The connection and operation of wind power plants produce some problems that are rising partly owing to large changeability of environment conditions, influencing the electrical energy supply from these sources. To be possible to study phenomena that are connected with wind power plants and impacts of their operation on the operation of distribution and transmission systems, it is necessary to do such as in other branches, different computer simulations. A grid connected wind power generation scheme using doubly fed induction generator is studied. The aim is modelling and simulation of DFIG operating in two quadrants (torque-speed) by a suitable control technique to control the rotor current. This method will also replace the conventional converter by Indirect Matrix Converter.

1. DFIG CONTROL OF WIND ENERGY CONVERSION
SYSTEM USING INDIRECT MATRIX CONVERTER
A Thesis submitted to
KIIT UNIVERSITY
(Declared under section 3 of UGC Act, 1956)
in fulfillment of the requirement for the award of the degree of Master Of Technology
in
Power & Energy System
By
Kuldeep Behera
Roll # 1458015, Registration # 14013532472
Under the supervision
of
Prof. Subrat Behera
Assistant Professor, School Of Electrical Engineering,
Campus-3, KIIT University,
Bhubaneswar, Odisha
&
Dr. Manoj Kumar Maharana
Associate Professor, School Of Electrical Engineering,
Campus-3, KIIT University,
Bhubaneswar, Odisha
SCHOOL OF ELECTRICAL ENGINEERING, KIIT UNIVERSITY,
BHUBANESWAR 751024, ODISHA, INDIA

2. ©KALINGA INSTITUTE OF INDUSTRIAL TECHNOLOGY
KIIT UNIVERSITY, BHUBANESWAR
ALL RIGHTS RESERVED

3. CERTIFICATE
This is to certify that the thesis entitled, "DFIG control of wind energy
conversion system using indirect matrix converter", submitted by Mr.
Kuldeep Behera, Roll #1458018 and Registration# 14013532472 for the
award of degree of Master of Technology in Power & Energy System of KIIT
University, is based on his own original research work under our supervision
and that neither his thesis nor any part of it has submitted for any degree or any
other academic award elsewhere.
Dr. C. K. Panigrahi
Dean, Professor
School of Electrical Engg.
KIIT University
Prof. Subrat Behera
Guide, Asst. Professor
KIIT University
Dr. M. K. Maharana
Co-Guide, Associate Professor
KIIT University
External Examiner

4. DECLARATION
I certify that the work presented in the thesis entitled "DFIG control of wind energy
conversion system using indirect matrix converter" in fulfilment of the requirement for
the award of degree of Master Of Technology in Power & Energy System in the School Of
Electrical Engineering and submitted to KIIT University, Bhubaneswar is an authentic
record of my own work carried out under the supervision of Prof. Subrat Behera, Assistant
Professor & Dr. Manoj Kumar Maharana, Associate Professor, School Of Electrical
Engineering, KIIT University, Bhubaneswar.
The matter embodied in this thesis has not been submitted by me for the award of any
other degree of this or any other University / Institute.
(Kuldeep Behera)

5. Acknowledgement
It gives me immense pleasure to express my deepest gratitude and sincere thanks to
my respected guide Prof. Subrat Behera, Asst. Professor, School of Electrical
Engineering, KIIT University, Bhubaneswar, for giving his valuable guiding encouragement
and help for this work. His instructive suggestions and careful guidance have helped me to
solve various technical problems. His continuous support and motivation has helped me to
face difficulties during this work.
I am equally indebted to Dr. M. K. Maharana, Associate Professor, School of
Electrical Engineering, for the valuable information provided by them in their respective
fields.
I would like to thank Dr. C. K. Panigrahi, Dean, School of Electrical Engineering
for giving the opportunity to work with different laboratories in the department on time and
care.
I am thankful to Prof. Tapas Roy, Professor and all staff members of the School of
Electrical Engineering, KIIT University for their cooperation in this work.
I cordially thank my classmates for giving me a wonderful company throughout my
stay at KIIT University. I enjoyed every bit of campus life and refreshing moments outside
my project because of them.
I would also like to express my sincere thanks to my loving family members for their
encouragement and providing me all moral support and necessary help whatever I have
achieved in my life.
Kuldeep Beher

6. i
ABSTRACT
The connection and operation of wind power plants produce some problems that are rising
partly owing to large changeability of environment conditions, influencing the electrical
energy supply from these sources. To be possible to study phenomena that are connected
with wind power plants and impacts of their operation on the operation of distribution and
transmission systems, it is necessary to do such as in other branches, different computer
simulations. A grid connected wind power generation scheme using doubly fed induction
generator is studied. The aim is modelling and simulation of DFIG operating in two
quadrants (torque-speed) by a suitable control technique to control the rotor current. This
method will also replace the conventional converter by Indirect Matrix Converter.
Proposed control of an Indirect Matrix Converter (IMC) is combined with predictive
rotor current control of a DFIG to achieve a very good dynamic response as the rotor
currents smoothly, which consists of an input side matrix converter and an output side
voltage source converter. The proposed method leads to a reduction in the commutation
losses in the output converter and reduced common mode voltage. For the input converter,
soft switching commutation is obtained by synchronizing the input and output converter
pulse width-modulation patterns. Taking a comparison study of all PWM techniques we
choose the space vector pulse width modulation as the best one because of its low switching
losses and high harmonic density, power factor & switching frequency. The output voltage,
output current waveforms, voltage transfer ratio and THD spectrum of switching waveforms
connected to load are to be analyzed by using MATLAB/ SIMULINK software. Hence
further the closed loop control of doubly feed induction generator is to be performed for the
wind energy conversion system connected to grid.

7. ii
CONTENTS
Page No.
Abstract i
List of Figures v
List of Tables vii
Abbreviation
viii
CHAPTER 1 : INTRODUCTION
1.1 Introduction 1
1.2 Objective 1
1.3 Scope of work 1
1.4 Motivation 2
1.5 Thesis Methodology 2
1.6 Thesis Outline 2
1.7 Literature review 3
1.8 Summary 6
CHAPTER 2 : SPACE VECTOR MODULATION
2.1 Space vector modulation 9
2.2 Modulation scheme in SVM 9
2.3 SVM of a voltage source inverter 12
2.4 Conclusion 13
CHAPTER 3 : MATRIX CONVERTER
3.1 Matrix converter 14
3.2 Development of Indirect matrix converter 15
3.3 Topology of Indirect matrix converter 17
3.4 Operation of bidirectional switch in matrix converter 18

8. iii
3.5 Voltage source inverter 19
3.6 Indirect modulation scheme of matrix converter 20
3.7 Conclusion 22
CHAPTER 4 : COMMUTATION SCHEME OF MATRIX CONVERTER
4.1 Indirect matrix converter 23
4.2 Commutation scheme of IMC 23
4.3 DC-link formation of IMC 26
4.4 Dwell time calculation 30
4.5 Simulation results and discussion 32
4.6 Conclusion 36
CHAPTER 5 : WIND ENERGY CONVERSION SYSTEM
5.1 Wind energy conversion system 37
5.2 Types of wind turbines in WECS 39
5.3 Operating region of wind turbines 39
5.4 Power of a wind turbine 40
5.5 Wind power versus speed characteristics 42
5.6 Turbine design 43
CHAPTER 6 : DOUBLY-FED INDUCTION GENERATOR
6.1 Doubly-fed induction generator in WECS 44
6.2 DFIG equivalent circuit 45
6.3 DFIG Mathematical Modelling 46
CHAPTER 7 : VECTOR CONTROL METHOD OF DFIG
7.1 Vector control method of DFIG 49
7.2 Theory of vector control phenomena 50

9. iv
7.3 Direct vector control method 51
7.4 Indirect vector control method 52
CHAPTER 8 : MATLAB IMPLEMENTATION OF INDIRECT MATRIX
CONVERTER WITH DFIG
8.1 MATLAB implementation of Indirect matrix converter with DFIG 55
8.2 Simulation results 58
CHAPTER 9
Conclusion 65
References 66

10. v
LIST OF FIGURES
Page No.
Fig. 2.1: Sector division in space vector modulation 9
Fig. 2.2: Voltage source inverter topology 12
Fig. 3.1: Classification of AC to AC converters 14
Fig. 3.2: First topology of Indirect Matrix Converter 15
Fig. 3.3: Topologies of Direct Matrix Converter 16
Fig. 3.4: Topology of Indirect Matrix Converter modulation scheme 17
Fig. 3.5: Four step commutation scheme of a bidirectional switch 18
Fig. 3.6: Voltage source inverter 21
Fig. 3.7: Application of voltage and current vectors over Ts 22
Fig. 3.8: generation of switching signals 22
Fig. 4.1: Topology of Indirect Matrix Converter 24
Fig. 4.2: Current flow for positive power flow in one leg of IMC 25
Fig. 4.3: Current flow for negative power flow in one leg of IMC 25
Fig. 4.3: Power flow in IMC 26
Fig.4.4: Behaviour of dc-link voltage and three phase input voltage
with average dc-link voltage 27
Fig. 4.5: Sector diagram comprising of vectors 29
Fig. 4.6: Switching diagram for the generation of voltage and current
over a section 30
Fig. 4.7: DC link voltage between rectifier and inverter stage 32
Fig. 4.8: Output phase voltage 33
Fig. 4.9: Magnified values of output phase voltage 33
Fig. 10: Output line voltage 34
Fig. 4.1: Output current 34
Fig. 4.12: Harmonic profile of output current 35
Fig. 4.13: Simulated phase voltage with various modulation indexes 36
Fig. 5.1: Block diagram of wind energy conversion system 37
Fig. 5.2: Wind turbines 38
Fig. 4.3: Power curve of a variable speed wind turbine 40

11. vi
Page No.
Fig. 5.3: Power versus Speed characteristics of wind turbine 42
Fig. 6.1: Equivalent circuit of DFIG 45
Fig. 7.1: Direct vector control of DFIG 52
Fig. 7.2: Indirect vector control of DFIG 54
Fig. 8.1: Model block representation of full system 55
Fig. 8.2: MATLAB/SIMULINK model of experiment 56
Fig. 8.3: MATLAB/SIMULINK model of Indirect matrix converter 57
Fig.8.4: Space vector modulation generation in MATLAB/SIMULINK 57
Fig.8.5: Rotor speed characteristics of machine in pu 58
Fig. 8.6: Rotor torque characteristics of machine 58
Fig 8.7: Stator active and reactive power 59
Fig 8.8: Rotor active and reactive power 59
Fig 8.9: Three phase stator current 60
Fig 8.10: Single phase stator current 60
Fig 8.11: Stator current in pu 60
Fig 8.12: Stator voltage phase A 61
Fig 8.13: Three phase rotor current 61
Fig 8.14: Single phase rotor current 61
Fig 8.15: Three phase rotor voltage 62
Fig 8.16: Single phase rotor voltage 62
Fig 8.17: DC-link voltage generated in converter 62
Fig 8.18: Output current of the converter 63
Fig 8.19: Output line voltage of converter 63
Fig 8.20: Generated reference current by vector control strategy 63
Fig 8.21: d-component of stator current phase A (pu) 64
Fig 8.22: q-component of stator current phase A (pu) 64

12. vii
LIST OF TABLES
Page No.
Table 2.1: Switching time of each transistor in VSI 11
Table 2.2: Vector sequence and voltage formation by SVM in inverter 12
Table 4.1: Output voltage over a period 27
Table 4.2: Switching sequence of IMC over a section 31
Table 4.3: Comparison of calculated and simulated output phase voltage 35
Table 8.1: Machine parameters 55
Table 8.2: Tabulation for various speed 56

13. viii
ABBREVIATIONS
BBC- Back to back converter
BPF- Band pass filter
CMC- Conventional matrix converter
DFIG- Doubly fed induction generator
FOC - Field oriented control
GSC - Grid side converter
HAWT - Horizontal axis wind turbine
IGBT- Insulated gate bipolar transistor
IMC- Indirect matrix converter
LPF – Low pass filter
MC- Matrix converter
PWM- Pulse Width Modulation
RSC - Rotor side converter
SMC - Sparse matrix converter
SMC- Sparse matrix converter
SPWM- Sinusoidal pulse width modulation
SRRF - Synchronously rotating reference frame
SVM- Space vector modulation
THD- Third harmonic distortion
USMC - Ultra sparse matrix converter
VAWT - Vertical axis wind turbine
VSI - Voltage source inverter
VSMC - Very sparse matrix converter
WECS - Wind energy conversion system

14. 1
CHAPTER 1
1.1 Introduction
India now ranks 4th in the world after Germany, USA and Spain with a wind power installed
capacity of 4434 MW. The 10th Plan aim at 1500 MW grid-interactive wind power has been
exceeded as capacity deployed up to 31.12.2005 exceeded 2800 MW taking the cumulative
deployment to over 4500 MW. India’s wind power potential has been assessed at around
45,000 MW assuming 3 percent land availability for wind farms requiring @12 hector/MW
in sites having wind power density in excess of 250W/sq. meter with 50 meters hub-height.
Power quality relates to factors which describe the variability of the voltage level, as
well as the distortion of voltage and current waveforms. When it comes to the power quality
of wind turbine generators only some specific power quality problems are relevant. Many
people have been investigating those problems with works concerning the power quality
improvement of wind farm and power quality and grid connection of wind.
The first part will introduce an indirect matrix converter to control which is a direct
AC to AC converter. Second part of the thesis will contain an introduction into wind energy
conversion system with Doubly Fed Induction and the advantages of DFIG rather to other
generating systems and the overall efficiency will be simulated through MATLAB/
SIMULINK.
1.2 Objective
The main objective of this thesis is modelling and simulation of DFIG with suitable control
technique using indirect matrix converter to reduce the switching losses and harmonics. This
will increase the efficiency of power conversion which will be analytically verified.
1.3 Scope of work
The present work describes the wind energy conversion system with considering the doubly
fed induction generator (DFIG) as because of its various advantages and producing energy
effectively. Further to control the rotor we introduce a matrix converter instead of
conventional back to back converters. The switching phenomenon of matrix converter is
obtained with space vector modulation technique. The application of MATLAB and

15. 2
implementation of system in MATLAB/ SIMULINK are to be studied and performance
results are to be justified from simulation result.
1.4 Motivation
Matrix converters are devices which could be used for real world up to 100kw in controlling
DFIG to enhance the efficiency of Wind energy conversion system in terms of output
voltage, current, switching frequency, harmonic distortion, power factor, active-reactive
power and device technology will increase magnetism for research.
1.5 Thesis methodology
Firstly Indirect Matrix Converter modulation strategy has been developed in MATLAB. The
space vector modulation algorithm by MATLAB coding is implemented and outputs are
determined. The factors residing with converter has verified and analysis was conducted.
A basic model of WRIG is tested in SIMULINK. The characteristics of machine with
mathematical equations are investigated in literature. This basic model is extended applying
the indirect matrix model replacing the ideal voltage source to WRIG rotor circuit thus built
a complete model of DFIG. This model is simulated according to our operating condition.
A wind turbine has been developed by considering the generalised equation of wind
power. The parameters are set for a fixed speed of wind. Further to synchronize the system
with utility grid the vector control Phase locked loop is enhanced. The coordinated control of
rotor and stator is possible by vector control strategy of DFIG. The analysis of complete
system is presented in the thesis with conclusion and recommendation.
1.6 Thesis outline
The contents of the chapters described in this thesis are as follows: In chapter 1 a
comprehensive literature review of indirect matrix converter and wind generator technology
priority on doubly fed induction generator are presented. The outline of thesis work is being
described.
An overview of space vector modulation control strategy is presented in chapter 2.
The necessity calculations of a normal inverter are described.

16. 3
Chapter 3 shows the development of indirect matrix converter. The topology
description, bidirectional operation of IGBTs is being described. The combination of VSI
and CSI operation for building a indirect matrix converter is performed.
The complete space vector modulation scheme of the developed converter topology
is presented in chapter 4. The dc-link formation technology has described. The pulses
generation and calculations are made, results are shown and analyzed.
Chapter 5 describes the basic theory of DFIG and equivalent circuit modelling of
general induction machine.
The reactive power compensation, pulses generation, voltage regulation, rotor current
control strategy is presented in vector control technique of DFIG in chapter 6.
Finally in chapter 7 using collated results from the research presented, the simulation
of the system, recommendations are made. This will set the foundation for further in future
studies.
1.7 Literature review
P.C.Krause [13]: This book gives overview about the mathematical modelling of various
machines including induction machine. This book also discuss in detail about the various
reference frames and necessary transformations required for transferring the quantities from
one reference frame to another. This book also incorporates the overview about the computer
simulations of various electrical machines.
Rubén Peña, Roberto Cárdenas, Eduardo Reyes, Jon Clare, Patrick Wheeler [1]: This
paper presents a control strategy for a doubly fed induction generator (DFIG) using an
indirect matrix converter. “Virtual dc link” voltage levels are exploited between the rotor
side converter and grid side converter. The presented method leads to a reduction in the
commutation losses in the output converter and reduced common mode voltage. Soft
switching commutation is obtained by synchronizing the input and output converter pulse
width modulation patterns. This presented modulation strategy is particularly applicable in
DFIG applications because the required rotor voltage decreases when the DFIG speed is

17. 4
close to the synchronous speed. The complete control strategy is experimentally validated
using a 2-kW rig.
Rubén Peña, Roberto Cárdenas, Eduardo Reyes, Jon Clare, Patrick Wheeler [10]: In
this paper, a topology for a grid-connected generation system, based on two doubly fed
induction machines, is presented. The proposed scheme is implemented using an indirect
matrix converter (IMC) consisting of an input stage, a three-to-two matrix converter, and
two output stages consisting of a pair of voltage source inverters. Steady-state and transient
operation is discussed with the system running at below and above synchronous speed. The
results demonstrate the feasibility of the proposed scheme for variable speed energy systems.
SVM algorithm used for the inverters is designed to provide soft switching operation in the
input converter. Simulation and experimental results obtained from a 2.5-kW experimental
prototype are presented.
Benjamin J Harris, University of Wollongong: This paper begins with the presentation of
existing DFIG system using back to back PWM converters connected between rotor circuit
and grid. By adopting a matrix converter the electrical losses are reduced as the power
conversion takes place at a single stage process. This also presents existing variable speed
generator technology with a focus on DFIG systems. Finally the MC excited DFIG control
system is adapted to provide reactive power compensation to the system for the regulation of
voltage in distribution network. Simulation and analysis are conducted in the PSCAD
environment.
M. Rivera, J. L. Elizondo, M. E. Macías, O. M. Probst, O. M. Micheloud, J. Rodriguez,
C. Rojas, A. Wilson [12]: In this paper a simple and intuitive Doubly Fed Induction
Generator (DFIG) predictive rotor current control scheme is presented. Predictive control of
an Indirect Matrix Converter (IMC) is combined with predictive rotor current control of a
DFIG to achieve a very good dynamic response as the rotor currents smoothly follow the
applied reference in a ±30% range of the generator nominal rpm. Simulation results are
presented for constant torque and rotational speed, as well as for variable rotational speed
corresponding to a 10 kW generator dynamic response. Derivation and conjunction of each
model equations are also presented along with a delay error compensation strategy to counter
the practical implementation issue implicit in discrete time control computation.

18. 5
J.Karpagam, J.Karpagam, V.Kumar Chinnaiyan [2]: This paper analyses the performance of
matrix converter with three different modulation techniques such as PWM, SVPWM and
SVM. The basic principle and switching sequence of these modulation techniques are
presented in this paper. The output voltage, output current waveforms, voltage transfer ratio
and THD spectrum of switching waveforms connected to RL load are analyzed by using
Matlab/Simulink software. The simulated results are analyzed and shows that the THD is
better for SVM technique.
Xinyan Zhang, Weiqing Wang, Dagui Liu, Haiyun Wang, Xuan Cao, Shan He [14]:
This paper prove via simulation that the matrix converter can be used in the DFIG and the
control method described here can realize the average power and the reactive power
decoupled control. The indirect space vector modulation strategy and the constant switch
frequency power control based on the matrix converter were proposed. The simulation also
verified that the control structure is simple, the control need not the PI control. The machine
parameters have little influence to the control and the harmonics content is minor. The on
grid power energy quality requirement about the wind power can be satisfied is also verified.
Vlastimil Šantín [15]: This paper deals with mathematical modelling of wind power plant
with asynchronous generator. The modelling procedure is briefly explained, mathematical
descriptions and SIMULINK models of the wind power plant basic parts are shown and the
model of the whole system is presented.
Andreas petersson, Chalmers University of Technology, Sweden [16]: This thesis deals
with the analysis, modelling, and control of the doubly-fed induction generator for wind
turbines. Different rotor current control methods are investigated with the objective of
eliminating the influence of the back EMF, which is that of, in control terminology, a load
disturbance, on the rotor current. This method also has the best stability properties. In
addition it is found that this method also has the best robustness to parameter deviations. The
energy production of the DFIG wind turbine is investigated and compared to that of other
wind turbine systems. The result found is that the energy capture of the DFIG wind turbine is
almost the same as for an active stall-controlled fixed-speed (using two fixed speeds) wind
turbine. Compared to a full-power-converter wind turbine the DFIG wind turbine can deliver
a couple of percentage units more energy to the grid. It has been found that the energy
production cost of the investigated wind turbines with voltage sag ride-through capabilities

19. 6
is between 1–3 percentage units higher than that of the ordinary DFIG wind turbine without
the ride-through capability.
Arushi Shahani, University of Minnesota: This thesis presents a lossless source based
commutation strategy along with a modulation technique that minimizes the frequency of
leakage inductance commutation. It also results in the soft switching of the output converter
(Zero current switching: ZCS). The topology along with the proposed control has been
analyzed, simulated and verified through experimental results. The topology based on the
indirect modulation of matrix converters uses minimum amount of copper and has relatively
less number of semiconductor switches.
1.8 Summary
Power Electronic is a field of Electrical Engineering which mainly focuses on the control
and conversion of electric power. The power conversion system in power electronics mainly
deals with the following systems:
1. AC to DC conversion (Rectifier)
2. DC to AC conversion (Inverter)
3. DC to DC conversion (Chopper)
4. AC to AC conversion
The AC to AC converter find application where input to output frequency and
voltage need to be controlled like V/F control of induction motor. This thesis work has
importance on AC to AC conversion system. Back to back converter, cyclo-converter,
matrix converter are different topological schemes of AC to AC power conversion.
Two types of back to back converter exist depending upon the type of input to
rectifier and inverter stage. In voltage source back to back converter (VBBC) the input to
rectifier stage is a voltage source. The rectified output is filtered with a capacitor and
becomes the input to the inverter stage. Depending on the ripple quantity in rectified output,
the size of the capacitor is decided and it is called as DC-link capacitor. In current source
back to back converter (CBBC) he input to rectifier is a current source. The rectified output
filtration is done using inductor in series which becomes input to the inverter. The cyclo
converters are direct AC to AC converter without any dc-link passive component in between
them. The demerits of cyclo-converter are requirement of large numbers of switching

20. 7
devices and complex control strategies for large three phase cyclo-converter. Further using
cyclo-converter the output frequency can be varied only to 1/3rd of the input frequency.
The matrix converter topological scheme has a unique inherent bidirectional power
flow capability. By using proper modulation strategies desirable sinusoidal output voltage
can be generated by this converter. Further the input modulation can be controlled easily.
This technology can be used in all variable speed drives.
As of 2011, electric motor drives are used 64% of the world wide industrial energy.
Out of these over 90% are AC motor drives used in industries. Elevators, cranes, escalators,
paper mill, power plant drives etc needs bi-directional power flow. While the wind energy
power generation, air conditioner, production industries, aviation industries etc
unidirectional power flow. So this shows that there requirement of efficient and low cost
drive system in industries. Hence matrix converters can prove to be an efficient solution for
this area.
There are two main topologies of matrix converters. One is direct matrix converter (DMC)
and another is indirect matrix converter(IMC). The DMC topology looks similar to cyclo-
converter topology but the control technique of DMC is totally different that of the cyclo-
converter. With the development of IMC, different topologies came into existence with
lower number of switches named as Sparse matrix converter, Very sparse matrix converter
Ultra sparse matrix converter etc.
The control strategy of IMC requires coordination between the control of rectifier
and inverter stage unlike VBBC. The space vector control based control strategy for MC
gives better performance compared to carrier based control strategy. Further the zero current
switching of IMC can be easily achieved in space vector based control strategy. The
advantage of zero current switching compared to forced commutation process is that the
switching loss is less. This strategy also gives a control on the output voltage amplitude and
frequency.
There are many different varieties of configuration according to the need of power
generation. However mainly they are two types: fixed speed generators(FSG) and
adjustable/variable speed generators(VSG). Some common generator configurations are:
1. Danish concept(FSG)
2. Direct-in-line generation (VSG)

21. 8
3. DFIG based generation
Danish concept is a method of conversion using a squirrel cage induction machine
where stator is connected directly to grid. So the speed of the generator has to be regulated.
It is possible by pitch control technique. It is not much efficient system because the
maximum availability of wind power is wasted for the reason that the generator speed could
not vary to observe the maximum power. But still these methods are applicable for low
power application such as pump, small lightening system.
To effectively transfer the wind power and the problems experienced in Danish
concept adjustable speed generators are implemented now a days. Varying the speed of
generator are possible by power electronic converters which allow the rotor of generator at
variable speed. So the generator is able to produce power at various wind speed and 100%
wind power can be captured.
The direct-in-line system incorporates a squirrel cage induction generator which is
connected to grid via an AC to AC power converter. The AC to Ac converter must be
designed largely to match the power rating of generator. Generally it is greater than 1 p.u.
Filter designing is compulsorily required to remove the switching component in current
waveforms. For this reason the size of the generator is limited within a range.
The VSG system is doubly fed induction generator (DFIG) which overcomes the
downfall of Danish concept and direct-in-line method of wind power generation. So more
energy can be extracted from wind and delivered to grid. DFIG uses a wound rotor induction
generator (WRIG) where the stator is directly connected to grid and rotor is connected to
grid via AC to AC converter. It is also called Scheribus drive system and they are 2% to 3%
more efficient than the direct-in-line system. The speed range is 33% of the grid
synchronous speed. Typical modern high power generators are rated up to 5 MW.

22. 9
CHAPTER 2
2.1 Space vector modulation
Space vector modulation is an advanced control technique to create AC waveform better
than conventional PWM technique. In other hand we can say that it is a digitally enhanced
technique for generating AC waveform from DC, most commonly to drive three phase AC
motors with variable speed or variable DC. The main principle of this modulation is it treats
the sinusoidal voltage as a constant amplitude vector rotating at constant frequency. Using
this modulation technique possesses the advantage of a wide linear modulation range and
less switching loss. The THD in the spectrum of switching is less compared to other
conventional modulation technique. Though it is a digital enhanced control technique the
computational calculation is less[2].
2.2 Modulation scheme in SVM
The SVM has a flexibility of selection of switching vector for the control of both input
current and output voltage. Also this technique is helpful for a unbalanced condition. The
reference voltage vector is selected by some set of stationary vectors for an interval of time
and it is free to rotate around the space. The change in position of vector is decided by the
timing calculation during a complete cycle. The reference voltage vector corresponds to new
set of stationary vectors while it changes its angular position. By this continuous process the
desired voltage vector being synthesized. Meanwhile the selected stationary vectors can also
give desirable phase shift between input voltage and current. The overall key point of this
technique is selection of this switching vectors and calculation of the vector time interval.
Fig. 2.1: Sector division in space vector modulation

23. 10
The set of vectors are defined as instantaneous space vector. These are created by
various states. Relating the three phase voltages and current in terms of wt is difficult to
handle directly. So it can be transformed to stationary two reference frame (d-q) by park's
transformation and their relational equation is-
𝑓𝑑𝑞0 = 𝐾𝑠 𝑓𝑎𝑏𝑐
" f " is a function of voltage or current.
𝐾𝑠 = 2
3
1 − 1
2 − 1
2
0 3
2
− 3
2
1
2
1
2
1
2
In this frame there are six stationary vectors (V1, V2.....V6) and two zero vectors (V0,
V7) at centre. There are two possible vectors called as zero vector and active vector. With the
help of those eight possible vectors the reference voltage (Vref) is to be positioned. The
following steps to be followed while implementing the SVM
Step 1: Determination of Vd, Vq, Vref and angle(α).
𝑉𝑑 = 𝑉𝑎𝑛 − 𝑉𝑏𝑛 cos 60 − 𝑉𝑐𝑛 cos 60
= 𝑉𝑎 𝑛 − 𝑉𝑏𝑛 cos 60 − 𝑉𝑐 𝑛 cos 60
𝑉𝑞 = 0 + 𝑉𝑏𝑛 cos 30 − 𝑉𝑐𝑛 cos 30
=
3
2
𝑉𝑏𝑛 −
3
2
𝑉𝑐 𝑛
𝑉𝑟𝑒𝑓 = Vd
2
+ Vq
2
𝛼 = tan−1
𝑉𝑑
𝑉𝑞
Vd
Vq
= 2
3
1 − 1
2 − 1
2
0 3
2 − 3
2
Van
Vbn
Vcn

24. 11
Step 2: Determination of the time durations T1, T2, T0.
Switching time at any duration can be illustrated by-
𝑇1 =
3𝑇𝑧 𝑉𝑟𝑒𝑓
𝑉𝑑𝑐
sin
𝜋
3
− 𝛼 +
−𝜋
3
=
3𝑇𝑍 𝑉𝑟𝑒𝑓
𝑉𝑑𝑐
sin
𝜋
3
− 𝛼
=
3𝑇𝑍 𝑉𝑟𝑒𝑓
𝑉𝑑𝑐
sin
𝜋
3
cos 𝛼 − cos
𝜋
3
sin 𝛼
𝑇2 =
3𝑇𝑧 𝑉𝑟𝑒𝑓
𝑉𝑑𝑐
sin 𝛼 − (
−𝜋
3
)
3𝑇𝑍 𝑉𝑟𝑒𝑓
𝑉𝑑𝑐
− cos 𝛼 sin
−𝜋
3
+ sin 𝛼 cos
−𝜋
3
𝑇0 = 𝑇𝑧 − (𝑇1 − 𝑇2)
Step 3: Determination of switching time of each transistors
Table 2.1: Switching time of each transistor in VSI
Sector Upper switch Lower switch
1
S1= T1+T2+T0/2 S4= T0/2
S3= T2+T0/2 S6= T1+T0/2
S5= T0/2 S2= T1+T2+T0/2
2
S1= T1+T0/2 S4= T2+T0/2
S3= T1+T2+T0/2 S6= T0/2
S5= T0/2 S2= T1+T2+T0/2
3
S1= T0/2 S4= T1+T2+T0/2
S3= T1+T2+T0/2 S6= T0/2
S5= T2+T0/2 S2= T1+T0/2
4
S1= T0/2 S4= T1+T2+T0/2
S3= T1+T0/2 S6= T2+T0/2
S5= T1+T2+T0/2 S2= T0/2
5
S1= T2+T0/2 S4= T1+T0/2
S3= T0/2 S6= T1+T2+T0/2
S5=T1+T2+T0/2 S2= T0/2
6
S1= T1+T2+T0/2 S4= T0/2
S3= T0/2 S6= T1+T2+T0/2
S1= T1+T0/2 S2= T2+T0/2

25. 12
2.3 SVM of a voltage source inverter
The division of sectors in a space has been already shown in figure. Now it is important to
know about the vector notation and selection of the vector sequence to change the angular
position of the reference vector. While naming the vector always the positively connected
switches are taken in to consideration.
Fig. 2.2: Voltage source inverter topology
For the current flow from the inputs side to the load it can be noticed from figure that
either upper 2 switches with lower 1 switch or upper 1 switch with lower 2 switches are kept
on at one particular time interval. The table 2.2 describes the detail about all vectors.
Table 2.2: Vector sequence and voltage formation by SVM in inverter [2]
Voltage
vector
Switch status Line to line voltage
A+ B+ C+ VAB VBC VCA
V0 0 0 0 0 0 0
V1 1 0 0 Vdc 0 - Vdc
V2 1 1 0 0 Vdc - Vdc
V3 0 1 0 - Vdc - Vdc 0
V4 0 1 1 - Vdc 0 Vdc
V5 0 0 1 0 - Vdc Vdc
V6 1 0 1 Vdc - Vdc 0
V7 1 1 1 0 0 0

26. 13
2.4 Conclusion
Because of switching losses high frequency (>20kHz) are less efficient than lower frequency
(100Hz). Though it is an advanced control technique still filter requirements are necessary
otherwise the system efficiency will decrease. Switching losses can be reduced by
modifying the topology with less number of switches or multi level inverters. But this might
result with greater harmonics or poor power factor. If the system needs further reduction in
switching losses then another technique based on stopping the control pulses of SVM for
some duration and this duration depends upon angle of the load power factor.

27. 14
CHAPTER 3
3.1 Matrix converters
Generally transformers are used as isolation device between two different voltage level
systems and to provide galvanic isolation which is necessary for safety purpose. Line
frequency transformers are often used at high power system which is a most expensive
component. Replacement of the low frequency transformer with its high or medium
frequency counterpart along with power electronic converter leads to dramatic increase in
power density. The increase in availability high frequency and low density magnetic
materials and reduction in the cost of semi conductor devices leads to design various
structure having comparable efficiency and economic viability. Also due to addition in
feature like reactive power support, voltage and frequency regulation these semiconductor
devices has an enabling technology for modernization of electric power distribution system.
High power density electric motor drives for example, electric traction, wind power, medium
voltage ASD are the major area of application of these semiconductor devices.
In case of wind turbines in replacement of low frequency transformers, power
electronic transformers are located at bottom of tower and eliminate the quantity of copper
loss occurred in carrying the generated power at low voltage. But the high current still
remains throughout the system. These devices or topologies can be used either in series or
parallel say modular units or multilevel structures to match with the grid voltage and rated
power. Reduction in efficiency, power density, reliability is also some of the additional
features that can be experienced by using these topologies.
Fig. 3.1: Classification of AC to AC converters

28. 15
3.2 Development of indirect matrix converter
The development of indirect conventional matrix converter with bidirectional switches was
done by Venturini and Alesina in 1980. This topology was used by many other researchers
for making it more efficient by using different modulation techniques. In 1985 Kastner and
Rodriguez and Neft and Schauder showed the implementation of 9 switches CMC for vector
control of induction machines. Mean while in 1983 Rodriguez developed a diffenent control
technique based on 'fictitious dc link'. In this method the switching is arranged so that the
output line is switched between the most positive and most negetive input lines using PWN
technique as used in conventional VSI.
Therefore in 1986 a primitive IMC was put up by Ziogas which was very much
similar to voltage source back to back converter without a dc link capacitor. The topology
given by Ziogas was analyzed by Kim et al in 1998. It was found that this converter
topology can't provide sinusoidal input current. Hence the topology was later named as
fundamental frequency front end converter by Gopfrich and Rebereh in 2003.
Meanwhile in those years academic researchers mostly focused on the CMC
topology and tried to devise new modulation for CMC. This modulation scheme was mostly
classified into direct frequency conversion scheme and indirect frequency conversion
scheme. In indirect frequency conversion scheme the conversion is fictitiously divided into a
voltage fed rectifier at input stage and an inverter at output stage with impressed output. This
idea was implemented by Limori et al, which is presently known as two stages IMC. This
IMC is a VBBC inspired by the technology and concept of CMC.
(a) (b)
Fig. 3.2: First topology of Indirect Matrix Converter (a) Indirect Matrix Converter with suppressed dc
link component (b) Two stage Indirect Matrix Converter topology [3]

29. 16
(a)
(b)
Fig. 3.3(a),(b): Topologies of Direct Matrix Converter [3]

30. 17
3.3 Topology description of Indirect Matrix Converter
In a few years the matrix converter has bring considerable attention for its featured operation
and efficiency. Basically Matrix converter is a combination of semiconductor switches
which gives three phase ac output directly from three phase ac input. It is an alternative to
the conventional back to back converter generally used in drives. Indirectly it can be
described as a force commutated Cyclo converter. This type of converter also called as
single stage AC-AC converter because the input and output currents and sinusoidal. There is
no energy storage element between converter and inverter side of the topology. Also the
capacitor sizing is a difficult and expensive task in normal back to back converter. The
switching scheme of the individual devices in such a way that a high virtual dc link voltage
is created. It can be reduced by either changing the modulation strategy of the converter or
inductive-resistive load. Direct Matrix Converter and Indirect Matrix Converter are two
different topologies of MC. The performance of IMC is similar to DMC considering input
current distortion, no. of devices and bidirectional power flow. Only a drawback of this
converter is the input to output voltage ratio is 87% for sinusoidal input and output. Several
modulation techniques like PWM, SVPWM, SVM has already been experimentally
implemented by many people. However a digital logic called space vector modulation is
successfully applied to matrix converter.
Fig. 3.4: Topology of Indirect Matrix Converter modulation scheme
The topology described in the thesis is a combination of current source inverter (grid side
converter) and voltage source inverter (load side converter) and the virtual dc link between
the two stages of conversion is chopped with a 50% duty cycle by GSC. The load side

31. 18
converter first rectifies the high frequency AC to get back the virtual DC link and then
inverts it to generate adjustable speed and magnitude. Any transition of the load side needs
commutation of leakage energy resulting in output voltage loss, common mode voltage
switching and reduction in switching frequency. Here a novel space vector modulation
technique has been developed to minimize the frequency of leakage commutation.
3.4 Operation of bidirectional switch in Matrix Converter
Matrix converter is a direct ac-ac converter that converts a balanced three phase ac voltage to
balanced three phase modulated ac voltage with adjustable magnitude and frequency. The
four quadrant operation of a bidirectional current flow is described below. The switch is
implemented as a common emitter of two IGBTs. The switching of one leg using four step
commutation.
Fig. 3.5: Four step commutation scheme of a bidirectional switch
Here the case, when leg current positive is considered, i>0 the Q1,Q2 are conducting
pair of IGBT and Q3,Q4 are non conducting pair of IGBT.
Step 1: Turn off Q2.
Step 2: Turn on Q3, If Vab>0 then no switching takes place otherwise Vab<0, natual
commutation will occur.
Step 3: Turn off Q1.
Step 4: Turn on Q4.
The switching of single leg is independent in a matrix converter. At a particular time
interval one switch of single leg is turned on to avoid the short circuiting. Another important

32. 19
thing is at least one switch should be on all time in one leg to ensure the smooth current
flow. In fig SaA, SbB, ScC are on that means the switching state will be [b b c].
But our proposed converter topology is different from the direct modulation method.
So it is said as indirect modulation method and the topology name is indirect matrix
converter. Before understanding the indirect commutation method it is important to
understand the modulation of voltage source inverter.
3.5 Voltage source inverter
The structure of VSI describes that, it consist of three legs. Each leg consists of series
connection of two IGBTs with anti parallel diode. Each switch in VSI allows bidirectional
current flow and blocks voltage in one direction. A three phase balanced output with variable
magnitude and frequency can be generated by space vector modulation. (3.1) denotes the
voltage space vector and (3.2) denotes balanced line to neutral voltage. ω is angular
frequency.
𝑉0 = v 𝑎𝑛0 + v 𝑏𝑛0 𝑒 𝑗2𝜋 3
+ v 𝑐𝑛0 𝑒−𝑗2𝜋 3
(3.1)
𝑉𝑎 𝑛 = 𝑉0 cos 𝜔𝑡 + ∅
𝑉𝑏𝑛 = 𝑉0 cos 𝜔𝑡 − 2𝜋
3
+ ∅ (3.2)
𝑉𝑐 𝑛 = 𝑉0 cos 𝜔𝑡 +
2𝜋
3
+ ∅
𝑉𝑟𝑒𝑓 = 𝑉𝑎𝑛 + 𝑉𝑏𝑛 𝑒 𝑗2𝜋/3
+ 𝑉𝑐𝑛 𝑒−𝑗2𝜋/3
(3.3)
=
3
2
𝑉0 𝑒 𝑗 𝜔𝑡 +∅
One of the important phenomena is only one switch state is to be change when
moving from one switching state to another. Therefore there are 6 active switching states
with 2 zero switching state. The switching states of a VSI are:
Zero states: [0 0 0], [1 1 1]
Active states: [1 0 0], [1 1 0], [0 1 0], [0 1 1], [0 0 1], [1 0 1]

33. 20
A switching state [1 1 0] implies SA1, SB1 and SC2 are on as shown in Fig. 3.6. As the neutral
of the three-phase load is the floating, sum of the three line currents must be zero (ia + ib +
ic= 0). As the load is balanced it is possible to express the line neutral voltages in terms of
the pole voltages. When state [1 1 0] is applied VaN = Vdc, VbN = Vdc and VcN = 0. This is the
vector V2 corresponding to the active state [1 1 0].
𝑉𝐴 =
1
3
2𝑉𝑎 𝑛 − 𝑉𝑏𝑛 − 𝑉𝑐 𝑛
𝑉𝐵 =
1
3
2𝑉𝑏𝑛 − 𝑉𝑐 𝑛 − 𝑉𝑎 𝑛 (3.4)
𝑉𝐶 =
1
3
2𝑉𝑐 𝑛 − 𝑉𝑎 𝑛 − V𝑏𝑛
Similarly it is possible to compute voltage vectors corresponding to all other five active
switching states.
3.6 Indirect modulation scheme of matrix converter
The presented modulation of the power electronic device in this thesis is based on the
indirect modulation of matrix converter and the topology we can say it as indirect matrix
converter, where the switches perform the four quadrant operation similar to voltage source
inverter. that means they have to block voltage in one direction and allow the flow of current
in both direction. This is possible by common emitter connection of two IGBTs.
Indirect matrix converter can be explained by the figure shown. Here a three phase
rectifier is connected with a voltage source inverter through what is called virtual dc link.
The rectifier is connected generally with grid to modulate the three phase AC or grid voltage
or it simply rectifies the AC voltage to a virtual dc to synthesize the average input current
space vector aligned along the input voltage. The space vector modulation is responsible for
input power factor correction and adjustable frequency and magnitude in the output which
can be fed to load end.
There are 18 active combinations of switches of the indirect matrix converter as
specified later. Each active combination is said as a switching state which is directly in
relation with vector selection. For example V2 [1 1 0] means (SA1, SB1, SC2) is applied on
VSI and (Sb1, Sc2 are on) is applied to rectifier.

34. 21
Fig. 3.6: Voltage source inverter
Sampling cycle both Iin and Vref are in the following respective switching state over
one sampling cycle where dI1, dI2, dV1, dV2 are obtained from
𝑑𝐼1 =
𝐼1
𝐼𝑑𝑐
sin(60 − 𝛽)
𝑑𝐼2 =
𝐼1
𝐼 𝑑𝑐
sin(𝛽) (3.5)
And
𝑑𝑉1 =
3𝑉0
𝑉𝑑𝑐
sin( 60 − 𝛽)
𝑑𝑉2 =
3𝑉0
𝑉 𝑑𝑐
sin( 𝛽) (3.6)
The input converter or rectifier functions as a CSI is responsible to create a virtual dc
link in case of the hypothetical converter implementation indirect modulation as described.
The output side converter acts as VSI to generate AC by receiving back the dc link voltage.
Minimising the switching transitions of the system in order to minimize the frequency of
leakage commutation is the main objective of the modulation. The application of voltage and
current vectors over a sample time is described in the next chapter. In short we can say that
inverter is switched only once over a sample time and zero vectors are applied with the help
of input converter. It is called the free-wheeling time. Sv1 represent the switching pulse
corresponding to V1 vector of the output converter shown and the vector sequence or
selection of vector over a complete cycle is shown below.

35. 22
Fig. 3.7: Application of voltage and current vectors over Ts
Fig. 3.8: Generation of switching signals
3.7 Conclusion
The chapter provides a brief introduction to various matrix converters. The capabilities,
advantages, disadvantages, features also a brief discussion about the historical time-line,
technological development is presented. The detailed commutation or modulation of Indirect
Matrix Converter will be discussed in next chapter.

36. 23
CHAPTER 4
4.1 Indirect Matrix converter
In a few years the matrix converter has bring considerable attention for its featured operation
and efficiency. Basically Matrix converter is a combination of semiconductor switches
which gives three phase ac output directly from three phase ac input. It is an alternative to
the conventional back to back converter generally used in drives. Indirectly it can be
described as a force commutated Cyclo converter. This type of converter also called as
single stage AC-AC converter because the input and output currents and sinusoidal. There is
no energy storage element between converter and inverter side of the topology. Also the
capacitor sizing is a difficult and expensive task in normal back to back converter. The
switching scheme of the individual devices in such a way that a high virtual dc link voltage
is created. It can be reduced by either changing the modulation strategy of the converter or
inductive-resistive load. Direct Matrix Converter and Indirect Matrix Converter are two
different topologies of MC. The performance of IMC is similar to DMC considering input
current distortion, no. of devices and bidirectional power flow. Only a drawback of this
converter is the input to output voltage ratio is 87% for sinusoidal input and output. Several
modulation techniques like PWM, SVPWM, SVM has already been experimentally
implemented by many people. However a digital logic called space vector modulation is
successfully applied to matrix converter.
4.2 Commutation scheme of IMC
The source from grid feeds the input terminals of converters where as the output terminals
are linked to three phase machine like induction motor. The size of capacitive filter on the
voltage feed side and inductive filter on the current feed side are inversely proposal to
switching frequency if the MC. The capacitive filter on the voltage- fed side and the
inductive filter on the current- fed side represented in the scheme of MC are intrinsically
necessary. Their size is inversely proportional to the matrix converter switching frequency.

37. 24
(a)
(b)
Fig. 4.1: Topology of Indirect Matrix Converter, (a) Indirect matrix converter, (b) Single leg of
indirect matrix converter
The IMC is assembled by series connected two mutually anti-parallel connected
current link converters and a two level-six switch voltage source converter. Instead of special
sensing mechanism of current and voltage, IMC can commutate offering a reduced
complexity of choosing modulation. IGBT with reverse blocking have recently available for
construction of bi-polar switch having two anti-parallels connected transistors.

38. 25
Fig. 4.2: Current flow for positive power flow in one leg of IMC [3]
Fig. 4.3: Current flow for negative power flow in one leg of IMC [3]

39. 26
Fig. 4.3: Power flow in IMC
4.3 DC-link formation in IMC
The inverter input state and rectifier input state have to be performed in order to avoid short
circuit and dead time between transistor turn-on for a particular switching state. To change
from one switching state to another it should to care about that, there should not be any
bidirectional path among any input lines having a continuous path for current flow. A
reference voltage is provided using a rotating reference vector. This orientation of reference
vector is chosen in order to control the fundamental component of frequency and magnitude
in the line side. The most efficient dc link voltage generated by this modulation contains less
number of harmonic distortions. The objective of any modulation scheme is to generate
variable output with maximum fundamental component and minimum harmonics.
IMC provide freedom in control strategy which reduces the complexity in
communication problem. The important technique that has to be considered is that, in the
free-wheeling time of inverter stage the rectifier should commutate with zero dc-link current
with no overlapping in transistor switching. Thus reduces the losses in switching of the
system. Further the number of switches has also reduced and many new topologies are being
developed named as SMC, VSMC, USMC etc.

40. 27
Fig.4.4: Behaviour of dc-link voltage and three phase input voltage with average dc-link voltage [3]
The concept of modulation described here can establish zero dc-link current and the
commutation is applicable to IMC. For the maximum output voltage formation one phase
input is hold on to positive or negative dc-link bus in a particular interval and phase voltage
has highest absolute value shown in table.
Table 4.1: Output Voltage over a Period
ωt = φ Up Un U
0 ... π/6 Ua Ub, Uc Uab, Uac
π/6....2π/6 Ua, Ub Uc Uac, Ubc
2π/6....3π/6 Ub, Ua Uc Ubc, Uac
3π/6....4π/6 Ub Uc, Ua Ubc, Uba
4π/6....5π/6 Ub Ua, Uc Uba, Ubc
5π/6....6π/6 Ub, Uc Ua Uba, Uca
6π/6....7π/6 Uc, Ub Ua Uca, Uba
7π/6....8π/6 Uc Ua,Ub Uca, Ucb
8π/6....9π/6 Uc Ub,Ua Ucb, Uca
9π/6....10π/6 Uc, Ua Ub Ucb,Uab
10π/6....11π/6 Ua, Uc Ub Uab, Ucb
11π/6....12π/6 Ua Ub, Uc Uab, Uac

41. 28
Now considering the symmetry of the topology the three phase input having angular
frequency ω amplitude U1 is;
Ua = U1 cos θ
Ub = U1 cos θ −
2π
3
(4.1)
Uc = U1 cos θ +
2π
3
Where, Ua + Ub + Uc = 0
Now instead of considering the total rotating field of the reference vector we will
limit our consideration in the interval 0 to π/6. Here the Ua is clamped on with maximum
positive voltage and Uac, Uab are two line-line voltage segments. The voltage generated for
this state having two different levels assuming the instant average value of current as
constant. The total interval (0 to π/6) is denoted by Tp. Further the Tp is divided into many
segments depending on the vector selection or switching pattern and denoted by Δ.
Switching of the rectifier takes place during the free-wheeling interval for the
coordinated commutation of rectifier and inverter stage. This can be achieved by turning on
the transistor of one leg simultaneously, assuming input currents ia, ib, ic = 0 and Dab+Dac =
1, where Dab, Dac are relative on times for generating Uab, Uac. Simpler commutation can be
implemented by changing all switching state of rectifier linking with the inverter free-
wheeling interval. In similar way inverter stage can be operated.
ia = Dac + Dab i , ib = − Dab i, ic = −(Dac )i
Dac = −
ic
ia
= −
Uc
Ua
and Dab = −
ib
ia
= −
Ub
Ua
(4.2)
Now the result in output can be achieved by two active vectors V(100) and V(110)
and either one of the free-wheeling state V(000) or V(111). So we can write dc-link voltage
as U = Uac and U = Uab and time period as
∆ 𝑎𝑏 = 𝐷𝑎𝑏
𝑇𝑝
2
And ∆ 𝑎𝑐 = 𝐷𝑎𝑐
𝑇𝑝
2
(4.3)
In each voltage segment the pattern of turning on and turning off states of devices are
changed considering that there should be only one state change at each time. And each
change in state is denoted by δ.

42. 29
so, δ100,ac =
∆100 ,ac
∆ac
and δ100,ab =
∆100 ,ab
∆ab
(4.4a)
Similarly
δ110,ac =
∆110 ,ac
∆ac
and δ110,ab =
∆110 ,ab
∆ab
(4.4b)
Taking U100 = 2
3 U and U110 = 2
3 Uejπ/3
the output formed in time Tp/2 is
U∗
=
2
3
Tp
2
Uac ∆100,ac + Uab∆100,ab + e
jπ
3 Uac ∆110,ac + Uab ∆110,ac (4.5)
Considering above equations-
U∗
= Uac Dac + Uab Dac δ100 + Uab Dab + Uac Dac ejπ/3
δ110 (4.6)
And average value is
U = Uab Dab + Uac Dac
so, U∗
=
2
3
[Uδ100 + Ue
jπ
3 δ100] (4.7)
Fig. 4.5: Sector diagram comprising of vectors

43. 30
Fig. 4.6: Switching diagram for the generation of voltage and current over a section [3]
4.4 Dwell time calculation
Time interval of active switching states can be calculated by directly referring local average
values. To calculate on time intervals of active switching states we could directly refer local
average value of the dc link voltage. Referring to the dwell time interval of two level inverter
T =
Vref
Vdc
sin π
3−α
sin π
3
Ts (4.8)
Where U = Vdc, U2
∗
= U∗
and U2
∗
= Vref
Therefore
δ100 = 3
U2
∗
U
cos π
6 + α (4.9)

44. 31
And
δ110 = 3
U2
∗
U
sin α (4.10)
From (4.8) , (4.9) and (4.10)
∆100,ac =
−1
3
U∗
U
2 Tp cos π
6 + α Uc (4.11)
∆100,ab =
−1
3
U∗
U
2 Tp cos π
6 + α Ub (4.12)
∆110,ac =
−1
3
U∗
U
2 Tp sin α Uc (4.13)
∆110,ab =
−1
3
U∗
U
2 Tp sin α Ub (4.14)
In similar way we can calculate the dwell time for all intervals from π/6 to 2π/6, 2π/6 to
3π/6.........11π/6 to 2π. We can observe that the output voltage formed is √3/2 times of U1.
Therefore the modulating index of complete analysis can be taken as
M =
U
U1
≤
3
2
Table 4.2: Switching sequence of IMC over a section

45. 32
4.5 Simulation results and discussion
In this section the MATLAB results of indirect matrix converter are presented. The
specifications of circuit is kept the same that of theoretical study. The waveform of different
parameter has been analyzed. The simulation has been done with three phase star connected
R= 5 ohm and L= 6 mH with modulation index 0.8.
The dc-link varies between the maximum and minimum values since it is formed by
voltage difference between two phases as discussed in theory. The maximum and minimum
dc-link voltages are Umax = 207volt, Umin = 180volt.
The voltage appearing across the R-L load of one phase is shown. The output phase
voltage contains 5 levels. The peak of the output dc voltage is 2
3 Umax . The peak value of
output phase voltage is 2
3 𝑋 207 = 138.5 v. The second level is 1
3 Umax = 69.2v
Fig. 4.7: DC link voltage between rectifier and inverter stage

46. 33
Fig. 4.8: Output phase voltage
Fig. 4.9: Magnified values of output phase voltage.

47. 34
Fig.10. Output line voltage
The current through RL load is shown. The peak value of current is calculated as
𝐼 =
𝑈
𝑍
=
𝑈
𝑅2 + 𝑋𝑙
2
Fig. 4.11: Output current

48. 35
Fig. 4.12: Harmonic profile of output current
The THD percentage without any filter circuit is verified to be 16.3% which is quite
appreciable. The output phase voltage has also been analyzed with respect to that of
modulation index. The variation in modulation index has been achieved by keeping the input
phase voltage constant and changing output phase voltage shown in table 4.3.
Table 4.3: Comparison of calculated and simulated output phase voltage
Modulation
index
Calculated output
phase voltage
Input voltage
Simulated phase
output voltage
0.8 96 120 91.26
0.7 84 120 81.44
0.6 72 120 69.94
0.5 60 120 58.29
0.4 48 120 46.62
0.3 36 120 34.97
0.2 24 120 23.3
0.1 12 120 11.6

49. 36
Fig. 4.13 Simulated phase voltage with various modulation index
4.6 Conclusion
A control strategy for modulation of Indirect Matrix converter has been experimentally
verified. The sizing of capacitor has been omitted, thus results in reduction of cost. Also
stabilize the frequency variations. Though more number of switches is used, but the
switching losses can be reduced by this soft switching control algorithm which is
experimentally verified.
0
10
20
30
40
50
60
70
80
90
100
0 0.2 0.4 0.6 0.8 1
Simulatedoutputphasevoltage
Modulation Index

50. 37
CHAPTER 5
5.1 Wind energy conversion system
Wind Energy Conversion System (WECS) is a combination of electronic, electrical and
mechanical system that converts the useful mechanical energy to electrical energy to drive
various electrical equipments. In simpler way we can say that it is an electricity generating
system from wind. Wind power is an alternative to conventional fossil fuel which is plentily
available, renewable, easily available. The generation of power produces no green house
gases. So it is a clean energy. The space used for its production is quite small compared to
traditional method of electricity generation from renewable sources.
From historical data sheet 'Denmark' generates 40% of its electricity from wind by
2015 which is largest in the world wide. Except Denmark 83 other countries around world
produces electricity from wind and supply power to grid. First wind mill used for the
production of electricity was built in 'Scotland' in July 1887 by Prof. James Blyth.
The offshore wind energy production is more efficient and gives large amount of
energy. But it is quite complex and expensive method. Generally the onshore wind firms are
comparatively less expensive and transmission of energy to grid is easy.
Fig 5.1: Block diagram of wind energy conversion system
Wind Energy Conversion System (WECS) is a combination of electronic, electrical
and mechanical system that converts the useful mechanical energy to electrical energy to
drive various electrical equipments. In simpler way we can say that it is an electricity
generating system from wind. From the physical setup viewpoint, we can classify them in to
two categories. They are horizontal axis wind turbines and vertical axis wind turbines.
Initially, vertical axis designs were considered due to their advantages of having gears and
generating equipments at the tower base and do not need yaw-system arrangement.

51. 38
However, the following disadvantages caused the VAWT to have a diminished presence in
the commercial market.
 Less aerodynamic efficiency: The blade surface is much closer to the axis.
 Housing usually at ground level. So it is not feasible to have the gearbox at ground
level because of the weight and cost of the transmission shaft.
In HAWT, the wind turbine blades rotate about an axis parallel to the ground and
wind flow. So the energy accumulated from wind is sufficiently more than a VAWT. Almost
all the larger generation capacity wind turbines employed in modern wind farms are HAWT.
They are more suitable for harnessing more wind energy. However, HAWT are subjected to
reversing gravitational loads which impose a limit on the size of such turbines. The rotation
of both HAWT and VAWT can be powered primarily by lift or drag force depending on the
design of the blade.
(a) (b)
Fig. 5.2: Wind turbines (a) Horizontal axis wind turbine, (b) Vertical axis wind turbine
Depending on the application there are two common ways of generating power from
wind turbine. Geared wind turbine and direct drive turbine. Direct drive turbine need a huge
generator and output directly proportional to the wind speed. But in case of geared turbine
the gear box helps to step up the speed and generator can operate at constant speed. More
energy can be collected by the help of efficient power electronic converters.

52. 39
Now days the most challenging scenario is to draw the most possible energy from the
variable speed wind turbine. Thus the conventional sources of energy will be saving for the
coming generation. The basic flow of the generation is represented here. In this thesis work
we have followed the HAWT. The generator, power electronic converter are discussed in
chapter 3, 4 and 6.
5.2 Types of wind turbines in WECS
Wind Turbine Generators in the current market can be classified into three types according
to their operation speed and the size of the associated converters as[16]:
 Fixed Speed Wind Turbine (FSWT)
 Variable Speed Wind Turbine (VSWT) with:
 Partial Scale Frequency Converter Wind Turbine (PSFCWT)
 Full Scale Frequency Converter Wind Turbine (FSFCWT)
Fixed speed wind turbine generator cost is less and low maintenance is required. Fixed speed
wind turbine generators are simple, robust and reliable. But main disadvantages of the
system are relatively low energy conversion efficiency, high mechanical stress and high
fluctuations to grid.
Variable speed wind turbine generators advantages are it has high energy conversion
efficiency, improved power quality and reduced mechanical stress. But the main
disadvantages of this system are its cost is comparatively higher than the fixed speed wind
turbine generator and losses are there due to use of converters. Its control system is more
complex.
Variable-speed variable-pitch wind turbines utilizing DFIG, also called PSFCWT,
are the most popular in the wind power industry especially for multi-megawatt wind turbine
generators. The DFIG consists of a wound rotor induction generator with the stator side
connected directly to the constant frequency three-phase grid and the rotor windings
connected to grid through a bidirectional back-to-back ac/dc/ac IGBT voltage source
converter .Its output power can be controlled via pitch control as well as back to back
converter control.

53. 40
5.3 Operating region of wind turbines
The operating region of a variable-speed variable-pitch wind turbine can be illustrated by
their power curve, which gives the estimated power output as function of wind speed as
shown in Figure 1 Three distinct wind speed points can be noticed in this power curve:
 Cut-in wind speed: The minimal wind speed at which wind turbine can start to
generate power.
 Rated wind speed: Wind speed at which the wind turbine generates the rated power,
which is usually the maximum power wind turbine can produce.
 Cut-out wind speed: Wind speed at which the turbine ceases power generation and
is shut down (with automatic brakes and/or blade pitching) to protect the turbine
from mechanical damage.
Fig. 4.3: Power curve of a variable speed wind turbine
Wind turbine is the main component of Wind energy system. Wind turbines produce
electricity by using the power of the wind. The kinetic energy of the wind is converted into
mechanical energy by the blade of the wind machine. This mechanical energy is converted to
rotational energy by the shaft of the electromechanical drive. The generator then convert this
energy to electrical energy. The gear drives are used to maintain the constant speed at the
generator shaft to protect it from the problems arising due to the wind speed variation.

54. 41
5.4 Power of a wind turbine
Wind turbines convert the kinetic energy present in the wind into mechanical energy by
means of producing torque. Since the energy contained by the wind is in the form of kinetic
energy, its magnitude depends on the air density and the wind velocity. The wind power
developed by the turbine is given by the following equations [16]-
Wind energy system converts the kinetic energy of the wind into the electrical energy. The
kinetic energy produced by a moving object is expressed as
𝐸𝑘𝑖𝑛 =
1
2
𝑚𝑣2
(5.1)
In this case, m is the mass of air and v is the wind velocity. The mass m could be derived
from
𝑚 = 𝜌 𝐴𝑑 (5.2)
where
𝜌 = air density (kg/m3).
A = area covered by the rotor blade.
d = distance travelled by the wind.
The mechanical power of the wind turbine (𝑃𝑤 ) is defined as the kinetic energy over the
time (t), thus Pw is expressed as
Pw =
Ekin
t
=
1
2
ρAdv2
t
=
1
2
ρAv3
(5.3)
𝑃𝑤 is the ideal power captured by the wind turbine. The actual power of the wind turbine
depends on the efficiency of the turbine represented by 𝐶𝑝 𝜆, 𝛽 which is the function of the
tip speed ratio 𝜆 and pitch angle 𝛽 of the rotor blades. Cp is the performance coefficient
of the turbine and generally less than 0.5. The tip speed ratio is defined as the𝝺, the wind
speed and is given by
𝜆 =
𝜔𝑅
𝑣
(5.4)
where, ω is the turbine rotational speed, and R is the radius of the turbine. Therefore, the
actual power captured by the wind turbine is given by,
𝑃 =
1
2
𝐶𝑝 𝜆, 𝛽 𝜌𝐴𝑣3
(5.5)
The torque of the wind turbine could be expressed as
𝑇 =
1
2
𝐶𝑡 𝜆, 𝛽 𝜌𝐴𝑅𝑣2
(5.6)

55. 42
where 𝐶𝑡 𝜆, 𝛽 = 𝐶𝑝 𝜆, 𝛽 𝜆 is the torque coefficient of the wind turbine.
The turbine power coefficient 𝐶𝑝 𝜆, 𝛽 is a nonlinear function and expressed by a generic
function
𝐶𝑝 𝜆, 𝛽 = 0.5176
116
𝜆 𝑖
− 0.4𝛽 − 5 𝑒
−21
𝜆 𝑖 + 0.0068𝜆 (5.7)
where,
1
𝜆 𝑖
=
1
𝜆+0.08𝛽
−
0.035
𝛽3+1
5.5 Wind power versus speed characteristics
Figure below describes the curves of the wind turbine power versus the rotor speed (ω) for
the different wind speeds. From the figure we can obtained that the different power curves,
the maximum powers are achieved at the different rotor speeds. Therefore, the rotor speed
should be operated at the optimum speed. This technique is called as MPPT (Maximum
Power Point Tracking) technique.
Fig. 5.3: Power versus Speed characteristics of wind turbine[16]
The above fig illustrates 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. At the base speed of turbine (1200
rpm), maximum power at the base speed is obtained. Therefore, the turbine output power is
directly proportional to the rotor speed.

56. 43
The various control techniques used in wind turbines are pitch control, yaw control and stall
control. But in the modern variable speed-variable pitch wind turbines, pitch control is the
most popular control scheme. In this control scheme, the horizontal axis wind turbine blades
are rotated around its tower to orient the turbine blades in upwind or down wind direction.
5.6 Turbine design
To accumulate or extract maximum energy from wind it is necessary to follow the
specifications of the design of wind turbine. The aerodynamics of turbine blades, height of
turbine, selection of generator, gearbox ratio, power converters are the important building
block of a wind turbine. Though the behaviour of wind flow is not straight forward
throughout the year, so it is important to put some safety factors of wind turbines in
designing it. Some of the control factors for the design of an efficient wind energy
conversion system are[15]
 Turbine speed: It depends on blade pitch angle (variable speed turbine) and stall
regulated control (fixed speed turbine).
 Shaft speed: It depends on the gear box ratio. The ratio of the number of tooth to
convert a low speed rotating shaft (turbine blade side) to high speed rotating
shaft (generator side).
 Generation system: There are various types of generators used according to the
user need. For example induction generator, synchronous generator, doubly fed
induction generator.
 Safety control: Yaw control mechanism to move the turbine towards the wind
direction. Braking system is to stop the turbine in case of natural disaster.

57. 44
CHAPTER 6
6.1 Doubly-fed induction generator in WECS
With increasing of wind power into electrical grids, DFIG based wind turbines are largely
deployed due to their dynamic response and operating with various speed feature. Wind
turbines are subjected to variation of load and impact of sudden change in wind speed with
respect to time due to the non linear behaviour of environment and increase in population. So
the necessity of wind power to grid has been increasing day by day.
The term "Doubly Fed" refers to the fact that the voltage on the stator is fed from the
grid and the voltage on the rotor is also induced indirectly by grid via the power converter.
This system allows a variable-speed operation over a large, but restricted, range. The
converter compensates the difference between the mechanical and electrical frequencies by
injecting a rotor current with a variable frequency . Hence, the operation and behaviour of
the DFIG is governed by the power converter and its controllers.
6.1.1 Advantages
1) Power factor control can be implemented in this system. Because it has ability to control
reactive power and ability of decouple control of active and reactive power by independently
controlling the rotor excitation current.
2) DFIG is wound rotor induction machine which is simple in construction and cheaper than
the synchronous machine. In DFIG, converter rating is typically 25-30 % of total system
power which results: reduced converter cost, less harmonics injection to the connected grid
and improved overall efficiency (approx. 2-3% more than full scale frequency converter) of
the wind turbine system
3) It can operate in Generator/Motor mode for both super synchronous and sub synchronous
speed mode with four possible operating conditions.
4) It is not necessarily to be magnetized from the power grid since it can be magnetized from
the rotor circuit too.
5) A speed variation of ±30% around synchronous speed can be obtained by the use of
power converter of 30% of nominal generated power.

58. 45
6) High energy conversion efficiency.
6.1.2 Disadvantages
1) Inevitable need of slip rings and gear box which requires frequent maintenance.
2) Limited reactive power capability and fault ride through capability.
6.2 DFIG equivalent circuit
Fig. 6.1: Equivalent circuit of DFIG
Applying Kirchhoff's voltage law to the circuit
𝑉𝑠 = 𝑅𝑠 𝐼𝑠 + 𝑗 𝜔1 𝐿 𝑠𝜆 𝐼𝑠 + 𝑗𝜔1 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 (6.1)
𝑉𝑟
𝑠
= 𝑅 𝑟 𝑠 𝐼𝑟 + 𝑗 𝜔1 𝐿 𝑟𝜆 𝐼𝑟 + 𝑗 𝜔1 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 (6.1.1)
0 = 𝑅 𝑚 𝐼 𝑅𝑚 + 𝑗𝜔1 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 (6.1.2)
Where
Vs =stator voltage, Rs = stator resistance
Vr = rotor voltage, Rr = rotor resistance
Is = stator current, Rm = magnetizing resistance
Ir = rotor current, Lsλ = stator leakage inductance
IRm = magnetizing resistance current, Lrλ = rotor leakage inductance
ω1 = stator frequency, Lm = magnetizing inductance

59. 46
Slip = (w1 – wr) / w1 = w2 / w1 (6.2)
Where, wr is the rotor speed and w2 is the slip frequency. Moreover, if the air-gap fluxes,
stator flux and rotor flux are defined as
Air gap flux (𝛹𝑚 ) = 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 (6.3)
Rotor flux (𝛹𝑟) = 𝐿 𝑟𝜆 I 𝑟 + 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 = 𝐿 𝑟𝜆 𝐼𝑟 + 𝛹𝑚 (6.4)
Stator flux (𝛹𝑠) = 𝐿 𝑠𝜆 𝐼𝑠 + 𝐿 𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼 𝑅𝑚 = 𝐿 𝑠𝜆 𝐼𝑠 + 𝛹𝑚 (6.5)
The equations describing the equivalent circuit can be rewritten as:
𝑉𝑠 = 𝑅𝑠 𝐼𝑠 + 𝑗𝜔1 𝛹𝑠 (6.7)
𝑉𝑟
𝑠
= 𝑅 𝑟 𝑠 𝐼𝑟 + 𝑗𝜔1 𝛹𝑠 (6.7.1)
0 = 𝑅 𝑚 𝐼 𝑅𝑚 + 𝑗𝜔1 𝛹𝑚 (6.7.2)
The resistive losses of the induction generator are
𝑃𝑙𝑜𝑠𝑠 = 3 𝑅𝑠 𝐼𝑠
2
+ 𝑅 𝑟 𝐼𝑟
2
+ 𝑅 𝑚 𝐼 𝑅𝑚
2
(6.8)
And it is possible to express the electro-mechanical torque (Te) as
𝑇𝑒 = 3𝑛 𝑝 𝐼 𝑚 𝛹 𝑚 𝐼 𝑟∗ = 3𝑛 𝑝 𝐼 𝑚 𝛹𝑟 𝐼 𝑟∗ (6.9)
np = Number of pole pair
6.3 DFIG Mathematical Modelling
Vds = rsIds − ωsλqs +
d
dt
λds (6.10)
Vqs = rsIqs + ωsλds +
d
dt
λqs (6.11)
Vdr = rrIdr − ωs − ωr λqr +
d
dt
λdr (6.12)
Vqr = rrIqr + ωs − ωr λdr +
d
dt
λqr (6.13)

60. 47
where
𝑉𝑑𝑠 , 𝑉𝑞 𝑠 = d-axis , q-axis stator voltage respectively
𝑉𝑑𝑟 , 𝑉𝑞 𝑟 = d-axis , q-axis rotor voltage
𝐼𝑑𝑠 , 𝐼𝑞𝑠 = d-axis , q-axis stator current
𝐼𝑑𝑟 , 𝐼𝑞𝑟 = d-axis , q-axis rotor current
𝜆 𝑑𝑠 , 𝜆 𝑞𝑠 = d-axis , q-axis stator fluxes
𝜆 𝑑𝑟 , 𝜆 𝑞𝑟 = d-axis , q-axis rotor fluxes
𝑟𝑠 , 𝑟𝑟 = stator and rotor resistance.
𝜔𝑠 = Rotational speed of synchronous reference frame.
Solving equation 3.17, 3.18, 3.19, 3.20 we will get,
𝜆 𝑑𝑠 = 𝐿𝑙𝑠 𝐼𝑑𝑠 + 𝐿 𝑚 𝐼𝑑𝑠 + 𝐼𝑑𝑟 = 𝐿 𝑠 𝐼𝑑𝑠 + 𝐿 𝑚 𝐼𝑑𝑟 (6.14)
𝜆 𝑞𝑠 = 𝐿𝑙𝑠 𝐼𝑞𝑠 + 𝐿 𝑚 𝐼𝑞𝑠 + 𝐼𝑞𝑟 = 𝐿 𝑠 𝐼𝑞𝑠 + 𝐿 𝑚 𝐼𝑞𝑟 (6.15)
𝜆 𝑑𝑟 = 𝐿𝑙𝑟 𝐼𝑑𝑟 + 𝐿 𝑚 𝐼𝑑𝑟 + 𝐼𝑑𝑠 = 𝐿 𝑚 𝐼𝑑𝑠 + 𝐿 𝑟 𝐼𝑑𝑟 (6.16)
𝜆 𝑞𝑟 = 𝐿𝑙𝑟 𝐼𝑞𝑟 + 𝐿 𝑚 𝐼𝑞𝑠 + 𝐼𝑞𝑟 = 𝐿 𝑚 𝐼𝑞𝑠 + 𝐿 𝑟 𝐼𝑞𝑟 (6.17)
Where
𝐿 𝑠 = 𝐿𝑙𝑠 + 𝐿 𝑚 And 𝐿 𝑟 = 𝐿𝑙𝑟 + 𝐿 𝑚
Now representing all equations in state space matrix form[2]
λds
λqs
λ dr
λqr
=
Ls 0 Lm
0 Ls 0
Lm
0
0 m
Lm
Lr
0
0
Lm
0
L r
ids
iqs
idr
iqr
Vds
Vqs
=
Rs 0
0 Rs
id
iq
+
d
dt
λds
λqs
+
0 −ωe
ωe 0
λds
λqs
Te =
3
2
PLm iqs idr − ids iqr

61. 48
By the construction the rotor winding turn ration is 2 to 3 times of the stator. So the
stator voltage is higher and current is lower compared to rotor. , the rated current of the
converter is accordingly lower which leads to a lower cost of the converter, in the typical ±
30% operational speed range around the synchronous speed. The drawback here is the
controller operation beyond the operational speed range is impossible because the rotor
voltage is higher than rated voltage. As a summary, as the rotor circuit is controlled by a
power electronics converter, the induction generator is able to both import and export
reactive power which helps in improving power stability and allows machine to operate with
grid during sever voltage disturbance. The synchronism with grid does not hamper due to
this dual side control of machine.

62. 49
CHAPTER 7
7.1 Vector control method of DFIG
Now a days more than 60% of all the electrical energy generated in the world is used by cage
induction machines have been mostly used at fixed speed for more than a century. On the
other hand, D.C machines have been used for variable speed applications. In DC machines
mmf axis is established at 90˚ electrical to the main field axis. The electromagnetic torque is
proportional to the product of field flux and armature current. Field flux is proportional to
the field current and is unaffected by the armature current because of orthogonal orientation
between armature mmf and field mmf .Therefore in a separately excited DC machine , with a
constant value of field flux the torque s directly proportional to the armature current. Hence
direct control of armature current gives direct control of torque and fast response. Hence
they are simple in control and offer better dynamic response inherently. Numerous
economical reasons, for instance high initial cost, high maintenance cost for commutators,
brushes and brush holders of DC motors call for a substitute which is capable of eliminating
the persisting problems in dc motors. Freedom from regular maintenance and a brushless
robust structure of the three phase squirrel cage induction motor are among the prime
reasons, which brings it forward as a good substitute. The ac induction motors are the most
common motors used in industrial motion control systems, as well as in main powered
appliances. Simple and rugged design, low cost and low maintenance are some of the main
advantages of 3 phase ac induction motors. The speed and torque control of three phase
induction motors require great understanding of design and characteristics of these motors.
In separately-excited DC machine the flux and torque can be controlled
independently. Linearization of toque can be done by armature current control with constant
field. In high performance domains such as robotics, rolling mills and tracking systems
where fast dynamic torque control is required DC motors have been widely used. But AC
machines are simpler and more robust construction; there are no mechanical commutators.
However, the electrical structures of ac machines are highly nonlinear and involve
multivariable inputs and outputs. In practice, intricate control algorithms are involved if ac
drives have to match the dynamic performance of dc drives

63. 50
7.2 Theory of vector control phenomena
The realization of fast decoupling control requires that both the magnitude and phase of the
machine currents be controlled accurately. Depending on the type of ac machine, there can
be many different approaches to synthesize the machine currents to provide fast decoupling
control. Among the different approaches of torque and flux decoupling control techniques,
yields the best overall performance. The FOC is the most widely accepted method of control
in high performance ac drive domains.
The principle behind the field oriented control or the vector control is instantaneous
stator currents are transformed to a reference frame rotating at synchronous speed aligned
with the rotor stator or air gap flux vectors. To produce a d-axis component current and a q-
axis component current the stator current space vector is split into two decoupled
components, one controls the flux and the other controls the torque respectively. An
induction motor is said to be in vector control mode, if the decoupled components of the
stator current space vector and he reference decoupled components defined by the vector
controller in the SRRF match each other respectively. Alternatively instead of matching the
reference and actual current in SRRF, the close match can also be made in the three phase
currents in the stationary reference frame. Hence instead of non-linear and highly interacting
multivariable control structure of induction machine, its control has becomes easy with the
help of FOC. Therefore FOC technique operates the induction motor like a separately
excitedly DC motor.
In general, there exists three possibilities for such selection and hence, three vector
controls. They are stator flux oriented control, rotor flux oriented control and magnetizing
flux oriented control. As the torque producing component in this type of control is controlled
only after transformation is done and is not the main input reference, such control is known
as indirect torque control. The most challenging and ultimately, the limiting feature of field
orientation is the method whereby the flux angle is measured or estimated. Depending on the
method of measurement, the vector control is sub divided into two sub categories: direct
vector and indirect vector control. In direct vector control, the flux measurement is done by
using flux sensing coils or the hall devices.

64. 51
FOC uses a d-q coordinates having the d-axis aligned with rotor flux vector that
rotates at the stator frequency. The particular solution allows the flux and torque to be
separately controlled by the stator current d-q components. The rotor flux is a flux of the d-
axis component stator current dsi .The developed torque is controlled by the q – axis
component of the stator current qsi .The decoupling between torque and flux is achieved
only if the rotor flux position is accurately known. This can be done using direct flux sensors
or by using a flux estimator.
The synchronously rotating reference frame can be aligned with the stator flux or
rotor flux or magnetizing flux (field flux) space vectors respectively. Accordingly, vector
control is also known as stator flux oriented control or rotor flux oriented control or
magnetizing flux oriented control. Generally in induction motors, the rotor flux oriented
control is preferred. . This is due to the fact that by aligning the SRRF with the rotor flux, the
vector control structure becomes simpler and dynamic response of the drive is observed to be
better than any other alignment of the SRRF. The vector control can be classified into (i)
Direct vector control and (ii) indirect vector control.
7.3 Direct vector control method
In direct vector control method we have seen that it determines the magnitude and position
of the rotor flux vector by direct flux measurement or by a computation based on terminal
conditions. It also called flux feedback control is method in which required information
regarding the rotor flux is obtained by means of direct flux measurement or estimation. The
flux is measured by the sensors like Hall Effect sensor, search coil and this is a part of the
disadvantages. Because fixing of number of sensors is a tedious job and this increases the
cost factor. The quantities generated from flux sensors are used in the outer loop of the drive
control structure. Alternatively, in place of flux sensors, the flux models can also be used for
which the stator currents and voltages become the feedback signals and he rotor flux angle is
given as its estimated output. Fig. 7.1 shows a simplified block diagram of a field control
scheme.
The two axis reference currents,

qsi and

dsi are the demanded torque and flux components
of stator current, respectively and are governed by the outer control loops. Currents

qsi and

65. 52

dsi undergo a coordinate transformation to two phase stator based quantities, followed by
two phase to three phase transformation which generates the stator reference currents
***
,, csbsas iii .These reference current are reproduced in the stator phases by the current
controlled inverter. Thus the external reference currents

qsi and

dsi are reproduced within
the induction motor. Control is executed in terms of these direct and quadrature axis current
components to give decoupled control of flux and torque as in a dc machine.
Fig. 7.1: Direct vector control of DFIG
7.3.1 Disadvantages
1. Fixing of number of sensors is a tedious job.
2. The sensors increase the cost of the machine.
3. Drift problem exist because of temperature.
4. Poor flux sensing at lower temperatures.
These disadvantages lead to another technique called in-direct vector control technique.
7.4 Indirect vector control method
The motor speed is used as feedback signal in the controller. The controller calculates
reference values of the two decoupled components of stator current space vector in the SRRF
which are iqs
*
and ids
*
for the control of torque and flux respectively. The two components of

66. 53
the currents are transformed into three phase currents which are ias
*
, ibs , ics
*
in the stationary
reference frame of reference. Now as a balanced load, two of the phase currents are sensed
and the third one is calculated from the two sensed currents. The current controller controls
the reference currents close to sensed three phase currents in the stationary reference frame
and operates the voltage source inverter to feed three phase induction motor. This ensures a
high level of performance of the vector controlled induction motor (VCIMD).Because of the
smooth, efficient and maintenance free operation of VCIMDs, such drives are finding
increasing applications in many drive application s such as air conditioning, refrigeration,
fans blowers, pumps, waste water treatment plants ,elevators, lifts traction motors, electric
vehicles, etc.
A triangular carrier wave is generated at the required switching frequency (fs). The
point of intersection of the triangular carrier wave and modulating signals acts as the point of
state change over for the resulting PWM signals, which are fed to the driver circuit of VSI
feeding an induction motor. The indirect vector controlled induction motor is shown in
figure below with blocks consists of the speed sensor, speed controller ,limiter, the field
weakening controller , the two phase rotating frame to three phase stationary frame
converter, PWM current controller, CC-VSI and three phase squirrel cage induction motor.
The field-weakening controller receives the speed signal ( r ) as an input signal and
provides reference value of the excitation current (
*
mri ) as an output signal. Therefore the
two signals are the reference signals for the vector controller. In the vector controller the d-
axis component (

dsi ) and the q- axis component (

qsi ) of the stator current signals are
computed which are responsible for the flux and torque control respectively. The slip
frequency signal (
*
2 ) is also computed in vector controller to evaluate the flux angle. The
slip angle is computed using slip frequency ( *
2 ), rotor speed ( r ) and sampling period (
T ). These signals of flux (

dsi ) and torque (

qsi ) are in the synchronously rotating
reference frame and these are transformed into stationary reference three phase currents (
***
,, csbsas iii ). For current controlled VSI fed vector controlled induction motor, the reference
currents
***
,, csbsas iii and sensed currents ( csbsas iii ,, ) are fed into the pulse width modulated
(PWM) current controller.

67. 54
Fig. 7.2: Indirect vector control of DFIG

68. 55
CHAPTER 8
8.1 MATLAB implementation of Indirect matrix converter with DFIG
Fig. 8.1: Model block representation of full system
In this section the implementation of control strategies has been discussed. The technology
simulation has been done using SIMULINK. The closed loop control has been done with
necessary parameters and results are shown. The simulation is carried out with wind speed
12m/s. The model is designed for 100 kilowatt generation capacity and generator is
asynchronous wound rotor machine. The stator, rotor parameters are taken standardised as
shown in table. The overall system is represented with blocks as shown in figure 8.1.
Table 8.1: Machine parameters
DFIG block parameters
Sl.No. Machine parameter Rating
1 Nominal power 100 KW
2 Stator resistance 0.95 Ω
3 Stator inductance 94mH
4 Rotor resistance 1.8 Ω
5 Rotor inductance 88 mH
6 Mutual inductance 82 mH
7 Pole pairs 6

69. 56
Synchronous speed =
120 f
P
For 50HZ, 6 pole machine the synchronous speed is 1000 rpm. The rotor speed in
p.u., torque, stator current in p.u. is found from the bus selector port. The speed gradually
increases and reaches the steady state. The synchronous speed of machine is 1000rpm. For a
wind speed 12m/s the rotor speed is found to be 1.4 p.u. or 1400 rpm.
The above table shows stator and rotor active power for different wind speed. Now
we limit our consideration for a fixed wind speed. The stator input power is fed from grid
and same as grid side power. Both active and reactive power of stator side and rotor side are
shown in below figure.
Table 8.2: Tabulation for various speed
Sl.No. Speed (pu) Rpm
Stator
power
Rotor
power
DC-link
voltage
1 1.1 1145 987 83 800
800 1.3 1336 1385 240 800
3 1.5 1623 2983 252 800
4 1.8 1718 3550 510 800
The SIMULINK model of the system has shown in figure. The subsystem incorporates with
MATLAB programme for the commutation of matrix converter.
Fig. 8.2 : MATLAB/SIMULINK model of experiment

70. 57
Fig. 8.3: MATLAB/SIMULINK model of indirect matrix converter
Fig.8.4: Space vector modulation generation in MATLAB/SIMULINK

71. 58
8.2 Simulation results
From the figure below we can see that the rotor current and voltage are 48% of the stator
current and voltage. Both three phase and single phase voltage and current are shown.
Fig.8.5 Rotor speed characteristics of machine in pu
Fig. 8.6: Rotor torque characteristics of machine

72. 59
Fig 8.7: Stator active and reactive power
Fig 8.8: Rotor active and reactive power

73. 60
Fig 8.9: Three phase stator current
Fig 8.10: Single phase stator current
Fig 8.11: Stator current in pu

74. 61
Fig 8.12: stator voltage phase A
Fig 8.13: Three phase rotor current
Fig 8.14: Single phase rotor current

75. 62
Fig 8.15: Three phase rotor voltage
Fig 8.16: Single phase rotor voltage
Fig 8.17: DC-link voltage generated in converter

76. 63
Fig 8.18: Output current of the converter
Fig 8.19: Output line voltage of converter
Fig 8.20: Generated reference current by vector control strategy

77. 64
Fig 8.21: d-component of stator current phase A (pu)
Fig 8.22: q-component of stator current phase A (pu)

78. 65
CHAPTER 9
Conclusion
In this thesis work the details of indirect matrix converter has been discussed. The
advantages of indirect matrix converter compared to that of back to back converter are
shown. It is observed that indirect matrix converters are capable of providing sinusoidal
input and output current without the DC-Link capacitor. This is a major advantage regarding
reduction in size and cost of AC-AC converter topologies. Further the complexity of
designing a power electronic converter with capacitor sizing was really a difficult and
expensive job for the designers. Due to the easier way of designing the new converter they
can be rapidly used in wind energy conversion system and also any other power circuit.
The experiment was carried out for 100kw wing energy conversion system. The necessity
generator control scheme was implemented. The complete system was integrated with user
grid. From this thesis work it has been concluded that these hybrid topologies can be utilized
for better performance of AC-AC converters.
The main objective of researchers was to achieve a topology which can be able to work
without the DC-Link energy storage elements and also does not provide complexity for large
3-phase circuits is successfully done.
The Space Vector based control Strategy is one of the most popular control technique for
power converters. The simulated results were verified with that of the calculated theoretical
results and are found to be of the same range.

79. 66
References
[1] Rubén Peña, Roberto Cárdenas, Eduardo Reyes, Jon Clare and Patrick Wheeler, "Control
of a Doubly Fed Induction Generator via an Indirect Matrix Converter With Changing DC
Voltage", IEEE Transactions On Industrial Electronics, Vol. 58, No. 10, October 2011.
[2] J.Karpagam, Dr.A.Nirmal Kumar and V.Kumar Chinnaiyan," Comparison of Modulation
Techniques for Matrix Converter," IACSIT International Journal of Engineering and
Technology, Vol.2, No.2, April 2010.
[3] Johann W. Kolar, Simon D. Round, "Novel Three-Phase AC–AC Sparse Matrix
Converters," IEEE Transactions On Power Electronics, Vol. 22, No. 5, September 2007.
[4] Mahmoud Hamouda, Farhat Fnaiech and Kamal Al-Haddad, “Space Vector Modulation
Scheme for Dual-Matrix Converters using Safe-Commutation Strategy”, IECON 2005, IEEE
31st Annual Conference on Industrial Electronics, pp.1060-1065, Nov 2005.
[5] L. Helle, K. B. Larsen, A. H. Jorgensen, S. Munk-Nielsen, and F. Blaabjerg, “Evaluation
of modulation schemes for three-phase to three-phase matrix converters,” IEEE Trans. Ind.
Electron., vol. 51, Feb. 2004.
[6] Apap, M. Clare, J.C. Wheeler and P.W. Bradley, K.J. “Analysis and Comparison of AC-
AC Matrix Converter Control Strategies”, PESC03, IEEE 34th Annual conference on Power
Electronics, Vol. 3, pp. 1287-1292, June 2003.
[7] P. Wheeler, J. Rodriguez, J. Clare, L. Empringham, and A. Weinstein, "Matrix
converters: A technology review" IEEE Trans. Ind. Electron., vol. 49, Apr 2002.
[8] P. Zwimpfer and H. Stemmler, “Modulation and realization of a novel two-stage matrix
converter,” in Proc. Brazilian Power Electronics Conf., Florianópolis, Brazil, Nov. 11–14,
2001.
[9] Gurmeet Kaur, Neeshu chahal, Izhar Ahmed, S.K. Goel, "Matrix Converter, A Review"
ISTP Journal of Research in Electrical and Electronics Engineering.

80. 67
[10] Roberto Cárdenas, Rubén Peña, Patrick Wheeler, Jon Clare, Greg Asher, "Control of
the Reactive Power Supplied by a WECS Based on an Induction Generator Fed by a Matrix
Converter", IEEE transactions on industrial electronics, vol. 56, no. 2, february 2009.
[11] E. Reyes, R.Pena, R Cardenas, J. Claret, P. Wheeler, "Control of a Doubly-Fed
Induction Generator via a Direct TwoStage Power Converter", Electrical Engineering
Department, University of Magallanes.
[12] M. Rivera, J. L. Elizondo, M. E. Macías, O. M. Probst, O. M. Micheloud, J. Rodriguez,
C. Rojas, A. Wilson," Model Predictive Control of a Doubly Fed Induction Generator with
an Indirect Matrix Converter" 2009, IEEE.
[13] P.C.Krause, "Analysis of Electrical machines and Drive systems", Prentice Hall, 1985.
[14] Xinyan Zhang, Weiqing Wang, Dagui Liu, Haiyun Wang, Xuan Cao, Shan He," Matrix
Converter Control Study of Doubly-fed Induction Wind Turbine Generator System", IEEE
PEDS 2015, Sydney, Australia.
[15] Vlastimil Šantín," Model of wind power plant with asynchronous generator in simulink
platform", Intensive programme on “Renewable Energy Sources”, May 2011, University of
West Bohemia.
[16] Andreas Petersson, "Analysis, Modelling and Control of Doubly-Fed Induction
Generators for Wind Turbines", A thesis for the degree of doctor of philosophy, Chalmers
University of Technology, Sweden.