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

A DISSERTATIONON

SUB-SYNCHRONOUS CONTROL INTERACTIONS BETWEEN TYPE-3 WINDTURBINES AND SERIES COMPENSATED AC TRANSMISSION SYSTEMS

Submitted in partial fulfillment of the requirements for the award of the degree of

MASTER OF TECHNOLOGYIN

POWER SYSTEMS

Submitted by

YAKKALURI DHARMA TEJA(Reg.N0: 11206103)

Under the Guidance of

DR. P. LINGAREDDYPROFESSOR

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

K L UNIVERSITY

GREEN FIELDS, VADDESWARAM, GUTNTUR.

2013

DEPARTMENT OF

ELECTRICAL & ELECTRONICS ENGINEERING

K L UNIVERSITY, GUNTUR.

2013

CERTIFICATE

This is to certify that the project work entitled “SUB-SYNCHRONOUS CONTROLINTERACTIONS BETWEEN TYPE-3 WIND TURBINES AND SERIESCOMPENSATED AC TRANSMISSION SYSTEMS” submitted by Y.DHARMA TEJA(11206103) in partial fulfillment of the MASTER OF TECHNOLOGY IN POWER SYSTEMSin the Department of Electrical & Electronics Engineering during the academic year 2012-2013, is a bonafide work done by him.

Dr. P. Lingareddy, Dr. M. Uma Vani,Professor Professor & HOD

KL University. KL University.

External Examiner

ACKNOWLEDGEMENT

It is a great pleasure to express my sincere gratitude to my supervisor, Dr. P.

Lingareddy Garu, Professor in KL University, Guntur, for his valuable advice, directions,

encouragements and supports throughout the program. My enthusiasm in this subject is inspired

by his profound knowledge in this area. I am truly honored to work on this thesis under his

supervision.

I also wish to thank to Professor Dr. M. Uma Vani, Head of Department of Electrical

& Electronics Engineering, K L University, Guntur, all the Asst Professor and support staff in the

Department of Electrical & Electronics Engineering for their help during my studies there.

I express my gratitude to Professor Dr. M. Venu Gopala Rao, for her help and support

in Project during my study.

I would like to thank Dr. G. L Dutta, Chancellor of KL University and all the faculty

members of the Department of Electrical & Electronics Engineering for their direct or indirect

support for helping me in completion of this Thesis.

I am greatly obliged to our KL University that has provided me a healthy environment

to drive me to achieve my goals and ambitions.

Last but not least I wish to convey my thanks to one and all who are concerned directly

or indirectly for helping me in the successful completion of this Thesis.

Y. DHARMA TEJA

ID. No. 11206103

KL UNIVERSITYGUNTUR (ANDHRA PRADESH)

Department of Electrical & Electronics Engineering

Duration :2012-2013 Academic YearDate of Start :August, 2012Date of Submission :July,2013Dissertation carried out at : KL University

Title of Project : Sub-Synchronous Control Interactions betweenType-3 Wind Turbines and Series CompensatedAC Transmission Systems

ID No./ Name of the student : 11206103Y. Dharma Teja

Name and Designation ofthe Guide/ co-guide andProfessional experts : Dr. P. Lingareddy, Garu.

Key Words : SSCI, SERIES COMPENSATION.

Dissertation Ares(s) : Control and Power

Abstract :This project gives the overview of the SSCIPhenomenon.

The most recent project experience andstudies have shown that Type 3 wind turbinegenerators with power electronic converters andcontrols that operate near the series compensatedtransmission lines are susceptible to un-damped sub-synchronous oscillations.

The project simulated on the MATLABplatform using a Type 3 wind turbine model are usedto demonstrate SSCI, the design of an SSCI dampingcontroller is presented to help mitigate the problemsthat arise during the process.

Signature of the Student Signature of the GuideDate: Date:

i

CONTENTS

Chapter 1 Introduction 1

1.1. Theme of thesis 51.2. Background Literature survey 61.3. Thesis Layout 81.4. Conclusions 8

Chapter 2 Wind Turbine Systems 9

2.1. Introduction 102.2. Wind Turbines 102.3. Wind Turbine Topologies 12

2.3.1. Fixed speed wind turbine (Type A) 122.3.2. Variable speed wind turbine 13

2.3.2.1. Type B wind turbine 142.3.2.2. Type C wind turbine 152.3.2.3. Type D wind turbine 16

2.4. Typical characteristics of the wind turbine 162.4.1. Power versus speed Characteristics 162.4.2. Power coefficient versus TSR Characteristics 172.4.3. Torque versus speed Characteristics 20

2.5. Conclusions 21

Chapter 3 DFIG System 22

3.1. Introduction 233.2. Vector or Field Oriented Control Theory 23

3.2.1. D-Q Theory 233.2.1.1. Transformation of three phase stationary to two phase stationary

Axes. 24

3.2.1.2. Transformation of two phase stationary to two phase synchronouslyrotating axes. 25

3.2.2. Mathematical modelling of Induction Generator 263.2.2.1. Modelling of DFIG in synchronously rotating frame 263.2.2.2. Dynamic modelling of DFIG in state space equations 28

3.2.3. Principle of Vector control 323.3. DFIG System 34

3.3.1. Double-fed Induction Generator 343.3.2. Voltage source converter 333.3.3. Grid side converter control 363.3.4. Machine side converter control 38

3.4. Conclusions 42

ii

Chapter 4 MATLAB /SIMULINK MODELLING 43

4.1. INTRODUCTIONTO MATLAB/SUMULINK 444.1.1. Development Environment 444.1.2. The MATLAB Mathematical Function Library

4.2. The MATLAB Language 454.2.1. Graphics 454.2.2. The MATLAB Applications Program interface (API) 454.2.3. MATLAB Documentation 45

4.3. MATLAB tools 46

Chapter 5 Problem Description & Results 48

5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION 495.2. ANALYSIS OF CONTROL INSTABILITY 515.3. DESIGN OF SSCI DAMPING CONTROLLER 535.4. OTHER SSCI MITIGATION ALTERNATIVES 555.5. RECOMMENDATIONS 575.6. MATLAB SIMULINK MODELS & RESULTS 585.7. CONCLUSIONS 60

Chapter 6 Fuzzy logic Controller 61

6.1 INTRODUCTION TO THE FUZZY LOGIC 62A. Fuzzy model, Fuzzy controller, and Fuzzy observer 62B. Fuzzy control system 62C. TS Fuzzy Model with Parameter Uncertainties 63

6.2 INTRODUCTION TO MY PROJECT EXTENSION 656.3 CONCLUSIONS 69

Chapter 7 Conclusions 70

7.1. INTRODUCTION 717.2. RESULTS 727.3. CONCLUSIONS 72

REFERENCES 73

APPENDIX 74

PUBLICATIONS 75

PUBLICATION PAPER

LIST OF FIGURES

S.NO NAME PAGE NO1 Fig 1.1. Statistical data of total installed wind capacity in world 32 Fig 1.2. Growth rate of wind power in Global market 33 Fig 1.3. World share of cumulative installed wind power for different wind

turbine concept (Approximate data) 4

4 Fig 1.4. The overall view of wind energy system 45 Fig 1.5. The Power flow diagram of DFIG 56 Fig 2.1. Horizontal axis turbine 117 Fig 2.2. Schematic diagram of a fixed speed wind turbine 138 Fig 2.3. Schematic diagram of Type B wind turbine 149 Fig 2.4. Schematic diagram of Type C wind turbine 15

10 Fig 2.5. Schematic diagram of Type D wind turbine 1611 Fig 2.6. The typical power versus speed characteristics of a wind turbine

17

12 Fig 2.7. The typical curves of Cp versus for various values of the pitchangle 17

13 Fig 2.8. The torque versus speed characteristics of wind turbine (horizontalaxis turbine) 20

14 Fig 3.1. Transformation of a-b-c to ds-qs axes 2415 Fig 3.2. Transformation of stationary ds-qs axes to synchronously rotating

frame d-q axes 25

16 Fig 3.3. Dynamic d-q equivalent circuit of DFIG (q-axis circuit) 2617 Fig 3.4. Dynamic d-q equivalent circuit of DFIG (d-axis circuit) 2718 Fig 3.5. Implementation of vector control principle 3319 Fig 3.6. Overall DFIG System 3420 Fig 3.7. Schematic diagram of Grid side Converter 3621 Fig 3.8. Vector control structure for Grid side Converter 3722 Fig 3.9. Vector control structure for Machine side Converter 3923 Fig 3.10. Vector diagram showing stator and rotor current components of

DFIG in voltage oriented co-ordinate 39

24 Fig.5.1. Simulated SSCI Event: Wind Plant Point of Interconnection Real Power, ReactivePower, and RMS Voltage (8% series compensation) 50

25 Fig.5.2.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls53

26 Fig.5.2.1. Revised Controls including SSCI Damping Controller and changes in Rotor SideCurrent Feedback Control Loop 53

27 Fig.5.3. Simulated SSCI Event After Controller Changes: Wind Plant Point ofinterconnection Real Power, Reactive power, and Rms Voltage (50% series compensation) 55

28 Fig.5.4. Example of a blocking filter in parallel with series capacitor 5629 Fig.5.5.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls) Using

a MATLAB Platform 58

v

30 Fig.5.5.1.Simulated SSCI Event When there is no SSCI damping controller: Wind PlantPoint interconnection Real Power, Reactive power, and RMS Voltage 58

31 Fig.5.6. Revised Controls including SSCI Damping Controller and changes in Rotor SideCurrent Feedback Control Loop Using a MATLAB Platform 59

32 Fig.5.6.1. Simulated SSCI Event After Controller Changes: Wind Plant Point ofinterconnection Real Power, Reactive power, and RMS Voltage 59

33 Fig 6.1. Fuzzy contorl system 6234 Fig 6.1.1 Equivalent Fuzzy model architecture with two inputs and one

output 6335 Fig6.1.2 Normalized triangular membership functions used in Fuzzification. 64

36 Fig 6.2.1 Fuzzy interface system editor 66

37 Fig 6.2.2 FIS with input membership function editor 66

38 Fig 6.2.3 FIS with output membership function editor 6639 Fig 6.2.4 FIS with rule editor 6640 Fig 6.2.5 Rule viewer individual 6641 Fig 6.2.6 Surface viewer of all the rules combined 6642 Fig.6.2.8. Revised Controls including SSCI Damping Controller and changes in Rotor Side

Current Feedback Control Loop Using a MATLAB Platform when Fuzzy logic controlleris introduced.

68

43 Fig.6.2.9. Simulated SSCI Event After Controller Changes: Wind Plant Point ofinterconnection Real Power, Reactive power, and RMS Voltage when fuzzy logiccontroller is introduced

68

NOMENCLATURE

Pair Power contained in windρ The air densityA The swept areaV The wind velocity without rotor interferenceCp Power coefficient Tip speed ratioω Rotational speed of rotorR The radius of the swept aread-q Synchronously rotating reference frame direct and quadrature

axesds-qs Stationary reference frame direct and quadrature axes (or -

axes)ds-axis stator voltageqs-axis stator voltageds-axis rotor voltageqs-axis rotor voltaged-axis stator voltageq-axis stator voltaged-axis rotor voltageq-axis rotor voltage

B Damping constantJ Rotor inertiaTL Load torqueTe Electromagnetic torqueP Number of polesLm Magnetizing inductanceLr Rotor inductanceLs Stator inductanceLlr Rotor leakage inductanceLls Stator leakage inductancef Supply frequencyb Angular frequencym Rotor mechanical speedr Rotor electrical speede Synchronous speedRr Rotor resistance with respect to stator.Rs Stator resistanceθ Angle of stationary reference frameθe Angle of synchronously rotating frame qr q-axis rotor flux linkage dr d-axis rotor flux linkage qs q-axis stator flux linkage

ds d-axis stator flux linkagei dr d-axis rotor currenti qr q-axis rotor currentXm Magnetizing reactanceXr Rotor reactanceXs Stator reactanceXlr Rotor leakage reactanceXls Stator leakage reactancePcus Stator copper lossPcur Rotor copper lossm2 Modulation index of machine side converterm1 Modulation index of supply side convertervdc DC-link voltageC DC-link capacitanceL Line inductanceR Line resistanceiq q-axis grid currentid d-axis grid currentvq q-axis grid voltagevd d-axis grid voltageQs Reactive power in the gridPs Active power in the grid

ds-axis stator currentqs-axis stator currentds-axis rotor currentqs-axis rotor current

i ds d-axis stator currenti qs q-axis stator current

ABSTRACT

This project gives the overview of the Sub-Synchronous control interaction (SSCI)

phenomenon. The most recent project experience and studies have shown that Type 3 wind

turbine generators with power electronic converters and controls that operate near the series

compensated transmission lines are susceptible to un-damped sub-synchronous oscillations.

The project simulated on the MATLAB platform using a Type 3 wind turbine model

are used to demonstrate SSCI, the design of an SSCI damping controller is presented to mitigate

the problems that arise during the process.

Chapter 1 Introduction

1

CHAPTER-1

INTRODUCTION

1.1. Theme of thesis 51.2. Background Literature survey 61.3. Thesis Layout 81.4. Conclusions 8


2

CHAPTER 1Introduction

Conservation of non-renewable resources motivate to explore the new avenues of

resources for electricity generation which could be clean, safe and most valuable to serve

the society for a long period. The option came with huge number of hands up a source

which is part of our natural environment and eco friendly is the Renewable Energy Sources.

These sources can be better replacement of the polluted non-renewable sources in order to

meet the growing demand for power due to rapidly growing economy and expanding

population.

As per World Energy Outlook (WEO)-2010 the prospects for renewable energy based

electricity generation hinge critically on government policies to encourage their

development. Worldwide, the share of renewables in electricity supply increases from 19%

in 2008 to 32% in 2035 in the New Policies Scenario; it reaches only 23% in the Current

Policies Scenario, but 45% in the 450 Scenario. In all three scenarios, rising fossil-fuel

prices and declining costs make renewables more competitive with conventional

technologies. Hydropower has been the dominant renewable source of electricity for over a

century. The recent strong growth in new technologies for wind power and solar photo

voltaic (PV) has created expectations among policy makers and the industry alike that these

technologies will make a major contribution to meet growing electricity needs in the near

future. It has also been forecasted that the increase in electricity generation from renewable

sources between 2008 and 2035 will be primarily derived from wind and hydro power,

which will contribute 36% and 31% of the additional demand respectively.

Wind power is projected to supply 8% of global electricity in 2035 up from just 1% in

2008. In the year 2010 the wind capacity has reached 196.630GW worldwide and it had

reached 240GW by the end of 2011 as shown in Fig 1.1.

In order to address the problem of rapidly growing demand for power, India has also

taken its step forward along with other countries. Total power generation capacity is

reached to173626.40MW. Out of the total capacity India’s installed wind power generation

capacity stood at about 13065MW as of March 2011.


3

pow

erca

paci

ty[G

W]

Total Installed wind Capacity (MW) in world

300000

250000

200000

150000

100000

50000 24322 31181 3229547693 59024

7412293927

240000

196630

159766

120903

02001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Fig 1.1. Statistical data of total installed wind capacity in world

Since the 2003 Electricity Act, the wind sector of India has registered a compound

annual growth rate of about 29.5%. The growth rate of wind power in global market is

forecasted for five years by Global Wind Energy Council (GWEC) and the report is

published in the Global wind report 2010[3]. The forecasting data is shown in Fig1.2.

Focusing on wind market penetration in to the global market, an investigation made on

share of the most commonly applied wind turbine concept over the years. The large

increasing electrical penetration of large wind turbines in to EPS is inspiring designers to

develop generators along with power electronics converters and the modern control system

Strategies.

500

450

400

350

22.5 21.4

15.9

19.518

25

20

16.7 15.6 15

300

250

11.1 10 9.7 8.8 10

448.8 5200

150

100 194.4235.9

282332.7

388.3

0

-550 35.8 -7

041.5 46.1 50.7 55.6 60.5

-102010 2011 2012 2013 2014 2015

Year

Annual capacity [GW] Cumulative capacity [GW]

Annual capacity growth rate [%] Cumulative capacity growth rate [%]

Fig 1.2. Growth rate of wind power in Global market


4

shar

eof

cum

ulat

edin

stal

led

pow

erin

%

The most commonly applied wind turbine designs in the industry today can be

categorized into four wind turbine concepts (Type A, B, C, D) (to be discussed in Chapter

2). There is an obvious trend towards the configuration using a DFIG (Type C) with

variable speed and variable pitch control as per the statistical data shown in Fig 1.3.

100

9080

7060

50

40

3020

10

01995 1997 1999 2001 2003 2005 2007 2009 2011

Year

Type A

Type B

Type C

Type D

Fig 1.3. World share of cumulative installed wind power for different wind turbine concept

(Approximate data)

Internet survey says that the top wind turbine manufacturing companies like Vestas

(Denmark), Gamesa (Spain), Nordex (Germany) etc. are employing mostly Type C & D

turbines in their recent products. For example Vestas and Gamesa have added V90-3.0MW

offshore (DFIG) & V164-7.0MW offshore (PMSG), G10X- 4.5MW (PMSG) & G9X-

2.0MW (DFIG) respectively to the growing wind market recently. Fig 1.4 shows a

schematic diagram of wind energy system. The picture shows the flow of energy from the

generation end to the consumer end.

Transformer Substations

House

Wind TurbinesThe wind turns the blades,which spin a shaft, whichconnects to a generator andmakes electricity

Electricity GridThe high-voltage transmission systems carryelectricity from the power plants and transmit ithundreds of miles away, and the lower-voltagedistribution systems draw electricity from thetransmission lines and distribute it to individualcustomers

Fig 1.4. The overall view of wind energy system


5

1.1.Theme of Thesis

The successful entry of DFIG based wind turbine into the competitive wind market

stimulates to study the performance of the overall DFIG system under different operating

and critical conditions. The DFIG system consists of a Wound Rotor Induction Generator

(WRIG) with the stator windings directly connected to the constant frequency three-phase

grid and with the rotor windings connected to grid through a bidirectional back-to-back

IGBT based voltage source converter.

This system allows a variable speed operation over a large range. The converter

compensates the difference between the mechanical angular frequency and grid frequency

by injecting a rotor current with a variable frequency. Both during normal operation and

faults the behaviour of the generator is thus governed by the power converter and its

controllers. The power converter consists of two converters, the machine-side converter and

grid-side converter, which are controlled independently of each other. The main idea behind

the total system (DFIG with back-to-back converters)(to be discussed in Chapter 3) is that

the machine-side converter controls the active and reactive power by controlling the rotor

current components, while the grid-side converter controls the dc-link voltage and ensures

the operation at unity power factor (i.e. Zero reactive power). By means of a

bidirectional converter in the rotor circuit the DFIG is able to work as a generator in both

sub-synchronous and super-synchronous modes.

Depending upon the operating condition of the drive, power is fed into or out of the

rotor (which is the case of super synchronous mode), then it flows from the rotor via the

converter to the grid. Where as in sub-synchronous mode it flows in opposite direction as

shown in Fig 1.5. In both modes the stator feeds energy in to utility grid.

Fig 1.5.The Power flow diagram of DFIG

(Sub-synchronous (left) & super-synchronous (right) generating mode)


6

The DFIG based wind turbine is used under study because of its obvious advantages.

1. It has the ability to control reactive power and to decouple active and reactive

power control by independently controlling the rotor excitation current.

2. The DFIG has not necessarily to be magnetized from the power grid; it can

be magnetized from the rotor circuit, too. It is also capable of generating reactive

power that can be delivered to the stator by the grid-side converter. However, the

grid-side converter normally operates at unity power factor and is not involved in

the reactive power exchange between the turbine and the grid.

3. In the case of a weak grid, where the voltage may fluctuate, the DFIG may be

ordered to produce or absorb an amount of reactive power to or from the grid, with

the purpose of voltage control.

a. The main objective of this thesis is the performance analysis of the DFIG for a

wind turbine application both during steady state operation and transient operation

(during the case of SSCI). The transient conditions for which the system is

analysed are given below,

i. Sudden change of reactive power demand by the machine

ii. Sudden change of supply frequency in the utility grid.

In order to analyse the overall DFIG system during steady state and transient state

operation both the modelling and controlling of the system are important issues. Hence the

control and modelling (to be discussed detail in Chapter 3) are also the part of this thesis

work. As a part of the thesis work the overall system is simulated using MATLAB

environment. In simulation work the system is modelled using different state equations and

the controlled PWM pulses for grid side as well as machine side converters are found using

PI controller using MATLAB.

1.2.Background Literature survey

The obvious adoptability led the people to study on the DFIG based wind turbine.

Though the basic features are explained in many literatures and text books, some of the

specific issues and the remedial actions taken by the researcher are highlighted in this

survey.

The energy of the wind is used for more than thousand years. The first history proven

usage has been around the year 650 in Tibet for religious aims. These early models are

vertical axis wind turbines based on the principle of scoop drag-type devices which are

today used only in anemometers. At the beginning of the second millennium horizontal axis


7

Wind mills became popular mainly in southern Europe and the Netherlands for pumping

water.

The first production of electrical energy with wind power was done in 1887 by Charles

Brush in Cleveland, Ohio. The rated Power of the used dc-generator was 12kW and was

designed to charge batteries. The induction machine was used for the first time in 1951. The

development of the induction machine in wind power technology from a squirrel cage

machine to a Doubly-fed Induction Machine (DFIM) shows the tremendous potential of this

kind of electrical generator. The first wind turbines with squirrel cage machine were built in

the late 1980s with a rated power of less than 100kW. The state of the art wind turbines with

doubly fed induction machine have a rated power up to 3.0MW. Theses turbines are

constructed for a very high efficiency, performance and very low maintenance in order to go

offshore with the next generation of wind turbines.

DFIM using an AC-AC converter in the rotor circuit (Schrebius drive) has long been a

standard drive option for high power applications involving a limited speed range. The

power converters only handle the rotor power. In 1980 Leonhard explains the vector control

technique used for the independent control of torque and excitation current. The

converter design, and control technique are well explained in. Following Jones and Jones

have shown the technique to decouple active and reactive power drawn from the utility grid.

Pena, Clare and Asher gave the detail design of DFIG using back-to-back PWM voltage

source converters in the rotor circuit and also they have validated the system experimentally

considering a grid connected system and stand-alone system. The option using current fed

DC-link converter with DFIG system is analysed. Since the DFIG system used under the

study is grid connected, it has to satisfy the grid code requirements such as grid stability,

fault ride through, power quality improvement, grid synchronization and ease of power

control. To solve the issues related to utility grid, the grid side converter plays a vital role in

taking the grid issues as key factor, and the control technique is adopted to solve the very

cause. Wu, Dewan and Slemon use the traditional voltage oriented control in grid side

converter to study the cause effect analysis under balanced three phase grid. Besides the

voltage oriented control, another controller called Linear Quadratic (LQ) controller is

synthesized to improve the fault ride through capability as well as the performance of the

generator under unbalance grid voltage . Nasiri and Abdel-Baqi used a series converter on

the stator terminal to mitigate the effect of the short circuit on the wind turbine.


8

1.3.Thesis Layout

Following the chapter on Introduction, the rest of the thesis is delineated as follows.

Chapter 2 Provides the fundamental concepts of wind electricity generation along with

different types of turbines used for the generation such as Type A, B, C, D. It also derives

the mathematical expression used for the maximum mechanical power extracted from the

wind. The characteristic curves to illustrate the relation between torque-speed, power-speed

are also the part of this chapter.

Chapter 3 Explains the modelling of the overall DFIG system in detail and also

focuses on the control techniques used for the grid side as well as machine side converter. In

this chapter the detail explanation is made using block diagrams and different algebraic

equations.

Chapter 4 This chapter deals with the Software MATLAB. The project has done in this

software platform and detailed overview of this software and the blocks that I have used in

the simulation were explained briefly.

Chapter 5 This chapter describes the Type 3 Wind Turbine and its parameters and

finally how the SSCI damping controller was developed and results were simulated

respectively. Conclusions were drawn.

Chapter 6 This chapter deals with the combination of PI controller and

Fuzzy controller which are used to damp out the SSCI concerns. Results were

simulated respectively and were drawn.

Chapter 7 Conclusions and Recommendation are given in this chapter

1.4. ConclusionsIn this chapter a brief Introduction is given to the Wind Turbines, and how

they are in progress. Layout of my thesis is briefly presented.

Chapter 2 Wind Turbine Systems

9

CHAPTER-2

WIND TURBINE SYSTEMS

2.1. Introduction 102.2. Wind Turbines 102.3. Wind Turbine Topologies 12

2.3.1. Fixed speed wind turbine (Type A) 122.3.2. Variable speed wind turbine 13

2.3.2.1. Type B wind turbine 142.3.2.2. Type C wind turbine 152.3.2.3. Type D wind turbine 16

2.4. Typical characteristics of the wind turbine 162.4.1. Power versus speed Characteristics 16

2.4.2. Power coefficient versus TSR Characteristics 172.4.3. Torque versus speed Characteristics 20

2.5. Conclusions 21


10

CHAPTER 2Wind Turbine Systems

2.1.Introduction

Now-a-days global warming is the most burning issue found in many of the climate

summit. Many researchers, scientists are working their own relevant areas to reduce the

effect due to global warming by using different techniques. Effective mitigation of climate

change will require deep reductions in greenhouse gas emissions. The electricity system is

viewed as being easier to transfer to low-carbon energy sources than more challenging

sectors of the economy such as surface and air transport and domestic heating. Hence the

use of cost-effective and reliable low carbon electricity generation sources is becoming an

important objective of energy policy in many countries. This is only possible by utilizing

renewable sources as the key sources for the generation of electricity. The total statistical

survey of renewable energy sources is highlighted briefly in chapter 1. The survey conveys

that, over the past few decades wind energy has shown the fastest rate of growth of any

form of electricity generation with its development stimulated by concerns of national

policy makers over climate change, energy diversity and security of supply. This chapter

discusses detail about the wind energy system. Basically this chapter explains about

different types of wind turbine used to achieve fastest growth in the world market. The basic

concepts of the turbines, maximum power extractable from wind, characteristics of wind

turbine are also the part of this chapter. A layman’s concept states that wind energy system

means it is the combination of turbines, generators, the mediator power electronic

converters and the brain called controller. The technical aspects of generators and other

devices except turbines will be the part of next chapter.

2.2. Wind turbines

Wind turbines produce electricity by using the power of the wind to drive an electrical

generator. Wind passes over the blades, generating lift and exerting a turning force. The

rotating blades turn a shaft inside the nacelle, which goes into a gearbox. The gearbox

increases the rotational speed to that which is appropriate for the generator, which uses

magnetic fields to convert the rotational energy into electrical energy. The power output

goes to a transformer, which converts the electricity from the generator at around 700V.


11

The appropriate voltage for the power collection system, typically 33 kV. A wind turbine

extracts kinetic energy from the swept area of the blades (Fig 2.1).

FREE WIND

Fig 2.1.Horizontal axis turbine

The power contained in the wind is given by the kinetic energy of the flowing air mass

per unit time [25]. That is

21 / 2 ( )airP airmassperunittime windvelocity21/ 2( AV )( )V (2.1)

31 / 2 * AV

Where Pair is the power contained in wind (in watts) , ρ is the air density (1.225

kg/m3 at 15°C and normal pressure), A is the swept area in (square meter), and

is the wind velocity without rotor interference, i.e., ideally at infinite distance from the

rotor (in meter per second).Although Eq. (2.1) gives the power available in the wind, the power transferred to the

wind turbine rotor is reduced by the power coefficient, Cp

Windturbinep

air

PC

P (2.2)

3* 1/ 2*Windturbine p air pP C P C AV (2.3)

A maximum value of Cp is defined by the Betz limit, which states that a turbine can

never extract more than 59.3% of the power from an air stream. In reality, wind turbine


12

Rotors have maximum Cp values in the range 25-45%. It is also conventional to define a tip

Speed ratio as

(2.4)

Where is rotational speed of rotor (in rpm), R is the radius of the swept area (in

meter).The tip speed ratio and the power coefficient CP are the dimensionless and so can

be used to describe the performance of any size of wind turbine rotor.

2.3.Wind turbine Topologies

There are a large number of choices of topologies available to the designer of a wind

turbine and, over the years, most of these have been explored. However, commercial

designs for electricity generation have now converged to horizontal axis, three-bladed,

upwind turbines. The largest machines tend to operate at variable speed whereas smaller,

simpler turbines are of fixed speed. For a fixed-speed system the turbulence of the wind will

result in power variations, and thus affect the power quality of the grid where as in a

variable-speed wind turbine the generator is controlled by power electronic equipment,

which makes it possible to control the rotor speed. In this way the power fluctuations caused

by wind variations can be more or less absorbed by changing the rotor speed and thus power

variations originating from the wind conversion and the drive train can be reduced. Hence,

the power quality impact caused by the wind turbine can be improved compared to a fixed-

speed turbine.

Modern electricity generating wind turbines now use three-bladed upwind rotors,

although two bladed, and even one-bladed, rotors were used in earlier commercial turbines.

Reducing the number of blades means that the rotor has to operate at a higher rotational

speed in order to extract the wind energy passing through the rotor disk. Although a high

rotor speed is attractive in that it reduces the gearbox ratio required, a high blade tip speed

leads to increased aerodynamic noise and increased blade drag losses. Most importantly,

three-bladed rotors are visually more pleasing than other designs and so these are now

always used on large electricity generating turbines.

2.3.1. Fixed speed wind turbine (Type A)

This type of turbines are also called Type A turbine. Fixed-speed wind turbines are

electrically fairly simple devices consisting of an aerodynamic rotor driving a low-speed

shaft, a gearbox, a high-speed shaft and an induction (sometimes known as asynchronous)


13

generator. From the electrical system viewpoint they are perhaps best considered as large

fan drives with torque applied to the low-speed shaft from the wind flow. Fig 2.2 illustrates

the configuration of a fixed-speed wind turbine. It consists of a squirrel-cage induction

generator coupled to the power system through a turbine transformer. The generator

operating slip changes slightly as the operating power level changes and the rotational speed

is therefore not entirely constant. However, because the operating slip variation is generally

less than 1%, this type of wind generation is normally referred to as fixed speed.

Squirrel-cage induction machines consume reactive power and so it is conventional to

provide power factor correction capacitors at each wind turbine. The function of the soft-

starter unit is to build up the magnetic flux slowly and so minimize transient currents during

energization of the generator. Also, by applying the network voltage slowly to the

generator, once energized, it brings the drive train slowly to its operating rotational speed.

Fig 2.2.Schematic diagram of a fixed speed wind turbine

2.3.2.Variable speed wind turbine

During the past few years the variable-speed wind turbine has become the dominant

type among the installed wind turbines. Variable-speed wind turbines are designed to

achieve maximum aerodynamic efficiency over a wide range of wind speeds. With a

variable-speed operation it has become possible continuously to adapt (accelerate or

decelerate) the rotational speed ω of the wind turbine to the wind speed .. This way,

the tip speed ratio is kept constant at a predefined value that corresponds to the maximum

power coefficient. Contrary to a fixed-speed system, a variable-speed system keeps the

generator torque fairly constant and the variations in wind are absorbed by changes in the


14

generator speed. The electrical system of a variable-speed wind turbine is more complicated

than that of a fixed-speed wind turbine. It is typically equipped with an induction or

synchronous generator and connected to the grid through a power converter. The power

converter controls the generator speed; that is, the power fluctuations caused by wind

variations are absorbed mainly by changes in the rotor generator speed and consequently in

the wind turbine rotor speed. The advantages of variable-speed wind turbines are an

increased energy capture, improved power quality and reduced mechanical stress on the

wind turbine. The disadvantages are losses in power electronics, the use of more

components and the increased cost of equipment because of the power electronics. The

introduction of variable-speed wind-turbine types increases the number of applicable

generator types and also introduces several degrees of freedom in the combination of

generator type and power converter type .

Most common variable speed wind turbine configurations are as follows.

1. Limited variable speed(Type B)

2. Variable speed with partial scale frequency converter (Type C)

3. Variable speed with full scale frequency converter (Type D)

2.3.2.1. Type B wind turbine

Fig 2.3.Schematic diagram of Type B wind turbine

This configuration corresponds to the limited variable speed wind turbine with variable

generator rotor resistance. It uses a wound rotor induction generator (WRIG) and has been

used by the Danish manufacturer Vestas since mid-nineties. The generator is directly


15

connected to the grid. A capacitor bank performs the reactive power compensation. A

smoother grid connection is achieved by using a soft-starter. The unique feature of this

concept is that it has a variable additional rotor resistance, which can be changed by an

optically controlled converter mounted on the rotor shaft. Thus, the total rotor resistance is

controllable. This optical coupling eliminates the need for costly slip rings that need brushes

and maintenance.

The rotor resistance can be changed and thus controls the slip. This way, the power

output in the system is controlled. The range of the dynamic speed control depends on the

size of the variable rotor resistance. Typically, the speed range is 0 to10% above

synchronous speed. The energy coming from the external power conversion unit is dumped

as heat loss. Wallace and Oliver (1998) describe an alternative concept using passive

components instead of a power electronic converter. This concept achieves a 10% slip, but

it does not support a controllable slip. Fig 2.3 shows the schematic diagram of type B wind

turbine.

2.3.2.2. Type C wind turbine

Fig 2.4.Schematic diagram of Type C wind turbine

This configuration, known as DFIG based wind turbine, corresponds to the limited

variable speed wind turbine with a WRIG and partial scale frequency converter (rated at

approximately 30% of nominal generator power) on the rotor circuit. The partial scale

frequency converter performs the reactive power compensation and the smoother grid

connection. It has a wider range of dynamic speed control compared with that of Type B

wind turbine, depending on the size of the frequency converter. Typically, the speed range


16

comprises synchronous speed -40% to +30 %. The smaller frequency converter makes this

concept attractive from an economical point of view. Its main drawbacks are the use of slip

rings and protection in the case of grid faults. The schematic diagram is shown in Fig 2.4.

2.3.2.3. Type D wind turbine

This configuration corresponds to the full variable speed wind turbine, with the

generator connected to the grid through a full-scale frequency converter. The frequency

converter performs the reactive power compensation and the smoother grid connection. The

generator can be excited electrically (WRSG/WRIG) or by a permanent magnet (PMSG).

Some full variable-speed wind turbine systems have no gearbox. In these cases, a direct

driven multi pole generator with a large diameter is used. The wind turbine companies

Enercon, Made and Lagerwey are examples of manufacturers using this configuration. The

schematic configuration is shown in Fig 2.5.

Fig 2.5.Schematic diagram of Type D wind turbine

2.4.Typical characteristics of wind turbines

The following characteristic curves are plotted to explain the behaviour of wind

turbine at different wind speeds [25].

2.4.1. Power versus speed Characteristics

The wind turbine power curves shown in Fig 2.6 illustrate how the mechanical power can be

extracted from the wind depends on the rotor speed. For each wind speed there is an optimum

turbine speed at which the extracted wind power at the shaft reaches its maximum.


17

Fig 2.6.The typical power versus speed characteristics of a wind turbine

2.4.2. Power coefficient versus TSR Characteristics

For a given wind turbine the power coefficient depends not only on TSR but also on the

blade pitch angle. Fig 2.7 shows the typical variation of the power coefficient with respect

to TSR (lambda) with blade pitch control.

Fig 2.7.The typical curves of Cp versusfor various values of the pitch angle

For a wind turbine with radius R Eq. 2.3 can be expressed as

2 31/ 2m pP C R V (2.5)

For a given wind speed the power extracted from the wind is maximized if Cp ismaximized. Always there is a optimum value of TSR for a optimum value of Cp (Cp-

optimum). This means for varying wind speed the rotor speed should be adjustedproportionally to follow to the optimum value of TSR (λoptimum) for maximum mechanicalpower output from the turbine.


20

Using Eq. 2.4 the maximum value of shaft mechanical power for any wind speed can

be expressed as

5 3 3max 1/ 2 (R / )optimump optimum

P C

(2.6)

Thus the maximum mechanical power that can be extracted from wind is proportional

to the cube of the rotor speed, i.e., 3maxP

2.4.3. Torque versus speed characteristics

The typical torque versus speed characteristics of horizontal axis (two blade

propeller type) Wind turbine is shown in the Fig 2.8.

Fig 2.8.The torque versus speed characteristics of wind turbine(horizontal axis turbine)

The curves shown in Fig 2.8 follow the power curve shown in Fig 2.6 because there is a

direct relationship exists between power and torque. The relation is given in Eq. 2.7.

(2.7)

Using the optimum values of Cp & λ, from Eq. 2.6 and 2.7 the maximum value

of aerodynamic torque can be expressed as

25

max 3

1

2 p optimumoptimum

RT C

(2.8)

The curve in Fig 2.8 shows that for any wind speed the torque reaches a maximum

value at a specific rotational speed, and this maximum torque varies approximately as the

square of rotational speed. In the case of electricity production the load torque depends on


21

the electrical loading. The torque can be made to vary as the square of the rotational speed

by choosing the load properly.

2.5.Conclusions

This chapter explains different types of wind turbine briefly. The important

mechanical characteristics as power versus speed characteristics, CP versus and torque

versus speed characteristics which will be required for the subsequent chapters are also

explained here using different mathematical expressions.

Chapter 3 DFIG System

22

CHAPTER - 3

DFIG SYSTEM

3.1. Introduction 223.2. Vector or Field Oriented Control Theory 23

3.2.1. D-Q Theory 233.2.1.1. Transformation of three phase stationary to two phase stationary

Axes. 24

3.2.1.2. Transformation of two phase stationary to two phase

Synchronously rotating axes. 253.2.2. Mathematical modelling of Induction Generator 26

3.2.2.1. Modelling of DFIG in synchronously rotating frame 263.2.2.2. Dynamic modelling of DFIG in state space equations 28

3.2.3. Principle of Vector control 323.3. DFIG System 34

3.3.1. Double-fed Induction Generator 343.3.2. Voltage source converter 333.3.3. Grid side converter control 363.3.4. Machine side converter control 38

3.4. Conclusions 42


23

CHAPTER 3DFIG System

3.1.Introduction

The most common machine which is widely used in these days is Doubly-fed Induction

Machine. These types of machines can be used resolutely as a generator or motor. Though

demand in the direction of motor is less because of its mechanical wear at the slip rings but

they have gained their prominence for generator application in wind and water power plant

because of its obvious adoptability capacity and nature of tractability. In this section detail

analysis of overall DFIG system along with back to back PWM voltage source converters

has been made. Prior to the analysis of DFIG a brief enquiry on vector control theory is also

included in this chapter.

3.2.Vector or Field Oriented control Theory

The overall control strategy of the machine is divided in two ways, one is scalar control

and the other is vector control. The limitations of scalar control give an importance to vector

control. Though the scalar control strategy is simple to implement but the inherent coupling

effect gives sluggish response. The inherent problem is being solved by the vector control.

The vector control is invented in the beginning of 1970s. Using this control strategy an IM

can be performed like dc machine. Because of dc machine like performance vector control

is also known as decoupling, orthogonal or Trans vector control.

The basic of the vector control theory is d-q theory. To understand vector control

theory knowledge about d-q theory is necessary.

3.2.1. D-Q theory

The d-q theory is also known as reference frame theory. The history says in 1920 R. H.

Park proposed a new theory to overcome the problem of time varying parameters with the

ac machines. He formulated a change of variables which in effect replace the variables

associated with the stator windings of a synchronous machine with variables associated with

fictitious winding rotating with the rotor at synchronous speed. Essentially he transformed

the stator variables to a synchronously rotating reference frame fixed in the rotor. With such

transformation (Park’s transformation) he showed that all the time varying inductances that


24

ds qs

v

s

qs

occur due to an electric circuit in relative motion and electric circuit with varying magnetic

reluctances can be eliminated. Later in 1930s H. C. Stanley showed that time varying

parameters can be eliminated by transforming the rotor variables to the variables associated

with fictitious stationary windings. In this case the rotor variables are transformed to the

stationary reference frame fixed on the stator. Later G. Kron proposed a transformation of

both stator and rotor variables to a synchronously rotating reference frame that moves with

the rotating magnetic field. Latter, Krause and Thomas shown that the time varying

inductances can be eliminated by referring the stator and rotor variables to an arbitrary

reference frame which may rotate at any speed.

3.2.1.1. Transformation of three phase stationary to two phase stationary axes

Consider a symmetrical three phase induction machine with stationary a-phase, b-

phase and c-phase axes are placed at 120° angle to each other as shown in Fig 3.1. The main

aim is to transform the three phase stationary frame variables into two phase stationary

frame variables (ds-qs) and then transform these to synchronously rotating reference frame

variables (d-q), and vice versa.

Fig 3.1.Transformation of a-b-c to ds-qs axes

Let ds-qs axes are oriented at an angle θ from a-b-c axes as shown in Fig 3.1. The

voltage (v s and v s) can be resolved into a-b-c components and can be represented in the

matrix form as

v a

cosθ

οsinθ

ο1 s s

v b cosθ 120 sinθ 120 1v ds (3.1)

v c cosθ 120ο sinθ 120ο 1 v 0s


25

s vmsin(θe φ)s

vqs vmsinφ

v v ds

vs vmcosqs

v

v

v e

v e

qs

v

qs

qs

The corresponding inverse relation is

s cosθ cosθ 120ο cosθ 120ο v s 2

ο ο a

vds 3 sinθ sinθ 120 sinθ 120 vb

(3.2) s 0s

0.5

s

0.5 0.5

c

Where v0s is added as the zero sequence component. Other parameters like current,

flux linkages can be transformed by similar manner. It is more convenient to set θ=0°, so

that q-axis is aligned with the a-axis in this case (The alignment of the axes are optional, d-

axis can also be aligned with a-axis). The sine components of d and q parameters will be

replaced with cosine values, and vice versa if d-axis coincides with a-axis.

3.2.1.2.Transformation of two phase stationary to two phase synchronously rotating

axes

vd vmsinφ

(θe φ)

Fig 3.2.Transformation of stationary ds-qs axes to synchronously rotating frame d-q axes

Fig 3.2 shows the synchronously rotating d-q axes which rotate at synchronous speed

e with respect to ds-qs axes. The two phase windings are transformed into the fictitious

windings mounted on the d-q axes.

The voltages on the ds-qs axes can be converted into d-q axes as follows;

vqss cos vs

dssin e (3.3)

vdss sin vs

dscos e (3.4)


26

s r m

Again resolving the rotating frame parameters into a stationary frame the relations are

svqs

vsds

vqs

cos e vds

sin e

vqs

sin e vds

cos e

(3.5)

(3.6)

3.2.2. Mathematical modelling of Induction Generator

In this section the basic mathematical modelling of DFIG is explained in detail.

From the previous section we confirm that the three phase parameters can be represent

in two phase parameters and vice versa using certain fundamental rules. In this section the

machine modelling is explained by taking two phase parameters into consideration. Though

the basic concepts behind the DFIG system is explained briefly in Chapter 1, in short we

can say the DFIG is a wound rotor type induction machine its stator consists of stator frame,

stator core, poly phase (3-phase) distributed winding, two end covers, bearing etc. The

stator core is stack of cylindrical steel laminations which are slotted along their inner

periphery for housing the 3-phase winding. Its rotor consists of slots in the outer periphery

to house the windings like stator. The machine works on the principle of Electromagnetic

Induction and the energy transfer takes place by means of transfer action. So the machine

can represent as a transformer but rotatory not stationary.

3.2.2.1. Modelling of DFIG in synchronously rotating frame

The equivalent circuit diagram of an induction machine is shown in Fig 3.3 and 3.4. In

this figure the machine is represented as two phase machine, it has already been discussed

before that a three phase machine can be represent as two phase machine obeying certain

rules. For the modelling of DFIG in synchronously rotating frame we need to represent the

two phase stator (ds- qs) and rotor (dr-qr) circuit variables in a synchronously rotating (d-q)

Frame.

L Lls Lm L L Llr

e ds ( e r ) dr

Fig 3.3.Dynamic d-q equivalent circuit of DFIG (q-axis circuit)


27

s r mL Lls

Lm L L Llr

eqs (e r)qr

Fig 3.4.Dynamic d-q equivalent circuit of DFIG (d-axis circuit)

The stator circuit equations are given below,

s s d svqs Rsiqs dtqs (3.7)

s s d svds Rsids dtds

s s

(3.8)

Where qs and dsare q-axis and d-axis stator flux linkages, respectively. Converting

Eq. (3.7) and (3.8) to d-q frame the following equations can be written as

dv

qs Rsi

qs

dt

qs (

e

ds)

dvds Rsids dt

ds (eqs )

(3.9)

(3.10)

Where all the variables are in synchronously rotating frame. The bracketed terms are

defined as the back e.m.f. or speed e.m.f or counter e.m.f. due to the rotation of axes as in

the case of DC machines. When the angular speed e is zero the speed e.m.f due to d and q

axis is zero and the equations changes to stationary form.

Owing to the rotor circuit, if the rotor is blocked or not moving, i.e. r=0, the machine

equations can be written in similar way as stator equations:

dvqr R riqr dt

qr (edr )

dvdr R ridr dt

dr (eqr )

(3.11)

(3.12)

Where all the parameters are referred to the primary circuit, which is stator in this case.

Let the rotor rotates at an angular speed r, then the d-q axes fixed on the rotor fictitiously

will move at a relative speed e r to the synchronously rotating frame.


28

The d-q frame rotor equations can be written by replacing

follows:

e r in place of e as

vqr

vdr

R riqr

R ridr

d

dt qr

d

dt dr

(e

r)

dr

(e

r)

qr

(3.13)

(3.14)

The flux linkage expressions in terms of current can be written from Fig 3.3 and 3.4 as

follows:

qs

ds

qr

dr

Llsiqs Lm (iqs iqr )

Lsiqs Lmiqr

Llsids Lm (ids idr )

Lsids Lmidr

Llriqr Lm (iqs iqr )

Lriqr Lmiqs

Llridr Lm (ids idr )

Lridr Lmids

(3.15)

(3.16)

(3.17)

(3.18)

qm Lm (iqs iqr )

dm Lm (ids idr )

(3.19)

(3.20)

Eq. (3.7) to (3.20) describes the complete electrical modelling of DFIG. Where as Eq.

(3.21) express the relations of mechanical parameters which are essential part of the

modelling.

The electrical speed r cannot be treated as constant in the above equations. It can be

connected to the torque as

Te TL Jdm

dt Bm TL

2J

d r

P dt

2 B r

P(3.21)

3.2.2.2. Dynamic modelling of DFIG in state space equations

The dynamic modelling in state space form is necessary to carried out simulation using

different tools such as MATLAB. The basic sate space form helps to analyse the system in

transient condition.

The basic definition says, the space whose co-ordinate axes are nothing but the „n‟ state

variables with time as the implicit variable is called the state space. The variables of the


29

e

e

qs

m

qs

state space (state variables) are involved to determine the state of the dynamic system.

Basically these are the energy storing elements contained in the system. The fundamental

equation of the state space is as follows:

Xt AXt BUt (3.22)Yt CXt DUt

Eq. (3.22) is in linear time invariant system, where A, B, C, D are constant matrices and Eq.

(3.23) is for linear time variant system, where A, B, C, D are time dependent matrices.

Xt AtXt BtUt (3.23)Yt CtXtDtUt

In the DFIG system the state variables are normally currents, fluxes etc. In the

following section the state space equations for the DFIG in synchronously rotating frame

has been derived with flux linkages as the state variables.

Since the machine and power system parameters are nearly always given in ohms or

percent or per unit of base impedance, it is convenient to express the voltage and flux

linkage equations in terms of reactances rather than inductances. The above stated voltage

and flux equations can be reworked as follows:

vqs

1 Rsi

qs

b

d

dt qs b

ds

(3.24)

vds1

Rsids b

d

dtds b

qs (3.25)

1 d e r vqr R r iqr qr b dt dr

b

(3.26)

1 d e r vdr R r idr b dt dr b

qr (3.27)

Equations related to flux linkage i.e. Eq. (3.15)-(3.20) can be written in terms of

reactances as follows:

qs Xls iqs Xmi

iqr

(3.28)

ds Xlsids X ids i

dr

(3.29)

qr Xlr iqr Xm

i

iqr

(3.30)


30

ls

m

m X

dr Xlridr X ids i

dr

(3.31)

qm Xmiqs iqr (3.32)

dm Xmids idr (3.33)

Where reactances (Xls, Xlr, Xm) are found by multiplying base frequency b with

inductances (Lls, Llr, Lm).

From Eq. (3.28)-(3.33) we can find the expressions for currents in terms of flux

linkages and also the mutual flux linkages (qm ,dm) are found using current expressions.

The equations are given as follows.

qs qmiqs X

(3.34)ls

qr qmiqr X

(3.35)lr

ids

idr

ds dm

Xls

dr dm

Xlr

(3.36)

(3.37)

Substituting Equations (3.34)-(3.37) in (3.32)-(3.33) we get,

qm Xm

Xm

qs qm

Xls

Xm

qr qm

Xlr

Xm Xm qm Xlsqs Xls

qm Xlrqr Xlr

qm Xm Xm Xm Xmqm qm qm qs qr

Xls

Xm

Xlr

Xm Xm

Xls

Xm

Xlr

qm 1

Xls

Xlr Xls

qs Xlrqr

Xqm

lsXlr XmXlr X X m

Xmqs

qr

Xls

XlsXlr

Xlr XmXlr

XmX

Xls

ls Xm

Xlr

Xm qmXm

XlsXlr Xm

Xls

qs Xlrqr

(3.38 contd.)


31

r

r

r

r

qm XmXeq

XmXlsqs

XmXlrqr

(3.38)

qmXeq qsXls

Xeq qr Xlr

Similarly we can find the value of dm as follows

dm

Xeq

Xlsds

Xeq

Xlrdr (3.39)

Substituting the current equations from (3.34)-(3.37) in voltage equations (3.24)-(3.27)

we will get,

v qs R s

X ls

R

qs qm 1

b

d qs

dt

d

e

b

ds (3.40)

v ds s

X lsds

1 dm

b

ds e

dt b

qs (3.41)

R r

1 d qr e v qr

X lr qr qm

b dt b dr (3.42)

R r

1 d dr e v dr X lr

dr dm dt

b b

qr (3.43)

The state variables can be expressed using the above equations as follows

d qs e R s b v qsdt

ds

b

X ls

qs qm

(3.44)

d ds e R s dt

b v ds

qs

b

X ls

ds dm (3.45)

d qr e R r b v qr

dt b dr X lr

qr qm

(3.46)

d dr e R r b v dr dt b

qr X lr

dr dm

(3.47)


32

The state space matrix can be written as follows

R s e 0 0 X ls b R

R s 0 X ls R

qs e

s

0 0 qs 1 0 0 0v qs 0s

ds b X ls ds

0 1 0 0v ds X ls qm

R 0 0 1 0v

R qr 0

r e0

r qr qr r0 dm

dr

X lr drb

0 0 0 1 v dr X

lr

0 0

e r R r R r

0 b X lr X lr

(3.48)

The electromotive torque is developed by the interaction of air-gap flux and the rotor

mmf. At synchronous speed the rotor cannot move and as a result there is no question of

induced emf as well as the current, so the torque becomes zero, but at any speed other than

synchronous speed the machine will experience torque which is the case of motor, where as

in case of generator electrical torque in terms of mechanical is provided by means of prime

mover which is wind in this case.

The torque expression can be written in terms of flux linkages and currents as follows

Te 3 P 2 2 dsiqs qsids

3 P

2 2Lm iqsidr idsiqr

(3.49)

3 P 2 2 driqr qridr

Equation (3.49) can be written in terms of state variables as follows

3 PTe 1 iqs qsi 2 2 b

ds ds(3.50)

3 P 1 iqr qri 2 2 b

dr dr

Eq. (3.44) - (3.50) describe the complete DFIG model in state space form, where

qs, ds, qr, dr are the state variables.

3.2.3.Principle of Vector Control

The fundamentals of implementation of vector control technique can be explained

using the Fig 3.5. In this figure the machine model is in synchronously rotating frame. The

vector control uses unit vectors to obtain the appropriate control action. The main role of


33

d

q

s

unit vector is to convert the 2-phase model to 3-phase model and vice versa. Though the

control techniques used for DFIG uses two axes parameters as explained in the

modelling via vector control but the model is virtual representation of the original

machine. The control signals which will be fed to the original machine or converters should

be in three axes form, so the process requires repeated conversion of two-phase to

three-phase parameter or vice versa following the necessary action being taken for the

system. There are essentially two general method of vector control.

Direct or feed back method (which is invented by Blaschke )

Indirect or feed forward method ( which is invented by Hasse)

The two methods are different from each other by the process of generating unit vector

for control. Unit vectors (cosθe, sinθe) are generally generated using the flux vectors, but it

can also be generated using voltage vectors. The name of the orientation of unit vector is

given according to the vector taken for generation of θe. The names of the orientations used

are given below.

Rotor flux orientation

Stator flux orientation

Air gap flux orientation

Voltage orientation

dd q

q tods qs

s ds qs tos abc

a b c

ds qs

tod q

s a bcq to

ds qs

a bc

d

q

Fig 3.5.Implementation of vector control principle


34

The detail vector control strategy is shown in Fig 3.5. The a, b, c components are

generated from the controlled components a*, b*, c* respectively using vector control

techniques. The machine terminal parameters (either voltages or currents) are converted to

ds-qs components by 3-phase to 2-phase transformation. These are then converted to

synchronously rotating frame by the unit vector before applying to the 2-phase machine

model. The controller makes two stage of inverse transformation as shown, so that the

control components d* and q* corresponds to the machine parameters d and q respectively.

3.3.DFIG System

The overall system is shown in Fig 3.6. The basic components of the system are as

follows.

1. DFIG (Wound rotor type Induction machine)

2. PWM Voltage source converters (Grid side converter and Machine side converter)

3. Utility grid

4. PI controller

Fig 3.6.Overall DFIG System

3.3.1.Doubly-fed Induction Generator

The modelling of DFIG has been discussed in 3.2.2. The state space equations are taken

into account for modeming of Induction Machine. The modeming is carried out using

MATLAB/SIMULINK.


35

r

The model uses flux linkages as the state variables as discussed above. Though the generator

can generate in both sub and super synchronous mode, here the speed is taken as super

synchronous speed, where the power can be extracted from the stator as well as rotor

circuit. The machine uses two back to back converters in the rotor circuit. The main purpose

of the machine-side converter is to controls the active and reactive power by controlling the

d-q components of rotor current (i.e. idr and iqr), while the grid-side converter is to control

the dc-link voltage and ensures the operation at unity power factor by making the reactive

power drawn by the system from the utility grid to zero.

3.3.2. Voltage source converter

Two back to back voltage-fed current regulated converters are connected to the rotor

circuit as shown in Fig 3.6. The firing pulses are given to the devices (IGBTs) using PWM

techniques. Two converters are linked to each other by means of DC-link capacitor.

Realization of vector control principle for decoupling of generator’s active and reactive

power , improvement of overall power factor, operation at synchronous speed by injecting

dc current into the rotor, less distortion in currents are the functional characteristics of the

back to back converters. Basically converter 1 controls the grid parameters where as the

converter 2 serves for machine. As a duo both are responsible for overall control. The

converters use six IGBTs (for three phase bridge type) as the controlled device for its

obvious advantages. Each control device has an antiparallel diode, to permit active and

reactive power flow in either direction.

The PWM technique uses the controlled voltage va*, vb

*, vc* as the reference voltages

for the generation of pulses. The triangular career waves are being compared with

sinusoidal reference waves to ensure pulses for the devices. The modulation indices are

different for the both converters. These are decided from the Eq. (3.51). The career

frequency is taken as 3 kHz where as the frequency of the reference waves are decided by

the supply frequency, which is 50Hz in this case.

Vs m1

Vdc 3

2 2

(3.51)

V sVs m2

Vdc s nm2

n 2 2 m1 3

Where Vs and Vr are the per phase stator and rotor voltages respectively, m1 and m2 are

the modulation index of the grid side and machine side converter respectively, s is the slip,

and Vdc represents DC-link voltage.


36

3.3.3. Grid side Converter Control

When the voltages in the grid changes due to different unbalance conditions, it

makes an effect on the dc link voltage. The relation between stator voltage and the dc link

voltage is shown in the equation (3.51). Since the machine is grid connected the grid voltage

as well as the stator voltage is same, there exist a relation between the grid voltage and dc

link voltage.

The main objective of the grid side converter is to maintain dc-link voltage constant for the

necessary action. The voltage oriented vector control technique is approached to solve this

issue. The detail mathematical modeming of grid side converter is given below. The control

strategies are made following the mathematical modelling and it is shown in Fig. 3.8. Phase

Locked Loop block is used to measure the system frequency and provides the phase

synchronous angle θ for the d-q transformations block. The PWM converter is current

regulated with the direct axis current is used to regulate the DC link voltage where as the

quadrature axis current component is used to regulate the reactive power. The reactive

power demand is set to zero to ensure the unit power factor operation. Fig. 3.7 shows the

schematic diagram of the grid side converter.

Fig 3.7.Schematic diagram of Grid side Converter

The voltage balance across the line is given by Eq. (3.52), where R and L are the line

resistance and reactance respectively. Using d-q theory the three phase quantities are

transferred to the two phase quantities.

va ia

ia v

v

R

Ld a'

(3.52) b ib dt ib vb'

v i

i v

c c c c'


37

The mathematical modelling of the grid side converter is shown in the following equations.

vd Rid Ldiddt

diq

eLiq v

d1

(3.53)

vq Riq Ldt eLid vq1

Where vd1 and vq1 are the two phase voltages found from va‟,vb‟ and vc‟ using d-q

theory. Since the dc link voltage needs to be constant and the power factor of the overall

system sets to be unity, the reference values are to be set accordingly. The d and q reference

voltages are found from the Eq. (3.54).

v* v i* R i*eL v d d d q d'

(3.54)v* vq i* R i*eL v q q d d'

Fig 3.8.Vector control structure for Grid side Converter

The control scheme utilizes current control loops for id and iq with the id demand being

derived from the dc-link voltage error through a standard PI controller. The iq demand

determines the displacement factor on the grid side of the choke. The iq demand is set to

zero to ensure unit power factor. The control design uses two loops, i.e. inner current loop

and outer voltage


38

v

d d

line resistance and reactance, where as dc link capacitor is taken as the plant for the voltage

loop. The plants for the current loop and the voltage loop are given in Eq. (3.55) and (3.56)

respectively.

Fs

id (s)

vd'(s)

iq (s)

vq' (s)

1Ls R

(3.55)

v (s)Gs dc

3m1 (3.56)id (s) 2 2Cs

The active and reactive power is controlled independently using the vector control

strategy. Aligning the d-axis of the reference frame along the stator voltage position is

found by Eq. (3.57), vq=0, since the amplitude of supply voltage is constant the active

power and reactive power are controlled independently by means of id and iq respectively

following Eq. (3.58).

sq

tane vsd

(3.57)

Ps 3 v2 did vqiq

(3.58)

Qs3 v iq vqi

2

3.3.4. Machine side Converter Control

The control strategy made for the machine side converter is shown in Fig.3.9. The main

purpose of the machine side converter is to maintain the rotor speed constant irrespective of

the wind speed and also the control strategy has been implemented to control the active

power and reactive power flow of the machine using the rotor current components. The

active power flow is controlled through idr and the reactive power flow is controlled through

iqr. To ensure unit power factor operation like grid side converter the reactive power demand

is also set to zero here.

The standard voltage oriented vector control strategy is used for the machine side

converter to implement control action. Here the real axis of the stator voltage is chosen as

the d-axis. The vector diagram is shown in Fig. 3.10. The mathematical modelling of the

machine side converter is given in the following equations.


39

i

r

v

T

e m

e

( )L i L i

Q**

Q qr

ds

'qr

r dr*

(e r )

riqr

*

iqrRr

' i

vqr

R*

idrr

vdr dr r

*

Ls idr ( )L i L i i

dr i

*s Lm

ee r m qs r qr

iqr

( )

abcr

(e r )e r

r

Vabcs

ids i

iqs

Fig 3.9. PWM Control for Mechanical side converter

Fig 3.10.Vector diagram showing stator and rotor current components of DFIG in voltage oriented co-ordinate

Since the stator is connected to the utility grid and the influence of stator resistance

is small, the stator magnetizing current im can be considered as constant. Under voltage

orientation the relationship between the torque and the dq axis voltages, currents and fluxes


40

L

s

s

dr qr

ddr

can be written as follows. The stator flux Equations are written in Eq. (3.59) neglecting

leakage inductances.

ds 0

qs Lsiqs Lmiqr

L L i L i

ls m qs m qr

Llsiqs iqs iqr Lm

Lmim

(3.59)

The equations of rotor fluxes are given in Eq. (3.60) following the vector diagram

shown in Fig.3.10. The derivation of Eq. (3.60) is given in Appendix I.

qr Lm qs Lriqr

Ls 2

Lm im Lriqr Ls

dr Lm Ls ds Lri

dr Lridr

Where 1

2m

Ls L r

(3.60)

The rotor voltage Eq. (3.13) and (3.14) can be written by substituting the values of dr

and qr from the Eq. (3.60) as follows.

d L2 vqr Rriqr

m im Lriqr e r Lridrdt L

Rriqr

0 Lriqr e r Lridt

d Rriqr Lr dt

iqr e r Lridr (3.61)

di 2

v R ri Lrdr e r

Lm im Lriqr

dr dr dt L

(3.62)

The unit vector is found in similar way as in the case of grid side converter. The

reference value v *

(3.61) and (3.62).

and v * are given in Eq. 3.63 and 3.64 which are being found from Eq.


41

v v

ds

T e

* 'qr qr iqr R r r idr Lr Lmids

(3.64)

Where v‟dr and v‟qr are found from the current errors processing through standard PI

controllers. The reference current i*dr can be found either from the reference torque given

by Eq. (3.66) or form the speed errors (for the purpose of speed control) through standard PI

controllers. Similarly i*qr is found from the reactive power errors. The reactive power and

speed is controlled using the current control loops.

The electromagnetic torque can be expresses as follows

3 PTe

2 23 P

dsiqs qsids qsi

2 2

3 Pqs

Lm i

dr 2 2 Ls

3 P Lm i

(3.65)

2 2 Lsqs dr

*The value of idr

* Ls

is found using Eq. (3.65)

i* drTeqs Lm

P P

(3.66)

Where * mechr

loss

Ploss Mechanical Losses Electrical Losses(PCur PCus )

Mechanical losses include friction and wind-age losses whereas electrical losses

include stator copper loss and rotor copper losses.

The maximum mechanical power given by Eq. (2.6) can be extracted from the wind is

proportional to the cube of the rotor speed.

The plant for the current loop is decided by the line resistance and reactance, where as

dc link capacitor is taken as the plant for the voltage loop. The plants for the current loop

and the voltage loop are given in Eq. (3.67) and (3.68) respectively.

Fs

idr (s)

vdr' (s)

iqr (s)

vqr'(s)

1

Lr Rr (3.67)

G(s)

3PLm K

4Lsqs Js B Js B (3.68)


42

where K 3PLm

4Lsqs

3.4.Conclusions

This chapter explains the transformation theory for conversion of three-phase

parameters to two-phase and vice versa. Detail modelling of the DFIG system was analysed

in this chapter. The control strategy made for the grid side and machine side converter was

also explained.

Chapter- 4 MATLAB/Simulink Modelling

43

CHAPTER-4

MATLAB/SIMULINKMODELLING

4.1. INTRODUCTIONTO MATLAB/SUMULINK 444.1.1. Development Environment 444.1.2. The MATLAB Mathematical Function Library

4.2. The MATLAB Language 454.2.1. Graphics 454.2.2. The MATLAB Applications Program interface (API) 454.2.3. MATLAB Documentation 45

4.3. MATLAB tools 46


44

CHAPTER 4MATLAB/ Simulink Modelling

4.1. INTRODUCTION TO MATLAB/SIMULINK

MATLAB is a high-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use environment where problems

and solutions are expressed in familiar mathematical notation. Typical uses include-

Math and computation

Algorithm development

Data acquisition

Modeling, simulation, and prototyping

Data analysis, exploration, and visualization

Scientific and engineering graphics

MATLAB is an interactive system whose basic data element is an array that does not

require dimensioning. This allows solving many technical computing problems, especially

those with matrix and vector formulations, in a fraction of the time it would take to write a

program in a scalar non-interactive language such as C or FORTRAN.

The MATLAB system consists of six main parts:

4.1.1. Development Environment

This is the set of tools and facilities that help to use MATLAB functions and files. Many

of these tools are graphical user interfaces. It includes the MATLAB desktop and Command

Window, a command history, an editor and debugger, and browsers for viewing help, the

workspace, files, and the search path.


45

4.1.2. The MATLAB Mathematical Function Library

This is a vast collection of computational algorithms ranging from elementary

functions, like sum, sine, cosine, and complex arithmetic, to more sophisticated functions like

matrix inverse, matrix Eigen values, Bessel functions, and fast Fourier transforms.

4.2. The MATLAB Language

This is a high-level matrix/array language with control flow statements, functions, data

structures, input/output, and object-oriented programming features. It allows both

"programming in the small" to rapidly create quick and dirty throw-away programs, and

"programming in the large" to create large and complex application programs.

4.2.1. Graphics

MATLAB has extensive facilities for displaying vectors and matrices as graphs, as well

as annotating and printing these graphs. It includes high-level functions for two-dimensional

and three-dimensional data visualization, image processing, animation, and presentation

graphics. It also includes low-level functions that allow to fully customize the appearance of

graphics as well as to build complete graphical user interfaces on MATLAB applications.

4.2.2. The MATLAB Application Program Interface (API)

This is a library that allows writing in C and FORTRAN programs that interact with

MATLAB. It includes facilities for calling routines from MATLAB (dynamic linking), calling

MATLAB as a computational engine, and for reading and writing MAT-files.

4.2.3. MATLAB Documentation

MATLAB provides extensive documentation, in both printed and online format, to help

to learn about and use all of its features. It covers all the primary MATLAB features at a high

level, including many examples. The MATLAB online help provides task-oriented and

reference information about MATLAB features. MATLAB documentation is also available in

printed form and in PDF format.


46

4.3. Matlab tools

(i) Three phase source block

The Three-Phase Source block implements a balanced three-phase voltage source with

internal R-L impedance. The three voltage sources are connected in Y with a neutral connection

that can be internally ground.

(ii) VI measurement block

The Three-Phase V-I Measurement block is used to measure three-phase voltages and

currents in a circuit. When connected in series with three-phase elements, it returns the three

phase-to-ground or phase-to-phase voltages and the three line currents

(iii) Scope

Display signals generated during a simulation. The Scope block displays its input

with respect to simulation time. The Scope block can have multiple axes (one per port); all axes

have a common time range with independent y-axes. The Scope allows you to adjust the

amount of time and the range of input values displayed. You can move and resize the Scope

window and you can modify the Scope's parameter values during the simulation


47

(iv). Three-Phase Series RLC Load

The Three-Phase Series RLC Load block implements a three-phase balanced load as

a series combination of RLC elements. At the specified frequency, the load exhibits constant

impedance. The active and reactive powers absorbed by the load are proportional to the square

of the applied voltage.

Three-Phase Series RLC Load

(v) Three-Phase Breaker block

The Three-Phase Breaker block implements a three-phase circuit breaker where the

opening and closing times can be controlled either from an external Simulink signal or from an

internal control signal.

Three-Phase Breaker block

(vi) Gain block

Gain block

The Gain block multiplies the input by a constant value (gain). The input and the gain

can each be a scalar, vector, or matrix.

Chapter- 5 Problem Description & Result

48

CHAPTER-5

PROBLEM DESCRIPTION &RESULTS

5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION 495.2. ANALYSIS OF CONTROL INSTABILITY 515.3. DESIGN OF SSCI DAMPING CONTROLLER 535.4. OTHER SSCI MITIGATION ALTERNATIVES 555.5. RECOMMENDATIONS 575.6. MATLAB SIMULINK MODELS & RESULTS 585.7. CONCLUSIONS 60


49

CHAPTER 5Problem Description & Result

5.1. INTRODUCTION TO THE SIMULATION MODEL DESCRIPTION

To analyse SSCI, a simple and non- proprietary test system was designed in MATLAB.

The real time disturbances were applied to change network configuration and excite unstable

operation modes.

A. System Model

This system uses a generic Type 3 (DFIG) wind turbine model developed by me. The

model includes vector controls and a back-to-back converter connected to the rotor.

The control model was taken from the base paper [10].

The control model has been used extensively in non-series compensated systems, and

performs well even into weak systems with a low short-circuit MVA. The generator is

connected to the radial series compensated system through a unit transformer and a station

transformer. The degree of series compensation can be varied from 0 to 100%, and the

series capacitor is equipped with bypass logic to remove or insert the capacitor as required.

Table I shows a summary of the key parameters in the example system.

TABLE ISYSTEM PARAMETERS

System quantities Values

Nominal Frequency 60 HzTotal wind generator power 450 MW (3MW x 150 units)

Rated turbine voltage (L-L,rms) 0.69 kVCollector voltage (L-L,rms) 33 kV

Station Transformer 600 MVA, 345/33/13.8 kV,12% Impedance

Unit Transformer 3.4 MVA scalable, 33/0.69 kV345 kV Line Impedance (pu

values on 100 MVA base)Approx. 100 Ω (R = 0.0075 pu, X =

0.084 pu, B = 1.25 pu)

Series Capacitor Impedance 0 - 100 ΩReceiving end system 345 kV, 1800 MVA /85° (at 1st

and 3rd harmonic)


50

B. Simulation of Disturbance

In order to excite the instabilities caused by SSCI in the modelled system, the system

was started with the series capacitor set to a small compensation value of 8%, and bypassed.

The simulation was given time to initialize properly before a bypass breaker was opened

across the capacitor at 5 seconds. The results are shown in Figure 2.

Fig.5.1. Simulated SSCI Event: Wind Plant Point of InterconnectionReal Power, Reactive Power, and RMS Voltage (8% series compensation)

Strong sub-synchronous oscillations develop and continue to grow for approximately 0.2

seconds, before the machines lose stability. If there are no protection system operations, the

current oscillations can continue to grow to very large levels and be maintained for many

seconds. It is noted that the oscillations are most evident in the real and reactive power and

currents. Voltage oscillations are evident but to a much lesser extent.

The generic wind turbine model is found to be unstable for any realistic compensation

level (6% or higher caused oscillations, where typical series compensation levels would be on

the order of 40% and higher), with oscillations developing in the current at the tuned SSR

series resonant frequency. The performance of this generic model is expected to be slightly

pessimistic, since current transducers and other forms of control filtering are not included in

this model as they would be in real turbines.


51

5.2. ANALYSIS OF CONTROL INSTABILITY

Analysis of the generic DFIG turbine models shows that SSCI interactions occur with the

following mechanism

1. The series capacitor and the electrical (inductive) system result in a sub-synchronous

electrical series resonant circuit.

2. Distorted or phase shifted components of voltage and current are measured and are seen

inside the wind turbine controllers.

3. The wind turbine controllers process this information through its controls.

4. The output of the controllers is an equivalent voltage source signal (or possibly a current

reference in some designs), which are compared to PWM (pulse-width modulation)

waveforms, and ultimately fire IGBTs in the VSC (voltage source converter) circuit on

the turbine rotor.

5. The closed-loop response (of the system, controller, and IGBT firing) results in negative

damping, which causes oscillations (at SS frequencies) to grow.

It is noteworthy that the frequency of the un-damped oscillations will change as the system

inductance changes – for example under heavy or light load conditions, or under contingency

conditions. The worst case is a radial system configuration, where the wind farm is

completely in series with the series capacitor and then the system, although SSCI can develop

for cases with parallel (non-series) paths as well.

To determine the precise control loops that are affected by the instability, the generic control

model was analysed when the current oscillations were growing, and the outputs of each

major control loop was analysed to see if the frequency was visible. Next, a test was

performed where the turbine was in steady state (so all controller outputs are constant) and

then the series capacitor bypass breaker was opened – this puts a small disturbance onto the

system, and initiates the SSR resonance. As a test, the output of each control loop was frozen

individually. If the oscillation stopped or if a significant change in the damping was observed

as a result of the control loop being locked, then this indicates the control loop has a significant

influence on SSCI.

The most significant control loops were identified as the rotor side current feedback

loops. A simplified representation of this control loop is shown in Figure 3.


52

The instantaneous measured ABC rotor side currents are converter to the DQ domain,

which requires a PLL (Phase Locked Loop) input – this process is direct and does not

introduce any filtering or delays. A sub-synchronous oscillation in the rotor currents would

appear as an oscillation on the measured DQ currents.

Next, the DQ measured components of current are compared to DQ current orders, which

come from higher level PI controllers which control real or reactive power (P or Q).

The difference is sent to PI controllers (or PID). The proportional gain of this inner PID

controller means there is a direct pass-through of the oscillation into the URDQ voltage

reference signals.

The URDQ voltage references are converted back to ABC domain (again a direct

conversion) and are compared with PWM carrier signals, resulting in firing pulses to the IGBT

converters. It is suspected that the tuning experience of the control designers is often limited

to inductive systems, whereas the introduction of the series capacitor introduces a phase

inversion, with unstable results.

Oscillations were also evident in the measured real and reactive power outputs, which can

pass through the proportional gain of the first set of PI controllers. This outer loop has also

been shown to have an impact on SSCI, although the effect is not the dominant effect.

It is the fast, direct nature of the current control loop which is the primary cause of the

SSCI problem. Topologies similar to the above described controls are common to all type

3 DFIG wind turbines. This explains why the problem is wide-spread amongst type 3 turbines

from most manufacturers. Type 4 (full converter) wind turbines do not use a rotor side

controller, and therefore do not exhibit the SSCI problem.

It has been shown that control changes in type 3 wind turbines can mitigate SSCI [9][10].

The following section describes several improvements that can be made to type 3 wind

turbine controls to mitigate SSCI.


53

Fig.5.2.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls

Fig.5.2.1. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current

Feedback Control Loop

5.3 DESIGN OF SSCI DAMPING CONTROLLER

The earlier results showed the nature of the SSCI instability, and identified the major

control loops which were the cause. To fix this problem, four changes were made to the


54

controls in the generic type 3 model. These changes are shown in Figure 4 and are described

as follows:

1. Reduction/optimization of the proportional gains in the rotor current DQ PI controller

loops. The original gains were 1.0 and were reduced to 0.4 pu.

2. A first order real pole was added to the IRD and IRQ measurement signals – the gain was

1.0 and the time constant was 0.01 seconds.

3. 2nd order low-pass filtering was added to the real power measurement signal (PGX in

Figure 4 - this filtering was already in place for the reactive power measurement signal

but is not shown)

4. A damping controller was added, which takes the real power error signal (input to the

first PI controller), passes it through a lead-lag control block (transfer function =

G*(1+sT1)/(1+sT2), where the G = 0.2, lead time constant T1 = 0.02, and lag time

constant T2 =

0.002), and then adds this signal to the output of the voltage signal reference (URQ

Ordered in Figure 4).

The generic model used in these tests is comprised of standard PSCAD control blocks for

PLLs, filters, etc. These may not function in exactly the same manner as real controls. Even

measurements such as Rms voltages, or P and Q flows can be performed in many different

ways and will be unique to each manufacturer.

With the 4 controller changes, the DFIG was able to operate radially into the series

compensated test system with more than 50% series compensation levels, without the

build-up of SSCI oscillations, as shown in Figure 5. It is noted that even though the

simulation shows stable operation with no growing sub-synchronous oscillations, the

transient response following the disturbance at 5 seconds is much more severe than that

seen when using the un- modified controls. This is due to a reduction in speed and increased

damping being introduced into the fast rotor current control loop, and illustrates that a

trade-off exists between reducing SSCI interactions and the speed the device is able to

respond to disturbances. For this reason, these control changes would not be made lightly,

and will require careful tuning by the wind turbine manufacturer. It is likely that additional

improvements and optimizations are possible, and results will vary from one manufacturer to

the other depending on their specific controller topologies and tuning.


55

Fig.5.3. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,

Reactive power, and Rms Voltage (50% series compensation)

5.4. OTHER SSCI MITIGATION ALTERNATIVES

Although the primary mitigation of SSCI should be accomplished by means of a

controller adjustment in the type 3 wind turbine rotor converter (the controls are the source of

the instability), there are other precautions and mitigations which may be adopted as required.

A. Addition of bypass filters across series capacitor

A sub-synchronous bypass filter across the series capacitor may be effective. A parallel

LC impedance (tuned to fundamental) in series with a damping resistor is placed in parallel

with the main series capacitor. The tuned LC path is an open circuit at fundamental

frequency (to minimize losses) – low frequencies components will pass through the filter

so the resistor adds sub-synchronous damping. The use of such a filter (example shown in

Figure 6) may lead to additional losses, and the RLC filter must be insulated to the full line

voltage and sit on an insulated platform in the same fashion as the series capacitor. Although

passive filters can be readily designed, such filters have not been implemented in the field.


56

Other bypass filter topologies can also be used. The wind turbine also may employ series

SSR blocking filters, but these can be expensive and may not be 100% effective.

The 60 Hz blocking filter is comprised of two or more blocking filters so that detuning is

minimized when a filter capacitor fails. The large inductors of the 60 Hz blocking component

of the filter may require iron cores, which could add an extra cost if they are too heavy to

mount on the platform and must be insulated for full line voltage.

B. Combination of wind turbine models

Recent study work has shown that full converter turbines (type 4) have been shown to add

positive damping at sub- synchronous frequencies, which could offset the negative

damping added by

Fig.5.4. Example of a blocking filter in parallel with series capacitor

D. Install SSCI protection relays

As a minimum, any wind turbine that is operated near a series capacitor should employ an

SSCI protection circuit. If sub-synchronous oscillations are detected, then either the wind

farm can be tripped or the series capacitor bypassed to avoid damage. This should be

considered a fail-safe protection mechanism, similar to SSR relays commonly installed in

gas turbine generators, rather than a mitigating solution. The oscillations have been observed

to ramp up very quickly (in seconds rather than minutes), so SSCI protection is required to be

faster than conventional SSR protection circuits, which operate over longer timeframes.

Ultimately, a combination of these mitigation methods may be required for a successful

project. It is important that the SSR behaviour of the system is studied with detailed

EMT models. Conventional transient stability programs do not demonstrate SSCI problems

as they cannot represent the electrical resonance. At present, this is not a requirement in most

wind interconnection standards. Since some of the mitigation solutions can be expensive and

require equipment to be purchased or control upgrades to be performed, the studies may need

to be performed relatively early in the overall project development schedule.


57

5.5. RECOMMENDATIONS

In order to ensure future wind and transmission projects are not impeded by SSCI

concerns when used in conjunction with series compensated transmission systems, the

following specific recommendations are made

1. Detailed EMT models of the turbine should be obtained directly from the manufacturer

during project planning stages. This may require non-disclosure agreements to be signed,

but is essential for a complete understanding of performance, and evaluation of potential

problems. The best models directly use the real code from the actual controller hardware.

In this case, the source code can be compiled and imbedded directly in the EMT tool,

complete with all measurement methods, controllers, protection functions etc. This has

been successfully done for several major wind turbine manufacturers. The method is

highly accurate and relatively easy to develop, but beyond the scope of this paper.

2. Wind turbine manufacturers are encouraged to aggressively research SSCI and see

if improvements can be made in their turbine controls.

3. Wind developers must be aware of potential problems of turbines operating near series

compensated lines and be aware of the potential complexities this introduces.

4. Transmission providers should update their interconnection standards to require

EMT/SSCI analysis to be performed when turbines are connected near series compensated

lines, and to ensure the proper protection systems are in place.

5. Transmission planners should include the additional costs for SSCI related problems

when comparing lines with series capacitors to higher voltage AC lines, or DC solutions.


58

5.6. MATLAB SIMULINK MODELS & RESULTS

Fig.5.5.Simplied Rotor Side Current Feedback Loop (No SSCI Damping Controls)

Using a MATLAB Platform

Fig.5.5.1.Simulated SSCI Event When there is no SSCI damping controller: Wind Plant Point of

interconnection Real Power, Reactive power, and RMS Voltage


59

Fig.5.6. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current Feedback

Control Loop Using a MATLAB Platform

`

Fig.5.6.1. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,

Reactive power, and RMS Voltage


60

5.7 CONCLUSIONS:

In this chapter, I used Type 3(DFIG) Wind turbine to analyse these SSCI Concerns.

First of all these SSCI Concerns were introduced into the system by the conditions that were

mentioned in the base paper. Afterwards, the design of the SSCI damping controller was done

and introduced it into the system as per the parameters that are mentioned in the 5.3. According

to the author of the base paper, he has implemented some of the changes to the SSCI damping

controller shown in the Figures 5.1 and 5.2. The same has implemented in to the system as per

my model explained in the section 5.6.

I designed my own Type 3 wind turbine system (Plant), and implemented the same

procedure in the Matlab/Simulink. The results were compared as shown in the Figures 5.1.1

and 5.5.1 and found that both the results are same.

So after implementing the changes in the controller, The SSCI concerns were damped out

earlier as compared with the previous controller

Chapter 6 Fuzzy Logic Controller

61

CHAPTER-6

FUZZY LOGIC CONTROLLER

6.1 INTRODUCTION TO THE FUZZY LOGIC 62A. Fuzzy model, Fuzzy controller, and Fuzzy observer 62B. Fuzzy control system 62C. TS Fuzzy Model with Parameter Uncertainties 63

6.2 INTRODUCTION TO MY PROJECT EXTENSION 656.3 CONCLUSIONS 69


62

CHAPTER- 6FUZZY LOGIC CONTROLLER

6.1 INTRODUCTION TO THE FUZZY LOGIC

A.TS Fuzzy Model, Fuzzy Controller, And Fuzzy Observer

In this section, we give a brief background of fuzzy logic control, TS fuzzy logic control,

and fuzzy observers.

B. Fuzzy Control Systems

Traditional control theory is quite limited in modeling and controlling complex

dynamical systems. On the contrary, fuzzy control theory has demonstrated potential in these

kinds of non-traditional applications. Fuzzy logic technology allows the designers to build

controllers even when their understanding of the system is still incomplete. Fig. 6.1 shows the

fuzzy controller which includes a fuzzification block, a knowledge base (fuzzy sets, rule base), a

fuzzy inference engine, and a defuzzification block. The fuzzy process maps a crisp point of real

meaning such as measured data, into fuzzy sets, by the knowledge of the input membership

functions. The fuzzy inference engine then uses the rules in the rule base to produce fuzzy sets at

output, corresponding to input fuzzy sets. The fuzzification interface modifies the inputs so that

they can be interpreted and compared to the rules in the rule-base. The defuzzification interface

converts the conclusions reached by the inference mechanism into the inputs to the plant. The

knowledge base of the fuzzy system stores the expert knowledge on how to control the wind

turbine. All the inputs and the outputs are normalized with tuning (Burns., 2001).

Fig 6.1. Fuzzy contorl system


63

C. TS Fuzzy Model with Parameter Uncertainties

A nonlinear control system can be represented as a TS fuzzy plant model-based system. It

consists of a TS fuzzy plant model (Takagi. 1985) and a fuzzy controller (Tanaka. 1992)

connected in a closed-loop. The TS fuzzy plant model describes the dynamic properties of a non-

linear plant through fuzzy rules that have linear systems as consequent parts. The inferred system

is expressed as a weighted sum of a number of linear subsystems. A fuzzy controller can thus be

designed such that the inferred output of the fuzzy controller is a weighted sum of a number of

linear sub-controllers. Consider an uncertain non-linear system that can be described by the

following TS fuzzy model. With parametric uncertainties, sensor faults, and disturbance. The

figure 6.2 below shows the TS of Fuzzy model with two inputs and a one output.

Fig 6.1.1 Equivalent Fuzzy model architecture with two inputs and one output


64

Fig.6.1.2 shows the normalized triangular membership functions used in Fuzzification. Fig.

6.1.2(a) for e and ce and Fig. 6.1.2(b) for δImax

Fig (a) error and change in error

Fig (b) Change in reference current

Fig 6.1.2 Normalized triangular membership functions used in Fuzzification.


65

6.2 INTRODUCTION TO MY PROJECT EXTENSTION

Due to the strong requirement from the wind energy field, fault detection of the wind

turbine components has received significant attention in recent years. Fault detection becomes

even more complex when multivariable nonlinear wind energy conversion systems (WECS) are

subject to parameter uncertainties. Uncertainties often degrade system performance and may

even lead to instability and so, in order to overcome these kinds of difficulties, different

techniques have been developed in the last two decades.

The problem of Sub-synchronous control interactions and damping has also been greatly

studied and still remains an active research area. As such, the combination of PI and Fuzzy based

scheme is presented to detect and accommodate faults in wind turbines. This paper extends

previous work of damping these Sub-synchronous controlled interactions with a Fuzzy logic

controller. In the previous work, only PI controller is used to damp-out SSCI concerns. Where as

in extension, a combination of both PI controller and Fuzzy controller for the better results.

This fuzzy logic controller can be designed in two methods rule based and model based,

mamdani is a rule based system and sugeno is a model based system. For my thesis, I used

mamdani based fuzzy logic controller which is a rule based system. In description to the

mamdani model it consists a FIS editor, Membership function editor, rule editor, Rules viewer

and Surface viewer.

FIS editor:

In FIS editor we have to mention how many inputs we are taking for the required output,

and we have to give the specific names to the inputs and outputs as per the system.


66

Fig 6.2.1 Fuzzy interface system editor

Fig 6.2.2 FIS with input membership

function editor

Fig 6.2.3 FIS with output membership

function editor

Fig 6.2.4 FIS with rule editor

Fig 6.2.5 Rule viewer individual

Fig 6.2.6 Surface viewer of all the rules

combined


67

Membership Function editor:

In membership Function editor we have formed a membership functions for each input

and output that we mentioned in the FIS editor. For each input and output we have to give the

Range and display range in the membership editor so that output is displayed as required.

The above shown Figures 6.2(1-6) are from the MatLab/Simulink platform. How we edit

the membership functions and form the rules in the rule editor are shown in the figures.

error ( e )

chan

ge in

the

erro

r c (e

)

NB NM NS ZE PS PM PB

NB NB NB NB NB NM NS ZE

NM NB NB NB NM NS ZE PS

NP NB NB NM NS ZE PS PM

EZ NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PB

PM NS ZE PS PM PB PB PB

PB ZE PS PM PB PB PB PB

Table 6.2.7 Rules table for by fuzzylogic controller

The above shown table is Rule tabe for the fuzzy logic controller for my thesis output.

Basing on the rules, fuzzy logic controller takes the decession what to do and what not to. These

rules are formed as per the required output for my thesis.

Fuzzy logic controller based on the above rules was introduced into the system shown in the

Figure 6.2.8, and respective results are shown in the Figure 6.2.9


68

Fig.6.2.8. Revised Controls including SSCI Damping Controller and changes in Rotor Side Current Feedback

Control Loop Using a MATLAB Platform when Fuzzy logic controller is introduced.

Fig.6.2.9. Simulated SSCI Event After Controller Changes: Wind Plant Point of interconnection Real Power,

Reactive power, and RMS Voltage when fuzzy logic controller is introduced


69

6.3 CONCLUSIONS:

In this chapter, I used a combination of PI controller and fuzzy logic controller

(Intelligent controller) into the system to damp out the SSCI Concerns. I designed the fuzzy

controller using Matlab/Simulink. Using a Fuzzy editor I formed the Inputs and outputs and

procedure was explained in the section 6.2. Afterwards the combination of PI controller and

Fuzzy logic controller was introduced in to the system as shown in the Fig 6.2.7 and results were

simulated.

The simulated results were shown in the figure 6.2.8 and were compared with the

previous chapter results (Chapter 5). By the comparison, it is found that usage of Fuzzy logic

controller SSCI concerns were damped out much faster than using a PI controller alone [10].

Chapter-7 Conclusions

70

CHAPTER-7

Conclusions

7.1. INTRODUCTION 717.2. RESULTS 727.3. CONCLUSIONS 72

REFERENCES 73

APPENDIX 74

PUBLICATIONS 75

PUBLICATION PAPER


71

CHAPTER- 7Conclusions

7.1 INTRODUCTIONIn this chapter, results obtained in all other chapters are explained and

Recommendations are given.

7.2 RESULTS

SSCI (Sub-Synchronous Control Interactions) is a new phenomenon, where wind

turbines/controls have been observed to interact with nearby series capacitors, resulting in un-

damped/fast growing oscillations. This is a widespread and serious problem, affecting turbines

from most major manufacturers. Worldwide, there are a large number of transmission

expansion projects relying on series capacitors, yet the majority of wind turbines are unstable

under these conditions. Furthermore, standard transient stability studies (performed as per the

interconnection standards) do not show this problem (as they use fundamental frequency

phasor solutions). Recent real system projects have experienced damage to turbines and

transmission equipment due to SSCI.

This paper demonstrates that the negative damping observed in the SSCI phenomena is

largely due to the wind turbine rotor side current controller in the type 3 topology. Controller

changes and damping controllers are proposed which help to mitigate the instability.

Fuzzy logic controller is introduced along with the PI controller into the system to damp

out the SSCI concerns. Fuzzy logic controller is an intelligent controller, by basing on the

rules give in the system it will act accordingly without the human interface. Analysis were

drawn using the MatLab/Simulink and comparison were done with the previous one. Both the

results were compared. By using the Fuzzy logic controller we achieved 30% improvement in

the system output, i.e., these SSCI are damped out in a very little time compared to the

previous one. So using a Fuzzy logic controller it is help full for the system to damp these

SSCI concerns in the future.

In all cases of potential SSCI, it is highly recommended that detailed EMT models of

the turbine be obtained directly from the manufacturer. Modern tools such as PSCAD/ EMTDC

are capable of directly imbedding code from the actual hardware into simulation models, such

that excellent predictions of SSCI phenomena may be produced. Increased awareness of SSCI


72

is critical, along with backup protection schemes capable of preventing equipment damage in

the event of SSCI.

7.3 CONCLUSIONS

The results from the chapter 5 and chapter 6 were compared and found that using the

fuzzy logic controller we can achieve fast damping of SSCI Concerns. This thesis results were

compared with base paper [10] results found that the damping of the SSCI 30% faster.


73

REFERENCES

[1] IEEE Committee Rep., "Reader’s guide to sub-synchronous resonance,” IEEE Trans.Power Syst., Vol. 7, No. 1, pp. 150-157, Feb. 1992.

[2] IEEE Working Committee Rep., "Third supplement to a bibliography for the study ofsub-synchronous resonance between rotating machines and power systems," IEEETrans. Power Syst., Vol. 6, No. 2, pp. 830–834, May 1991.

[3] P. Kundur, “Power System Stability and Control," McGraw-Hill Companies, 1994.

[4] R. K. Varma, S. Auddy, and Y. Semsedini, "Mitigation of sub- synchronousresonance in a series-compensated wind farm using FACTS controllers," IEEE Trans.Power Del., Vol. 23, No. 3, pp. 1645–1654, Jul. 2008

[5] R. M. Mathur, R. K. Varma, “Thyristor-based FACTS Controllers for ElectricalTransmission Systems”, IEEE Wiley-Interscience, 2002

[6] G. D. Irwin, "Sub-Synchronous Interactions with Wind Turbines," Technical Conference- CREZ System Design and Operation, January 26, 2010, Taylor, Texas, USA.http://www.ercot.com/calendar/2010/01/20100126-TECH

[7] W. Wong, J. Daniel, "ABB presentation on CREZ Reactive Study- ERCOT RPGMeeting,"March12,2010,Austin,Texas,USAhttp://www.ercot.com/calendar/2010/03/20100312-RPG

[8] G. Reed, "CREZ Project Overview," January 26, 2010, Taylor, Texashttp://www.ercot.com/calendar/2010/01/20100126-TECH.

[9] E. Larsen, "Wind Power on series-compensated lines," 2010 Wind- Power Conf andExhibition, Dallas, TX, USA, May 23-26, 2010

[10] A. K. Jindal, G. D. Irwin and D. A. Woodford, "Sub-Synchronous Interactions withWind Farms connected near series compensated AC lines", 9th Int. Workshop on Large scaleintegration of wind, Quebec City, Canada, pp. 559-564, Oct 18-19, 2010.

74

APPENDIX

A) Specifications of DFIGTABLE I

SYSTEM PARAMETERS

System quantities Values

Nominal Frequency 60 HzTotal wind generator power 450 MW (3MW x 150 units)

Rated turbine voltage (L-L,rms) 0.69 kVCollector voltage (L-L,rms) 33 kV

Station Transformer 600 MVA, 345/33/13.8 kV,12% Impedance

Unit Transformer 3.4 MVA scalable, 33/0.69 kV345 kV Line Impedance (pu

values on 100 MVA base)Approx. 100 Ω (R = 0.0075 pu, X =

0.084 pu, B = 1.25 pu)

Series Capacitor Impedance 0 - 100 ΩReceiving end system 345 kV, 1800 MVA /85° (at 1st

and 3rd harmonic)

B) Fuzzy Logic controller rule box

error ( e )

chan

ge in

the

erro

r c (e

)

NB NM NS ZE PS PM PB

NB NB NB NB NB NM NS ZE

NM NB NB NB NM NS ZE PS

NP NB NB NM NS ZE PS PM

EZ NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PB

PM NS ZE PS PM PB PB PB

PB ZE PS PM PB PB PB PB

75

PUBLICATIONS

Y. Dharma Teja, Dr. P. Linga Reddy, “Sub-Synchronous Control Interactions between

Type 3 Wind Turbines with Fuzzy Logic Controller and Series Compensated AC

Transmission Systems” IJEE international Journal Of Electrical, Electronics and

Telecommunication Engineering, issued on june 2013.

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

Education

wind turbine systems

wind turbines

type d wind turbine

type b wind turbine

type c wind turbine

wind turbine generators

wind turbine model

wind turbine topologies