Detail analysis and design point of vie on wind power plant

Expected learning outcome
The Trainer will be able to understand
• Basic Wind resource assessment
• fundamental liner momentum and
aerodynamics theory of wind turbine
• Electric power extraction from wind
• Wind turbine types, components and their
operation.
• Wind turbine farm, siting and wind energy
economics
3

Introduction to Wind Energy
• The role played by electricity for the sole
functioning of the industries, that the existing
development of the world is relied at, is
increasing.
• The energy demand across the globe is also rising
along with its side effects to the atmosphere and
this requirement leads the world to look forward
for an extensive and environmental friendly
electrical energy sources like that of the
renewable energy sources
4

It is estimated that, at least for about 3000 years the
power of the wind has been used, windmills were
used regardless of the functions they perform like for
water pumping and sailing ships.
From around 1990, regardless of the available oil at a very
low price, the main driver for the extraction and use of wind
turbines to generate electrical power was raised due to the
very low CO2 emissions and the potential of wind energy to
help in controlling the climate change.
5

6
Then from around 2006 the very high oil price
and concerns over security of energy supplies
led to a further increase of interest in wind
energy and a succession of policy measures
were put in place in many countries to
encourage its use.
In 2007 the European Union declared a policy
that 20% of all energy should be from
renewable sources by 2020.

The studiesw and reports for 2011 presented that, the
growth regarding wind energy in the world is accelerating
at a rate which is much higher than the other renewable
sources of energy.
The worldwide wind capacity, extended to 215 GW by
the end of June 2011 and at the end of the year it went
to 236.749 GW. Worldwide wind capacity grew by 9.3 %
within six months and by 22.9 % on an annual basis,
whereas, the annual growth rate in 2010 was 23.6 %.
7

8
The total installed wind capacity in the whole world was 283
GW by the end of the year 2012. This capacity can cover
almost 3 % of the electricity demand all over the world. And
it went to 318 GW in 2013.
According to the estimation conducted by WWEA, at least 44
countries added a combined 45GW of capacity (more than
any other renewable technology), increasing the global total
by 19% to 283 GW in 2012 and around 12.37% in 2013.
Figure 1.1 shows the growth of the world wind potential
from 1996 till the end of 2013.

Energy can come from coal, oil, and other sources. But we
also have an abundance of wind, sunshine, and other
natural sources of energy that do not result in pollution.
We measure our energy consumption by the kilowatt-
hour (kW-hr). One kilowatt-hour is the amount of energy
that a 100-W light bulb consumes in 10 hours. Pollution,
in the form of generating CO2, from coal is 0.712 kg
(1.57lb) per kW-hr.
This means that the energy required to light each 100-W
light bulb for only 10 hr if it comes from a coal plant
generates 1.57lb of CO2.
coming from a coal plant, the energy to power each 100-
W light bulb for only 10 hr generates 1.57 lb of CO2.
10

Any renewable energy, although abundant, suffers
from two major drawbacks:
It is a low-level energy and it is not
continuously available. Being a low-level
energy implies that we cannot expect to
have a wind turbine with the same capacity
as a thermal plant.
11

12
A thermal plant (steam and gas turbines) can have a capacity of
500 MW(1 megawatt 1,000,000 watts) or more with only one or
a few turbines, whereas for that capacity we may need at least
200 wind turbines in an onshore wind farm.
Moreover, a 500 MW thermal power plant is normally capable
of delivering that much power on a continuous basis, whereas
the output of a wind turbine depends on the wind and
fluctuates with the time of the day and the month of the year.
The very first condition for a wind farm is that it has
good wind and is appropriate for installation of wind
turbines. To verify this, the first thing to do is to collect
wind data.
area for wind power generation

A piece of land may look windy and seem to be a
potential place for developing a wind farm. A single
observation, however, is not sufficient for a project that
can cost hundreds of millions of dollars.
Wind data in basic form can be found from historical data
and wind resource maps that show the average wind
speeds for various regions in a country.
Further and more specific wind monitoring should be
done on a piece of land that has been identified as a
potential site for a wind farm.
13

Meteorological studies are necessary for wind
monitoring. A meteorological tower with measurement
instruments that record wind speed and direction is
installed and wind data are collected and recorded.
A meteorological tower (abbreviated as met tower) is a
single tower, similar to a communication tower,
supported by guy wires, at the top of which
measurement instruments are installed. These towers
can vary in height from 10 m (33 ft ) to 70 m (230 ft ).
For better and more reliable results, if no data from a
region are available, this study can continue for 3 years.
Depending on the history of the region, this may be
reduced to 2 years or 1 year.
Based on the analysis of data and economic analysis of
the cost of a project a go-ahead decision can be made14

A second condition to be verified is the availability of a
transmission line. In fact, this is more a line capacity
verification and access reservation, rather than a
question of whether or not a transmission line exists.
A transmission line that has reached its maximum
capacity cannot be used for new projects, even though
it physically exists.
Among other preconstruction activities for a wind farm
is formal agreements with authorities for matters such
as aviation, broadcasting, distance from public roads,
distance from residential areas, and so on, as well as
agreements with landowners if the land is not owned
by the developer (which is most often the case).
15

 After a site has been regarded as having the potential for a
wind farm, it is necessary to perform soil studies in order
to design the appropriate foundation for the turbines.
 Site design, turbine selection, and interconnection to the
electrical grid are part of the engineering work for a
project.
 The initial cost of developing wind farms is high. For this
reason, in order to facilitate it for companies and persuade
them to invest in wind projects, governments introduce
incentives in the form of “tax breaks” and “accelerated
cost recovery” for companies.
 These mechanisms stimulate investments in renewable
energy, without which the cost per kilowatt-hour of
generated energy can be higher than that from
nonrenewable power plants. 16

WIND POTENTIAL STUDIES IN ETHIOPIA
Ethiopia depend on heavily on a limited set of renewable energy
resources to meet its energy requirements: principally biomass for
thermal energy in the residential and commercial sector and large
hydropower for electricity.
The Government of Ethiopia has planned to scale up and diversify
the Renewable energy mix, to minimize hydropower dependency;
thus the focus has been shifted to Renewable energy sources to
fulfill the demand. The planned Renewable energy mix for 2015,
presented 860 MW of energy is expected to be generated from Wind
Energy
17

18
The Ethiopian Government had prepared a Master Plan for wind and solar energy
for investigating the available wind and solar energy resource, which recommends
the major policy options to be developed for wind and solar energy expansion
along with recommendation of 51 wind projects having a total planned capacity of
6,820 MW

Planned renewable energy mix for 2015
Distribution of average wind speed at 50 m
19
In addition to the growing economic attractiveness of wind energy, there are major
essential arguments for its use throughout the world, such as:
• Wind energy is one of the renewable energy systems with the lowest cost of electricity
production and with the largest resource available.
• Wind-power plants emit absolutely no CO2, the major pollutant when fuels are
burned.

• The operation of wind turbines leaves behind
no dangerous residues as do nuclear plants.
• Decommissioning costs of wind turbines are
much smaller than those of many other types
of power plants, especially compared with
those of nuclear generators.
• Land occupied by Wind Farms can find other
simultaneous uses like agriculture
20

Wind resource
• Most renewable energy ultimately comes from the sun.
Winds are produced by uneven solar heating of the
earth’s surface. Such irregular heating of earth’s surface
creates a circulated air: and that air flows from areas of
high pressure to areas of low pressure. That movement of
air is named as wind. From 1-2 % of the sun’s energy
reaching the earth is converted into wind
• Wind results from expansion and convection of air as solar
radiation is absorbed on Earth. On a global scale these
thermal effects combine with dynamic effects from the
Earth’s rotation to produce prevailing wind patterns.
21

Characteristics of the wind
• Wind resources are particularly high in coastal areas
because wind can move unhindered across the smooth
surface of the sea.
• Furthermore, temperature differences between water
and land cause local compensating streams.
• The sunlight heats the land more quickly than the water
during the day.
• The results are pressure differentials and compensating
winds in the direction of the land. These winds can
reach up to 50 km inland.
• During the night the land cools much faster than the
sea; this causes compensating winds in the opposite
direction.
22

Table 1: wind speed classification
23

All countries have national meteorological services that
record and publish weather related data, including wind
speeds and directions.
The methods are well established and co-ordinated
within the World Meteorological Organization in
Geneva, with a main aim of providing continuous runs
of data for many years.
Consequently only the most basic data tend to be
recorded at a few permanently staffed stations using
robust and trusted equipment.
Unfortunately for wind power prediction,
measurements of wind speed tend to be measured only
at the one standard height of 10 m,
24

Therefore to predict wind power conditions at a specific site,
standard meteorological wind data from the nearest station are only
useful to provide first order estimates, but are not sufficient for
detailed planning.
Usually careful measurements around the nominated site are needed
at several locations and heights for several months to a year.
These detailed measurements can then be related to the standard
meteorological data, and these provide a long-term base for
comparison.
In addition, information is held at specialist wind power data banks
that are obtained from aircraft measurements, wind power
installations and mathematical modeling, etc.
Such organized and accessible information is increasingly available
on the Internet. 25

• A standard meteorological measurement of wind speed
measures the ‘length’ or ‘run’ of the wind passing a 10m
high cup anemometer in 10 min. Such measurements may
be taken hourly, but usually less frequently.
• Such data give little information about fluctuations in the
speed and direction of the wind necessary for accurately
predicting wind turbine performance.
• Continuously reading anemometers are better, but these
too will have a finite response time.
• A typical continuous reading trace shows the rapid and
random fluctuations that occur.
• Transformation of such data into the frequency domain
gives the range and importance of these variations. 26

Variation of wind speed with height
 The wind speed is usually recorded at a height of 10 m. Changes
in elevation can change the wind speed in a distance of only a
few hundred meters. Hills or mountains influence the wind speed
significantly.
 Obstacles, plants or hills near a wind generator site can slow the
wind significantly.
 Single obstacles are no problem if the total rotor area is over
three times higher than the obstacle or if there is sufficient
distance between the wind generator and the obstacle.
 Without proper clearance, wind turbulence can reduce the
usable wind energy.
27

The wind speed increases with the height from ground
because the wind is slowed down by the roughness of
the ground.
Wind generators usually have hub heights of more
than 10 meters. For the estimation of the wind
potential, additional wind speed measurements at
other heights are necessary.
However, if the type of ground cover is known, the
wind speed at other heights can be calculated.
The wind speed v(h2) at height h2 can be calculated
directly with the roughness length, Zo of the ground
cover and the wind speed v(h1) at height h1:
28

• Obstacles can cause a displacement of the boundary layer from the
ground
• This displacement can be considered by the parameter d. For
widely scattered obstacles, parameter d is zero. In other cases d
can be estimated as 70 percent of the obstacle height.
• The roughness length z0 describes the height at which the wind
is slowed to zero. In other words, surfaces with a large roughness
length have a large effect on the wind. Table 2 shows the
classification of various ground classes depending on the
roughness length.
29

The wind speed decreases significantly with rising roughness
lengths Z0; thus, it does not make any sense to install wind power
plants in built-up areas or large forests. The wind speed also
increases significantly with height. For instance, the wind speed at a
height of 50 m is 30 per cent higher than at 10 m for ground class 4.
This must be considered for the installation of large wind turbines.
The usable wind speed at the top of large wind towers is much
higher than at the common measurement height of 10 m.
Wind turbines of the megawatt class come with hub heights of
between 50 and 70 m for coastal areas (ground class 1 to 3) and
even higher for inland areas with higher roughness lengths.
The wind speed usually becomes independent of the height, where
the wind becomes known as geostrophic wind, at heights
significantly exceeding 100 m from the ground.
30

Table 2 Roughness Lengths Zo for different ground
classes
31

32
Table 3: Decrease in Wind Speed v(h2) at Height h2 = 10 m as a
function of the Ground Class for v(h1) = 10 m/s at h1 = 50 m

Wind Direction
Direction of wind is an important factor in the sitting of a
wind energy conversion system. If the major share of
energy available in the wind is received from a certain
direction, it is important to avoid any obstructions to the
wind flow from this side.
Wind vanes were used to show the direction of wind in
earlier days of wind distribution data collection. However,
most of the anemometers used today have provisions to
record the direction of wind along with its velocity.
Information on the speed and direction of wind, in a
combined form, can be presented in the Wind Roses. The
Wind Rose is a chart which indicates the distribution of
wind in different directions
34

Wind Speed Distribution
The performance of wind turbine generators (WTG) on a
particular site can be determined by the site’s distribution of
wind speeds and the corresponding WTG power curve.
As stated in the above section the wind is never constant at any
site. It is influenced by weather system, the local land terrain, and
its height above the ground surface.
Wind speed varies within the minute, hour, day, season, and even
by year. Since wind velocity varies it is necessary to capture this
variation in the model used to predict energy production.
The variations of this wind speed are best described by the
Weibull probability distribution function with two parameters,
shape parameter and the scale parameter
36

Weibull Probability Distribution
The probability density function (PDF) of wind speeds is a
mathematical function describing the range and relative frequency
of wind speeds at a particular location.
The probability of wind speed being U during any time interval is
given by the following equation
Where, K is a constant known as the shape factor, C is the scale factor (m/s) and
U represents the wind speed (m/s). As the value of k increases the curve will
have a sharper peak and the larger the scale parameter, the more spread out
the distribution
37

From experience and multiple observations of sites, the typical
values the shape factor will range from 1 to 3 and for the specified
site the value of k considered is 2 . The typical values for the
shape factor are shown in the table below
After k is determined, the scale factor (C) can be calculated using the following
equation
38

WIND TURBINE POWER, ENERGY, AND TORQUE
44
Underlying features of conversion process
• Aerodynamic lift force on the blades  net positive torque on a
rotating shaft  mechanical power  electrical power in a
generator.
• No energy is stored – output is inherently fluctuating with the
wind variability (though can limit output below what wind could
produce at any given time).
• Any system turbine is connected to must be able to handle this
variability.

Typical size, height, diameter and rated
capacity of wind turbines
45

46
The mass flow rate dm/dt of air of density  and velocity U through a rotor disk of
area A is:
The kinetic energy per unit time, or power, of the flow is:
The wind power per unit area,
P/A or wind power density is:
Estimation of the potential wind resource
Note: density is generally taken as 1.225 kg/m3 (15oC
at sea level). Actual power output is only about 45% of
this available wind power for even the the best turbines

474747
•A wind turbine obtains its power input by
converting the force of the wind into a
torque (turning force) acting on the rotor
blades.
• The amount of energy which the wind
transfers to the rotor depends on the density
of the air, the rotor area, and the wind speed.
• The kinetic energy of a moving body is
proportional to its mass (or weight). The
kinetic energy in the wind thus depends on
the density of the air, i.e. its mass per unit of
volume.
In other words, the "heavier" the air, the
more energy is received by the turbine.

48
Power per unit area
available from
steady wind
Maps of annual average wind speeds  maps of average wind
power density. More accurate estimates can be made if hourly
averages, Ui, are available for a year. The average wind power
density, based on hourly averages is

49
where U is the annual average wind speed and Ke is called
the energy pattern factor. The energy pattern factor is
calculated from:
where N = number of hours in a year = 8,760
Typical qualitative magnitude evaluations of the wind
resource are:
P / A < 100 W/m2 - poor
P / A ~ 400 W/m2 - good
P / A > 700 W/m2 - great

Wind turbine schematic
• ..,
From left to right: a horizontal axis (propeller) type turbine,(a), and two vertical axis machines a
Gyromill,(b) and a Darrieus,(c).
50
Large no. blades
to produce high torque
Savonius Darrieus
1,2,3 and 4 blades
to produce high speed
50

Wind Power
Wind power is very strongly dependent on its speed
ρ - is a variable quantity which varies under different pressure
= 1.225 kg/m3
m - rate of air flow
V - speed of air under no obstacle in infinite distance
Maximum wind power available of which we should think to extract
21
;
2
P mV
21
;
2
AV V  
31
;
2
P AV  A V∞
Power contained in wind:
5151

Bornayl Principle – in pressure difference
Trust
2 21 1
2 2
V P v P  
   
2 2
2
1 1
2 2
V P v P  
  
 2 2
2
1
2
P P V V 
  
   2 2
2
1
2
T A P P A V V 
   
Idealized wind energy extractor , Disc / Converter
V∞
P∞
v
P+ P -
V2
P∞
5252

   
   
 
2 2
2 2
2 2
2
1
2
1
2
T m V V A V V
A V V Av V V
v V V

 
 
 

   
  
 
Defining the axial induction factor a as the fractional
decrease in wind velocity between the free stream and the
rotor plane:
   
   
   
2
2
1 ............................. 1
1
1
2
1 2 ............................. 2
v V a
V a V V
V V a

 

 
  
 
5353

Drop in kinetic energy
Power extracted
 
   
 
2 2
2
22 2
3 2
3 2 3
2
1
2
1
1 1 2
2
1
1 1 1 4 4
2
1
4 8 4
2
3 4 1 0
1
1;
3
P Av V V
AV a V V a
AV a a a
P AV a a a
dP
a a
da
a





  


 
    
 
      
    
   

3
3
1 4 1 4
8
2 3 9 27
1 16
2 27
P AV
P AV




 
    
 
   
Power contained in the wind
Two possibilities
Betz limit
5454

If we consider in trust principle
V∞
u
If the receded with speed u,
 
 
 
2
2
2
2 2
3
Force C A V V
C A V
Force C A V
C A V
C A V 4V 3 ;
V
1
: 1;
3
1
C AV
8
22 7
F
F
F
F
F
F
u
Power u u
dP u
u u
du
Two solutions
P




 

 



 




 
 
   

.FC Force coeff
For trust principle working turbine the power coefficient is
8/27
5555

u
vwind
-u
ω - relative wind
FD
FL
v
As much as we reduce the surface
Area of wind hits we reduce the drug force
component which can be done by pitch angle
56
Aerodynamic principle (not thrust) in which modern wind turbine works

Aerodynamic principle (not thrust) in which modern wind turbine works
Airofoil
FD
FL
u
vwind
-u
ω - relative wind
FD
FL
v
F
An airfoil or wing directed to
the wind direction
By Bornayl Principle
An airfoil or wing directed to
different to the wind direction
In properly designed airfoil FL
much larger than FD
The major Force responsible the turbine to rotate
5757

Lift force - defined to be perpendicular to direction of the
oncoming airflow. The lift force is a consequence of the
unequal pressure on the upper and lower airfoil surfaces
Drag force - defined to be parallel to the direction of
oncoming airflow. The drag force is due both to viscous
friction forces at the surface of the airfoil and to unequal
pressure on the airfoil surfaces facing toward and away
from the oncoming flow
58

Pressure on an airfoil.
The angle between the
wind direction and the
reference line is called
the angle of attack, α.
A lift component (normal to the velocity)
PL and PD are determined experimentally in
wind tunnels under specified conditions.
CL and CD, called, respectively, the lift
coefficient and the drag coefficient, it depends
on the shape of the object.
A drag component (parallel to the velocity)
5959

21
2
D b DdF dA C 
cos sinT L DdF dF I dF I 
sin cosM L DdF dF I dF I 
 sin cosL DdM r dF I dF I 
21
2
L b LdF dA C 
ρ = 1.2 kg/m3
Actual wind turbine has similar force vector diagram for each elements
u1
m1
u12
m12
Area of the blade element
Lift coeff.
Depends on
shape and
design
Wind tunnel used for measuring
coeff. Airfoil characteristics
In WWW. Stuttgart….
drr
mdM r dF
dP dM


u
u
DdF

LdF
dF
TdF
MdF
v
I
Total force
Thrust force
the tower stand
Moment
producing force
Linear velocity of blade
Є
60
Linear wind speed

61
Characteristics of a NACA 4412 Airfoil
Reynolds number = 9 million table 3

The tip speed ratio, λ = ω R/v1, is one of the major parameters to be selected. Up to
certain limit, the larger the λ, the better the system . However, too large a lambda
will cause ωR to exceed the speed of sound.. Actually, λ must be sufficiently low to
avoid undue noise and undue stresses.
Tip speed ratio/TSR/, [λ]
1
1
Tip speed ratio,
2
Speed of the tip
un affected V
RRn
V v
Power Output
Power Coefficient
Power Contained





 

Tip speed ratio (TSR), λ
16
27
PC
1 2 3 4 5 6 7 8
TSR 1.5 – 2 for water pumping
TSR 6 – 9 for electric production
(TS of the turbine much higher than wind speed)
Darrieus
HWT
Savonius
6262

Calculate the total thrust and aerodynamics power
developed in a 3- blade wind turbine at a wind
velocity of 9 m/s.
The machine specs. Are as follows:
 Diameter = 9 m
 Rotational speed = 100 rpm
 Blade length = 4 m
 TSR = 5.23
 Chord length = 0.45 m
 Pitch angle = 5o
 Aerofoil secction = NACA 230/8
 Distance from shaft to inner edge = 0.5 m
Example 1.
6464

1 432
1 m 1 m 1 m 1 m
4 m
By Betz theory
v = 2/3 * 9 = 6 m/s dAb= 0.45 m2
Rotational speed 100 rpm = 100/60 = 1.66 rps.
I1 = tan-1 6/(2π *1*1.66 )= 29.81o
I2 = tan-1 6/(2π *2*1.66 )= 15.98o
I3 = tan-1 6/(2π *3*1.66 )= 10.81o
I2 = tan-1 6/(2π *4*1.66 )= 8.15o
i1 = 24.81o ; i2 = 10.98o i1 = 5.81o i1 = 3.15o
CL1 = 0.95
CL2 = 1.20
CL3 = 0.75
CL4 = 0.46
CD1 = 0.0105
CD2 = 0.0143
CD3 = 0.0092
CD4 = 0.0078
From the table 3 for specific Aerofoil:
The angles b/n Relative
wind and Direction of
rotation, dFL & v
The angles of attack
for each of the blade element
Angle of incidence
i = I - α
Angle of attack
6565

66
One blade of a
horizontal axis wind
turbine. This one
rotates clockwise when
driven by a wind
blowing into the page.
 1 sin cosL DdP r dF I dF I 
 21
sin cos
2
b L Dr dA C I C I   
198.2 watt
2 3 4886.14 ; 1190.52 ; 1213.38 ;dP W dP W dP W  
 1 2 3 43Total Power dP dP dP dP   
10,466 10W kW 
1 2 3 433.96 ; 154.24 ; 212.94 ; 229.96 ;T T T TdF N dF N dF N dF N   
 1 2 3 33T T T T TF dF dF dF dF    
1893.4N
Power developed in each blade element
In the inner side
In the outer side
In the inner side In the outer side
66

I = This is the angle between the relative wind and
the direction of rotation 𝛼 =the angle between
the actual position with the relative wind that is
the angle of attack, clear. So, the actual position as
different from the direction of the relative wind
that is the angle of attack
• In order to get the angle between the chord
line and the relative wind. = I – pitch angle
• There is another important thing that you would like
to calculate. How much should be the strength of
the tower that holds the whole wind turbine and
that is dependent on the thrust that tries to topple
the tower 67

68
i
For particular foil
Angle of attack which is different for each element
68

Yaw Control
Tin-Airfoil Troposkien shaped
Generator system
Guy wire
Tensile stress
VWT
H
VWT at sea level its effective in power production
2D
D
HWT
H
HWT has orientation system
69

Darrieus Rotor which needs the first starting torque
FL
FD
FL
FL
FL
FD
FD
FD
ω
ω
ω
ω
-u
-u
-u
-u
v
v
v
v
V∞
Still in positive
torque direction
70

supp
a
useful power extructed from the wind
power lied by the wind
 
 
 
sin cos
sin
cos sin
M
T
L D
L D
L
u dF
v dF
u dF
v dF
u dF I dF I
v dF I dF
dividing by dF I
I







1 cot
cot
tan
cot
1 tan cot
cot
cot tan
1 tan cot
1 tan tan
max tan min
D
L
D
L
D D
L L
a
a
a
u I
v I
u
I
dF
dF
dF
dF
dF
v
I
I
I
I
I
wh n
C
e
dF C







 
 
 
 
 
 
 
 




 

 
 
Aerodynamic efficiency, ηa
71

The angle of attack
http://aerospace.illinois.edu/m-selig/propid.html
72

73
ᵋ
i = I - α
i
CD
CL
CL
CD

The final power output
A is in terms of diameter1/4 pi D sq
For easy and quick cal., a good, well design wind
turbine by not having all the above constants
74
3
2 3
0
1
2
1
8
p m e
p m e
p m e
AV
D V
P P C
C
C
 
 
 

 


   

 


 
Example: P = 4 kW; V∞ = 7 m/s ; Cp = 0.4 ; ηm = 0.9 ; ηe = 0.95 ; D = 8.3 m
P = 0.2 D2 V∞
3
For P = 1 MW D = ?

 High solidity is for water pumping mills
 Low solidity is for electricity production
 The Lower the solidity the higher rotational speed
 So the no. of blades should be less
75
;
Blade area
Solidity
Swept area

a bt t
bt Time taken by the distributed wind to pass
at time taken by a blade to move to
the position of the proceding blade

b
d
t
v

2
; .at n no of blade
n


 
Solidity
Disturbed wind results
in torque pulsation

For inner edge
For outer edge etc.
 For large capacity turbine these parameter
changes due to wind speed as a result a
continuous pitch angle variation should be there
76
 For lower rated turbine rotor, its possible to manufacture from wood of PVC materials
How wind turbines are made
 For higher rated turbine rotor, its possible to manufacture from fiber glass materials
Є , i - to be optimal
Є = tan Dd /Cl
i = I - α
Pitch angle
incidentof attack Angle of attack
u
u

v
I
u
u

v
I
u
u

v
I
u
u

v
I
Chord length

Tower Design
Tower should withstand all mechanical loads, oscillations and various frequencies
77
 Weight of all components
 Thrust forces
 Gear box frequencies
 Generator frequency
 Natural oscillation of the tower
2D
D
Up wind
Down wind

Wind Energy Conversion Systems
78WECS with horizontal-axis wind turbine
Tower
Yaw control to face the wind
Pitch control to
adjust pitch angle
1:25
1:30
brake
Acces
hole

79
3
.
2 3
.
2 3
.
5
3
. 3
1
2
1
2
1
2
1
2 opt
mech p
mech p
mech p
mech p
opt
P AV C
P R V C
P R V C
R
P C

 
 
  




 
 
 
 
Power
coefficient
Tip speed ratio, λ
16
27
λ
Cp P max operating at this point
R
V




Torque = Pm/n
Pm
n- rotational speed
R
V

 
Power-speed and Torque-speed characteristics of the wind turbines

Mechanical torque
80
5
2
3
.
1
2 optm p
opti
R
T C  

 
.mech mP T  
Tm
n- rotational speed per min
TL
TL
10 m/s
8 m/s
5 m/s
TL = k n2
K - Constant of proportionality

8181
TYPES OF WIND MACHINES
Generally, modern wind turbines are classified into two
basic groups:
1. Horizontal axis
wind turbines
(HAWT)
2. Vertical axis wind
turbines (VAWT)
81

82
HAWT
• Rotor axis of rotation is in line
with the prevailing wind direction
• Uses vane for orienting the turbine
towards prevailing wind direction
• Also called “directional windmill”

83
HAWT ADVANTAGES
• Variable blade pitch gives the blades the optimum angle of
attack.
• Allowing the angle of attack to be remotely adjusted gives
greater control to collect the maximum amount of wind
energy for the time of day and season.
• The tall tower base allows access to stronger wind in sites.
• For every 10 meters up, the wind speed can increase by
20% .
83

84
HAWT DISADVANTAGES
• Difficult operation in near ground, turbulent winds.
• The tall towers and blades up to 90 meters long are
difficult to transport.
• Tall HAWTs are difficult to install.
• Their height disrupts the appearance of the landscape and
sometimes creating local opposition.
• HAWTs require an additional yaw control mechanism to
turn the blades toward the wind.
84

85
VAWT
• Shaft rotation is along the
vertical axis perpendicular to
prevailing wind direction
• Non-directional due to absence
of vane
• Accept wind from any direction
• Power is available even in
ground level( lower height)
85

8686
Starting Torque of a VAWT
 The lift-force VAWT does not experience any
starting torque!!! This may be a critical issue for
certain applications.
 Turbines connected to the electricity grid can
use the electric generator as a starting motor.
In stand-alone configurations, either electricity
storage devices (again using the generator as
a starting motor) or integrated drag-force
turbines (as start turbines) can be applied in
order for the VAWT to spin up to a point where
the lift force can take over.

87
VAWT ADVANTAGES
• No massive tower structure is needed.
• No yaw mechanism is needed.
• Can be located nearer the ground,
making it easier to maintain the moving
parts.
• VAWTs do not need to turn to face the
wind if the wind direction changes.
87

88
VAWT ADVANTAGES
• VAWTs have lower wind startup speeds than
HAWTs. Typically, they start creating
electricity at 6 m.p.h. (10 km/h).
• VAWTs are less likely to break in high
winds.
• May be built at locations where taller
structures are prohibited.
88

VAWT DISADVANTAGES
• Most VAWTs produce energy at only 50% of the efficiency of
HAWTs because of the additional drag that they have as their
blades rotate into the wind.
• VAWTs will rotate faster in stronger winds at higher elevations as
they rotate at least as fast as the wind velocity.
89
89

9090
Machine Elements and Electrical Generators for Wind Turbines

9292
Gear Box
• The power from the rotation of the wind
turbine rotor is transferred to the generator
through the power train, i.e. through the main
(low speed) shaft, the gearbox and the high
speed shaft
• The gearbox increases the slower speed of the
wind turbine to the higher speed required by the
generator (1200 rpm for 50 HZ).

939393WECS with horizontal-axis wind turbine
Tower
Yaw control to face the wind
Pitch control to
adjust pitch angle
1:25
1:30
brake

Yawing
Horizontal axis wind turbines must always follow the direction of
the wind, in contrast to vertical axis wind turbines.
The orientation of the rotor blades must be chosen so that the
rotor blades face the wind at the optimal angle. This can be a
problem for pitch-controlled wind turbines if the direction of the
wind changes very fast or is gusty. Hence, high power fluctuations
can occur and must be cushioned by changes in the rotor speed.
The position of the rotor can be upwind or downwind. The position
of the rotor relative to the tower for upwind turbines is before the
tower in the direction of the wind, and for downwind turbines it is
behind.
The disadvantage of the downwind rotor is that the rotor blades
have to continually pass the sheltered zone of the tower. This
produces high mechanical strains and noise emissions due to
turbulence from the tower and the nacelle. 94

Therefore, most large wind turbines are upwind turbines.
Downwind turbines have the advantage that wind pressure adjusts
the rotating rotor blades optimally to the wind.
Small wind turbines can use wind vanes for passive yawing. The
wind vane moves the rotor of an upwind turbine always to a
position perpendicular to the wind.
To move a horizontal axis wind turbine in the yaw direction, the
whole nacelle with rotor, gearbox and generator must be movable
on top of the tower.
Wind measuring equipment on the nacelle estimates the wind
speed and direction and a control unit decides when an electric or
hydraulic yaw drive moves the nacelle and rotor azimuth.
When the nacelle reaches its optimal position, azimuth brakes hold
this position. In reality there are always small deviations of the
direction of the wind and the optimal position of the rotor. This
deviation is called the yaw angle and is usually about 5°. 95

9696
Cooling Unit
• The cooling unit contains an electric fan
which is used to cool the electrical generator
• In addition, it contains an oil cooling unit
which is used to cool the oil in the gearbox
• Some turbines have water-cooled generators.

9797
Ideal power output Curve
 The turbine is usually designed to reach full rated
power at wind velocities of around 12–15 m/s.
 It actually runs at part-load most of the time, as the
wind speeds are mostly below the nominal value.
 On the other hand, in stronger winds the turbine
must decrease its output to protect the generator
from overloading.
 The ideal and optimum power curve for a typical
wind turbine would look like this

9898
Ideal power output Curve
Cut-In Speed
 The wind speed at which a wind turbine begins to produce power
Rated Speed
 The "rated wind speed" is the wind speed at which the "rated power" is achieved
and generally corresponds to the point at which the conversion efficiency is near its
maximum .
 In most cases, the power output above the rated wind speed is maintained at a
constant level.
Cut-Out Speed
The cut-out speed is the wind speed at which the turbine may be shut down to
protect the rotor and drive train machinery from damage, or high wind stalling
characteristics;

99
P Output
Wind speed (m/s)
kW
TL
3
P V
(m/s)
Controling power
Rated Power
Rated Speed
Cut-in speed Cut-Out speed
or Furling wind speed
Dangerous speed
Pitch angle should be changed in
wrong way slightly to maintain power to be stable
Stalling region
- Active stall
- passive stall
Applied for small WT
Without pitch adjustment

Limiting power output and storm protection
The power that can be taken from the wind varies with the wind
speed. After reaching the nominal power, the power should
remain constant for wind speeds greater than the nominal wind
speed because the turbine and generator cannot handle more
power. Therefore, a wind power plant must limit the power with
one of the two following methods:
• stall control
• pitch control.
100

• Many manufacturers of wind turbines prefer pitch control,
although the technical effort is much higher than for stall
control. However, since pitch control is an active control, it
can be adjusted to suit the conditions, in contrast to stall-
controlled systems. Pitch control directly increases or
lowers the pitch angle of the rotor and therefore the angle
of attack. The rotor blade is turned into the wind at higher
wind speeds lowering the angle of attack and actively
decreasing the power input of the rotor blade.
• Pitch controlled wind turbines are more difficult to
manufacture because the rotor blades must twist inside the
rotor hub. Small systems often use mechanically controlled
pitch mechanisms using centrifugal forces. An electric
motor moves the rotor blade to the desired position in large
systems.
102

If the wind generator is stopped due to storm protection, the pitch
control can pitch the rotor blade towards the feather position. This
reduces the power input and avoids damage to the wind turbine.
Stall-controlled systems often have additional aerodynamic brakes.
For instance, the rotor tip can bend. During storms, the tip bends by
90° and slows the wind turbine.
Rotor Blade Positions for Different Wind Speeds for a Pitch-controlled System 103

Wind Measurement
The device measurement relies on thrust force produced by the wind
Small taco-generator to produce a voltage proportional to the wind
Or a disc having holes at the periphery- and an integrated data logging devices
104
The Robinson cup anemometer
hr.
m/s
104

Low-power wind generation
• Power output of each generation unit in the order of a few kW. Power profile is
predominately stochastic.
• Originally they were used for nautical and rural applications with dc generators. Cost
is relatively low.
• More modern systems use permanent-magnet generators.
Air-X 400
400 W
Rotor diameter: 1.15 m
SW Windpower
Whisper 200
1 kW
LNP 6.4-5000
5 kW
108

Low-power wind generation
Bergey Excel
7.5 kW
Solerner
3 kW
YM-CZ3kW
3 kW
SW Windpower
Whisper 500
3 kW
Wind generators
In Tokyo
109

Wind generators model
• The output in all types of generators have an ac component.
• The frequency of the ac component depends on the angular speed of the wind
turbine, which does not necessarily matches the required speed to obtain an output
electric frequency equal to that of the grid.
• For this reason, the output of the generator is always rectified.
• The rectification stage can also be used to regulate the output voltage.
• If ac power at a given frequency is needed, an inverter must be also added.
• There are 2 dynamic effects in the model: the generator dynamics and the wind
dynamics.
110

Classifications of Electrical machine
ELECTRICAL MACHINES
AC MACHINES
ASYNCHRONOUS
(INDUCTION)
MACHINE
DC MACHINES
SYNCHRONOUS
MACHINE
Mostly Exist in
Generator mode
Mostly Exist in
Motor mode
111

Wind generator
•Synchronous generator
•Induction generator
112

PERMANENT MAGNET GENERATORS
A permanent magnet generator is like the synchronous or ac
generator except that the rotor field is produced by permanent
magnets rather than current in a coil of wire.
This means that no field supply is needed, which reduces costs. It
also means that there is no I2R power loss in the field, which
helps to increase the efficiency.
One disadvantage is that the reactive power flow cannot be
controlled if the PM generator is connected to the utility
network. This is of little concern in an asynchronous mode, of
course. The magnets can be cast in a cylindrical aluminum rotor,
which is substantially less expensive and more rugged than the
wound rotor of the conventional generator.
No commutator is required, so the PM generator will also be less
expensive than the dc generator of the previous section.
These advantages make the PM generator of significant interest
to designers of small asynchronous wind turbines. 113

CommercialWindTurbines
• 3 phase induction generators are industry standard
• Require multistage gearboxes
– Gearboxes fail before designed lifetime of 20
years and account for majority of system losses
– High operation and maintenance costs
• Variable speed operation is expensive
• Direct drive permanent magnet generators present
an efficient alternative
Need for Renewable Energy
Need for Alternative Generators
inWindTurbines
Problem Definition
114

where Xs is the synchronous reactance, Rs is the winding
resistance, and Ra is the resistance of one leg or one phase of
the load resistance. The neutral current In is given by the sum
of the other currents
In = Ia + Ib + Ic A
If the load is balanced, then the neutral current will be zero. In
such circumstances, the wire connecting the neutrals of the
generator and load could be removed without affecting any of the
circuit voltages or currents.
The asynchronous system will need the neutral wire connected,
however, because it allows the single-phase voltages Va, Vb, and
Vc to be used for other loads in an unbalanced system. Several
single-phase room heaters could be operated independently, for115

 It is desirable to maintain the three line currents at about the same value to minimize
torque fluctuations. It is shown in electrical machinery texts that a three-phase generator
will have a constant shaft torque when operated under balanced conditions.
 A single-phase generator or an unbalanced three-phase generator has a torque that
oscillates at twice the electrical frequency.
 This makes the generator noisy and tends to shorten the life of the shaft, bearings, and
couplers.
 This is one of the primary reasons single-phase motors and generators are seldom seen
in sizes above about 5 kW.
 The PM generator will have to be built strongly enough to accept the turbine torque
fluctuations, so some imbalance on the generator currents should not be too harmful to
the system, but the imbalance will need to be minimized to keep the noise level down, if
for no other reason.
Permanent-magnet generator connected to a resistive load
116

AC GENERATORS
The standard type of generator for all power generation at the commercial level,
except in wind turbines, is a three-phase synchronous generator
The specific difference between a synchronous generator and an asynchronous
generator is that a synchronous generator must be rotated at a constant rpm in
order to be connected to a grid. Otherwise the frequency of the generated
electricity, which depends on the rpm, is not going to be constant and fixed at a
required value.
It is impossible to have different frequencies in agrid. Indeed, it is impossible to
connect an AC generator to a grid with a frequency other than that of the grid. At
a lower level, it is impossible to interconnect two AC generators having two
different frequencies.
119

• This does not mean that a synchronous generator cannot
provide electricity when it is rotated at different rpm. In an
isolated application where frequency is not important, a
synchronous generator can be used. Suppose that in a remote
location a single wind turbine is to provide electricity for
heating and lighting. Heating and lighting are less affected by
frequency. In such a case, a three-phase or single-phase
synchronous AC generator can be employed.
• The major difference from permanent magnet generator is
that the induced emfs are no longer proportional to speed
only, but to the product of speed and flux. In the linear case,
the flux is directly proportional to the field current If , so the
emf Ea can be expressed as
120

 Basic parts of a synchronous generator:
• Rotor - dc excited winding
• Stator - 3-phase winding in which the ac emf is generated
 The manner in which the active parts of a synchronous
machine are cooled determines its overall physical size and
structure
TYPES
 Salient-pole synchronous machine
 Cylindrical or round-rotor synchronous machine
121

1. Most hydraulic turbines have to turn at low speeds
(between 50 and 300 r/min)
2. A large number of poles are required on the rotor
Hydrogenerator
Turbine
Hydro (water)
D  10 m
Non-uniform
air-gap
N
S S
N
d-axis
q-axis
Salient-Pole Synchronous Generator
122

Salient-Pole Synchronous Generator
Stator
123

L  10 m
D  1 mTurbine
Steam
Stato
r
Uniform air-gap
Stator winding
Rotor
Rotor winding
N
S
 High speed
 3600 r/min  2-pole
 1800 r/min  4-pole
 Direct-conductor cooling (using
hydrogen or water as coolant)
 Rating up to 2000 MVA
Turbogenerator
d-axis
q-axis
Cylindrical-Rotor Synchronous Generator
124

Cylindrical-Rotor Synchronous Generator
Stator
Cylindrical rotor 125

Operation Principle
The rotor of the generator is driven by a prime-mover
A dc current is flowing in the rotor winding which
produces a rotating magnetic field within the machine
The rotating magnetic field induces a three-phase
voltage in the stator winding of the generator
126

Generated Voltage
The generated voltage of a synchronous generator is given by
where f= flux in the machine (function of If)
fe = electrical frequency
Kc= synchronous machine constant
Saturation characteristic of a synchronous generator.
ec fKE f
If
E
127

Equivalent Circuit_1
o The internal voltage Ef produced in a machine is not usually the
voltage that appears at the terminals of the generator.
o The only time Ef is same as the output voltage of a phase is
when there is no armature current flowing in the machine.
o There are a number of factors that cause the difference between
Ef and Vt:
– The distortion of the air-gap magnetic field by the current flowing
in the stator, called the armature reaction
– The self-inductance of the armature coils.
– The resistance of the armature coils.
– The effect of salient-pole rotor shapes.
128

generator
motor
Ia
Ia
Ef
Eres
Vt
jX jXl Ra
+
+
+
Equivalent Circuit_2
Equivalent circuit of a cylindrical-rotor synchronous machine
129

Phasor Diagram
Phasor diagram of a cylindrical-rotor synchronous generator,
for the case of lagging power factor
Lagging PF: |Vt|<|Ef| for overexcited condition
Leading PF: |Vt|>|Ef| for underexcited
condition 130

Three-phase equivalent circuit of a cylindrical-rotor
synchronous machine
The voltages and currents of the three phases are 120o apart in angle,
but otherwise the three phases are identical.
+
Ia1
Ef1 jXs Ra+
VL-L
VL-L =3Vt
Vt
131

SELF-EXCITATION OF THE INDUCTION GENERATOR
 Induction generator is generally simpler, cheaper, more reliable, and
perhaps more efficient than either the ac generator or the dc
generator.
 The induction generator and the PM generator are similar in
construction, except for the rotor, so complexity, reliability, and
efficiency should be quite similar for these two types of machines.
 The induction generator is likely to be cheaper than the PM generator
by perhaps a factor of two, however, because of the differences in the
numbers produced.
 Induction motors are used very widely, and it may be expected that
many will be used as induction generators because of such factors as
good availability, reliability, and reasonable cost
132

 An induction machine can be made to operate as an
isolated ac generator by supplying the necessary
exciting or magnetizing current from capacitors
connected across the terminals of the machine
133

Doubly-Fed Induction Generators (DFIG)
• Doubly-fed electric machines are basically electric machines that
are fed ac currents into both the stator and the rotor windings.
Most doubly-fed electric machines in industry today are three-
phase wound-rotor induction machines.
• Doubly-fed induction generators have a number of advantages
over other types of generators when used in wind turbines.
 The primary advantage of doubly-fed induction generators when used in wind
turbines is that they allow the amplitude and frequency of their output voltages
to be maintained at a constant value, no matter the speed of the wind blowing
on the wind turbine rotor.
 Because of this, doubly-fed induction generators can be directly connected to
the ac power network and remain synchronized at all times with the ac power
network.
 Other advantages include the ability to control the power factor (e.g., to
maintain the power factor at unity), while keeping the power electronics devices
in the wind turbine at a moderate size. 134

• The same operating principles apply in a doubly-fed
induction generator as in a conventional (singly-fed)
induction generator. The only difference is that the
magnetic field created in the rotor is not static (as it is
created using three-phase ac current instead of dc
current), but rather rotates at a speed
137

Interaction between the rotor speed and the frequency of the rotating magnetic field
created in the rotor windings of a doubly-fed induction generator 139

Modes of operation of wind turbines
• The way a wind turbine is connected to a grid depends on the type of the
generator employed and the design specifications of the turbine. This
determines what other equipment is necessary and what control strategy may be
utilized.
• We call the various ways practiced by wind turbine manufacturers the modes of
operation.
1.Those that use synchronous generators, and
2. Those that use asynchronous generators.
In the first category the modes are: direct drive mode, fixed speed mode, and
variable speed mode.
In the second category, there are also three different modes that wind turbine
generators are put to work. In one of them, a squirrel-cage generator is used, and
in the other two, the generator is a wound-rotor induction machine.
Thus, we can refer to these modes as (a) squirrel-cage generator mode, (b) variable
slip mode, and (c) variable slip with doubly fed induction generator mode.
146

Direct drive mode
As the name implies, in this mode of operation the turbine and generator
are directly connected to each other, and there is no gearbox between
them.
A three-phase transformer stands between the generator and the grid, to
increase the voltage from the generator to the grid voltage.
A difficult condition to be satisfied here in such a mode is the necessity
for the turbine and the generator speed to be the same. Such a
requirement implies that the design speed of a turbine be high and a
generator with a large number of poles be used.
As we can recall, a generator with a large number of poles (similar to
those used in water turbines) has a relatively large diameter. Also,
operating a turbine at a high speed creates a lot of noise, which is not
desirable.
New designs try to overcome the problem of speed match by other
possible means such as hydraulic converters, or using permanent magnet
generators. Employing permanent magnets eliminates the need for higher
speeds of a generator in order to provide the rotor magnetic field.
However, the frequency of the generated AC electricity is low and,
147

Therefore, a frequency converter must be employed to raise the frequency to
that of the grid. Most recently Siemens introduced a permanent magnet
(synchronous) generator for wind turbines used in variable speed mode , but
connected directly to the turbine rotor. This generator has other design features
such as placing the permanent magnets on the outside of the stator winding.
148

Fixed speed mode
In fixed speed mode a synchronous generator is connected to the turbine
by means of a gearbox .
The gearbox increases the slow speed of a wind turbine to a high speed,
matching that of the generator.
In this sense, a smaller size generator can be used compared to the direct
drive, but still the necessity of running the turbine at a fixed speed is there.
This mode was practiced before the induction generators found their place
in wind power generation.
Since there can be a considerable difference in the amount of power at high
wind speeds compared to low wind speeds, in some turbines two
generators were involved, a small generator for low wind speed and a large
generator for high wind speeds.
A switching mechanism was required to disengage one and bring in the
other at a certain wind speed. This arrangement is no longer utilized
presently in today’s more sophisticated and more powerful wind turbines
149

Variable speed mode
In order to capture wind power at a wider range of wind speeds the
variable speed mode is utilized by some turbine manufacturers.
This method relaxes the tight condition of turbine speed control.
Variable speed turbines use electronic converters to change the
generated AC electricity (which can be at any frequency, depending
on the wind speed) to DC and then convert the DC back to three-
phase AC.
With such a design there is no restriction on the speed at which a
turbine runs, except that it should not overload the generator and
the electronic components. Converting AC to DC is performed by a
rectifier, and converting DC to AC is carried out by an inverter. The
two of them together, as utilized in the variable speed mode, is
sometimes called a frequency converter, since the initial AC is
converted to a second alternating-current electricity with a different
frequency. 150

One of the disadvantages of the variable speed turbine is the
initial cost of the electronic devices involved, since these devices
must be able to handle the full power of the turbine. This cost
can constitute a considerable percent of the total cost, and can
be prohibitive.
151

Variable slip mode
• From the discussion of the induction machines it can be
seen that if the slip of a machine is altered by introducing
external resistance in series with the rotor winding it is
possible to better adapt the operating point of an
induction generator to the maximum point of the turbine
characteristic curve.
• This method has been implemented in some turbines in
order to have the turbine operate more efficiently and
near the maximum point of its characteristic curve,
152

Variable slip with doubly fed induction generator
 We have already had a discussion of how the doubly fed induction generators work,
Suppose that a squirrel-cage induction generator can work at wind speeds between 4
m/sec and 20 m/sec.
 This implies that the cut-in speed is 4 m/sec and the turbine does not have any
production below this speed, and the cut-out speed is 20 m/sec and the turbine must
stop if the wind speed exceeds this.
 Now, if a same size induction generator with a wound rotor is used instead, because the
rotor winding is accessible, we can connect the rotor winding to external circuits. The
squirrel-cage generator had to be stopped at a 20 m/sec wind speed because the higher
speed wind would cause the generator to overload or the speed would go beyond the
limit, increasing the frequency.
 With the wound-rotor generator, part of the available energy is extracted from the rotor
winding, and at a 20 m/sec wind speed the generator has not yet reached its maximum
capacity; it can continue to generate electricity, say, up to 23 m/sec wind speed.
 In addition to that, at lower-end wind speeds instead of stopping production at a 4 m/sec
wind speed, this generator is still capable of continuing to work until wind speed drops to,
say, 3 m/sec; thus, grasping more wind power within a wind regime
153

In a doubly fed induction generator, a portion of the generated
electricity is from the stator. This portion can be up to about 70% of
the generator power rating. The rest, reaching a maximum of 30% of
the generator power rating, comes from the rotor winding.
The portion generated by the stator is formed by the same principle
as the squirrel-cage generator and the performance of the generator
and its circuitry are similar to those of a squirrel-cage generator.
On the other hand, the frequency and the voltage of the portion of
electricity from the rotor are not compatible with those of the grid.
In order to feed this portion into the grid both the frequency and
the voltage must be changed. This is done in a similar manner to
what was discussed for the variable speed mode of operation. The
alternating current electricity from the rotor is first converted to DC
with a rectifier and, in turn, the DC voltage is converted back to AC
with the required frequency and voltage.
154

As we can see, the electricity from the stator is connected directly to the grid, whereas
the electricity from the rotor must pass through the back-to-back converters for AC-to-
DC-to-AC conversion.
The back-to-back converter works both ways. It consists of two programmable
converters that can convert AC to DC or DC to AC, based on the requirement, according
to the wind speed. The converters are connected together by a capacitor, which
performs as a DC source. The voltage of this capacitor is kept at a constant value by one
of the converters performing as a source while the other converter acts as a load.
At higher wind speeds where the generator rotor rpm is higher than the synchronous
speed (based on the grid frequency), the converter connected to the rotor winding acts
as an AC-to-DC converter and supplies the DC source.
155

• At lower wind speeds, when the generator rotor rpm drops, the
actions of the two converters are switched. An alternating current
with appropriate frequency is generated by the converter attached
to the rotor winding and is injected to the rotor windings.
• In this case, the converter attached to the rotor winding becomes
a consumer (a load) and the other converter becomes a source.
The advantage of this mode over the variable speed mode,
described earlier, lies in the fact that the cost of the electronic
components in this mode is much lower than in the variable speed
mode, since they must be rated for only 30% of the power.
• This is a remarkable advantage of doubly fed induction generators
used in wind turbines compared to variable speed mode using
synchronous generators.
156

ELECTRICAL SYSTEM CONCEPTS
Grid monitoring
The grid data is detected by the electrical quantity collection
module equipped with power converters and monitored by the
controller. The grid data detection is divided into the following five
aspects.
Voltage: The three phase voltage is detected continuously all the
time. These detection values are stored after calculating. The
voltage measuring and calculation value is also used for monitoring
over voltage and under voltage in order to protect the wind
generating set.
Current: The three phase current is detected continuously all the
time. These detection values are calculated and stored. The
voltage measuring and calculation value, the current measuring
and calculation value and some other data are used together to
calculate the output and consume of wind generating set.
157

Frequency: The frequency is used to detect the three phase
continuously. These detection values are calculated, stored and
compared to the specified value for calculation. Once the
frequency detected higher than or lower than the specified
value, the wind generating set will stop at once.
Active power output: The three phase output
power is detected continuously. These detection
values are stored and used to perform different
calculation of average. The total three phase output
power is calculated according to the measured value
of each phase of output power, in order to calculate
the output and consume of active electric degree.
The active power value also serves as the stop
condition for overload or under load of wind
generating set.
158

Reactive power output: Continuous detection of three
phase reactive power is done then stored and used to
perform different calculation of average. The total three
phase output power is calculated according to the
measured value of each phase of output power.
Bridge rectifier
The rectifier system used in AWF is six phase full bridge
rectifier system. Converts the six phase AC output comes
from generator to DC output. The rectifier system is
consisted up of using twelve uncontrolled diode
components. Rectifiers are characterized as non linear
loads causing harmonics in the wind farm operation.
However, as compared to the three phase rectifier system,
the six phase rectifier used in AWF is expected to have
lower du/dt effect. Hence, it may results low emission of
harmonics effects relatively.
159

Six phase system also has more stable and increased
amount of DC- link voltage production than three
phase system. This has been proved mathematically
as follows. For three phase system, the voltage is
given as,(AWF)
160

Frequency Converter (AWF)
The connection of the wind farm to the public grid is done by a frequency converter system
and a transformer. The frequency converter has been specially designed for the use
together with synchronous generators. It allows a complete separation of the generator
operation from the grid system. So variable speed operation of generator in a speed range
of 9 to 17.3 rpm is possible. At the generator output side, a 12 – pulse uncontrolled rectifier
with a subsequent step-up converter is used to avoid voltage peaks (du/dt loads) in the
generator windings, which has a very simple, but robust layout. Main circuit of the converter
system adopts AC-DC-AC structure, and sends the energy of PMSG to the grid.
The main circuit diagram of the converter system is as follows.
162

TURBINE PLACEMENT
 The production of large quantities of electricity will require the installation of many wind
turbines. There are many economic benefits if these turbines are installed in the clusters
that we call wind power plants or wind farms.
 That is, installation can proceed more efficiently than if the turbines are widely distributed.
Operation and maintenance can be done with minimum personnel. Collection of the
electricity generated can be accomplished efficiently.
 The larger amounts of concentrated power can be more easily transformed to higher
voltages and distributed on the utility grid.
 Turbines will typically be placed in rows perpendicular to the prevailing wind direction.
Spacing within a row may be as little as two to four rotor diameters if the winds blow
perpendicular to the row almost all the time.
 If the wind strikes a second turbine before the wind speed has been restored from striking an
earlier turbine, the energy production from the second turbine will be decreased relative to
the unshielded production. The amount of decrease is a function of the wind shear, the
turbulence in the wind, the turbulence added by the turbines, and the terrain.
 This can easily be in the range of five to ten percent for downwind spacing’s of
around ten rotor diameters. Spacing the turbines further apart will produce more
power, but at the expense of more land, more roads, and more electrical wire.163

We will define two turbine spacing’s,
Dcw as the crosswind spacing within a row of turbines,
Ddw as the downwind spacing between rows of turbines.
These are calculated as a constant times the number of rotor
diameters Dr. The terms are shown in Fig. below
• It appears that a reasonable spacing is four rotor diameters
between turbines in a row and
• Ten rotor diameters between rows.
• The rows would be aligned across the prevailing wind direction,
usually in a east-west direction in this part of the world where
strong winds are usually from the north or south.
• We will consider that spacing's less than 3Dr in a row or 8Dr
between rows will need special justification. 164

Dimensions of Turbines in a Wind farm
165

SITE PREPARATION
• The first step in constructing a wind farm is to acquire the right
to use the land. Land may be either purchased or leased,
depending on the circumstances.
• It holds the capital costs down to a minimum. It may be the only
practical method of acquiring large tracts of ground from many
owners if a large wind farm is planned.
• Depending on the type of turbine and the spacing, most of the
land may still be usable for agricultural purposes.
166

• On the other hand, multi mega watt turbines have not proven
themselves cost effective, so wind farms are installed with smaller
turbines, mostly in the 50 - 500 kW range.
• The smaller turbines will have a much greater density on the land
and therefore affect with farming operations to a greater extent.
• For example, the Carter 300, a guyed turbine rated at 300 kW,
with a crosswind spacing of 4 diameters and a downwind spacing
of 10 rotor diameters, would have 8 rows of 20 turbines each on a
square mile of land.
• The access roads and guy wires would make it very difficult to
grow row crops.
• It may be best to buy the land, plant it to grass to minimize
erosion, and perhaps harvest the grass for cattle feed.
167

• There may be some sites which do not require access roads
because of rocky or sandy soil conditions, but most sites will
require graded roads with a crushed rock or gravel surface so
work vehicles can reach a turbine site in any kind of weather.
• The minimum length of access roads would be the total length
of all the turbine rows plus the distance across the wind farm
perpendicular to the rows plus the distance from the nearest
existing road to the Wind farm.
• Some turbine types, such as the Carter 300, may require two
access roads per row of turbines. One road would be for access
to the base of the turbine and the other road would be to reach
the guy point from which the turbine is lowered to the ground
for maintenance.
168

• While the length of access roads and the length of electrical wire
required to interconnect the turbines is easy to calculate for a given
site with a given turbine layout, detailed economic studies involving
different wind farm sizes, perhaps with different turbines, are more
easily performed with simple formulas which determine these
lengths for given assumptions.
• We will therefore develop the notation which will allow such studies
to be performed in an efficient fashion. We define the power rating
of an individual turbine as P tur and the number of turbines in the
wind farm as Nt farm. The total power rating of the wind farm, Pwf, is
then
169

• Each row will have some length Drow as determined by land
and electrical constraints.
• In the Great Grasslands, county and township roads usually
have a distance between road centerlines of one mile (5280 ft)
so a row length of 5000 ft would allow the end turbines to be
140 ft from the road.
• This would usually be the practical maximum row length in this
part of the world.
• The tentative number of turbines in a row, Ntrow, for a tentative
row spacing Dcw, would be given by
170

• This calculation should be treated as integer arithmetic. That is, a result of 9.62
would be interpreted as either 9 or 10 turbines per row.
• Other constraints may require either a smaller or larger value. If four turbines are
to be operated from a single transformer, for example, then it may be
economically desirable to have the number of turbines in a row be some multiple
off four, say 8 or 12 for our tentative calculation of 9.62 turbines per row.
• One design choice which must be made is whether to hold the turbine separation
at exactly four rotor diameters, for example, and let the row length be less than
the maximum possible value, or to fill all available space and let the turbine
separation differ from exactly four rotor diameters.
• One generally wants to use all available land but there may be cases where a
small wind farm is to be installed on a large piece of ground that one would just
use the nominal turbine spacing.
• Once the actual number of turbines per row, Ntrow, has been selected, along
with the actual row length Drow, the actual turbine spacing in a row Dcw is given
by
171

• The number of rows and the corresponding length of a column of wind turbines,
Dcol, will be determined in a similar fashion.
• The size of the piece of land and zoning requirements will determine the
maximum column length.
• The maximum number of rows would be used to compute the total number of
turbines in the wind farm and the total electrical power rating.
• There may be financial or technical limitations on the number of turbines or the
total power, so fewer rows may be necessary.
• There may also be a requirement for an even or odd number of rows for
economic efficiency of wind farm layout.
• A rectangular piece of ground would be expected to have the same number of
turbines in each row although local terrain features may require some turbines
to be omitted from the spot they would otherwise occupy.
• There may need to be some iteration between the calculation of the number of
turbines per row and the number of rows.
• Once the column length Dcol and the number of rows Nrows has
been selected, the actual down wind spacing Ddw can be calculated.
172

• The length of a rectangular fence around the perimeter of the wind
farm would be
• where ht is the hub height of a turbine and Dr is the
rotor diameter. Increasing the fence length by the hub
height plus half the rotor diameter on each side will
allow each turbine to be laid down in any direction
without the rotor striking the fence.
• If the turbines do not fill the entire purchased area,
then the fence would be longer since it would normally
be placed at the boundary. If a section of land was
purchased, the length of fence would be approximately
four miles. 173

ECONOMICS OF WIND ENERGY
• There are two types of costs for a wind energy project.
• The first category is the initial costs. Initial costs are associated
with the purchase and installation of wind turbines up to the point
that they are ready for production.
• It is normally a one-time expense that a developer must pay for at
the beginning of a project.
• However, in addition to the price of a turbine and the installation
cost, there are other costs that are not so evident, and that one
may overlook.
• We may categorize the initial cost, thus, into direct and indirect
costs, as discussed here. Direct costs are for turbine(s) and its
ancillary components (controls, transformers, etc.), turbine
foundation and installation, transportation, and connection to the
grid.
174

• Indirect costs are for the purchase of land and/or the site,
roads to access the site, extra cost if the site is far from
the grid, legal fees, and so on.
In this section we consider the various initial costs of a wind
energy development project
• The cost of a turbine is what one must pay to the manufacturer for
all the components of a turbine.
• Normally a turbine is sold as a whole, like an automobile. So,
although the blades, the gearbox, the generator, the nacelle, and
the tower can be manufactured by different companies, they are
already matched together and are delivered to a customer.
• At delivery to the site, however, a turbine is not yet assembled
because of the large size. Each major component is delivered
separately, and the assembly takes place on site only after the
foundation is ready 175

• The cost for a turbine, thus, is the price one
must pay for: tower (including what is inside the
tower, such as ladder, cables, lights and so on);
gears and motors for yaw motion; nacelle
(containing all auxiliary parts as oil heat
exchangers, space heaters, etc.); generator;
gearbox; rotor (hub, blades, all the controls
inside them); turbine controller; pad mount
transformer; and all other small components for
measurements, instrumentation,
communication, and control.Installation
176

Installation of a turbine consists of
1. Foundation construction
2. Erecting the turbine
3. Connection to the grid, testing, and commissioning
• The foundation of turbine is a giant block of concrete that must
be able to hold the turbine; that is, it must withstand and transfer
to ground all the force of weight and the lateral forces that a
turbine gets from wind.
• The diameter of a turbine tower can be around 10–12 ft (3–3.6
m), whereas the diameter of the foundation can reach 50–55 ft
(15–17 m). The depth of the foundation is accordingly
proportional.
.
177

• In this regard, the bulk of the foundation is hidden in
the ground, covered by soil.
• Only the part of the foundation a turbine is bolted to
shows from outside, like an iceberg, only the tip of
which is out of the water.
• Considering the size, weight, and the forces exerted on
a turbine, the weight of the foundation block must be
comparative.
• The dimensions of the foundation, depending on the
type of soil and the ground condition, are determined
to withstand the forces
178

• In this respect, the construction of the foundation implies digging the ground and
replacing the soil with thousands of cubic yards of reinforced concrete.
• Obviously, the cost of this operation is not trivial. But it is a one-time expense that
comprises a significant percentage of the initial cost of a turbine After the
foundation is ready, erection of a turbine is usually carried out by setting up the
base (lowest segment) of the tower.
• The tower arrives to the site in three or four segments, depending on the height
and the design—the base, one or two middle segments, and the top.
• The base is fixed to the bolts mounted in the foundation.
• This follows by fixing one by one the other segments of tower on top of each
other, and bolting each to the previous one.
• After the tower is completed, the nacelle, the gearbox, the generator, and other
components, depending on the way a turbine is designed, are lifted and fixed in
their places.
• Finally, the rotor, which was assembled on the ground, is lifted and attached to
the nacelle.
• All the lifting must be done by strong and large cranes that are able to reach
higher than the nacelle .
• This installation of the turbine is also costly and the operation counts for a non-
negligible percentage of the initial cost.
179

Transportation
• Another portion of the initial cost is the expense of transporting the
turbine(s) to the site. That is, from the manufacturing site to the wind farm.
Whereas the previous two cost items are almost the same for two identical
turbines, this cost can be very different and depends on factors such as the
distance from the manufacturer, how far the site is from major roads, and
how difficult access is to the site.
• All the pieces of a turbine are either heavy or long. For on-road
transportation of a large turbine (over 1 MW), each blade is carried
separately and each segment of the tower is also carried separately on a
special truck for long loads.
• On large roads and highways, this is normally not a problem provided that the
highway safety code is respected. On smaller roads and in mountainous
regions, nevertheless, a long vehicle may have difficulties in turning, in
addition to disturbing the other traffic, which can lead to travel time
limitations and long delays. As well, if no appropriate road exists from a main
route to the site, new temporary roads must be constructed. These are the
extra costs that cannot be avoided.
180

Grid connection
• The same thing that was mentioned for the transportation and road factor is
true also for connection to a grid.
• That is to say, if a transmission line exists in the vicinity of a wind farm,
connecting the farm to the grid is much less expensive than if a wind farm is in
an area where either there is no transmission line or there is no more capacity
for an existing transmission line. Installing transmission lines, when necessary,
adds to the cost of a project.
• For a wind farm, all the generation, that is, the output electricity from turbines,
is put together in a collector. The collector, which operates like a substation, is
connected to a grid. The cost of the substation and the cables from turbines
(usually buried underground cables) is included in the initial cost of a wind farm.
Legal and other costs
Among the indirect initial cost of a turbine there also are those
expenses for legal issues such as right of way, agreements with land
owners where the turbines are located, various contracts, insurance
for operations, and similar items. This cost is not very high, but still
has to be a counted for when a wind farm is to be developed 181

Operating cost
The operating cost or running cost for any plant or business activity, including a
wind farm, is the regular day-to-day expenditure for running the business. For a
general plant, this is normally addressed as operations and maintenance. The
breakdown of this cost depends on the type of the activity. The cost associated
with a wind power plant can more specifically be categorized into:
• Operations
• Maintenance
• Insurance
• Lease and Royalty
• Taxes
For a production or manufacturing plant, normally the cost of raw material must
also be added to the list. For an activity that requires people, the building to
accommodate them, heating, office supplies, and so on are to be also added.
For a power plant, in addition to these there is a larger cost for fuel. Compared
with gas, fossil, coal, and nuclear power generation plants, the fuel for a wind
turbine is wind, which is free. With the others, one has to pay for gas, coal, oil,
or uranium.
Compared with gas, fossil, coal, and nuclear power generation plants, the fuel
for a wind turbine is wind, which is free. 182

Running cost
• We consider here the other wind turbine operating costs except the
maintenance for further discussion.
• When a set of wind turbines are in production they work in open air
in the land where they are installed. In many cases, this land does
not belong to the developer of the wind farm. It can belong to one
or more owners. Based on a contract, a yearly amount is paid to the
owner of the land in the form of rent or lease for the land. At
today’s rate this amount is $5000 to $6000 for each turbine.
• A second item of this cost is the amount to be paid for the
insurance.
• Insurance of an operating turbine is necessary. Again, this is based
on the content of the insurance policy. It could be for the coverage
on the equipment failure, damage to surrounding area, injury to
people, fi re, and so on. This could be much more than the
aforementioned figure for rent, for each turbine. 183

• A third item that comes into effect is the tax that a company must
pay.
• Tax is usually calculated based on the income of a corporation. For
a wind farm however, certain tax breaks are granted by
governments to help or persuade companies to invest in clean
energy.
• The tax sometimes makes a big difference in the financial status of
a wind energy project. Companies seriously take this into account,
since the tax to pay determines a “go” or “no go” decision for a
project.
• The salary to be paid to technicians for the maintenance and
upkeep of a turbine can be regarded as part of the maintenance
cost.
• Nevertheless, supposing that there is no repair for a turbine, but
technicians are paid and are available to do any repair job, it could
be considered a part of this cost category.
184

Maintenance cost
• Like any other machine, wind turbines can break every now and
then and they need to be fixed.
• Also, regular maintenance such as inspection of parts and
changing oil are necessary for proper work of a turbine.
• Maintenance, in general, falls into two types: fault correction
maintenance (or corrective maintenance) and preventive
maintenance. Corrective maintenance refers to bringing back a
turbine to working order after a part has failed and has caused
the machine to shut down; preventive maintenance, on the other
hand, is beforehand scheduled inspection, detection, correction,
and repair of machine parts in order to prevent future
breakdowns and failures that could be more costly.
• In preventive maintenance, some parts that are prone to fail soon
are replaced, even if they are still working. The cost of
maintenance can become very high and prohibitive, and
companies must reduce this cost to a minimum by paying careful
attention to what the causes of problems are and eliminate them185

• The cost of maintenance, as we’ll see here, is not just
the price of the items that need to be replaced and the
labor.
• Here we can again categorize this into direct and
indirect classes. When a turbine shuts down because of
a fault or for maintenance the following costs are
involved:
a. Loss of revenue for the whole period of downtime.
b. The cost involved for the problem to be fixed.
• Since turbines are normally remote from the offices and
people to maintain them, it takes a long time for
technicians to reach a turbine and diagnose the
problem.
186

• Climbing a turbine with the proper safety gear on also adds to the
required time.
• Moreover, the size and weight of a piece to be replaced, and the
time of the year (consider below-freezing temperature in a windy
region with a lot of snow on the ground) directly influence the
downtime and the amount of revenue lost.
• If a major component, such as a blade, gearbox, generator, and so
on needs a repair, the cost is very high and in most cases requires a
crane to be brought to the site.
• This is a noticeable cost for a wind turbine. By properly looking
after the turbine and doing scheduled inspection and preventive
maintenance, the maintenance cost can be minimized.
• Figure below depicts how the maintenance cost for a turbine can
be kept to a minimum, whereas it can skyrocket to a much higher
amount.
• This figure illustrates the effect of preventive maintenance
(scheduled maintenance) for a turbine in a number of years
187

Proper scheduled maintenance can eliminate many unnecessary costs and revenue losses.
188

Comparison with other energy sources
• A distinct difference between a wind power generation facility and a conventional fossil
power plant of the same size is the initial cost. The initial cost for a wind farm is much
higher than the initial cost for a fossil power plant. Since the initial cost has to be paid
up-front, it makes it more difficult for investment.
• Nevertheless, since one has to pay for the fuel, but wind is free, the difference gradually
changes the course.
• Each year the cost of maintenance, other running costs, and the price for fuel adds up
to the amount of expenditure from an economical standpoint; that is, the invested
capital.
• The total cost of a project, thus, can be shown by adding all the cost in each year to the
cost of the previous year.
• The result is an ascending curve. Figure below illustrates the matter in broad terms
(that is, without any variation of the cost from one year to the other) for a typical wind
farm and a fossil plant. In this figure the price of oil (gas, coal) is considered to remain
constant over the 20 years that the graph shows. Also, no inflation of prices is taken into
account for more clarity of the comparison.
• According to this graph, after 15 years the cost of the fossil plant exceeds that of the
wind farm. In reality, inflation is not zero and the increase in the oil price cannot be
ignored.
• These will affect the number of years one surpasses the other. A plant is expected to be
productive for 20 to 25 years. In practice, it may perform well beyond that, say, up to 30
years. Considering the total cost of a fossil plant after this time, it is obvious from figure
below that the cost of a wind farm is much lower than the cost of a fossil plant.
189

Comparison of total long-term cost of a fossil power plant with that of a wind power plant.
190

• Any industrial plant (power generation or manufacturing) comes to the end of its useful
life, and operations will be stopped when the cost of running the plant exceeds the
revenue from the plant. In such a case, the plant will be abandoned or salvaged.
• The 20 to 25 years, mentioned above, is for many large projects. For an advancing
industry such as wind turbines, a plant can become outdated before that period. The rule
of scan for industrial machines, and a wind turbine is not an exception, is that the larger a
unit, the more efficient it is.
• For wind turbines, the new generations are around 2–3 MW, compared to those at 500–
750 kilowatts. So, it will be no surprise if a wind turbine is decommissioned (put out of
work) even before its life expectancy has ended.
Cost per unit
• It is sometimes necessary to know the cost per unit for an item. For instance, what is the
cost for a 2-MW turbine? Or, what is the cost per watt in a wind farm?
• the initial cost of wind turbines was analyzed and the various components of the cost
were explained.
• From that discussion it is easy to realize that the cost associated with a single running
turbine depends on a number of factors, and it is not easy to just assign a number to the
cost. In other words, the cost for each individual case can be specific for that case.
191

• For two wind farms, the cost of purchase of a turbine may not change that much,
but the cost of transportation and connection to the grid can be significantly
different.
• Consider two wind farms, one with 150 turbines and one with only 10 turbines.
The cost of constructing access roads and pavement to bring the turbines to the
site, and the cost of a substation for grid connection, will be shared between 150
units in the first case, whereas it is for only 10 turbines in the latter.
• On the other hand, when comparing the older turbines with a smaller capacity
with today’s larger turbines, a difference must be observed for advancement of
technology, increase of efficiency due to the larger size, and decrease in cost of
installation for less number of turbines (consider installation of 300 units of 400-
kW turbines versus 60 units of 2-MW turbines, both totaling 120 MW of installed
energy).
• Thus a figure for the average cost, based on the total cost of many wind farm
projects, can be obtained. This figure can be used as an index or a rule of thumb in
order to roughly determine the cost of a project, or compare past and present
costs.
• At today’s prices one can say that the cost of a wind turbine is 1.2–1.4 dollars per
watt. Thus, for example, the cost of a 2-MW turbine is about $2.6 million.
192

A case study
In this study, we take the example of a wind farm with a number of turbines. We
want to see if the project of developing this wind farm makes a profit, or if it should
be rejected. Each turbine to be installed is 2 MW and the total cost of developing the
farm is based on the simpler value of $1 per watt. In this sense, calculation can be
made for one dollar, but here for the sake of simplicity it is carried out for one
turbine at $2M. The following data are necessary (numbers are all assumptions):
• Years of operation _ 25
• Interest rate =7%
• Operating cost =5% (100,000$/year)
• Selling price per kilowatt-hour =$0.04
• Capacity production per year =40%
Note that the installed power is 2 MW. But, the production is less than the installed
power. Production varies during 24 hours and also it varies based on the season.
For this project there are three items that we must consider and find their values to
compare: (a) the cost of investment (initial capital), (b) the cost of operations, and (c)
the income from selling the product. If the total cost after 25 years is less than the
total income, the project is not profitable; otherwise the difference shows the profit
after 25 years. The first year is considered the development stage and neither the
operating cost nor the income are considered.
193

Project cost and income in 25 years (electricity at 4 cents per kilowatt-hour).
195

illustrates the above numbers and how the cost and income are
related. Note that instead, we can subtract the cost each year from
the income, and use the same formula for the difference, which is
the net profit each year. The reason it was done separately is that
we may want to see if the electricity is sold at a different rate, then
what the income would be. For example, consider that the sale
price is 5 cents per kilowatt-hour, instead of 4. Then the income
from sales will be (no tax or tax break is considered)
196

Project financial details (electricity at 5 cents per kilowatt-hour). 197

The corresponding graph is shown in Figure
above. Instead of finding the values of the
investment and net income after 25 years, it is
possible to base the calculations on the present
values of them.
In this way, the net present value can be found. It
is another way of doing the calculations based on
today’s worth of money. The results lead to the
same conclusion. That is, for a price of 4 cents
per kilowatt-hour there is a loss, but for 5 cents
per kilowatt-hour there is a profit.
198

Detail analysis and design point of vie on wind power plant

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