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

©KALINGA INSTITUTE OF INDUSTRIAL TECHNOLOGY

KIIT UNIVERSITY, BHUBANESWAR

ALL RIGHTS RESERVED

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

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)

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

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.

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

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

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

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

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

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

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

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

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.

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

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.

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

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

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)

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.

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

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 = 𝐾𝑠𝑓𝑎𝑏𝑐

" f " is a function of voltage or current.

𝐾𝑠 = 23

1 −1

2 −12

0 32 − 3

2

12

12

12

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

= 𝑉𝑎𝑛 − 𝑉𝑏𝑛 cos 60 − 𝑉𝑐𝑛 cos 60

𝑉𝑞 = 0 + 𝑉𝑏𝑛 cos 30 − 𝑉𝑐𝑛 cos 30

= 3

2𝑉𝑏𝑛 −

3

2𝑉𝑐𝑛

𝑉𝑟𝑒𝑓 = Vd2 + Vq

2

𝛼 = tan−1𝑉𝑑𝑉𝑞

Vd

Vq = 2

3

1 −12 −1

2

0 32 − 3

2

Van

Vbn

Vcn

11

Step 2: Determination of the time durations T1, T2, T0.

Switching time at any duration can be illustrated by-

𝑇1 = 3𝑇𝑧 𝑉𝑟𝑒𝑓

𝑉𝑑𝑐sin

𝜋

3− 𝛼 +

−𝜋

3

= 3𝑇𝑍 𝑉𝑟𝑒𝑓

𝑉𝑑𝑐sin

𝜋

3− 𝛼

= 3𝑇𝑍 𝑉𝑟𝑒𝑓

𝑉𝑑𝑐sin

𝜋

3cos𝛼 − cos

𝜋

3sin𝛼

𝑇2 = 3𝑇𝑧 𝑉𝑟𝑒𝑓

𝑉𝑑𝑐sin 𝛼 − (

−𝜋

3)

3𝑇𝑍 𝑉𝑟𝑒𝑓

𝑉𝑑𝑐 − cos𝛼 sin

−𝜋

3+ sin𝛼 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

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

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.

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

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]

16

(a)

(b)

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

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

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

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 = v𝑎𝑛0 + v𝑏𝑛0𝑒𝑗2𝜋 3 + v𝑐𝑛0𝑒

−𝑗2𝜋 3 (3.1)

𝑉𝑎𝑛 = 𝑉0 cos 𝜔𝑡 + ∅

𝑉𝑏𝑛 = 𝑉0 cos 𝜔𝑡 − 2𝜋

3+ ∅ (3.2)

𝑉𝑐𝑛 = 𝑉0 cos 𝜔𝑡 +2𝜋

3+ ∅

𝑉𝑟𝑒𝑓 = 𝑉 𝑎𝑛 + 𝑉 𝑏𝑛 𝑒𝑗2𝜋/3 + 𝑉 𝑐𝑛𝑒

−𝑗2𝜋/3 (3.3)

=3

2𝑉0𝑒

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]

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 2𝑉𝑎𝑛 − 𝑉𝑏𝑛 − 𝑉𝑐𝑛

𝑉𝐵 =1

3 2𝑉𝑏𝑛 − 𝑉𝑐𝑛 − 𝑉𝑎𝑛 (3.4)

𝑉𝐶 =1

3 2𝑉𝑐𝑛 − 𝑉𝑎𝑛 − 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.

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 =𝐼1𝐼𝑑𝑐

sin(60 − 𝛽)

𝑑𝐼2 =𝐼1

𝐼𝑑𝑐sin(𝛽) (3.5)

And

𝑑𝑉1 = 3𝑉0

𝑉𝑑𝑐sin( 60 − 𝛽)

𝑑𝑉2 = 3𝑉0

𝑉𝑑𝑐sin(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.

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.

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.

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.

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]

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.

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

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= 𝐷𝑎𝑏𝑇𝑝

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.

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 = 23 U and U110 = 2

3 Uejπ/3 the output formed in time Tp/2 is

U∗ =2

3

Tp2 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/3δ110 (4.6)

And average value is

U = Uab Dab + Uac Dac

so, U∗ =2

3 [U δ100 + U e

jπ

3 δ100 ] (4.7)

Fig. 4.5: Sector diagram comprising of vectors

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 π3

Ts (4.8)

Where U = Vdc, U2∗ = U∗ and U2

∗ = Vref

Therefore

δ100 = 3U2

∗

U cos π 6 + α (4.9)

31

And

δ110 = 3U2

∗

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

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

33

Fig. 4.8: Output phase voltage

Fig. 4.9: Magnified values of output phase voltage.

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 + 𝑋𝑙2

Fig. 4.11: Output current

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

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

Sim

ula

ted

outp

ut

phas

e vo

ltag

e

Modulation Index

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.

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.

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.

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.

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

2𝑚𝑣2 (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

2ρAd v2

t=

1

2ρAv3 (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

2𝐶𝑝 𝜆,𝛽 𝜌𝐴𝑣3 (5.5)

The torque of the wind turbine could be expressed as

𝑇 = 1

2𝐶𝑡 𝜆,𝛽 𝜌𝐴𝑅𝑣2 (5.6)

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

𝜆𝑖− 0.4𝛽 − 5 𝑒

−21

𝜆𝑖 + 0.0068𝜆 (5.7)

where, 1

𝜆𝑖=

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.

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.

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.

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 = 𝑅𝑠𝐼𝑠 + 𝑗 𝜔1𝐿𝑠𝜆𝐼𝑠 + 𝑗𝜔1𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 (6.1)

𝑉𝑟

𝑠= 𝑅𝑟 𝑠 𝐼𝑟 + 𝑗 𝜔1𝐿𝑟𝜆 𝐼𝑟 + 𝑗 𝜔1𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 (6.1.1)

0 = 𝑅𝑚 𝐼𝑅𝑚 + 𝑗𝜔1𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 (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

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) = 𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 (6.3)

Rotor flux (𝛹𝑟) = 𝐿𝑟𝜆 I𝑟 + 𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 = 𝐿𝑟𝜆 𝐼𝑟 + 𝛹𝑚 (6.4)

Stator flux (𝛹𝑠) = 𝐿𝑠𝜆𝐼𝑠 + 𝐿𝑚 𝐼𝑠 + 𝐼𝑟 + 𝐼𝑅𝑚 = 𝐿𝑠𝜆𝐼𝑠 + 𝛹𝑚 (6.5)

The equations describing the equivalent circuit can be rewritten as:

𝑉𝑠 = 𝑅𝑠𝐼𝑠 + 𝑗𝜔1𝛹𝑠 (6.7)

𝑉𝑟

𝑠= 𝑅𝑟 𝑠 𝐼𝑟 + 𝑗𝜔1𝛹𝑠 (6.7.1)

0 = 𝑅𝑚 𝐼𝑅𝑚 + 𝑗𝜔1𝛹𝑚 (6.7.2)

The resistive losses of the induction generator are

𝑃𝑙𝑜𝑠𝑠 = 3 𝑅𝑠 𝐼𝑠 2 + 𝑅𝑟 𝐼𝑟

2 + 𝑅𝑚 𝐼𝑅𝑚 2 (6.8)

And it is possible to express the electro-mechanical torque (Te) as

𝑇𝑒 = 3𝑛𝑝𝐼𝑚 𝛹𝑚 𝐼𝑟∗ = 3𝑛𝑝𝐼𝑚 𝛹𝑟𝐼𝑟∗ (6.9)

np = Number of pole pair

6.3 DFIG Mathematical Modelling

Vds = rsIds −ωsλqs +d

dtλds (6.10)

Vqs = rsIqs + ωsλds +d

dtλqs (6.11)

Vdr = rrIdr − ωs − ωr λqr +d

dtλdr (6.12)

Vqr = rrIqr + ωs − ωr λdr +d

dtλqr (6.13)

47

where

𝑉𝑑𝑠 ,𝑉𝑞𝑠 = d-axis , q-axis stator voltage respectively

𝑉𝑑𝑟 ,𝑉𝑞𝑟 = d-axis , q-axis rotor voltage

𝐼𝑑𝑠 , 𝐼𝑞𝑠 = d-axis , q-axis stator current

𝐼𝑑𝑟 , 𝐼𝑞𝑟 = d-axis , q-axis rotor current

𝜆𝑑𝑠 , 𝜆𝑞𝑠 = d-axis , q-axis stator fluxes

𝜆𝑑𝑟 , 𝜆𝑞𝑟 = 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,

𝜆𝑑𝑠 = 𝐿𝑙𝑠𝐼𝑑𝑠 + 𝐿𝑚 𝐼𝑑𝑠 + 𝐼𝑑𝑟 = 𝐿𝑠𝐼𝑑𝑠 + 𝐿𝑚 𝐼𝑑𝑟 (6.14)

𝜆𝑞𝑠 = 𝐿𝑙𝑠𝐼𝑞𝑠 + 𝐿𝑚 𝐼𝑞𝑠 + 𝐼𝑞𝑟 = 𝐿𝑠𝐼𝑞𝑠 + 𝐿𝑚 𝐼𝑞𝑟 (6.15)

𝜆𝑑𝑟 = 𝐿𝑙𝑟 𝐼𝑑𝑟 + 𝐿𝑚 𝐼𝑑𝑟 + 𝐼𝑑𝑠 = 𝐿𝑚 𝐼𝑑𝑠 + 𝐿𝑟𝐼𝑑𝑟 (6.16)

𝜆𝑞𝑟 = 𝐿𝑙𝑟 𝐼𝑞𝑟 + 𝐿𝑚 𝐼𝑞𝑠 + 𝐼𝑞𝑟 = 𝐿𝑚 𝐼𝑞𝑠 + 𝐿𝑟𝐼𝑞𝑟 (6.17)

Where

𝐿𝑠 = 𝐿𝑙𝑠 + 𝐿𝑚 And 𝐿𝑟 = 𝐿𝑙𝑟 + 𝐿𝑚

Now representing all equations in state space matrix form[2]

λds

λqs

λ drλqr

=

Ls 0 Lm

0 Ls 0Lm

00 m

Lm

Lr0

0Lm

0L r

ids

iqs

idriqr

Vds

Vqs =

Rs 00 Rs

id

iq +

d

dt λds

λqs +

0 −ωe

ωe 0 λds

λqs

Te =3

2PLm iqs idr − ids iqr

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.

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

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.

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

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

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.

54

Fig. 7.2: Indirect vector control of DFIG

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

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

57

Fig. 8.3: MATLAB/SIMULINK model of indirect matrix converter

Fig.8.4: Space vector modulation generation in MATLAB/SIMULINK

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

59

Fig 8.7: Stator active and reactive power

Fig 8.8: Rotor active and reactive power

60

Fig 8.9: Three phase stator current

Fig 8.10: Single phase stator current

Fig 8.11: Stator current in pu

61

Fig 8.12: stator voltage phase A

Fig 8.13: Three phase rotor current

Fig 8.14: Single phase rotor current

62

Fig 8.15: Three phase rotor voltage

Fig 8.16: Single phase rotor voltage

Fig 8.17: DC-link voltage generated in converter

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

64

Fig 8.21: d-component of stator current phase A (pu)

Fig 8.22: q-component of stator current phase A (pu)

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.

66

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