Modelling and Simulation of Fuzzy-PI Control System for a Variable

Speed Wind Power Generator

By

Md. Maruf Billah

A thesis submitted for the fulfillment of a

Master of Engineering (by Research)

Supervisors:

Dr. Mehran Motamed Ektesabi

Dr. Nasser Hosseinzadeh

Faculty of Engineering and Industrial Sciences (FEIS)

Swinburne University of Technology

Hawthorn, Victoria, Australia

November, 2012

i

ABSTRACT

This thesis serves the main objective of modelling and simulation of a variable speed wind

power generator. Induction generators are considered to be most popular type of generator

for wind energy system nowadays. Both squirrel cage induction generator (SCIG) and

wound rotor induction generator (WRIG) can be used for wind power production. Doubly

fed induction generator (DFIG) is a special type of WRIG. Both SCIG and DFIG are

considered here for this research and a comprehensive simulation model has been

completed for both types of induction generators.

The control system of the wind power generator is considered as the most important

subsystem for simulation and modelling purpose. Apart from the traditional PI type

controllers, a newly improved intelligent fuzzy-PI control system is utilized here in active

power, reactive power and DC-link voltage control loops. By introducing fuzzy logic

control in the designed controllers, the simulated system becomes more adaptive and more

agile to follow the nonlinear relationship of the system quantities. Both SCIG and DFIG

systems with these fuzzy-PI type controllers are simulated in fixed and variable wind speed

criteria. The significant system quantity response observation and analysis are carried out to

demonstrate the correct working capabilities of the proposed control system. In terms of

these system quantities, the proposed model response is compared with traditional PI

controller based model. This insight brings out the clear improvement in a sense that, when

fuzzy logic controllers are added with PI controllers, it can give better tracking of reference

value thus improving the system quantity response. Apart from this, the authenticity of

using this improved fuzzy-PI controllers in wind energy system can be claimed in a fault

associated condition. The simulation shows that, system dynamics improve after a fault is

cleared while the controllers are fuzzy-PI type rather than just the traditional PI type.

Along with this analysis of significant system quantities in a steady state condition, several

other important relationships were established among different system quantities. These

relationships are important for a better understanding of the correct working status of the

ii

proposed control system. Alteration of these relationships will affect the ideal operation of

the system a great deal. Significant system quantity responses are simulated and compared

with and without a controller. This represents the importance of using a control system in a

variable speed wind power generator operation. Also a noise reduction capability of the

designed control system is demonstrated in this research. This proves the compatibility of

the proposed model to withstand inserted noise coming from external atmosphere via

sensors.

The last important finding of this research concerns the relationship of the inertia constant

to the system’s initial start-up response. It has been shown in this thesis that the inertia

constant affects fixed and variable speed operation in different ways. For variable speed

operation, increasing the inertia constant does increase the time for system quantity to reach

steady state level but helps to reduce oscillation. For the fixed speed case it has been shown

that the oscillation is negligible and the time to reach the steady state is only affected by

changing inertia constant. This relationship can help to select practical equipment with the

proper inertia constant which will bring a tradeoff between the amount of oscillation and

the time to reach to steady state level.

In the appendix, a full chapter is devoted to the discussion on the experimental setup which

was developed for the next phase of this research (future work). Initial experimental works

have been carried out and mentioned with proper data and analysis.

iii

ACKNOWLEDGEMENTS

This research work has been carried out at and supported by the Faculty of Engineering and

Industrial Sciences (FEIS) of the Swinburne University of Technology.

In the very beginning, I would like to express my gratitude to my both supervisors, Dr.

Mehran Motamed Ektesabi and Dr. Nasser Hosseinzadeh for their continuous

encouragement, support and patience. I would also like to thank Mr. Mikhail Mayorov from

Power System Lab at Swinburne. I would like to thank my colleagues, Mr. Md. Ayaz

Chowdhury and Mr. Mehedi Al Emran Hasan for their advice and comments. My special

thanks go to my parents and my wife, Shirin Sultana, for being my inspiration.

iv

DECLERATION

I hereby declare that I am the sole author of this thesis and to the best of my knowledge, it

contains no material that has been published by others previously except where necessary

references have been mentioned. No material of this thesis work has been submitted or

accepted for any other degree of diploma at any university.

Md. Maruf Billah

November 2012

v

LIST OF PUBLICATIONS

Peer reviewed Conference Proceedings:

“Modelling of a Doubly Fed Induction Generator (DFIG) to Study its Control

System” speech presentation on 08.12.10 at Australasian Universities Power

Engineering Conference (AUPEC-2010 December), Christchurch, New Zealand. By

Md.MarufBillah, Dr. Nasser Hosseinzadeh, Dr. Mehran Motamed Ektesabi.

“Variable Speed DFIG Modelling and Parameter Dependency of Initial Transient

Response” published at 3rd International Conference on Power Electronics and

Intelligent Transportation System Conference (PEITS-2010, November), Shenzhen,

China by Md. MarufBillah, Dr. Nasser Hosseinzadeh, Dr. Mehran Motamed

Ektesabi.

“Dynamic DFIG Wind Farm Model with an Aggregation Technique” published at

6th International Conference of Electrical and Computer Engineers Conference

(ICECE-2010, December), Dhaka, Bangladesh by M. A. Chowdhury, M. M. Billah,

N. Hosseinzadeh and S. A. Haque.

Seminar Presentations:

“Induction Generator Modelling and Simulation”poster and speech presentation on

03.11.2009 at Post Graduate (PG) Conference in Swinburne University of

Technology, Hawthorn, Australia by Md. Maruf Billah, Dr. Nasser Hosseinzadeh,

Dr.Mehran Motamed Ektesabi.

“Detail Variable speed DFIG model Outlining the Important Internal Parameter

Variation on Generator Response ”paper and speech presentation on 09.11.2010 at

Post Graduate (PG) Conference in Swinburne University of Technology, Hawthorn,

Australia by Md. MarufBillah, Dr. Nasser Hosseinzadeh, Dr. Mehran Motamed

Ektesabi.

vi

TABLE OF CONTENTS

1 Introduction..........................................................................................................1

1.1 Wind Power Generators……………………………………………………………..2

1.2 Thesis Outline………………………………………………………………………..4

1.3 Literature Review……………………………………………………………………5

1.4 Applied Control System and Algorithm…………………………………………….7

1.5 Wind Farms and Grid Connection…………………………………………………11

2 Wind Power And Wind Scenario Analysis…………………………...13

2.1 Source of Wind…………………………………………………………………….13

2.2 Different Parts of a Wind Turbine System…………………………………………15

2.3 Wind Turbine………………………………………………………………………16

2.3.1 Vertical Axis Turbine………………………………………………………17

2.3.2 Horizontal Axis Turbine……………………………………………………18

2.3.3 Fixed Speed Turbine………………………………………………………..19

2.3.4 Variable Speed Turbine…………………………………………………….20

2.4 Extractable Wind Power…………………………………………………………...21

2.5 Torque Derivation from Wind Power……………………………………………...22

2.6 Tip Speed Ratio…………………………………………………………………….24

2.7 Various Aerodynamic Power Controls…………………………………………….27

2.7.1 Pitch Control………………………………………………………………..28

2.7.2 Yaw Control………………………………………………………………..29

2.7.3 Stall Control………………………………………………………………...29

2.7.4 Active Stall Control………………………………………………………...29

2.8 Electricity Production from Wind………………………………………………….30

2.9 Global Wind Energy Scenario Analysis……………………………………….......31

2.10 Wind Energy Scenario in Australian Perspective………………………………….35

vii

3 Induction Generator Modelling………………………………………....39

3.1 Introduction………………………………………………………………………...39

3.2 General Aspects of Modelling……………………………………………………..40

3.3 Modelling Approaches……………………………………………………………..41

3.4 Three Axes to Two Axes Transformation (d-q transformation)………………….42

3.4.1 Transformation in d-q Stationary Reference Frame………………………..44

3.4.2 Transformation in d-q Synchronously Rotating Reference Frame…………45

3.4.3 Transformation in d-q Rotor Reference Frame…………………………….46

3.5 Voltage Transformation Equation………………………………………………….49

3.6 Current Transformation Equation………………………………………………….52

3.7 Power Transformation Equation…………………………………………………...54

3.8 Equivalent Circuit of Induction Generator…………………………………………55

3.9 d-q axes Induction Generator Model……………………………………………....58

3.9.1 DFIG with Partial Scale Power Electronic Converter……………………...62

3.9.2 SCIG with Full Scale Power Electronic Converter………………………...63

3.10 Two Mass Model for the Gearbox System………………………………………...64

3.11 Aerodynamic Power Calculation (Block Design)………………………………….65

3.12 Control System Block Design……………………………………………………...67

3.12.1 Pitch Angle Controller……………………………………………………...67

3.12.2 Rotor Side Controller……………………………………………………..67

3.12.3 Grid Side Controller………………………………………………………..68

3.13 Grid System Modelling…………………………………………………………….69

4 Control of Induction Generator…………………………………………73

4.1 Control Aspects…………………………………………………………………….73

4.2 Controllable System Quantities…………………………………………………….74

4.3 Power Electronics for Control……………………………………………………...75

4.4 Full Scale Converter and Partial Scale Converter………………………………….77

4.5 Power Losses……………………………………………………………………….78

4.6 Vector Control Approach…………………………………………………………..79

viii

4.6.1 Stator Flux Orientation……………………………………………………..79

4.6.2 Stator Voltage Orientation………………………………………………….79

4.7 Different Parts of Conventional PI Control System………………………………..80

4.7.1 Rotor Side Converter Control………………………………………………80

4.7.1.1 Active and Reactive Power Controller……………………………….81

4.7.1.2 Speed Controller……………………………………………………..83

4.7.1.3 Rotor Side Current Controller………………………………………..85

4.7.2 Grid Side Converter Control………………………………………………..86

4.7.2.1 Grid Side Current Controller…………………………………………87

4.7.2.2 DC Link Voltage Controller………………………………………….88

4.7.3 Pitch Angle Control………………………………………………………...89

4.8 Fuzzy Control System……………………………………………………………...89

4.9 Implemented Fuzzy-PI Control Structure………………………………………….90

4.10 Generic Block Diagram of a Whole Wind Generator System with Control unit…..99

5 Result Analysis and Significant System Quantity Response

Characterisation……………………………………………………………101

5.1 Defining Significant System Response…………………………………………...101

5.2 The Impact on System Quantity Responses with and without Controller………..102

5.3 Analysis of Significant System Quantity Responses for DFIG (With Partial Scale

Converter)…………………………………………………………………………104

5.3.1 Fixed Speed Case………………………………………………………….105

5.3.2 Variable Speed Case………………………………………………………107

5.4 Analysis of Significant System Quantity Response for SCIG (With Full Scale

Converter)…………………………………………………………………………109

5.4.1 Fixed Speed Case………………………………………………………….109

5.4.2 Variable Speed Case………………………………………………………111

5.5 Correlation of Rotor Side Converter Power and Grid Side Converter Power with q-

axis Rotor Current………………………………………………………………...113

5.6 Correlation between P and Te and Analogy Behind………………………………114

ix

5.7 Constant DC Voltage Topology…………………………………………………..115

5.8 Variation of Rotational Speed/Active Power for Wind Speed…………………....117

5.9 The Impact of Reactive Power Reference on the System Simulation……………118

5.10 Noise Elimination…………………………………………………………………119

5.11 Start-up System Transient Time Response Analysis……………………………..122

5.12 Fault Comparison scenario in Fuzzy-PI controller and Tradition PI Controller….125

5.13 Model Comparison between Traditional PI Controllers and Fuzzy-PI Controllers127

6 Conclusions……………………………………………………………..…….130

6.1 Result Discussion………………………………………………………………….130

6.2 Remarks……………………………………………………………………………132

6.3 Future Work Suggestion…………………………………………………………..133

REFERENCES……………………………………………………………………..….134

Appendix………………………………………………………………………..……..144

A1. Experimental Hardware Setup Overview………………...………..144

1. Introduction……………………………………………………………………….144

2. Laboratory Equipments for Wind Energy Test Bench……………………………144

3. Wind mill Controller Unit………………………………………………………...145

4. Test Bench Setup………………………………………………………………….147

5. Three-phase Windmill Induction Generator Performance at no Load……………149

5.1 Effect of Capacitance in Induction Generator Performance………………150

5.2 Effect of Inductance in Induction Generator Performance………………..152

6. Three-Phase Windmill Induction Generator Performance at Load……………….154

7. Relation of Total Efficiency with the Load……………………………………….157

A2. Nomenclature…………………………………………………………..……159

A3. System Parameter’s value…………………………………...………….162

x

LIST OF FIGURES

Fig. 1 Various associated blocks in electrical power generation from wind power……….1

Fig. 2 Different generator technology used for wind energy system………………………2

Fig. 3 Schematic diagram of a wind turbine system connected to grid line [104]………..12

Fig. 4 Wind velocity and pressure status in a turbine [53]………………………………..15

Fig. 5 Various parts associated with wind energy systems [55]………………………….16

Fig. 6 Vertical axes wind turbine…………………………………………………………18

Fig. 7 Horizontal axes wind turbine………………………………………………………19

Fig. 8 Wind turbine output power vs. rotational speed [70]………………………………23

Fig. 9 Wind turbine output torque vs. rotational speed curve [70]……………………….24

Fig. 10 Curve showing relationship between power coefficients and tip speed ratio……...25

Fig. 11 Bar diagram of the probability of wind speed for a certain amount of time (Weibull

representation, total probability adds up to 100%)………………………………...27

Fig. 12 Figure showing electricity production from a wind turbine (Practical view) [75]…32

Fig. 13Wind energy production trend (Installed Capacity) throughout the years………….33

Fig. 14 Market growth rate comparisons…………………………………………………..33

Fig. 15 Wind energy installation for the last 5 years for Australia………………………...36

Fig. 16 Vector control implementation principle with machine (d-q) model………………44

Fig. 17 d-q transformation in a stationary reference frame [60]…………………………...46

Fig. 18 d-q transformation in a synchronously rotating reference frame [60]……………..47

Fig. 19 Voltage vector with its component in direct and quadratic axes [60]……………...49

Fig. 20 Current vector with its component in direct and quadratic axes [60]……………...52

Fig. 21 Voltage and current vector (power representation) with their components on direct

and quadratic axes………………………………………………………………….55

Fig. 22 Thevenin’s equivalent circuit of an induction generator…………………………...55

Fig. 23 Equivalent circuit for squirrel cage induction generator…………………………...56

Fig. 24 Equivalent circuit for wound rotor induction generator or DFIG………………….56

Fig. 25 d-q model of DFIG system in block representation………………………………..59

Fig. 26 Vector diagram for DFIG in d-q reference frame (synchronously rotating)……….60

xi

Fig. 27 Block diagram of a fixed or variable speed DFIG with partial power electronics

converter……………………………………………………………………………63

Fig. 28 Block diagram of a fixed or variable speed SCIG with full rating power electronics

converter……………………………………………………………………………64

Fig. 29 Two mass model representation of a gearbox……………………………………...64

Fig. 30 Schemetic representation of wind turbin control [87]……………………………...65

Fig. 31 Pitch Angle Controller (block diagram)……………………………………………67

Fig. 32 Rotor Side Controller (RSC) block diagram……………………………………….68

Fig. 33 Grid Side Controller (GSC) block diagram..............................................................69

Fig. 34 Grid model used in this research created in Simulink environment……………….70

Fig. 35 Transmission line π- model used for transmission line block design……………...71

Fig. 36 Typical Power Electronics Converter connected to the wind generation system

[104]………………………………………………………………………………..76

Fig. 37 Full scale converter connected to a variable speed wind power generation

system........................................................................................................................77

Fig. 38 Partial scale converter connected to a variable speed wind power generation

syste………………………………………………………………………………...77

Fig. 39 PI active power controller in RSC side…………………………………………….82

Fig. 40 PI reactive power controller in RSC Side………………………………………….83

Fig. 41 PI Speed controller in RSC side……………………………………………………84

Fig. 42 MPPT control for power tracking in terms of different wind speed [97]………….84

Fig. 43 Current control loop of stator side controller………………………………………88

Fig. 44 DC link voltage control loop……………………………………………………….88

Fig. 45 Pitch angle controller………………………………………………………………89

Fig. 46 Block diagram of a fuzzy control system…………………………………………..90

Fig. 47 Block diagram of a fuzzy-PI active power controller……………………………...93

Fig. 48 Block diagram of fuzzy-PI reactive power controller……………………………...93

Fig. 49 Membership functions for the input and output quantities for active power

controller; (a) Error in active power, (b) Rate of change of error in active power, (c)

q-axis rotor reference current……………………………………………………....94

Fig. 50 Surface view in FIS editor for active power fuzzy controller……………………...95

xii

Fig. 51 Membership functions for the input and output quantities for reactive power

controller; (a) Error in reactive power, (b) Rate of change of error in reactive

power, (c) d-axis rotor reference current…………………………………………...96

Fig. 52 Surface view in FIS editor for fuzzy reactive power controller……………………97

Fig. 53 Block diagram of DC-Link Voltage fuzzy-PI Control…………………………….98

Fig. 54 Membership functions for the input and output quantities for DC-Link Voltage

Controller; (a) Error in DC Voltage, (b) d-axis reference grid current…………….98

Fig. 55 Surface view in FIS editor for fuzzy DC-link Voltage controller………………….99

Fig. 56 Equation flow diagram of a generic DFIG wind turbine system…………………100

Fig. 57 Parameter characterization with and without controller………………………….104

Fig. 58 DFIG with fixed speed case, (a) wind speed, (b) rotational speed, (c) active power,

(d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) DC-Link

Voltage, (h) slip…………………………………………………………………...106

Fig. 59 DFIG with variable speed case, (a) wind speed, (b) rotational speed, (c) active

power, (d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g)

DC-Link Voltage………………………………………………………………….108

Fig. 60 SCIG with fixed speed case, (a) wind speed, (b) rotational speed, (c) active power,

(d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) slip….110

Fig. 61 SCIG with variable speed case, (a) wind speed, (b) rotational speed, (c) active

power, (d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g)

slip………………………………………………………………………………...112

Fig. 62 Relation between grid and rotor side converter power with q-axis rotor current...114

Fig. 63 Correlation between active power and electromagnetic torque…………………..116

Fig. 64 Constant DC voltage topology……………………………………………………117

Fig. 65 Variation of rotational speed and active power…………………………………...118

Fig. 66 Noise elimination capability of the controller in variable wind speed……………120

Fig. 67 Noise elimination capability of the controller in fixed wind speed………………121

Fig. 68 Initial transient time response for different inertia constant (represented by

rotational speed) (a) for variable speed case and (b) fixed speed case…………...124

Fig. 69 Rotational speed curve with same inertia constant (H = 5 sec) for both fixed and

variable speed operations…………………………………………………………124

xiii

Fig. 70 Comparison between system responses during fault in traditional PI controller based

system and fuzzy-PI controller based system, (a) rotational speed, (b) active power,

(c) reactive power, (d) electromagnetic torque, (e) DC-Link Voltage……………125

Fig. 71 Comparison between system responses in traditional PI controller based system and

fuzzy-PI controller based system, (a) wind speed, (b) rotational speed, (c) active

power, (d) reactive power, (e) electromagnetic torque, (f) DC-Link Voltage……128

Fig. 72 Wind Mill Controller Unit (MV4250) from TERCO…………………………….145

Fig. 73 Single line diagram of the Wind Mill Controller Unit arrangement……………...146

Fig. 74 Equipment connection diagram for experimental setup…………………………..148

Fig. 75 Picture of hardware setup in the laboratory………………………………………148

Fig. 76 Relation between generated AC voltage and rotational speed for no load case….150

Fig. 77 Measurement of rotational speed requires to generate AC voltage for different

capacitance level………………………………………………………………….151

Fig. 78 Measurement of AC voltage in different inductance level……………………….153

Fig. 79 Measurement of AC current in different inductance level………………………..153

Fig. 80 Relation among DC load voltage and rotational speed for loading to the system..155

Fig. 81 Voltage and current relationship in case of loading by keeping the rotational speed

constant…………………………………………………………….……………..156

Fig. 82 Effect of DC voltage, total efficiency and rotational speed in terms of increasing

load to the system…………………………………………………………………158

xiv

LIST OF TABLES

Table. 1 Comparison of different generator technologies in terms of important

parameters…………………………………………………………………...3

Table. 2 Converter option and control schemes for various generator systems………8

Table. 3 Summary in a tabular form of the wind energy status of the leading countries

[74]………………………………………………………………………..34

Table. 4 Energy growth rate chart for different renewable energy share in

Australia……………………………………………………………………36

Table. 5 Satewise wind energy production analysis of Australia…………………...37

Table. 6 Relationship of slip and operating mode and indication of mechanical, stator

and rotor power for sub and super synchronous speed zone……………….57

Table. 7 Rule base law for active power fuzzy controller block…………………….95

Table. 8 Rule base law used for fuzzy reactive power controller…………………...97

Table. 9 Rule base law for fuzzy DC-Link Voltage contorller……………………...99

Table. 10 Parameter’s value for AC voltage generation for no load case…………...149

Table. 11 Generated AC voltage relation with rotational speed for no load case…...149

Table. 12 Relation of AC voltage generation to rotational speed in different

capacitance for no load case………………………………………………151

Table. 13 Relation of AC voltage and current measurement to rotational speed in

different inductance for no load case……………………………………..152

Table. 14 Measurement of DC load current, voltage and rotational speed at different

load introduced to the system……………………………………………..154

Table. 15 Measurement of loading by keeping the rotational speed fixed………….156

Table. 16 Measurement of different parameters (speed, DC current, DC voltage, DC

power, shaft power and efficiency) for load case…………………………157

1

Chapter One

Introduction

From ancient times wind has been considered as a source of power. In the age of ape-men,

strong wind was considered as the spiritual power coming directly from God. Modern

science has discovered many ways of extracting power from wind. Electricity is one of the

modern discoveries without which life is unthinkable. Conventional sources of electricity

generation are fossil fuels like coal, oil and gas.

Fig. 1 various associated blocks in electrical power generation from wind power.

The problem associated with the continuous consumption of finite fossil fuels and their

harmful effect on the environment have led to a search for secure, renewable and green

energy sources. Wind is regarded as the most prominent source of electricity generation. It

is unlimited and environmental friendly and creates less pollution or environmental hazard.

In a typical wind energy production unit, a three phase transformation of energy is taking

place (illustrated in the Fig. 1). Wind power rotates the turbine rotor and the kinetic energy

of wind is converted to mechanical energy. The generator is connected to the rotor shaft,

which produce the electrical energy from the mechanical energy. In Fig. 1, different

associated blocks are presented, which take part in wind power generation.

Wind Turbine Rotor Blade

Drive Train or

Gear Box

Power Electronics Converter

Transmission Grid

Load/ Consumer

Generator

Wind Power

Mechanical Power

Electrical Power

Mandatory Parts Optional Parts

2

1.1 Wind Power Generators

The generator is the most vital part of a wind energy generation system. A wind farm can

operate in either fixed speed or in variable speed. In case of variable speed operation certain

advantages can be achieved compared to fixed speed generators such as, more power

production, wide operational range, more stability and smoother operation etc. Though

there are some disadvantages like complex system design and required constant observation

and care for the system. On the other hand the fixed speed wind generators are more robust

and cheap with maximum life limit. The power production range is low compared to the

variable speed type but if the issues of continuous operation or stability of operation can be

taken care of, then fixed speed type can also become a very good option due to its low cost

benefit ratio. However both solutions have their advantages and disadvantages which will

be highlighted later in the following chapters. In Fig. 2, a tree diagram for wind generators

classification is illustrated. Here the classification is done on the basis of speed of rotation.

Fig. 2 Different Generator technology used for wind energy system.

The main two categories are synchronous speed or asynchronous speed generator.

Synchronous speed generators are rarely used as they require a large permanent magnet and

produce AC voltage which needs to be connected to the grid directly. In a synchronous

generator the system frequency and the grid frequency needs to be exactly matched with

each other and as most of the wind farms are on remote areas and also it is advantageous to

transfer DC electricity rather AC electricity, so it is better to use an asynchronous

3

generator. The asynchronous generators are mainly divided into two types, one is the

squirrel cage generator (SCIG) which is used to for fixed speed operation and the other one

is the wound rotor induction generator (WRIG) which is used for variable speed operation.

Doubly Fed Induction Generator (DFIG) is a special kind of wound rotor generator which

is connected to the grid via both stator and rotor. This DFIG is modelled and used here as

the main intended topic for this research. Along with modelling of the DFIG, the squirrel

Cage Induction Generator (SCIG) is also modelled and analysis has been carried out.

Table. 1 Comparison of different generator technology in terms of important

parameters

Generator Type

Operation of Speed

Reactive Power

Control

Active Power

Control

Investment Maintenance

Permanent Magnet

Synchronous Generator,

PMSG (KW)

Variable Speed

Operation is possible

Yes (unless there is a

back to back converter)

Yes High High

Doubly Fed Induction Generator, DFIG (kW

to MW)

Variable Speed

Operation is possible

Yes Yes High Almost low

Induction Generator, IG (kW to

MW)

Variable Speed

operation is possible only with certain

configuration. Not Common in usual case.

Yes (to generate

energy and to stabilize the output

voltage and frequency)

Limited Low Low

Synchronous Generator, SG (KW to

MW)

Variable Speed

Operation is possible

Yes Yes Low High

4

In Table. 1, a comparative analysis has been stated of different kinds of wind power

generators in terms of operational speed, reactive and active power control capability,

amount of investment required and maintenance required. Here it shows that DFIG requires

high investment and low maintenance but SCIG on the other hand requires high

maintenance but less investment. Both fixed and variable speed operation is possible for

DFIG and SCIG, but it is more common for DFIG, where SCIG’s are mostly operated on

fixed speed.

1.2 Thesis Outline

There are five chapters and an appendix in this thesis. Chapter 2 discusses how wind energy

systems work and details wind energy scenario across the world and especially in Australia.

It also discusses the different turbine types and contains a brief introduction of control

blocks used in the system. Chapter 3 mainly focuses on the modelling prerequisite of the

thesis. Starting from the d-q model transformation of different variables like voltage,

current and power from real to imaginary d-q axes, the induction generator model (Both

DFIG and SCIG), the aerodynamic model used in the research and the generator controllers

are described. Chapter 4 deals with the control system. The main control systems are the

rotor side converter control and the grid side converter control. Also the internal loop

design and characteristic equation of internal controller unit has been demonstrated in detail

in this chapter. Apart from using the conventional PI controllers, a new type of fuzzy-PI

controllers has been used in this thesis. We also discusses the semiconductor device and the

modeling approach. The pitch angle controller block is another important subsection of this

chapter. Where needed, a block diagram or equation flow diagram is provided to make the

thesis easily understood by the readers. Chapter 5 is the result and outcome section where

various simulation results have been plotted for different scenarios. Both DFIG and SCIG

have been modelled in the simulation program and both fixed and variable speed operations

have been demonstrated. Different important criteria for ideal operation are considered, and

justification of the used model has been made by comparing the system performance in the

ideal condition. Also some distinct analysis of two or more parameters was carried out to

represent a new relationship among those parameters. In another simulation the noise

5

reduction capability of the proposed controller has been demonstrated. The system initial

startup transient response time is observed for different inertia constant value for both fixed

and variable wind speed. The important characteristics of a system response like rise time,

settling time and overshoot has been considered and compared for various simulation plots

and relationship among the inertia constant with system initial response time has been

mentioned for both fixed and variable speed case. Designed model with fuzzy-PI controller

has been compared with the traditional PI controller model and the improvement of system

response in active power and reactive power output is seen. In the last simulation, the fault

scenario analysis of the both type of controllers are carried out to show the distinct

improvement of the modelled system compared to the conventional model. An

experimental test bench is initially established which can be further used for the next step

of this research. A wind mill control unit and associated generators, power supply unit and

other accessories have been collected and some initial experiments have been carried out to

observe the very basics of a test bench implementation. As that is not the scope of work for

this research so those initial basic test cases and experiments are mentioned here in the

appendix. Before that appendix, chapter 5 ends with the overall result analysis and some

future work suggestions.

1.3 Literature Review

According to previous research, like [1, 2] a variable speed DFIG can achieve around 30%

greater energy production compare to fixed speed SCIG. This research was mostly

conducted by focusing more on DFIG capabilities. On the other hand in the following

research [3, 4], it is shown here the SCIG can also produce a reasonable amount of energy

production with a reduced investment and longer life time. For DFIG focused research, the

other generator system (SCIG) is considered as very simple and basic with less or reduced

amount of control ability [5, 6]. On the other hand the papers where the SCIG is said as

advantageous, DFIG structure has been considered as expensive and reduced control

capable and omit the continuous maintenance section of SCIG [4]. Various criteria like

selection of maximum operation speed of wind turbine, turbine blade profile, speed control

technology, missing base parameter assumption etc. are affecting a proper comparison

6

among both systems. In this research both SCIG and DFIG are simulated and modelled

with both fixed and variable speed capability. SCIG can also operate in variable wind speed

but only under certain conditions. Some important system response is plotted against the

time and analysis has been carried out for those in a steady state condition. In this research,

only the initial startup transient is shown for the figures which are required to start and

reach to the steady state for the system.

All the research shows that the complexity is much higher for the DFIG model compared to

the SCIG model. It is mainly due to the fact the DFIG requires complex control model as

both rotor and stator are connected to the grid, where in SCIG only grid side is connected

[3]. Also the partial rating converter used for DFIG also demands more careful design. One

common way of controlling the rotor current for the DFIG rotor is by means of field

oriented (vector) control. Several vector control approaches have been proposed for the

DFIG system. Among them stator flux orientation (SFO) is one which is suggested by the

following research [5, 7-9]. It is also shown that if the stator resistance is considered as

small, stator flux orientation can be considered as stator voltage orientation (SVO) as well

[10, 11]. Some researchers tried to differentiate these two vector control schemes but others

say that under certain boundary conditions they are both the same [8, 9]. Xu et al. [12] have

shown in his simulation that variation in stator supply as well as load change affects the

flux distribution. Liu et al. [13] have shown that for stator flux orientation, DFIG system

may be unstable in some certain condition. Here in this research basically SFO is followed

as the vector control for the modelling of the system, but the research shows that omitting

the negligible stator resistance can work as a SVO vector control of the system as well.

Most commonly used DFIG models are either 3rd order [14, 15] or 5th order model [15, 16].

A 5th order DFIG model is the vivid and most detail model with all the flux linkage, current

and voltage equations for both d and q axis of rotor and stator quantity. A 3rd order DFIG

model is simplified where order has reduced. In the most shorten way, a single order DFIG

model can be described as the swing equation. Here in this model a detail 5th order DFIG

model is selected to explain the model clearly.

7

There is not much literature on the comparisons of the parameter’s response for DFIG and

SCIG for both fixed and variable speed operation. In this research both DFIG and SCIG

have been operated in both fixed and variable wind speed to get the comparative study. The

variable wind speed model has been used according to the reference [17] and the wind

speed is modelled by a ‘signal builder’ block in Simulink environment. The response

analysis shows the justification of using this wind speed model. Also different inter

parameter relationship has been established. It brings out some interesting insights of the

response where it shows a sure correlation of different parameters. The electromagnetic

torque and active power have got an inversely proportional relationship to each other. In

steady state condition these relationships can comment on perfect working capabilities of

the simulated model. The startup time response and relationship to main characteristics

(such as, rise time, overshoot, settling time etc.) with inertia constant was also carried out

for fixed and variable speed. This analysis was not clearly stated in any of the literature. For

simulation work it is important to note the time constant which the system requires to reach

a steady state. The simulation model utilized a control structure which is modelled by using

both PI and a fuzzy logic controller to provide a more accurate reference value for the

system. Some literature has focused on a combined fuzzy and PI controller system, but no

one has shown the fault scenario comparative analysis where this fuzzy-PI controller is

showing improvement in system response during a fault condition. This analysis has been

carried out in this research. The comparison of system response between a traditional PI

controller based system and a fuzzy-PI based system is another novel simulation effort

which will be discussed in this thesis.

1.4 Applied Control System and Algorithm

Both DFIG and SCIG can be equipped with various control schemes and converter options.

In Table. 2 a list of available options of different controller’s type for different generator

solution are given. Converter options from the diode bridge rectified converter to the

advanced matrix converter have been utilized for modelling of a DFIG or SCIG system. For

example reference [8, 9, 18, 19] used back to back PWM or pulse width modulation

converters for DFIG modelling. Reference [4] used a PWM converter for SCIG modelling.

8

Table. 2 Converter option and control scheme for various generator systems[3].

Converter Options Generator Types Control Schemes

Diode Bridge/SCR Converter

PMSG Simple firing angle control of one converter

DFIG Sliding mode control SG Nothing IG Nothing

SCR Rectifier

PMSG Simple firing angle control of both converter

DFIG Dual thyristor firing angle control

SG Nothing IG Nothing

Diode bridge/ Hard Switching Rectifier

PMSG MPPT wind prediction control, vector control of

supply side DC link capacitor’s voltage

DFIG Nothing SG Phase angle displacement

and supply voltage control IG Nothing

Back-to-back hard switching rectifer (normal

or reduced switch)

PMSG MPPT, vector control of both converters, MPPT

inverter current controlled through PI controllers

DFIG PWM MPPT or rotor and stator side space vector

control SG Grid side reactive and

active power control and electromagnetic torque

control IG Using fuzzy logic

controllers and model adaptive reference system

vector control

Matrix Converter

PMSG Nothing DFIG Vector control of stator and

rotor side double space vector PWM switching

SG Nothing IG Vector control of supply

side space vector

9

This PWM converter control design is the most commonly used and effective way to model

the converter control. DPC or direct power control is another way to replace the PWM

converter control. Reference [7, 20, 21] discusses the DPC control scheme. Reference [21]

discussed a modified way to use DPC where discrete space vector modulation technique

has been utilized. It shows the possibility of synthesizing a large number of voltage vectors

in space DPC technique without needing the PWM converter control. Reference [18, 22]

used a vector converter (VC) control scheme. IGBT voltage source back to back converter

has been used in reference [23]. Paper [24] also propose a new hysteresis control loop for

the power controller to improve the harmonic elimination. For this research the most

commonly used converter control scheme PWM has been selected for converter design

because of its flexibility and simplicity. For induction generator, a diode bridge rectifier

cannot be used unless there is a capacitor bank at the generator side to control the voltage

and frequency. A diode rectifier introduction to the IG system means a unidirectional power

flow and therefore no reactive power control for the generator.

The most common control scheme used by the researchers is the PI controller [2, 5, 25, 26].

Though it is the most basic type of controller, it is widely used because of the simplicity of

its control loops and its optimum performance. In most of the control loops like active

power control, reactive power control and current control loop, PI controller has been

extensively used by researchers. PLL also been used in speed loops by some researchers.

Reference [18, 27] can be mentioned among many. In reference [27] Fadaeinedjad et. al.

mentioned the dependencies between rotational speed and active power need but didn’t

define a relationship among them. Also he defined the term electrical disturbance (which

comes from tower vibration) but didn’t show the effect of the system quantity responses

like rotational speed, active power etc. Sub and super synchronous speed level dynamic of

quantities is illustrated in [28] which is mostly done for DFIG system. In this research both

DFIG and SCIG system is considered for sub and super synchronous speed operation. A

tabular form of different converter option and various possible control schemes for different

type of wind energy generators is shown in Table. 2. Due to the short comes of PI

controllers like, non-adaptive and non-responsive to system’s non-linear relationship,

different intelligent controller system is adopted by the researchers. Fuzzy logic controller

10

has been used in some research [3, 29, 30] where a fuzzy function has been used to design

the controller. Both Takagi-Sugeno fuzzy logic and Mamdani fuzzy logic has been utilized

for controller design. Another control scheme used is Matrix converter [3, 31]. Neural

network is mostly used in aerodynamic control blocks where an intelligent neural network

has been used to get the power output from the turbine speed [32, 33]. Intended controllers

for this thesis are fuzzy logic controllers and PI controllers. Conventional PI controllers

only are not been able to provide ideal performance due to system’s non-linear parameter

changes and being difficult to adjust due to poor self-adaptive capability. Thus the

performance of a system used with PI controllers only is not up to the mark. Alternatively

an adaptive controller can handle the system non-linear parameter changes as well. Thus a

fuzzy-PI controller is used for this research to model the control system. This can simplify

things and make it easier to see how controllers work with the adaptive and non-linear

parameter changes handling capability of the system. Some literature suggests the

successful application of fuzzy logic controllers in power system, mainly in nonlinear and

complex processes. In reference [34-36], the authors have used Takagi-Sugeno (TS) fuzzy

logic controllers to model the control system for variable speed wind turbine generators.

Also reference [37-40] has used the Mamdani type fuzzy logic controllers for the wind

power generators. In reference [39, 41], concept of fuzzy-PI controllers has been used. The

approach they followed is to tune the Kp and Ki gain of the PI controllers by the fuzzy logic.

This directly affects the PI controller characteristics. In this thesis the PI controllers was

kept as original and a separate fuzzy controller block has been utilized in the control block

which will give a more accurate reference value compared to tuning Kp and Ki parameters

only. Also neither of these papers has compared the fault analysis scenario between this

fuzzy-PI controller based system and only PI controller based system which has been

simulated here. Only reference [37] has mentioned various system responses for fault

occurring in different places in the bus. All these mentioned literatures has only emphasized

on active and reactive power controller loops and utilized fuzzy controllers over there, but

this research also used another fuzzy logic controller in the DC-Link Voltage control loop

to get steady DC voltage output.

11

For wind speed tracking, MPPT (Maximum Power Point Tracking) technique is followed

here, which has been followed by most of the researchers [1, 42]. Induction generator

model order can be varied in terms of either 5th order or 3rd order model. The higher the

order number, the more detail the model is. Complete model with high order has been

followed in the references [15, 16, 43, 44]. On the other hand some reference followed

lower third order model [15, 22, 45, 46]. In this research a complete 5th order detail model

was considered for modelling purpose. The wind speed model has been followed by the

reference where a wind speed is simulated for 30 sec of simulation by using the ‘Signal

Builder’ simulation block.

1.5 Wind Farms and Grid Connection

Wind farms are basically a group of wind turbines combined and working together in a

specific region. An individual stand-alone wind turbine can generate electricity in very

small amounts (depending on the generator rating). It also has to face the uncertainty of the

wind pattern. As the consumer or the utility distribution system where the wind turbine is

giving power needs a constant amount of power throughout the time so it is not viable to

depend solely on a single wind turbine unit. Also in case of any fault or operational

mismatch a single wind power plant most often cannot participate in that voltage dip. In

financial terms, operating a single wind turbine is not viable for the owner. Thus the

concept of wind farm arises, where a large number of wind turbines are operated and the

total amount of power production is transferred to the transmission line or to the utility

distribution system as required. Obviously a central and rugged controlling and monitoring

system needs to be implemented for the whole wind farm to ensure continuous operation of

the whole system. Important advantages of building a total farm include more power

production, more control ability on produced power, participation on fault control of the

whole system and last not least greater profit margins. The land where the wind turbines are

installed can be used for agriculture or for other purposes as well. As a minimum of 8 to 10

m/sec of wind speed is required to rotate the turbine and produce electricity, so a

combination of different speed wind turbines in a wind farm can be a good aggregation

12

process. Wind speed is high in higher altitude as the drag force is less, so wind turbines

with greater height can yield more electricity than low altitude turbines.

Another important consideration for any wind farm is the analysis of site specific and

meteorological wind data analysis. It is necessary to analysis wind statistics for a particular

area of land for at least a year to get an idea of the wind input. The usual range of power

production for each turbine is around 2-5 MW nowadays, and from 20 to 100 MW rated or

even more single wind turbines can be grouped together to form a wind farm.

In Fig. 3, a schematic diagram of a single wind generation plant connected to the

distribution line is depicted.

Fig. 3 Schematic diagram of a wind turbine system connected to grid line [104].

13

Chapter two

Wind Power and Wind Scenario Analysis

2.1 Source of Wind In general terminology, movement of atmospheric air can be defined as the source of wind.

Compared to the polar region, air in the equator region (at and around 0 degree latitude),

are warmer due to the sun. Thus this hot air from the tropical region rises towards the upper

atmosphere and travels towards the pole. This air moves towards the east. On the other

hand, cool surface air is also affected by the rotation of the earth around its own axis and

around sun. This cool air tends to move from the polar region to the equator and hence tries

to shift to west because of its own inertia. This results in a large circulation of air flow in

the anticlockwise direction towards the low pressure regions in the northern hemisphere

and clock wise direction in the southern hemisphere [47]. The earth is inclined at an angle

of 23.5 degree to the axis of rotation around the sun. This causes the seasonal changes in

strength and direction of the air flow and the difference in heat radiation from the sun

towards different portion of the earth [48, 49].

Apart from this there is another air flow which is called “Local Wind” [50]. It is created by

the temperature difference between water regions (sea, river etc.) and regions of land. In the

day time, the sand or land portion of the earth gets warm more quickly than the water

portion. Thus the air above the land portion becomes hot and rises to the high atmospheric

region. This phenomenon creates a vacuum in the atmospheric region close to the land. To

fill up this, comparatively cool air above the water portion flies towards the atmospheric

region above the land portion. This particular air flow is named as “Sea Breeze”. It alters

the direction in the night time as radiation of heat takes longer time over water compared to

sand. Similar air flow is also created around valleys and mountains where the warm air

rises up along the slope of valley or mountain. Local wind flow may seem insignificant

compared to the global wind flow (due to the temperature difference from heat of sun), but

in a wind farm the impact cannot be ignored.

14

Meteorological estimation shows that, among the total incoming solar radiation, only 1% is

converted into wind, in terms of energy. But the solar energy which is received by earth in

10 days is equivalent to the total energy consumed by the fossil fuels (including coal, oil

and gas) [51]. The amount of fossil foils is decreasing day by day but on the other hand the

energy consumption by the world is increasing continuously. So a large demand and supply

gap has been created and is increasing in terms of energy requirements. As an estimation of

1990, only single percentage of wind energy can supply the whole energy demands of the

earth. This simple analogy gives us optimism to meet the energy crisis world is facing now

a days. Continuous research is going on to provide mankind with an effective and

environment friendly energy solution. Wind is certainly one of the top alternative sources

of energy to mitigate this energy scarcity. It is possible to eliminate the energy crisis of the

world by using wind energy only regardless of the concern of pollution and other side

effect of fossil fuels.

In Fig. 4, a representation of velocity and pressure of wind flowing through the wind

turbine is displayed [53]. The swept area increases as the wind passes the wind turbine

blades. As a result the wind velocity decreases after the wind turbine blades. This figure

shows that the wind speed is at maximum before coming to the rotor turbine blade and at

the point, when it hits the turbine blade it is at optimum speed. It reaches to a minimum

speed when it passes the turbine. As to maintain the constant pressure theorem, the pressure

tends to increase as the wind swept area increases until the wind hits the turbine blades. But

going pass the turbine blades the pressure is maximum negative and it turns to be normal as

the wind passes the turbine blade by quite a distance where there is no effect of wind

turbine blades [52].

15

Fig.4 Wind velocity and pressure status in a turbine [53].

2.2 Different Parts of a Wind Turbine System

Here a pictorial overview of a wind turbine system is given in Fig. 5 [54]. Various parts of

the whole system are numbered and highlighted. Along with the important parts like

generator, turbine blade, tower, gear box, some other associated parts like an anemometer,

pitch, brake, nacelle etc. are notified. The mechanical control system for the rotor blade

likes a yaw and pitch control is shown here but the generator control systems all together

are combined inside a controller block. This is connected to the grid transmission line for

distribution of electrical energy to the grid system.

16

Fig. 5 Various parts associated with wind energy system [54].

2.3 Wind Turbine

A wind turbine is a mechanical structure with a long stand and rotor blades. Blades rotate

as a consequence of incoming wind. The idea of a wind turbine started around 200 BC. in

Persia [55], when the Persian were using it for lifting water from underground, crushing

seeds to extract oil, grinding grains, etc. It was generally used for domestic household

purposes. In 1887 Scottish academic James Blyth [56] used the wind turbines to extract

wind power and make electricity from wind. The speed of wind turbine rotors was quite

slow compared to modern wind turbines. Turbine blades utilize the air force (either lift or

drag force) to rotate. A shaft is connected to rotor hub which is further connected to the

generator part via a drive train. Depending on the air force, the turbines might be high

17

speed (for lift force) or low speed (for drag force). In case of lift force, the turbine blades

can rotate in linear direction greater by several times than the wind speed. While in the case

of drag force the linear speed cannot exceed the wind speed [57, 58].

From a mechanical or structural point of view wind turbines can be divided into two major

subclasses. These are;

2.3.1 Vertical Axis Turbine

The oldest wind turbine structure is the vertical axis wind turbine. Around 1920 a French

electrical engineer named G.J.M. Darrieus [59] first designed this type of wind turbine for

power production. A typical vertical axis wind turbine is shown in Fig. 6. Usually it has

two or three blades. The C-shaped rotor which rotates around the long pole (tower support)

forms the vertical axis wind turbine. It might have strengthened wire (guy wires) to hold the

structure stand. The gearbox and the generator were usually deployed at the base of the

tower support [60]. The advantage of this kind of wind turbine is the rotor blades receive

wind from any direction independent of any control mechanism to move the direction of

blades towards the wind (in terms of vertical wind turbine). Also the vertical structure

makes it easy and simple to install the generator and gear box close to ground. It eventually

aids the less technical difficulties to further electricity transmission [61]. The height of a

vertical axis turbine is limited because it requires guy wires to keep it upright. It is

unsuitable for off-shore application and only operates effectively close to the ground where

air speeds are low. So it is not efficient in terms of large and continuous electricity

production. Moreover in case of high or gusty wind speeds, the output power cannot be

easily controlled as the only the mechanism of changing pitch can be utilized here.

Research shows that by using variable pitch blades, this problem can be overcome. Along

with that high wind speed can be utilized by installing a vertical axis wind turbine over a

tall building or structure [50].

18

Fig. 6 Vertical axes wind turbine.

2.3.2 Horizontal Axis Turbine

Horizontal axis wind turbines are those in which the rotation is along the horizontal axis.

That means the turbine blade rotates in parallel along the wind direction. Presently most of

the wind turbines are of this type. Horizontal axis wind turbines also can be divided into

two types depending on the direction of wind coming towards the rotor blades (as in Fig.

7). If the wind is coming from the front then the turbine is called an upwind machine type,

while if the wind comes from the rear part of the turbine, it is called a downwind machine

type [48, 62]. Though the extractable wind energy amount is dependent upon the turbine

parameters and the data sheet of the wind farms, it can be said that increasing the number of

blades can increase the energy captured (dual blade has got 10% more energy capture than

single blade, while the triple blade has got 5% more energy capture than dual blade). As

this type of turbines is independent of guy wires, it can be installed at heights where there is

more air flow although the pole will need to be wider and stronger. This turbine type can

extract high wind speed far above from the ground level. It is also good for off shore

installation and application. Apart from usual pitch control, stall control technology is

utilised here which gives more power control in terms of high wind speed [63].

19

Fig. 7 Horizontal axes wind turbine

In another criterion, based on operating speed of wind, the turbines can be divided into two

broad sections. These are;

2.3.3 Fixed Speed Turbine

Fixed speed wind turbine is the system where the turbine speed remains fixed throughout

the whole operation period. Control system in the turbine rotors is implemented in such a

way that it keeps the rotational speed constant irrespective of the wind. Generally stall

control turbines run at fixed speeds. The amount of power production remains constant. It

uses a squirrel cage induction generator. The SCIG is connected to the turbine rotor via a

multiple stage gear box which is further connected to the transformer or grid system

directly [4]. SCIG usually operates on a narrow speed range around a synchronous speed

level. In the 1980s many Danish manufacturers built their turbines by following this

process [64]. As the SCIG is operating on a fixed speed range so the turbine connected to

this system is called fixed speed turbine. In this system the generator draws reactive power

from the grid. So a capacitor bank is used to supply the reactive power to the system which

makes the system operate smoothly. It is sometime referred to as “Danish” concept. This

utilizes a self-regulated machine to operate around a constant speed range so the frequency

remains stable when connected to a large grid system. Also the construction of this system

is simple, easy and robust and mass production is possible. Stall control wind turbines are

used for this system but pitch angle control or active stall controls can also be introduced in

20

this system. The disadvantage is the system operates in a narrow speed range which creates

several demerits like torque pulsation, shadowing, high mechanical stress to the turbine and

gear box etc. Because of this constant speed operation the optimum wind power production

cannot be achieved in this turbine system and it cannot capture or cope up with the variable

wind speed scenario. The multistage gear boxes also added heavy weight on the nacelle and

require a large investment as well. As the reactive power is supplied from the grid so this

system is incapable to participate in the voltage control in case of grid disturbance [49, 65].

2.3.4 Variable Speed Turbine

A variable speed wind turbine system operates on variable wind speed and adjusts the

turbine blade rotation according to variability of wind speed [58, 63, 65]. As the wind speed

generally varies throughout the year and even at different times of day. The control system

implemented here modifies the turbine speed to maximize power production. It require

complex and advance control technology to be implemented in the turbine blade and even

in the generator part as well. Here pitch angle control system is used in the turbine rotor to

control the turbine rotation based on the wind speed. A power electronics converter system

is attached to the system. Depending on the rating of the power electronics converter either

full scale (where stator is connected to the grid via power electronics converter) or partial

scale (where rotor is connected to the grid via the converter and stator is directly connected)

system can be implemented [19, 66]. Advantages of this system in general are the

capability to operate on variable wind speeds and more control over the system. It can

operate in a wide speed range (around 30 percent) around synchronous speed level thus

more power production is possible. Overall cost of electricity production gets reduced by a

good amount. This kind of wind turbine system can contribute to the voltage control of the

grid and the converter supply reactive power to the system. There are several

disadvantages. Slip rings are used here which require continuous observation and

maintenance. The operation becomes more complex and involves more power electronics.

The variable speed wind turbine is the recent trend and currently is the selected type for

many projects. More research is going on to make it more efficient [22, 60].

21

2.4 Extractable Wind Power

Wind is basically the movement of air and air has mass. Thus there is kinetic energy

production by the movement of air of a certain mass. The rotor blade rotates due to this

kinetic energy and as a result of this it rotates the turbine shaft. The kinetic energy is

converted into mechanical energy [60, 67]. The rotation of the turbine shaft cuts the flux in

the induction generator. Hence the electrical energy production occurs in the generator part

which is transmitted later on.

According to the physics, the kinetic energy of wind is given by,

𝐾𝐸 = 12 𝑚𝑣𝑤𝑖𝑛𝑑2 (1)

Where m is the mass of the air in Kg and 𝑣𝑤𝑖𝑛𝑑 is the speed of air in m/sec.

As the power is the rate of energy, so by doing the derivation the wind power is equal to,

𝑃𝑤𝑖𝑛𝑑 = 𝑑𝑑𝑡𝐾𝐸𝑎𝑖𝑟 = 1

2𝑑𝑚𝑑𝑡𝑣𝑤𝑖𝑛𝑑2 (2)

dmdt

is the mass flow rate of air per second which has a unit of Kg/sec. If the volume rate of

air flow per second is multiplied with the density of air through which it flows, then it will

be equal to mass flow rate of air per second [60].

Thus, 𝑑𝑚𝑑𝑡

= 𝜌 𝑑𝑞𝑑𝑡

= 𝜌 ∗ 𝐴 ∗ 𝑣𝑤𝑖𝑛𝑑, where A is the swept area by the turbine rotor blades in m2.

Thus the wind power,

Pwind = 12ρ*A*vwind3. (3)

This is the extractable wind power for a particular wind speed and in the area swept by

the turbine rotor blade is m2.

The air density can be considered as the function of temperature and pressure of air. Both

of these terms are dependent upon the height of the air above sea level [60].

ρ(z) = P0RT

e�-gzRT� (4)

Where,

22

ρ(z)= Air Density as a function of altitude kgm-3

P0 = Standard sea level atmospheric density1.225kgm-3

R = Specific gas constant for air 287.05 JKg-1K-1

g = Gravity Constant 9.81 ms-2

T = Temperature K

z = Altitude above sea level m

This wind power is considered as the total available energy per unit of time, where the

velocity v is considered as the wind velocity at the rotor (which is lower than the free

stream wind velocity). In this ideal case scenario, where one dimensional calculation of

total wind speed throughout the whole turbine blade is considered is not true in real time

analysis. So a compensation factor needs to be introduced. The theoretical optimum wind

power utilisation was first calculated by Betz in 1926 [68, 69], where he included a factor

called “Power Coefficient” which will compensate this issue. According to the Betz law, if

without considering the mechanical and other losses in a wind turbine system, the

maximum power that can be extracted is

Pbetz=12ρ*A*vwind3*Cp,betz=12ρ*A*v

3*0.59 (5)

That means theoretically, if no losses are considered the maximum wind power can be

extracted is 59% of the actual total power available in the wind for a particular speed and

sweeping a particular radius area.

2.5 Torque Derivation from Wind Power

Depending a lot on the system parameters, there are two major factors that determine the

power production of a wind turbine. These factors are the cut in speed and rated wind

power. The cut in speed is the speed at which the wind turbine starts to operate and the

rated power is the maximum power rating which can be attained by that wind turbine. As

the relationship of wind power and wind speed suggested the wind power varies with the

cube of wind speed. A typical figure showing the variation of turbine power compared to

23

the shaft speed in different wind speed is showing in Fig. 8. So if wind speed increases

twice the wind power varies 8 times from the original speed. Depending on the

characteristic parameters of a particular wind turbine, the rated wind speed generally is

reached in 12-16 m/sec.

Fig. 8 Wind turbine output power vs. rotational speed [70].

The power production on that rated speed is the maximum rated power for that wind

turbine. So the turbine mechanics are controlled in such a way that this rated power will be

maintained whether the wind speed increases or decreases from this rated value. There

always is a cut off value at which the turbine stops its operation and power production

comes to zero immediately (for safety reasons). This idea of an immediate stop occurs in

case of a storm or gusty wind. When this happens, the wind turbine needs to be started from

the very beginning again and it might experience a substantial delay depending upon the

turbine technology. Thus a single wind turbine operation for continuous electricity

production is not feasible. Hence the idea of wind farms (where there are large numbers of

wind turbines running at the same time) comes into action [42]. In case of an aggregated

wind farm, the immediate fall in power production can be eliminated and depending of the

position of the turbines and technologies the slope of decreasing power curve can be

controlled [70].

24

Fig.9 Wind turbine output torque vs. rotational speed curve [70]

The torque production in the wind turbine happens because of the aerodynamic shape of the

rotor blades. The blades diameter increases from the centre to the periphery. At low shaft

speed the angle of incidence on a blade is large, so only a small amount of driving force is

created. As a result the production of torque is low. As the shaft speed increases, the

velocity of wind hitting the rotor blade increases. Thus the angle of incidence reduces and

the torque production increases. But as the shaft speed increases further the angle of the

incidence reduces towards to zero as the free wind velocity is now very low compare to the

shaft speed. As the torque production is proportional to the angle of the incidence so the

torque production reduces to zero level at high wind speed. This variation of torque

production compared to the shaft speed variation at particular wind speed is demonstrated

in Fig. 9 [70].

Thus this toque is calculated by, T = P/ωr

Where is the wind turbine velocity in rad/sec.

2.6 Tip Speed Ratio

Tip speed ratio (TSR) is the rate at which the rotor blades turn in a tangential direction

compared to the free speed wind [26, 62]. The possible energy extraction or the force

25

creation on the rotor blade depends on the angle of incidence between the relative wind

speed and moving rotor plane. So with the simple geometry the angle of incidence can be

calculated by the blade speed and incoming wind speed. This is represented by a simple

term Tip Speed Ratio like,

TSR = vm/vwind or equal to (ωr*R/vwind) (6)

As the wind created by the rotation of rotor blades is taken into account so the tip speed

ratio controls the operating condition of the wind turbine. It shows the tangential speed of

the rotor blade compared to the undistributed free speed wind.

A Graph of tip speed ratio and power coefficient is given (Fig. 10), which will indicate that

at the change of wind speed, the tip speed ration changes and hence the power coefficient

also changes. So around the rated wind speed the wind power coefficient is highest for a

certain tip speed ratio, which means the angle of incidence is at sharp angle. So the angle of

incidence can be calculated by,

φ = arc tan(1λ) = arctan (Vwind)

ωr*R (7)

Fig. 10 Curve showing relationship between power coefficient with tip speed ratio.

26

In modern wind turbines the rotor pitch angle Beta (β), can be controlled by a control

mechanism. Thus by changing the rotor pitch angle, the force on the wind turbine blades

can be controlled as the angle of attack of wind can be changed by changing β. Given that

the power coefficient equation can be modified and written as a function of tip speed ration

and rotor pitch angle

Cp = ∫(λ,β) (8)

Now Cp becomes a nonlinear power function of tip speed ratio (λ ) and pitch angle (β ). A

positive side of this relation is that, it is independent of the turbine parameters or

characteristics as these quantities can be normalised.

For old wind turbines, where the pitch angle was fixed, thus the power coefficient become

only a function of tip speed ratio for that particular pitch angle. This is shown in the graph

above. Thus if the Cp Vs λ curve is known for any wind turbine with the information of

rotor blade radius, power coefficient against the rotor speed can easily be constructed. So

the optimal rotation speed will be,

ωr,opt = λopt*vwindR

(9)

It shows that optimal rotor speed has a proportional relation with the tip speed ratio at a

fixed wind speed and has an inversely proportional relation with the rotor blade radius. In

terms of variable speed wind turbines, tip speed ratio is maintained at its optimal value.

This means that the rotational speed of turbine blade is adjusted over a wide range of wind

speed. Therefore the obtainable power coefficient reaches its maximum position for a

large range of wind speed and thus production of mechanical power becomes higher

compared to the fixed speed wind turbines. So in the case of a variable speed wind turbine

at a high wind speed, the mechanical power production is kept at an optimum rated level by

utilising the control technology. While in terms of a fixed speed wind turbine, at high speed

the power production becomes zero [71]. So keeping the other parameters the same, the

variable speed wind turbine can yield more power production at the cost of complex control

mechanism of rotor blades.

27

2.7 Various Aerodynamic Power Controls

As the output power of a wind turbine depends on the amount of wind speed attainable, so

the wind turbine output power can be considered as a function of wind speed. By

calculating the large statistical data of wind speed (lowest, highest, and average) for a long

period of time in the area where the wind farm is deployed, an operational range of wind

speed for that wind farm is determined. In the Fig. 11, a histogram is plotted which covers

the probability of wind speed over a year. Since it covers from zero wind speed to

maximum wind speed so the sum of the height is 1 or 100%. This means that the

probability of wind speed within that histogram is 100% (including zero wind speed). For

an example, the probability of wind speed between 4.5 to 5.5 m/s is 0.104 or

(0.104*8760=910 hours) year. Here the curve is plotted in a histogram as not enough

precise wind speeds were considered mainly non fractional values were taken. If more

intermittent points are taken in the histogram, the curve will become a continuous one,

which can be fitted to a Weibull distribution function [72].

Fig. 11 Bar diagram of the probability of wind speed for a certain amount of time (Weibull

representation, total probability adds up to 100%).

For a operated wind turbine a minimum wind speed is chosen as cut in speed (around 4 to 5

m/s ), when the wind turbine rotor will start to rotate. Also there need to be a fixed

28

maximum wind speed limit selected called cut off speed (around 25 to 30 m/s ) at or after

which the wind turbine should stop. Within this region, the wind turbine can be fixed to

rotate in a single optimal speed or it can rotate by following an optimum power coefficient

𝐶𝑝 curve. The first type is called a fixed speed wind turbine and second type is called a

variable speed wind turbine. In the case of a turbine with a fixed wind speed, the output

power will not be continuous as wind speed will vary [58]. A variable speed wind turbine

follows the power coefficientCp, which will indicate the optimum power production at

every wind speed. So a nominal wind speed at which maximum power production is

achieved is calculated and the Power coefficient Cp changes for every wind speed to get

that maximum power production for that certain wind speed. Thus the wind turbine

operates through a particular wind speed range to maintain that optimum power coefficient

[65]. The amount of cut in and cut off speed is dependent on the policy of the particular

wind farm considering the amount of power loss. This policy depends on the structure type,

environmental data, expected power production, type of load distribution etc.

As the equation and theory suggested, the wind power is proportional to the cube of wind

speed [5]. So if the wind speed increases twice, the wind power delivered is eight times

bigger. This creates problem in high or gusty wind speed. So a control system is very

important in the wind turbine design to limit the huge wind power in high wind speed to

protect the machine. The main control mechanisms used in modern wind turbines are

described below.

2.7.1 Pitch Control

Wind turbine blade pitch can be controlled in case of change in wind speed by the pitch

control system. Here the change of wind speed is sensed by sensors or from an automatic

control system (from the weather data and wind directions from satellite) and based on that

sensed signals, the whole blade or a portion of the blade is pitched away or into the wind

from their longitudinal axes [3]. If the captured power becomes too high for high wind

speed, the pitch is turned away from the wind or if the captured power becomes too low,

29

then the pitch is turned into the wind. Generally it is operated by using hydraulics. The

pitch control mechanism is advantageous because of good power control performance,

assisted start-up and emergency power reduction. The biggest disadvantage is that the pitch

mechanism is complex and requires sensitive sensors and signal transmission.

2.7.2 Yaw Control

The mechanism of yawing or tilting the rotor blade from wind rotation in case of excessive

wind speed is named as yaw control. It reduces the cross section of the wind flowing into

the blade [60]. This control system is utilized more in vertical axis wind turbines.

2.7.3 Stall Control

Stall Control technology is basically turbine rotor blade design dependent. The rotor blade

can be design in such way that when it is experiencing a high wind speed and the electrical

and mechanical rating of the blade is about to exceed its limit, the blade will automatically

stall [66]. Though the angle of rotor blade is fixed due to the aerodynamic design it will

create turbulence on the opposite side to the wind flow. So an opposite force will be created

against the rotor speed. Thus the rotor blades will stalled and stop rotating thus it will not

activate at high wind speeds and will retain the electrical and mechanical ratings. The

advantages of this kind of control are that it is robust, cheap, less complex, has fewer

moving parts and effective in high wind speed. On the other hand the disadvantages are this

control type is less effective in low wind speed and a sudden wind gust can destroy the

entire mechanical structure. Also it requires complex research into the aerodynamic shape

of the rotor blades [60].

2.7.4 Active Stall Control

As the normal stall control is risky to deploy in areas with sudden wind change, a

modification of stall control has been developed where the rotor blades are twisted

30

gradually along its length from the periphery to the centre [60]. This considerably decreases

the shock of sudden wind change and smooths the operation of a wind turbine in speed

changing state. This control technology is called active stall control.

2.8 Electricity Production from Wind

This section is a brief description of electricity production from the wind. Wind of a certain

mass and velocity flows through the turbine blades and makes the blades rotate. The shaft is

connected to the turbine blade which will also rotate by the blade rotation. The shaft is also

connected to the generator (gear box can be used in between). The generator’s rotor rotates

as the shaft of the wind turbine rotates. The rotation of torque creates a load torque or shaft

torque. Also the rotor electromagnetic torque is produced as the rotor rotates. The

differences between these two torques create the rotation speed. Relative difference in

rotation of rotor and stator creates an electromagnetic field in between the air gaps of the

rotor and the stator. This electromagnetic field induces and produces electricity if the

rotation is different than the synchronous speed. The stator is connected to the grid either

directly or via a power electronics converter. Depending on the amount of speed compared

to synchronous speed level (higher or lower than synchronous speed), the electricity

produced can be directed outwards towards the grid or inwards to the system. If the

rotational speed is greater than the synchronous speed, the difference in speed level (Slip) is

negative and the current flowing is observed outwards (towards grid). If the slip is positive

the electricity is flowing towards the system. If a converter is used, it can produce reactive

power and supply this to the system otherwise the grid system needs to be capable of

providing reactive power. Depending on the operation, converters can be used between

stator and grid (full scale) or between rotor and grid (partial scale). This is a very generic

overview of power production from the wind. Furthermore transformers are used to

upgrade the voltage level of the produced power and then, via a transmission grid network,

it can be directed to another location where a step down distribution transformer is used to

distribute the electricity which further supply to the utilities [19, 42, 68].

31

2.9 Global Wind Energy Scenario Analysis

Because it is a renewable source of energy and is easily available in unlimited quantities the

wind has drawn much attention as an alternative source. It is a prime source of clean

energy. It is still considered as the most lucrative solution throughout the whole world but

most of the new advancements and significant achievements have been accomplished by

advanced countries [73]. A pictorial view of a wind turbine is showing in Fig. 12. Until

2009 North America and Europe had the dominant share of wind energy production while

China and India were considered as the emerging countries which could contribute to

production of electricity and to technological advancement. Wind Energy was gaining an

increasing growth rate (showing in Fig. 14) for a long period of time (especially in the last

decade) until 2010 when a decreasing growth rate has been experienced in terms of new

wind farm installation and production of electricity from wind. After 2009 the growth was

31.7% and decreases to 23.6% after 2010. Although there was negative growth in

worldwide wind market, new countries like China (Growth rate 100%), Romania (Growth

Rate 120%), and Bulgaria (Growth Rate 112%) have contributed to the market. After

China, Eastern Europe and North America still retain the major share of wind energy while

Latin America, the rest of Asia, the Pacific region, Oceania and Africa still lag far behind

[74]. In terms of new market installation, China now holds the number one position with

total addition of 18.9GW, for a total market share of 50.3% (around half) of the total

amount. USA was the holder of the highest share (25.9%) in terms of new installation

capacity in 2009 but in 2010 was down by 14.9% of market share. They have only installed

around new 10GW wind energy farms. Among other countries, Germany, Spain, India etc.,

were making good progress in terms of new installation. In terms of installation capacity

per person or capacity per land area or capacity per GDP, eastern European Countries like

Denmark, Germany, Spain, Portugal etc. were the leading countries. In terms of total

electricity production throughout the whole world from any fuel sources, Wind Source still

lags far behind as by the end of 2010, it only represents 2.5% of the total electricity

generation. By the end of 2010, it is estimated that a total of 430 TWh electricity will be

produced by wind. Among the two types of wind energy farms, on shore wind farms are

dominating by far as the offshore farms are only 1.6% of the total installation capacity at

32

the end of 2010In continental terms, Asia holds the first position as it achieves 50.6% of

growth as a continent compare to North America (16.3%) and Europe (13.4%). Seen from

this point of view a good future rate forecast for wind energy resources. It is anticipated

that by the end of 2015, a global capacity of 600 000 MW is possible which is expected to

reach at least 1500 000 MW by 2020 (showing in Fig. 13) [51].

Fig. 12 Figure showing electricity production from a wind turbine (Practical view) [75].

Though the year 2010 was frustrating for new capacity increment of wind energy plants

there is hope for a better future. Among the positive sides are;

• World leaders are still promising to get more investment in the wind energy sector.

• World economy is on its way to a recovery after the recent inflation and crisis.

• Continuous decrease of fossil fuel reserve level at an alarming rate.

• Public support throughout the whole world is positive and increasing for the use of

clean and environment friendly energy sources.

• New countries are increasing their market share. Thus new emerging countries are

participating more in terms of wind farm installation and capacity increment.

• The idea of wind energy is becoming more popular in every corner of the world.

33

• Technological advancement is continuing and extensive and elaborate research is

going on this sector.

Fig. 13 Wind energy production trend (Installed Capacity) throughout the years.

Fig. 14 Market growth rate comparisons 1995-2010

34

Table. 3 Summary in a tabular form of the wind energy status of the leading countries

[74].

Position 2010 Country

Total Offshore Capacity 2010

(MW)

Added Offshore Capacity

2010 (MW)

Growth Rate 2010 (%)

Total Offshore Capacity

2009 (MW)

Total Offshore Capacity

2008 (MW)

1 United

Kingdom 1341 653 94.9 688 574 2 Denmark 854 190.4 28.7 663.6 426.6 3 Netherlands 249 2 0.8 247 247 4 Belgium 195 165 550 30 30 5 Sweden 164 0 0 164 134 6 China 123 100 434.8 23 2 7 Germany 108.3 36.3 50.4 72 12 8 Finland 30 0 0 30 30 9 Ireland 25 0 0 25 25

10 Japan 16 15 1500 1 1 11 Spain 10 0 0 10 10 12 Norway 2.3 0 0 2.3 0

Worldwide wind energy scenario has been tabulated in Table. 3. In the last year, there were

two major disasters which significantly affect the advancement of wind energy production.

Those were Oil leaks in the Gulf Sea near New Mexico and near New Zealand and the

nuclear disaster in Fukushima, Japan. Billions of dollars were wasted with serious

environmental and natural hazard with long time impact. These incidents surely will turn

the thoughts of world leaders to get the clean and environment friendly energy source as

soon as possible [76]. Future progress in towards wind energy sector relies heavily on the

perfect combination of advance technology and strong leadership in the right track. New

technologies can be utilizes to install and maintain the wind farms. To make it happen,

more concern and fund is needed to be available in this sector.

35

2.10 Wind Energy Scenario in Australian Perspective

Negative growth rate around the world in the wind energy sector also affects the Australian

wind energy sector. Australia was falling behind compared to the rest of the world in this

industry and after 2010 this scenario deteriorated further [73]. While after 2009, the total

installed wind energy capacity was around 555 MW, it added only 11.8 MW after 2010

(graphs are showing in Fig. 15). So the decrease in growth rate was sharp and frustrating

for the requirement of clean energy. As a continent, Australia has potentially got the most

prosperous future in the wind energy sector because of its long coast line. Compared to

other renewable energy sources, wind energy has a high potential to grow (showing in

Table. 4). Also, in terms of greenhouse gas emission, Australia is the highest emitter of

greenhouse gases per capita among the other developed countries in the world (Australia

emits 25.8 ton Carbon-Di-Oxide per person annually) [77]. The Australian government

announced a Mandatory Renewable Energy Target (MRET) to fill 20% of electricity

demand from renewable energy sources by 2020 [78]. In 2011 this target is divided into

two group, one is LRET (Large Scale Renewable Energy Target) and SRES (Small-scale

Renewable Energy Scheme) [78]. The new target set by government is to achieve 20% of

power from renewable sources by the end of 2020 (as promised in the Kyoto Protocol). If

the availability of wind is considered as the basic requirement, then Australia surely is a

very good place as over the entire coastline above 50m height (approximate rotor hub

height) there is a constant wind speed of around 8-9 m/s. This criterion makes Australia a

very lucrative place to install new and wind farms with large capacity. Compared to the

rest of the world Australia place 15th in terms of total capacity, added capacity, growth rate

at the end of year 2010 [79, 80]. Though compared to 2009, they have moved forward by

one position (from position 14th to position 15th), this is mostly because of the reluctant and

stagnant advancement of wind energy sector in the whole world.

36

Fig. 15 Wind energy installation for the last 5 years for Australia.

Table.4 Energy growth rate chart for different renewable energy share in Australia.

Renewable Energy Type

Growth 2006-07 (%)

2006-07 (PJ)

Biogas/Liquids 4.1 13 Hydro -9.9 52 Solar/Wind 230.2 28 Biomass 6.9 205 Total 10.3 298

In Australia wind farms are spread around the various states. A statewide energy production

analysis has been charted in Table. 5. Among the states South Australia (SA) has got the

most number of existing wind farms (wind energy contributing around 15% of the total

demand in SA). The installed capacity in SA is around 740 MW. Victoria holds the second

position with the installed capacity of 380 MW. Other states contributing significantly are

Western Australia and Tasmania. The forecast scenario is very hopeful for Victoria as there

is a future proposal of a new 2632 MW total capacity wind power plant. As of now wind

energy contributes very little (around 1%) to the national grid nationwide and a grid code

37

for wind generation is yet to be identified and finalized. The main problem behind this was

the unwillingness of the Australian government.

Table.5 State wise wind energy production analysis of Australia[74].

Stat

e/

Terr

itory

Wind Power Capacity Proposed Projects' Publicly Announced Status

(MW) Installed capacity

Feas

ibili

ty

Seek

ing

Appr

oval

Plan

ning

Ap

prov

ed

Und

er T

ende

r

Aban

done

d or

Su

spen

ded

Und

er

Cons

truc

tion

Proj

ects

Turb

ines

Tota

l MW

Pene

trat

ion

(%)

SA 14 435 907 19.4 890 Nill 725 Nill 117 296 VIC 9 267 428 4.3 846 275 1369 165 120 487 WA 14 142 202 1.2 99 2 142 Nill Nill Nill NSW 7 116 187 1 525 269 1315 Nill 80 92 TAS 6 68 143 4.7 190 Nill 130 Nill 160 168 QLD 2 22 12 0.1 52 Nill 624 Nill Nill Nill AAT 1 2 1 Nill Nill Nill 0.3 Nill Nill Nill NT 0 0 0 Nill Nill Nill Nill Nill Nill Nill ACT 0 0 0 Nill Nill Nill Nill Nill Nill Nill Australia 52 1052 1880 2602 545 4304 165 477 1043

Being the biggest Coal producer country, the Australian power generation industry was and

till now is based on coal driven power plants. The coal industry is very influential in

Australia [81], but a rise in public awareness of environmental issues has increases pressure

on the government to increase renewable energy market share. In the last parliament

election the Green party made coalition government with the liberal part. That brings a

positive attitude to the policy makers towards more funding in renewable energy sector.

Previously it was anticipated wrongly that per kWh electricity generated from a wind farm

costs more compare to the coal farm. Eventually researchers have demonstrated that this

propaganda actually is not true if we consider the environmental factor, reduction in

greenhouse gases, improvement in human life. If we only to consider the life cycle of a

typical wind farm (around 20 year) and the area utilized for that wind farm, it can be seen

that wind energy is far more cost effective than a coal fired energy plant. Another

38

significant step towards the clean energy was taken when in the last quarter of 2011,

government imposed a carbon tax on the industries [82]. Though normal industry seems not

to be taking this positively but at least it demonstrates willingness by the government to

reduce carbon emissions. So the scenario is quite optimistic for the renewable energy

sector.

39

Chapter Three

Induction Generator Modelling

This chapter discusses the modelling approaches where important modelling aspects and

criteria are discussed. The Induction Generator modelling (DFIG mainly and SCIG as well)

is done in a d-q synchronously rotating reference frame. The reference frame theory, the

transformation of parameters from actual a-b-c phase to an imaginary d-q reference frame,

the voltage, current and power measurement is also discussed here. The equivalent circuit

for the DFIG modelling is carried out based on the vector control approach. The block

diagram representation of the whole system with different internal blocks is elaborated.

DFIG and SCIG systems with both full scale and partial scale converters are presented to

clarify the difference between them. After that the aerodynamic power generation block is

modelled separately and explained in detail. Then a small description of the grid side

converter control, rotor side converter control and pitch angle control (3 main control units

for this research) is given. At the end of this chapter, the grid model is discussed in detail

with each component as well as transmission line model.

3.1 Introduction

The induction generator is an essential part of the whole wind power system. The electricity

generation depends mostly on the proper and correct modelling of a generator system along

with other associated subsystems. As the wind is variable in nature, to deal with this it is

necessary to model the induction generator in a proper way where each and every aspect is

taken care of. Initially variable speed AC drives were mainly used for general household

applications of less demand. Then the industrial application started for variable speed AC

machines. For the production of power DC generators are often preferred. But in the recent

past, the high growth of power electronics equipment, and greater demand for renewable

energy systems, wind energy is being regarded as one of the potential source of electricity

generation. When the question of generation arises, the induction machines are regarded as

much more importance because of their lower maintenance cost, rigid structure, small and

40

easy deployment, simple architecture etc. Basically induction generators are divided into

two basic categories,

1. Wound Rotor Induction Generator

2. Squirrel Cage Induction Generator.

These two categories have their certain advantages and disadvantages. Based on the actual

scenario and amount of power production required, both of them can be utilized in the

designed system [65, 83, 84].

Here in this chapter, the general aspects of induction generator modelling is discussed first,

followed by the axes transformation from real time three phase to imaginary two phase

transformation. This transformation is essential to facilitate the modelling in an easy and

more understandable way. This transformation is defined as the direct axis and quadrate

axis or d-q transformation. Later this d-q transformation, based on the speed of the system

is differentiated into 3 more categories (synchronously rotating, stationary and rotor

reference frame). Most of the simulation work in this thesis is carried out based on the

synchronously rotating reference frame, which is the most convenient and acceptable and

widely used system by others. After that the voltage and current transformations are shown

in terms of mathematical equations. Then the d-q modelling of the induction generator,

DFIG and SCIG model is elaborated. In the last part, the other associated subsystems, like

the aerodynamic power system, generic control system and grid system are explained in

brief.

3.2 General Aspect of Modelling

Computer simulation is nowadays regarded as a required stage for any application oriented

process. Before exposing the whole physical system directly to the practical environment,

simulation work is carried out in almost every sector. It saves a lot more money, effort,

potential risk and threat to environment and the system and human life as well. So a

successful project outcome depends a lot on the proper simulation of the system in a

computer software environment. It gives a clear idea about the real life scenario. Often data

41

and parameters from the real life environment are taken and used to understand the system

behavior and characteristics [26, 83]. The thing which need to be considered while

performing any simulation work are mainly, but not limited to, clear concept of the whole

system and its behavior, consideration of the real time parameters and data, consideration

of different probable outcomes and their effect on the system, proper understanding and

analysis of the simulation results, etc. It should be always kept in mind that this simulation

work is the prototype of the real system, but it will not necessarily be the same. The

modelling details and structure may vary for different outcomes and can be modified

according to the requirements of the project. For this reason simulation results might

slightly differ when using different models. Different subsystems structure might be

different for various operations. Most importantly a general base design is important where

various aspects are considered and where project-wise alteration can be performed.

To model a total Wind Energy Conversion System (WECS), an in depth knowledge of all

the associated parts of the wind farm, their operation characteristics, behavior and general

modelling information is essential. In this work, a detailed WECS model is completed and

each and every subsystem is defined elaborately. Various considerations or boundary

conditions are defined with each subsystem with appropriate explanation.

3.3 Modelling Approaches

Converter and induction generator modelling can be performed in various ways. In a

broader sense, it can be divided into two basic categories. One of them is the mathematical

functional model and another one is the mathematical physical model [85].

The functional model is mainly based on the relationship between the system input and

output and associated parameters related to the system. A mathematical relationship is

developed and hence the separate block by block approach of a system is not used as it

would be hard to differentiate. The main advantage of this approach is the simplicity and

fast operation time of the model in the time domain. However, the disadvantages are mainly

due to complex mathematical equitation derivation of the system and the reduced accuracy

42

in some cases. The functional model may be developed for a specific operating condition,

which may then lose its accuracy when applied to other operation conditions. As the

boundary conditions of the system are considered as ideal, in some cases it might overlook

some special scenarios in this type of modelling approach. In the case of DFIG/SCIG

converter design, it is a convenient approach as the actual power electronics converter

design and model is not taken into consideration, rather, the system response of the power

electronics converters are considered as reference. In this approach, the converters are

considered as ideal and also assumed to have constant voltage between the DC link

capacitor. On the rotor side converter, controllable voltage or current can be considered as

the input signal, based on the particular control system.

The mathematical physical model, on the other hand is mostly block diagram or equations

of the system oriented. This approach considers different blocks or subsystems of the whole

system in a separate way and also inter subsystem’s relationship among those are

recognized. Depending of the various analyses that need to be carried out, the system

behavior and responses vary in this approach. Thus the constitution of the physical model

varies in terms of steady state, fault condition or transient condition. With this approach it

is easier to achieve accurate results so that certain conditions can be identified which can

contribute to a realistic solution to a problem. Though this approach is rather complex

compared to the functional model approach, it is essential to apply this model approach to

perfectly identify the boundary or rated condition of any system. This approach will

uncover the insights of the system to get the mathematical equation representation.

3.4 Three Axes to Two Axes Transformation

In the language of mathematics transformations are utilized to make a complex system into

a simple system, with which the calculations and outcome processing becomes much easier

and user friendly. After obtaining the desired outcome, the inverse transformation can be

used to get this outcome into real system [86].

43

In electrical machine analysis, to get the system outcome in a user friendly and applicable

way (for simulation purpose) and to achieve more command on analysis of parameters, the

three-axes to two-axes transformation are carried out. Among the previous research works

for induction machine modelling and transformation, some are regarded as pioneers in this

field e.g. R. H Park, H. C Stanley, G. Kron and D. S. Brereton etc.

R.H Park formulated a variable change, where he replaced the variables (voltage, current,

flux) of a stator associated synchronous machine with a rotating rotor winding which is

fictitious. In the late 1930s, H. C. Stanley employed a change of variables in the analysis of

induction machines [62], where rotor variables are transformed to a reference frame fixed

to the stator. G. Kron utilized a new reference frame rotating at a synchronous speed with

the rotating magnetic field, which eventually eliminated the time varying inductances. D. S.

Brereton employed the Park transformation into the induction machine, where he

eliminated the time varying inductances by transforming the stator variables to a reference

frame fixed in the rotor side.

All of these transformations were used for any certain or particular scenario until 1965 [60],

it was discovered that all these transformation of induction machine analysis can be

contained into one general transformation which eliminates all time varying inductances by

referring the stator and rotor variables to a new reference frame. This reference frame might

stand still or rotate at an angular velocity. Thus, appropriate assigning of speed to the

reference frame is all that is needed for transformation to different scenarios. This is called

an arbitrary reference frame [5, 86, 87]. In Fig. 16 implementation of the vector control in

an arbitrary reference frame is shown. It can be seen that the transformation of variables

from real axes to imaginary axes and inverse transformation of vice versa is carried out for

stator current.

44

Fig. 16 Vector control implementation principle with machine (d-q) model.

3.4.1 Transformation in d-q Stationary Reference Frame

Considering a three phase induction machine with stationary stator winding axes as, bs and

cs with voltages along these axes𝑣𝑎𝑠, 𝑣𝑏𝑠, 𝑣𝑐𝑠 . After transformation to a d-q reference, the

voltages would consecutively be vqss and vdss along the q and d- axis. Let the angle

difference be θ among the voltage vas andvqss . So the direct and quadratic axis voltages

can be written as [86],

�vasvbsvcs� = �

cos θ sinθ 1cos�θ-120∘� sin�θ-120∘� 1

cos(θ+ 120∘) sin(θ+ 120∘) 1� �

vqss

vdss

v0ss� (10)

45

The corresponding inverse relationship is,

�vqss

vdss

v0ss� = �

cos θ cos�θ-120∘� cos(θ + 120∘)sinθ sin�θ-120∘� sin(θ+ 120∘)0.5 0.5 0.5

� �vasvbsvcs� . [13] (11)

From this relationship, the voltage of each axes (d and q) in the stationary rotating reference

frame can easily be calculated as,

vqse = vqss cos θe-vdss sinθe (12)

vdse = vqss sin θe-vdss cos θe (13)

Resolving the rotating frame parameters into stationary frame,

vqss = vqs cos θe + vqs sinθe (14)

vdss = - vqs sin θe + vds cos θe (15)

Writing the line to line voltages in trigonometric way,

vas = vm cos(ωet + ϕ) (16)

vbs = vm cos �ωet- 2π3

+ ϕ� (17)

vcs = vm cos �ωet + 2π3

+ ϕ� (18)

From equation 14 and 15,

vqss = vm cos(ωet + ϕ) (19)

vdss = -vm sin(ωet + ϕ) (20)

So placing the value of,𝑣𝑞𝑠𝑠 , 𝑣𝑑𝑠𝑠 in those equations,

vqs = vmcosϕ (21)

vds = -vmsinϕ (22)

46

This shows that sinusoidal variables appear as DC quantities in a stationary reference

frame. So the magnitude of this sinusoidal voltage is the maximum voltage value, which is,

�V→� = Vm (23)

Fig. 17 shows the vector representation of the d-q transformation in a stationary reference

frame. Where, the phase difference is theta between real a-axis of stator quantity and the

imaginary q-axis in stationary reference frame. The q-axis is leading the d-axis by 90

degree.

Fig. 17 d-q transformation in a stationary reference frame [60].

3.4.2 Transformation in d-q Synchronously Rotating Reference Frame

In Fig. 18, the d-q transformation of a synchronously rotating reference frame is

represented via a vector diagram. It shows that the rotational angle between the

synchronously rotating reference frame and the stationary reference frame is θ , the angular

rotation in synchronous speed. So now the quantities which have been transferred to the

stationary reference frame are transferred from this reference frame to the synchronously

rotating reference frame.

47

Fig. 18 d-q transformation in a synchronously rotating reference frame [60].

The stator circuit equations can be written as,

vqss = Rs iqss + ddtψqs s (24)

vdss = Rsidss + ddtψdss (25)

Where, ψqss is the q axis flux linkage and ψdss is the d axis flux linkage.

vqs = Rsiqs + ddtψqss + ωeψds (26)

vds = Rsids + ddtψdss -ωeψqs (27)

If the rotor is not rotating, the rotor equations will be as,

vqr = Rriqr + ddtψqrs + ωeψdr (28)

vdr = Rridr + ddtψdrs + ωeψqr (29)

48

If rotor rotates then the equations will be,

vqr = Rriqr + ddtψqrs + (ωe-ωr) ψdr (30)

vdr = Rridr + ddtψdrs + (ωe-ωr) ψqr (31)

3.4.3 Transformation in d-q Rotor Reference Frame

The rotor reference frame is that reference frame where the transformation of the system is

done based on the rotation of the rotor. In this type of reference frame the rotational speed

becomes ω = ωr.

So the stator voltage will be

vqs = Rsiqs + ddtψqss + ωrψds (32)

vds = Rsids + ddtψdss -ωrψqs (33)

Rotor equations for both d and q axes voltages if the rotor does not rotate,

vqr = Rriqr + ddtψqrs + ωrψdr (34)

vdr = Rridr + ddtψdrs + ωrψqr (35)

Rotor equations for both d and q axes voltages when the rotor rotates are as follows.

vqr = Rriqr + ddtψqrs (36)

vdr = Rridr + ddtψdrs (37)

49

3.5 Voltage Transformation Equation

Fig. 19 Voltage vector with its component in direct and quadratic axes [60].

In Fig. 19, the d and q axis stator voltage is indicated as a vector diagram in the d-q

reference frame. For a balanced network with three phase pure sinusoidal voltage supply,

the total sum of these three phases becomes zero. In this kind of system the voltage

transformation from a-b-c to d-q axis can be written as [60, 69],

�vqs

vds� = 2

3�1 -1

212

0 -√32

√32

� �vavbvc� (38)

For balance system,

va + vb + vc = 0 (39)

In trigonometry, the three phase sinusoidal voltage inputs can be written as,

va = Vm cosωet (40)

vb = Vm cos(ωet- 2π3

) (41)

vb = Vm cos(ωet + 2π3

) (42)

50

So substituting these values in the previous equation, we can get the d and q axis voltage

values,

vqs = 23

(va- vb2

- vc2

) (43)

vds = 23

(√32

(-vb + vc))

𝑜𝑟, 𝑣𝑑𝑠 =1√3

(𝑣𝑐 − 𝑣𝑏)

or, vds = 1√3

(Vm cos(ωet + 2π3

) -Vm cos(ωet- 2π3

)) (44)

According to Euler’s identity, converting a trigonometric equation into exponential form, it

can be written as,

vds = Vm√3

(ej�ωet+

2π3 �+e-j�ωet+

2π3 �

2- e

j�ωet-2π3 �+e-j�ωet-2π3 �

2) (45)

After simplifying equation 43 and 45, we get,

vds = -Vm sinωet (46)

vqs = Vm cosωet (47)

For a balanced system considered here, the d-axis and q-axis voltages are always at right

angle to each other and also as the equation suggested, they hold the same peak as a-b-c

phase voltages.

So d-q resultant voltage, if we consider the vector average,

Vdq = vqs-jvds = Vm(cosωet + j sinωet) = Vmeωet (48)

So in the 1st quadrant the resultant voltage vector for the stationary reference frame is

shown in the Fig. 19. If the d-axis voltage is along the real or x-axis, then the q-axis voltage

will always be at a right angle to it that means along the-axis or imaginary axis. The

51

resultant will be in middle of it which will be rotating at an angle θe or ωet from the d-axis

voltage value.

For ideal scenario where the system is balanced, it can be written as,

Vdqs = �((vds2) + (vqs

2)) (49)

So substituting the values of d and q-axis voltages,

𝑉𝑑𝑞 = 𝑉𝑚

The RMS value will be,

Vrms = 0.707Vdq (50)

So it can be said that, for the balanced system the RMS value can also be calculated if the

instantaneous value of a-b-c phase voltage is known and the resultant d-q voltage

magnitude is just equal to the peak voltage of three-phase system for a balance condition.

In the other representation, if the line to line voltage is measured or given as a reference,

the relationship for line to line voltage to the phase voltage can easily be calculated for a

three phase system. And then once we get the phase voltage the relation are procedure to

get the d-q axis voltage is just like previous case.

So for a balance system,

𝑣𝑎𝑏 + 𝑣𝑏𝑐 + 𝑣𝑐𝑎 = 0

𝑣𝑎𝑏 = 𝑣𝑏 − 𝑣𝑎

𝑣𝑏𝑐 = 𝑣𝑐 − 𝑣𝑏

𝑣𝑐𝑎 = 𝑣𝑎 − 𝑣𝑐

52

𝑣𝑎 =13

(𝑣𝑎𝑏 − 𝑣𝑏𝑐)

vb = 13�vbc-vca� (51)

𝑣𝑐 =13

(𝑣𝑐𝑎 − 𝑣𝑎𝑏)

3.6 Current Transformation Equation

The d and q axis stator current vectors are shown in Fig. 20. For the current transformation

into d-q reference of a three phase system, [60, 69],

�iqs

ids

i0s� = 1

3�2 -2 -10 -√3 √31 1 1

� �iaibic� (52)

Considering no current flowing through the neutral phase for balanced system, the previous

equation can be written as,

�iqs

ids� = 2

3�1 -1

2-12

0 -√32

√32

� �iaibic� (53)

Fig. 20 Current vector with its component in direct and quadratic axes [60].

53

For balanced condition,

𝑖𝑎 + 𝑖𝑏 + 𝑖𝑐 = 0

So,

isq = 2

3�ia- ib

2- ic2� = ia (54)

ids = 1√3�ic-ib� (55)

ia = Im cos(ωet-∅) (56)

ib = Im cos(ωet- 2π3

-∅) (57)

ic = Im cos(ωet + 2π3

-∅) (58)

So substituting these values, we can get the q and d axis currents as,

iqs = Im cos(ωet-∅) (59)

𝑖𝑑𝑠 =𝐼𝑚√3

�cos(𝜔𝑒𝑡 +2𝜋3− ∅)− cos(𝜔𝑒𝑡 −

2𝜋3− ∅)�

Or, ids = Im√3

(ej�ωet+

2π3 -∅�+e-j�ωet+

2π3 -∅�

2- e

j�ωet-2π3 -∅�+e-j�ωet-2π3 -∅�

2)

Or, ids = -Im sin(ωet-∅) (60)

So it means that, both d-axis and q-axis currents are 90 degree apart from each other and d

axis current leads the q axis current. Also, it proves that for a balanced system. In the case

of current transformation similar to voltage transformation, as well, the peak value remains

unchanged. So the resultant current in stationary d-q axis can be written as,

𝐼𝑑𝑞 = 𝑖𝑞𝑠 − 𝑗𝑖𝑑𝑠 = 𝐼𝑚(cos(𝜔𝑒𝑡 − ∅) + 𝑗 sin(𝜔𝑒𝑡 − ∅)) = 𝑉𝑚𝑒𝑗(𝜔𝑒𝑡−∅)

Here the angle ∅ is the angle between the resultant voltage and resultant current value and

calculated in degrees.

So like previous case, the d-q axis resultant current has a maximum peak value of 𝐼𝑚 and

rotates at an angle 𝜔𝑒 from the d axis. Also like the previous case,

54

Idq = �((ids2) + (iqs

2)) (61)

𝐼𝑑𝑞 = 𝐼𝑚

Irms = 0.707Idq (62)

Thus also for current conversion case, the RMS current can easily be measured from the

instantaneous value of peak value of phase current. As it is considered a balanced system so

if only the two phase current value is given, the 3rd phase current value can easily be

calculated. Also if the line to line current is given as a reference the line current can be

calculated from them and the same approach can be followed to get the d-q stationary axis

current from the a-b-c, three phase current value.

3.7 Power Transformation Equation

Since the peak values remain unchanged from three axis systems to two axis systems, so

only by multiplying the power of the two axis system by 3/2 the actual power of a two axis

system can be calculated. The condition here is that, it is assumed the voltage and current

values in the two axes d-q reference frame is known [60, 86]. In Fig. 21, the resultant

current and resultant voltage vectors of stator side in d-q axis is represented to obtain the

idea of measurement of power delivered by the stator.

So, P = 32

(idsvds + iqsvqs)

Replacing the values of q- and d-axis currents and voltages, we can get the power

expression as,

P = 32

ImVm cos∅ (63)

55

Fig. 21 Voltage and current vector (power representation) with their components on direct

and quadratic axes.

3.8 Equivalent circuit of Induction generator

VoltageStator Voltage

Impedance (Z’) stator current

Fig. 22 Thevenin’s equivalent circuit of an induction generator.

Equivalent circuit representation is important to realize the electrical circuit connection and

diagram for any system. A Thevenin’s equivalent circuit (showed in Fig. 22) can be a

simple representation of an induction generator. Here also an equivalent representation is

made for both squirrel cage induction generator and wound rotor induction generator. From

the grid point of view the induction generator is seen as a voltage source where VS is the

56

voltage and current IS flows through the impedance Z. For a squirrel cage induction

generator, the rotor is short circuited and the stator is connected to the grid. So the

equivalent circuit is represented in Fig. 23 [88].

jω1Lsλjω1Lrλ

jω1Lm

Rs

RmRr/s

Is Ir

+

_

Vs Ir m

Fig .23 Equivalent circuit for squirrel cage induction generator.

For the wound rotor induction generator (equivalent circuit is represented in Fig. 24), the

rotor is not short circuited, instead it contributes to the power production. So the rotor also

has a voltage source here. It shows both stator and rotor circuit together where the mutual

resistance and inductance are also represented. Here a Y-connected DFIG is represented in

the equivalent circuit diagram (Fig. 24). In the equivalent circuit, Vs is the stator phase

voltage applied, Is is the stator current, Iris the rotor current, Rs is the stator resistance, Rr is

the rotor resistance, Lsλ is the stator leakage inductance, Lrλ is the rotor leakage

inductance, Rm is the mutual or magnetizing resistance, Lm is the magnetizing inductance,

ω1 is the stator angular frequency and s is the slip.

jω1Lsλjω1Lrλ

jω1Lm

Rs

Rm

Is Ir

+

_

Vs

+

_

Vr/SIr m

Fig. 24 Equivalent circuit for wound rotor induction generator or DFIG.

57

The relative speed between the synchronous speed and rotor speed is described as slip.

s = (ωe-ωr)/ωe So slip represents the relative speed of the rotor compared to the

synchronous speed of the generator. Usually the synchronous speed of any system is fixed

and dependent upon the system frequency and number of poles, Ns = 120f/P .

When the rotor is not short circuited (in terms of wound rotor induction generator), the

rotation of rotor also affects the stator circuit. But this phenomenon does not directly affect

the resistance or inductance value. Rather it affects the relative current and voltage value.

For simplicity or convenience it is advantageous to refer all the quantities either to the

stator or to the rotor side. Now for the resistances and inductances multiplying by the turn

ratio is enough to convert it from rotor to stator side or vice versa. But for voltage and

current values it is necessary to multiply the rotor values by the slip amount and then we

will get the relative current or voltage value of the rotor circuit in terms of the stator side. It

is because the amount of power production is only the slip times of actual power for the

rotor circuit to handle. [89].

Table.6 Relationship of slip and operating mode and indication of Mechanical, stator

and rotor power for sub and super synchronous speed zone.

Slip Operating mode Mechanical

power

Stator Power Rotor Power

0< <1 (Sub-

synchronous)

motor <0 <0 >0

generator >0 >0 <0

<0 (Super-

synchronous)

motor <0 <0 <0

generator >0 >0 >0

So for a double fed induction generator the bidirectional power electronics converter of

partial rating is used which connects the rotor circuit to the grid [90]. For a super

synchronous speed operation, the rotor speed is greater than the synchronous speed

(𝜔𝑟>𝜔𝑒) so the slip becomes negative (s<0). So in this case if both rotor and stator power

production is positive (here positive means towards the grid) the system will operate as

58

generator. But on the other hand if both stator and rotor are receiving power from the grid

(power production is negative) then the system works as a motor.

For sub synchronous speed where the rotor speed is less than the synchronous speed

(ωr < ωe) the slip becomes positive (s>0). In this condition if the stator is producing

power (i.e. the stator power is positive) the system will operate in generator mode

regardless the sign of rotor power. Similarly, if the stator is absorbing power from the grid

(power production is negative), the system will operate in a motor mode regardless of the

power production sign of the rotor. Table. 6 is used here to simplify this analogy.

As mentioned earlier the rotor side only handles a partial amount of power produced by the

stator, usually the slip times. So the net power or total power for this kind of system

depends on both stator and rotor power. In the table it is represented clearly.

𝑃𝑟𝑜𝑡𝑜𝑟= - s𝑃𝑠𝑡𝑎𝑡𝑜𝑟 (64)

Protor = Pgrid/(1-s) (65)

The total mechanical power can be represented as,

Pmech = Protor�1-s�s

= Protor+Pstator (66)

3.9 d-q axes Induction Generator Model

Induction machine modelling has been described in different ways in the literature [70, 85,

91-93]. There are lots of different approaches but the most common and recommended

approach is the “Park Model”[94, 95]. Thus the “Park model” which is a two axis model or

d-q representation has been selected here to model both DFIG and SCIG. Also the order of

the model varies depending on the various approaches. Some researchers have taken the 3rd

order [15] model as their considered one while others have chosen the 5th order model. Due

to the increased number of order, a 5thorder [14] model is a more detail representation for

59

the induction generator modelling. It is recommended as the most appropriate model. Thus,

in this thesis a fifth order Park model is simulated here. All the parameters used for the

simulation of this thesis are mentioned in the appendix A3. Transformation from a real

static a-b-c axis to an imaginary but rotating d-q axis makes it easier to model induction

generator in simulation works. Depending upon the speed of rotation of the d-q reference

frame it can be differentiated into three categories [63]. These reference frames also vary as

researchers have considered each one based on their own advantages and requirements.

Synchronously rotating reference frame selection is appropriate here and selected for the

design purpose for this research because the system considered is not stationary. Thus, it

becomes easier for us to define various rotating parameters. The rotor reference frame has

not been selected as all the parameters are referred to the stator side not to the rotor side.

The generator convention of sign has been implied for the equations, which means while

fed into the grid the real or reactive power has a positive sign. In Fig. 26 the phasor diagram

is represented, where F denotes the vector for different variables of the system (voltage,

current or flux linkage.). This is the vector representation of all the variables in one

reference frame (here synchronously rotating reference frame). The d-axis is the real axis

and q-axis is the imaginary axis. The angles are calculated from the d-axis for different

parameters. Also it can be noted that the rotation of this reference frame is counter

clockwise and the q-axis quantity always leads d-axis quantity by 90 degrees.

GEAR BOX

DFIG

Turbine Rotor

RSC(AC/DC)

GSC(DC/AC)

Grid

CONTROL

PITCH ANGLE

CONTROL Vr Vgc

Fig. 25 d-q model of DFIG system in block representation.

60

d-axis

Stator α-axis

Stator β-axis

Rotor α-axis

Rotor β-axis

Source Voltage

vector, Vs

Flux Linkage

vector, ψs

Variable vector, F

ωs

ωrθr

θs

Fig.26 Vector diagram for DFIG in d-q reference frame (synchronously rotating).

The generator voltage, flux linkage and current equations in an arbitrary reference frame

can be stated as below and can be found in the following references. The voltage equations

in d-q reference frame can be written as [2, 63, 91, 96],

vqs = 1ωb

ddtψqs + ω

ωbψds-

rsxls

(ψmq-ψqs) (67)

vds = 1ωb

ddtψds-

ωωbψqs-

rsxls

(ψmd-ψds) (68)

vqr = 1ωb

ddtψqr + ω-ωr

ωbψdr-

rrxlr

(ψmq-ψqr) (69)

vdr = 1ωb

ddtψdr-

ω-ωrωb

ψqr-rrxlr

(ψmd-ψdr) (70)

The mutual flux linkage equations are,

ψmq = xm(iqs + iqr) (71)

ψmd = xm(ids + idr) (72)

From equations 1-4 and 5, the current equations can be derived as,

iqs = 1xls

(ψqs-ψmq) (73)

ids = 1xls

(ψds-ψmd) (74)

iqr = 1xlr

(ψqs-ψmq) (75)

idr = 1xlr

(ψdr-ψmd) (76)

The flux linkage equation thus becomes,

61

ψqs = xmiqr + xsiqs

ψds = xmidr + xsids (77)

ψqr = xmiqs + xriqr

ψdr = xmids + xridr

The electrical torque equation can be written as (following the generator sign convention)

Te = -polepair*(ψds*iqs-ψqs*ids) (78)

The rotational speed of the generator can be calculated by the following equation which is

known as swing equation.

ωr = ωb/2H*(∫(Te-Tm)dt) (79)

The active and reactive power for both stator and rotor can be calculated by following

equations,

Ps = vdsids + vqsiqs

Qs = vqsids-vdsiqs (80)

Pr = vdridr + vqriqr

Qr = vqridr-vdriqr

vqs, vds, vqr, vdr,ψqs,ψds,ψqr,ψdr, iqs, ids, iqr, idr denotes stator and rotor d- and q- axis

voltages, fluxes and currents consecutively. ω,ωr and ωb are the arbitrary, rotor and base

rotational speed. r and xl denotes the resistance and leakage reactance while subscript s or r

denotes the stator or rotor quantities. Mutual inductances (both in q- and d-axis) are

represented by xm. Now as Stator Flux Orientation (SFO) is utilized here to facilitate the

vector control design for the DFIG, so the q-axis flux linkage vector is oriented along the q-

axis of synchronously rotating reference frame (Fig. 26), thus ψqs = 0 and ψds =

62

ψs (total stator flux linkage) [9]. The stator current both in q- and d-axis can be rewritten

as,

iqs = - xmxs

iqr (81)

ids = ψsxs

- xmxs

idr (82)

Stator resistance is assumed to be negligible thus having a very small effect on the stator

voltages. Thus in steady state, the stator winding voltages can be simplified as𝑣𝑞𝑠 = 𝑣𝑠

(total stator voltage) and 𝑣𝑑𝑠 = 0 (This also implies the Stator Voltage Orientation (SVO)

vector representation). Substituting these current expressions, simplified electric torque,

stator active and reactive power equations can be derived as follows,

Te = xmxsψsiqr (83)

Ps = - xmxs

vsiqr (84)

Qs = Vsψsxs

- xmxs

vsidr (85)

Thus SFO vector control of the DFIG is achieved. The equation flow block diagram of the

DFIG system along with the aerodynamic wind turbine model and the converter set is

shown in a figure later.

3.9.1 DFIG with Partial Scale Power Electronic Converter

In this system type the wound rotor induction generator is used as the generator. The stator

is directly connected to the grid model or via a transformer. There is an AC-DC-AC

converter connected in the rotor side of the generator. It is connected to the grid through a

DC link voltage and is bidirectional. That means the power can flow both ways into the

generator or away to the grid. Thus the rotor circuit is also participating in the power

production of the system. A block diagram of the whole DFIG system is shown in Fig. 27

where both fixed and variable wind speed in the same block will be different for fixed and

variable speed DFIG system. The aerodynamic power block diagram takes input wind and

63

converts the mechanical power from it. This further is considered as the input to the system.

Maximum power point tracking (MPPT) is considered for the mechanical power production

based on the wind speed [97]. The power electronics converter used in this scheme is of

partial rating (usually 30% of full power) [1, 60]. It also can supply reactive power to the

system.

Aerodynamic Power

Calculation Block

Wound Rotor Induction Generator

Block

Rotor Side Controller

Block

Grid Side Controller

Block

DC link Capacit

or

Grid Connection and

Transmission Line Block

Fixed Wind Speed

Power Electronics Converter of partial rating

Variable Wind Speed

or

Fig. 27 Block diagram of a fixed or variable speed DFIG with partial power electronics

converter.

To model the variable wind speed, a signal builder block from Simulink library has been

chosen according to the reference. The output of the block is now variable wind speed and

further fed into aerodynamic block of the system. It is important to ensure that the control

system will work with this kind of variable input to visualize the real time scenario.

3.9.2 SCIG with full scale power electronics converter

For a SCIG system, the rotor of the generator is short circuited. Thus only the stator is

contributing to the power production of the system. Here the power electronics converter is

connected in between the grid and stator circuit. So in this case the full scale power

electronics converter system is used. A block representation for both the fixed wind speed

and variable wind speed system is shown in the Fig. 28, where the wind speed can be

selected as the input of the SCIG system. Wind power is given as the input to the system

through the aerodynamic power calculation block [3].

64

Aerodynamic Power

Calculation Block

Squirrel Cage Induction Generator

Block

Rotor Side Controller

Block

Grid Side Controller

Block

DC link Capacit

or

Grid Connection and

Transmission Line Block

Variable Wind Speed

Power Electronics Converter of Full rating

Reactive power source

(capacitor bank)

Fixed Wind Speed

or

Fig. 28 Block diagram of a fixed or variable speed SCIG with full rating power electronics

converter.

3.10 Two Mass Model for the Gearbox System

The gear box is an essential part of a wind power generation unit as it matches the wind

turbine speed with the generator speed [90]. The gear box can be modelled in many

different ways. Here two mass model is considered (see Fig. 29). It considers the turbine

and generator as separate entities and rotational speed between turbine and generator is

converted. A lumped quantity of turbine inertia JT (Nms2/rad), generator inertia JG

(Nms2/rad), turbine friction damping DT (Nms/rad), generator friction damping DG

(Nms/rad) and shift stiffness Ksh (Nm/rad) is recorded. All the parameters are referred to

the turbine side in this model.

Fig. 29 Two mass model representation of a gearbox.

65

The simplified equation of this model can be written as,

TT-Ksh�θT-θG�-DTωT = JTdωTdt

(86)

Ksh�θT-θG�-TG-DGωG = JGdωGdt

(87)

Tsh = Ksh�θT-θG� (88)

Here, TT,TG and Tsh are turbine, generator and shaft torques in Nm, ωG is the generator

angular speed in rad/sec, θT and θG are the angular position of turbine and generator in

radian respectively.

3.11 Aerodynamic Power Calculation (Block Design)

Fig. 30 Schemetic representation of wind turbine control [87].

The kinetic energy of the wind flowing through the rotor turbine blade which is converted

into wind power can be expressed according to reference [87] as,

66

Pwind = 12ρ*A*vwind3 (89)

Where, Pwind is the power possessed in the wind of the swiped area ( 2^R×π ). Extractable

mechanical power from this amount of wind power is defined by the following equation,

Pmech = 12ρ*π*R2*Cp(λ,β)*vwind3 (90)

This mechanical power is dependent upon the power coefficient, Cp. Theoretically

(According to Betz’ law), the maximum value of Cp that can be achieved equals to 16/27 or

0.59. In terms of functionality, Cp is dependent upon tip speed ration ( λ ) and pitch angle (

β ), which can be defined as follows [98],

Cp = 0.73 �151λi

-0.58β-0.002β2.14-13.2� *exp (-18.4/λ) (91)

λi = 11

λ-0.02β-0.003β3+1

(92)

Lambda ( λ ) is Tip Speed Ratio where the denominator is the wind speed and numerator is

the blade tip’s circumferential velocity [99].

𝜆 = 𝜔𝑟∗𝑅

𝑣 (93)

In this thesis, the nominal value of λ and maximum value of Cp is recorded as 6.9 and

0.4412 pu.

These values were chosen to find out the maximum power coefficient value for a certain

nominal tip speed ratio value. As the nonlinear curve of power coefficient is taken from

reference [63] by observing the power coefficient versus. tip speed ratio curve, it is found

that for λ = 0.4412 pu., the maximum power coefficient recorded as 6.9 pu. Finally the

mechanical torque can be written as [7],

Tm = 12*λ

(ρ*π*R3*vwind2 *Cp(λ,β)) (94)

By choosing the nominal value of λ in an optimal point the desired maximum Cp value can

be obtained for a defined pitch angle [60]. It is necessary to control rotor speed in different

wind speeds to maximize the output mechanical power from the rotor. Rotor pitch angle

control comes into action in this point, where it maximizes the output power when the wind

speed is below the nominal wind speed range (low wind speed) and it controls or optimizes

67

the output mechanical power to a certain value when the wind speed exceeds the nominal

wind speed (high wind speed). With the change of wind speed, the frequency of the

converter also changes. This is to keep the system frequency in a fixed quantity throughout

the whole simulation period. The system frequency is taken as 50 Hz. While the system,

synchronous speed changes, and the frequency of the system also changes. It has been

shown in the figure for slip. As slip changes from super synchronous region to sub

synchronous region. But the control system of the converter keeps the system frequency

constant when the system reaches the steady state level. After reaching the steady state

level, the slip continues to carry a fixed value and hence the frequency of the system

stabilizes and other system parameters (like active power, rotational speed, torque etc.)

show steady results.

3.12 Control System Block Design

3.12.1 Pitch Angle Controller

A generic way of control is selected to design the pitch control system where the rotational

speed feedback is used to control the pitch angle. The power speed characteristics curve is

used to follow the maximum power production so the pitch angle is kept at zero up to a

certain point. This point is defined as the maximum output power point and beyond this

point the pitch angle changes proportionally with the deviation of speed change. At pitch

angle value “zero” the tip-speed ratio gives the maximum value of power coefficient Cp, on

which the maximum power production from the wind turbine is dependent. The block

diagram of pitch angle controller including pitch gain and rate limiter is drawn in Fig. 31.

PITCH ANGLE CONTROLLER

(PI TYPE)+ -

PITCH GAIN

RATE LIMITER

Pitch angle max

Pitch angle minRotational speed

Speed fo Max Power

In1

In2

Out1

Fig. 31 Pitch Angle Controller (block diagram).

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3.12.2 Rotor Side Controller

Rotor Side Controller (RSC) is supposed to control both the real and reactive power (and

voltage) of the generator. A power-speed characteristics curve is designed to optimize the

power output at different rotational speed for different wind speeds [100]. This optimum

power is taken as the reference and compared with the measured electrical output power.

Fig. 32 shows the block diagram of the control scheme for RSC controller. After

comparison, by using a controller, this will give the output of quadrature axis reference

rotor current( iqr_ref).On the other side, the measured output voltage or reactive power is

compared with the reference values (which we provide as input) and ended up with

providing direct axis rotor current ( idr_ref ) after going through the fuzzy logic and PI

controller. Both ( iqr_ref) and ( idr_ref)will be entered into the current controller (PI) to

produce the ultimate q-axis and d-axis rotor voltage signals (vqr and vqr , accordingly).

vr(having two components, vqr and vdr) will be the rotor side controller voltage output

signal which will feed back to the generator. As the active power and reactive power

controlling is done separately. Thus it achieves the de-couple control capability of DFIG

[1].

Reactive Power,

Q regulator

Active Power, P regulator

In1

In2

Out1

Out2

RotorCurrent

Regulator

Out1Out3

Idq_r

Idq_s

Iαβ_r

Iαβ_s

Idr_ref

Iqr_ref

Idqr_ref Vdqr_ref

Vd_r

Vq_r

Dq to αβ transformation

Fig. 32 Rotor Side Controller (RSC) block diagram.

3.12.3 Grid Side Controller

The grid side converter performs its work to control the DC link voltage in a constant

value. Fig. 33 shows the block diagram of the grid side controller scheme [1]. From the

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power available in the DC link capacitor (Pgrid-Protor) and by using the capacitor value, the

DC voltage is calculated. In the GSC, the calculated DC voltage value is compared with the

constant given DC voltage value and regulation is done using a fuzzy-PI controller. The

output here is the grid side converter d-axis current(idg_ref). As per design the grid side

converter q-axis current(iqg_ref) is assumed as zero (means no reactive power transfer via

the grid side converter). Both of these currents are used as an input in the grid side current

controller to provide the output as the grid side converter voltage (vd_gridand vq_grid)

signals. vgrid(having two components, vd_gridand vq_grid) will be the grid side converter

controller signal. Another option of GSC control is to provide or absorbing reactive power

to or from the grid. This can be accomplished by changing the q-axis current of grid side

controller accordingly.

÷⊗

C1

S1+In1

In2

In3

In4

Out1

Out2

Vdc_ref

PGSCVdc

Idg_ref

Iqg_ref

Vd_grid

Vq_grid

DC Voltage

Regulator

Grid Current

Regulator

PRSC

-

Fig. 33 Grid Side Controller (GSC) block diagram.

3.13 Grid System Modelling

In this section, a grid system is modeled to get the idea of a simple grid system with a

transmission line model [101]. So the transmission line model is included in grid system

model and will not be discussed separately. The grid model simulated here is the simple

model which contains a generation unit, transmission line, low voltage to high voltage

transformer and a load. The idea of grid modeling recorded as per the Matlab/Simulink

model of wind power system and its Simulink block diagram is shown in Fig. 34. A voltage

source of three phases is considered as the grid source of a constant voltage. Here 25kV

voltage source with 50Hz frequency is selected as the constant voltage source. A three

phase mutual impedance block for coupling requirement is added with the voltage source.

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In this block the positive and zero sequence resistances and inductances are defined for

mutual impedances. A common three phase bus bar is defined for the system. This bus bar

has a constant voltage level of 25 kV. Along with a transmission line has been modeled of a

10 km line. The Pi model is adopted for the modelling of the transmission line. Usually in

the network the resistances and inductances are distributed throughout the whole

transmission line. But for convenience it is considered that the resistances and inductances

are lumped together in one part. The shunt capacitors are assumed to be connected to both

ends from line to ground. This is followed for all three phases. This method assumes the

system has balance voltage that means the three phases are having balanced supply flowing

through the transmission line. Line parameters R, L and C are specified as both zero and

positive sequence parameters that take into account the inductive and capacitive coupling

between the three phase conductors as well as ground parameters.

Fig. 34 Grid model used in this research created in Simulink environment (Adopted from

the Matlab model).

If we consider,

The positive and zero sequence resistance are r1 and r0 in per unit length (ohm/Km)

The positive and zero sequence inductance are l1 and l0 in per unit length (ohm/Km)

The positive and zero sequence capacitance are c1 and c0 in per unit length (ohm/Km)

Frequency is f (Hz)

Line section length is lsec (Km)

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Then, the total positive and zero sequence RLC parameters including hyperbolic

corrections are first evaluated:

R1=r1.lsec.kr1

L1=l1.lsec.kl1

C1=c1. lsec.kc1

R0=r0. lsec.kr0

L0=l0, lsec.klo

C0=c0. lsec.kc0

Here kr1, kl1, kc1, kr0, kl0, kc0 are defined as the hyperbolic correction factors. To get the

actual line representation, for the long line (>50km) it is required to take these hyperbolic

parameters into account. But here in this model the line length is considered of only 10km.

So in this case it is actually a short transmission line. Thus it is considered the hyperbolic

parameters as equal to unity.

The RLC line sector parameter then can be computed as following,

𝑅𝑠 = (2𝑅𝑙 + 𝑅0)/3

𝐿𝑠 = (2𝐿𝑙 + 𝐿0)

𝑅𝑚 = (𝑅0 − 𝑅𝑙)/3

𝐿𝑚 = (𝐿0 − 𝐿𝑙)/3

𝐶𝑝 = 𝐶𝑙

𝐶𝑔 = 3𝐶𝑙𝐶0/(𝐶𝑙 − 𝐶0)

These parameters are given as input to model the transmission line model for the grid

system.

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Fig. 35 Transmission line π- model used for transmission line block design.

After the transmission line model a transformer is added to the system. This transformer is

a step up transformer seeing from the generator end. It can step up the voltage level of the

wind power generation plant from 660V to 25 kV to match the transmission line voltage

level. The lower voltage side is connected in delta connection and the higher voltage side is

connected by a Wye (Y) connection. The winding parameters like resistance, inductances

for both high and lower voltage side, turn ratio and frequency, etc., are defined in the

Simulink block to model this transformer. After this transformer a load of three phases is

connected in parallel with the transmission line. The nominal phase voltage is defined as

the voltage of the transformer’s lower voltage. The load is required to consume the

produced electricity from the wind power generation unit. Here the load is designed as 660

kW. This load is the last block for the grid system. After that a common bus bar is placed

which will have the voltage level of 660 V. The three phase voltage output from the wind

power generation unit will be connected to this common bus bar where the total grid system

is also connected. So, to the left of this bus bar the model is a grid model and to the right of

this bus bar a wind power generation unit model [102]. A three phase fault block can be

added to locate faults that may occur in the grid or transmission line. The block can be

defined for different types of fault in various conditions. In this research the ideal fault

block has been used to compare different responses of the system with the PI controllers

and with the Fuzzy-PI controllers.

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Chapter Four

Control of Induction Generator

4.1 Control Aspects

The classical power systems are equipped with large power generation plants located at

remote and regional places of a certain grid. Those generation plants produce most of the

power which is then transferred to the national grid. The national power grid line is built to

cover the whole geographical location around any country or a large portion of the country.

The central control and monitoring system is installed and placed to control the power in

the grid [103]. The grid lines are basically the transmission lines of electricity. In a certain

region, a distribution generation unit and step down transformer unit is placed which takes

power from the national grid line and supply to the utility services of a lower voltage rating.

This traditional system has a constant pattern of production as in most of these systems

fossil fuel is used to rotate the turbine for electricity generation. Thus a central control and

monitoring system is well established for these types of grid lines. As the amount of

renewable energy share is increasing day by day, so the traditional grid line needs to be

upgraded. Due to many reasons the increment of renewable power share in the electricity

generation market eventually will change the grid codes. Wind is one of the main sources

of renewable energy. Due to the availability of wind in nature, it seems to be a lucrative

solution for clean energy and can be considered as the answer of the future energy crisis.

But, due to the uncertainty and uncontrollable nature of wind, any power grid with only

wind power generation units cannot be a feasible and stable option. Along with the fixed

base load demand the seasonal peak load demand added on top of it. Peak load demands

generally occur on a certain period of day or in a certain time of a year. Due to these

criteria, the control system is an essential part of the wind power generation unit. The

control system is required to determine, control and monitor the power production to a

rated level based on requirement [100]. Also it will protect the generator, rotor, turbine and

drive train from sudden changes in the system.

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In the early age of wind power generation, the ratings of wind turbines were very low and

the generator used was mostly squirrel cage induction generator. Thus the variation of the

wind was transferred directly to the grid. For high wind speed, the power production could

increase above the rated level which resulted in a compulsory shut down of the wind

turbine. When the wind speed became normal again the wind turbine started from the

beginning. The control system was basically the mechanical control to turbine rotor and

some elementary electrical control of the wind generator. Those types of generators could

not contribute too much to the grid control system rather created problems in terms of

sound operation. But as wind turbines have increased both in number and capacity, the

control system needs to be improved and modified as the wind turbines contribute as an

active part to the grid. More control on the active and reactive power, voltage, frequency,

phase, etc. has been achieved so that a wind power plant can be considered similar to the

other power plants from the grid point of view. Another important aspect of control is to

maximize the power production by exploiting variable wind speed generators. To maintain

the rated output power in variable wind speed, it requires complex control technology to be

installed in a wind turbine. Previously when a fault was found the turbines were

disconnected and the operation of the wind generation system was disrupted. To overcome

this problem fault ride through technology has been improved and a modern wind turbine

nowadays is not disconnected from the grid in case of a fault. So it can be said that the

control technology is the brain of a wind power generation system and a truly essential part

of the system [104].

4.2 Controllable System Quantities

There are several controllable quantities in a wind generation system. In general there are

some parameters which might be important to observe and can give a clear indication of the

perfect operation of the system. A continuous and close observation of those quantity

responses can give an indication whether the wind generation system is operating smoothly

or not. Among these quantities, active power, reactive power of the grid, voltage level,

current level of the grid, frequency, phase angle etc. are considered as primary indicators.

There are also some other parameters on turbine rotor and wind generator parts which are

75

also very important. From the turbine rotor part; tip speed ratio, angle of attack, power

coefficient, mechanical torque, rotational speed of turbine, etc. and form the generator part;

stator and rotor voltage, current, fluxes and electromagnetic torque are all important. This

thesis will focus on the analysis of these indicative quantities, which will be called

‘significant system quantities’.

4.3 Power Electronics for Control

Power electronics equipment is generally used to modify a form of electrical energy (for

example; change the voltage level or current or frequency) [105]. Compared with

“Classical” electronics equipment, which is used to carry only information, the power

electronics equipment carries power. Though at the very early stage, the power electronics

equipment were made up from “Mercury arc”, but nowadays semiconductor switching

devices like diodes, thyristors, and transistors are used as power electronics devices. It is an

essential part of any control application. The major criteria and advantages for using power

electronics might be;

• It is a rapidly developing technology with regular improvements in this sector.

• The modern power electronics components can handle higher current and voltage

ratings.

• The power losses in the switching activity in the power electronic device are being

reduced as power electronics become more efficient.

• The control technologies of the power electronics equipment are simple and power

amplification in large scale is possible.

• The price and power ratio is also coming down rapidly and makes it more attractive

in wind power application.

Due to the continuous improvement and research on semiconductor devices and

microprocessor units, more efficient models or versions of power electronics equipment are

coming to the market. From the power equation (P=V*I), the instantaneous dissipation of

power of a device depends on the voltage across the device and current flowing through it.

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For power electronics too the instantaneous power would be this much. From this

calculation, an indication of losses can be found. As we want to keep the power loss or

power dissipation as low as possible, so the device is operated mostly around “On-Stage”

when the voltage across it is zero or “Off-Stage” when the current flowing through it is

zero. By this arrangement the power dissipation can be limited to a minimum. A typical

power electronics system consist a source connected to the input, a load connected to the

output and a control unit.

Fig. 36 Typical Power Electronics Converter connected to the wind generation system

[104].

In terms of wind energy conversion system, the power electronics converter is connected

between the generator/load and the grid with bidirectional power flow capabilities.

Continuous advantages can be achieved through using a power electronics semiconductor

built control unit as the price per kW is decreasing and efficiency over power handling

capacity is increasing [104]. In the wind energy application area the most commonly used

power electronics are; Diode Bridge, SCR Inverter, SCR rectifier, Diode Bridge/Hard

Switching Inverter, DC boost/bulk inverter, Back to Back Inverter and Matrix Converter.

Based on the generators (SCIG, PMSG, DFIG etc.) and different output requirements,

different power electronic devices are used. This simulation model is designed to use IGBT

based power electronic converters in the system.

77

4.4 Full Scale Converter and Partial Scale Converter

The power electronic converter is connected between the generator/load and the grid. Based

on the requirement it can be positioned in such a way where it can have full power flowing

through it to and from the grid [104]. This type of setup is called a full scale converter

setup. The full scale converter is the ultimate solution for utilizing the maximum of variable

wind as it can operate at a good percentage (around 30%) of the speed above and below the

synchronous speed level. As the asynchronous speed generators are the most suitable

choice, so they usually operate above or below the synchronous speed level. In terms of sub

synchronous speed level, both stator and rotor will operate in power conversion (to and

from the grid). A full scale converter system can significantly improve technical

performance but the problem is the power losses increase proportionally and this adds extra

cost for converter rating.

Fig. 37 Full scale converter connected to a variable speed wind power generation system.

Fig. 38 partial scale converter connected to a variable speed wind power generation system.

A partial scale converter is placed in such a position or in such a setup where the partial

power to and from the grid will pass through it. It also can operate below and above the

synchronous speed level but with less range. The partial scale converters only need partial

78

rating power electronics equipment with a lower cost compared with full scale converters.

Also the relative power production compared to the full scale converter equipment is

reasonable. So the technical difficulties are greatly reduced.

4.5 Power losses

When taking into account the total loss of a wind power generation system there are couple

of subsystems which are responsible for power losses [106].

Total system loss can be summed up in general as,

Ploss = Ploss,gen + Ploss,gear + Ploss,rsc + Ploss,gsc (95)

Where,

Ploss,gen is equal to the loss in the generator. It depends on the type, size and rating of

generator.

Ploss,gear is the loss which occurs in the gear box where wind power is transformed into

mechanical power.

Ploss,rsc is the loss in the rotor side converter as power flows through it.

Ploss,gsc is the loss in the grid side converter as it is connected between the grid and the

system.

Also there are losses in the slip rings and friction losses. After connecting the wind turbine

to the grid line there are some losses in the transmission line. In this research a common

and accumulated loss is taken into consideration and it is subtracted as a single quantity

from the power production. Also some losses, like friction loss are not taken into account.

The average value of total wind power can be found by integrating the wind power for a

particular wind speed with respect to the wind speed distribution function (normally

Rayleigh distribution) from zero wind speed to infinite wind speeds.

79

4.6 Vector Control Approach

Vector control approach facilitates a better and easier modelling approach of the control

system for the wind power plants. As the generator is associated with the moving parts so

to design the machine parameters, vector control approach is more beneficial than scalar

control [107]. It treats the flux, voltage or current parameter of either stator or rotor as a

vector quantity which helps to design the controller. Using the vector control approach to

control the generator parameters like the rotor current, the reference frame has to be aligned

with a flux linkage. It might be either aligned with the stator flux linkage (thus stator flux

orientation) or the air gap flux linkage [108]. The resistance value of the stator can be

considered very small which means stator flux orientation can also be oriented with stator

voltage.

4.6.1 Stator Flux Orientation

The stator flux orientation can be defined as the orientation where the whole stator flux

vector is aligned with the real axis of the rotating reference frame, that means (𝜓𝑠) is

aligned with the d-axis of the rotation and there is no component along the q-axis of the

rotation [109]. In this orientation system the grid voltage is at an angular distance with the

q-axis of the rotation. That angle is the angle between the stator flux and the grid flux

vector. By measuring the stator and rotor current quantity along with the rotor position, this

angle can easily be calculated.

4.6.2 Stator Voltage Orientation

In the case of stator voltage orientation (which is sometimes referred as grid flux

orientation), the stator flux vector is at an angle different to the real axis of the rotating

reference frame [109]. Thus the stator voltage vector of the system is aligned totally with

the imaginary axis of the rotating reference frame. That means there is no component of

stator voltage along the d-axis but the total component of the stator voltage is aligned with

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the q-axis. If it is referred to as a grid flux orientation, it can be said that the grid flux is

aligned totally with the real or d axis or rotating reference frame. If we consider the stator

resistance to be negligible (as it is very small), so the angle between the stator flux and the

grid flux vector become insignificant (almost zero). Under this circumstances both stator

flux orientation and stator voltage orientation becomes same.

4.7 Different Parts of a Conventional PI Control System

Initially the controller blocks with conventional PI controller are described with the aid of a

block diagram. Later the proposed and used fuzzy-PI controllers are described with an

updated control system block diagram.

4.7.1 Rotor Side Converter Control

The rotor side converter is mainly responsible for the active and reactive power control of a

wind power generation unit. A decouple control of the active and reactive power control is

possible as the d-axis and q-axis current component is bisected and controlled separately.

RSC also has the inner current control loop in which the rotor side current is compared with

the rotor side reference current and the output is the rotor side reference voltage [16, 91,

92]. Another controllable parameter or control block is the speed controller. As this block

experiences the mechanical quantity so the time response is slow for the speed controller as

the mechanical time constant is high compare to the electrical time constant. In the speed

controller the rotational speed of the system is calculated compared to the output power

generation of the system. A power tracking system called as MPPT power tracking

algorithm is utilized here for calculating the rotation speed of the system for each power

output at different wind speeds. The output of this controller is the power reference which

will feed to the active power controller for more control work. All the controllers are

described here under RSC control below.

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4.7.1.1 Active and Reactive Power Controller

In a conventional power generation unit active power is considered to be of more

significance where the reactive power control does not take much attention. Due to the

characteristics of wind power generation system, the active power and the reactive power

are given equal priority. As in the conventional power generation systems, the reactive

power is supplied by the grid and handled separately. But in wind power generation

systems, the power electronics converter is capable of supplying the reactive power to the

system as well. Thus the wind power generation system and the power electronics converter

can contribute to the voltage control of the grid in case of voltage sag or other fault.

Previously wind power generators were disconnected from the system during fault and

connected again when the fault is cleared. But now the modern wind turbines with reactive

power control capability can adequately contribute when fault occur as well as normal

operating condition. To excite the rotor for induction generators in wind energy system it is

required to supply some reactive power. A system connected to the grid can draw reactive

power from the grid but an isolated system requires large capacitor banks connected to the

system to supply the reactive power. The power electronics converter connected via a DC

link capacitor can produce enough excitation for the rotor thus eliminating the requirement

of extra capacitor banks to be connected to the system.

The traditional active power control block with PI controller is described here. For active

power control, it can be written as per generator modelling equations, the stator active and

reactive power is,

Ps = Vsqisq (96)

Qs = Vsqisd (97)

In the same way the rotor active power Pr and reactive power Qr can be expressed as,

Pr = Vrqirq + Vrdird (98)

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Qr = Vrqirq-Vrdird (99)

The RSC or rotor side converter is actually a voltage source converter model. Here the

switching dynamics on the power electronics are neglected. Also the equations indicates

that both active and reactive power control can be done independently as it depends on the

q-axis stator current and d-axis stator current consequtively.

The output of the speed control, stator power referecne Ps_ref is compared with the actual

stator power PS via a PI controller. The output of this controller is the q-axis rotor current

reference Irq_ref. Further this q-axis rotor current reference is compared with the actual q-

axis rotor current in the current control loop [88]. To compensate for the effect of the d-axis

rotro flux density, the decoupling term is added to the output of the current control loop.

This provides the q-axis rotor Voltage Vrq.It is referred in Fig. 39.

Fig. 39 PI active power controller in RSC side.

For the reactive power control loop (referred in Fig. 40), the stator reactive power (which is

usually defined as input to the system based on the requirement) is compared with the

actual q-axis reactive power. Here after PI reactive power controller the output is the d-axis

rotor reference current. This is further compared with the d-axis actual rotor current with a

PI current control loop. The decoupling compensation factor to compensate the q-axis rotor

flux lingake is added with the output of the current control loop and to provide the d-axis

roor reference voltage Vrd. This is the reactive power control controller [110].

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Fig. 40 PI Reactive power controller in RSC Side.

Usually both the active and the reactive power controllers are part of rotor side controller

(RSC). The q-axis and d-axis rotor reference voltages are two different output from active

and reactive power controller and it is independent of each other thus calling as decoupled

control system. Or in other wards, d-axis and q-axis rotor voltage can be decoupled and

achieved as a outcome of two different controller. Both d-axis and q-axis rotor reference

voltages are considered as the rotor voltage input and using the d-q to a-b-c transformation,

three phase rotor voltages can be calculated.

4.7.1.2 Speed Controller

The time response of a speed controller is slower than an active power controller. This is

because the electrical time constant is smaller than the mechanical time constant. As in the

speed controller the mechnical power calculation is involved so it requires more time. Here

the Power-Speed graph is used as the reference from which the reference rotational speed

of the generator is deduced from the stator power. Further this reference rotational speed of

the generator is compared to the actual generator speed and the output signal is fed to a PI

controller (speed controller) to get the stator reference active power value [85]. This stator

reference active power is the input to the active power control loop (block diagram showed

in Fig. 41).

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Fig. 41 PI Speed controller in RSC side.

Fig. 42 MPPT control for power tracking in terms of different wind speed [97].

Stator Power output vs. rotational speed graph is depicted here in Fig. 42. It is called MPPT

(Maximum power Point tracking) algorithm [97]. Based on the wind speed, rotational

speed versus power output graph is drawn first. Here it is shown that as the rotational speed

increases, the power output increases for a certain fixed wind speed. Also in high wind

speed the power output is higher. Now in every power output graph for each wind speed,

the maximum value is taken and a locus is drawn by connecting those maximum points. At

the very low wind speed the output power is kept fixed for a certain rotational speed and

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after that, the maximum power points are followed up to a certain wind speed. The

minimum wind speed up to which the power production is kept in zero level is called the

cut in speed. It is the wind speed from when the turbine starts to produce power output.

Also there is a maximum wind speed considered when the output power reaches to its

maximum value (here 1 pu.). After that wind speed, it is forced to keep the power level

constant whether the wind speed is increasing or remains same. A power vs. rotational

speed curve for different wind speed is shown in Fig. 42, to depict the idea of MPPT

tracking of power at various wind speeds. This wind speed is called the cut off wind speed.

Operating point of the wind power plant follows the locus of this point and hence the

MPPT tracking for rotational speed for maximum power at different wind speed is

achieved. In Matlab and Simulink, a look up table is formed to represent these conditions

for MPPT tracking.

4.7.1.3 Rotor side Current Controller

As previously mentioned, calculating rotor voltages is necessary to keep the switching

frequency constant. It is possible to generate rotor reference voltage from the reference

rotor current. This can be fed to the plant block to get the actual rotor current [106]. It

forms a close loop system where this actual rotor current is compared with the reference

rotor current and gives input to the controller to get the reference rotor voltage. To aid the

simplicity of the calculation of the current controller, eliminating stator current, and

rotor flux linkage 𝜓𝑟 is advantageous.

From the voltage equation of the induction generator,

vs = -rsiR + dψsdt

+ ( rLM

+ jω1)ψs (100)

vr = (rr + rS + jω2Lσ)iR + LσdiRdt

+ E (101)

E = vs-(rsLM

+ jωr)ψs (102)

E is the back EMF. If we decouple the d-axis and q-axis component, and arrange it in terms

of transfer function, the equation of d-axis and q-axis rotor current becomes,

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ddt

idre = 1rr+sσ(Lσ)

v'dre (103)

ddt

iqre = 1rr+sσ(Lσ)

v'qre (104)

Therefore the transfer function becomes,

C(x) = 1rr+sσ(Lσ)

(105)

Kp = αcL�σ (106)

Ki = αc(R�R + R�s + Rα) (107)

Where, αc is the bandwidth of the current dynamics.

So the gain of transfer function becomes,Gcl(p) = pp+αc

Considering this transfer functions the Kp and Ki parameters for the PI controller is selected.

The current controller gives the rotor side reference voltage. This went through the d-q to a-

b-c conversion block to give the reference rotor voltage output in actual three phase system.

4.7.2 Grid Side Converter Control

The prime object of the other converter which is named as the Grid Side Converter is to

control the DC link voltage. Both RSC and GSC are connected via a DC link capacitor

which performs the duty of a storage device and acts as the bridge between the rotor side

converter and grid side converter. In GSC initial controller is the current control block

which response fast and situated at the inner part of system. In the outer part, the slow DC

link voltage control block is operating [3]. Here the SVO or Stator Voltage Orientation is

followed. That means the grid current components are bisected into both q-axis component

and d-axis components. The reference frame of the GSC is aligned with the grid flux

density vector. The q-axis component of the grid side current will control the active power

and d-axis of the current will control the reactive power. This implies that the current

controller will be dealing with the q-axis component of the current and DC link voltage

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controller will consider d-axis current component of grid current. So basically these two

control blocks will be discussed in the GSC or Grid Side Converter part as shown below.

4.7.2.1 Grid Side Current Controller

Similar to rotor side current controller, the grid side current controller also compares the

reference stator current and actual stator current and gives input to the PI type current

controller [23]. The output of this PI controller is the stator reference voltage which will go

through the converter and to the system or plant. The output of the plant is the actual stator

current which was considered first for the comparison with the reference stator current

value to get the input to the controller. Thus it actually forms a closed loop system. For

both the d-axis and q-axis stator current the simplified transfer function gain can be written

as

G� =ddtids

e

(R+Ls) ddtids

e =ddtiqs

e

(R+Ls) ddtiqs

e = 1R+Ls

(108)

This is the gain of the transfer function

As per reference [23],

kp = αcsLkcs

(109)

ki = αcsRkcs

(110)

Here the closed circuit gain parameter is Kcs = M1L2Vtri

In the simulation the rotor resistance and inductance of the grid of line is lumped and

considered as a fixed value. So the current controller is designed for the grid side converter

by taking into account of the Kp and Ki gain and after that it will further give the reference

voltage in the d-axis and q-axis stator reference frame.

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Fig. 43 Current control loop of stator side controller.

4.7.2.2 DC Link Voltage Controller

A DC link capacitor is connected in between the rotor side converter and grid side

converter. A linear system can be simplified by considering both grid side converter power

and rotor side converter power and the capacitance value. It is,

12

CdcdWdt

= PGSC-PRSC (111)

A reference DC voltage is taken and the actual output DC voltage is compared with this and

fed into the DC voltage controller. The proportional and integral gain of this controller can

be written as [85],

Fig. 44 DC link voltage control loop.

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4.7.3 Pitch Angle Control

The stator power is compared to the rated power and the pitch angle reference is given as

output after a PI controller. This reference pitch angle is limited at its rate in terms of Servo

time constant, and implemented into a closed loop feedback system. The pitch angle

maximum and minimum values are limited from 0 degree to 90 degree. This output pitch

angle will control the output stator power as the wind speed varies. Here the rated rotational

speed is considered as constant at 1.21 pu. thus the pitch angle operates when this rotational

speed tends to increase with the wind speed increment. Here thing to be remembered as, for

the turbine mass, inertia and size, the rate of change of pitch angle is slow [89].

Fig. 45 Pitch angle controller.

4.8 Fuzzy Control System

Fuzzy based control system considers linguistic variable command which is similar to

human reasoning. It can handle data which is often uncertain or imprecise and may need

some tolerance. The output of this type of control system can be very satisfactory

depending how well the model is built considering expert experiences. A significant

advantage of fuzzy logic control is that it does not require a detailed mathematical model of

the system which is often very hard to formulate for a complex nonlinear system. Rather an

expert knowledge of the system and input-output nature is the only requirement for this

type of controller. Fuzzy controllers also have the inherent capabilities to deal with

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nonlinear data or where noise maybe incorporated into the input data. Mainly two types of

fuzzy inference system are considered, one of them is the Takagi-Sugeno and the other one

is the Mamdani type fuzzy inference method. The Mamdani type fuzzy inference method is

the most widely used. In this system both the input and output variables need to be fuzzy

set. After the fuzzy inference rule based conditions each fuzzy output are defuzzified by

finding the centroid of a two dimensional aggregate output function. On the other hand, the

main variation for the Takagi-Sugeno fuzzy inference system is, the output membership

functions are either linear or constant.

Fig. 46 is a block diagram of a fuzzy controller based on Mamdani method. The system has

four major parts. For the fuzzification block, fuzzy input signals are taken as the input to

the system. Then fuzzy inference engine and knowledge base condition process these

inputs. At the end a defuzzification block has been used to defuzzify the fuzzy outputs.

Fig. 46 Block diagram of a fuzzy control system

4.9 Implemented Fuzzy-PI Control Structure

The PI controllers are rigid to the sudden change in parameters and do not incorporate the

dynamic behavior of the system quantities very well. As a result often system responses

cannot incorporate proper dynamics when there is a rapid change in the system due to fault

or etc. Thus a modified control system is necessary. Due to this inflexible response of the

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conventional PI controller loop only, a fuzzy–PI control system is proposed and

implemented in this thesis.

Active power, reactive power, DC voltage, current controllers are traditionally designed

using PI control loop which were described previously. For finer tuning of the parameters,

three control loops has been selected, where a fuzzy logic controller has been utilized and

the output of that fuzzy logic controller has been added with the output of the PI

controller’s output. The improvement in system quantity responses is visible compared to

the control loop with PI based controller only. The significant outcome of this practice can

be illustrated in case of fault occurring condition. All the result analysis will be described in

chapter 5. Here fuzzy logic control blocks and associated rule and surface view are

described.

The fuzzy controller used in this thesis aids the traditional PI controller to provide more

reliable output for the RSC. The main operation of RSC is to control the active and reactive

power. So in both active and reactive power loops the fuzzy controller has been used. The

output of the fuzzy controllers are added to the traditional PI controller’s output to get more

precise reference level of quantity for each controllers. In next chapter, the comparisons of

system quantity responses are simulated to authenticate this statement. Fuzzy sets used in

the input and output variable here are NB, N, Z, P and PB, which consecutively represents

linguistic variables negative big, negative, zero, positive and positive big. Membership

functions of the inputs and output has normalized universe of discourse over the time

interval. In the FIS simulation editor, total a 25 of if-then rules are defined for each fuzzy

controller. For an example, in the fuzzy active power controller, if for a time interval, the

error of active power reference and actual active power (diff (P)) and rate of change of this

error (∆diff (P)) both are ‘PB’ (meaning positive big) the output of the fuzzy active power

controller (∆I_qr_ref) is PB or positive big. The linguistic meaning of this rule is when the

reference active power is too high compared to the actual reference power and the rate of

change is also too high, that means the rate of change is also increasing to a high value then

the output q-axis reference current needs to produce a high value of current, so that the

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actual active power increases. This way the entire linguistic variables from an expert

opinion have been incorporated in the fuzzy controller.

For the implementation of a fuzzy logic based controller, an important consideration is the

determination of universes of discourse for input and output variables. Possible minimum

and maximum values of any respective variable needs to be determined within which the

universe of discourse should be constrained. For a Mamdani type fuzzy logic control the

limiting value of the universe of discourse for a variable can be determined by the

following process. One of the inputs to this fuzzy power controller is the error signal,

diff (x) = P_ref (x) – P_actual (x). (112)

So the maximum and minimum value of this error signal can be found like,

diff_max = P_ref_max – P_actual_min (113)

diff_min = P_ref_min – P_actual_max (114)

By the same manner, the rate of change of error, which is the other input to the system is,

∆diff (x) = diff (x) – diff (x-1). So the operating range for the second input can be found by,

∆diff_max = diff_max – diff_min (115)

∆diff_min = diff_min – diff_max (116)

Also the output signal is,

∆I_qr_ref (x) = I_qr_ref (x) – I_qr_ref (x-1). (117)

So the operating range is,

∆I_qr_ref_max = I_qr_ref_max - I_qr_ref_min (118)

∆I_qr_ref_min = I_qr_ref_min - I_qr_ref_max (119)

By observing the respective values of required system quantities from the previous

simulation with conventional PI controllers only, these limiting values have been defined

and used in the fuzzy logic controller. The membership functions were taken as the

trapezoidal and triangular function to get better output and the peak and limiting range for

each linguistic variable are tune by continuous iterative process. This is done manually to

get the fine tuning and get the system response as possible to the optimum.

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In the rotor side controller both active power and reactive power control loops have been

modified by introducing an additional fuzzy logic control block.

Fig. 47 Block diagram of a fuzzy-PI active power controller

Fig. 48 Block diagram of fuzzy-PI reactive power controller

In the block diagram shown above (Fig. 47 and 48), the active and reactive power control

blocks with additional fuzzy logic controller are visible. The inputs to the fuzzy controller

for the active power loop are difference between the reference active power and actual

active power and derivative of this difference. The output here is the q-axis reference rotor

current which has been added with the q-axis reference rotor current from PI controller.

Thus a new modified q-axis reference rotor current is found which has been used as the

actual reference current for other blocks in the system. Same as for reactive power control

loop, two inputs, difference between reference and actual reactive power and derivative of

that quantity has been selected to the fuzzy reactive controller. The output of this fuzzy

controller is the d-axis reference current, which has been added with the d-axis reference

current from the traditional PI controller to get the modified d-axis reference current. This

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modified reference current is considered as the actual reference for the d-axis rotor

reference current and fed to the other subsystems.

For the active power fuzzy controller, the inputs and the output membership functions and

rule based law are listed below,

(a)

(b)

(c)

Fig. 49 Membership functions for the input and output quantities for active power

controller; (a) Error in active power, (b) Rate of change of error in active power, (c) q-

axis rotor reference current

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Table. 7 Rule based law for active power fuzzy controller block

∆I_qr_ref ∆diff(P)

NB N ZE P PB

NB NB NB N N ZE

diff(P) N NB N N ZE P

ZE N N ZE P P

P N ZE P P PB

PB ZE P P PB PB

Fig. 50 Surface view in FIS editor for active power fuzzy controller

For the reactive power fuzzy controller, the inputs and the output membership function and

the rule based laws are listed below,

96

(a)

(b)

(c)

Fig. 51 Membership functions for the input and output quantities for reactive power

controller; (a) Error in reactive power, (b) Rate of change of error in reactive power, (c)

d-axis rotor reference current

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Table. 8 Rule based law used for fuzzy reactive power controller

∆I_dr_ref ∆diff(Q)

NB N ZE P PB

NB NB NB N N ZE

diff(Q) N NB N N ZE P

ZE N N ZE P P

P N ZE P P PB

PB ZE P P PB PB

Fig. 52 Surface view in FIS editor for fuzzy reactive power controller

In the Grid Side controller in addition to the traditional PI controller, a fuzzy controller is

added to get the modified output of the d-axis grid reference current. This modified

reference current is used as the d-axis grid reference current and fed to the grid side current

control loop to get the reference voltage signal. The input of the new fuzzy control block is

the difference between reference DC-link voltage and actual DC-link voltage and the output

of this fuzzy control block is the reference d-axis grid current. The input and output

membership functions and rule based viewer and surface viewer is listed below. For this

DC-link voltage fuzzy controller, only one input variable is chosen, this is the error signal

of DC voltage (Vdc_ref – Vdc_actual) in actual unit (Volt (V)). The output is the d-axis reference

grid current. This output is further added to the traditional PI controller’s output signal to

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get the revised reference current for the system. Three linguistic variables are defined for

the input signal and seven linguistic variables are defined for output variables. The rule

used for this fuzzy controller is illustrated in table. 9. For example, if the input error signal

is positive, then the output d-axis reference signal can be either positive high or moderate or

low.

Fig. 53 Block diagram of DC-Link Voltage fuzzy-PI Control.

(a)

(b)

Fig. 54 Membership functions for the input and output quantities for DC-Link Voltage

Controller; (a) Error in DC Voltage, (b) d-axis reference grid current.

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Table. 9 Rule base law for fuzzy DC-Link Voltage contorller.

∆V_dc POS POS POS OK NEG NEG NEG

I_dg_ref POS_H POS_M POS_L OK NEG_L NEG_M HEG_H

Fig. 55 Surface view in FIS editor for fuzzy DC-link Voltage controller.

4.10 Generic Block Diagram of a Complete Wind Generator System

with Control Unit

Here (in Fig. 56) a generic block diagram of the whole system is depicted which show the

different subsystems and how they interact. It is important to note that, each subsystem is

dependent on the others but modeled individually. The operation and modelling of each

subsystem is equally important. As a whole the total wind energy conversion system stands

as a total system. The controller part takes input from different subsystems like generator

model, aerodynamic model, grid model and gives the control signal output the system. The

aerodynamic subsystem takes wind speed as an input and calculates the mechanical torque

to give as an input to the system. The generator part is modeled based on the mathematical

equation of the wound rotor or squirrel cage induction generator model and generate

electrical power. The grid system model also takes electrical power from the generator sub

system, the voltage and current of the output nodes can be measured from here. For

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convenience, the modelling is done in two axis virtual reference frame as the three phase

machine modelling is mathematically complex so conversion blocks which will convert

parameters from three axes to two axes and vice versa is also another important subsystem.

Overall the control algorithm design is also necessary as the stabilization and accuracy of

the entire model depends on it.

Stator Flux

linkage and

Current equation

Rotor Flux linkage

and Current

equation

Mutual Flux linkage equation

and Electrical torque equation

Swing equation

abc to dq transformation dq to abc

transformation

Va

Vb

Vc

Ia

Ib

Ic

Vds Vqs

Ids

Iqs

IqrIdr

ω

ω

ω

Te

Tm ωr

ωr

ωr

Ψd,qs

Ψd,qrΨd,qm

Ψd,qm

Rotor Side

converterCrotor

Grid Side converter

Cgrid DC Link CapacitorVdc

Vdr

Vqr

Wind Turbine Model

ωr

CONTROL

PITCH ANGLE

VrVgc

Fig. 56 Equation flow diagram of a generic DFIG wind turbine system.

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Chapter Five

Result Analysis and Significant System Quantity Response

Characterization

5.1 Defining Significant System Response

System responses observation is significant for building up the accurate model. It is

necessary to understand the behavior of a system’s internal responses of various quantity

and explain the changes or patterns of different responses for different system inputs or in

different system conditions [111]. If a relationship among the significant system responses

can be established and explained with model characterization, then it will help researchers

to understand system behavior under different conditions. This will make the process

characterization and understanding of the behavior of the system much simpler and easier

to anticipate any changes that may occur. This approach will add an extra advantage in the

actual scenario and will be beneficial for better process implementation and critical

condition handling. The system model is conceived as a whole wind energy conversion

system, where all the important subsystems are considered and modeled individually. The

responses of different significant system characteristics can help us to draw the perfect

working capability of the system in steady state condition. In this model system responses

are defined as:

1. Input system quantity

2. Output system quantity

3. System response quantity

Input system quantities are considered as the inputs given to simulated system. Often these

quantities designate the system nature. For example, wind speed can be considered as the

input system quantity which can be either fixed or variable. Based on these types, the

simulated system can be called as fixed speed wind generator or variable speed wind

generator model. Output system quantities define the performance of the system based on

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certain predefined conditions and specific type of input system quantity designated system.

The output system quantities are dependent on the system configuration and amount of

input system quantity. For example active power can be considered as the output system

quantity which is dependent on the wind speed type (fixed or variable) as well as generator

type (SCIG or DFIG). Observations of output system quantities are important as these are

the ultimate outcomes of the system. Based on these outcomes a simulated system can be

decided as performing up to the task or not. Adjustment on different conditions and various

parameters are often carried out by observing the output system quantities. The system

response quantities are third type of response which is considered as the key system

responses. These quantities are not considered as the output of the simulated system rather

considered as the indicator of the system response. For example, rotational speed is one of

the system response quantities which define at which speed range (sub- or super-

synchronous speed) the system is running. To simulate the model accurately, these

categories of responses are very important to observe. When to achieve a desired output,

any predefined conditions or system parameters are adjusted, observation of system

response quantity can authenticate the adjustment.

5.2 The Impact of Significant Quantity Responses with and without

Controller

As mentioned earlier a complete induction generator model was built in Matlab and

Simulink environment. Simulation is carried out in steady state by considering ideal

conditions. In this section, a DFIG system is modelled and some selective significant

quantity responses are considered (as shown in Fig. 48). An ideal fixed wind speed (14

m/sec.) is given as the input quantity to the system (for simplicity) for demonstrating the

complete controllability of the controllers for DFIG. In one system, all the three major

controllers (RSC, GSC and pitch angle controller) are considered (with controller) and in

another system the GSC is excluded (without controller). The idea behind this exclusion

was to demonstrate system behaviours when rotor circuit side is connected directly to the

grid side without any controller unit. It was considered here only the rotor side controller is

operating and output of the RSC is further converted to AC quantity using a generic

103

Simulink block and connected to the grid. The GSC keeps DC voltage quantity in desired

level to save the system from grid oscillations and harmonics. It was initially assumed that,

other system quantities might be unaffected. But actually the other system quantities along

with DC voltage quantity are affected by this exclusion of GSC from the system. DC

voltage quantity as suspected is not responding to the desired reference level and also

incorporated oscillations. For an ideal condition, both the rotor side converter power and

grid side converter power becomes identical and depends on q-axis rotor current (later

described in this thesis). But here for the system without GSC, this relationship is voided,

thus the absence of the GSC affects the rotor current quantity which in terms affects the

other system response quantity like rotational speed, electromagnetic torque etc. Because of

not having a rotor circuit feedback to the actual power output which is the main feature of

the DFIG system, this arrangement without GSC lacks its characteristics of performing as a

DFIG system. On the other hand, it is not actually a SCIG system as in case of SCIG

arrangement, RSC and GSC is connected in the stator side and rotor side is short circuited.

Fig.57 represents selective system quantity responses for both system arrangements (with

and without the controller). Red dotted graphs are system quantity responses without the

GSC controller and blue solid graphs are system quantity responses with all the controllers.

Rotational speed curves are plotted in Fig. 57b. For the system with all controllers

rotational speed response shows ideal behaviour. It started from a starting value 0.8 pu. and

after the step response time, reaches its stable steady state level of 1.21 pu. These levels are

defined in the speed-power characteristics curve in the simulation model. But for the

system without GSC controller, the maximum level it can reach is around 1 pu. As it is not

a perfect SCIG arrangement, rotational speed never settles in a steady state value rather an

oscillation is occurring. Same as, the torque responses also never gets steady in case of

simulation without GSC. Active power output also reflects similar characteristics for

system without the controller arrangement. The required time for all the system quantities

reach to its steady state level is defined here as the start-up system response time. This is

required in a simulation to let the responses become stable. More analysis on the start-up

transient time and its characteristics will be covered later in this chapter. Obviously this

high frequency oscillation in system responses does not comply with reality but this can

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certainly show the requirement of using a complete set of controllers in the system

simulation.

Fig. 57 Parameter characterization with and without controller.

5.3 Analysis of Significant System Quantity Responses for DFIG (With

Partial Scale Converter)

For a DFIG which utilized a partial scale converter between rotor circuit and grid the

significant system quantity responses are listed in this section. In the first section fixed

wind speed is used as the system input quantity and system output and response quantities

are examined and plotted. In the second section, variable wind speed is selected to

demonstrate the variable speed workability of the DFIG system and same quantities are

105

examined and plotted. The fuzzy-PI controller is used in active power, reactive power and

DC-Link voltage control loops.

5.3.1 Fixed Speed Case

In Fig. 58, eight significant quantity responses are plotted. Here wind speed is the input

system quantity Active power, reactive power and DC link voltage are output system

quantities and rotational speed, electromagnetic torque, mechanical torque and slip are

system response quantities.

Various parameters value or system ideal conditions for model design are taken from the

reference [25] and mentioned in Appendix A3. For DFIG system modelling in this and

other simulation in this research same reference parameters and conditions have been

maintained. Any differences will be mentioned in the discussion. As a fixed wind speed

DFIG model the wind speed is selected as 14 m/sec. It is selected over the speed compared

to the consecutive synchronous speed level. The general idea behind this selection is to

demonstrate the super synchronous speed operation capability of the DFIG system. At the

beginning, the system is at sub synchronous speed level. Later when the system quantity

responses reach its steady state level, the system goes into the super synchronous speed

level. Due to the selection of input wind speed above the base wind speed level, the system

responses continues to stay and operate after reaching its super synchronous speed level

throughout the whole simulation period. It is important to demonstrate DFIG operating both

sub and super synchronous operating range as both stator and rotor participate in power

production in super synchronous speed range. It is reflected in the rotational speed graph,

where the total range of rotational speed is 0.8 pu. to 1.2 pu. This depends on the system

parameters value and defined condition of MPPT operation. Due to the generator

convention which has been used, both electromagnetic and mechanical torques (Both

measured in pu.) are in the negative region. The active power is also positive as per the

expectation. This is just below the one pu. level, mainly due to the losses considered. In the

practical case it might be lower than this level as well. In this system, the reactive power

reference level is given as zero. It has been done as the model was considered as the ideal

one which is not exposed to the fault condition.

106

Fig. 58 DFIG with fixed speed case, (a) wind speed, (b) rotational speed, (c) active power,

(d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) DC-Link Voltage,

(h) slip.

107

It was considered that there is no need for a reactive power transfer from the wind power

system to the grid or vice versa. In the reactive power plot, the simulation shows that the

reactive power maintains its level at zero throughout the whole simulation period. Slip is

plotted next as this gives a clear indication of the operational speed of the generation

system. As it was seen earlier for sub synchronous speed level of operation the slip should

be positive and for the super synchronous speed level of operation the slip should be

negative. The last subplot is the DC link Capacitor voltage. This quantity response can give

a clear idea of the perfect and accurate workability of the control system. This link

capacitor is connected between the rotor side and grid side converter and in the ideal

scenario which has been followed here, it should maintain its reference level to keep both

converters working in balance. This is what happened for the last subplot which shows that

the DC reference voltage is kept at 1200V throughout the whole simulation period. In a

summary, this figure is demonstrating an ideal and perfect working condition of a DFIG

system in fixed wind speed condition.

5.3.2 Variable Speed Case

In a practical scenario the wind speed is variable in its nature. Thus the capability to act

properly in case of variable wind speeds emphasizes the most important attributes for any

DFIG wind turbine. But the problem arises when this variable wind speed is required to be

simulated in a simulation model. Modelling a practical, real time wind profile requires a

complex arrangement of equipment and a large volume of statistical data taken for a long

time throughout the year. For any simulation model it is not possible to generate a proper

variable wind speed model without having a group of statistical data set with all the

atmospheric and metrological information. For this research, the variable wind speed

profile has been followed based on reference [17], where the author has given a wind

profile over the 30 sec of simulation time. That wind profile has been used as the variable

wind speed profile throughout this simulation work. In Fig. 59 six significant output

quantity responses or system quantity responses, which were examined before for constant

wind speed were plotted.

108

Fig. 59 DFIG with variable speed case, (a) wind speed, (b) rotational speed, (c) active

power, (d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) DC-Link

Voltage.

109

The basis was the input system quantity which is the variable wind speed in this case. By

closely observing the system response quantities and system output quantities, it resembles

that simulated model is working perfect for the variable wind speed. Only the mechanical

torque curve is affected by the variability of wind speed. Because the aerodynamic

subsystem is directly having wind speed as input and calculate mechanical torque. Also the

amount of mechanical torque is directly dependent upon the wind speed (which is the cause

of turbine rotation). Thus the mechanical torque curve shows the total variability in its

behavior. For other subplots, the shapes and values match quite perfectly with the outcomes

as anticipated, similar for the constant wind speed figure. By dealing with this type of wind

speed, the designed DFIG system established its effectiveness of working capability for

variable wind speed as well. The energy conversion or the voltage and current conversion

in the converters has not been discussed as it has been assumed those are following normal

procedure. The DC link capacitor has been chosen of 1000 µF and DC link voltage

reference of 1200 V. The waveforms are converter from AC to DC before the DC link

capacitor and again transferred from DC to AC after the DC link capacitor. Due to the ideal

behavior, as there is no energy transfer among the converters and it is a fault free condition,

so the DC link voltage is showing the reference value for the whole simulation period. At

the starting of the each system responses, a quick fluctuation is visible. It is mainly due to

the initial system inertia effect at the starting of the generator. This behavior is more related

to the transient analysis of the system and has not been covered in this thesis. In a future

scope of the extending this work, the transient analysis of this phenomenon can be analyzed

more and compared with a practical small wind generator prototype.

110

5.4 Analysis of Significant System Quantity Responses for SCIG (With

Full Scale Converter)

5.4.1 Fixed speed SCIG The Squirrel Cage Induction Generator has the simplest architecture among the induction

generators. In the SCIG the stator side is directly connected to the grid system and the rotor

side is short circuited. The aerodynamic model is kept the same for this simulation. Five

significant system quantity responses have been plotted these are; rotational speed,

electromagnetic torque, active power, reactive power and slip. Corresponding with the

different wind speeds (both fixed and variable wind speed) other system output quantity

and system response quantity have been simulated and plotted in Fig. 60 and 61. In Fig. 60,

it can be seen that though the initial transition time is very small for this SCIG arrangement,

the system quantity responses shows a different start up transient response compared to the

DFIG operated at a fixed speed. In the fixed speed operation it is seen that the quantity

responses are quite stable after the system reaches stability. Obviously the SCIG cannot run

above the synchronous speed level and thus the rotation speed curve reaches maximum

level of 1 pu. Total power is transferred via the full scale converter and there is no division

in power transformation between stator and rotor circuit.

111

Fig. 60 SCIG with fixed speed case, (a) wind speed, (b) rotational speed, (c) active power,

(d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) slip

112

As a result the converter loss is increased. Also this system can only operate below or equal

to the synchronous speed level range (sub synchronous speed range), so it can operate in

lower wind speeds and thus power capture is low compared to the same fixed speed

operation of a DFIG system. The Complete SCIG model is demonstrated and simulated

here. In the first case, a constant wind speed of 14 m/sec has been applied as an input to the

system. As this wind speed is higher than the corresponding synchronous speed for the

generator, the pitch angle controller acts at the point, where the rotational speed tries to

exceed the predefined value ( here <~1pu or synchronous speed). Thus the mechanical

power extraction is limited and hence the rotational speed is maintained in a constant value.

Also the subplot of slip shows that the when the system reaches to a steady state condition

the amount of slip is reduced to almost zero. It is not exactly zero because at the exact zero

level of slip the rotational speed will become the same as the synchronous speed and the

machine will stop generating power. The reactive power response has also been plotted for

reference purposes. The reactive power reference is given as zero, anticipating no reactive

power transformation required by the system. Exactly same response occurs over here as

the reactive power always presents value “zero” throughout the entire simulation period.

5.4.2 Variable Speed SCIG

To simulate the SCIG system with variable wind speed same five system response

quantities (rotational speed, active power, electromagnetic torque, mechanical torque,

reactive power and slip) have been plotted here. The reference level is kept around 1 pu. for

the rotation speed and other response quantities are also reflecting the same level. But the

most significant variations over here are the amount of oscillation present in the system

response. For the SCIG setup the system is connected with a full scale converter and using

variable wind speed (shown at Fig. 61). The system response quantities are not quite stable

as those were for the DFIG case. It reflects the reduced operational capabilities of the SCIG

system with variable wind speed.

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Fig. 61 SCIG with variable speed case, (a) wind speed, (b) rotational speed, (c) active

power, (d) reactive power, (e) electromagnetic torque, (f) mechanical torque, (g) slip.

114

5.5 Correlation of Rotor Side Converter Power and Grid Side Converter

Power with q-axis Rotor Current

The rotor side converter power and grid converter power have a proportional relationship

with the q-axis rotor current. There is a positive correlation between RSC power and GSC

power. For a fault free condition if the value is considered, both are providing ideal

response and giving same power output. As dependent on the value of q-axis rotor current,

both power curves change in exactly the same way based on the q-axis rotor current value

change. Positive correlation is the relationship among two different individual functions

which are showing a linear relationship in their parameter or value changes. This is what

happens for these two power quantities. Reactive power transformation via the rotor circuit

to and from the system is not considered here. This is demonstrated to get the ideal scenario

and analyze the characteristics of the system in a fault free condition. Because of that, the

DC voltage controller will always get the constant DC voltage as the rated value (here

1200V). Also, the rotor side and grid side converter power needs to be equal to keep the

DC voltage at a constant level for the ideal system.

𝑃𝐺𝑆𝐶 = ∑�𝑉𝑑𝑞_𝑔𝑟𝑖𝑑_𝑐𝑜𝑛𝑣 ∗ 𝐼𝑑𝑞_𝑔𝑟𝑖𝑑_𝑐𝑜𝑛𝑣�

𝑃𝑅𝑆𝐶 = ∑(𝑉𝑑𝑞_𝑟𝑜𝑡𝑜𝑟_𝑐𝑜𝑛𝑣 ∗ 𝐼𝑑𝑞_𝑟𝑜𝑡𝑜𝑟_𝑐𝑜𝑛𝑣)

For a system which is not participating in reactive power transformation, 𝐼𝑞_𝑟𝑜𝑡𝑜𝑟_𝑐𝑜𝑛𝑣 and

𝐼𝑑_𝑔𝑟𝑖𝑑_𝑐𝑜𝑛𝑣 can be considered as same quantity. From the equations of rotor side converter

power and grid side converter power, it can be written that, for a defined system, the

voltage (stator and grid) quantities are constant and given. Also the current in direct axis for

both the stator and rotor depends on the active power output of the system. As this system

is contributing to the active power transformation, so the current quantities can also be

considered as a constant value. So only left is the quadrature axis rotor current. With the

variation of this quantity, the rotor side converter power and grid side converter power will

also vary. The shape and value of both rotor and grid side converter power curves are

exactly the same and match the shape of the q-axis rotor current curve as well (suggested in

Fig. 62). The difference in the value of those quantities with the q-axis current quantity is

the amount of constant which can be calculated from other known quantities. Thus it can be

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stated that the rotor and grid side converter power is proportional with the quad axis rotor

current. It can be said that there is a positive correlation among these system quantities.

Fig. 62 Relation between grid and rotor side converter power with q-axis rotor current.

5.6 Correlation between P and Te and Analogy Behind

From equation 84, the electromagnetic torque and active power can be written as,

𝑇𝑒 =𝑥𝑚𝑥𝑠𝜓𝑠𝑖𝑞𝑟

𝑃𝑠 = −𝑥𝑚𝑥𝑠𝑣𝑠𝑖𝑞𝑟

It can be shown that the electrical torque and active power both are proportional to the q-

axis rotor current in per unit. So 𝑇𝑒 𝛼 𝑖𝑞𝑟 and 𝑃 𝛼 − 𝑖𝑞𝑟. In the case of stator flux or stator

voltage orientation vector representation the flux (𝜓𝑠) and voltage (𝑣𝑠) quantities are

considered constant and as reactance is fixed, so both active power and electromagnetic

torque quantities are dependent upon iqr. But the value of the source voltage vector is larger

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than the flux linkage vector, thus the active power has a higher value compared to the

electric torque. As the generating sign is followed, so the electric torque is negative (to the

generator) and active power is positive (to the grid). In Fig. 63, both Active power (P) and

electromagnetic torque in negative scale (-Te) are plotted together. To resemble the

proportionality the electromagnetic torque is plotted in negative scale. It seems that both the

function of active power, f (P) and the function of electromagnetic torque, f (-Te) have a

strong correlation between them. As both quantities are dependent upon q-axis rotor

current, so the active power is positively proportional to that and the electromagnetic torque

is negatively proportional to q-axis rotor current. If there is any problem in the simulation

block building of the system, this proportional relationship would not be visible. On the

other hand, for SCIG system, this relationship cannot be observed as the rotor is short

circuited, so there is no such relation between the active power or electromagnetic torque

and the q-axis rotor current.

Fig. 63 Correlation between active power and electromagnetic torque.

5.7 Constant DC Voltage Topology

The grid side controller is required to keep the DC voltage around the DC-link capacitor

constant in the desired reference value. In an ideal system, the rotor side converter and grid

side is supposed to transfer the same amount of power. If both rotor side controller and grid

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side controllers are delivering the same power towards the grid or towards the rotor (in any

direction), then it will keep the DC link voltage constant. At t=0 sec, there is a big spike in

the DC voltage quantity. This is the initialisation period of the machine and this is

momentarily at zero second when the machine starts. After this, for every second, the ideal

characteristics of system is maintained and both rotor and grid side converter power seem

to be exactly the same. As DC link voltage calculation takes both these converter powers

into consideration, so we can see a constant DC voltage. This criterion is uniform in both

transient and steady state conditions for ideal case. The analogy behind this is the converter

power is dependent on the reactive power transformation of the system. As a fault free ideal

system is considered here, so there is no anticipated fault present in the system. Thus there

is no need to transfer any reactive power to or from the grid system. As a result, both

converters are supplying ideal and equal amounts of power to the system. This will make it

possible to keep the DC link voltage at a constant level throughout the simulation period. It

is verified here in Fig. 64. Here both rotor side converter power and grid side converter

power are plotted against time and they present exactly the same values. The DC link

voltage (Fig. 64) shows a constant value throughout the whole operating region in this

steady state simulation.

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Fig. 64 Constant DC voltage topology.

5.8 Variation of rotational speed/Active power for wind speed

As the aerodynamic power control is established here for this simulation model, the

minimum and maximum power is defined as the reference value. The pitch angle controller

is activated when the rotor speed reaches 0.8 pu. where the power set point is minimum. It

continues to increase until the power set point reaches its maximum value (where the

rotational speed is defined as 1.21 pu.). Within this range, the rotational speed increases

with the simulation time following the slope. This is defined as the active range generator

(where the generator works or produces power). After that speed limit of the pitch angle

controller is activated and keeps the rotational speed constant, regardless of the wind speed.

This region is called the saturation region. It is depicted in Fig. 65. This figure shows the

rotational speed starts from 0.8 pu and continues till 1.21 pu. After that the rotational speed

maintains a constant speed of 1.21 pu. for the whole simulation period as the system

reaches its steady state condition. Same for the active power curve, it started from zero at

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cut in speed and continues until cutoff speed and after that it continues to deliver constant

power for the whole simulation period. These two quantities are considered very

significant. Both are related to each other and a positive proportional relationship is always

kept between them. This simulation is done for a fixed speed DFIG system. The same

criterion is seen in the variable speed DFIG and both the fixed and variable speed SCIG as

well. But for the SCIG system, the maximum rotational speed is reached at a point just

above the synchronous speed and the active power level is also less compared to the DFIG

system.

Fig. 65 Variation of rotational speed and active power.

5.9 The Impact of Reactive Power Reference on the System Simulation

The model is simulated here in Volt-Ampere (VA) mode. That means the main observation

for this simulation work is to see the amount of active power production from the system to

the grid. Here the reactive power reference is kept at zero level. So the system is not

considering any change in reactive power reference level. It is an indicator for the

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controllers used in this system. The actual reactive power output (after the calculation of

system equation) shows it keeps a constant zero level throughout the whole simulation

period. Reactive power reference will define whether the system will participate in reactive

power generation or absorption to or from the system. As the power electronic converters

are used for control purposes, so it has the capability to take part in the reactive power

production for the system. But for the Volt-Ampere mode of operation we are not

considering any change of reactive power levels for the system. It is considered here the

system is fault free. To observe the effect of reactive power reference the system should be

modelled in the Volt-Ampere Reactive (VAR) mode, where the reactive power reference

can be given as either positive or negative level. It will then indicate that the system will

provide reactive power to the system (for positive reactive power reference) or absorb

reactive power from the grid (for negative reactive power reference). This practice is more

suitable for a fault condition where, voltage sag happens and the system needs to either

provide or absorb reactive power. This simulation model in this thesis is operating in Volt-

Ampere (VA) mode and not performing the reactive power exchange.

5.10 Noise elimination

In the case of a very simple simulation, wind speed is considered as constant or fixed,

however, it will not be constant in real scenario. Wind varies and is dependent upon

numerous types of parameters. However, a DFIG system should be capable of dealing with

the variable nature of the wind. This has already been demonstrated in the variable speed

operation of the DFIG.

Another significant aspect of accurate modelling and proper limit verification of controllers

would be the introduction of noise. In the system any noise can be introduced to the system

from the environment. Usually in a practical system, various sensors are used to gathered

actual input data of system responses such as wind speed, shaft toque, rotational speed of

rotor, shaft power etc. These sensors are the main source for insertion of noise to the

system. The sensors provide the sensed signal to the control unit to perform the control

activities, thus noise is introduced to the control system. In the simulation here, with wind

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speed, a noise has been incorporated to get an idea of the real scenario (as real time wind

velocity modelling is complicated and required sophisticated software package and

numerous data). It is done by adding band limited white noise of power spectral density

(PSD) of noise 0.01 pu. and sample time 0.1sec and a starting speed of random number

generator. It has been carried out for both variable and fixed wind speed operations of

DFIG in Fig. 66 and 67, respectively. The same set of significant quantities (like rotational

speed, electromagnetic torque, mechanical torque, active power, slip and DC link voltage)

are simulated and plotted to show the rejection of noise in the wind speed by the controller.

Fig. 66 Noise elimination capability of the controller in variable wind speed.

The variable wind speed idea has been taken from a Matlab demo model. A step input

response has been considered here as the input wind speed of the system and white band

limited noise has been added. The wind speed variation is only reflected in the mechanical

torque plot (both Fig. 66 and 67) as it is directly calculated from the wind power (Equation

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21), so noise is affecting the mechanical torque plot. For other system quantities, the

controller nullified the effect of noise and other system quantities are kept well safe from

this oscillation (As suggested from other plots of rotational speed, electromagnetic torque,

active power, slip and DC voltage). As this Gaussian white noise block adds noise to the

input wind speed with not big amplitude, so the sudden change of wind speed in a large

variation did not occur. The fuzzy-PI controller is tuned to provide smooth reference value

as the controller outputs. So it can be said that, the controllers reject the oscillation of the

wind variation in the steady state operation mode. Thus, the noise reduction capability of

the DFIG is demonstrated. The same experiment can be conducted for SCIG case as well as

the noise level is deducted by the controllers. This noise elimination analysis is helpful for

observing the noise deduction capability of the system. The reasons recorded for possible

sources of noise are not capable of introduce any noise of high magnitude and that is why

Gaussian white noise block has been used in this simulation.

Fig. 67 Noise elimination capability of the controller in fixed wind speed.

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5.11 Startup System Transient Time Response Analysis

For simulation work, it is important to consider the startup transient time response as it will

give us idea about how fast the system will reach saturation or steady state condition. This

start up transient happens initially for the simulation of a system, when the different

individual blocks start to work and through iteration and after performing internal

calculation, it will reach the steady state condition. Here it is found that for both the fixed

and variable wind speed simulation models, startup transient time response varies with the

variation of the inertia constant (H) of the system. For both variable and fixed wind speeds,

startup transient response shows similar result though they vary in terms of overshoot of the

parameters.

For a system impulse response analysis three important characteristics can be considered

and examined. These are rise time, percentage of overshoot and settling time. Rise time is

the time which is required for a system response move from a specific lower value to a

specific higher value. For various types of system the definition or actual amount of

specific limiting values are different. It is considered for an under damped system, the

lower value is the 0% of the system value and the upper value is the 100% of the system

value. This is 5% and 95% for critically damped condition and 10% to 90% for an over

damped condition. Here the system responses for constant wind speed can be considered as

under the damped scenario as there is no significant overshoot of the parameters. But the

system responses for variable wind speed is an over damped scenario as there is a

significant amount of overshoot. The percentage of overshoot can be described as a

percentage of how much the maximum deviation is from the expected system response. It

can be formulized as(𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒𝑠𝑡𝑒𝑝 𝑣𝑎𝑙𝑢𝑒

− 1 ∗ 100%). This formula has been used for

calculating the overshoot for variable wind system response. The last characteristic is

settling time, which can be defined as the required time for the system response to reach

and continue within a certain percentage (2% or 5%) of the final value.

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By observing the rotational speed curves the characteristics seems similar to a system

impulse response curve for which the target level is 1.21 pu. In the power-speed

characterizations curve, 1.21 pu. is given as the maximum reachable rotational speed for

this system. After the simulation has started, when the parameters are saturated the

rotational speed reached to its maximum stable position of 1.21 pu. For fixed wind speed

simulation, three different values of inertia constant are chosen and rotational speed curve

is plotted in Fig. 68. It is very clear that the increasing the amount of inertia constant (H= 3,

5 and 7 sec) is causing an increase in the rise time (8, 12.5 and 15 sec) of the system

response. As there is no overshoot in the system responses, so the percentage of overshoot

is zero and settling time is the same as the rise time. For variable wind speed simulation,

the system response is considered as an over damped system. It affects the calculation of

the rise time. But still to reach the parameters value from 10% to 90%, it takes almost the

same amount of time (8, 12.5 and 15 sec consecutively for inertia constant value of 3, 5 and

7 sec). But the percentage of overshoot is 3.30%, 2.75% and 2.06% for the inertial constant

in an increasing order. In the same order the settling time is 28, 25 and 22.5 sec. So it is

clear that, for variable wind speed condition, along with the rise time, the settling times of

the system response increase with the increment of inertia constant but the percentages of

overshoot decreases. The important characteristics found from this study is for fixed wind

speed simulation, keeping the inertia constant low will give better result in terms of

reaching the steady state period faster. But for variable wind speed simulation, it is required

to optimize the inertia constant in a reasonable level to get the moderate allowable

overshoot and comparable faster rise time and settling time.

So in a working system, the inertia constant of the whole system (turbine and generator)

should be considered to avoid undesirable overshoot and at the same time to gain quicker

settling and rise time. If the system response has high overshoot it will take longer time to

get settled and that will affect the steady power supply from the wind energy system to the

grid system. In practice though, the turbine and generator has a certain fixed amount of

inertial constant based on industrial rating, but this simulation will be helpful to select the

optimum combination when a new wind farm or wind generator is going to be established.

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In Fig. 69, for the same inertial constant (H = 5 sec), the rotational speed for both fixed and

variable wind speed systems is plotted. It is clear that though all the system parameters are

the same but except for wind speed variation there is a variation in the rotational speed

curve. For variable wind speed simulation, the rotational speed achieves ma greater speed

range compared to a fixed speed simulation case. Thus it is clear that, a doubly fed

induction generation can cover a bigger speed range for variable speed case than a fixed

speed scenario.

Fig. 68 Initial transient time response for different inertia constant (represented by

rotational speed) (a) for variable speed case and (b) fixed speed case.

Fig. 69 Rotational speed curve with same inertia constant (H = 5 sec) for both fixed and

variable speed operation

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5.12 Fault Comparison Scenario in Fuzzy-PI Controller and Tradition

PI Controller

Fig. 70 Comparison in system responses during a fault in the traditional PI controller based

system and fuzzy-PI controller based system, (a) rotational speed, (b) active power, (c)

reactive power, (d) electromagnetic torque, (e) DC-Link Voltage.

The effect of using a fuzzy controller with the PI controller is clearly visible in a fault

occurring scenario in the system. Here a three-phase line to line fault has been added in the

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grid bus system. This fault is introduced by using a ‘three-phase fault’ block from Simulink

Simpower library. The fault is added in the steady state period when all the system

parameter responses are at a steady state level. At 22 sec the fault was introduced and was

cleared after 0.2 sec. Simulation with this fault added was carried out on both systems, with

PI controllers only and with fuzzy-PI controller. Five significant system parameters were

scrutinized to represent the effect of faults on both systems. In Fig. 70, the blue colored

solid line responses are the system responses with fuzzy-PI controllers and red colored

dashed line responses are the system response with PI controllers only. As the fault was

introduced to the system in steady state, so before the fault, the system response was steady

and normal. At the time when the fault was occurred, the system response becomes

unstable and again after a certain time when the fault was cleared, the system response went

back to normal condition again. It is clearly seen that the overshoot of the parameters and

settling time required to get back to the steady state level is more in the traditional PI

controller used system compared to the system which has used fuzzy-PI controller. For

example, the rotational speed curve has an extra 0.02 pu. overshoot for the traditional PI

controllers compared to fuzzy-PI controller. Also in terms of the DC-link voltage figure,

the output using the fuzzy-PI controller required less time (within 0.08 sec) to settle

compared to the traditional PI controller (0.12 sec) only. So this suggested that the system

response improves by a good amount when the fuzzy-PI controllers have been used in the

system compared to PI controllers only. This is because in a fuzzy-PI controller system the

parameters have a more accurate reference output. As the linguistic rules in fuzzy

controllers have considered the expert opinion so it shaped the output more precisely. So in

case of a fault, when the parameter responses are changed in a drastic mode, this controller

can control the system response in a more agile and precise way. The problem with

traditional PI controllers only is that they cannot handle the sudden change parameters very

well, at the same time more suitable for linear equations only. But the total wind energy

conversion system has some non-linear operating equations as well. So when the fuzzy

controller are introduced to the system, which can handle rapid change of parameters and

nonlinear equations in better way compared to PI controllers, Thus system performance is

improved in fault occurring scenarios. Fault ride through condition has not been performed

or analyzed here. Still, due to the fault the parameter responses were disturbed in quite

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large amount. Fault ride through capability can be introduced by various means, such as by

adding an extra resistance to carry through the extra current due to the voltage sag in the

system. The main idea behind this fault analysis simulation scenario is to depict the

improvement of parameter responses in terms of overshoot and settling time. So to perform

fault ride through for fuzzy-PI controller based system, it required protecting equipment of

less rating. At the same time system can reach much quicker to the steady state condition.

The result will be in saving in price and time compared to traditional PI controller based

system. Thus the system will be more reliable and less fluctuation will experienced in a

faulty condition.

5.13 Model Comparison between Traditional PI and Fuzzy-PI

Controllers

The whole simulation was carried out for 30 sec for both types of controllers. To get a

comparison analysis of the parameter response for both controllers, only the last 5 sec

simulation has been shown over here to show the variation in a zoomed in view. In Fig. 71,

the red solid line is representing the parameter responses for the system with PI controllers

only and the blue dashed line represents the system parameter responses for the system

using fuzzy-PI controllers. Various system responses change according to the variation in

wind speed. As the fuzzy-PI controllers were included in both active and reactive power

control loop, so effect is clearest in these two responses. In terms of other system responses,

the variation is quite negligible. The rate of fall in wind speed is quite high in between 26.5

to 28 sec. At that time the active power output for PI controllers only shows quite a lot of

ripples or oscillation in the output characteristics, but the controller with fuzzy logic and PI

both behaves in a normal manner and the extra oscillations are not visible. By adding a

fuzzy logic controller in the active power loop, it is now capable of handling the nonlinear

equation well enough compared to a system with PI controllers only. So the output

responses are quite smooth and steady. Similarly for the reactive power curve, whenever

there is a change in wind speed ( at 26.2, 26.8, 28, 29 sec) the output reactive power for PI

controllers only experiences a large spike. On the other hand the fuzzy-PI controller output

reactive power doesn’t show such a sudden spike or rapid change in output quantity. The

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reason is the introduction of the fuzzy logic controller in the system actually incorporates

an intelligent expert opinion to the system and it is quite agile to the system’s sudden

change of input parameters.

Fig. 71 Comparison is system responses in traditional PI controller based system and fuzzy-

PI controller based system, (a) wind speed, (b) rotational speed, (c) active power, (d)

reactive power, (e) electromagnetic torque, (f) DC-Link Voltage.

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So the reference values after the fuzzy-PI controllers are more trained to follow the actual

value. Whereas the PI controller is quite robust and cannot always follow the sudden state

change of parameters. So introducing the fuzzy logic controller with the PI controllers into

the control loop improve significantly the parameter characteristics and add missing

features of PI controllers to the control structure. The traditional PI controller has been

selected in this thesis as this is the most commonly used and simplest controller unit. As a

traditional controller unit, PI controller is the easiest to work with. But the obvious failures

of PI controller are rigid behavior in the sudden parameter changes of the system and not

following properly for the nonlinear cases. These features can be well achieved if an

adaptive and agile fuzzy controller can be introduced to the system alongside the traditional

PI controllers. Hence in this thesis a comparison in the simulation results has been

demonstrated between these two controllers. At the same time it should be considered that,

this thesis is not focusing other updated or modified controllers. Using those controllers can

achieve more accurate and precise results by the cost of simplicity. More advance research

can be carried out to compare the result of fuzzy-PI controller to those complex controllers.

A trade off should also need to be analyzed among the simple and user friendly approach

with complex and fractional improvement in the system responses.

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Chapter Six

Conclusion

The variable speed operation of a wind power generation unit is described with modelling

its controller part (fuzzy-PI type). Literature reviews were carried out to summarise

important contributions in this field. Wind energy scenario worldwide and in Australia was

also discussed to report the current status in this sector. Important aspects and

considerations for modelling a variable speed wind power generator were mentioned to

demonstrate a whole picture of the system. Later modelling of the generator system along

with its controllers has been discussed before presenting the important findings. In chapter.

5, simulation results were articulated with proper analysis. Effective response of system

quantities with the fuzzy-PI controller compared to the traditional PI controllers was

recorded. In the Appendix A1 an initial experimental setup of a laboratory test bench is

described with some basic experiments which were carried out. More advanced

experiments will be conducted with this hardware setup as an extension of this research

work in future.

6.1 Result Discussion

Both types of induction generator (SCIG and DFIG) have been modelled and simulated

here to reflect the workability of these wind generators in the variable wind speeds. Along

with variable wind speed also fixed wind speed operation has been carried out to show the

difference. A fixed set of significant system response quantities comprising of rotation

speed, electromagnetic torque, mechanical torque, active power, reactive power, slip, DC

link capacitor voltage have been considered for each system with both fixed and variable

wind speed. The responses are recorded and analysed.

Traditional PI controllers and upgraded fuzzy-PI controllers which used in this research are

discussed in detail. The comparisons between the system response quantities is showing a

good amount of improvement in active and reactive power where the fuzzy-PI controllers

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have been used. The sudden change in input wind condition created spikes in the PI

controller based model, was eliminated by introducing fuzzy logic controllers in the system.

This aids better tracking of system reference value when there is a nonlinear change in

situation, a limitation of the traditional PI controllers. Also by observing the active power

curve, it can be said that, the system now becomes more adaptive as fuzzy logic controllers

are introduced. Thus the active power ripples are removed. In terms of a fault occurring

situation adopted fuzzy-PI controller demonstrates a reduction of the overshoot and settling

time. This is another important outcome of this research. As PI controllers are not capable

of dealing with the nonlinear equation very well, so introduction of the fuzzy-PI controller

improves the system performance in case of fault.

The rotational speed is in both sub and super synchronous speed levels for DFIG system

but for a SCIG, rotational speed is around unity. It is actually a bit more than unity as

induction generator will not operate at synchronous speed. Thus it reflects the DIFG can

operate in a bigger speed range than the SCIG system. Mechanical torque, electrical torque

and active power maintain the correct representation as well. The DC voltage level is kept

at its reference value and remains constant for the whole range of operation. All these

system response quantities demonstrate perfect behaviour of the system. The variable wind

has been uniquely modelled as the outcomes followed the expectation quite well. In another

Figure (Fig. 57), model responses with and without controller are shown for the DFIG case.

It is visible over there that, without using the GSC controller only, the system quantity

responses are not stable at all. There were oscillations throughout the whole simulation

time. So control system is an essential part of the whole system.

Some important relationship between various system responses were established which can

be used as the indication of perfect system behaviour and can be considered as the system

analysis criteria. Simulation shows that the active power and electromagnetic torque both

are dependent on the q-axis rotor current and both can be considered as proportional to the

q-axis rotor current for stator voltage orientation vector control. The electromagnetic torque

is a negative quantity as it follows the generation sign (towards the grid). Considering

magnitude only, it can be said that both active power and electromagnetic torque have a

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positive correlation in their responses. In the same way, both rotor side and grid converter

powers are dependent on the q-axis rotor current and have got a similarity in their value and

shape with q-axis rotor current. Similarly there is also a proportional relationship among the

shape and value of active power and rotational speed curves. On the other hand the DC link

capacitor voltage is dependent on the output of both the rotor and grid side converter

power. As it is considered here that the system is not taking part in the reactive power

transformation, so both rotor side converter power and grid side converter power are equal

and the main reason for the constant DC link voltage throughout the whole simulation

period. If these powers are not the same, then there will be variation in the DC link voltage.

Put another way, there will be power transfer from whichever is the higher one to the lower

one. Noise elimination capability of the controller system was also demonstrated in this

thesis. Gaussian white noises have been added and system response quantities simulated are

unaffected. The controllers were capable of deducting a certain amount of noise present in

the system. This idea can be utilised for test bench setup or using sensors to collect input

signal in the actual system.

Also, system initial start-up transient response analysis has been carried out. The inertia

constant is the main factor of controlling this response but depending on the wind speed the

characteristics of the start-up transient response varied a bit. It has been shown that for

fixed speed, the amount of overshoot is negligible and the inertia constant only change the

rise time of system response. On the other hand, for variable wind speed operation,

increasing the inertia constant does decrease the percentage of overshoot, but increase the

rise and settling time. So a trade-off needs to be considered when practical system will be

consider for component selection based on percentage of overshoot and system response

rise time.

6.2 Remarks

The system modelled and simulated here is the basic and ideal system. Some criteria are

taken into consideration and can be mentioned here.

1. For usual simulation system is considered as to be a fault free system.

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2. No reactive power transfer is carried out. Just a certain fixed reactive power

level is kept constant for the whole simulation period.

3. For assigning the limiting value of the membership functions of fuzzy logic

controllers, the limits are selected by a trial and error method, running the

system with PI controllers.

4. The grid system used here is modelled in a similar way to the Matlab/Simulink

model but some extra blocks have been added.

5. No transient analysis has been carried out for the overall system.

For the generator model, a 5th order model has been taken into consideration which is the

most detailed model

6.3 Future Work Suggestions

In the next phase of this research some certain things can be carried out. Here in this part a

suggestion for possible future work for this research is proposed.

1. Experimental setup for this is already established. In that setup some certain

things can be examined. For example, after operating the DFIG model, various

system response data can be gathered and plotted to get the results and those

results can be compared with results of the simulation work.

2. An experimental setup can be established comprised with a small capacity wind

generator (for example a 3 kW wind generator) can be introduced to obtain a

realistic data and to verify the idea of noise and harmonic reduction by the

controller.

3. Mamdani fuzzy-PI controllers have been used for active power and reactive

power and DC-Link capacitor control loops only. In the same way fuzzy current

controllers can be designed and inserted to the system.

4. More work could be done to examine the transient response of the system

quantity in the transient state. This will give an indication of more efficient fault

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clearance for the system. For this effort a realistic fault can be introduced to the

prototype system.

5. Permanent magnet synchronous generator (PMSG) can be used to compare the

results with DFIG system.

6. Smart grid connection and the impact of low frequency emitted from wind

generator on smart grid and rural population area can be observed to understand

the grid connection characteristics of the future type.

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137

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Appendix

A1. Experimental hardware Setup Overview

1 Introduction

In the laboratory, an experimental test bench setup is formed as a part of this research. The

initial works of setting up a simple system with a squirrel cage induction generator has been

completed and some basic experiments have been carried out to verify the working

procedure of a wind generation prototype system with squirrel cage induction generator

connected to the system. However, the implementation of a DFIG with its control system

was beyond the scope of this thesis. All the equipment was brought from TERCO, a

company which builds educational equipment. The equipment list that has been arranged is;

2 Laboratory Equipment’s for Wind Energy Test Bench

The following hardware and accessories were used for preparing the laboratory test bench

system;

Test Bench

Wind Mill Control Unit (MV4250)

Torque meter (MV 1054)

Induction Motor Squirrel Cage (MV1009)

Induction Motor Wound Rotor (MV 1007)

DC motor (MV 1034)

Synchronous Motor (MV 1027)

Resistive load (MV1010)

Capacitor Bank

Multi meter

Lamp

Power Pack (MV 1302)

148

IG Starter (MV 2306)

DC Machine (MV 1028)

DSP Board (DS1104) installed in a computer.

3 Wind Mill Controller Unit

The significant equipment of this setup is the TERCO Wind Mill Control Unit (MV4250).

It is a controller unit which has a 4-quadrate Rectifier and infinite bus system

connected/built inside. It is basically designed to be connected with a squirrel cage

induction generator which might be driven by another machine or may be connected to the

wind turbine rotor blade in a real environment. The controller unit will help to get the

excitation for the induction generator and can produce AC voltage of different frequencies

depending on the requirement. The actual equipment picture is given here for further

reference.

Fig. 72 Wind Mill Controller Unit (MV4250) from TERCO.

149

The principle single line diagram of the asynchronous wind mill controller unit is also

given here to demonstrate the working principle of this controller unit. Here it shows that

the induction generator is connected to the designated 3 ports for 3 phase system. There are

current and voltage measurement systems to give the output data indication after that. The

built-in capacitor bank for excitation control and compensating inductances are connected

in parallel with the system. The capacitor values can be changed to some defined level and

capacitance of the system can be increased gradually to compensate the effect of load

connected to the system. It will indicate that if the load is increased the system will need

more capacitor to give more reactive power supply to the system. The inductance basically

is required to keep the voltage level within a reasonable limit. In the actual wind energy

system, to limit the wind energy in a high wind scenario, It needs a compensating element

to control the system voltage. The inductance works here as that compensating element.

After that a three phase rectifier bridge is placed to supply a floating DC voltage (which is

dependent upon the input 3 phase ac voltage) to the output side of the system. A high

voltage DC line is modeled as built in for the system which can be altered between two

options, either short line or long line. It is an internal model and the transmission line

parameters are fixed for the system (both long and short DC voltage line model). The

transmission line is characterized by taking into account the effect of resistance and

inductances.

Fig. 73 Single line diagram of the Wind Mill Controller Unit arrangement.

As the capacitance is the concern for AC transmission line so it is omitted here for DC

transmission line designing. The distributed DC voltage can further be loaded into a built in

resistive load bank (Rl- PWM modulated resistive load). By using this load resistance

150

different operating or break down points for the generator operation can be decided and

selected. Also the distributed DC voltage can be connected alternatively to the 4-quadrate

rectifier which is further connected to a built in infinite bus system.

4 Test Bench Setup

The test bench setup is organized as below (picture given before wiring the whole system).

A block diagram of the system with connection line is also given here for further reference.

A voltage source (Power pack, MV1302) is used for the first power source. The DC

machine (MV 1034) is used in the experiment as the representation of wind turbine rotor

blade for actual scenario. The DC motor is considered as the turbine rotor which will

provide load torque to the system. It is coupled with the squirrel cage induction generator

(MV 1009). A torque meter and sensor unit is used in between this coupling process to get

the information of the load torque, rotational speed of the system and power dissipated in

the shaft. The voltage source has both DC and AC voltage input options to take from. As

the DC machine is considered as the motor and load torque provider, so the DC voltage

option is exploited and the voltage source is supplying DC system voltage to the armature

and the field is short circuited by using an external resistance block. The squirrel cage

induction machine is connected after the torque sensor where, the rotor side is short

circuited and stator side is connected via 3 phase to the wind mill control unit. There is

another capacitor bank connected to the stator in parallel to aid the voltage build up

process. Further a three phase load (Here lamp is used) is connected in parallel with the

stator in its three phases. The wind mill control unit connection is made according to the

equipment manual. The three phase outlet is connected from the three phase stator voltage

connector from the induction machine. Here the induction machine is connected in delta

connection. The measuring outlets of three phases are connected to each via jumper cables.

The HVDC (High Voltage DC) line model is selected as long and load resistance is kept at

zero position initially.

151

Fig: 74 Equipment connection diagram for experimental setup.

Fig. 75 Picture of hardware setup in the laboratory.

152

5 Three-phase Windmill Induction Generator Performance at No

Load

The first experiment carried out was to run the wind generation system at no load. That

means the load resistance (Rl) in the wind mill controller unit was kept at zero level for the

whole experiment process.

For the initial experiment after making the proper connection of the system with rechecking

the safety issue and connections, the system is powered up. From the potential meter in the

DC voltage source, the DC voltage was increased, thus the shaft speed of the system

increased. The induced voltage amount also increases and after building up a substantial

voltage in the induction machine, the lamp (three phase) glow up. The system parameters

and values were recorded as,

Table. 10 Parameter’s value for AC voltage generation for no load case.

Speed (RPM) Torque (Nm) Shaft Power (Kw)

DC Voltage (V)

AC Voltage (V)

1305 2.21 0.28 186 200

After reaching the maximum voltage (here 240V is taken as maximum limit as due to

safety concern it was not increased after that), to see the effect of speed for the induced AC

voltage generation. The table (Table. 11) below shows the result for different speed ranges.

The speed range is changed by varying the potentiometer of the DC voltage source and

measurements were taken from the torque measurement unit and a volt meter connected to

a single phase of the induction generator.

Table. 11 Generated AC voltage relation with rotational speed for no load case.

Speed (RPM)

1275 1240 1212 1158 1110 1050 1000 940

AC Voltage (V)

240 230 220 205 190 175 160 135

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Fig. 76 Relation between generated AC voltage and rotational speed for no load case.

The important finding is that as the speed increases of the system, the generated AC voltage

also increases. As the shaft of the ac generator is coupled with the DC motor which is

working here as a load torque provider, so the increment in shaft speed will increase the

cutting of flux in the AC generator (squirrel cage induction generator). Thus the voltage

will also increase. The analogy is matched with the theory and with the practical scenario.

Also in practice, as the wind energy increases, the amount of power production also

increases. But here no controller has been utilized so the generated AC voltage will

increase in an uncontrolled way. Also no load has been added to the system, so generated

voltage is proportional to the shaft speed. It is the representation of the system in the active

zone, where before saturation the voltage increase with the speed. After a certain defined

level, the controller will act and keep the voltage level constant irrespective of the

increment of speed limit.

5.1 Effect of Capacitance in Induction Generator Performance

Now, same experiment is done by changing magnetizing capacitance and compensating

inductance value. Here the value of capacitance and inductance can be varied in some

predefined levels which were kept at zero level initially.

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As not communicated from TERCO, the actual capacitor value was not known. But in

terms of percentage it can be said that, the capacitance values increase while we turn the

potentiometer from position 0 to 1 and so on. The following table (Table. 12) and graph

(Fig. 77) will demonstrate the results,

Table. 12 Relation of AC voltage generation with rotational speed in different

capacitance for no load case.

Capacitance Position

0 1 2 3

AC voltage (V) 220 220 220 220 Speed (Nm) 1250 1210 1195 1180

Fig. 77 Measurement of rotational speed requires to generate AC voltage for different

capacitance levels.

It shows that, if the capacitance value increases, the same amount of voltage build up in

induction generator happens faster than the original case with capacitance kept at zero

level. The theory says that, if the capacitance is increased of the system, it will aid in

reactive power increment, thus the actual voltage build up will be more. So if the

magnetizing capacitance of the system is increased, the magnetization will be quicker and

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eventually it will require a smaller amount of wind power, that means less amount of torque

or shaft speed, to get the desired voltage level.

5.2 Effect of Inductance in Induction Generator Performance

Now the compensating inductance is included to the system. Inductance is basically

limiting the generated voltage by a certain amount and it is affecting in an opposite way as

the capacitor works. For the next experiment, the system capacitance is kept at position 2,

with some certain magnetizing capacitance and the potentiometer of the compensating

inductance was changed to the defined level. It also does not tell the actual value of

inductance due to TERCO policy but can indicate that by increasing the level from 0 to 1

and so on will actually increasing the inductance values.

Table. 13 Relation of AC voltage and current measurement with rotational speed in

different inductance for no load case.

Inductance Position

0 1 2 3

Speed (Nm) 1187 1197 1204 1210 Voltage (V) 218 210 204 196 Current (A) 4.25 3.75 2.75 1.8

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Fig. 78 Measurement of AC voltage in different inductance level.

Fig. 79 Measurement of AC current in different inductance level.

The experimental result shows that, the inductance has a negative impact in the voltage

building scenario while the capacitance has a positive impact to the system. Also here

current values are considered. It is because; now the system has got two reactive current

components. One is capacitive current and another is inductive current. As the capacitance

value is fixed at position 2, so the capacitive current will be fixed. But if it is varying the

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inductive component so the inductive current will vary. Here actually the inductive current

is increased. So the resultant of the reactive current will be the vector addition of both

capacitive and inductive currents. Thus by increasing the inductive current, the total

reactive current of the system will decrease eventually. It shows the similarity with the

experimental results. As it can be seen from the chart, the resultant current is decreasing as

we increase the inductance to the system.

6 Three-Phase Windmill Induction Generator Performance at Load:

Now a load is included to the system. It is done by introducing the load resistance by

varying the load potentiometer from 0 to 100%. The first objective was to see the effect of

load to the system. It is obvious to say that, as the load is added to the system, so it will

require more speed to generate the same voltage output as it was for the no load status.

Here this phenomenon is verified and another significant finding is explained here. From

the DC voltage/current potentiometer it can be observed the DC voltage and current values

after the three phase rectifier. Regardless of the speed variation we tried to maintain a

constant DC current at a desired level (here 3Ampere). The effect is compensated by

adjusting the load via the Rl potentiometer. The values of DC voltage for different speed

level are mentioned here in the following Table. 14,

Table. 14 Measurement of DC load current, voltage and rotational speed at different

load introduced to the system.

Speed (Nm) 1195 1245 1295 1320 DC Current (Idc)

3 3 3 3

DC Voltage (Vdc)

265 285 300 310

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Fig. 80 relation among DC load voltage and rotational speed for loading to the system.

It shows that, at the low speed range, there is a reasonable amount of DC voltage variation

while keeping the DC current fixed at 3A by varying the load. So more load can be

introduced to the system at low speed level as it can compensate the effect of load. Whereas

for high speed level the voltage variation is not significant. Also the effect of load to the

system is not that much visible. It can be concluded that by increasing the rotational speed,

increasing the generation that means more interaction between the generator rotor and

stator. This will increase the capacity to handle more loads. But as the result suggests, this

relationship is not linear. As the speed is increased, the generator is reaching to a point

where the iron cores will be saturated. So the increments of magnetizing current at this

point increase very small increment in the voltage, which will result in a very small

increment in the load current. Thus the result shows the voltage difference is very small in

high speed operations compared to low speed operations. So overloading is not desirable

for the system, as for high speed operation we will need more inductance to limit the

voltage and in the low speed operation it will need more capacitance to aid the voltage

build up.

In another experiment, the rotational speed was kept constant and the DC load current is

changed by changing the Rl potentiometer. The observation here was the DC voltage and

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the effect of DC voltage by changing the load to the system. The results are shown in the

following graph,

Table. 15 Measurement of loading by keeping the rotational speed fixed.

Speed (Nm) 1250 1250 1250 1250 1250 DC Current (A)

1.5 2 2.5 3 3.5

DC Voltage (V)

305 300 295 290 285

Fig. 81 Voltage and current relationship in case of loading by keeping the rotational speed

constant.

It shows that as the load is increasing by load potentiometer (Rl) the load current increases

and the load DC voltage decreases with this. Thus it can be said that, the increment of load

is inversely proportional to the DC voltage and proportional to the DC load current. It

aligned with the theory as well.

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7 Relation of Total Efficiency with the Load

The effect of efficiency of the system is calculated for the system with load included. For

this arrangement the magnetizing capacitance in position 2, and the compensating

inductance is kept in position 0. The load is varied and different speed, DC current, shaft

voltage, load torque, DC voltage is charted. The DC power is calculated by multiplying the

DC current and DC voltage for each load. The efficiency can be calculated in percentage by

following this equation 𝜂𝑡𝑜𝑡𝑎𝑙 = 𝑃𝐷𝐶𝑃𝑠ℎ𝑎𝑓𝑡

Table. 16 Measurement of different parameters (speed, DC current, DC voltage, DC

power, Shaft Power and efficiency) for load case.

Speed (rpm)

1200 1150 1120 1090 1075

DC Current (Idc)

0.5 1 2 3 3.5

Pshaft (Kw) 0.53 0.85 0.96 1.12 1.17 Torque (Nm)

4.42 7.50 8.45 10.29 10.80

DC Voltage (Vdc)

300 260 250 220 205

DC Power (Pdc)

150 260 500 660 717.5

Total efficiency

28.83% 30.58% 52.20% 58.9% 61.38%

It shows that, as the load increases the load current also increases and the DC power will

also increase. It shows that with the increase in load the rotational speed decreases and the

efficiency also decreases. So the total efficiency is proportional with the rotational speed of

the system. Then the four-quadrate DC rectifier is connected to the system and it affects the

system in the desired way. It means that by increasing the load, the load current is increased

and load voltage is decreasing by increasing the load.

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Fig. 82 Effect of DC voltage, total efficiency and rotational speed in terms of increasing

load to the system.

These experiments were carried out for the squirrel cage induction generator setup. The

four-quadrate rectifier and the infinite bus was the built into system and there was no

tapping point in between these two components. It was the potential barrier for making the

system as the DFIG or wound rotor induction generator system. In the case of a DFIG

system it is necessary to connect the controller unit to the rotor side and the stator is

supposed to connect directly to the grid (in this case an infinite bus system). But as the total

control unit was a compact solution so it was not a DFIG system with this arrangement.

For further work in this project an arrangement can be made where a wound rotor induction

generator will be used as a generator and the rotor will be connected to the wind mill

controller unit. The output from this will be taken separately and added with the direct

connection with the stator connections. For this arrangement, it requires extensive research

including the high voltage signal handling capable circuit arrangement.

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A2. Nomenclature

Abbreviations

DFIG Doubly Fed Induction Generator

SCIG Squirrel Cage Induction Generator

pu. per unit

TSR Tip speed ratio

WT wind turbine

EMF Electro Magnetic Force

SVO Stator Voltage Orientation

SFO Stator Flux Orientation

PWM Pulse width modulation

RMS Root mean square

GSC Grid Side Converter

RSC Rotor Side Converter

IMC Internal Model Control

MPPT Maximum Power Point Tracking

Symbols

A Rotor blade swept area

Cp Power coefficient

KE Kinetic Energy

m Mass

vwind Speed of wind

vm Speed of rotor

R Radius of rotor blade

φ Angle of incidence

Pwind Wind power

d/dt Differential operator

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dmdt

Flow rate of air

ρ Air density constant

𝑇𝑒 Electromagnetic torque

𝑇𝑚 Mechanical torque

P Active power

Q Reactive power

ωr Rotational speed of rotor

ωe Synchronous rotational speed

β Pitch angle

λ Tip speed ratio (TSR)

s Slip

Ns Synchronous speed

f Frequency of the system

P Number of Pole

Protor Rotor side power

Pstator Stator side power

Pmech Mechanical power

𝑃𝐺𝑆𝐶 Grid side converter power

𝑃𝑅𝑆𝐶 Rotor side converter power

𝑃𝑟𝑎𝑡𝑒𝑑 Rated Power

H Inertia constant

𝑇𝑡,𝑇𝐺 , 𝑎𝑛𝑑 𝑇𝑠ℎ Turbine, generator and shaft torque

𝜃𝑇 Rotational angle of turbine

𝜃𝐺 Rotational angle of generator

𝜔𝑇 ,𝜔𝐺 Rotational speed of turbine and generator

𝐷𝑇 ,𝐷𝐺 Turbine friction damping, generator friction damping coefficient

Ksh Shift stiffness coefficient

Inertia constant for turbine and generator

lsec Line section length

Kp, Ki Proportional Constant and Integral constant

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G(x) Process

G^(x) Process model

𝑉𝑚, 𝐼𝑚 Maximum voltage, maximum current

𝑣𝑎, 𝑣𝑏 , 𝑣𝑐 Voltage across a, b and c axis with respect to neutral

𝑣𝑎𝑏, 𝑣𝑏𝑐 , 𝑣𝑐𝑎 3 Line to line voltages of a three phase system among different

phases

𝑖𝑎,𝑖𝑏,𝑖𝑐 current across a, b and c axis with respect to neutral

𝑖𝑎𝑏 , 𝑖𝑏𝑐, 𝑖𝑐𝑎 3 line to line currents of a three phase system among different phases

𝑣𝑞𝑠, 𝑣𝑑𝑠 , 𝑣𝑞𝑟 , 𝑣𝑑𝑟 Stator side q axis and d axis voltage, rotor side q axis and d axis

voltage

E Back EMF

𝑖𝑞𝑠, 𝑖𝑑𝑠, 𝑖𝑞𝑟 , 𝑖𝑑𝑟 Stator side q axis and d axis current rotor side q axis and d axis

current

𝜓𝑞𝑠,𝜓𝑑𝑠,𝜓𝑞𝑟 ,𝜓𝑑𝑟 Stator side q axis and d axis flux linkage, rotor side q axis and d axis

flux linkage

𝑟𝑠, 𝑟𝑟 , 𝑥𝑠, 𝑥𝑟 , 𝑥𝑙 Stator resistance, rotor resistance, stator reactance, rotor reactance,

mutual reactance.

Z, X Impedance and reactance

𝑣𝑟𝑚𝑠, 𝑖𝑟𝑚𝑠 RMS voltage level, RMS current level

𝑣𝑑𝑞 , 𝑖𝑑𝑞 Resultant voltage and current for d-q representation

Superscript e, s and r Voltage of subsequent side in synchronously rotating, stationary and

rotor reference frame.

Subscript s and r refers as stator side voltage and rotor side quantity.

Subscript ref Reference value.

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A3. System Parameter’s Value

Model parameters are taken from reference [25] as per below,

Turbine parameters,

Base power, 𝑆𝐵 660 kVA

Air density, ρ 1.12 Kg/m3

Rotor diameter, D 47 m

Rotor inertia, 𝐻𝑟 0.5 Sec

Shaft stiffness, 𝐾𝑟 0.35 p.u./rad

Shaft damping coefficient, Dm 5 p.u.

Induction Generator parameters,

Base voltage, vB 660 V

Stator resistance, rs 0.01 p.u.

Stator leakage reactance, Lls 0.04 p.u.

Rotor resistance, rr 0.01 p.u.

Rotor leakage reactance, Llr 0.05 p.u.

Mutual reactance, Lm 2.9 p.u.

Generator inertia, H 5 Sec

PI Controller parameters,

Active power controller

Reactive power controller

Q-axis current controller

D-axis current controller

Speed controller

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