sub-synchronous interactions between type 3 wind turbine using fuzzy logic

A DISSERTATION
ON
SUB-SYNCHRONOUS CONTROL INTERACTIONS BETWEEN TYPE-3 WIND
TURBINES AND SERIES COMPENSATED AC TRANSMISSION SYSTEMS
Submitted in partial fulfillment of the requirements for the award of the degree of
MASTER OF TECHNOLOGY
IN
POWER SYSTEMS
Submitted by
YAKKALURI DHARMA TEJA
(Reg.N0: 11206103)
Under the Guidance of
DR. P. LINGAREDDY
PROFESSOR
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
K L UNIVERSITY
GREEN FIELDS, VADDESWARAM, GUTNTUR.
2013

DEPARTMENT OF
ELECTRICAL & ELECTRONICS ENGINEERING
K L UNIVERSITY, GUNTUR.
2013
CERTIFICATE
This is to certify that the project work entitled “SUB-SYNCHRONOUS CONTROL
INTERACTIONS BETWEEN TYPE-3 WIND TURBINES AND SERIES
COMPENSATED AC TRANSMISSION SYSTEMS” submitted by Y.DHARMA TEJA
(11206103) in partial fulfillment of the MASTER OF TECHNOLOGY IN POWER SYSTEMS
in the Department of Electrical & Electronics Engineering during the academic year 2012-
2013, is a bonafide work done by him.
Dr. P. Lingareddy, Dr. M. Uma Vani,
Professor Professor & HOD
KL University. KL University.
External Examiner

ACKNOWLEDGEMENT
It is a great pleasure to express my sincere gratitude to my supervisor, Dr. P.
Lingareddy Garu, Professor in KL University, Guntur, for his valuable advice, directions,
encouragements and supports throughout the program. My enthusiasm in this subject is inspired
by his profound knowledge in this area. I am truly honored to work on this thesis under his
supervision.
I also wish to thank to Professor Dr. M. Uma Vani, Head of Department of Electrical
& Electronics Engineering, K L University, Guntur, all the Asst Professor and support staff in the
Department of Electrical & Electronics Engineering for their help during my studies there.
I express my gratitude to Professor Dr. M. Venu Gopala Rao, for her help and support
in Project during my study.
I would like to thank Dr. G. L Dutta, Chancellor of KL University and all the faculty
members of the Department of Electrical & Electronics Engineering for their direct or indirect
support for helping me in completion of this Thesis.
I am greatly obliged to our KL University that has provided me a healthy environment
to drive me to achieve my goals and ambitions.
Last but not least I wish to convey my thanks to one and all who are concerned directly
or indirectly for helping me in the successful completion of this Thesis.
Y. DHARMA TEJA
ID. No. 11206103

KL UNIVERSITY
GUNTUR (ANDHRA PRADESH)
Department of Electrical & Electronics Engineering
Duration :2012-2013 Academic Year
Date of Start :August, 2012
Date of Submission :July,2013
Dissertation carried out at : KL University
Title of Project : Sub-Synchronous Control Interactions between
Type-3 Wind Turbines and Series Compensated
AC Transmission Systems
ID No./ Name of the student : 11206103
Y. Dharma Teja
Name and Designation of
the Guide/ co-guide and
Professional experts : Dr. P. Lingareddy, Garu.
Key Words : SSCI, SERIES COMPENSATION.
Dissertation Ares(s) : Control and Power
Abstract :This project gives the overview of the SSCI
Phenomenon.
The most recent project experience and
studies have shown that Type 3 wind turbine
generators with power electronic converters and
controls that operate near the series compensated
transmission lines are susceptible to un-damped sub-
synchronous oscillations.
The project simulated on the MATLAB
platform using a Type 3 wind turbine model are used
to demonstrate SSCI, the design of an SSCI damping
controller is presented to help mitigate the problems
that arise during the process.
Signature of the Student Signature of the Guide
Date: Date:

i
CONTENTS
Chapter 1 Introduction 1
1.1. Theme of thesis 5
1.2. Background Literature survey 6
1.3. Thesis Layout 8
1.4. Conclusions 8
Chapter 2 Wind Turbine Systems 9
2.1. Introduction 10
2.2. Wind Turbines 10
2.3. Wind Turbine Topologies 12
2.3.1. Fixed speed wind turbine (Type A) 12
2.3.2. Variable speed wind turbine 13
2.3.2.1. Type B wind turbine 14
2.3.2.2. Type C wind turbine 15
2.3.2.3. Type D wind turbine 16
2.4. Typical characteristics of the wind turbine 16
2.4.1. Power versus speed Characteristics 16
2.4.2. Power coefficient versus TSR Characteristics 17
2.4.3. Torque versus speed Characteristics 20
2.5. Conclusions 21
Chapter 3 DFIG System 22
3.2. Vector or Field Oriented Control Theory 23
3.2.1. D-Q Theory 23
3.2.1.1. Transformation of three phase stationary to two phase stationary
Axes. 24
3.2.1.2. Transformation of two phase stationary to two phase synchronously
rotating axes. 25
3.2.2. Mathematical modelling of Induction Generator 26
3.2.2.1. Modelling of DFIG in synchronously rotating frame 26
3.2.2.2. Dynamic modelling of DFIG in state space equations 28
3.2.3. Principle of Vector control 32
3.3. DFIG System 34
3.3.1. Double-fed Induction Generator 34
3.3.2. Voltage source converter 33
3.3.3. Grid side converter control 36
3.3.4. Machine side converter control 38
3.4. Conclusions 42

ii
Chapter 4 MATLAB/SIMULINK MODELLING 43
4.1. INTRODUCTIONTO MATLAB/SUMULINK 44
4.1.1. Development Environment 44
4.1.2. The MATLAB Mathematical Function Library
4.2. The MATLAB Language 45
4.2.1. Graphics 45
4.2.2. The MATLAB Applications Program interface (API) 45
4.2.3. MATLAB Documentation 45
4.3.MATLAB tools 46
Chapter 5 Problem Description & Results 48
5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION 49
5.2. ANALYSIS OF CONTROL INSTABILITY 51
5.3. DESIGN OF SSCI DAMPING CONTROLLER 53
5.4. OTHER SSCI MITIGATION ALTERNATIVES 55
5.5. RECOMMENDATIONS 57
5.6. MATLAB SIMULINK MODELS & RESULTS 58
5.7. CONCLUSIONS 60
Chapter 6 Fuzzy logic Controller 61
6.1 INTRODUCTION TO THE FUZZY LOGIC 62
A. Fuzzy model, Fuzzy controller, and Fuzzy observer 62
B. Fuzzy control system 62
C. TS Fuzzy Model with Parameter Uncertainties 63
6.2 INTRODUCTION TO MY PROJECT EXTENSION 65
6.3 CONCLUSIONS 69
Chapter 7 Conclusions 70
7.1. INTRODUCTION 71
7.2. RESULTS 72
7.3. CONCLUSIONS 72
REFERENCES 73
APPENDIX 74
PUBLICATIONS 75
PUBLICATION PAPER

LIST OF FIGURES
S.NO NAME PAGE NO
1 Fig 1.1. Statistical data of total installed wind capacity in world 3
2 Fig 1.2. Growth rate of wind power in Global market 3
3 Fig 1.3. World share of cumulative installed wind power for different wind
turbine concept (Approximate data) 4
4 Fig 1.4. The overall view of wind energy system 4
5 Fig 1.5. The Power flow diagram of DFIG 5
6 Fig 2.1. Horizontal axis turbine 11
7 Fig 2.2. Schematic diagram of a fixed speed wind turbine 13
8 Fig 2.3. Schematic diagram of Type B wind turbine 14
9 Fig 2.4. Schematic diagram of Type C wind turbine 15
10 Fig 2.5. Schematic diagram of Type D wind turbine 16
11 Fig 2.6. The typical power versus speed characteristics of a wind turbine
17
12 Fig 2.7. The typical curves of Cp versus  for various values of the pitch
angle 
17
13 Fig 2.8. The torque versus speed characteristics of wind turbine (horizontal
axis turbine) 20
14 Fig 3.1. Transformation of a-b-c to ds-qs axes 24
15 Fig 3.2. Transformation of stationary ds-qs axes to synchronously rotating
frame d-q axes 25
16 Fig 3.3. Dynamic d-q equivalent circuit of DFIG (q-axis circuit) 26
17 Fig 3.4. Dynamic d-q equivalent circuit of DFIG (d-axis circuit) 27
18 Fig 3.5. Implementation of vector control principle 33
19 Fig 3.6. Overall DFIG System 34
20 Fig 3.7. Schematic diagram of Grid side Converter 36
21 Fig 3.8. Vector control structure for Grid side Converter 37
22 Fig 3.9. Vector control structure for Machine side Converter 39
23 Fig 3.10. Vector diagram showing stator and rotor current components of
DFIG in voltage oriented co-ordinate 39
24 Fig.5.1. Simulated SSCI Event: Wind Plant Point of Interconnection Real Power, Reactive
Power, and RMS Voltage (8% series compensation) 50
25 Fig.5.2.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls
53
26 Fig.5.2.1. Revised Controls including SSCI Damping Controller and changes in Rotor Side
Current Feedback Control Loop 53
27 Fig.5.3. Simulated SSCI Event After Controller Changes: Wind Plant Point of
interconnection Real Power, Reactive power, and Rms Voltage (50% series compensation) 55
28 Fig.5.4. Example of a blocking filter in parallel with series capacitor 56
29 Fig.5.5.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls) Using
a MATLAB Platform 58
v

30 Fig.5.5.1.Simulated SSCI Event When there is no SSCI damping controller: Wind Plant
Point interconnection Real Power, Reactive power, and RMS Voltage 58
31 Fig.5.6. Revised Controls including SSCI Damping Controller and changes in Rotor Side
Current Feedback Control Loop Using a MATLAB Platform 59
32 Fig.5.6.1. Simulated SSCI Event After Controller Changes: Wind Plant Point of
interconnection Real Power, Reactive power, and RMS Voltage 59
33 Fig 6.1. Fuzzy contorl system 62
34 Fig 6.1.1 Equivalent Fuzzy model architecture with two inputs and one
output 63
35 Fig6.1.2 Normalized triangular membership functions used in Fuzzification. 64
36 Fig 6.2.1 Fuzzy interface system editor 66
37 Fig 6.2.2 FIS with input membership function editor 66
38 Fig 6.2.3 FIS with output membership function editor 66
39 Fig 6.2.4 FIS with rule editor 66
40 Fig 6.2.5 Rule viewer individual 66
41 Fig 6.2.6 Surface viewer of all the rules combined 66
42 Fig.6.2.8. Revised Controls including SSCI Damping Controller and changes in Rotor Side
Current Feedback Control Loop Using a MATLAB Platform when Fuzzy logic controller
is introduced.
68
43 Fig.6.2.9. Simulated SSCI Event After Controller Changes: Wind Plant Point of
interconnection Real Power, Reactive power, and RMS Voltage when fuzzy logic
controller is introduced
68

NOMENCLATURE
Pair Power contained in wind
ρ The air density
A The swept area
V The wind velocity without rotor interference
Cp Power coefficient
  Tip speed ratio
ω Rotational speed of rotor
R The radius of the swept area
d-q Synchronously rotating reference frame direct and quadrature
axes
ds-qs Stationary reference frame direct and quadrature axes (or -
axes)
ds-axis stator voltage
qs-axis stator voltage
ds-axis rotor voltage
qs-axis rotor voltage
d-axis stator voltage
q-axis stator voltage
d-axis rotor voltage
q-axis rotor voltage
B Damping constant
J Rotor inertia
TL Load torque
Te Electromagnetic torque
P Number of poles
Lm Magnetizing inductance
Lr Rotor inductance
Ls Stator inductance
Llr Rotor leakage inductance
Lls Stator leakage inductance
f Supply frequency
b Angular frequency
m Rotor mechanical speed
r Rotor electrical speed
e Synchronous speed
Rr Rotor resistance with respect to stator.
Rs Stator resistance
θ Angle of stationary reference frame
θe Angle of synchronously rotating frame
 qr q-axis rotor flux linkage
 dr d-axis rotor flux linkage
 qs q-axis stator flux linkage

 ds d-axis stator flux linkage
i dr d-axis rotor current
i qr q-axis rotor current
Xm Magnetizing reactance
Xr Rotor reactance
Xs Stator reactance
Xlr Rotor leakage reactance
Xls Stator leakage reactance
Pcus Stator copper loss
Pcur Rotor copper loss
m2 Modulation index of machine side converter
m1 Modulation index of supply side converter
vdc DC-link voltage
C DC-link capacitance
L Line inductance
R Line resistance
iq q-axis grid current
id d-axis grid current
vq q-axis grid voltage
vd d-axis grid voltage
Qs Reactive power in the grid
Ps Active power in the grid
ds-axis stator current
qs-axis stator current
ds-axis rotor current
qs-axis rotor current
i ds d-axis stator current
i qs q-axis stator current

ABSTRACT
This project gives the overview of the Sub-Synchronous control interaction (SSCI)
phenomenon. The most recent project experience and studies have shown that Type 3 wind
turbine generators with power electronic converters and controls that operate near the series
compensated transmission lines are susceptible to un-damped sub-synchronous oscillations.
The project simulated on the MATLAB platform using a Type 3 wind turbine model
are used to demonstrate SSCI, the design of an SSCI damping controller is presented to mitigate
the problems that arise during the process.

Chapter 1 Introduction
1
CHAPTER-1
INTRODUCTION
1.1. Theme of thesis 5
1.2. Background Literature survey 6
1.3. Thesis Layout 8
1.4. Conclusions 8

2
CHAPTER 1
Introduction
Conservation of non-renewable resources motivate to explore the new avenues of
resources for electricity generation which could be clean, safe and most valuable to serve
the society for a long period. The option came with huge number of hands up a source
which is part of our natural environment and eco friendly is the Renewable Energy Sources.
These sources can be better replacement of the polluted non-renewable sources in order to
meet the growing demand for power due to rapidly growing economy and expanding
population.
As per World Energy Outlook (WEO)-2010 the prospects for renewable energy based
electricity generation hinge critically on government policies to encourage their
development. Worldwide, the share of renewables in electricity supply increases from 19%
in 2008 to 32% in 2035 in the New Policies Scenario; it reaches only 23% in the Current
Policies Scenario, but 45% in the 450 Scenario. In all three scenarios, rising fossil-fuel
prices and declining costs make renewables more competitive with conventional
technologies. Hydropower has been the dominant renewable source of electricity for over a
century. The recent strong growth in new technologies for wind power and solar photo
voltaic (PV) has created expectations among policy makers and the industry alike that these
technologies will make a major contribution to meet growing electricity needs in the near
future. It has also been forecasted that the increase in electricity generation from renewable
sources between 2008 and 2035 will be primarily derived from wind and hydro power,
which will contribute 36% and 31% of the additional demand respectively.
Wind power is projected to supply 8% of global electricity in 2035 up from just 1% in
2008. In the year 2010 the wind capacity has reached 196.630GW worldwide and it had
reached 240GW by the end of 2011 as shown in Fig 1.1.
In order to address the problem of rapidly growing demand for power, India has also
taken its step forward along with other countries. Total power generation capacity is
reached to173626.40MW. Out of the total capacity India’s installed wind power generation
capacity stood at about 13065MW as of March 2011.

3
powercapacity[GW]
Total Installed wind Capacity (MW) in world
300000
250000
200000
150000
100000
50000 24322 31181 32295
47693
59024
74122
93927
240000
196630
159766
120903
0
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Fig 1.1. Statistical data of total installed wind capacity in world
Since the 2003 Electricity Act, the wind sector of India has registered a compound
annual growth rate of about 29.5%. The growth rate of wind power in global market is
forecasted for five years by Global Wind Energy Council (GWEC) and the report is
published in the Global wind report 2010[3]. The forecasting data is shown in Fig1.2.
Focusing on wind market penetration in to the global market, an investigation made on
share of the most commonly applied wind turbine concept over the years. The large
increasing electrical penetration of large wind turbines in to EPS is inspiring designers to
develop generators along with power electronics converters and the modern control system
Strategies.
500
450
400
350
22.5 21.4
15.9
19.5
18
25
20
16.7 15.6 15
300
250
11.1 10 9.7 8.8
10
448.8 5200
150
100 194.4
235.9
282
332.7
388.3
0
-5
50 35.8 -7
0
41.5 46.1 50.7 55.6 60.5
-10
2010 2011 2012 2013 2014 2015
Year
Annual capacity [GW] Cumulative capacity [GW]
Annual capacity growth rate [%] Cumulative capacity growth rate [%]
Fig 1.2. Growth rate of wind power in Global market

4
shareofcumulatedinstalled
power
in%
The most commonly applied wind turbine designs in the industry today can be
categorized into four wind turbine concepts (Type A, B, C, D) (to be discussed in Chapter
2). There is an obvious trend towards the configuration using a DFIG (Type C) with
variable speed and variable pitch control as per the statistical data shown in Fig 1.3.
100
90
80
70
60
50
40
30
20
10
0
1995 1997 1999 2001 2003 2005 2007 2009 2011
Year
Type A
Type B
Type C
Type D
Fig 1.3. World share of cumulative installed wind power for different wind turbine concept
(Approximate data)
Internet survey says that the top wind turbine manufacturing companies like Vestas
(Denmark), Gamesa (Spain), Nordex (Germany) etc. are employing mostly Type C & D
turbines in their recent products. For example Vestas and Gamesa have added V90-3.0MW
offshore (DFIG) & V164-7.0MW offshore (PMSG), G10X- 4.5MW (PMSG) & G9X-
2.0MW (DFIG) respectively to the growing wind market recently. Fig 1.4 shows a
schematic diagram of wind energy system. The picture shows the flow of energy from the
generation end to the consumer end.
Transformer Substations
House
Wind Turbines
The wind turns the blades,
which spin a shaft, which
connects to a generator and
makes electricity
Electricity Grid
The high-voltage transmission systems carry
electricity from the power plants and transmit it
hundreds of miles away, and the lower-voltage
distribution systems draw electricity from the
transmission lines and distribute it to individual
customers
Fig 1.4. The overall view of wind energy system

5
1.1.Theme of Thesis
The successful entry of DFIG based wind turbine into the competitive wind market
stimulates to study the performance of the overall DFIG system under different operating
and critical conditions. The DFIG system consists of a Wound Rotor Induction Generator
(WRIG) with the stator windings directly connected to the constant frequency three-phase
grid and with the rotor windings connected to grid through a bidirectional back-to-back
IGBT based voltage source converter.
This system allows a variable speed operation over a large range. The converter
compensates the difference between the mechanical angular frequency and grid frequency
by injecting a rotor current with a variable frequency. Both during normal operation and
faults the behaviour of the generator is thus governed by the power converter and its
controllers. The power converter consists of two converters, the machine-side converter and
grid-side converter, which are controlled independently of each other. The main idea behind
the total system (DFIG with back-to-back converters)(to be discussed in Chapter 3) is that
the machine-side converter controls the active and reactive power by controlling the rotor
current components, while the grid-side converter controls the dc-link voltage and ensures
the operation at unity power factor (i.e. Zero reactive power). By means of a
bidirectional converter in the rotor circuit the DFIG is able to work as a generator in both
sub-synchronous and super-synchronous modes.
Depending upon the operating condition of the drive, power is fed into or out of the
rotor (which is the case of super synchronous mode), then it flows from the rotor via the
converter to the grid. Where as in sub-synchronous mode it flows in opposite direction as
shown in Fig 1.5. In both modes the stator feeds energy in to utility grid.
Fig 1.5.The Power flow diagram of DFIG
(Sub-synchronous (left) & super-synchronous (right) generating mode)

6
The DFIG based wind turbine is used under study because of its obvious advantages.
1. It has the ability to control reactive power and to decouple active and reactive
power control by independently controlling the rotor excitation current.
2. The DFIG has not necessarily to be magnetized from the power grid; it can
be magnetized from the rotor circuit, too. It is also capable of generating reactive
power that can be delivered to the stator by the grid-side converter. However, the
grid-side converter normally operates at unity power factor and is not involved in
the reactive power exchange between the turbine and the grid.
3. In the case of a weak grid, where the voltage may fluctuate, the DFIG may be
ordered to produce or absorb an amount of reactive power to or from the grid, with
the purpose of voltage control.
a. The main objective of this thesis is the performance analysis of the DFIG for a
wind turbine application both during steady state operation and transient operation
(during the case of SSCI). The transient conditions for which the system is
analysed are given below,
i. Sudden change of reactive power demand by the machine
ii. Sudden change of supply frequency in the utility grid.
In order to analyse the overall DFIG system during steady state and transient state
operation both the modelling and controlling of the system are important issues. Hence the
control and modelling (to be discussed detail in Chapter 3) are also the part of this thesis
work. As a part of the thesis work the overall system is simulated using MATLAB
environment. In simulation work the system is modelled using different state equations and
the controlled PWM pulses for grid side as well as machine side converters are found using
PI controller using MATLAB.
1.2.Background Literature survey
The obvious adoptability led the people to study on the DFIG based wind turbine.
Though the basic features are explained in many literatures and text books, some of the
specific issues and the remedial actions taken by the researcher are highlighted in this
survey.
The energy of the wind is used for more than thousand years. The first history proven
usage has been around the year 650 in Tibet for religious aims. These early models are
vertical axis wind turbines based on the principle of scoop drag-type devices which are
today used only in anemometers. At the beginning of the second millennium horizontal axis

7
Wind mills became popular mainly in southern Europe and the Netherlands for pumping
water.
The first production of electrical energy with wind power was done in 1887 by Charles
Brush in Cleveland, Ohio. The rated Power of the used dc-generator was 12kW and was
designed to charge batteries. The induction machine was used for the first time in 1951. The
development of the induction machine in wind power technology from a squirrel cage
machine to a Doubly-fed Induction Machine (DFIM) shows the tremendous potential of this
kind of electrical generator. The first wind turbines with squirrel cage machine were built in
the late 1980s with a rated power of less than 100kW. The state of the art wind turbines with
doubly fed induction machine have a rated power up to 3.0MW. Theses turbines are
constructed for a very high efficiency, performance and very low maintenance in order to go
offshore with the next generation of wind turbines.
DFIM using an AC-AC converter in the rotor circuit (Schrebius drive) has long been a
standard drive option for high power applications involving a limited speed range. The
power converters only handle the rotor power. In 1980 Leonhard explains the vector control
technique used for the independent control of torque and excitation current. The
converter design, and control technique are well explained in. Following Jones and Jones
have shown the technique to decouple active and reactive power drawn from the utility grid.
Pena, Clare and Asher gave the detail design of DFIG using back-to-back PWM voltage
source converters in the rotor circuit and also they have validated the system experimentally
considering a grid connected system and stand-alone system. The option using current fed
DC-link converter with DFIG system is analysed. Since the DFIG system used under the
study is grid connected, it has to satisfy the grid code requirements such as grid stability,
fault ride through, power quality improvement, grid synchronization and ease of power
control. To solve the issues related to utility grid, the grid side converter plays a vital role in
taking the grid issues as key factor, and the control technique is adopted to solve the very
cause. Wu, Dewan and Slemon use the traditional voltage oriented control in grid side
converter to study the cause effect analysis under balanced three phase grid. Besides the
voltage oriented control, another controller called Linear Quadratic (LQ) controller is
synthesized to improve the fault ride through capability as well as the performance of the
generator under unbalance grid voltage . Nasiri and Abdel-Baqi used a series converter on
the stator terminal to mitigate the effect of the short circuit on the wind turbine.

8
1.3.Thesis Layout
Following the chapter on Introduction, the rest of the thesis is delineated as follows.
Chapter 2 Provides the fundamental concepts of wind electricity generation along with
different types of turbines used for the generation such as Type A, B, C, D. It also derives
the mathematical expression used for the maximum mechanical power extracted from the
wind. The characteristic curves to illustrate the relation between torque-speed, power-speed
are also the part of this chapter.
Chapter 3 Explains the modelling of the overall DFIG system in detail and also
focuses on the control techniques used for the grid side as well as machine side converter. In
this chapter the detail explanation is made using block diagrams and different algebraic
equations.
Chapter 4 This chapter deals with the Software MATLAB. The project has done in this
software platform and detailed overview of this software and the blocks that I have used in
the simulation were explained briefly.
Chapter 5 This chapter describes the Type 3 Wind Turbine and its parameters and
finally how the SSCI damping controller was developed and results were simulated
respectively. Conclusions were drawn.
Chapter 6 This chapter deals with the combination of PI controller and
Fuzzy controller which are used to damp out the SSCI concerns. Results were
simulated respectively and were drawn.
Chapter 7 Conclusions and Recommendation are given in this chapter
1.4. Conclusions
In this chapter a brief Introduction is given to the Wind Turbines, and how
they are in progress. Layout of my thesis is briefly presented.

Chapter 2 Wind Turbine Systems
9
CHAPTER-2
WIND TURBINE SYSTEMS
2.2. Wind Turbines 10
2.3. Wind Turbine Topologies 12
2.3.1. Fixed speed wind turbine (Type A) 12
2.3.2. Variable speed wind turbine 13
2.3.2.1. Type B wind turbine 14
2.3.2.2. Type C wind turbine 15
2.3.2.3. Type D wind turbine 16
2.4. Typical characteristics of the wind turbine 16
2.4.1. Power versus speed Characteristics 16
2.4.2. Power coefficient versus TSR Characteristics 17
2.4.3. Torque versus speed Characteristics 20
2.5. Conclusions 21

10
CHAPTER 2
Wind Turbine Systems
2.1.Introduction
Now-a-days global warming is the most burning issue found in many of the climate
summit. Many researchers, scientists are working their own relevant areas to reduce the
effect due to global warming by using different techniques. Effective mitigation of climate
change will require deep reductions in greenhouse gas emissions. The electricity system is
viewed as being easier to transfer to low-carbon energy sources than more challenging
sectors of the economy such as surface and air transport and domestic heating. Hence the
use of cost-effective and reliable low carbon electricity generation sources is becoming an
important objective of energy policy in many countries. This is only possible by utilizing
renewable sources as the key sources for the generation of electricity. The total statistical
survey of renewable energy sources is highlighted briefly in chapter 1. The survey conveys
that, over the past few decades wind energy has shown the fastest rate of growth of any
form of electricity generation with its development stimulated by concerns of national
policy makers over climate change, energy diversity and security of supply. This chapter
discusses detail about the wind energy system. Basically this chapter explains about
different types of wind turbine used to achieve fastest growth in the world market. The basic
concepts of the turbines, maximum power extractable from wind, characteristics of wind
turbine are also the part of this chapter. A layman’s concept states that wind energy system
means it is the combination of turbines, generators, the mediator power electronic
converters and the brain called controller. The technical aspects of generators and other
devices except turbines will be the part of next chapter.
2.2. Wind turbines
Wind turbines produce electricity by using the power of the wind to drive an electrical
generator. Wind passes over the blades, generating lift and exerting a turning force. The
rotating blades turn a shaft inside the nacelle, which goes into a gearbox. The gearbox
increases the rotational speed to that which is appropriate for the generator, which uses
magnetic fields to convert the rotational energy into electrical energy. The power output
goes to a transformer, which converts the electricity from the generator at around 700V.

11
The appropriate voltage for the power collection system, typically 33 kV. A wind turbine
extracts kinetic energy from the swept area of the blades (Fig 2.1).
FREE WIND
Fig 2.1.Horizontal axis turbine
The power contained in the wind is given by the kinetic energy of the flowing air mass
per unit time [25]. That is
  2
1 / 2 ( )airP airmassperunittime windvelocity
2
1/ 2( AV )( )V   (2.1)
3
1/ 2* AV 
Where Pair is the power contained in wind (in watts) , ρ is the air density (1.225
kg/m3
at 15°C and normal pressure), A is the swept area in (square meter), and 
is the wind velocity without rotor interference, i.e., ideally at infinite distance from the
rotor (in meter per second).
Although Eq. (2.1) gives the power available in the wind, the power transferred to the
wind turbine rotor is reduced by the power coefficient, Cp
Windturbine
p
air
P
C
P
 (2.2)
3
* 1/ 2*Windturbine p air pP C P C AV   (2.3)
A maximum value of Cp is defined by the Betz limit, which states that a turbine can
never extract more than 59.3% of the power from an air stream. In reality, wind turbine

12
Rotors have maximum Cp values in the range 25-45%. It is also conventional to define a tip
Speed ratio as
(2.4)
Where is rotational speed of rotor (in rpm), R is the radius of the swept area (in
meter).The tip speed ratio and the power coefficient CP are the dimensionless and so can
be used to describe the performance of any size of wind turbine rotor.
2.3.Wind turbine Topologies
There are a large number of choices of topologies available to the designer of a wind
turbine and, over the years, most of these have been explored. However, commercial
designs for electricity generation have now converged to horizontal axis, three-bladed,
upwind turbines. The largest machines tend to operate at variable speed whereas smaller,
simpler turbines are of fixed speed. For a fixed-speed system the turbulence of the wind will
result in power variations, and thus affect the power quality of the grid where as in a
variable-speed wind turbine the generator is controlled by power electronic equipment,
which makes it possible to control the rotor speed. In this way the power fluctuations caused
by wind variations can be more or less absorbed by changing the rotor speed and thus power
variations originating from the wind conversion and the drive train can be reduced. Hence,
the power quality impact caused by the wind turbine can be improved compared to a fixed-
speed turbine.
Modern electricity generating wind turbines now use three-bladed upwind rotors,
although two bladed, and even one-bladed, rotors were used in earlier commercial turbines.
Reducing the number of blades means that the rotor has to operate at a higher rotational
speed in order to extract the wind energy passing through the rotor disk. Although a high
rotor speed is attractive in that it reduces the gearbox ratio required, a high blade tip speed
leads to increased aerodynamic noise and increased blade drag losses. Most importantly,
three-bladed rotors are visually more pleasing than other designs and so these are now
always used on large electricity generating turbines.
2.3.1. Fixed speed wind turbine (Type A)
This type of turbines are also called Type A turbine. Fixed-speed wind turbines are
electrically fairly simple devices consisting of an aerodynamic rotor driving a low-speed
shaft, a gearbox, a high-speed shaft and an induction (sometimes known as asynchronous)

13
generator. From the electrical system viewpoint they are perhaps best considered as large
fan drives with torque applied to the low-speed shaft from the wind flow. Fig 2.2 illustrates
the configuration of a fixed-speed wind turbine. It consists of a squirrel-cage induction
generator coupled to the power system through a turbine transformer. The generator
operating slip changes slightly as the operating power level changes and the rotational speed
is therefore not entirely constant. However, because the operating slip variation is generally
less than 1%, this type of wind generation is normally referred to as fixed speed.
Squirrel-cage induction machines consume reactive power and so it is conventional to
provide power factor correction capacitors at each wind turbine. The function of the soft-
starter unit is to build up the magnetic flux slowly and so minimize transient currents during
energization of the generator. Also, by applying the network voltage slowly to the
generator, once energized, it brings the drive train slowly to its operating rotational speed.
Fig 2.2.Schematic diagram of a fixed speed wind turbine
2.3.2.Variable speed wind turbine
During the past few years the variable-speed wind turbine has become the dominant
type among the installed wind turbines. Variable-speed wind turbines are designed to
achieve maximum aerodynamic efficiency over a wide range of wind speeds. With a
variable-speed operation it has become possible continuously to adapt (accelerate or
decelerate) the rotational speed ω of the wind turbine to the wind speed .. This way,
the tip speed ratio is kept constant at a predefined value that corresponds to the maximum
power coefficient. Contrary to a fixed-speed system, a variable-speed system keeps the
generator torque fairly constant and the variations in wind are absorbed by changes in the

14
generator speed. The electrical system of a variable-speed wind turbine is more complicated
than that of a fixed-speed wind turbine. It is typically equipped with an induction or
synchronous generator and connected to the grid through a power converter. The power
converter controls the generator speed; that is, the power fluctuations caused by wind
variations are absorbed mainly by changes in the rotor generator speed and consequently in
the wind turbine rotor speed. The advantages of variable-speed wind turbines are an
increased energy capture, improved power quality and reduced mechanical stress on the
wind turbine. The disadvantages are losses in power electronics, the use of more
components and the increased cost of equipment because of the power electronics. The
introduction of variable-speed wind-turbine types increases the number of applicable
generator types and also introduces several degrees of freedom in the combination of
generator type and power converter type .
Most common variable speed wind turbine configurations are as follows.
1. Limited variable speed(Type B)
2. Variable speed with partial scale frequency converter (Type C)
3. Variable speed with full scale frequency converter (Type D)
2.3.2.1. Type B wind turbine
Fig 2.3.Schematic diagram of Type B wind turbine
This configuration corresponds to the limited variable speed wind turbine with variable
generator rotor resistance. It uses a wound rotor induction generator (WRIG) and has been
used by the Danish manufacturer Vestas since mid-nineties. The generator is directly

15
connected to the grid. A capacitor bank performs the reactive power compensation. A
smoother grid connection is achieved by using a soft-starter. The unique feature of this
concept is that it has a variable additional rotor resistance, which can be changed by an
optically controlled converter mounted on the rotor shaft. Thus, the total rotor resistance is
controllable. This optical coupling eliminates the need for costly slip rings that need brushes
and maintenance.
The rotor resistance can be changed and thus controls the slip. This way, the power
output in the system is controlled. The range of the dynamic speed control depends on the
size of the variable rotor resistance. Typically, the speed range is 0 to10% above
synchronous speed. The energy coming from the external power conversion unit is dumped
as heat loss. Wallace and Oliver (1998) describe an alternative concept using passive
components instead of a power electronic converter. This concept achieves a 10% slip, but
it does not support a controllable slip. Fig 2.3 shows the schematic diagram of type B wind
turbine.
2.3.2.2. Type C wind turbine
Fig 2.4.Schematic diagram of Type C wind turbine
This configuration, known as DFIG based wind turbine, corresponds to the limited
variable speed wind turbine with a WRIG and partial scale frequency converter (rated at
approximately 30% of nominal generator power) on the rotor circuit. The partial scale
frequency converter performs the reactive power compensation and the smoother grid
connection. It has a wider range of dynamic speed control compared with that of Type B
wind turbine, depending on the size of the frequency converter. Typically, the speed range

16
comprises synchronous speed -40% to +30 %. The smaller frequency converter makes this
concept attractive from an economical point of view. Its main drawbacks are the use of slip
rings and protection in the case of grid faults. The schematic diagram is shown in Fig 2.4.
2.3.2.3. Type D wind turbine
This configuration corresponds to the full variable speed wind turbine, with the
generator connected to the grid through a full-scale frequency converter. The frequency
converter performs the reactive power compensation and the smoother grid connection. The
generator can be excited electrically (WRSG/WRIG) or by a permanent magnet (PMSG).
Some full variable-speed wind turbine systems have no gearbox. In these cases, a direct
driven multi pole generator with a large diameter is used. The wind turbine companies
Enercon, Made and Lagerwey are examples of manufacturers using this configuration. The
schematic configuration is shown in Fig 2.5.
Fig 2.5.Schematic diagram of Type D wind turbine
2.4.Typical characteristics of wind turbines
The following characteristic curves are plotted to explain the behaviour of wind
turbine at different wind speeds [25].
2.4.1. Power versus speed Characteristics
The wind turbine power curves shown in Fig 2.6 illustrate how the mechanical power can be
extracted from the wind depends on the rotor speed. For each wind speed there is an optimum
turbine speed at which the extracted wind power at the shaft reaches its maximum.

17
Fig 2.6.The typical power versus speed characteristics of a wind turbine
2.4.2. Power coefficient versus TSR Characteristics
For a given wind turbine the power coefficient depends not only on TSR but also on the
blade pitch angle. Fig 2.7 shows the typical variation of the power coefficient with respect
to TSR (lambda) with blade pitch control.
Fig 2.7.The typical curves of Cp versus for various values of the pitch angle

For a wind turbine with radius R Eq. 2.3 can be expressed as
2 3
1/ 2m pP C R V   (2.5)
For a given wind speed the power extracted from the wind is maximized if Cp is
maximized. Always there is a optimum value of TSR for a optimum value of Cp (Cp-
optimum). This means for varying wind speed the rotor speed should be adjusted
proportionally to follow to the optimum value of TSR (λoptimum) for maximum mechanical
power output from the turbine.

20
Using Eq. 2.4 the maximum value of shaft mechanical power for any wind speed can
be expressed as
5
3 3
max 1/ 2 (R / )optimump optimum
P C   
 (2.6)
Thus the maximum mechanical power that can be extracted from wind is proportional
to the cube of the rotor speed, i.e., 3
maxP 
2.4.3. Torque versus speed characteristics
The typical torque versus speed characteristics of horizontal axis (two blade
propeller type) Wind turbine is shown in the Fig 2.8.
Fig 2.8.The torque versus speed characteristics of wind turbine(horizontal axis turbine)
The curves shown in Fig 2.8 follow the power curve shown in Fig 2.6 because there is a
direct relationship exists between power and torque. The relation is given in Eq. 2.7.
(2.7)
Using the optimum values of Cp & λ, from Eq. 2.6 and 2.7 the maximum value
of aerodynamic torque can be expressed as
2
5
max 3
1
2 p optimum
optimum
R
T C  

 
  
  
(2.8)
The curve in Fig 2.8 shows that for any wind speed the torque reaches a maximum
value at a specific rotational speed, and this maximum torque varies approximately as the
square of rotational speed. In the case of electricity production the load torque depends on

21
the electrical loading. The torque can be made to vary as the square of the rotational speed
by choosing the load properly.
2.5.Conclusions
This chapter explains different types of wind turbine briefly. The important
mechanical characteristics as power versus speed characteristics, CP versus  and torque
versus speed characteristics which will be required for the subsequent chapters are also
explained here using different mathematical expressions.

Chapter 3 DFIG System
22
CHAPTER - 3
DFIG SYSTEM
3.2. Vector or Field Oriented Control Theory 23
3.2.1. D-Q Theory 23
3.2.1.1. Transformation of three phase stationary to two phase stationary
Axes. 24
3.2.1.2. Transformation of two phase stationary to two phase
Synchronously rotating axes. 25
3.2.2. Mathematical modelling of Induction Generator 26
3.2.2.1. Modelling of DFIG in synchronously rotating frame 26
3.2.2.2. Dynamic modelling of DFIG in state space equations 28
3.2.3. Principle of Vector control 32
3.3. DFIG System 34
3.3.1. Double-fed Induction Generator 34
3.3.2. Voltage source converter 33
3.3.3. Grid side converter control 36
3.3.4. Machine side converter control 38
3.4. Conclusions 42

23
CHAPTER 3
DFIG System
3.1.Introduction
The most common machine which is widely used in these days is Doubly-fed Induction
Machine. These types of machines can be used resolutely as a generator or motor. Though
demand in the direction of motor is less because of its mechanical wear at the slip rings but
they have gained their prominence for generator application in wind and water power plant
because of its obvious adoptability capacity and nature of tractability. In this section detail
analysis of overall DFIG system along with back to back PWM voltage source converters
has been made. Prior to the analysis of DFIG a brief enquiry on vector control theory is also
included in this chapter.
3.2.Vector or Field Oriented control Theory
The overall control strategy of the machine is divided in two ways, one is scalar control
and the other is vector control. The limitations of scalar control give an importance to vector
control. Though the scalar control strategy is simple to implement but the inherent coupling
effect gives sluggish response. The inherent problem is being solved by the vector control.
The vector control is invented in the beginning of 1970s. Using this control strategy an IM
can be performed like dc machine. Because of dc machine like performance vector control
is also known as decoupling, orthogonal or Trans vector control.
The basic of the vector control theory is d-q theory. To understand vector control
theory knowledge about d-q theory is necessary.
3.2.1. D-Q theory
The d-q theory is also known as reference frame theory. The history says in 1920 R. H.
Park proposed a new theory to overcome the problem of time varying parameters with the
ac machines. He formulated a change of variables which in effect replace the variables
associated with the stator windings of a synchronous machine with variables associated with
fictitious winding rotating with the rotor at synchronous speed. Essentially he transformed
the stator variables to a synchronously rotating reference frame fixed in the rotor. With such
transformation (Park’s transformation) he showed that all the time varying inductances that

24
ds qs
v
s
qs
 
occur due to an electric circuit in relative motion and electric circuit with varying magnetic
reluctances can be eliminated. Later in 1930s H. C. Stanley showed that time varying
parameters can be eliminated by transforming the rotor variables to the variables associated
with fictitious stationary windings. In this case the rotor variables are transformed to the
stationary reference frame fixed on the stator. Later G. Kron proposed a transformation of
both stator and rotor variables to a synchronously rotating reference frame that moves with
the rotating magnetic field. Latter, Krause and Thomas shown that the time varying
inductances can be eliminated by referring the stator and rotor variables to an arbitrary
reference frame which may rotate at any speed.
3.2.1.1. Transformation of three phase stationary to two phase stationary axes
Consider a symmetrical three phase induction machine with stationary a-phase, b-
phase and c-phase axes are placed at 120° angle to each other as shown in Fig 3.1. The main
aim is to transform the three phase stationary frame variables into two phase stationary
frame variables (ds
-qs
) and then transform these to synchronously rotating reference frame
variables (d-q), and vice versa.
Fig 3.1.Transformation of a-b-c to ds
-qs
axes
Let ds
-qs
axes are oriented at an angle θ from a-b-c axes as shown in Fig 3.1. The
voltage (v s
and v s
) can be resolved into a-b-c components and can be represented in the
matrix form as
va  
  

cosθ
ο
sinθ
ο
1 s 
 s 

v b   cosθ  120  sinθ  120  1vds  (3.1)
vc cosθ  120ο  sinθ  120ο  1 
v0s



25
s vmsin(θe φ)
s
vqs  vmsinφ
v 
v ds
vs  vmcos
qs
v
v 
 v e
 v e
qs
v
qs
qs


The corresponding inverse relation is
s cosθ cosθ 120ο  cosθ 120ο v 
 s  2 

ο ο  a 

vds  
3 sinθ sinθ 120  sinθ 120 v
b  (3.2)
 s 
 0s 
 0.5
s
0.5 0.5 


c 
Where v0s is added as the zero sequence component. Other parameters like current,
flux linkages can be transformed by similar manner. It is more convenient to set θ=0°, so
that q-axis is aligned with the a-axis in this case (The alignment of the axes are optional, d-
axis can also be aligned with a-axis). The sine components of d and q parameters will be
replaced with cosine values, and vice versa if d-axis coincides with a-axis.
3.2.1.2.Transformation of two phase stationary to two phase synchronously rotating
axes
v
d vmsinφ
(θe φ)
Fig 3.2.Transformation of stationary ds
-qs
axes to synchronously rotating frame d-q axes
Fig 3.2 shows the synchronously rotating d-q axes which rotate at synchronous speed
e with respect to ds
-qs
axes. The two phase windings are transformed into the fictitious
windings mounted on the d-q axes.
The voltages on the ds
-qs
axes can be converted into d-q axes as follows;
vqs
s cos   vs
ds
sin e (3.3)
v
ds
s sin   vs
ds
cos e (3.4)

26
s r m
Again resolving the rotating frame parameters into a stationary frame the relations are
svqs
vs
ds
 v
qs
cos e  v
ds
sin e
 v
qs
sin e  v
ds
cos e
(3.5)
(3.6)
3.2.2. Mathematical modelling of Induction Generator
In this section the basic mathematical modelling of DFIG is explained in detail.
From the previous section we confirm that the three phase parameters can be represent
in two phase parameters and vice versa using certain fundamental rules. In this section the
machine modelling is explained by taking two phase parameters into consideration. Though
the basic concepts behind the DFIG system is explained briefly in Chapter 1, in short we
can say the DFIG is a wound rotor type induction machine its stator consists of stator frame,
stator core, poly phase (3-phase) distributed winding, two end covers, bearing etc. The
stator core is stack of cylindrical steel laminations which are slotted along their inner
periphery for housing the 3-phase winding. Its rotor consists of slots in the outer periphery
to house the windings like stator. The machine works on the principle of Electromagnetic
Induction and the energy transfer takes place by means of transfer action. So the machine
can represent as a transformer but rotatory not stationary.
3.2.2.1. Modelling of DFIG in synchronously rotating frame
The equivalent circuit diagram of an induction machine is shown in Fig 3.3 and 3.4. In
this figure the machine is represented as two phase machine, it has already been discussed
before that a three phase machine can be represent as two phase machine obeying certain
rules. For the modelling of DFIG in synchronously rotating frame we need to represent the
two phase stator (ds
- qs
) and rotor (dr
-qr
) circuit variables in a synchronously rotating (d-q)
Frame.
L  L
ls
 Lm L  L L
lr
     

e ds ( e r )
dr
Fig 3.3.Dynamic d-q equivalent circuit of DFIG (q-axis circuit)

27
s r mL  L
ls
Lm L  L L
lr
eqs (e r)qr
Fig 3.4.Dynamic d-q equivalent circuit of DFIG (d-axis circuit)
The stator circuit equations are given below,
s s d svqs  Rsiqs 
dt
qs (3.7)
s s d sv
ds
 Rsi
ds

dt

ds
s s
(3.8)
Where qsand 
ds
are q-axis and d-axis stator flux linkages, respectively. Converting
Eq. (3.7) and (3.8) to d-q frame the following equations can be written as
d
v
qs
 Rsi
qs

dt

qs
 (
e

ds
)
d
v
ds
 Rsi
ds

dt

ds
 (
e

qs
)
(3.9)
(3.10)
Where all the variables are in synchronously rotating frame. The bracketed terms are
defined as the back e.m.f. or speed e.m.f or counter e.m.f. due to the rotation of axes as in
the case of DC machines. When the angular speed e is zero the speed e.m.f due to d and q
axis is zero and the equations changes to stationary form.
Owing to the rotor circuit, if the rotor is blocked or not moving, i.e. r=0, the machine
equations can be written in similar way as stator equations:
d
v
qr
 Rri
qr

dt

qr
 (
e

dr
)
d
v
dr
 Rri
dr

dt

dr
 (
e

qr
)
(3.11)
(3.12)
Where all the parameters are referred to the primary circuit, which is stator in this case.
Let the rotor rotates at an angular speed r, then the d-q axes fixed on the rotor fictitiously
will move at a relative speed e  r to the synchronously rotating frame.

28
The d-q frame rotor equations can be written by replacing
follows:
e  r in place of e as
v
qr
v
dr
 R ri
qr
 R ri
dr

d

dt qr

d

dt dr
 (
e
 
r
)
dr
 (
e
 
r
)
qr
(3.13)
(3.14)
The flux linkage expressions in terms of current can be written from Fig 3.3 and 3.4 as
follows:
qs
ds
qr
dr
 Llsiqs  Lm(iqs  iqr )
 Lsiqs  Lmiqr
 Llsids  Lm(ids  idr )
 Lsids  Lmidr
 Llriqr  Lm(iqs  iqr )
 Lriqr  Lmiqs
 Llridr  Lm(ids  idr )
 Lri
dr
 Lmi
ds
(3.15)
(3.16)
(3.17)
(3.18)
qm  Lm (iqs  iqr )

dm
 Lm (i
ds
 i
dr
)
(3.19)
(3.20)
Eq. (3.7) to (3.20) describes the complete electrical modelling of DFIG. Where as Eq.
(3.21) express the relations of mechanical parameters which are essential part of the
modelling.
The electrical speed r cannot be treated as constant in the above equations. It can be
connected to the torque as
Te  TL  J
dm
dt
 Bm  TL 
2
J
dr
P dt
2
 Br
P
(3.21)
3.2.2.2. Dynamic modelling of DFIG in state space equations
The dynamic modelling in state space form is necessary to carried out simulation using
different tools such as MATLAB. The basic sate space form helps to analyse the system in
transient condition.
The basic definition says, the space whose co-ordinate axes are nothing but the „n‟ state
variables with time as the implicit variable is called the state space. The variables of the

29
e
e





qs

m 
qs

state space (state variables) are involved to determine the state of the dynamic system.
Basically these are the energy storing elements contained in the system. The fundamental
equation of the state space is as follows:
Xt   AXt   BUt

  (3.22)
Yt CXt DUt

Eq. (3.22) is in linear time invariant system, where A, B, C, D are constant matrices and Eq.
(3.23) is for linear time variant system, where A, B, C, D are time dependent matrices.
Xt  AtXt BtUt
  (3.23)
Yt  CtXt DtUt

In the DFIG system the state variables are normally currents, fluxes etc. In the
following section the state space equations for the DFIG in synchronously rotating frame
has been derived with flux linkages as the state variables.
Since the machine and power system parameters are nearly always given in ohms or
percent or per unit of base impedance, it is convenient to express the voltage and flux
linkage equations in terms of reactances rather than inductances. The above stated voltage
and flux equations can be reworked as follows:
v
qs
1
 Rsi
qs


b
d
 
dt qs 
b

ds
(3.24)
vds
1
 Rsids 

b
d 
dt
ds 

b
qs (3.25)
1 d e  r 
vqr  R riqr  qr 
b dt 
dr
b
(3.26)
1 d e  r 
vdr
 R ridr   

b
dt dr 
b
qr (3.27)
Equations related to flux linkage i.e. Eq. (3.15)-(3.20) can be written in terms of
reactances as follows:
qs  Xlsiqs  Xm
i


 i
qr 

(3.28)

ds
 X
ls
i
ds  X i
ds
 i
dr


(3.29)

qr
 Xlriqr  Xm
i


 i
qr 

(3.30)

30


ls

m 


m X



dr
 X
lr
i
dr  X i
ds
 i
dr


(3.31)
qm  Xmiqs  iqr 

(3.32)

dm  Xmids  idr 

(3.33)
Where reactances (Xls, Xlr, Xm) are found by multiplying base frequency b with
inductances (Lls, Llr, Lm).
From Eq. (3.28)-(3.33) we can find the expressions for currents in terms of flux
linkages and also the mutual flux linkages (qm ,dm) are found using current expressions.
The equations are given as follows.
qs  qm
iqs 
X
(3.34)
ls
qr  qm
iqr 
X
(3.35)
lr
ids
idr
  
 ds dm
X
ls
  
 dr dm
Xlr
(3.36)
(3.37)
Substituting Equations (3.34)-(3.37) in (3.32)-(3.33) we get,

qm  Xm 

Xm
qs  qm
Xls
Xm
qr  qm  
  
Xlr  

Xm Xm 
qm 
X
ls
qs 
X
ls
qm  
X
lr
qr 
X
lr
qm 



Xm Xm Xm Xmqm  qm  qm  qs  qr 
Xls
 Xm
Xlr
Xm
 Xm
Xls
Xm
X
lr 


qm
1


X
ls

X
lr

 X
ls
qs  
X
lr
qr 


 X
qm
 lsXlr  XmXlr
 X X 
  m

Xmqs 

qr 

 X
ls
X
ls
X
lr
X
lr
 XmX
lr

 XmX
X
ls
ls
 Xm
X
lr 

Xm 
qmXm


XlsXlrXm

 Xls
qs  
Xlr
qr 







(3.38 contd.)

31

r
r
r 
r

 



qm 
Xm
Xeq

Xm
X
ls
qs 
Xm
Xlr
qr







(3.38)
qm
Xeq
 qs
Xls
Xeq 
 qr 
X
lr 

Similarly we can find the value of dm as follows
dm
Xeq

Xls
ds 

Xeq
X
lr
dr
(3.39)
Substituting the current equations from (3.34)-(3.37) in voltage equations (3.24)-(3.27)
we will get,
vqs 
R s
Xls
R
 qs   qm 
1
b
d qs
dt
d



e
b




 ds
(3.40)
vds 
s

X
ls
ds
1
 
dm


b
ds

e
dt b
 qs (3.41)
R r
 


1 d qr e   
v qr 
X
lr
 qr   qm  
b dt b
 dr (3.42)
R r
 


1 d dr
e   
v dr 
X lr
 dr   dm 
 dt


b b
 qr (3.43)
The state variables can be expressed using the above equations as follows
d qs e R s
 

 b v qs
dt 



 ds
b

X ls
 qs   qm 

(3.44)
d ds e R s
 

dt
 
b v
ds



 qs
b

Xls
 ds
 
dm 

(3.45)
d qr  e    
R r
 
 
b v qr 
dt 
b
 dr 
X lr
 qr   qm 

(3.46)
d dr  e    
R r
 
 
b v
dr

dt 
b
 qr 
X lr
 dr   dm 

(3.47)

32


The state space matrix can be written as follows
 R s  e 
  0 0 
 X ls  b 
  R 
 R s 
 0 
X ls 
 R 
qs  
e

s
0 0  qs  1 0 0 0v qs   0
s


ds
   b X ls  ds
 0 1 0 0v ds
  X ls  qm 
  
 R 

  

   
0 0 1 0

v
   R  
 qr   0
r e
0  
 r  qr    qr   r
0  dm 

dr 



X lr   dr
b 

0 0 0 1 v dr X 
 lr 



0 0

 e   r  R r 


R r 

0

  b X lr   X lr 


(3.48)
The electromotive torque is developed by the interaction of air-gap flux and the rotor
mmf. At synchronous speed the rotor cannot move and as a result there is no question of
induced emf as well as the current, so the torque becomes zero, but at any speed other than
synchronous speed the machine will experience torque which is the case of motor, where as
in case of generator electrical torque in terms of mechanical is provided by means of prime
mover which is wind in this case.
The torque expression can be written in terms of flux linkages and currents as follows
Te 
3 P

2 2 dsiqs  qsids 

3 P
2 2
Lm iqsidr  idsiqr 

(3.49)

3 P

2 2 dr
iqr  qridr


Equation (3.49) can be written in terms of state variables as follows
3 P
Te  1


iqs  qsi 
2 2 
b
ds ds
(3.50)

3 P 1


iqr  qri 
2 2 b
dr dr
Eq. (3.44) - (3.50) describe the complete DFIG model in state space form, where
qs, ds, qr, dr are the state variables.
3.2.3.Principle of Vector Control
The fundamentals of implementation of vector control technique can be explained
using the Fig 3.5. In this figure the machine model is in synchronously rotating frame. The
vector control uses unit vectors to obtain the appropriate control action. The main role of

33
d
q
s
unit vector is to convert the 2-phase model to 3-phase model and vice versa. Though the
control techniques used for DFIG uses two axes parameters as explained in the
modelling via vector control but the model is virtual representation of the original
machine. The control signals which will be fed to the original machine or converters should
be in three axes form, so the process requires repeated conversion of two-phase to
three-phase parameter or vice versa following the necessary action being taken for the
system. There are essentially two general method of vector control.
 Direct or feed back method (which is invented by Blaschke )
 Indirect or feed forward method ( which is invented by Hasse)
The two methods are different from each other by the process of generating unit vector
for control. Unit vectors (cosθe, sinθe) are generally generated using the flux vectors, but it
can also be generated using voltage vectors. The name of the orientation of unit vector is
given according to the vector taken for generation of θe. The names of the orientations used
are given below.
 Rotor flux orientation
 Stator flux orientation
 Air gap flux orientation
 Voltage orientation
d
d q
q to
ds qs

s ds qs
 to
s a bc
a b c




ds qs
to
d q
s a bc
q to
ds qs
a bc
d
q
Fig 3.5.Implementation of vector control principle

34
The detail vector control strategy is shown in Fig 3.5. The a, b, c components are
generated from the controlled components a*
, b*
, c*
respectively using vector control
techniques. The machine terminal parameters (either voltages or currents) are converted to
ds
-qs
components by 3-phase to 2-phase transformation. These are then converted to
synchronously rotating frame by the unit vector before applying to the 2-phase machine
model. The controller makes two stage of inverse transformation as shown, so that the
control components d*
and q* corresponds to the machine parameters d and q respectively.
3.3.DFIG System
The overall system is shown in Fig 3.6. The basic components of the system are as
follows.
1. DFIG (Wound rotor type Induction machine)
2. PWM Voltage source converters (Grid side converter and Machine side converter)
3. Utility grid
4. PI controller
Fig 3.6.Overall DFIG System
3.3.1.Doubly-fed Induction Generator
The modelling of DFIG has been discussed in 3.2.2. The state space equations are taken
into account for modeming of Induction Machine. The modeming is carried out using
MATLAB/SIMULINK.

35
r
The model uses flux linkages as the state variables as discussed above. Though the generator
can generate in both sub and super synchronous mode, here the speed is taken as super
synchronous speed, where the power can be extracted from the stator as well as rotor
circuit. The machine uses two back to back converters in the rotor circuit. The main purpose
of the machine-side converter is to controls the active and reactive power by controlling the
d-q components of rotor current (i.e. idr and iqr), while the grid-side converter is to control
the dc-link voltage and ensures the operation at unity power factor by making the reactive
power drawn by the system from the utility grid to zero.
3.3.2. Voltage source converter
Two back to back voltage-fed current regulated converters are connected to the rotor
circuit as shown in Fig 3.6. The firing pulses are given to the devices (IGBTs) using PWM
techniques. Two converters are linked to each other by means of DC-link capacitor.
Realization of vector control principle for decoupling of generator’s active and reactive
power , improvement of overall power factor, operation at synchronous speed by injecting
dc current into the rotor, less distortion in currents are the functional characteristics of the
back to back converters. Basically converter 1 controls the grid parameters where as the
converter 2 serves for machine. As a duo both are responsible for overall control. The
converters use six IGBTs (for three phase bridge type) as the controlled device for its
obvious advantages. Each control device has an antiparallel diode, to permit active and
reactive power flow in either direction.
The PWM technique uses the controlled voltage va
*
, vb
*
, vc
*
as the reference voltages
for the generation of pulses. The triangular career waves are being compared with
sinusoidal reference waves to ensure pulses for the devices. The modulation indices are
different for the both converters. These are decided from the Eq. (3.51). The career
frequency is taken as 3 kHz where as the frequency of the reference waves are decided by
the supply frequency, which is 50Hz in this case.
Vs  m1
Vdc 3 

2 2 




(3.51)
V  s
Vs
 m2
Vdc
 s   nm2 


n 2 2 m1 3

Where Vs and Vr are the per phase stator and rotor voltages respectively, m1 and m2 are
the modulation index of the grid side and machine side converter respectively, s is the slip,
and Vdc represents DC-link voltage.

36
3.3.3. Grid side Converter Control
When the voltages in the grid changes due to different unbalance conditions, it
makes an effect on the dc link voltage. The relation between stator voltage and the dc link
voltage is shown in the equation (3.51). Since the machine is grid connected the grid voltage
as well as the stator voltage is same, there exist a relation between the grid voltage and dc
link voltage.
The main objective of the grid side converter is to maintain dc-link voltage constant for the
necessary action. The voltage oriented vector control technique is approached to solve this
issue. The detail mathematical modeming of grid side converter is given below. The control
strategies are made following the mathematical modelling and it is shown in Fig. 3.8. Phase
Locked Loop block is used to measure the system frequency and provides the phase
synchronous angle θ for the d-q transformations block. The PWM converter is current
regulated with the direct axis current is used to regulate the DC link voltage where as the
quadrature axis current component is used to regulate the reactive power. The reactive
power demand is set to zero to ensure the unit power factor operation. Fig. 3.7 shows the
schematic diagram of the grid side converter.
Fig 3.7.Schematic diagram of Grid side Converter
The voltage balance across the line is given by Eq. (3.52), where R and L are the line
resistance and reactance respectively. Using d-q theory the three phase quantities are
transferred to the two phase quantities.
va  ia  ia  v 
v 
R 
L
d    a' 
(3.52) b  ib  
dt ib  v
b'
v 

i 

i 
 v 
 c   c   c  c'

37

The mathematical modelling of the grid side converter is shown in the following equations.
vd  Rid  L
did
dt
diq
 eLiq  v

d1





(3.53)
vq  Riq  L
dt
 eLid  vq1
Where vd1 and vq1 are the two phase voltages found from va‟,vb‟ and vc‟ using d-q
theory. Since the dc link voltage needs to be constant and the power factor of the overall
system sets to be unity, the reference values are to be set accordingly. The d and q reference
voltages are found from the Eq. (3.54).
v*  v  i*R  i*eL  v 
d d d q d'


(3.54)
v*  vq  i*R  i*eL  v 

q q d d'













Fig 3.8.Vector control structure for Grid side Converter
The control scheme utilizes current control loops for id and iq with the id demand being
derived from the dc-link voltage error through a standard PI controller. The iq demand
determines the displacement factor on the grid side of the choke. The iq demand is set to
zero to ensure unit power factor. The control design uses two loops, i.e. inner current loop
and outer voltage

38
v

d d 

line resistance and reactance, where as dc link capacitor is taken as the plant for the voltage
loop. The plants for the current loop and the voltage loop are given in Eq. (3.55) and (3.56)
respectively.
Fs

id (s)

vd'(s)
iq (s)
v
q'
(s)

1
Ls  R
(3.55)
v (s)
Gs dc 
3m1 (3.56)
id (s) 2 2Cs
The active and reactive power is controlled independently using the vector control
strategy. Aligning the d-axis of the reference frame along the stator voltage position is
found by Eq. (3.57), vq=0, since the amplitude of supply voltage is constant the active
power and reactive power are controlled independently by means of id and iq respectively
following Eq. (3.58).
s
q
tane 
vs
d
(3.57)
Ps 
3
v
2 did  vqiq






(3.58)
Q
s

3
v iq  vqi 
2
3.3.4. Machine side Converter Control
The control strategy made for the machine side converter is shown in Fig.3.9. The main
purpose of the machine side converter is to maintain the rotor speed constant irrespective of
the wind speed and also the control strategy has been implemented to control the active
power and reactive power flow of the machine using the rotor current components. The
active power flow is controlled through idr and the reactive power flow is controlled through
iqr. To ensure unit power factor operation like grid side converter the reactive power demand
is also set to zero here.
The standard voltage oriented vector control strategy is used for the machine side
converter to implement control action. Here the real axis of the stator voltage is chosen as
the d-axis. The vector diagram is shown in Fig. 3.10. The mathematical modelling of the
machine side converter is given in the following equations.

39
i
r
v


T
e m
e
(  )
L i L i 

Q*
*
Q
qr
 ds
'
qr
r dr


*
(e r )
r
iqr
*
iqrRr
' i
vqr
R
*
i
dr
r
v
dr dr r
*
Ls i
dr (  )
L i  L i  i
dr i
*
s Lm
e
e r m qs r qr
iqr
(  )
abcr
(e r )
e r
r
 V
abcs
i
ds i
iqs
Fig 3.9. PWM Control for Mechanical side converter
Fig 3.10.Vector diagram showing stator and rotor current components of DFIG in voltage oriented co-ordinate
Since the stator is connected to the utility grid and the influence of stator resistance
is small, the stator magnetizing current im can be considered as constant. Under voltage
orientation the relationship between the torque and the dq axis voltages, currents and fluxes

40

L
s
s
dr qr



d
dr
can be written as follows. The stator flux Equations are written in Eq. (3.59) neglecting
leakage inductances.
ds  0 
qs  Lsiqs  Lmiqr 
 L  L i  L i

ls m qs m qr 
 Llsiqs  iqs  iqr Lm 
 Lmim






(3.59)
The equations of rotor fluxes are given in Eq. (3.60) following the vector diagram
shown in Fig.3.10. The derivation of Eq. (3.60) is given in Appendix I.
qr 
Lm qs  Lriqr

Ls 
2 

Lm im  Lriqr 
Ls 

dr 
Lm 
Ls
ds
 Lri 
dr 

 Lridr
Where  1



2
m
Ls Lr
(3.60)
The rotor voltage Eq. (3.13) and (3.14) can be written by substituting the values of dr
and qr from the Eq. (3.60) as follows.
d  L2 
vqr  Rriqr   m im  Lriqr
  e  r Lridrdt  L 
 

 Rriqr 

0  Lriqr  e  r Lri
dt
d
 Rriqr  Lr dt
iqr  e  r Lridr (3.61)
di  2 


v  Rri  Lr
dr  e  r  Lm im  Lriqr

dr dr dt  L 
 

(3.62)
The unit vector is found in similar way as in the case of grid side converter. The
reference value v *
(3.61) and (3.62).
and v *
are given in Eq. 3.63 and 3.64 which are being found from Eq.

41
v  v

ds

T e
* '
qr qr  iqr R r   r i
dr
Lr  Lmi
ds



(3.64)
Where v‟dr and v‟qr are found from the current errors processing through standard PI
controllers. The reference current i*dr can be found either from the reference torque given
by Eq. (3.66) or form the speed errors (for the purpose of speed control) through standard PI
controllers. Similarly i*qr is found from the reactive power errors. The reactive power and
speed is controlled using the current control loops.
The electromagnetic torque can be expresses as follows
3 P
Te  
2 2
3 P
dsiqs  qsids 
  qsi
2 2
 

 
3 P
qs

L
m i 
dr 2 2

L
s 

3 P Lm
 i
(3.65)
2 2 Ls
qs dr
*
The value of idr
*  Ls
is found using Eq. (3.65)
i* 
dr
Te
qs  Lm
P  P
(3.66)
Where * mech
r
loss
Ploss  Mechanical Losses  Electrical Losses(PCur  PCus )
Mechanical losses include friction and wind-age losses whereas electrical losses
include stator copper loss and rotor copper losses.
The maximum mechanical power given by Eq. (2.6) can be extracted from the wind is
proportional to the cube of the rotor speed.
The plant for the current loop is decided by the line resistance and reactance, where as
dc link capacitor is taken as the plant for the voltage loop. The plants for the current loop
and the voltage loop are given in Eq. (3.67) and (3.68) respectively.
Fs

idr (s)

vdr'(s)
iqr (s)
vqr'(s)

1
Lr  R
r (3.67)
G(s)  

3PLm

K
4Ls qs Js  B Js  B (3.68)

42
where K 
3PLm
4Lsqs
3.4.Conclusions
This chapter explains the transformation theory for conversion of three-phase
parameters to two-phase and vice versa. Detail modelling of the DFIG system was analysed
in this chapter. The control strategy made for the grid side and machine side converter was
also explained.

Chapter- 4 MATLAB/Simulink Modelling
43
CHAPTER-4
MATLAB/SIMULINK
MODELLING
4.1. INTRODUCTIONTO MATLAB/SUMULINK 44
4.1.1. Development Environment 44
4.2. The MATLAB Language 45
4.2.1. Graphics 45
4.2.2. The MATLAB Applications Program interface (API) 45
4.2.3. MATLAB Documentation 45
4.3.MATLAB tools 46

44
CHAPTER 4
MATLAB/ Simulink Modelling
4.1. INTRODUCTION TO MATLAB/SIMULINK
MATLAB is a high-performance language for technical computing. It integrates
computation, visualization, and programming in an easy-to-use environment where problems
and solutions are expressed in familiar mathematical notation. Typical uses include-
 Math and computation
 Algorithm development
 Data acquisition
 Modeling, simulation, and prototyping
 Data analysis, exploration, and visualization
 Scientific and engineering graphics
MATLAB is an interactive system whose basic data element is an array that does not
require dimensioning. This allows solving many technical computing problems, especially
those with matrix and vector formulations, in a fraction of the time it would take to write a
program in a scalar non-interactive language such as C or FORTRAN.
The MATLAB system consists of six main parts:
4.1.1. Development Environment
This is the set of tools and facilities that help to use MATLAB functions and files. Many
of these tools are graphical user interfaces. It includes the MATLAB desktop and Command
Window, a command history, an editor and debugger, and browsers for viewing help, the
workspace, files, and the search path.

45
This is a vast collection of computational algorithms ranging from elementary
functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like
matrix inverse, matrix Eigen values, Bessel functions, and fast Fourier transforms.
4.2. The MATLAB Language
This is a high-level matrix/array language with control flow statements, functions, data
structures, input/output, and object-oriented programming features. It allows both
"programming in the small" to rapidly create quick and dirty throw-away programs, and
"programming in the large" to create large and complex application programs.
4.2.1. Graphics
MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well
as annotating and printing these graphs. It includes high-level functions for two-dimensional
and three-dimensional data visualization, image processing, animation, and presentation
graphics. It also includes low-level functions that allow to fully customize the appearance of
graphics as well as to build complete graphical user interfaces on MATLAB applications.
4.2.2. The MATLAB Application Program Interface (API)
This is a library that allows writing in C and FORTRAN programs that interact with
MATLAB. It includes facilities for calling routines from MATLAB (dynamic linking), calling
MATLAB as a computational engine, and for reading and writing MAT-files.
4.2.3. MATLAB Documentation
MATLAB provides extensive documentation, in both printed and online format, to help
to learn about and use all of its features. It covers all the primary MATLAB features at a high
level, including many examples. The MATLAB online help provides task-oriented and
reference information about MATLAB features. MATLAB documentation is also available in
printed form and in PDF format.

46
4.3. Matlab tools
(i) Three phase source block
The Three-Phase Source block implements a balanced three-phase voltage source with
internal R-L impedance. The three voltage sources are connected in Y with a neutral connection
that can be internally ground.
(ii) VI measurement block
The Three-Phase V-I Measurement block is used to measure three-phase voltages and
currents in a circuit. When connected in series with three-phase elements, it returns the three
phase-to-ground or phase-to-phase voltages and the three line currents
(iii) Scope
Display signals generated during a simulation. The Scope block displays its input
with respect to simulation time. The Scope block can have multiple axes (one per port); all axes
have a common time range with independent y-axes. The Scope allows you to adjust the
amount of time and the range of input values displayed. You can move and resize the Scope
window and you can modify the Scope's parameter values during the simulation

47
(iv). Three-Phase Series RLC Load
The Three-Phase Series RLC Load block implements a three-phase balanced load as
a series combination of RLC elements. At the specified frequency, the load exhibits constant
impedance. The active and reactive powers absorbed by the load are proportional to the square
of the applied voltage.
Three-Phase Series RLC Load
(v) Three-Phase Breaker block
The Three-Phase Breaker block implements a three-phase circuit breaker where the
opening and closing times can be controlled either from an external Simulink signal or from an
internal control signal.
Three-Phase Breaker block
(vi) Gain block
Gain block
The Gain block multiplies the input by a constant value (gain). The input and the gain
can each be a scalar, vector, or matrix.

Chapter- 5 Problem Description & Result
48
CHAPTER-5
PROBLEM DESCRIPTION &
RESULTS
5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION 49
5.2. ANALYSIS OF CONTROL INSTABILITY 51
5.3. DESIGN OF SSCI DAMPING CONTROLLER 53
5.4. OTHER SSCI MITIGATION ALTERNATIVES 55
5.5. RECOMMENDATIONS 57
5.6. MATLAB SIMULINK MODELS & RESULTS 58
5.7. CONCLUSIONS 60

49
CHAPTER 5
Problem Description & Result
5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION
To analyse SSCI, a simple and non- proprietary test system was designed in MATLAB.
The real time disturbances were applied to change network configuration and excite unstable
operation modes.
A. System Model
This system uses a generic Type 3 (DFIG) wind turbine model developed by me. The
model includes vector controls and a back-to-back converter connected to the rotor.
The control model was taken from the base paper [10].
The control model has been used extensively in non-series compensated systems, and
performs well even into weak systems with a low short-circuit MVA. The generator is
connected to the radial series compensated system through a unit transformer and a station
transformer. The degree of series compensation can be varied from 0 to 100%, and the
series capacitor is equipped with bypass logic to remove or insert the capacitor as required.
Table I shows a summary of the key parameters in the example system.
TABLE I
SYSTEM PARAMETERS
System quantities Values
Nominal Frequency 60 Hz
Total wind generator power 450 MW (3MW x 150 units)
Rated turbine voltage (L-L,rms) 0.69 kV
Collector voltage (L-L,rms) 33 kV
Station Transformer 600 MVA, 345/33/13.8 kV,
12% Impedance
Unit Transformer 3.4 MVA scalable, 33/0.69 kV
345 kV Line Impedance (pu
values on 100 MVA base)
Approx. 100 Ω (R = 0.0075 pu, X =
0.084 pu, B = 1.25 pu)
Series Capacitor Impedance 0 - 100 Ω
Receiving end system 345 kV, 1800 MVA /85° (at 1st
and 3rd harmonic)

50
B. Simulation of Disturbance
In order to excite the instabilities caused by SSCI in the modelled system, the system
was started with the series capacitor set to a small compensation value of 8%, and bypassed.
The simulation was given time to initialize properly before a bypass breaker was opened
across the capacitor at 5 seconds. The results are shown in Figure 2.
Fig.5.1. Simulated SSCI Event: Wind Plant Point of Interconnection
Real Power, Reactive Power, and RMS Voltage (8% series compensation)
Strong sub-synchronous oscillations develop and continue to grow for approximately 0.2
seconds, before the machines lose stability. If there are no protection system operations, the
current oscillations can continue to grow to very large levels and be maintained for many
seconds. It is noted that the oscillations are most evident in the real and reactive power and
currents. Voltage oscillations are evident but to a much lesser extent.
The generic wind turbine model is found to be unstable for any realistic compensation
level (6% or higher caused oscillations, where typical series compensation levels would be on
the order of 40% and higher), with oscillations developing in the current at the tuned SSR
series resonant frequency. The performance of this generic model is expected to be slightly
pessimistic, since current transducers and other forms of control filtering are not included in
this model as they would be in real turbines.

51
5.2. ANALYSIS OF CONTROL INSTABILITY
Analysis of the generic DFIG turbine models shows that SSCI interactions occur with the
following mechanism
1. The series capacitor and the electrical (inductive) system result in a sub-synchronous
electrical series resonant circuit.
2. Distorted or phase shifted components of voltage and current are measured and are seen
inside the wind turbine controllers.
3. The wind turbine controllers process this information through its controls.
4. The output of the controllers is an equivalent voltage source signal (or possibly a current
reference in some designs), which are compared to PWM (pulse-width modulation)
waveforms, and ultimately fire IGBTs in the VSC (voltage source converter) circuit on
the turbine rotor.
5. The closed-loop response (of the system, controller, and IGBT firing) results in negative
damping, which causes oscillations (at SS frequencies) to grow.
It is noteworthy that the frequency of the un-damped oscillations will change as the system
inductance changes – for example under heavy or light load conditions, or under contingency
conditions. The worst case is a radial system configuration, where the wind farm is
completely in series with the series capacitor and then the system, although SSCI can develop
for cases with parallel (non-series) paths as well.
To determine the precise control loops that are affected by the instability, the generic control
model was analysed when the current oscillations were growing, and the outputs of each
major control loop was analysed to see if the frequency was visible. Next, a test was
performed where the turbine was in steady state (so all controller outputs are constant) and
then the series capacitor bypass breaker was opened – this puts a small disturbance onto the
system, and initiates the SSR resonance. As a test, the output of each control loop was frozen
individually. If the oscillation stopped or if a significant change in the damping was observed
as a result of the control loop being locked, then this indicates the control loop has a significant
influence on SSCI.
The most significant control loops were identified as the rotor side current feedback
loops. A simplified representation of this control loop is shown in Figure 3.

52
The instantaneous measured ABC rotor side currents are converter to the DQ domain,
which requires a PLL (Phase Locked Loop) input – this process is direct and does not
introduce any filtering or delays. A sub-synchronous oscillation in the rotor currents would
appear as an oscillation on the measured DQ currents.
Next, the DQ measured components of current are compared to DQ current orders, which
come from higher level PI controllers which control real or reactive power (P or Q).
The difference is sent to PI controllers (or PID). The proportional gain of this inner PID
controller means there is a direct pass-through of the oscillation into the URDQ voltage
reference signals.
The URDQ voltage references are converted back to ABC domain (again a direct
conversion) and are compared with PWM carrier signals, resulting in firing pulses to the IGBT
converters. It is suspected that the tuning experience of the control designers is often limited
to inductive systems, whereas the introduction of the series capacitor introduces a phase
inversion, with unstable results.
Oscillations were also evident in the measured real and reactive power outputs, which can
pass through the proportional gain of the first set of PI controllers. This outer loop has also
been shown to have an impact on SSCI, although the effect is not the dominant effect.
It is the fast, direct nature of the current control loop which is the primary cause of the
SSCI problem. Topologies similar to the above described controls are common to all type
3 DFIG wind turbines. This explains why the problem is wide-spread amongst type 3 turbines
from most manufacturers. Type 4 (full converter) wind turbines do not use a rotor side
controller, and therefore do not exhibit the SSCI problem.
It has been shown that control changes in type 3 wind turbines can mitigate SSCI [9][10].
The following section describes several improvements that can be made to type 3 wind
turbine controls to mitigate SSCI.

53
Fig.5.2.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls
Fig.5.2.1. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current
Feedback Control Loop
5.3 DESIGN OF SSCI DAMPING CONTROLLER
The earlier results showed the nature of the SSCI instability, and identified the major
control loops which were the cause. To fix this problem, four changes were made to the

54
controls in the generic type 3 model. These changes are shown in Figure 4 and are described
as follows:
1. Reduction/optimization of the proportional gains in the rotor current DQ PI controller
loops. The original gains were 1.0 and were reduced to 0.4 pu.
2. A first order real pole was added to the IRD and IRQ measurement signals – the gain was
1.0 and the time constant was 0.01 seconds.
3. 2nd order low-pass filtering was added to the real power measurement signal (PGX in
Figure 4 - this filtering was already in place for the reactive power measurement signal
but is not shown)
4. A damping controller was added, which takes the real power error signal (input to the
first PI controller), passes it through a lead-lag control block (transfer function =
G*(1+sT1)/(1+sT2), where the G = 0.2, lead time constant T1 = 0.02, and lag time
constant T2 =
0.002), and then adds this signal to the output of the voltage signal reference (URQ
Ordered in Figure 4).
The generic model used in these tests is comprised of standard PSCAD control blocks for
PLLs, filters, etc. These may not function in exactly the same manner as real controls. Even
measurements such as Rms voltages, or P and Q flows can be performed in many different
ways and will be unique to each manufacturer.
With the 4 controller changes, the DFIG was able to operate radially into the series
compensated test system with more than 50% series compensation levels, without the
build-up of SSCI oscillations, as shown in Figure 5. It is noted that even though the
simulation shows stable operation with no growing sub-synchronous oscillations, the
transient response following the disturbance at 5 seconds is much more severe than that
seen when using the un- modified controls. This is due to a reduction in speed and increased
damping being introduced into the fast rotor current control loop, and illustrates that a
trade-off exists between reducing SSCI interactions and the speed the device is able to
respond to disturbances. For this reason, these control changes would not be made lightly,
and will require careful tuning by the wind turbine manufacturer. It is likely that additional
improvements and optimizations are possible, and results will vary from one manufacturer to
the other depending on their specific controller topologies and tuning.

55
Fig.5.3. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,
Reactive power, and Rms Voltage (50% series compensation)
5.4. OTHER SSCI MITIGATION ALTERNATIVES
Although the primary mitigation of SSCI should be accomplished by means of a
controller adjustment in the type 3 wind turbine rotor converter (the controls are the source of
the instability), there are other precautions and mitigations which may be adopted as required.
A. Addition of bypass filters across series capacitor
A sub-synchronous bypass filter across the series capacitor may be effective. A parallel
LC impedance (tuned to fundamental) in series with a damping resistor is placed in parallel
with the main series capacitor. The tuned LC path is an open circuit at fundamental
frequency (to minimize losses) – low frequencies components will pass through the filter
so the resistor adds sub-synchronous damping. The use of such a filter (example shown in
Figure 6) may lead to additional losses, and the RLC filter must be insulated to the full line
voltage and sit on an insulated platform in the same fashion as the series capacitor. Although
passive filters can be readily designed, such filters have not been implemented in the field.

56
Other bypass filter topologies can also be used. The wind turbine also may employ series
SSR blocking filters, but these can be expensive and may not be 100% effective.
The 60 Hz blocking filter is comprised of two or more blocking filters so that detuning is
minimized when a filter capacitor fails. The large inductors of the 60 Hz blocking component
of the filter may require iron cores, which could add an extra cost if they are too heavy to
mount on the platform and must be insulated for full line voltage.
B. Combination of wind turbine models
Recent study work has shown that full converter turbines (type 4) have been shown to add
positive damping at sub- synchronous frequencies, which could offset the negative
damping added by
Fig.5.4. Example of a blocking filter in parallel with series capacitor
D. Install SSCI protection relays
As a minimum, any wind turbine that is operated near a series capacitor should employ an
SSCI protection circuit. If sub-synchronous oscillations are detected, then either the wind
farm can be tripped or the series capacitor bypassed to avoid damage. This should be
considered a fail-safe protection mechanism, similar to SSR relays commonly installed in
gas turbine generators, rather than a mitigating solution. The oscillations have been observed
to ramp up very quickly (in seconds rather than minutes), so SSCI protection is required to be
faster than conventional SSR protection circuits, which operate over longer timeframes.
Ultimately, a combination of these mitigation methods may be required for a successful
project. It is important that the SSR behaviour of the system is studied with detailed
EMT models. Conventional transient stability programs do not demonstrate SSCI problems
as they cannot represent the electrical resonance. At present, this is not a requirement in most
wind interconnection standards. Since some of the mitigation solutions can be expensive and
require equipment to be purchased or control upgrades to be performed, the studies may need
to be performed relatively early in the overall project development schedule.

57
5.5. RECOMMENDATIONS
In order to ensure future wind and transmission projects are not impeded by SSCI
concerns when used in conjunction with series compensated transmission systems, the
following specific recommendations are made
1. Detailed EMT models of the turbine should be obtained directly from the manufacturer
during project planning stages. This may require non-disclosure agreements to be signed,
but is essential for a complete understanding of performance, and evaluation of potential
problems. The best models directly use the real code from the actual controller hardware.
In this case, the source code can be compiled and imbedded directly in the EMT tool,
complete with all measurement methods, controllers, protection functions etc. This has
been successfully done for several major wind turbine manufacturers. The method is
highly accurate and relatively easy to develop, but beyond the scope of this paper.
2. Wind turbine manufacturers are encouraged to aggressively research SSCI and see
if improvements can be made in their turbine controls.
3. Wind developers must be aware of potential problems of turbines operating near series
compensated lines and be aware of the potential complexities this introduces.
4. Transmission providers should update their interconnection standards to require
EMT/SSCI analysis to be performed when turbines are connected near series compensated
lines, and to ensure the proper protection systems are in place.
5. Transmission planners should include the additional costs for SSCI related problems
when comparing lines with series capacitors to higher voltage AC lines, or DC solutions.

58
5.6. MATLAB SIMULINK MODELS & RESULTS
Fig.5.5.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls)
Using a MATLAB Platform
Fig.5.5.1.Simulated SSCI Event When there is no SSCI damping controller: Wind Plant Point of
interconnection Real Power, Reactive power, and RMS Voltage

59
Fig.5.6. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current Feedback
Control Loop Using a MATLAB Platform
`
Fig.5.6.1. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,
Reactive power, and RMS Voltage

60
5.7 CONCLUSIONS:
In this chapter, I used Type 3(DFIG) Wind turbine to analyse these SSCI Concerns.
First of all these SSCI Concerns were introduced into the system by the conditions that were
mentioned in the base paper. Afterwards, the design of the SSCI damping controller was done
and introduced it into the system as per the parameters that are mentioned in the 5.3. According
to the author of the base paper, he has implemented some of the changes to the SSCI damping
controller shown in the Figures 5.1 and 5.2. The same has implemented in to the system as per
my model explained in the section 5.6.
I designed my own Type 3 wind turbine system (Plant), and implemented the same
procedure in the Matlab/Simulink. The results were compared as shown in the Figures 5.1.1
and 5.5.1 and found that both the results are same.
So after implementing the changes in the controller, The SSCI concerns were damped out
earlier as compared with the previous controller

Chapter 6 Fuzzy Logic Controller
61
CHAPTER-6
FUZZY LOGIC CONTROLLER
6.1 INTRODUCTION TO THE FUZZY LOGIC 62
A. Fuzzy model, Fuzzy controller, and Fuzzy observer 62
B. Fuzzy control system 62
C. TS Fuzzy Model with Parameter Uncertainties 63
6.2 INTRODUCTION TO MY PROJECT EXTENSION 65
6.3 CONCLUSIONS 69

62
CHAPTER- 6
FUZZY LOGIC CONTROLLER
6.1 INTRODUCTION TO THE FUZZY LOGIC
A.TS Fuzzy Model, Fuzzy Controller, And Fuzzy Observer
In this section, we give a brief background of fuzzy logic control, TS fuzzy logic control,
and fuzzy observers.
B. Fuzzy Control Systems
Traditional control theory is quite limited in modeling and controlling complex
dynamical systems. On the contrary, fuzzy control theory has demonstrated potential in these
kinds of non-traditional applications. Fuzzy logic technology allows the designers to build
controllers even when their understanding of the system is still incomplete. Fig. 6.1 shows the
fuzzy controller which includes a fuzzification block, a knowledge base (fuzzy sets, rule base), a
fuzzy inference engine, and a defuzzification block. The fuzzy process maps a crisp point of real
meaning such as measured data, into fuzzy sets, by the knowledge of the input membership
functions. The fuzzy inference engine then uses the rules in the rule base to produce fuzzy sets at
output, corresponding to input fuzzy sets. The fuzzification interface modifies the inputs so that
they can be interpreted and compared to the rules in the rule-base. The defuzzification interface
converts the conclusions reached by the inference mechanism into the inputs to the plant. The
knowledge base of the fuzzy system stores the expert knowledge on how to control the wind
turbine. All the inputs and the outputs are normalized with tuning (Burns., 2001).
Fig 6.1. Fuzzy contorl system

63
C. TS Fuzzy Model with Parameter Uncertainties
A nonlinear control system can be represented as a TS fuzzy plant model-based system. It
consists of a TS fuzzy plant model (Takagi. 1985) and a fuzzy controller (Tanaka. 1992)
connected in a closed-loop. The TS fuzzy plant model describes the dynamic properties of a non-
linear plant through fuzzy rules that have linear systems as consequent parts. The inferred system
is expressed as a weighted sum of a number of linear subsystems. A fuzzy controller can thus be
designed such that the inferred output of the fuzzy controller is a weighted sum of a number of
linear sub-controllers. Consider an uncertain non-linear system that can be described by the
following TS fuzzy model. With parametric uncertainties, sensor faults, and disturbance. The
figure 6.2 below shows the TS of Fuzzy model with two inputs and a one output.
Fig 6.1.1 Equivalent Fuzzy model architecture with two inputs and one output

64
Fig.6.1.2 shows the normalized triangular membership functions used in Fuzzification. Fig.
6.1.2(a) for e and ce and Fig. 6.1.2(b) for δImax
Fig (a) error and change in error
Fig (b) Change in reference current
Fig 6.1.2 Normalized triangular membership functions used in Fuzzification.

65
6.2 INTRODUCTION TO MY PROJECT EXTENSTION
Due to the strong requirement from the wind energy field, fault detection of the wind
turbine components has received significant attention in recent years. Fault detection becomes
even more complex when multivariable nonlinear wind energy conversion systems (WECS) are
subject to parameter uncertainties. Uncertainties often degrade system performance and may
even lead to instability and so, in order to overcome these kinds of difficulties, different
techniques have been developed in the last two decades.
The problem of Sub-synchronous control interactions and damping has also been greatly
studied and still remains an active research area. As such, the combination of PI and Fuzzy based
scheme is presented to detect and accommodate faults in wind turbines. This paper extends
previous work of damping these Sub-synchronous controlled interactions with a Fuzzy logic
controller. In the previous work, only PI controller is used to damp-out SSCI concerns. Where as
in extension, a combination of both PI controller and Fuzzy controller for the better results.
This fuzzy logic controller can be designed in two methods rule based and model based,
mamdani is a rule based system and sugeno is a model based system. For my thesis, I used
mamdani based fuzzy logic controller which is a rule based system. In description to the
mamdani model it consists a FIS editor, Membership function editor, rule editor, Rules viewer
and Surface viewer.
FIS editor:
In FIS editor we have to mention how many inputs we are taking for the required output,
and we have to give the specific names to the inputs and outputs as per the system.

66
Fig 6.2.1 Fuzzy interface system editor
Fig 6.2.2 FIS with input membership
function editor
Fig 6.2.3 FIS with output membership
function editor
Fig 6.2.4 FIS with rule editor
Fig 6.2.5 Rule viewer individual
Fig 6.2.6 Surface viewer of all the rules
combined

67
Membership Function editor:
In membership Function editor we have formed a membership functions for each input
and output that we mentioned in the FIS editor. For each input and output we have to give the
Range and display range in the membership editor so that output is displayed as required.
The above shown Figures 6.2(1-6) are from the MatLab/Simulink platform. How we edit
the membership functions and form the rules in the rule editor are shown in the figures.
error ( e )
changeintheerrorc(e)
NB NM NS ZE PS PM PB
NB NB NB NB NB NM NS ZE
NM NB NB NB NM NS ZE PS
NP NB NB NM NS ZE PS PM
EZ NB NM NS ZE PS PM PB
PS NM NS ZE PS PM PB PB
PM NS ZE PS PM PB PB PB
PB ZE PS PM PB PB PB PB
Table 6.2.7 Rules table for by fuzzylogic controller
The above shown table is Rule tabe for the fuzzy logic controller for my thesis output.
Basing on the rules, fuzzy logic controller takes the decession what to do and what not to. These
rules are formed as per the required output for my thesis.
Fuzzy logic controller based on the above rules was introduced into the system shown in the
Figure 6.2.8, and respective results are shown in the Figure 6.2.9

68
Fig.6.2.8. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current Feedback
Control Loop Using a MATLAB Platform when Fuzzy logic controller is introduced.
Fig.6.2.9. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,
Reactive power, and RMS Voltage when fuzzy logic controller is introduced

69
6.3 CONCLUSIONS:
In this chapter, I used a combination of PI controller and fuzzy logic controller
(Intelligent controller) into the system to damp out the SSCI Concerns. I designed the fuzzy
controller using Matlab/Simulink. Using a Fuzzy editor I formed the Inputs and outputs and
procedure was explained in the section 6.2. Afterwards the combination of PI controller and
Fuzzy logic controller was introduced in to the system as shown in the Fig 6.2.7 and results were
simulated.
The simulated results were shown in the figure 6.2.8 and were compared with the
previous chapter results (Chapter 5). By the comparison, it is found that usage of Fuzzy logic
controller SSCI concerns were damped out much faster than using a PI controller alone [10].

Chapter-7 Conclusions
70
CHAPTER-7
Conclusions
7.1. INTRODUCTION 71
7.2. RESULTS 72
7.3. CONCLUSIONS 72
REFERENCES 73
APPENDIX 74
PUBLICATIONS 75
PUBLICATION PAPER

71
CHAPTER- 7
Conclusions
7.1 INTRODUCTION
In this chapter, results obtained in all other chapters are explained and
Recommendations are given.
7.2 RESULTS
SSCI (Sub-Synchronous Control Interactions) is a new phenomenon, where wind
turbines/controls have been observed to interact with nearby series capacitors, resulting in un-
damped/fast growing oscillations. This is a widespread and serious problem, affecting turbines
from most major manufacturers. Worldwide, there are a large number of transmission
expansion projects relying on series capacitors, yet the majority of wind turbines are unstable
under these conditions. Furthermore, standard transient stability studies (performed as per the
interconnection standards) do not show this problem (as they use fundamental frequency
phasor solutions). Recent real system projects have experienced damage to turbines and
transmission equipment due to SSCI.
This paper demonstrates that the negative damping observed in the SSCI phenomena is
largely due to the wind turbine rotor side current controller in the type 3 topology. Controller
changes and damping controllers are proposed which help to mitigate the instability.
Fuzzy logic controller is introduced along with the PI controller into the system to damp
out the SSCI concerns. Fuzzy logic controller is an intelligent controller, by basing on the
rules give in the system it will act accordingly without the human interface. Analysis were
drawn using the MatLab/Simulink and comparison were done with the previous one. Both the
results were compared. By using the Fuzzy logic controller we achieved 30% improvement in
the system output, i.e., these SSCI are damped out in a very little time compared to the
previous one. So using a Fuzzy logic controller it is help full for the system to damp these
SSCI concerns in the future.
In all cases of potential SSCI, it is highly recommended that detailed EMT models of
the turbine be obtained directly from the manufacturer. Modern tools such as PSCAD/ EMTDC
are capable of directly imbedding code from the actual hardware into simulation models, such
that excellent predictions of SSCI phenomena may be produced. Increased awareness of SSCI

72
is critical, along with backup protection schemes capable of preventing equipment damage in
the event of SSCI.
7.3 CONCLUSIONS
The results from the chapter 5 and chapter 6 were compared and found that using the
fuzzy logic controller we can achieve fast damping of SSCI Concerns. This thesis results were
compared with base paper [10] results found that the damping of the SSCI 30% faster.

73
REFERENCES
[1] IEEE Committee Rep., "Reader’s guide to sub-synchronous resonance,” IEEE Trans.
Power Syst., Vol. 7, No. 1, pp. 150-157, Feb. 1992.
[2] IEEE Working Committee Rep., "Third supplement to a bibliography for the study of
sub-synchronous resonance between rotating machines and power systems," IEEE
Trans. Power Syst., Vol. 6, No. 2, pp. 830–834, May 1991.
[3] P. Kundur, “Power System Stability and Control," McGraw-Hill Companies, 1994.
[4] R. K. Varma, S. Auddy, and Y. Semsedini, "Mitigation of sub- synchronous
resonance in a series-compensated wind farm using FACTS controllers," IEEE Trans.
Power Del., Vol. 23, No. 3, pp. 1645–1654, Jul. 2008
[5] R. M. Mathur, R. K. Varma, “Thyristor-based FACTS Controllers for Electrical
Transmission Systems”, IEEE Wiley-Interscience, 2002
[6] G. D. Irwin, "Sub-Synchronous Interactions with Wind Turbines," Technical Conference
- CREZ System Design and Operation, January 26, 2010, Taylor, Texas, USA.
http://www.ercot.com/calendar/2010/01/20100126-TECH
[7] W. Wong, J. Daniel, "ABB presentation on CREZ Reactive Study- ERCOT RPG
Meeting,"March12,2010,Austin,Texas,USA
http://www.ercot.com/calendar/2010/03/20100312-RPG
[8] G. Reed, "CREZ Project Overview," January 26, 2010, Taylor, Texas
http://www.ercot.com/calendar/2010/01/20100126-TECH.
[9] E. Larsen, "Wind Power on series-compensated lines," 2010 Wind- Power Conf and
Exhibition, Dallas, TX, USA, May 23-26, 2010
[10] A. K. Jindal, G. D. Irwin and D. A. Woodford, "Sub-Synchronous Interactions with
Wind Farms connected near series compensated AC lines", 9th Int. Workshop on Large scale
integration of wind, Quebec City, Canada, pp. 559-564, Oct 18-19, 2010.

74
APPENDIX
A) Specifications of DFIG
TABLE I
SYSTEM PARAMETERS
System quantities Values
Nominal Frequency 60 Hz
Total wind generator power 450 MW (3MW x 150 units)
Rated turbine voltage (L-L,rms) 0.69 kV
Collector voltage (L-L,rms) 33 kV
Station Transformer 600 MVA, 345/33/13.8 kV,
12% Impedance
Unit Transformer 3.4 MVA scalable, 33/0.69 kV
345 kV Line Impedance (pu
values on 100 MVA base)
Approx. 100 Ω (R = 0.0075 pu, X =
0.084 pu, B = 1.25 pu)
Series Capacitor Impedance 0 - 100 Ω
Receiving end system 345 kV, 1800 MVA /85° (at 1st
and 3rd harmonic)
B) Fuzzy Logic controller rule box
error ( e )
changeintheerrorc(e)
NB NM NS ZE PS PM PB
NB NB NB NB NB NM NS ZE
NM NB NB NB NM NS ZE PS
NP NB NB NM NS ZE PS PM
EZ NB NM NS ZE PS PM PB
PS NM NS ZE PS PM PB PB
PM NS ZE PS PM PB PB PB
PB ZE PS PM PB PB PB PB

75
PUBLICATIONS
Y. Dharma Teja, Dr. P. Linga Reddy, “Sub-Synchronous Control Interactions between
Type 3 Wind Turbines with Fuzzy Logic Controller and Series Compensated AC
Transmission Systems” IJEE international Journal Of Electrical, Electronics and
Telecommunication Engineering, issued on june 2013.

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