thesis torque ripple reduction based direct torque control for induction motor drives a thesisdtc

8/17/2019 Thesis Torque Ripple Reduction Based Direct Torque Control for Induction Motor Drives A ThesisDTC

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Torque Ripple Reduction Based

Direct Torque Control for Induction

Motor Drives

A Thesis

Submitted to the College of Engineering University of Baghdad in

Partial Fulfillment of the Requirements for the Degree of Master ofScience in Electrical Engineering

By

Hayder S. Hameed

Supervised by Prof. Dr. J.H. Alwash Dr. Hanan M. Habbi

March 2014

REPUBLIC OF IRAQ

MINISTRY OF HIGHER EDUCATION AND SCIENTIFIC RESEARCH

UNIVERSITY OF BAGHDAD

COLLEGE OF ENGINEERING


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i

cknowledgement

First of all, I give my thanks forever to Allah Who Have Enabled me to

complete this work

I would like to express my sincere gratitude to my supervisors

Prof Dr J H Alwash and Dr Hanan M Habbi for their great help,

kind advice, guidance and encouragement during their supervision for this work.

I would like to thank my family who has given me support throughout my

academic years. Without them, I might not be the person I am today.

A special thanks to my wife for her kindness and support and without here

heartening I couldn’t finish this work.

Also, I would like to thank the staff of the department of Electrical

Engineering of University of Baghdad for their assistance and support.

Finally ,I would like to acknowledge all kind people who help me to complete

this work .

ayder Salim


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ii

ABSTRACT

Direct Torque Control (DTC) is a control technique used in AC drive systems

to obtain high performance torque control. The conventional DTC drive contains a

pair of hysteresis comparators, a flux and torque estimator and a voltage vectorselection table. The torque and flux are controlled simultaneously by applying

suitable voltage vectors, and by limiting these quantities within their hysteresis

bands, de-coupled control of torque and flux can be achieved. Conventional DTC

drives utilizing hysteresis comparators suffer from high torque ripple and variable

switching frequency.

Several techniques have been developed to improve the torque performance.

In this thesis, Proportional-Integral (PI) controller has been presented to improve

the system performance which gives better torque and flux response and also

reduces the undesirable torque ripple. The most common solution to high torque

ripple and variable switching frequency is to use the space vector pulse width

modulation (SV-PWM) that depends on the reference torque and flux. The

reference voltage vector is then realized by using a voltage vector modulator.

The conventional DTC and DTC with PI controller are implemented using

Xilinx System Generator (XSG) for MATLAB/Simulink environment through

Xilinx blocksets. The design was achieved in VHDL, based on a

MATLAB/Simulink simulation model.

The Hardware-in-the-Loop (HIL) method is used to verify the functionality

of the Xilinx FPGA estimator. The results are obtained and compared with

MATLAB/ Simulink results considering the implementation of the proposed model

on the Xilinx NEXYS2 Spartan 3E1200 FG320 Kit.

The simulations of the DTC-SVPWM were carried out using

MATLAB/ Simulink simulation package.

The design, implementation and simulation of the overall drive system is

performed using MATLAB/Simulink program version 7.13.0.564 (R2011ba) and

Xilinx ISE Design Suite 14.2.


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List of Contents

iii

List of Contents

UTitle Page

Acknowledgements ………………………………………………………........iAbstract ……… ……….………………...……………….….………………...ii

List of Contents ………… ………….…………….…………….…...….........iii

List of Abbreviations ………… …………………………….……….…….…..vi

List of Symbols ……… …………………………………..……………..…....vii

UChapter One: Introduction and Literature Survey

1.1

General Introduction …...………………….………………………....….…..1

1.2 Speed Control Techniques of Induction Motor …………………...…..…….2

1.3 Literature Survey …………………………………..………….……....…….7

1.4 Thesis Objective……………………………….……...…………………....12

1.5 Thesis Outline ………...……...………………….……...………………….12

UChapter Two: Direct Torque Control Technique and Xilinx System

Generator

2.1 Introduction …………………………………………………………..…....13

2.2 The Conventional DTC...… .……....………………………………………14

2.3 DTC Development …………………... …………………...…………….....16

2.3.1 Mathematical Model of Induction Motor.…….….…….………..…...16

2.3.2 Flux and Torque Estimator……...………………………………...….21

2.3.3 Torque and Flux Hysteresis Comparator ………………..……....…...23

2.3.4 Lookup Table……………………………………………………...….26

2.3.5 Three-Phase Voltage Source Inverter(VS……………………………27

2.4 Modified DTC Scheme …………………………………………………….29

2.5 Classic PI Controller………………….……..……………………………...30

2.6 Direct Torque Control With Space Vector Modulation (DTC – SVM)........31


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List of Contents

iv

2.7 Principle of Space Vector PWM …………………………………………..33

2.7.1 Step 1: Determining Vd , Vq , Vref , and Angle (α) ………..…………36

2.7.2 Step 2: Determining Time Duration T1, T2, T0 ………………….…38

2.7.3 Step 3 : Determining the Switching Time of Each

Transistor(S1toS6) ..……………………………………………………………39

2.8 Types of Different Schemes …………………………………………….…40

2.9 Field Programmable Gate Array ……………………………………….…44

2.10 Hardware in the Loop ……………………………………………………44

2.11 Usage of Xilinx System Generator in the Controller Design ……………44

2.12 System Modeling Using the Xilinx System Generator ………………..45

2.14 Integration in Xilinx Environment …………………………………….46

Chapter Three: Simulation Results of DTC and DTC-SVM

3.1 Introduction …………………………………………………….………….48

3.2 Implementation of DTC in MATLAB/Simulink …………………………48

3.2.1 Induction Motor ……………………………………………….…….49

3.3.2 Sector ,Flux and Torque estimator … ……….……....…….………..50

3.2.3 Flux and Torque Hysteresis Controller ………………………….…50

3.2.4 Lookup Table Using MATLAB/Simulink …...……....…………...…51

3.2.5 Voltage Source Inverter …………………………………………….51

3.3 Modified DTC Scheme Using MATLAB/Simulink ……………………...53

3.4 Modeling Space Vector PWM Using MATLAB/Simulink ....…………….54

3.5 Implementation DTC Using Xilinx Software ……………………………...56

3.5.1 Real Time System Modeling via Simulink…….……………..……...56

3.5.2 Xilinx Software Analysis ………….……………….…..…………....57

3.5.3 The MCode Block…………..........………………………………..…57

3.5.4 Implementation of Sector ,Flux and Torque Estimators Using

Xilinx/SIMULINK ………………………………………………………….....58

3.5.5 Flux and Torque hysteresis Controller ……………….....……..….….61


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List of Contents

v

3.5.6 Switching Table Using Xilinx Mcode Block …………………...……61

3.6 Modified DTC Scheme using Xilinx/SIMULINK ………………………...62

3.7 Hardware/Software Co-Simulation …….………………………………….63

3.8 Experiment Setup and Instrumentation…………………………………….66

3.9 Simulation Results for Conventional DTC…...….…………………………67

3.10 Simulation Results of DTC with Conventional PI Controller ……………71

3.11 Simulation Results of DTC-SVM ………………………………………..73

3.12 Simulation Results for CDTC Using Hardware/Software Co-Simulation

Xilinx Blocks …………………………………………………………………..75

3.13 Simulation Results of DTC-PI Controller Using Hardware/Software Co-

Simulation ………………………………………………………………….......77

3.14 Comparison among the Presented Controllers …………………………...79

Chapter Four: Conclusions and Suggestions for Future Works

4.1 Conclusions…………………………………………………………….......83

4.2 Suggestions for Future Work……..………………………………………..84

References ……………………………………………….………………….....85

Appendix A

Appendix B

Appendix C

Appendix D


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List of Abbreviations

vi

List of Abbreviations

DescriptionAbbreviation

Alternating CurrentAC

Configurable Logic BlockCLB

Direct CurrentDC

Digital Signal Processor DSP Direct Torque ControlDTC

Electric VehicleEV

Fuzzy LogicFL

Field Oriented ControlFOC

Field Programmable Gate Array FPGA

Hardware Description LanguageHDL

Hardware in the loopHIL

Induction MotorIM

Joint Test Action GroupJTAG

Look Up TableLUT

Magneto motive forcemmf

Metal-Oxide Semiconductor Field Effect TransistorsMOSFET

Proportional-IntegralPI

Proportional-Integral-DerivativePID

Pulse Width ModulationPWM

Sine Pulse Width ModulationSPWM

Space Vector Modulation SVM

Space Vector Pulse Width ModulationSVPWM

Total Harmonic Distortion THD

Very-high-speed Hardware Description LanguageVHDL


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List of Symbols

vii

List of Symbols

Symbol Description

d,q Rotating reference frame axes

d RsR,q Rs Stationary reference frame axes

f Frequency of AC Supply (Hz)

ia,ib,ic Stator Phase Currents (A)

iRqsR, iRdsR q and d–axis stator currents (A)

iRqr R, iRdr R q and d–axis rotor currents (A)

J Moment of Inertia (Kg.mP2P)

K R p Proportional Gain

K Ri Integral gain

LRm Mutual inductance

LRr Rotor Inductance (H)

LRs Stator Inductance (H)

m Modulation index

P Number of Poles

R Rr Rotor resistance( Ω)

Rs Stator Resistance (Ω)

s Stator variable

TR1R, TR2R, TRo Switching Time Intervals (sec)

TRe Electromechanical Torque (Nm)

TRL Load Torque (Nm)

TRs Sampling Time or Switching Time

1TVRaR,VR bR,VRc Stator Phase Voltages (V)


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List of Symbols

viii

Symbol Description

VRdc Supplied DC Voltage (V)

VRoR….VR7 Space Voltage Vectors

vRqsR, vRdsR q and d–axis stator voltages

vRqr R, vRdr q and d–axis rotor voltages

XRs Stator reactance ( Ω )

XRr Rotor reactance ( Ω )

XRm Magnetizing reactance ( Ω )

ΨRm Mutual flux (Wb)

ΨRdr d-axis Rotor Flux Linkage (Wb)

ΨRqr q-axis Rotor Flux Linkage (Wb)

ΨRds d-axis Stator Flux Linkage (Wb)

ΨRqs q-axis Stator Flux Linkage (Wb)

ΨRs Stator flux (wb)

ωe Stator angular electrical frequency (rad/sec)

ωRr Rotor angular electrical speed (rad/sec)

ωRs Synchronous Speed (rad/sec)

θ The angle of rotation

θR0 The initial angle offset

θRr Rotor angle(deg)

θRs Stator angle (deg)

θRsr Angle between the stator and rotor fluxes


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Chapter One Introduction and Literature Survey

1

Chapter One

Introduction and Literature Survey

U

1.1 General Introduction

Induction Motor (IM) drive is widely used in many residential, commercial

and high performance industry applications due to its compactness, offering many

benefits to industrial users, highest power density, high torque to inertia ratio and

dynamic control, and high efficiency over a wide speed range. There are two main

types of induction motors which are the wounded rotor and squirrel-cage design

and both of them are in widespread use. In the past, squirrel cage induction

machines were limited to constant speed applications, and were operated from a

fixed sinusoidal supply. The development of high power switching devices has

accelerated the growth in the market for variable speed drive systems incorporating

AC induction machines and variable speed drives . [1,2]

The simple control method is volt/hertz control, or scalar control. Vector or

field-oriented control (FOC) and direct torque control (DTC) are basically twomethods of electromagnetic torque controlled a.c. drives. The direct torque control

has been adopted in this thesis.

The concept of the vector control method or so called Field Orientation

method of AC motors was proposed by Hasse in 1969 and Blaschke in 1972, based

on making the well-established separately excited dc machine. Vector control

schemes have allowed the induction machine to achieve torque control performance similar to that of a separately excited DC machine and have led to the

replacement of the DC machine by the induction machine in many high

performance applications .The torque is defined as the cross vector product of the

magnetic field from the stator poles and the armature current. [1,3]


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Direct Torque Control concepts were proposed by Takashi and Noguchi in

1986 [4]. The idea of this method is based on comparing the measured stator flux

and torque with the theoretically desired bands. The vector differences will control

the subsequent switching sequence of the SVPWM inverter voltage based on the

switching logic table. That, however, restricts the means of the stator flux and

torque to fall in the pre-established bands.[2]

U1.2 Speed Control Techniques of Induction Motor

There are different ways to control the speed of a rotational or linear

alternating current (AC) electric motor . The classification of the electrical drives is

depending on the application ; some of them are fixed speed and some are variable

speed. Before the invention of power electronics devices, the variable speed drives

had various limitations such as poor efficiencies, larger space, lower speed ,

etc. But now, variable speed drive are constructed in smaller size, high

efficiency and high reliability [5]. The effective way of producing variable

induction motor speed drive is to supply the induction motor with three phase

voltages of variable frequency and variable amplitude. A variable frequency is

required because the rotor speed depends on the speed of the rotating magnetic

field provided by the stator. A variable voltage is required because the motor

impedance is reduced at the low frequencies and consequently , the current has to

be limited by means of reducing the supply voltages. A variable-frequency drive

(VFD) is a specific type of adjustable-speed drive .

The control of the speed is achieved by controlling the frequency of the

electrical power supplied to the motor drives. There are three major types of

variable frequency control techniques of IM: scalar control, vector control and

field acceleration method [6,7] as shown in Figure 1.1 .


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Scalar control: is known as V/f control which acts by imposing a constant

relation between voltage and frequency and it is the most widespread in the

majority of the industrial applications because it has simple structure and it is

normally used without speed feedback. The stator flux and the torque are not

directly controlled ,so this control does not achieve a good accuracy in both speed

and torque responses [8].

Vector Control: In this type of control, the control loops are used for

controlling both the torque and the flux. The controllers of this type use vector

transform such as either Park or Ku. The requirement of huge computational and

the compulsory good identification of the motor parameters are the main

disadvantages for this type of control [9] .

Field Oriented Control (FOC) was introduced for the first time by Blaschke in

the early 1970s. The main objective of this control method is, as in separately

excited DC machines, to independently control the torque and flux; this is done by

choosing a d-q rotating reference frame synchronously with the rotor flux space

vector [9,10].

Figure.1.1 : Overview of induction motor control methods.[11]


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FOC is based on maintaining the amplitude and the phase of the stator current

constants, avoiding electromagnetic transients. FOC involves controlling the stator

currents represented by vectors. FOC method is based on projections which

transform a three phase time and speed dependent system into a two co-ordinate

(d and q co-ordinates) time invariant system [12].

DTC main features are as follows:

• Direct control of flux and torque by selecting the appropriate inverter state.

• Indirect control of stator currents and voltages.

• Approximately sinusoidal stator fluxes and stator currents.

• High dynamic performance even at stand still.

The main advantages of DTC are:

• Absence of co-ordinate transforms.

• Absence of voltage modulator block, as well as other controllers such as PID for

motor flux and torque.

• Minimal torque response time, even better than the vector controllers.

However, some disadvantages are also present such as:

• Possible problems during starting.

• Requirement of torque and flux estimators, implying the consequent parameters

identification.

• Inherent torque and stator flux ripple.

One of the major applications of DTC is in the Electric Vehicle (EV); electric

vehicles are an important step towards solving the environmental problems

produced by cars with internal combustion engines. Another advantage of the EV

is its devoid of pollution and high energy efficiency. Indeed, an electric motor


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provides very fast response and can be controlled in a much better way. Therefore,

EV has definite advantages over the Internal Combustion Engine (ICE) driven

vehicles. The input of the IM controller is the reference speed, which is applied by

the vehicle pedal [13].

DTC control technique in its basic construction suffers from two major

problems: 1) variable switching frequency and 2) high torque ripple

The conventional DTC algorithm using the hysteresis-based voltage switching

method has relative merits of simple structure and easy implementation. Some

drawbacks such as large torque ripple in the low speed region and switching

frequency variation according to the change of the motor parameters and the motor

speed are exhibited. If the hysteresis bands of the torque and flux comparators

become relatively wide for high power applications with the low inverter switching

frequency, the resulting torque ripples are enlarged to an undesired level [14] .

In conventional DTC, the voltage vector selection is based on the torque and flux

errors, but small and large errors are not distinguished by the hysteresis controllers.

The voltage vectors are applied for the entire sample period; even for small errors,

resulting large torque overshoots in steady-state regime [15] .

In steady state with constant load, the active switching state causes the torque

to continue to increase past its reference value until the end of the switching

period. Then a zero voltage vector is applied for the next switching period causing

the torque to continue to decrease below its reference value until the end of the

switching period. That results in high torque ripple as shown in Figure 1.2 [16] .


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Figure 1.2 Conventional DTC

By removing the hysteresis comparators and performing the switching at

regular intervals is a widely adopted method to reduce the torque ripple and

at the same time maintaining a constant switching frequency. Instead ofapplying a single voltage vector for the whole sampling period, two or more

voltage vectors are applied.

Figure 1.3(a) shows the torque waveforms for hysteresis based controller

with the width of the hysteresis marked as ∆T. Due to the delay in the

microprocessor implementation or sensors, the torque overshoot and

undershoot beyond and below the hysteresis bands will occur. The positiveslope is high at low speed, which will increase the possibility of the torque

touching the upper band. In Figure 1.3(b), fixed switching is employed but

with the whole sampling period applied with a single voltage vector. This

technique will result in a high torque ripple with all additional torque

oscillation [17,18] .

Figure 1.3: Various switching strategies in DTC .(a)Hystresis-based controller

,(b)Fixed switching torque.


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U1.3 Literature Survey

During the last decade, many different techniques of control applied to IM

drives. The DTC technique has been recognized as an efficient alternative and

viable solution to get high performance in these drives. A lot of modifications have

been developed to conventional Direct Torque Control scheme. Therefore, a

literature survey for many previously published studies is presented as follows:

Toh, et al., 2003 [18] presented two simple controllers for the torque and flux

loops, which replaced the conventional hysteresis comparators. The controllers

work was based on waveform comparisons and hence retained the simple

control structure of the DTC. Simulations of the proposed controllers were

performed using MATLAB/SIMULINK simulation package. The results show

that the controllers managed to reduce the torque ripple significantly.

Rodriquez, et al , 2004 [19] presented a new method for Direct Torque Control

(DTC) based on load angle control . The use of simple equations to obtain the

control algorithm makes it easy to understand and implement. Fixed switching

frequency and low torque ripple are obtained using space vector modulation.

Buja, and Kazmierkowski , 2004 [11] presented a review of recently used direct

torque and flux control (DTC) techniques for voltage inverter fed induction and

permanent magnet synchronous motors. A variety of techniques and difference in

concept are described as follows: switching-table based hysteresis DTC, direct

self-control, constant switching frequency DTC with space-vector modulation

(DTC-SVM). Also, trends in the DTC-SVM techniques based on neuro-fuzzy logic

controllers are presented.

Garcia, and Arias, 2005 [20] presented a novel controller based on Direct Torque

Control (DTC) strategy. This controller is designed to be applied in the control of


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Induction Motors (IM) fed with a three-level Voltage Source Inverter (VSI). This

type of inverter has several advantages over the standard two-level VSI, such as a

greater number of levels in the output voltage waveforms, lower dV/dt, less

harmonic distortion in voltage and current waveforms and lower switching

frequencies. In the new controller, torque and stator flux errors are used together

with the stator flux angular frequency to generate a reference voltage vector.

Ismail, 2005 [7] studied, evaluated and compared the various techniques of the

DTC-SVM applied to the induction machines through simulations. The simulations

were carried out using MATLAB/SIMULINK simulation package. Evaluation was

made based on the drive performance, which includes dynamic torque and flux

responses, feasibility and the complexity of the system.

Paturca, et al, 2006 [15] presented a simple solution, which consists in the

modulation of the nonzero voltage vector duration over a sampling period,

according to the instant values of the torque and stator flux errors. The introduced

duty ratio is calculated using a relation containing terms proportional to these

errors. The presented results show the torque, flux and current ripple reduction

obtained by using the proposed method. Its main advantage is that it requires an

insignificant additional computation, preserving the simplicity of the conventional

DTC.

Kostic, et al, 2009 [21] presented different direct torque and flux control of

induction motor schemes (DTC). Classical DTC method, its modifications for

torque and flux ripple reduction, as well as modified DTC method with PI

controllers (PI-DTC) based on space vector modulation (SVPWM) are considered.

For each method, theoretical principles and experimental results, at laboratory

condition using dSPACE development tool realized, are presented.


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Tsoutsas, 2009 [22] An electromagnetic torque calculator of an induction motor is

designed in the MATLAB/ Simulink environment through XILINX block sets. The

accuracy of the torque estimator is verified using the Field Programmable Gate

Array (FPGA).

Kamble, and Bankar, 2010 [23] presented a Fuzzy Logic Direct Torque Control

(FLOTC) to improve the system performance which gives better torque and flux

response and also reduces the undesirable torque ripple in the conventional DTC.

Aarniovuori, 2010 [24] presented a coupled system simulator, based on analytical

circuit equations and a finite element method (FEM) model of the motor and it is

used to analyze a frequency-converter-fed industrial squirrel-cage induction motor.

Two control systems that emulate the behavior of commercial direct-torque-

controlled (DTC) and vector-controlled industrial frequency converters were

studied, implemented in the simulation software and verified by extensive

laboratory tests.

Zhang ,

and Zhu,2011 [25] presented a comparison between the performances of

three duty determination methods in detail and then proposed a very simple but

effective method to obtain the duty ratio. By appropriately arranging the sequence

of the vectors, the commutation frequency is reduced effectively without

performance degradation. To further improve the performance of system, a low-

pass filter-based voltage model with compensations of amplitude and phase is

employed to acquire accurate stator flux estimation.

Sutikno, et al, 2011 [26] presented an improved FPGA-based torque and stator

flux estimators for direct torque control (DTC) induction motor drives, which

permit very fast calculations. To avoid saturation due to DC offset present in the

sensed currents, the LP Filter is applied. The simulation results of DTC model in


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MATLAB/ SIMULINK, which performed double-precision calculations, are used

as references to digital computations executed in FPGA implementation. The

Hardware-in-the-loop (HIL) method is used to verify the minimal error between

MATLAB/SIMULINK simulation and the experimental results, and thus the well

functionality of the implemented estimators.

Alwadie, 2012 [27] presented a practical implementation for direct torque

control of induction motor drive. Control system experiment is proposed

using Digital Signal Processor. This control scheme directly determines the

switching states of the inverter and gives optimal characteristics for stator

flux and torque control.

Shah, et al,2012 [28] presented the application of FPGA in Direct Torque

control induction motor drive. Modern AC drives require a fast digital

realization of many mathematical operations concerning control and

estimator’s algorithms, which are time consuming. Therefore developing of

custom built digital interfaces as well as digital data processing blocks and

sometimes even integration of ADC converters into single integrated circuit is

necessary.

Kumar , and Babu, 2012 [29] presented control method of DTC implementation

and improvement using Space Vector Pulse Width Modulation (SVPWM) to give

constant switching frequency and reduces torque ripple. A d-q coordinate reference

frame locked to the flux space vector is used to achieve decoupling between the

motor flux and torque.

Krishna,et al, 2012 [30] presented the modeling and simulation of induction

motor drive employing SVM-DTC, carried it out using MATLAB/SIMULINK

simulation package and the results were compared with Conventional DTC.


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Sekhar , and Chandra, 2013 [31] presented a fuzzy logic duty ratio control

(FLDRC) and Space Vector Modulation (SVM) techniques to reduce torque ripple

in conventional DTC using a versatile simulation package, MATLAB/SIMULINK.

Sutikno, et al, 2013 [32] presented a novel direct torque control (DTC) approach

for induction machines, based on an improved torque and stator flux estimator and

its implementation using field-programmable gate arrays (FPGA). The DTC

performance is significantly improved by the use of FPGA, which can execute the

DTC algorithm at higher sampling frequency. The design was achieved in VHDL,

based on a MATLAB/Simulink simulation model. The Hardware-in-the-Loop

method is used to verify the functionality of the FPGA estimator. The design,

which was coded in synthesizable VHDL code for implementation on Altera

APEX20K200EFC484-2x device.

The presented work differs from the foregoing survey by the following:

1) The IM model, CDTC, and DTC- PI controller are designed with

MATLAB/ Simulink environment using m-file blocks which will make the

system design simple when implemented with Xilinx/Simulink because it

does not need to write the code in VHDL language.

2) The Hardware-in-the-Loop method is used to verify the whole system of

DTC algorithm without writing code for implementation on Xilinx

NEXYS2 Spartan 3E1200 FG320 Kit .

3) Different mechanical tests have been verified for the whole system with

MATLAB/ Simulink model and HIL model.


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U1.4 Thesis Objective

• Analyzing and proving (DTC) by means of MATLAB/SIMULINK and

Xilinx /SIMULINK .

• Reduce the torque and stator flux pulsations, and constant switching

frequency , with PI controllers (PI-DTC),and (DTC) based on Space Vector

Modulation (DTC-SVM)

• Implement a practical controller of the conventional direct torque control

(CDTC) method by using field programmable gate array (FPGA) with

Hardware/Software Co-Simulation in Xilinx/SIMULINK .

U1.5 Thesis Outline

The contents of the chapters are briefly introduced here:

Chapter Two concentrates on the fundamentals of the principle of DTC of

induction motors and Direct Torque Control with Space Vector Modulation

(DTC-SVM) control techniques.

Chapter Three covers the MATLAB /SIMULINK model and Xilinx System

Generator simulation technique and simulation results and discussion of

comparing of conventional DTC ,DTC with PI controller and DTC-SVM . The

simulation results are presented and compared to the theoretical values.

Chapter Four has the conclusions and suggestion for future works


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Chapter Two Direct Torque Control Technique and Xilinx System Generator

13

Chapter Two

Direct Torque Control Technique

and Xilinx System Generator

U2.1 Introduction

The concept of Direct Torque Control (DTC) was developed by Takahashi

and Dpenbrock [4,10].It has become a powerful control scheme for the control of

induction motor drives [27]. The scheme of DTC has good dynamic performance,

precise and quick control of stator flux and electromagnetic torque, robustness

against the motor parameter variations, and the simplicity of the algorithm [15].

The DTC aims to choose the best voltage vector in order to control both stator

flux and electromagnetic torque of machine simultaneously. Similar to hysteresis

band (HB)current control, there will be a ripple in current ,flux ,and torque . The

current ripple will give additional harmonic loss, and the torque ripple will try to

induce speed ripple in a low inertia system and possible problem during starting

.To improve the performance of DTC ,the torque ripple must be reduced [9].

This chapter discusses the mathematical model of the induction motor and the

principles, theories, mathematical equations, and procedures involved for the

software (MATLAB/Simulink package) implementation of the direct torque

control technique using different controllers (Conventional and modified DTC by

PI controller and SVPWM technique).

As field programmable gate array (FPGA) is used to run the algorithm, a

software Xilinx system generator, a toolbox of MATLAB/Simulink can be used.

It will simulate the hardware as well as generate the VHDL code needed for the

implementation in FPGA. It can automatically convert the model into VHDL


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code. In this chapter, the Rapid Control Prototyping tool Xilinx System

Generator that runs from Simulink is here investigated. Implementation of the

Direct Torque Control algorithm for controlling a motor serves as main subject for

the investigation. A library with ready-to-use blocks is created for having the

possibility to implement other control algorithms in the future in a fast, graphical,

intuitive and user friendly way. It shows the advantage of using an FPGA with its

parallelism and re-programmable characteristics when implementing a motor

control algorithm. It provides a high bandwidth and therefore a possibility to

control several motors with one FPGA.

By programming the FPGA with a Rapid Control Prototyping tool like Xilinx

System Generator, the opportunity to an easy way change of different parts

becomes obvious. To use Model Based Design and Rapid Control Prototyping

concepts extensive code writing is avoided. The gap between the software engineer

and the hardware engineer is reduced and the possibility to work in both of the

domains is given[28, 33].

U2.2 The Conventional DTC

The structure of the conventional DTC was shown in Figure 2.1 which

consists of two hysteresis comparator, torque and flux estimators, voltage vector

selector and voltage source inverter (VSI) [29].In this method, the best voltage

vector should be chosen to maintain the stator flux and torque within a hysteresis

band around the proper flux and torque magnitudes by the selection of proper

inverter switching state. The hysteresis band is used to control the flux


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15

and torque of the motor directly. So the drive system affected by the range of

hysteresis band control [14].

Figure 2.1: Block diagram of conventional DTC

The configuration is much simpler than the vector control system due to the

absence of coordinate transforms between stationary frame and synchronous

frame and PI regulators. It also does not need a PWM and position encoder,

which introduces delay and requires mechanical transducers respectively [4,34].

DTC based drives are controlled in the manner of a closed loop system without

using the current regulation loop.

S(K)

Torque hysteresis

IM

Vdc

2HBΨ

Flux hysteresis

2HBT

V_abc

EΨ

ETe

Look up

TableVSI

Te*

Ψs*

-

Ψs^ Sector, Flux

and Torque

Estimators

Te^

+

+

-

ia,ib

Sa

Sb

Sc


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16

The main advantages offered by DTC are

• Decoupled control of torque and stator flux .

•

Excellent torque dynamics with minimal response time.• Inherent motion-sensorless control method since the motor speed

is not required to achieve the torque control.

•

Absence of coordinate transform .

• Absence of voltage modulator as well as other controllers.

• Robust for rotor parameter variation. Only the stator resistance is

needed for torque and flux estimation.

The major drawback of the DTC drive is the steady state ripples in torque and

flux. In case of constant load, when the torque increases the reference value until

the end of the switching period because of the active switching state, then applying

the vector of zero voltage for the next switching period which lead to making the

torque to continue to decrease under its reference value until the end of the

switching period will result in high ripple in flux and torque [35].

U2.3 DTC Development

U2.3.1 Mathematical Model of Induction Motor

The mathematical model of an electric machine represents all the equations

that describe the relationships between electromagnetic torque and the main

electrical and mechanical quantities. The mathematical models with concentrated

parameters are the most popular and are consequently employed both in scientific

literature and practice. The equations stand on resistances and inductances, which

can be used further for defining magnetic fluxes, electromagnetic torque, etc.

These models offer results, which are globally acceptable but cannot detect


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17

important information concerning local effects. The family of mathematical

models with concentrated parameters comprises different approaches but two of

them are more popular: the phase coordinate model and the orthogonal (dq) model.

The first category works with the real machine. The equations include, among

other parameters, the mutual stator-rotor inductances with variable values

according to the rotor position. As a consequence, the model becomes non-linear

and complicates the study of dynamic processes. The orthogonal (dq) model began

with Park’s theory nine decades ago. These models use parameters that are often

independent to rotor position [36].

The dynamic equivalent circuit of the induction machine is used to understand

and analyze the transient behavior of the induction machine [3].The following

equivalent circuit is used to simulate a three-phase, P-pole, symmetrical induction

motor in the dqo reference frame which is known in the generalized machine

analysis as arbitrary reference frame.

Figure 2.2: The dynamic or d-q equivalent circuit of an induction machine


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18

The complexity of the voltage and torque equations can be reduced by

eliminating all time varying inductance [37].

This equivalent circuit model is used to make all the machine variables

controllable and every single equation will be represented in one block [38]. The

following equations can be written for stator:

vqs = Rsiqs + ddt +ωeΨds (2.1)vds = Rsids + ddt ωeΨqs (2.2)The rotor equations:

vqr = Rriqr + dΨdt + ( )Ψdr R R(2.3)vdr = Rridr + dΨdt (ωe ωr )Ψqr (2.4)The flux linkage expressions in terms of the currents can be written from figure 2.4

as follows:

Ψqs= L

si

qs+ L

mi

qs+ i

qr (2.5)

Ψqr = Lriqr + Lm(iqs + iqr) (2.6)Ψqm = Lm(iqs + iqr) (2.7)Ψds = Lsids + Lm(ids + idr) (2.8)Ψdr = Lridr + Lm(ids + idr) (2.9)

Ψdm = Lm(ids + idr) (2.10)

Using the two-axis notation and the matrix form, the voltage equations can be

represented by[9]:

vqsvdsvqrvdr = Rs + pLs ωeLs pLm ωeLmωeLs Rs + pLs ωeLm pLm

pLm (ωe ωr )Lm Rr + pLr (ωe ωr )Lr(ωe ωr )Lm pLm (ωe ωr )Lr Rr + pLr iqsidsiqridr

(2.11)


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19

The arbitrary reference frame rotates with electrical angle velocity of rotor (ωr );therefore, the electrical equation of the squirrel-cage induction motor becomes:

vqsvdsvqrvdr = Rs + pLs ωrLs pLm ωrLmωrLs Rs + pLs ωrLm pLm

pLm 0 Rr + pLr 00 pLm 0 Rr + pLr

iqsidsiqridr

(2.12)

In order to have fast simulation, the above equation should be represented in state

space form with currents as state variables as in the following [39]:

p[] = [L ]−1([] +ωr [])[] + [L ]−1[] (2.13)Where,

[

] = [i

qs i

qr i

ds i

dr]

, [V] = [v

qs v

qr v

ds v

dr]

, [R] =

Rs 0 0 00 R

s0 0

0 0 Rr 00 0 0 Rr

[L] = Ls 0 Lm 00 Ls 0 LmLm 0 Lr 00 Lm 0 Lr

, [] = 0 Ls 0 LmLs 0 Lm 00 0 0 0

0 0 0 0

Now the current equation of an induction motor in the two-axis stator referenceframe can be written as [40]:


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20

idsiqsidri

qr

= ∫⎩Ls 0 Lm 00 Ls 0 LmLm 0 Lr 00 L

m0 L

r

−1

=0

⎝vdsvqsvdrvqr

Rs 0 0 00 Rs 0 00

P2ωrLm Rr P2ωrLr P2ωrLm 0 P2ωrLr Rridsiqsidriqr ⎠⎭

(2.14)The electromagnetic torque equation is

T

e= 1.5

P2L

m(i

qsi

dr i

dsi

qr) (2.15)

The speed R RωRr Rcannot be normally treated as a constant .It can be related to the

torques asR:

Te = TL + J ddt = TL + 2P J ddt (2.16)Where

d: direct axis

q: quadrature axis

s: stator variable

r: rotor variable

LRs R:stator inductance

LRm R:mutual inductance

LR

rR

:rotor inductance

Rr: rotor resistance

Rs: stator resistance

vRqsR, vRdsR: q and d–axis stator voltages


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21

vRqr R, vRdr R: q and d–axis rotor voltages

iRqsR, iRdsR: q and d–axis stator currents

iRqr,R iRdr R: q and d–axis rotor currents

P: number of poles

J: moment of inertia

TReR: electrical output torque

TRLR: load torque

ωReR: stator angular electrical speed

ωRr R: rotor angular electrical speed

U2.3.2 Flux and Torque Estimator

The basic principle of the conventional DTC is to control the torque and the

modulus of the stator flux linkage directly by controlling the inverter switches

using the outputs of the hysteresis comparators and selecting the correct voltage

vector from the optimal switching table. Flux and torque estimators are used to

determine the actual value of torque and flux linkages. The VSI voltage vector

transformed to the d-q stationary reference frame.

The voltage across the stator coil can be expressed as follows [41]:

v

qs= R

si

qs+ L

s didt (2.17)

vds = Rsids + Ls didt (2.18)The terms Ls didt , Ls didt represent the change in stator flux in d and q axis ,

respectively. Reforming the above equations yields the following formulas


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22

vqs = Rsiqs + ddt (2.19)v

ds= R

si

ds+ ddt

(2.20)

The estimate of the stator q and d axis flux linkages are an integral of the

stator EMF which can be written by solving (2.19) and (2.20) for (Ψqs ,Ψds) togive the following equationsΨqs = ∫(vqs Rsiqs) (2.21)Ψds = ∫(vds Rsids) (2.22)The stator flux vector can be obtained as follows

Ψs = Ψqs2 +Ψds2 (2.23)θs = tan−1() (2.24)

The developed electric torque is calculated from the estimated flux linkage

components and the measured stator currents in the two-axis stationary reference

frame.

Te = 1.5 P2 (iqsΨds idsΨqs) (2.25)According to (2.24), the stator flux angle is used to divide the electrical revolution

into six sectors denoted from Sec R1 Rto SecR6 Ras shown in Figure 2.3.

These sectors can be distributed as follows in Table 2.1:


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Table 2.1 : Sectors distribution

U2.3.3 Torque and Flux Hysteresis Comparator

In the DTC, there is no fixed switching frequency but the average switching

frequency is controlled with flux linkage and torque hysteresis bands. The

hysteresis bands are controlled by the reference switching frequency to achieve the

desired average value. In the DTC, there is no predetermined switching pattern

either, and the frequency component content of the voltages is not known

beforehand [24]. The IM stator voltage equation can be written by:

vs = Rsis + ddt (2.26)Where vRs ,RiRsR, and ΨRsR are the stator voltage, current and stator flux

space vectors, respectively. If the stator resistance is small and can be

neglected, the change in stator flux,

∆Ψs will follow the stator voltage; i.e.,

∆Ψs = vs∆t (2.27)

Sector Degrees

1 -30 < θRs

R< 30Po

2 30Po

P< θRs R< 90Po

3 90Po

P < θRs R< 150Po

4 150Po

P < θRsR< 210Po

5 210Po

P < θRsR< 270Po

6 270Po

P < θRsR< 330Po


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Therefore, variation of stator flux space vector can be achieved by the

application of stator voltage vRsR for a time interval of ∆t. The stator flux is

controllable if a proper selection of the voltage vector is made. In Figure 2.3, the

stator flux plane is divided into six sectors where each one has a set of voltage

vectors.

Figure 2.3 :Six sectors with different set of voltages

The reference stator flux and torque values are compared with the estimated values

in hysteresis flux and torque controllers. The digitized output signals of the flux

(HRψR) and torque (HRTeR) controllers are as follows:

Hψ = 1 For Eψ ≥ + HBψ (2.28)Hψ = 1 For Eψ ≤ HBψ (2.29)H = 1 For ETe

≥ + HBTe (2.30)

H = 0 For HBTe ≤ ETe ≤ + HBTe (2.31)H = 1 For ETe ≤ HBTe (2.32)Where ERψ Rand ERTe Rare the flux R Rand torque errors, HBRψR and HBRTe Rare the

acceptable predefined flux and torque errors and 2HB RψR and 2HBRTeR are the total

hysteresis band width of the flux and the torque control [31].


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25

The flux error which is due to the difference between the estimated and

desired stator flux is fed to the 2–level hysteresis comparator which in turn

produces the flux error status. The error signal is processed in a comparator. If the

actual flux is smaller than the reference value, the comparator output is at state 1 ,

or else it will be at state -1. The states for Flux are shown in Figure 2.4.

Figure 2.4: Flux hysteresis states.

The instantaneous electromagnetic torque is a sinusoidal function of the

angle between the stator and rotor fluxes as given in the following equation:

Te = 32 P2 LΨsΨrL′ L sin θsr (2.33) The relation between Ψs and Ψr vectors can be illustrated by Figure 2.5where the angle between them is denoted by θ Rsr.

Figure 2.5: Space vector of stator and rotor fluxes

state

-1

1


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26

R RTorque is controlled within its 3-level hysteresis band as shown in Figure 2.6

[41,18].

Figure 2.6: Torque hysteresis states .

U2.3.4 Lookup Table

The stator flux angle in addition to the torque and flux hysteresis status are

used to determine the suitable stator flux sector in order to apply the correct

voltage vector to the induction motor operating under DTC. The selection of the

appropriate voltage vector is based on the switching table given in Table 2.1. The

input quantities are the stator flux sector and the outputs of the two hysteresis

comparators. [41].

The feedback flux and torque are calculated from the machine terminal

voltages and currents. The signal computation block also calculates the sector

number S(k) in which the flux vector Ψs lies. There are six sectors each 3 anglewide. The Look up table block in figure 3.1 receives the input signals H RψR, H RTeR and

S(k) and generates the appropriate control voltage vector for the inverter by a look

up table, which is shown in Table 2.2.

state

0

1

-1


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27

Table (2.2) Lookup table of inverter voltage vectors

If the stator flux lies in sector k with the motor rotating in counter clockwise,

active voltage vector V RS,k+l Ris used to increase both the stator flux and torque.

Voltage vector VRS,k+2

Ris selected to increase the torque but decrease the stator flux.

The two zero voltage vectors (V RS,7 Rand VRS,8R) are used to reduce the torque and at

the same time, freezes the stator flux. Reverse voltage vector V RS,k-2 Ris used to

decrease the torque and flux in forward braking mode. Whereas V RS,k.1 Rwill reduce

the torque and increase the flux[23].

U2.3.5 Three-Phase Voltage Source Inverter(VSI)

The VSI synthesizes the voltage vectors commanded by the switching table.

In DTC, this is quite simple since no pulse width modulation is employed, the

output devices stay in the same state during the entire sample period.

HRψ HRTe S(1) S(2) S(3) S(4) S(5) S(6)

1

1 VR2 VR3 VR4 VR5 VR6 VR1


-1 VR6 VR1 VR2 VR3 VR4 VR5

-1



-1 VR5 VR6 VR1 VR2 VR3 VR4


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28

There are many topologies for the voltage source inverter used in DTC

control of induction motors that give high number of possible output voltage

vectors but the most common one is the six step inverter [8,42]. A six step voltage

inverter provides the variable frequency AC voltage input to the induction motor in

DTC method. The DC supply to the inverter is provided either by a DC source like

a battery, or a rectifier supplied from a three phase (or single phase) AC source.

The switching devices in the voltage source inverter bridge must be capable of

being turned off and on. The power metal-oxide semiconductor field effect

transistors (MOSFETs) are used because they have this ability and in addition they

offer high switching speed with enough power rating. Each MOSFET has an

inverse parallel-connected diode. This diode provides alternate path for the motor

current after the MOSFET is turned off [43,16].

Each leg of the inverter has two switches; one is connected to the high side

(+) of the DC link and the other is connected to the low side (-). Only one of the

two can be on at any instant. When the high side gate signal is on, the phase is

assigned the binary number 1, and assigned the binary number 0 when the low side

gate signal is on. Considering the combinations of status of phases a, b and c, the

inverter has eight switching modes (VRaR VR bR VRcR=000-111): two are zero voltage

vectors VR0R (000) and VR7R (111) where the motor terminals is short circuited and the

others are nonzero voltage vectors VR1 Rto VR6R . The waveforms of the branch voltage

for 180P0

P conduction mode will be as shown in Figure 2.7.


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29

Figure 2.7: Leg voltage waveform of a three-phase (VSI).

From figure 3.7 for one cycle (360Po

P) the leg voltages will have six distinct and

discrete values because every state has been changed after an interval of (60 Po

P) [44].

U2.4 Modified DTC Scheme

When we need to regulate the speed of such a drive a speed controller is

needed. The speed controller takes the error signal between the reference and the

actual speed and produces the appropriate reference torque value. In Figure 2.8 we

can see the block diagram of the proposed drive, in speed control mode. A

reference speed signal ω Rr R* or, in other words, the speed command is given. The

actual speed ωRr R is estimated or measured with a speed encoder. This depends on

the precision requirements of each application. In this theses the classical PI

controller is also used for the comparison between the classic DTC and DTC-

SVM.

For that, it becomes essential to know the rotor mechanical speed. A

speed controller may be employed and augmented with the classical DTC


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30

scheme. The block diagram of the modified DTC scheme is as shown in

Figure 2.8.

Figure 2.8 : The block diagram of the modified DTC scheme

U2.5 Classic PI Controller

A classic Proportional plus Integral (PI) controller is suitable enough to adjust

the reference torque value TReRP*

P. Nevertheless, its response depends on the gains K R pR

and K RiR, which are responsible for the sensitivity of speed error and for the speed

error in steady state. During computer analysis, we use a controller in a discrete

S(K)

Torque Hysteresis

IM

Vdc

2HB

Flux hysteresis

2H

V_abc

E

ETeLook

up

Table

VSI

Te*

Ψs*

-

Ψs^ Sector, Flux

and Torque

EstimatorsTe^

+

+

+

-

-

ia,ib

PI

Controller

Wr

Wr*

Sa

Sb

Sc


40/115


31

system in order to simulate a digital signal processor (DSP) drive system. Its block

diagram is shown in Figure 2.9, where T is the sampling time of the controller.

Figure 2.9: Block diagram of a discrete classic PI speed controller.

The response of the PI speed controller, in a wide range area of motor speed,

is very sensitive to gains K R pR and K RiR and it needs good tuning for optimal

performance. High values of the PI gains are needed for speeding-up the motor and

for rapid load disturbance rejection. This results to an undesired overshoot of

motor speed. A solution is to use a variable gain PI speed controller. However, in

the case of using a variable gain PI speed controller, it is also necessary to know

the behavior of the motor during start up and during load disturbance rejection in

several operation points in order to determine the appropriate time functions for PI

gains. This method is also time-consuming and depends on the control system

philosophy every time [45].

U2.6 Direct Torque Control With Space Vector Modulation (DTC –

SVM)


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32

Direct Torque Control drives utilizing hysteresis comparators suffer from

high torque ripple and variable switching frequency. The most common solution to

this problem is to use the space vector that depends on the reference torque and

flux. Space Vector Modulation is one of the PWM technique in which when the

drive is excited by three phase, balanced currents produces a voltage space

vector which traces a circle with uniform velocity by sampling that rotating

reference voltage space vector with high sampling frequency different

switching can be possible. The reference voltage vector is then realized using a

voltage vector modulator. There are various types of direct torque control-space

vector modulation (DTC-SVM) schemes that have been proposed. Each scheme

will perform the different control technique but its aims are still similar, which are

to attain the constant switching frequency and to reduce the torque ripple. The

differences between various DTC-SVM are on how the reference voltage is

generated the reference voltage is then implemented using SVM. Space Vector

Modulation is used to define the inverter switching state or voltage vector positions

different from six standard positions [7,37].

The SVPWM has been widely used in three phase inverter control system

because it has a higher utility efficiency of DC-side voltage than the sine pulse

width modulation (SPWM). Although the SVPWM has many advantages, it is

difficult to implement. The most difficult factor is calculating the duty cycles for

each power switch, as well as determining the vector sector and pulse sequence in

each switching cycle. The duty cycle calculation for the three phase 2- level

inverter was presented in many papers, and the vector sequence can be determined

in many ways (for example, the center-aligned method, which can be easily

implemented in MCU platform) [46].


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33

The implementation of the conventional SVPWM is especially difficult

because it requires complicated mathematical operations. In the SVPWM

technique, the duty cycles are computed rather than derived through comparison as

in SPWM. The SVPWM technique provides more efficient use of supply voltage

compared with sinusoidal modulation technique as shown in Figure 2.10 [47].

The fundamental voltage can be increased up to a square wave mode where a

modulation index of unity is reached. Moreover, the utilization of the DC bus

voltage can be further increased when extending into the over-modulation region

of SVPWM .Three-phase voltage source pulse-width modulation inverters have

been widely used for DC to AC power conversion since they can produce outputs

with variable voltage magnitude and variable frequency. For example, modern

power electronics controllers have been rapidly moving toward digital

implementation. Typical solutions employ microcontrollers or DSPs [48].

SV PWM

√ Vdc Vdc

Sine PWM

a

b

c

d

q

Vdc


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34

Figure 2.10: Locus comparison of maximum linear control voltage in Sine PWM

and SVPWM.

U2.7 Principle of Space Vector PWM

The procedure for implementing a two-level space vector PWM can be

summarized as follows:

1. Calculate the angle α and reference voltage vector VRref R based on the input

voltage components.

2. Calculate the modulation index and determine if it is in the over-modulation

region.

3.Find the sector in which VR

refR

lies, and the adjacent space vectors of VR

k R

and VR

k

+ 1 R based on the sector angle α.

4. Find the time intervals T R1R and TR2R and TR0R based on TRzR, and the angle α.

5. Determine the modulation times for the different switching states [47] .

To implement the space vector PWM, the voltage equations in the abc

reference frame can be transformed into the stationary dq reference frame that

consists of the horizontal (d) and vertical (q) axes as depicted in Figure 2.11.

Figure 2.11: The relationship of abc reference frame and stationary dq reference

frame.

From this figure, the relation between these two reference frames is shown as:

d axis

q axis

b

c

a


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35

f dq0 = Ksf abc (2.34)

Where, Ks = 231 12 120 √ 32 √ 3212 12 12 , f dq0=[ f d f q f 0]

P

TP

, f dq0=[ f a f b f c]P

TP

, and f denoted

either a voltage or a current variable.

As described in Figure 2.11, this transformation is equivalent to an orthogonal

projection of [a, b, c]Pt

P onto the two-dimensional perpendicular to the vector

[1, 1, 1] Pt

P (the equivalent d-q plane) in a three-dimensional coordinate system. As a

result, six non-zero vectors and two zero vectors are possible. Six nonzero vectors(V1- V6) shape the axes of a hexagonal as depicted in Figure 2.12,and feed electric

power to the load. The angle between any adjacent two non-zero vectors is 60

degrees.

Figure 2.12: Basic switching vectors and sectors.

α

V3 (010) V2 (110)

V1 (100)

V6 (101)V5 (001)

V4 (011)V7 (111)

V0 (000)

q axis

d axis

(1/3,1/ 3) Vref

(2/3)Vdc

(1/3,1/ 3)

( 13

,1/ 3) (13

,1/ 3)

(2/3,0) (2/3,0) 1

2

3

4

5

6


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36

Meanwhile, two zero vectors (V0 and V7) are at the origin and apply zero

voltage to the load. The eight vectors are called the basic space vectors and are

denoted by V0, V1,V2, V3, V4, V5, V6, and V7. The same transformation can be

applied to the desired output voltage to get the desired reference voltage vector Vref

in the d-q plane. The objective of space vector PWM technique is to approximate

the reference voltage vector Vref using the eight switching patterns. One simple

method of approximation is to generate the average output of the inverter in a

small period; T is to be the same as that of Vref in the same period. Therefore, space

vector PWM can be implemented by the following steps:

Step 1. Determine Vd , Vq , Vref , and angle (α)

Step 2. Determine time duration T1, T2, T0

Step 3. Determine the switching time of each transistor (S1to S6)

U2.7.1 Step 1: Determining Vd, Vq, Vref , and Angle (α)

From Figure 2.13, the Vd , Vq , Vref , and angle (α) can be determined as

follows:

V = V V60 V60 = V 12V 12V (2.35)V = 0 + V30 V30 = V + √ 32 V √ 32 V (2.36)vvq = 23 1 12 120 √ 32 √ 32

vanvbnvcn (2.37)

|V ref | = V2 + Vq2 (2.38)


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37

α = tan−1 VV = = 2πf , where f= fundamental frequency

Figure 2.13: Voltage Space Vector and its components in (d,q) .

It is necessary to know in which sector the reference output lies in order to

determine the switching time and sequence. The identification of the sector where

the reference vector is located is straightforward. The phase voltages correspond to

eight switching states: six non-zero vectors and two zero vectors at the origin.

Depending on the reference voltages Vd and Vq , the angle of the reference vector

can be used to determine the sector as shown in Table 2.3.

Table 2.3: Sector Definition.

Sector Degrees

1 0 < α ≤ 60Po

2 60Po

P< α ≤ 120Po

3 120P

oP

< α ≤ 180P

o

4 180P

oP < α ≤ 240P

o

5 240Po

P < α ≤ 300Po

6 300Po

P < α ≤ 360Po

a, d axis

V

d

→ refVq α

q axis

b

c


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U2.7.2 Step 2: Determining Time Duration T1, T2, T0

The duty cycle computation is done for each triangular sector formed by twostate vectors. The magnitude of each switching state vector is 2Vdc/3 and the

magnitude of a vector to the midpoint of the hexagon line from one vertex to

another is Vdc/√ 3 .From Figure 2.14, the switching time duration can be calculated as follows:

Switching time duration at sector 1

∫ V ref =T0 ∫ V 1 +T0 ∫ V 2 +T+TT ∫ V oTT+T (2.39)For sufficiently high switching frequency, the reference space vector V ref is

assumed constant during one switching cycle. Taking into account that the states

V 1 and V 2 are constant, one finds (see Figure 2.14):V ref T = V 1 T1 + V 2 T2 (2.40)23 T1V 10+ 23 T2 V �cos(π/3)sin(π/3) = T|V ref | � cos(α)sin(α) (2.41)(where , 0≤ α ≤60P

oP)

T1 = T sin (−)sin () (2.42)T2 = T sin

(

)

sin () (2.43)T0 = T (T 1 + T2), where, T = 1f and = |V |V Switching time duration at any sector


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39

T1 = √ 3 T |V |V sin 3 α + −13 π = √ 3 T |V |V sin(3 π α) = √ 3

T |

V |

V sin 3 π . cosα 3 π . α (2.44)T2 = √ 3 T |V ref |

V sin α 13 π =

√ 3 T |V |V α. −13 π sin −13 π . cosα (2.45)T

0= T

T

1 T

2 where, n=1 through 6 (that is, Sector 1 to 6)

For the sectors II-VI, the same rules apply [49].

Figure 2.14: Reference vector as a combination of adjacent vectors at sector 1.

U2.7.3 Step 3: Determining the Switching Time of Each

Transistor (S1to S6)

It is necessary to arrange the switching sequence so that the switching

frequency of each inverter leg is minimized. There are many switching patterns

that can be used to implement SVPWM. To minimize the switching losses, only

two adjacent active vectors and two zero vectors are used in a sector [50,51]. To

meet this optimal condition, each switching period starts with one zero vector and

end with another zero vector during the sampling time Tz. This rule applies


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normally to three-phase inverters as a switching sequence. Therefore, the switching

cycle of the output voltage is double the sampling time, and the two output voltage

waveforms become symmetrical during Tz. Table 2.4 presents asymmetric

switching sequence.

Referring to this table, the binary representations of two adjacent basic

vectors differ in only one bit, so that only one of the upper transistors switches is

closed when the switching pattern moves from one vector to an adjacent one. The

two vectors are time-weighted in a sample period Tz to produce the desired output

voltage.

Table 2.4: Seven-Segment Switching Sequence

Sector Switching Segment

1 2 3 4 5 6 7

1 V 0 , [000] V 1 , [100] V 2, [110] V 7, [111] V 2, [110] V 1 , [100] V 0 , [000] 2 V 0 , [000] V 3 , [010] V 2, [110] V 7, [111] V 2, [110] V 3 , [010] V 0 , [000] 3 V 0 , [000] V 3 , [010] V 4, [011] V 7, [111] V 4, [011] V 3 , [010] V 0 , [000] 4 V

0 , [000] V

5 , [001] V

4, [011] V

7, [111] V

4, [011] V

5 , [001] V

0 , [000]

5 V 0 , [000] V 5 , [001] V 6, [101] V 7, [111] V 6, [101] V 5 , [001] V 0 , [000] 6 V 0 , [000] V 1 , [100] V 6, [101] V 7, [111] V 6, [101] V 1 , [100] V 0 , [000] U2.8 Types of Different Schemes

There are two modes of operation available for the PWM waveform:

symmetric and asymmetric PWM. The pulse of an asymmetric edge aligned signal

always has the same side aligned with one end of each PWM period. On the other

hand, the pulse of symmetric signals is always symmetric with respect to the center

of each PWM period. The symmetrical PWM signal is often preferred because it

has been shown to have the lowest total harmonic distortion (THD). Output

patterns for each sector are based on a symmetrical sequence. There are different


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schemes in space vector PWM and they are based on their repeating duty

distribution. In order to reduce the switching loss of the power components of the

inverter, it is required that at each time only one bridge arm is switched. After re-

organizing the switching sequences, the switching pulse patterns of six different

sectors in Figure 2.15 are shown for the upper and lower switches of a three-phase

inverter.

It is obvious that in the odd sector the active state sequence is in ascending-

descending order; whereas, it is in a descending-ascending order in an even sector.

For example:

1. In an odd sector 1, the state sequence of space vectors is in the order

V 0, V 1, V 2, V 7, V 7, V 2, V 1, V 0.2. In an even sector 2, the state sequence of space vectors is:

V 0, V 3, V 2, V 7, V 7, V 2, V 3, V 0.Following the same procedure, we have the switching sequence summarized

in Table 2.5 for all six sectors.

Table 2.5: Switching Sequence for Three-Phase PWM Technique

Sector Switching Sequence of the Three Phase Modulation

1 V 0 V 1 V 2 V 7 V 2 V 1 V 0 2 V 0 V 3 V 2 V 7 V 2 V 3 V 0 3 V 0 V 3 V 4 V 7 V 4 V 3 V 0 4 V

0 V

5 V

4 V

7 V

4 V

5 V

0

5 V 0 V 5 V 6 V 7 V 6 V 5 V 0 6 V 0 V 1 V 6 V 7 V 6 V 1 V 6


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Figure 2.15 shows space vector PWM switching patterns at each sector.

(a)Sector 1 (b)Sector 2

(c)Sector 3 (d)Sector 4

(e)Sector 5 (f)Sector 6


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Figure 2.15 Space Vector PWM switching patterns at each sector.

Based on Figure 2.15 and according to the principle of symmetrical PWM, the

switching sequence in Table 2.6 is shown for the upper and lower switches and it

will be built in Simulink model to implement SVPWM.

Table 2.6 Switching Time Calculation at Each Sector

Sector Upper switches (S1,S3,S5) Lower switches (S4,S6,S2)

1S1=2(T1+T2)+T0 S3=2T2+T0

S5=T0

S4=T0 S6=2T2+T0

S2=2(T1+T2)+T0

2

S1=2T2+T0

S3=2(T1+T2)+T0

S5=T0

S4=2T2+T0

S6=T0

S2=2(T1+T2)+T0

3

S1=T0 /2

S3=2(T1+T2)+T0

S5=2T2+T0

S4=2(T1+T2)+T0S6=T0

S2=2T2+T0

4

S1=T0

S3=2T2+T0

S5=2(T1+T2)+T0

S4=2(T1+T2)+T0

S6=2T2+T0S2=T0

5

S1=2T2+T0

S3=T0

S5=2(T1+T2)+T0

S4=2T2+T0

S6=2(T1+T2)+T0S2=T0

6

S1=2(T1+T2)+T0

S3=T0

S5=2T2+T0

S4=T0

S6=2(T1+T2)+T0

S2=2T2+T0


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U2.9 Field Programmable Gate Array

A Field Programmable Gate Array (FPGA) is a silicon device that containslogic. It is constructed of cells called Configurable Logic Block (CLB); each

configurable logic block contains more or less a Look Up Table (LUT), a Flip-Flop

and a multiplexer. In-between the CLBs, there are interconnections and at the

borders input and output cells. An FPGA is normally programmed with a

Hardware Description Language (HDL) like VHDL or Verilog. An FPGA can be

re-programmable and several tasks can be executed at the same time; in other

words, parallel programming can be applied to it.

U2.10 Hardware in the Loop

Hardware in the loop (HIL), or FPGA in the loop, is a concept that as

revealed by the name uses the hardware in the simulation loop. This leads to easy

testing and the possibility to see how the actual plant is behaving in hardware. By

having the stimuli in a software on the PC, implementing a part of the loop inhardware and then receiving the response from hardware back in the software, a

good indication of the design’s performance is given [52].

U2.11 Usage of Xilinx System Generator in the Controller Design

MATLAB SIMULINK software package provides a powerful high level

modeling environment for people who are involved in system modeling and

simulations. Xilinx System Generator Tool developed for MATLAB SIMULINK

package is widely used for algorithm development and verification purposes in

Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs).

System Generator Tool allows an abstraction level algorithm development while


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keeping the traditional SIMULINK blocksets, but at the same time automatically

translating designs into hardware implementations that are faithful, synthesizable,

and efficient.

Here in this study, a direct field and torque controlled induction machine

driven by a Voltage Source Inverter (VSI) is analyzed by using a MATLAB

SIMULINK model. The control signals for the VSI in the related model are

generated by the Xilinx FPGA chip. But, the FPGA chip needs Very-high-speed

Hardware Description Language (VHDL) codes to generate the control signals for

the related controller. Normally, MATLAB SIMULINK Package does not provide

an interface for the VHDL needed for the controller to be embedded in the FPGA

chip. However, the Xilinx System Generator Tool provides such an interface; i.e., a

control algorithm developed Xilinx System Generator Tool convenient to be used

with traditional Simulink blocksets can be translated to the VHDL codes needed

for the controller to be embedded in the FPGA chip. The following section briefly

introduces system modeling using the Xilinx System Generator Tool.

U2.12 System Modeling Using the Xilinx System Generator

The formation of a DSP design begins with a mathematical description of the

operations needed for the controller and ends with the hardware realization of the

algorithm. The hardware implementation is rarely faithful to the original functional

description, instead it is faithful enough. The challenge is to make the hardwarearea and speed efficient, while still producing acceptable results. In a typical

design flow supported by System Generator, the following steps are followed:

1. Describe the algorithm in mathematical terms;


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2. Realize the algorithm in the design environment, initially using double

precision;

3. Trim double precision arithmetic down to fixed point;

4. Translate the design into efficient hardware .

U2.14 Integration in Xilinx Environment

The experimental application presents certain problems caused by the external

noise interference and the appearance of constant offsets at the waveforms. The

flux estimation is achieved by the integration of the stationary voltage and the

current waveforms. However, if there is an offset at the input of the integrator, a

ramp error occurs at the output of the integration [53] .

The implementation of the integral operator1+1 in real time application is yet

another problem to be sorted out. In general, the digital implementation includes

several hardware limitations, such as limited memory, finite precision, and limited

speed execution. Operations that require a finite amount of data and make the

algorithm computable are necessary.

According to the Euler approximation technique, a transfer function in the

differential operator (s) can be transformed into a discrete time transfer function in

the time delay operator (z) by substituting :

s = 1−z

T (2.46)

In Equation (2.46) ,Ts is the sampling interval. Let the clock frequency of the

FPGA be 0.2 MHz and consequently the sampling interval be 5* 10P-6

P sec.


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By substituting Equation (2.46) in the integral operator 1+1 , it is obtained:1+1 = 1 +1 = 1+1 =

5x101.000005−z = 4.999975x101−0.999995z (2.47)In time domain, Equation (2.47) is implemented by the difference equation:

[

] = 0.999995y[n

1] + 4.99x10−6

[

] (2.48)

Equation (2.48) yields the following block diagram realization:

Figure 2.17: Block diagram realization of equation (2.48) [22].


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Chapter Three System Implementation and Simulation Results

48

Chapter Three

System Implementation and Simulation Results

3.1 Introduction

This chapter deals with the implementation of DTC and examination of the

performance of DTC using differen

thesis torque ripple reduction based direct torque control for induction motor drives a thesisdtc

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