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MODELING AND SIMULATION
OF WIND TURBINES
A Thesis Submitted to the
Graduate School of Natural and Applied Sciences of
Dokuz Eyll University
In Partial Fulfillment of the Requirements for
the Degree of Master of Science in Electrical & Electronics Engineering,
Electrical & Electronics Engineering Program
by
Osman Oral KIVRAK
February, 2003
IZMIR
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M.Sc. THESIS EXAMINATION RESULT FORM
We certify that we have read this thesis and MODELING AND
SIMULATION OF WIND TURBINES completed by OSMAN ORAL
KIVRAK under supervision of PROF. DR. MUSTAFA GNDZALP and that in
our opinion it is fully adequate, in scope and in quality, as a thesis for the degree of
Master of Science.
Prof. Dr. Mustafa GNDZALP
Supervisor
(Committee Member) (Committee Member)
Approved by the
Graduate School of Natural and Applied Sciences
Prof. Dr. Cahit HELVACI
Director
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I
ACKNOWLEDGMENTS
I wish to thank to my supervisor Prof. Dr. Mustafa GNDZALP for his
guidance and understanding throughout my project.
I wish also thank to Prof. Dr. Eyp AKPINAR for his support on critical points.
I am also grateful to my family and colleagues for their advices.
Osman Oral KIVRAK
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II
ABSTRACT
Increasing worldwide energy deficiency causes raising importance of
development of new energy resources. It is foreseen that new energy resources
should not harm environment and natural life beside meeting present and future
energy demand. Accordingly, a great tendency towards renewable energy resources
took place in the market.
Wind energy has become the most popular resource in the last decade by its purity
and sustainability. Wind energy conversion systems convert the aerodynamic power
in an air stream into the electric power. Principally, a wind energy conversion system
consists of blade(s), which captures the aerodynamic power in the wind, shaft,
which transfers the torque created by the turning action of blade(s) and generator,
which converts this torque into electric power.
Unlike other energy production systems, wind, as a source of energy for wind
energy conversion systems, has a structure of showing sudden changes depending on
climatic conditions. These sudden changes in wind speed may cause some unwanted
mechanical or electrical damages, therefore it is necessary to supervise produced
power curve continuously. Several power control methods are developed for this
purpose. Pitch control opening and closing of blades along their longitudinal axes -
is the most efficient and popular power control method especially for variable-speed
wind turbines.
In this project, status and importance of wind energy conversion systems
throughout the world, the energy conversion operation in wind turbines and
components of them are investigated. Then, wind turbines are classified according to
different categories. At final, a megawatt size, variable-speed wind turbine is
modeled and its operation is observed by using MATLAB v5.2 SIMULINK
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III
software. Output power curve regulation is carried out by pitch control method.
The prototype for the simulation is VESTAS V80 2.0 MW model wind turbine.
Keywords: Wind energy, renewable, turbine, variable speed, pitch control,
energy conversion, MATLAB.
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IV
ZET
Enerji aiginin her geen gn arttigi dnyamizda, yeni enerji kaynaklari
gelistirmenin nemi de her geen gn artmaktadir. Olusturulacak yeni enerji
kaynaklarinin, mevcut ve gelecekteki enerji ihtiyacini karsilamasi ile birlikte, evreyi
ve dogal yasami da olumsuz ynde etkilememesi ngrlmektedir. Bu dogrultuda,
enerji sektrnde yenilenebilir enerji kaynaklarina ynelim artmaktadir.
Rzgar enerjisi, temizligi ve srekliligi ile, son 10 yilda en popler kaynak
olmustur. Rzgar enerjisi dnsm sistemleri, rzgarin iinde bulundurdugu
aerodinamik gc elektriksel gce dnstrrler. Bir rzgar enerjisi dnsm
sistemi, prensip olarak, rzgardaki aerodinamik gc yakalayan kanat(lar), kanatlarin
dnme hareketi ile olusan torku ileten saft ve bu mekanik torku elektriksel gce
eviren jeneratrden olusmaktadir.
Diger enerji retim sistemlerinden farkli olarak, rzgar enerjisi dnsm
sistemlerinde enerji kaynagi olarak kullanilan rzgar, iklim kosullarina bagli olarak
ani degisimler gsterebilen bir yapidadir. Bu ani degisimler, sistemde mekaniki ve
elektriki birok hasara yol aabileceginden, retilen g egrisinin srekli denetim
altinda bulundurulmasi gerekmektedir. Bu amala, esitli g kontrol yntemleri
gelistirilmistir. Pitch kontrol trbin kanatlarinin kendi dikey eksenlerinde ailip
kapatilmasi -, zellikle degisken hizlarda alisan rzgar trbinleri iin en verimli ve
popler g kontrol yntemidir.
Bu projede, rzgar enerjisi dnsm sistemlerinin nemi ve dnyadaki durumu,
rzgar trbinlerinde gereklesen enerji dnsm islemi ve trbin aksamlari
incelenmistir. Daha sonra rzgar trbinleri esitli kategorilere gre siniflandirilmistir.
Son olarak, MATLAB v5.2 SIMULINK yazilimi kullanilarak, degisken hizlarda
alisan megawatt boyutunda bir rzgar trbini modellenerek alismasi gzlenmistir.
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V
ikis gc ayari pitch control yntemiyle gereklestirilmistir. Modelde prototip
olarak VESTAS V80 2.0 MW model rzgar trbini alinmistir.
Anahtar Kelimeler: Rzgar enerjisi, yenilenebilir, trbin, degisken hizli, ai
kontrol.
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VI
CONTENTS
Page
Contents... VI
List of Tables... X
List of Figures..... XI
Chapter One
INTRODUCTION
1.1 Historical Background......... 4
1.2 Functional Structure of Wind Turbines........ 6
Chapter Two
COMPONENTS OF WIND TURBINES
2.1 Common Components........ 8
2.1.1 Nacelle.......... 82.1.2 Blade............. 8
2.1.3 Low Speed Shaft........... 11
2.1.4 High Speed Shaft.......... 11
2.1.5 Disc Brake............ 11
2.1.6 Generator.......... 12
2.1.7 Tower............ 12
2.2 Optional Components..... 13
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VII
2.2.1 Gear Box........ 13
2.2.2 V / Hz Converter....... 13
2.2.3 Yaw Assembly...... 14
2.2.4 Pitch Control Mechanism...... 14
2.2.5 Electronic Controller......... 15
Chapter Three
ELECTROMECHANICAL ENERGY CONVERSION
3.1 Aerodynamics of Wind Turbines......... 183.1.1 Aerodynamic Forces............. 18
3.1.1.1 Drag Forces............... 19
3.1.1.2 Lift Forces......... 19
3.1.2 Aero-Foils............. 20
3.2 Energy and Power in The Wind....... 22
3.2.1 Power Coefficient ............ 25
3.2.2 Tip Speed Ratio................ 273.2.3 Effect of The Number of Blades...................................................... 28
3.3 Generator Theory......... 33
3.3.1 DC Machines............ 33
3.3.1.1 Theory........... 33
3.3.1.2 DC Generator Applications in Wind Turbines. 36
3.3.2 Synchronous AC Machines (Alternators) 36
3.3.2.1 Theory................... 37
3.3.2.2 The Rotation Speed of a Synchronous Generator. 39
3.3.2.3 Internal Voltage of a Synchronous Generator.. 40
3.3.2.4 The Equivalent Circuit of an Alternator 42
3.3.3 Asynchronous (Induction) AC Machines. 44
3.3.3.1 Equivalent Circuit of an Induction Machine 46
3.3.3.1.1 Rotor Circuit Model...... 48
3.3.3.1.2 Final Equivalent Circuit 50
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VIII
3.3.4 Recent Developments in Generators for Wind Turbines. 56
3.3.4.1 Dual Generators 56
3.3.4.2 Direct-Drive Generators 57
3.4 Grid Integration.... 58
3.4.1 Frequency Converter Systems...... 59
3.4.1.1 Power Semiconductors for Frequency Converters 63
3.4.1.1.1 Semiconductor Diodes...... 64
3.4.1.1.2 Thyristors...... 65
3.4.1.1.3 Transistors............................................................................. 65
3.4.1.2 Characteristics of Power Converters 67
Chapter Four
CLASSIFICATION OF WIND TURBINES
4.1 Classification by Axis of Rotation........... 69
4.1.1 Horizontal Axis Wind Turbines (HAWT)........ 70
4.1.2 Vertical Axis Wind Turbines (VAWT)........ 71
4.2 Classification by Rotor Speed...... 72
4.2.1 Variable Rotor Speed........... 73
4.2.2 Constant Rotor Speed........... 74
4.3 Classification by Power Control... 75
4.3.1 Pitch Control. 80
4.3.2 Stall Control.. 81
4.4 Classification by Location of Installation.... 83
4.4.1 On-Shore Wind Turbines. 83
4.4.2 Off-Shore Wind Turbines. 84
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IX
Chapter Five
EXPERIMENTAL WORK
5.1 Sub-Systems in The Model.......... 89
5.1.1 Yaw Control Block........... 89
5.1.2 Turbine Efficiency Block......... 90
5.1.3 Pitch Control Block...... 91
5.1.4 Angular Speed Calculation Block........................................................ 93
5.1.5 Cp ? Selection Block. 95
5.2 Simulation Results 95
Chapter Six
CONCLUSIONS
6.1 Future Prospects........... 106
References............. 108
Appendices.... 110
Appendix A Flowchart of The Simulated System..... A
Appendix B VESTAS V80 2.0 MW Wind Turbine....... B
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X
LIST OF TABLES
Page
able 1.1 World Electricity Consumption with Estimations...... 2
able 1.2 Wind Power Installations Worldwide..... 3
able 1.3 Wind Energy Capacity Leaders Worldwide by End 2001...... 4
able 2.1 Number of Blades for Commercial Wind Turbine Designs 11
able 3.1 Speed Definitions 27
able 3.2 Common Synchronous Speeds for Generators... 55
Table 3.3 Characteristics and Maximum Ratings of Switchable Power
Semiconductors... 67
Table 4.1 Descriptions of Operational Regions for a Typical Wind Turbine. 77
Table 4.2 Pitch vs. Stall Issues 82
Table 5.1 Modelled Wind Turbine Simulation Results.......................... 103
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XI
LIST OF FIGURES
Page
Figure 1.1 World electricity consumption with estimations .... 1
Figure 1.2 Wind power installations worldwide............... 2
Figure 1.3 Power transfer in a wind energy converter.................. 6
Figure 2.1 Wind turbine types by rotor assemblies.. 7
Figure 2.2 Nacelle................. 8
Figure 2.3 Horizontal axis wind turbines according to number of blades 10
Figure 2.4 A typical gear.. 13
Figure 2.5 AC AC signal conversion............. 14
Figure 2.6 A typical wind turbine in detail (VESTAS V27 / 225 kW).... 16
Figure 3.1 A typical wind turbine showing all components. 17
Figure 3.2 Lift and drag forces acting on rotor blade........... 19
Figure 3.3 Components of wind power acting on rotor blade.. 21
Figure 3.4 Cylindrical volume of air passing at velocity V (10 m/s) through
a ring enclosing an area, A, each second.. 23
Figure 3.5 Wind flow through a wind turbine.. 25
Figure 3.6 Power coefficient versus tip speed ratio for a constant speed wind
turbine.. 31
Figure 3.7 Power coefficient versus tip speed ratio for a variable speed wind
turbine for different pitch angles from 0 to 15 degrees by 0.5
degree increments.... 32
Figure 3.8 The equivalent circuit for DC motors.. 34
Figure 3.9 A salient six-pole rotor for a synchronous machine 38
Figure 3.10 A non-salient two-pole rotor for a synchronous machine... 39
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XII
Figure 3.11 a. Plot of flux vs. field current for synchronous generators
b. The magnetization curve for synchronous generators.
41
Figure 3.12 A simple circuit for alternators 42
Figure 3.13 The per-phase equivalent circuit for synchronous generators. 43
Figure 3.14 Cutaway diagram for a wound-rotor induction machine. 45
Figure 3.15 Cutaway diagram for a squirrel-cage induction machine 45
Figure 3.16 Transformer model for an induction machine. 47
Figure 3.17 Magnetization curve for an induction machine compared to that
for a transformer.. 47
Figure 3.18 The rotor circuit model for induction machines.. 49
Figure 3.19 The rotor circuit model with all the frequency (slip) effectsconcentrated in resistor RR ..... 49
Figure 3.20 The per-phase equivalent circuit for induction machines 51
Figure 3.21 Torque-Speed curve for a MW-size induction machine.. 52
Figure 3.22 Electrical energy conversion by power converters.. 60
Figure 3.23 Basic wiring diagram for direct frequency converters 62
Figure 3.24 Indirect frequency converters.. 63
Figure 4.1 Horizontal and vertical axis wind turbines.. 70Figure 4.2 Horizontal axis wind turbine configurations... 71
Figure 4.3 Vertical axis wind turbine configurations... 72
Figure 4.4 Operating regions of a typical wind turbine 76
Figure 4.5 Rotor diameter vs. power output. 78
Figure 4.6 Swept area by rotor blades.. 79
Figure 4.7 Pitch Control 81
Figure 4.8 Stall Control. 81
Figure 4.9 Stall & Pitch controlled power schemes.. 83
Figure 5.1 Overview of the wind turbine simulation.... 88
Figure 5.2 Yaw control block....... 90
Figure 5.3 Turbine efficiency block.............. 90
Figure 5.4 Turbine efficiency characteristics correspond ing to wind speed.... 91
Figure 5.5 Graphical demonstrations for the response of pitch control
mechanism....................................................................................... 92
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XIII
Figure 5.6 Pitch control block with 0-15 degrees adjustment interval. 93
Figure 5.7 Angular speed calculation block..................................................... 94
Figure 5.8 Wind speed values filtered by yaw control block... 96
Figure 5.9 Aerodynamic power in the wind. 96
Figure 5.10 Captured wind power by the turbine (Input power to generator) 97
Figure 5.11 Angular speed variation of the turbine in respect of each wind
speed change (Change of input torque)... 97
Figure 5.12 Angular shaft speed of the turbine... 98
Figure 5.13 Rotational speed of turbine shaft before gearbox 98
Figure 5.14 Rotational speed of turbine shaft after gearbox (Rotational speed
of generator rotor) 99Figure 5.15 Tip speed ratio..... 99
Figure 5.16 Blade pitch angle (a)... 100
Figure 5.17 Power coefficient (Cp). 100
Figure 5.18 Tip speed ratio vs. power coefficient.......... 101
Figure 5.19 Turbine wind speed power characteristics....... 101
Figure 5.20 Turbine efficiency vs. wind speed... 102
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1
CHAPTER ONE
INTRODUCTION
World electrical energy consumption gets higher as the technology being
developed and the human lifes dependency on electricity is growing. Predictions
say that world electrical energy demand will continue to increase in the following 20
years period as shown in Figure 1.1. So, electrical energy supplies will beinsufficient to respond this demand. Therefore, new and cost-reduced energy
supplies must be introduced into the market.
World Electricity Consumption
0
6000
12000
18000
24000
1990 1995 2000 2005 2010 2015 2020
Years
NetElectricalEnergyCons
umption
(GWh)
Figure 1.1 World electricity consumption with estimations
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Table 1.1 World Electricity Consumption with Estimations
World Electricity Consumption Annual Consumption (GWh)
1990 10,549
1998 12,725
1999 12,833
2005* 15,182
2010* 17,380
2015* 19,835
2020* 22,407
* Estimated values.
Wind energy offers the potential to generate substantial amounts of electricity
without the pollution problems of most conventional forms of electricity generation.
The scale of its development will depend critically on the care with which wind
turbines are selected and sited. (Boyle, 1996, p.267)
Figure 1.2 shows that, for about 10 years, generating electricity from wind sites is
one of the most popular methods to provide demanded electricity of the world.
Wind Power Installation History 1991 - 2002
0
4000
8000
12000
16000
20000
24000
28000
32000
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Year
InstalledMW
Annual Installation
Cumulative Installation
Figure 1.2 Wind power installations worldwide
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3
Table 1.2 Wind Power Installations Worldwide
WECS
InstallationsAnnual Installation (MW) Cumulative Installation (MW)
1991 2,223
1992 338 2,561
1993 480 3,041
1994 730 3,771
1995 1,290 5,061
1996 1,292 6,353
1997 1,568 7,921
1998 2,597 10,518
1999 3,922 14,440
2000 4,495 18,935
2001 6,824 25,759
2002* 6,000 31,759
* Estimated value.
Since 1996, global wind power capacity has continued to grow at an annualcumulative rate close to 40%. Over the past decade, installations have roughly
doubled every two and a half years. During 2001 alone, close to 6,800 MW of new
capacity was added to the electricity grid worldwide. (EWEA, European Wind
Energy Association, 2002, p.11)
By the end of 2001, global wind power installed had reached a level of almost
25,000 MW. This is enough power to satisfy the needs of around 14 millionhouseholds, over 35 million people. Europe accounts for around 70% of this
capacity, and for two-thirds of the growth during 2001. But other regions are
beginning to emerge as substantial markets for the wind industry. Over 45 countries
around the world now contribute to the global total, and the number of people
employed by the industry world-wide is estimated to be around 70,000. (EWEA,
European Wind Energy Association, 2002, p.11)
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Table 1.3 Wind Energy Capacity Leaders Worldwide by End 2001
COUNTRY Installed MW
Germany 8,734
USA 4,245
Spain 3,550
Denmark 2,456
India 1,456
Italy 700
UK 525
China 406
Greece 358
Japan 357
Turkey 19
Others 2,121
TOTAL 24,927
1.1 HISTORICAL BACKGROUND
Wind energy has been used for thousands of years for milling grain, pumping
water, and other mechanical power applications. Today there are over one million
windmills in operation around the world; these are used principally for water
pumping. Whilst the wind will continue to be used for this purpose, it is the use of
wind energy as a pollution-free means of generating electricity on a potentially
significant scale that is attracting most current interest in the subject. Strictly
speaking, a windmill is used for milling grain, so modern windmills tend to be
called wind turbines, partly because of their functional similarity to other types of
turbines that are used to generate electricity. They are also sometimes referred to as
wind energy conversion systems (WECS) and those used to generate electricity are
sometimes described as wind generators or aero-generators. For utility-scale sources
of wind energy, a large number of wind turbines are usually built close together to
form a wind plant.
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Attempts to generate electricity from wind energy have been made (with various
degrees of success) since the end of the nineteenth century. Small wind machines for
charging batteries have been manufactured since the 1940s. It is, however, only since
the 1980s that the technology has become sufficiently mature. An extensive range of
commercial wind turbines is currently available from over 30 manufacturers around
the world. Several electricity providers today use wind plants to supply power to
their customers. (Boyle, 1996, p.267)
Wind turbines, like windmills, are mounted on a tower to capture the most energy.
At 30 meters or more above ground, they can take the advantage of faster and less
turbulent wind. Turbines catch the winds energy with their propeller-like blades.Usually, two or three blades are mounted on a shaft to form a rotor.
A blade acts much like an airplane wing. As wind blows, a pocket of low-pressure
air forms on the downwind side of the blade. The low-pressure air pocket then pulls
the blade toward it, causing the rotor to turn. This is called lift. The force of the lift is
actually much stronger than the wind's force against the front side of the blade,
which is called drag. The combination of lift and drag causes the rotor to spin like apropeller, and the turning shaft spins a generator to make electricity.
Wind turbines can be used in stand-alone applications, or they can be connected to
a utility power grid or even combined with a photovoltaic (solar cell) system. Stand-
alone wind turbines are typically used for water pumping or communications.
However, homeowners or farmers in windy areas can also use wind turbines as a way
to cut their electric bills.
The cost of wind energy equipment fell steadily between the early 1980s and the
early 1990s. The technology is continually being improved to make it both cheaper
and more reliable, so it can be expected that wind energy will tend to become more
economically competitive over the coming decades.
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An understanding of machines that extract energy from the wind involves many
fields of knowledge, including meteorology, aerodynamics, electricity and planning
control, as well as structural, civil and mechanical engineering.
1.2 FUNCTIONAL STRUCTURE OF WIND TURBINES
Figure 1.3 Power transfer in a wind energy converter
As shown in Figure 1.3, blades of a wind turbine rotor extract some of the flow
energy from air in motion, convert it into rotational energy then deliver it via a
mechanical drive unit (shafts, clutches and gears) to the rotor of a generator and
thence to the stator of the same by mechanical-electrical conversion. The electrical
energy from the generator is fed via a system of switching and protection devices,
leads and any necessary transformers to the mains, to the end user or to some means
of storage. (Heier, 1998, p.21)
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CHAPTER TWO
COMPONENTS OF WIND TURBINES
A wind turbine converts the kinetic energy of the wind firstly to the rotational
mechanical energy then to the electrical energy. All of these duties are carried out by
special components.
The rotor assembly may be placed either;
1. Upwind of the tower and nacelle, so receiving wind unperturbed by the tower
itself or,
2. Downwind of the tower, which enables self alignment of the rotor with the
wind direction (yawing), but causes the wind to be deflected and made
turbulent by the tower before arriving at the rotor (tower shadow).
Figure 2.1 Wind turbine types by rotor assemblies
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The lifetime of a rotor is related to variable loads and environmental conditions
that it experiences during service. Therefore, the rotor's inherent mechanical
properties and design will affect its useful service life.
2.1. COMMON COMPONENTS
2.1.1. NACELLE
Nacelle contains the key components of a wind turbine, including the gearbox,
and electrical generator. Service personnel may enter the nacelle from the tower of
the turbine in order to make maintenances. Towards the other side of the nacelle,there is wind turbine rotor, i.e. rotor blades and the hub.
Figure 2.2 Nacelle
2.1.2. BLADE
Rotor blade design has advanced with knowledge from wing technology, and
utilizes the aerodynamic lift forces that an airfoil experiences in a moving stream of
air. The shape of the blade and its angle in relation to the relative wind direction both
affect its aerodynamic performance.
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The materials used in modern wind turbine blade construction may be grouped
into three main classes;
Wood (including laminated wood composites)
Synthetic composites (a polyester or epoxy matrix reinforced by glass fibers)
Metals (predominantly steel or aluminum alloys)
Rotor blades should have the optimum design in order to capture maximum
amount of wind and so to provide maximum rotation of the shaft. Wind turbines can
have different number of rotor blades. The principle rule is; the lower the number of
rotor blades the faster turns the rotor. The measure for this is called tip speed ratio, ,
which is defined as rotor tip speed divided by the wind velocity. If = 1, the blade
tip velocity is as high as the wind speed. Rotors of wind turbines should have
rotational speeds as high as possible to reduce the masses of gearboxes and
generators. So, the number of rotor blades is low and in general not more than three.
Most of todays wind turbines have blade tip speeds of less than 65 m/s. In the old
prototypes of large wind turbines, designers tried to increase the blade tip speed more
and more because the shaft torque reduces with increasing rotational speed, but high
blade tip speeds have the disadvantage of high noise emissions and physical damages
of the rotor.
3-bladed rotors are the most common ones all over the world. The main reason to
use 3 blades is the constant inertia moment of the rotor for all circumferential
azimuth angles in relation to operational motions around the longitudinal axis of thetower. (German Wind Energy Institute - DEWI, 1998, p.40)
2-bladed rotor offered the chance to reduce the cost for the rotor, but
unfortunately the dynamic behaviour of the 2-bladed rotor caused additional efforts
that increase again the overall cost. (German Wind Energy Institute - DEWI, 1998,
p.41)
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As compared to 3-bladed rotors, 1-bladed rotors have tip speed two times that of
3-bladed ones. This means a 1-bladed wind turbine is several times noisier than a 3-
bladed one. Additionally, the rotor blade can be fixed to the hub by a single hinge
that allows for a movement that reduces structural loads on the blade. On the other
hand, 1-bladed rotors principally have an aerodynamic unbalance, which introduces
additional motions, causes loads and needs complicated hub constructions to keep
the movements under control. (German Wind Energy Institute - DEWI, 1998, p.41)
a. One-Bladed b. Two-Bladed c. Three-Bladed
Figure 2.3 Horizontal axis wind turbines according to number of blades
If 1, 2 or 3 bladed rotors are designed for similar tip speeds (as they have not been
in the past but would require to be in the future for European land based applicationssubject to current sound limits), then the blades of the 3-bladed rotor are more highly
stressed than for the 2 or 1 bladed system and thus rotor blade costs will be high for
the 3 bladed system.
Table 2.1 illustrates the relative proportion of 1, 2 and 3 bladed designs among
present commercially available wind turbines of over 30 kW rated output. If the data
were presented as the proportion of operational machines the dominance of the 3-
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bladed designs would be still more pronounced. (European Commission Directorate-
General for Energy, 1997, pp.5-6)
Table 2.1 Number of Blades for Commercial Wind Turbine Designs
Number of Blades % of Designs
1 2
2 24
3 74
Conventional wisdom holds that three-bladed machines will deliver more energy
and operate more smoothly than either one or two bladed turbines. They will also
incur higher blade and transmission costs as a result. Some experiments say that
rotors with three blades can capture 5% more energy than two-bladed turbines while
encountering less cyclical loads than one and two bladed turbines.
2.1.3. LOW SPEED SHAFT
While transferring the primary torque to the gear train from the rotor assembly,the main shaft is usually supported on journal bearings. Due to its high torque
loadings, the main shaft is susceptible to fatigue failure. Thus, effective pre-service
non-destructive testing procedures are advisable for this component.
2.1.4. HIGH SPEED SHAFT
The high-speed shaft rotates with over 1,000 revolutions per minute (rpm) anddrives the electrical generator. It is equipped with an emergency mechanical disc
brake.
2.1.5. DISC BRAKE
This may be situated either on the main shaft before the gearbox, or on the high-
speed shaft after the gearbox. The latter arrangement requires a smaller (and cheaper)
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brake assembly in order to supply the necessary torque to slow down the rotor.
However, this arrangement does not provide the most immediate control of the rotor,
and in the event of a gearbox failure, braking control of the rotor is lost.
2.1.6. GENERATOR
The generator converts the mechanical energy of the input shaft to electrical
energy. It must be compatible at input with the rotor and gearbox assemblies, but at
output with the utility's power distribution (if connected to a grid) or to local power
requirements (if the turbine is part of a stand alone system).
The generator can be either DC, synchronous or induction (asynchronous). DC
machines are used for stand alone systems such as battery charging which do not
need to produce grid compatible electricity. Synchronous machines are generally
used for high synchronous speeds, but induction machines can be used for low
variable speeds. Generally for wind turbines, induction generators are used for the
opportunity of controlling the system under different wind speeds. This situation is
the result of unstable wind speeds. In some systems, permanent magnet generatorscan also be used.
2.1.7. TOWER
The tower of a wind turbine carries the nacelle and the rotor. Generally, it is an
advantage to have a high tower, since wind speeds increase farther away from the
ground. For example, a typical modern 600 kW turbine will have a tower of 40 to 60
metres (the height of a 13-20 story building).
Towers may be either of tubular or lattice types. Tubular towers are safer for the
personnel that have to maintain the turbines, as they may use an inside ladder to get
to the top of the turbine. The advantage of lattice towers is primarily that they are
cheaper.
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2.2. OPTIONAL COMPONENTS
2.2.1. GEAR BOX
Gearboxes are used for non-direct drive designs. In general, the transmission gear
is used to adapt WECS to low wind speeds in order to help the rotational speed
getting close to the frequency of the grid system. But, this adaptation brings the
addition of mechanical machinery parts (Large gearboxes, coupling elements etc.) to
be installed.
Figure 2.4 A typical gear
Gearboxes are not intrinsic to wind turbines. Designers use them only because
they need to increase the speed of the slow-running main shaft to the speed required
by mass-produced generators. Manufacturers can produce for special purpose, slow-
speed generators and drive them directly without using a transmission. For this
reason, specially designed permanent-magnet alternators have revolutionized the
reliability and serviceability of small wind turbines.
2.2.2. V / Hz CONVERTER
The AC-AC converter includes a rectifier and an inverter to control the frequency.
Its aim is to keep the generated system voltage near grid frequency (50 or 60 Hz). A
controlled rectifier-inverter group converts the generated AC voltage to a DC signal
and then again to an AC signal. The controlling principle is based on the controlling
of the inverter elements (IGBTs, thyristors etc.).
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Figure 2.5 AC AC signal conversion
2.2.3. YAW ASSEMBLY
It is necessary for the rotor axis to be aligned with the wind direction in order to
extract as much of the wind's kinetic energy as possible. The smallest upwind
machines (up to 25 kW) most commonly use tail vanes to keep the machine aligned
with the wind. However, larger wind turbines with upwind rotors require active yaw
control to align the machine with the wind. To enable this, when a change in wind
direction occurs, sensors activate the yaw control motor, which rotates the nacelle
and rotor assembly until the turbine is properly aligned.
Downwind machines of all sizes may possess passive yaw control, which means
that they can self-align with the wind direction without the need for or a tail vane or
yaw drive.
Yaw system can also be used to shut down the wind turbine in order to save it
from the physical effects of very high wind speeds.
2.2.4. PITCH CONTROL MECHANISM
This mechanism is used on wind turbines for active power control. At a
sufficiently high level of wind, a blade pitch adjuster ensures that the turbine speed is
kept roughly constant by altering the blade angle.
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For reasons of stability and to reduce the component loading, this mechanism
changes the blade pitch angle along its longitudinal axis to limit the input torque
loading to turbine blades.
A simple pitch control design can be achieved by using a hydraulic or mechanical
centrifugal governor.
2.2.5. ELECTRONIC CONTROLLER
It contains a computer, which continuously monitors the condition of the wind
turbine and controls the pitch and yaw mechanisms. In case of any malfunction, (e.g.overheating of the gearbox or the generator), it automatically stops the wind turbine
and calls the turbine operator's computer via a telephone modem link.
Another important characteristic of the electronic controller is to control the AC-
AC converter elements (i.e. firing angles of thyristors). At this point, electronic
controller takes on the frequency synchronization duty between generated signal and
grid.
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Figure2.6
Atypicalwindturbineindetail(VESTASV2
7/225kW)
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CHAPTER THREE
ELECTROMECHANICAL ENERGY
CONVERSION
Electromechanical energy conversion is carried out by the full operation of wind
turbine. In case of any components failure, either the complete energy conversion
stopped or some losses must be taken into account.
Figure 3.1 A typical wind turbine showing all components
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As shown in Figure 3.1, the wind blade(s) is able to capture the wind energy and
rotates itself. This rotation of the blade is transferred to the generator shaft or namely
to the rotor by an optional gearbox. This box increases the rotational speed of the
shaft, which provides more electrical energy production. The high-speed generator
(asynchronous or synchronous) is connected to the V/Hz converter to keep the
frequency of the generated voltage in the order of the grid frequency.
The sequence of events in the generation and transmission of wind power can be
summarized as follows:
1.A torque is produced as the wind interacts with the rotor,2.The relatively low rotational frequency of the rotor is increased via a gearbox,
3.The gearbox output shaft turns a generator,
4.The electricity produced by the generator passes through the turbine controller
and circuit breakers and is stepped up to an intermediate voltage level
(generally 690 V) by the turbine transformer,
5.The site cabling system delivers the electricity to the site transformer via the
site control and circuit breaker system,6.The site transformer steps up the voltage to the grid value,
7.The grid system transmits the electricity to the locality of its end use,
8.Transformer substations reduce the voltage to domestic or industrial values,
9.Local low voltage networks transmit the electricity to homes, offices and
factories.
3.1. AERODYNAMICS OF WIND TURBINES
3.1.1. AERODYNAMIC FORCES
An object in an air stream experiences a force that is imparted from the air stream
to that object. This force can be considered to be equivalent to two component
forces, acting in perpendicular directions, known as the drag force and the lift force.
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The magnitudes of drag and lift forces depend on the shape of the object, its
orientation to the direction of the air stream, and the velocity of the air stream.
Figure 3.2 Lift and drag forces acting on rotor blade
3.1.1.1. DRAG FORCES
Drag forces are in line with the direction of the air stream. For example, a flat
plate in an air stream experiences maximum drag forces when the direction of the air
flow is perpendicular to the flat side of the plate. When the direction of the air stream
is in line with the flat side of the plate, the drag forces are at a minimum. (Boyle,
1996, p.284)
For wind turbine blades, the objective is to minimize drag forces.
3.1.1.2. LIFT FORCES
Lift forces are perpendicular to the direction of the air stream. They are termed
lift because they are the forces that enable aero planes to lift off the ground and fly.
Lift forces acting on a flat plate are smallest when the direction of the air stream is at
a zero angle to the flat surface of the plate.
At small angles relative to the direction of the air stream (that is, when the so
called angle of attack is small), a low pressure region is created on the downstream
side of the plate as a result of an increase in the air velocity on that side. In this
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situation, there is a direct relationship between air velocity and pressure: The faster
the air flow, the lower the pressure. This phenomenon is known as the Bernoullis
Effect. The lift force thus acts as a suction or pulling force on the object. Lift
forces are the principal that cause a modern wind turbine to operate. (Boyle, 1996,
p.284)
3.1.2. AERO-FOILS
The angle that an object makes with the direction of an air flow, measured against
a reference line in the object, is called the angle of attack or angle of incidence. The
reference line on an aero-foil section is usually referred to as the chord line . Archingor cambering a flat plate will cause it to induce higher lift forces for given angle of
attack, but the use of so-called aero-foil sections is even more effective. When
employed as the profile of a wing, these sections accelerate the air flow over the
upper surface. The high air speed thus induced results in a large reduction in pressure
over the upper surface relative to the lower surface. (Boyle, 1996, p.284)
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Figure 3.3 Components of wind power acting on rotor blade
The lift force, in a direction at right angles to the air stream, is described by the
lift coefficient CL, and is defined by Equation (3.1);
L2L AV?
L2C
= (3.1)
where
CL : Lift coefficient
: Air density (kg/m2)
AL : Area of aero-foil in plan (m2)
V : Wind speed (m/s)
L : Lift force (N)
Similarly, the drag force is described by the drag coefficient CD by Equation (3.2);
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D2D AV?
D2C
= (3.2)
where
CD : Drag coefficient
: Air density (kg/m2)
AD : Area of aero-foil in plan (m2)
V : Wind speed (m/s)
D : Lift force (N)
Horizontal and vertical axis wind turbines both make use of the aerodynamicforces generated by aero-foils in order to extract power from the wind, but each
harnesses these forces in a different way.
In a fixed pitch horizontal axis wind turbine, the angle of attack at a given position
on the rotor blade stays constant throughout its rotation cycle.
In a vertical axis wind turbine, the angle of attack at a given position on the rotorblade is constantly varying throughout its rotation cycle.
3.2 ENERGY AND POWER IN THE WIND
A wind turbine obtains its power input by converting the force of the wind into
torque (turning force) that is 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, andthe wind speed.
Power can be defined as the rate at which energy is used or converted and it can
therefore be expressed as energy per unit of time;
sj1W1 = (3.3)
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The energy contained in the wind is its kinetic energy;
2Vm21E = (3.4)
where m is the mass and V is the velocity with which this mass is moving.
It can be considered that the air is passing through a circular ring (enclosing a
circular area, say 100 m2) at a velocity V (say 10 m/s) as shown in Figure 3.4;
Figure 3.4 Cylindrical volume of air passing at velocity V (10 m/s) through a
ring enclosing an area, A, each second
As the air is moving at a velocity of 10 m/s, a cylinder of air with a length of 10 m
will pass through the ring each second. Therefore, a volume of air equal to
100x10=1000 cubic meters will pass through the ring each second. By multiplying
this volume by the air density, the mass of the air moving through the ring each
second can be obtained.
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In other words;
Mass of air per second = air density x volume of air passing each second
= air density x area x length of cylinder of air
passing each second
= air density x area x velocity
VA = ?m (3.5)
where
: Air density (kg/m3)
A : Rotor disk Area (m2)
V : Wind velocity (m/s)
Consequently the kinetic energy formula becomes;
3VA21E = ? (3.6)
However, energy per unit of time is equal to power (1 W = 1 j/s), so above
formula is also the expression for the power in the wind;
3VA21P = ? (3.7)
An airstream moving through a turbine rotor disc cannot give up all of its energyto the blades because some kinetic energy must be retained in order to move the
airstream away from the disc area after interaction. In addition, there are frictional
effects, which produce heat losses. Thus, a turbine rotor will never extract 100 % of
the wind's energy.
There are some new parameters to be introduced into calculations in order to
express the system efficiency.
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3.2.1. POWER COEFFICIENT
The ability of a turbine rotor to extract the wind's power depends upon its
"efficiency". Thus, to express the power output of the turbine, a non-dimensional
power co-efficient Cp is included.
Also, rotors reduce the wind velocity from the undisturbed wind speed V1 far in
front of the rotor to a reduced air stream velocity V2 behind the rotor as shown in
Figure 3.5;
Figure 3.5 Wind flow through a wind turbine
The difference in the wind velocity is a measure for the extracted kinetic energy
which turns the rotor and at the opposite end of the drive train, the connected
electrical generator.
By including the losses, the power theoretically extracted by the wind turbine can
be described by Equation (3.8);
31VApC2
P =?
(3.8)
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where
? : Air density (kg/m3)
pC : Non-dimensional power coefficient
: Mechanical / Electrical efficiency
A : Rotor disk area (m2)
V1 : Undisturbed wind velocity in front of the rotor (m/s)
This describes the fraction of the wind's power per unit area extracted by the rotor,
governed by the aerodynamic characteristics of the rotor and its number of blades.
As the air stream interacts with the rotor disc and power is extracted, the air
stream speed is reduced by an amount described by the axial interference factor, a.
This is the ratio of the upstream to the downstream wind speed. Equation (3.9)
expresses the power using the axial interference factor;
)a1(aVA2P 231 = ? (3.9)
where "a" is the dimensionless axial interference factor.
Thus, by substitution, the power co-efficient Cp may be defined as;
)a1(a4C 2p = (3.10)
By differentiating (3.10) with respect to a, the maximum value of Cp occurs when
a = 0.33. Thus, Cpmax = 16/27 = 0.593.
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3.2.2. TIP SPEED RATIO
The speed of rotation of a wind turbine is usually given in either revolutions per
minute (rpm) or radians per second (rad/s). The rotation speed in rpm is usually
symbolized by nr and the angular velocity in rad/s is by ? r.
Table 3.1 Speed Definitions
Definition Symbol Unit
Rotational Speed nr rpm
Angular Speed ? r rad/s
1 rpm =60
2 rad/s = 0.10472 rad/s
Another measure of a wind turbines speed is its tip speed, U, which is the
tangential velocity of the rotor at the tip of blades, measured in meters per second. It
is the product of the angular velocity, ? r, of the rotor and the tip radius, r.
Alternatively, it can be defined as;
60
nr2U r
= (3.11)
By dividing the tip speed, U, by the undisturbed wind velocity, V, at the upstream
of the rotor, the very useful non-dimensional ratio known as the tip speed ratio,
which is usually symbolized by is obtained. This ratio provides us with a useful
measure with which to compare wind turbines of different characteristics. (Boyle,
1996, p.283)
If a rotor turns very slowly, it will allow wind to pass unperturbed through the
gaps between the blades. Likewise, a rotor turning very rapidly will appear as a solid
wall to the wind. Therefore, it is necessary to match the angular velocity of the rotor
to the wind speed in order to obtain maximum efficiency.
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The relationship between the wind speed and the rate of rotation of the rotor is
characterized by a non-dimensional factor, known as the tip speed ratio, , given by
Equation (3.12). Note that this factor arises from the full aerodynamic theory of wind
power extraction;
V
U
V
r
SpeedWind
SpeedTipBlade r=
== (3.12)
where
r : Rotor radius measured at the blade tip (m)
? r : Angular speed of the blade tip (rad/s)
U : Blade tip speed (m/s)
V : Wind Speed (m/s)
3.2.3. EFFECT OF THE NUMBER OF BLADES
The optimum tip speed ratio may be inferred however by relating the time taken
for the disturbed wind to re-establish itself tw, to the time taken for a blade of
rotational frequency omega to move into the position occupied by its predecessor t b.
For an n-bladed rotor, the time period for the blade to move to its predecessor's
position is given by Equation (3.13);
rb
n2t
= (3.13)
where
tb : Time period for the blade to move its predecessors position (sec)
? r : Angular speed of the blade tip (rad/s)
n : Number of blades
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If the length of the strongly disturbed airstream upwind and downwind of the
rotor is d, then the time for the wind to return to normal is given by Equation (3.14);
V
dtw = (3.14)
where
tw : Time period for the wind to return to normal (sec)
d : Length of disturbed air stream (m)
V : Wind Velocity (m/s)
Maximum power extraction occurs when these time periods are equal (If tb
exceeds tw, then some wind is unaffected. If tw exceeds tb, then some wind is not
allowed to move through the rotor). For this case, Equation (3.15) applies;
d
2
V
n r
(3.15)
where
? r : Angular speed of the blade tip (rad/s)
n : Number of blades
d : Length of disturbed air stream (m)
V : Wind velocity (m/s)
Therefore, for optimum power extraction, the rotor must turn at a frequency which
is related to the speed of the oncoming wind. This rotor frequency decreases as the
radius of the rotor increases, and may be characterized by calculating the optimum
tip speed ratio by Equation (3.16);
d
r
n
20 (3.16)
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where
0 : Optimum tip speed ratio
r : Blade tip radius of rotation (m)
n : Number of blades
d : Length of disturbed air stream (m)
If we substitute a constant k for the term (r/d), which practical results have shown
to be approximately 2 for an n bladed machine, then the optimum tip speed ratio is
defined by Equation (3.17);
n4
0 (3.17)
Thus, for a two-bladed rotor, the maximum power extracted from the wind (at
Cpmax) occurs at a tip speed ratio of about 6, and for a four-bladed machine at a tip
apeed ratio of about 3. If the aerofoil is carefully designed, the optimum tip speed
ratios may be about 30% above these values. (De Montfort University-
http://www.iesd.dmu.ac.uk/wind_energy/m32extex.html, 1996).
Most modern horizontal axis wind turbine rotors consist of two or three thin
blades. These are known as "low solidity" rotors, due to the low fraction of the swept
area which is solid. This arrangement gives a relatively high tip speed ratio in
comparison to rotors with a high number of blades (such as those used in water
pumps, which require a high starting torque), and gives an optimum match to the
frequency requirements of modern electricity generators. This minimizes the size of
the gearbox required and increases efficiency.
Figure 3.6 shows the relationship between rotor efficiency (Cp) and the tip speed
ratio for a typical wind turbine; as wind speed increases, it is necessary for the rotor
to speed up in order to remain near the optimum tip speed ratio. However, this is in
conflict with the requirements of most generating systems, which require a constant
generator frequency in order to supply electricity of a fixed frequency. Thus, the
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wind turbine which has a generator directly coupled to the grid operates for much of
the time with a tip speed ratio which is not optimized.
Figure 3.6 Power coefficient versus tip speed ratio for
a constant speed wind turbine
The alternative is to decouple the generator from the grid by an intermediate
system which facilitates variable speed operation. Some manufactures are producing
variable speed turbines (where the rotor speeds up with the wind velocity), in order
to maintain a tip speed ratio near the optimum. These turbines utilize electronic
inverter/rectifier based control systems to stabilize the fluctuating voltage from the
turbine before feeding into the grid supply.
For a variable-speed turbine, the objective is to operate near maximum efficiency,
where the resulting target power can be expressed as;
3r
3
etargtetargt,petargt
rCApC2
P
=
? (3.18)
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where
? : Air density (kg/m3)
pCtarget : Power coefficient target
: Mechanical / Electrical efficiency
A : Rotor disk area (m2)
r : Rotor radius measured at the blade tip (m)
? r : Angular speed of the blade tip (rad/s)
target : Tip speed ratio target
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
TSR
Cp
Figure 3.7 Power coefficient versus tip speed ratio for a variable speed wind
turbine for different pitch angles from 0 to 15 degrees by 0.5 degree increments
Figure 3.7 illustrates the Cp- relationship for a variable-speed wind turbine at
different pitch angles. For constant-speed turbines, only one of the curves will be
valid and an attempt is made to design the rotor blades to operate near maximum
efficiency (Cpmax) at wind speeds that occur most frequently at the design site. The
rotor speed varies by only a few percent, but the wind speed varies over a wide
range. Therefore, the operating point is rarely, and randomly, at for Cpmax . It is
apparent from Equation (3.18) and Figure 3.7 that the power at any wind speed is
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maximized by operating near the tip-speed ratio which results in the maximum
power coefficient. For a variable-speed turbine, this means that as the wind speed
changes, the rotor speed should be adjusted proportionally.
3.3. GENERATOR THEORY
All generators produce electricity by Faraday Law of electromagnetic induction:
A magnetic field cuts a wire with a relative velocity, so inducing an electric potential
difference in the wire. If this wire forms a circuit, then an electrical current is
produced. The magnitude of the current is being increased with the strength of the
field, the length of wire cut by the field and the relative velocity.
Of the wind turbine systems currently being manufactured, their generating
systems may be classed as follows;
3.3.1. D.C. GENERATORS
3.3.1.1. THEORY:
DC machines convert mechanical power to dc electric power, and vice versa.
Most dc machines are like ac machines in that they have ac voltages and currents
within them dc machines have a dc output only because a mechanism exists that
converts the internal ac voltages to dc voltages at their terminals. Since this
mechanism is called commutator, dc machinery is also known as commutating
machinery.
DC generators are dc machines used as generators. There is no real difference
between a generator and a motor except for the direction of power flow. (Chapman,
1999, p.566)
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Figure 3.8 The equivalent circuit for DC motors
In Figure 3.8, the armature circuit is represented by an ideal voltage source EA
and a resistor RA. This representation is really the Thevenin equivalent of the entire
rotor structure, including rotor coils, interpoles and compensating windings, if
present. The brush voltage drop is represented by a small battery Vbrush opposing the
direction of current flow in the machine. The field coils, which produce the magnetic
flux in the generator, are represented by inductor LF and resistor RF. The separate
resistor Radj represents an external variable resistor used to control the amount of
current in the field circuit. (Chapman, 1999, p.508)
The internal generated voltage in a DC machine is given by Equation (3.19);
=
a2
PZEA (3.19)
where Z is the total number of conductors and a is the number of current pathsin the machine. This equation is sometimes rewritten in a simpler form that
emphasizes the quantities that are variable during machine operation. This simpler
form is;
= KEA (3.20)
where K is a constant representing the construction of the machine.
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The induced torque developed by the machine is given by;
Aind IK = (3.21)
Equations (3.20) and (3.21), the Kirchhoffs Voltage Law equation of the
armature circuit and the machines magnetization curve, are all the tools necessary to
analyze the behaviour and performance of a dc motor. (Chapman, 1999, p.508)
There are five major types of dc generators, classified according to the manner in
which their field flux is produced:
1.Separately Excited Generator: In a separately excited generator, the field flux
is derived from a separate power source independent of the generator itself.
2.Shunt Generator: In a shunt generator, the field flux is derived by connecting
the field circuit directly across the terminals of the generator.
3.Series Generator: In a series generator, the field flux is produced by
connecting the field circuit in series with the armature of the generator.
4.Cumulatively Compounded Generator: In a cumulatively compoundedgenerator, both a shunt and a series field are present, and their effects are
additive.
5.Differentially Compounded Generator: In a differentially compounded
generator, both a shunt and a series field are present, but their effects are
subtractive.
These various types of dc generators differ in their terminal (voltage-current)characteristics, and therefore in the applications to which they are suited. DC
generators are compared by their voltages, power ratings, efficiencies,and voltage
regulations. Voltage regulation (VR) is defined by Equation (3.22);
%100V
VVVR
fl
flnl
=
(3.22)
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where Vnl is the no-load terminal voltage of the generator and Vfl is the full-load
terminal voltage of the generator. It is a rough measure of the shape of the generator's
voltage-current characteristica positive voltage regulation means a drooping
characteristic, and a negative voltage regulation means a rising characteristic.
All generators are driven by a source of mechanical power, which is usually called
the prime mover of the generator. A prime mover for a dc generator may be a wind
or steam turbine, a diesel engine, or even an electric motor. Since the speed of the
prime mover affects the output voltage of a generator, and since prime movers can
vary widely in their speed characteristics, it is customary to compare the voltage
regulation and output characteristics of different generators, assuming constant-speed
prime movers. (Chapman, 1999, pp.566-567)
3.3.1.2. DC GENERATOR APPLICATIONS IN WIND TURBINES
Small scale stand-alone wind turbines are the most commonly used to charge
batteries at relatively low voltages. They use simple DC generators. In these systems,
the rotating generator shaft (connected to the turbine blades either directly or througha gearbox) turns the rotor within a magnetic field produced by either the field coil
windings or by an arrangement of permanent magnets on the armature. The rotation
causes an electric current to be set up in the rotor windings as the coils of wire cut
through the magnetic field. This current (whose magnitude depends upon the number
of turns in the windings, the strength of the magnetic field and the speed of rotation)
is drawn off from the commutator through graphite brushes and fed directly to the
battery, sometimes via a voltage regulator which smoothes out fluctuations in the
generated voltage.
3.3.2. SYNCHRONOUS AC MACHINES (ALTERNATORS)
AC generators employ a rotary magnetic field, known as a rotary field. This may
be obtained by the use of a rotating permanent magnet or by rotary excitation using a
current fed via so-called brushes and slip-rings. In stationary conductorsthe stator
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windings of the generatorsuch rotary fields excite electric currents that vary with
the frequency of rotation. In these synchronous generators, coils are set (spatially) at
e.g. 120 intervals or an integral multiple thereof. The voltage is dependent on the
construction of the generator, the speed of rotation of the rotary field, the excitation
and the load characteristics, and in isolated and stand-alone operation can be
regulated by varying the excitation. When connected to the public supply, both
voltage and frequency are dictated by the grid.
If the three-phase alternating current stator of a generator is supplied with
alternating current from the grid, it also sets up a rotary field. This excites currents in
the rotor windings of the generator, which vary with a frequency corresponding tothe difference between the field rotation frequency and the mechanical speed of
rotation. These currents cause torques on the rotor, which, in synchronous machines,
have a damping effect.
3.3.2.1. THEORY
A synchronous generator or alternator is a device for converting mechanicalpower from a prime mover to AC electric power at a specific voltage and frequency.
The term synchronous refers to the fact that this machine's electrical frequency is
locked in or synchronization with its mechanical rate of shaft rotation. The
synchronous generator is used to produce the vast majority of electric power used
throughout the world. (Chapman, 1999, p.316)
In a synchronous generator, a dc current is applied to the rotor winding, which
produces a rotor magnetic field. The rotor of the generator is then turned by a prime
mover, producing a rotating magnetic field within the machine. This rotating
magnetic field induces a three-phase set of voltages within the stator windings of the
generator.
Two terms commonly used to describe the windings on a machine are field
windings and armature windings. In general, the term "field windings" applies to
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the windings that produce the main magnetic field in a machine, and the term
"armature windings" applies to the windings where the main voltage is induced. For
synchronous machines, the field windings are on the rotor, so the terms "rotor
windings" and "field windings" are used interchangeably. Similarly, the terms "stator
windings" and "armature windings" are used interchangeably.
The rotor of a synchronous generator is essentially a large electromagnet. The
magnetic poles on the rotor can be of either salient or non-salient construction. The
term salient means "protruding" or "sticking out" and a salient pole is a magnetic
pole that sticks out from the surface of the rotor. On the other hand, a non-salient
pole is a magnetic pole constructed flush with the surface of the rotor. Non-salientpole rotors are normally used for two- and four-pole rotors, while salient-pole rotors
are normally used for rotors with four or more poles. (Chapman, 1999, pp.250-252)
Figure 3.9 A salient six-pole rotor for a synchronous machine
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Figure 3.10 A non-salient two-pole rotor for a synchronous machine
A DC current must be supplied to the field circuit on the rotor. Since the rotor isrotating, a special arrangement is required to get the DC power to its field windings.
There are two common approaches for supplying this DC power;
1.Supply the DC power from an external DC source to the rotor by means of slip
rings and brushes.
2.Supply the DC power from a special DC power source mounted directly on the
shaft of the synchronous generator.
3.3.2.2. THE ROTATION SPEED OF A SYNCHRONOUS GENERATOR
Synchronous generators are by definition synchronous, meaning that the electrical
frequency produced is locked in or synchronized with the mechanical rate of rotation
of the generator. A synchronous generators rotor consists of an electromagnet to
which direct current is supplied. The rotor magnetic field points in whatever
direction the rotor is turned. Now, the rate of rotation of the magnetic fields in the
machine is related to the stator electrical frequency by;
120
pnf me
= (3.23)
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where
fe : Electrical frequency (Hz)
nm : Mechanical speed of the magnetic field (rpm)
(equals the speed of the rotor for synchronous machines)
p : Number of poles
Since the rotor turns at the same speed as the magnetic field, this equation relates
the speed of the rotor rotation to the resulting electrical frequency. (Chapman, 1999,
pp.254-255)
3.3.2.3. INTERNAL VOLTAGE OF A SYNCHRONOUS GENERATOR
The magnitude of the voltage induced in a given stator phase is;
fN2E CA = (3.24)
In solving problems with synchronous machines, this equation is sometimes
rewritten in a simpler form that emphasizes the quantities that are variable during
machine operation. This simpler form is;
= KEA (3.25)
where K is a constant representing the construction of the machine. If ? is
expressed in radians per second, then
2
pNK C
= (3.26)
The internal generated voltage EA is directly proportional to the flux and to the
speed, but the flux itself depends on the current flowing in the rotor field circuit. The
field current IF is related to the flux in the manner shown in Figure 3.11 (a). Since EA
is directly proportional to the flux, the internal generated voltage EA is related to the
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field current as shown in Figure 3.11 (b). This plot is called the magnetization curve
or the open-circuit characteristic of the machine.
Figure 3.11 a. Plot of flux vs. field current for synchronous generators
b. The magnetization curve for synchronous generators
The voltage EA is the internal generated voltage produced in one phase of a
synchronous generator. However, this voltage EA is not usually the voltage that
appears at the terminals of the generator. In fact, the only time the internal voltage EAis the same as the output voltage VF of a phase is when there is no armature current
flowing in the machine. (Chapman, 1999, pp.255-256)
There are number of factors that cause the difference between EA and VF ;
1.The distortion of the air-gap magnetic field by the current flowing in the stator,
called armature reaction2.The self inductance of armature coils
3.The resistance of armature coils
4.The effect of salient-pole rotor shapes
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3.3.2.4. THE EQUIVALENT CIRCUIT OF AN ALTERNATOR
Figure 3.12 A simple circuit for alternators
The armature reaction voltage on a phase is;
AA IXjEV = (3.27)
In addition to the effects of armature reaction, the stator coils have a self
inductance and resistance. If the stator self inductance is called LA (and its
corresponding reactance is called XA) while the stator resistance is called RA, then
the total difference between EA and VF is given by;
AAAAAA IRIXjIXjEV = (3.28)
The armature reaction effects and the self inductance in the machine are both
represented by reactances, and it is customary to combine them into a single
reactance, called the synchronous reactance of the machine;
AS XXX += (3.29)
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Therefore, the final equation describing VF is;
AAASA IRIXjEV = (3.30)
Figure 3.13 The per-phase equivalent circuit for synchronous generators
The way in which a synchronous generator operates in a real power system
depends on the constraints on it. When a generator operates alone, the real and
reactive powers that must be supplied are determined by the load attached to it, and
the governor set points and field current control the frequency and terminal voltage,
respectively. When the generator is connected to an infinite bus, its frequency and
voltage are fixed, so the governor set points and field current control the real and
reactive power flow from the generator. In real systems containing generators of
approximately equal size, the governor set points affect both frequency and power
flow, and the field current affects both terminal voltage and reactive power flow.
A synchronous generator's ability to produce electric power is primarily limited
by heating within the machine. When the generator's windings overheat, the life of
the machine can be severely shortened. Since here are two different windings
(armature and field), there are two separate constraints on the generator. The
maximum allowable heating in the armature windings sets the maximum
kilovoltamperes allowable from the machine, and the maximum allowable heating in
the field windings sets the maximum size of EA. The maximum size of EA and the
maximum size of IA together set the rated power factor of the generator. (Chapman,
1999, p.316)
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Capacitors connected between the output and the earth enable autonomous self-
excited generation (some residual magnetism in the system is necessary),
A small synchronous generator may be run in parallel, which may (if diesel,
fuelled, for example) then provide power at times of inadequate wind.
Figure 3.14 Cutaway diagram for a wound-rotor induction machine
Figure 3.15 Cutaway diagram for a squirrel-cage induction machine
3.3.3.1. EQUIVALENT CIRCUIT OF AN INDUCTION MACHINE
An induction machine relies for its operation on the induction of voltages and
currents in its rotor circuit from the stator circuit (transformer action). Because the
induction of voltages and currents in the rotor circuit of an induction machine is
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essentially a transformer operation, the equivalent circuit of an induction machine
will turn out to be very similar to the equivalent circuit of a transformer. An
induction machine is called a singly excited machine (as opposed to a doubly excited
synchronous machine), since power is supplied to only the stator circuit. Because an
induction machine does not have an independent field circuit, its model will not
contain an internal voltage source such as the internal generated voltage EA in a
synchronous machine.
It is possible to derive the equivalent circuit of an induction machine from the
knowledge of transformers and the variation of rotor frequency with speed in
induction machines. (Chapman, 1999, p.365)
A transformer per-phase equivalent circuit, representing the operation of an
induction machine, is shown in Figure 3.16. Like any transformer, there is a certain
resistance and self-inductance in the primary (stator) windings, which must be
represented in the equivalent circuit of the machine. The stator resistance will be
called as R1 and the stator leakage reactance will be called as X1. These two
components appear right at the input to the machine model. Also, like anytransformer with an iron core, the flux in the machine is related to the integral of the
applied voltage E1. The curve of magnetomotive force versus flux (magnetization
curve) for this machine is compared to a similar curve for a power transformer in
Figure 3.17. Notice that the slope of the induction machine's magnetomotive force-
flux curve is much shallower than the curve of a good transformer. This is because
there must be an air gap in an induction machine, which greatly increases the
reluctance of the flux path and therefore reduces the coupling between primary and
secondary windings. The higher reluctance caused by the air gap means that a higher
magnetizing current is required to obtain a given flux level. Therefore, the
magnetizing reactance Xm in the equivalent circuit will have a much smaller value
(or the susceptance Bm will have a much larger value) than it would in an ordinary
transformer.
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primarily in the effects of varying rotor frequency on the rotor voltage ER and the
rotor impedances RR and jXR. (Chapman, 1999, pp.366-367)
3.3.3.1.1. ROTOR CIRCUIT MODEL
In an induction machine, when the voltage is applied to the stator windings, a
voltage is induced in the rotor windings of the machine. In general, the greater the
relative motion between the rotor and the stator magnetic fields, the greater the
resulting rotor voltage and rotor frequency. The largest relative motion occurs when
the rotor is stationary, called the locked-rotor or blocked-rotor condition, so the
largest voltage and rotor frequency are induced in the rotor at that condition. Thesmallest voltage (0 V) and frequency (0 Hz) occur when the rotor moves at the same
speed as the stator magnetic field, resulting in no relative motion. The magnitude and
frequency of the voltage induced in the rotor at any speed between these extremes is
directly proportional to the slip of the rotor. Therefore, if the magnitude of the
induced rotor voltage at locked-rotor conditions is called ER0, the magnitude of the
induced voltage at any slip will be given by Equation (3.31);
0RR EsE = (3.31)
and the frequency of induced voltage at any slip will be given by Equation (3.32);
er fsf = (3.32)
This voltage is induced in a rotor containing both resistance and reactance. The
rotor resistance RR is a constant (except for the skin effect), independent of slip,
while the rotor reactance XR is affected in a more complicated way by slip.
(Chapman, 1999, p.367)
The reactance of an induction machine rotor depends on the inductance of the
rotor and the frequency of the voltage and current in the rotor. With a rotor
inductance of LR, the rotor reactance is given by;
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RrRrR Lf2LX == (3.33)
Substituting Equation (3.32) into Equation (3.33);
( )
0RR
ReR
ReR
XsX
Lf2sX
Lfs2X
=
=
=
(3.34)
where XR0 is the blocked-rotor rotor reactance.
Figure 3.18 The rotor circuit model for induction machines
Figure 3.19 The rotor circuit model with all the frequency (slip) effects
concentrated in resistor RR
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3.3.3.1.2. FINAL EQUIVALENT CIRCUIT
To produce the final per-phase equivalent circuit for an induction machine, it is
necessary to refer the rotor part of the model over to the stator side. The rotor circuit
model that will be referred to the stator side is shown in Figure 3.19, which has all
the speed variation effects concentrated in the impedance term.
In an ordinary transformer, the voltages, currents and the impedances on the
secondary side of the device can be referred to the primary side by means of the turns
ratio of the transformer:
s2
s
ssp
ssp
ZaZ
Ia
1II
VaVV
=
=
=
=
=
(3.35)
where the prime refers to the referred values of voltage, current and impedance.
Exactly the same sort of transformation can be done for the induction machines
rotor circuit. If the effective turns ratio of an induction machine is aeff, then the
transformed rotor voltage becomes;
0ReffR1 EaEE == (3.36)
and the rotor current becomes;
eff
R2
a
II = (3.37)
and the rotor impedance becomes
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+= 0R
R2eff2 jX
s
RaZ (3.38)
so
0R2eff2
R2eff2
XaX
RaR
=
= (3.39)
Figure 3.20 The per-phase equivalent circuit for induction machines
In wind energy conversion systems, depending on the speed of the wind, the
generator may act either as a generator, supplying power to the grid, or as a motor
(acting as a sink of power from the grid). In either case, there will be a difference in
speed between the shaft speed nr and the output ns. This is known as generator slip,
and may be expressed as;
s
rs
n
)nn(s
= (3.40)
where
ns : Electrical speed of the magnetic field (or stator speed) (rpm)
nr : Rotor mechanical speed (rpm)
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The slip is defined as negative when the machine is acting as a generator, and
positive when acting as a motor. (Chapman, 1999, pp.369-370)
Figure 3.21 Torque-Speed curve for a MW-size induction machine
The torque-speed characteristic curve in Figure 3.21 shows that, if an induction
motor is driven at a speed greater than synchronous speed by an external effect (i.e.
wind), the direction of its induced torque will reverse and it will act as a generator.As the torque applied to its shaft increases, the amount of power produced by that
generator increases. There is a maximum possible induced torque in the generator
mode of operation. This torque is known as the pushover torque of the generator. If
a torque is applied to the shaft of the induction generator which is greater than the
pushover torque, the generator will over-speed. (Chapman, 1999, p.436)
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As a generator, an induction machine has severe limitations. Because it lacks a
separate field circuit, an induction generator cannot produce reactive power. In fact,
it consumes reactive power, and an external source of reactive power must be
connected to it at all times to maintain its stator magnetic field. This external source
of reactive power must also control the terminal voltage of the generatorwith no
field current, an induction generator cannot control its own output voltage. Normally,
the generator's voltage is maintained by the external power system to which it is
connected.
The one great advantage of an induction generator is its simplicity. An induction
generator does not need a separate field circuit and does not have to be drivencontinuously at a fixed speed. As long as the machine's speed is some value greater
than synchronous speed for the power system to which it is connected, it will
function as a generator. The greater the torque applied to its shaft (up to a certain
point), the greater its resulting output power. The fact that no fancy regulation is
required makes this generator a good choice for windmills, heat recovery systems,
and similar supplementary power sources attached to an existing power system. In
such applications, power-factor correction can be provided by capacitors, and thegenerator's terminal voltage can be controlled by the external power system.
(Chapman, 1999, p.437)
Wind machines driving electrical generators operate at either variable or constant
speed. In variable-speed operation, rotor speed varies with wind speed. In constant-
speed machines, rotor speed remains relatively constant, despite changes in wind
speed. (Gipe, 1995, p.211)
Small wind turbines typically operate at variable speed. This simplifies the
turbines controls while improving aerodynamic performance. When these small
wind machines drive an induction generator, both the voltage and frequency vary
with wind speed. The electricity they produce is incompatible with the constant-
voltage, constant-frequency alternating current (AC) produced by the utility, but can
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be used as is for resistive heating or pumping water at variable rates, or it can be
rectified to direct current (DC) for charging batteries.
If a grid-connected turbine is fitted with an AC generator, this must produce
power that is in phase with the utility's grid supply. Many commercial grid-
connected turbines use induction AC generators, whose magnetizing current is drawn
from the grid, ensuring that the generator's output frequency is locked to that of the
utility and so controlling the rotor speed within limits. Synchronous generators
produce electricity in synchronization with the generator's rotating shaft frequency.
Thus, the rotor speed of grid-connected turbines must exactly match the utility
supply frequency.
To generate utility-compatible electricity, the output from a variable-speed
generator must be conditioned. Although it is possible to use rotary inverters for this
task, variable-speed turbines typically use a form of synchronous inverter to produce
constant-voltage 50 or 60 Hz AC like that of the utility. Most of these inverters use
the utilitys alternating current as a signal to trigger electronic switches that transfer
the variable-frequency electricity at just the right moment to deliver 50 or 60 Hz ACat the proper voltage.
Although some manufacturers of medium-sized wind turbines build variable-
speed turbines, most operate the rotor at or near constant speed. These machines
produce utility-compatible power directly via induction (asynchronous) generators.
Induction generators have two advantages over alternators;
They are inexpensive.
They can supply utility-compatible electricity without complicated controls.
For AC generators, a critical design factor, that is synchronous speed, must be
considered. AC generators produce alternating current, the frequency of which varies
directly with the speed of the rotor and indirectly with the number of poles in the
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generator. For a given number of poles, frequency increases with increasing
generator speed.
p
f120sn
= (3.41)
where
ns : Synchronous or stator speed (rpm)
f : Grid frequency (Hz)
p : Number of poles
Manufacturers should decide the number of poles of the generator (for either
synchronous or asynchronous) for optimum conditions.
Table 3.2 Common Synchronous Speeds for Generators
Pole Number Europe (50 Hz) North America (60 Hz)
4-pole 1500 rpm 1800 rpm
6-pole 1000 rpm 1200 rpm
An induction generator begins producing electricity when it is driven above its
synchronous speed which is generally 1000 or 1500 rpm in Europe (1200 or 1800
rpm in North America). Induction generators are not true constant-speed machines.
As torque increases, generator speed increases 2 to 5 %, or 20 to 50 rpm on a 1000-
rpm generator. This increase of 1 to 3 rpm in rotor speed is imperceptible in a wind
turbine operating at a nominal speed of 50 rpm. As torque increases, the magneticfield in the induction generator also increases. This continues until the generator
reaches its limit, which is about 5 % greater than its synchronous speed. Induction
generators are readily available in a range of sizes and are easily interconnected with
the utility. Medium-sized wind turbines use induction generators almost exclusively.
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3.3.4. RECENT DEVELOPMENTS IN GENERATORS FOR WIND
TURBINES
As well as applying to the basic process of energy conversion, technological
development also relates to the design and size of machines used for the generation
of electric p