range 3 m/s to 25 m/s
6. Power control Active blade pitching
7. Type of generator Induction generator
8. Generator Speed 1000 rpm / 1500 rpm
9. Generator rating 1 MW
10. Annual Energy Output 1.8 to 2 GWh
11. Machine cost About Rs. 4.2 Crores
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 Example 1
• Compare the energy at 15˚C, 1 atm pressure, contained in
1m2 of the following wind regimes:
a) 100 hrs of 6 m/s winds (13.4 mph)

1 1
Energy(6m / s) = ρAv 3 ∆t = X 1.225 X 1X 63 X 100 = 13,230Wh
2 2
b) 50 hours at 3 m/s plus 50 hours at 9 m/s(i.e. an average
wind speed of 6 m/s)

1 1
Energy(3m / s ),50hrs ρAv 3 ∆t = X 1.225 X 1X 33 X 50 = 827Wh
2 2
1 1
Energy(9m / s ),50hrs ρAv 3 ∆t = X 1.225 X 1X 93 X 50 = 22,326Wh
2 2
Total Energy= 827+22326=23,152Wh 60

Example 2

• A 40 m, three bladed wind turbine produces 600 kW at a

wind speed of 14 m/s. Air density is the standard 1.225
kg/m3. Under these conditions,
a) At what rpm does the rotor turn when it operates with a
TSR of 4.0?
TSRx60v 4 x60 s / min x14m / s
rpm = = = 26.7 rev / min
πD 40πm / rev

b) What is the Tip speed of the rotor?

26.7 rev / min xπ 40m / rev
Tipspeed = = 55.9m / s
60 s / min

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c) If the generator needs to turn at 1800 rpm what gear
ratio is needed to match the rotor speed to the generator
speed?

generatorrpm 1800
GearRatio = = = 67.4
Rotorrpm 26.7
d) What is the efficiency of the complete wind turbine
(blades, gear box, generator) under these conditions?

1 1 π
Pw = ρAv 3 = x1.225 x x 40 2 x14 3 = 2112kW
2 2 4
Overall efficiency=
600kW
Overallefficiency = = 0.284 = 28.4%
2112kW

NOTE: Rotor efficiency : 43% and gear box times the efficiency of 62
generator would be 66% (43%x66%=28.4)

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 Types of Wind Turbines

According to orientation of axis of the rotors

Horizontal Axis Wind Turbine (HAWT)
Vertical Axis Wind Turbine (VAWT)
According to aerodynamic operations they can be grouped
Lift type (high speed turbines)
Drag type (low speed turbines)
According to the type of rotors used
Multiblade type
Propeller type
Savonious type
Darrieus type
According to the direction of wind
Up-wind turbine
Down-wind turbine
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Types of Wind Turbine

Fig. Horizontal axis wind turbines (HAWT) are either upwind machines (a) or
downwind machines (b). Vertical axis wind turbines (VAWT) either accept
the wind from any direction (c).
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 HAWT

Upwind turbine Downwind turbine

Complex yaw control Let the wind control left-right
motion
Keep blade facing wind Orient itself correctly to wind
direction
Operate more smoothly Wind shadowing effect by the
tower, cause the blade to flex.
Deliver more power Increase noise and reduce power
output

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Yaw Control

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 Pitch Control

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Power Conversion - MPPT

Techniques to limit the produced power in high wind:
Stall control
Active stall control
Pitch control (replace stalling)

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 70
Horizontal axis wind turbines

Number of Blades

Multi-blade windmill need high starting torque and low wind

speed for continuous water pumping function.

As rpm increases, turbulence caused by one blade affects

efficiency of the blade that follows.

Fewer blades allow the turbine to spin faster smaller

generator.

Two and three blades are the most common in modern wind
turbine.

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 VAWT
• French engineer G. M. Darrieus who first developed the
turbines in the 1920s.

• 500-kW, 34-m diameter machine, was undertaken in the

1980s by Sandia National Laboratories in the United
States.

• They don’t need any kind of yaw control to keep them

facing into the wind.

• The heavy machinery contained in the nacelle (the housing

around the generator, gear box, and other mechanical
components) can be located down on the ground, where it
can be serviced easily.

• The tower can be lightened even further when guy wires

are used, which is fine for towers located on land but not for
offshore installations. 72

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Vertical axis wind turbines

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 Power Extracted From the Wind

• Rotor Efficiency

• Tip Speed Ratio

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Temperature Correction for Air Density

Table: Density of Dry Air at a Pressure of 1 Atmosphere

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 Altitude Correction for Air Density

Table: Air Pressure at 15◦C as a Function of Altitude

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Impact of Tower Height

Table: Friction Coefficient for Various Terrain Characteristics

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 Table: Roughness Classifications

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Fig. Increasing (a) wind speed and (b) power ratios with height for various
friction coefficients α using a reference height of 10 m 79

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 Optimizing Rotor Diameter and Generator
Rated Power
• Tradeoff between Rotor diameter and generator Size
Rated power is reached at lower wind speed
Increases the output of the power with the same generator
Increasing generator size increases the power and emphasizing
the higher wind speeds.
In areas with higher wind speed, it may better to increase the
generator size.

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Wind Hours @ Vi Fractio of Hrs @ Vi X Fraction of (Vi)^3 X fraction Hrs

Speed per Yr Vi Hrs @ Vi (Vi)^3 @ Vi
0 24 0.002739726 0 0 0
1 276 0.031506849 0.03150685 1 0.031506849
2 527 0.060159817 0.12031963 8 0.481278539
3 729 0.083219178 0.24965753 27 2.246917808
4 869 0.099200913 0.39680365 64 6.348858447
5 941 0.107420091 0.53710046 125 13.42751142
6 946 0.107990868 0.64794521 216 23.3260274
7 896 0.102283105 0.71598174 343 35.08310502 1000
8 805 0.091894977 0.73515982 512 47.05022831
900
9 690 0.078767123 0.70890411 729 57.42123288
10 565 0.064497717 0.64497717 1000 64.49771689 800
11 444 0.050684932 0.55753425 1331 67.46164384
700
12 335 0.038242009 0.45890411 1728 66.08219178
13 243 0.027739726 0.36061644 2197 60.94417808 600
14 170 0.019406393 0.2716895 2744 53.25114155 500
15 114 0.013013699 0.19520548 3375 43.92123288
16 74 0.008447489 0.13515982 4096 34.60091324 400
17 46 0.005251142 0.08926941 4913 25.79885845 300
18 28 0.003196347 0.05753425 5832 18.64109589
19 16 0.001826484 0.0347032 6859 12.52785388
200
20 9 0.001027397 0.02054795 8000 8.219178082 100
21 5 0.000570776 0.0119863 9261 5.285958904
0
22 4 0.000456621 0.01004566 10648 4.862100457
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526
23 2 0.000228311 0.00525114 12167 2.777853881
24 2 0.000228311 0.00547945 13824 3.156164384
25 0 0 0 15625 0
8760 7.00228311 657.4447489 Probability density function
Pav 7m/s 210.0875

Pav 657 402.4125 1.915451895 81

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 f(v)
different K Values and C=8
v 1 2 3
0 0 0 0
1 0.110312113 0.03076551 0.00584794
2 0.083545273 0.05871332 0.02307414
3 0.079152003 0.08145141 0.05002551
4 0.071768793 0.0973501 0.08273408
5 0.064688416 0.10572404 0.11475256
6 0.057957156 0.10683428 0.13833619
7 0.051706042 0.1017282 0.14692781
8 0.04598493 0.09196986 0.13795479
9 0.040801954 0.07933021 0.11428142
10 0.036140656 0.06550356 0.08310361
11 0.031970796 0.05189849 0.05267938
12 0.028255179 0.03952471 0.02887154
13 0.024953943 0.0289724 0.01355731
14 0.022027207 0.02046215 0.00540207
15 0.019436646 0.01393557 0.00180823
16 0.017146365 0.00915782 0.00050319
17 0.015123324 0.00581016 0.00011518
18 0.013337474 0.00356046 2.1454E-05
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20
0.011761725 0.0021082
0.010371803 0.00120653
3.2162E-06
3.8376E-07
Weibull P.D.F.
21 0.009146062 0.00066759 3.6043E-08
22 0.00806526 0.00035721 2.6347E-09
23 0.007112338 0.00018487 1.4821E-10
24 0.006272202 9.2557E-05 6.3434E-12
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25 0.005531508 4.4837E-05 2.0423E-13

f(v)
different C Values and K=2
v 4 6 8
0 0 0 0
1 0.117426633 0.05403358 0.03076551
2 0.194700196 0.09942659 0.05871332
3 0.213668559 0.12980013 0.08145141
4 0.183939721 0.14248453 0.0973501
5 0.131007117 0.13870883 0.10572404
6 0.079049418 0.12262648 0.10683428
7 0.040924295 0.09970168 0.1017282
8 0.018315639 0.07511703 0.09196986
9 0.00712093 0.05269961 0.07933021
10 0.002413068 0.03454251 0.06550356
11 0.000714415 0.02120353 0.05189849
12 0.000185115 0.01221043 0.03952471
13 4.20357E-05 0.00660541 0.0289724
14 8.37396E-06 0.00336019 0.02046215
15 1.46465E-06 0.00160871 0.01393557
16 2.2507E-07 0.00072532 0.00915782
17 3.04029E-08 0.00030815 0.00581016
18 3.61176E-09 0.00012341 0.00356046
19 3.7748E-10 4.6609E-05 0.0021082
20 3.47199E-11 1.6606E-05 0.00120653
21 2.81117E-12 5.5826E-06 0.00066759
22 2.00412E-13 1.7713E-06 0.00035721 Rayleigh P.D.F
23 1.25828E-14 5.3057E-07 0.00018487
24 6.95857E-16 1.5005E-07 9.2557E-05
25 3.39017E-17 4.0071E-08 4.4837E-05
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 Wind Speed Cumulative Distribution Function
• Total area under a probability density function is equal to one.
• The area between any two wind speed is the probability that the
wind is between those speeds.
• Probability that some wind speed is less than specified wind speed
is given by

• F(V) is named cumulative distribution function. It represents the time

fraction or probability that the wind speed is smaller than or equal to
a given wind speed.
• Probability that wind speed is less than 0 is 0, then F(0)=0
Probability that wind speed is less than infinite is 1, then F(∞)=1
• The cumulative distribution function for Weibull statistics is

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• For Rayleigh Statistics k=2 & C = 2V / π

K=2,
C=6

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• The probability that the wind speed is greater than certain value

• For Weibull Statistics

• For Rayleigh Statistics

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Example
The probability that the wind speed is below cut-in 4 m/s is
 π  V 2   π  4 2 
F (VC ) = prob (v ≤ VC ) = 1 − exp −  C   = 1 − exp −    = 0.1181
 4  v    4  10  
Hours (v ≤ 4m / s ) = 8760 X 0.1181 = 1034h / yr

The probability that the wind speed is higher than 25 m/s is

 π  V 2   π  25  2 
Hours (v ≥ 4m / s ) = 8760. exp −  F   = 8760. exp −    = 65h / yr
 4  v    4  10  
The wind speed is between 14m/s and 25 m/s produces a rated
power of 1000kW. The number of hrs that the wind speed is higher
than 14m/s is
 π  14  2 
Hours (v ≥ 14m / s ) = 8760. exp −    = 1897 h / yr
 4  10  
The no. of hrs that the wind blow between 14m/s and 25 m/s is
1897-65=1814 h/yr.
Energy = 1000kW *1814h / yr = 1.814 X 106 kWh / yr 87

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Capacity Factor

Actual Energy Delivered

CF =
PR X 8760

Average Power
CF =
Rated Power

1.81 * 106
CF = = 0.21
1000 * 8760

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