55390761 Modeling and Simulation of Wind Turbines

7/30/2019 55390761 Modeling and Simulation of Wind Turbines

1/128

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


2/128

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


3/128

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


4/128

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


5/128

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.


6/128

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.


7/128

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.


8/128

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


9/128

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


10/128

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


11/128

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


12/128

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


13/128

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


14/128

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


15/128

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


16/128

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


17/128

2

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


18/128

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)


19/128

4

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.


20/128

5

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.


21/128

6

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)


22/128

7

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


23/128

8

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.


24/128

9

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)


25/128

10

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-


26/128

11

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)


27/128

12

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.


28/128

13

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.).


29/128

14

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.


30/128

15

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.


31/128

16

Figure2.6

Atypicalwindturbineindetail(VESTASV2

7/225kW)


32/128

17

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


33/128

18

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.


34/128

19

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


35/128

20

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)


36/128

21

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);


37/128

22

D2D AV?

D2C

= (3.2)

where

CD : Drag coefficient


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)


38/128

23

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.


39/128

24

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


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.


40/128

25

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)


41/128

26

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.


42/128

27

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.


43/128

28

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)


n : Number of blades


44/128

29

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




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)


45/128

30

where

0 : Optimum tip speed ratio

r : Blade tip radius of rotation (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


46/128

31

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)


47/128

32

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)


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


48/128

33

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)


49/128

34

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.


50/128

35

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)


51/128

36

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


52/128

37

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


53/128

38

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


54/128

39

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)


55/128

40

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


56/128

41

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


57/128

42

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)


58/128

43

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)


59/128


60/128

45

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


61/128

46

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.


62/128


63/128

48

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;


64/128

49

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


65/128

50

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


66/128

51

+= 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)


67/128

52

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)


68/128

53

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


69/128

54

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


70/128

55

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.


71/128

56

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

55390761 Modeling and Simulation of Wind Turbines

Documents

Transcript of 55390761 Modeling and Simulation of Wind Turbines