-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
1/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 1
SPEED CONTROLLER OF INDUCTION MOTOR
USING GENETIC ALGORITHMS
A Thesis
Submitted in partial fulfillment of the
Requirements for the award of the Degree of
MASTER OF TECHNOLOGY
In
ELECTRICAL AND ELECTRONICS ENGINEERING
(POWER ELECTRONICS ENGINEERING)
By
D. NAGESWARA RAO
11011D4318
Under the esteemed guidance of
Dr. A. JAYA LAXMI
DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
COLLEGE OF ENGINEERING
(AUTONOMOUS)
HYDERABAD 500085
ANDHRA PRADESH
Year 2011 - 2013
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
2/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 2
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
COLLEGE OF ENGINEERING
(AUTONOMOUS)
HYDERABAD 500 085
ELECTRICAL AND ELECTRONICS ENGINEERING
CERTIFICATE
Certified that this is a bonafide record of the dissertation
work entitled, SPEED CONTROLLER OF
INDUCTION MOTOR USING GENETIC ALGORITHM, done by D. NAGESWARA
RAObearing Admn.
No: 11011D4318 submitted to the Faculty of Electrical
Engineering,in partial fulfillmentof therequirements
for the Degree of MASTER OF TECHNOLOGY with specialization in
POWER ELECTRONICS
ENGINEERING from Jawaharlal Nehru Technological University
Hyderabad, College of Engineering
(Autonomous), Hyderabad.
Signature of the Head of the Department
Dr. M. SUSHAMAM Tech, Ph.D(JNTUH),M.I.S.T.E
M.S.S.I,M.I.E.T.E
Professor & Head, JNTUCEH
Signature of the Supervisor
Dr. A. JAYA LAXMIM. Tech, Ph. D, M.I.E,M.I.S.T.E
Professor
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
3/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 3
ABSTRACT
In the power system, some things like testing process, operator
training, apparatus modeling, costly
failures, integrating a subsystem into the system without any
fault are some of the concerns of engineers that
can be harmful and cost effective. Research on high level
modeling, new converter-inverter topologies and
control strategies are the major research areas in electrical
drives. So according to expressed problems there are
some rational reasons for creating digital control on electrical
machines and drives. A particular merit of this
approach is that it even permits a gradual change from
simulation to actual application, as it allows to start from
a pure simulation and to gradually integrate real electrical and
mechanical subsystems into the loop as they
become available. A simulation can help reduce development
cycles, cut overall cost, prevent costly failures,
increase repeatability through controlled environment and test a
subsystem exhaustively before integrating it
into the system.
Today, it is more common to test controllers using simulated
motor models in a real-time environment.
This methodology offers several distinct advantages. For
example, the simulated motor drive can be tested with
borderline conditions that would damage a real motor, often a
costly prototype. While testing, a controller is
interfaced with the real-time simulated motor drive through a
set of proper I/Os. Such motor drive simulation is
required for motor drive manufacturers to accelerate development
and testing time, by using real-time
simulation before making tests on physical prototypes.
The project involves Simulation of Induction Motor drive Using
Genetic Algorithms with compared
Artificial Intelligence Techniques Such as Fuzzy and Adaptive
Neuro-Fuzzy Inference System (ANFIS).
The dissertation work entries the following:
(a) Mathematical modeling and Simulation of Induction Machine
Drives with conventional controller
using MATLAB/SIMULINK.
(b) Static and Dynamic Analysis of Induction Motor, using
conventional controller.
(c) Implementation of simulation of Induction Machine drives
using speed controlled of induction motor
using genetic algorithms, fuzzy, ANFISN are presented in this
thesis.
(d) Comparison of dynamic performance of induction motor drive
using artificial intelligence controller
such as fuzzy, ANFIS, genetic algorithm.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
4/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 4
ACKNOWLEDGEMENT
I owe a great many thanks to great peoples who helped and
supported me during the project. This
acknowledgement is not just a position of words but also an
account of confession.
I would like to express my deepest respect and sincere gratitude
to my supervisor, Dr. A Jaya Lakshmi for
guiding and correcting various documents of mine with attention
and care.
I wish to express my sincere gratitude to Dr. M. SUSHAMA
Professor and Head of electrical and electronic
engineering College of JNTUHfor providing me an opportunity to
do my project work.
I thank Mr. Prashant Menghalone of my best friends for sharing
his valuable time and for giving me helpfulinformation to finish
this project. Thank you.
Last but not least I wish to avail myself of this opportunity,
express a sense of gratitude towards my parents for
their kind co-operation and encouragement which helped me in
completion of this project. I don't always show
it but they know that I do appreciate how much the both of them
have helped me with my life, and given me all
of the things that have gotten me here. Thank you Mom and
Dad.
D.NAGESWARA RAO
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
5/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 5
D. NAGESWARA RAO
Contents
CHAPTER ONE
........................................................................................................................................................
11
INTRODUCTIONTOINDUCTIONMOTOR DRIVES
....................................................................................................11
1.1 INTRODUCTION OF INDUCTION MOTOR
DRIVE.................................................................................................................
121.2 SYNCHRONOUS SPEED
...............................................................................................................................................................
121.3 SLIP
.....................................................................................................................................................................................................
14
1.4 TORQUE CURVE
.............................................................................................................................................................................
14
1.4.1 LOCKED ROTOR TORQUE
......................................................................................................................................................
15
1.4.2 PULL-UP TORQUE
......................................................................................................................................................................
15
1.4.3 BREAKE-DOWN TORQUE
........................................................................................................................................................
15
1.4.4 FULL-LOAD TORQUE
...............................................................................................................................................................
15
1.5 OBJECTIVES
.....................................................................................................................................................................................
16
1.6 CHAPTER BREAK UP
.....................................................................................................................................................................
16
1.7 SPEED CONTROL METHOD
..........................................................................................................................................................
17
A) POLE CHANGING METHOD
.........................................................................................................................................................
17
B) STATOR VOLTAGE CONTROL
.....................................................................................................................................................
19
C) VARIABLE FREQUENCY CONTROL
..........................................................................................................................................
20
D) EDDY CURRENT CONTROL
..........................................................................................................................................................
21
E) ROTOR RESISITANCE CONTROL
................................................................................................................................................
21
F) SLIP ENERGY RECOVERY SCHEME
..........................................................................................................................................
221.8CONCLUSION
.................................................................................................................................................................23
CHAPTER TWO
......................................................................................................................................................
24
DYNAMICMODELLING&SIMULATIONOFINDUCTIONMOTORDRIVES.........................................................24
2.1DYNAMICMODELLINGOFINDUCTIONMOTOR...............................................................................................25
2.2 DYNAMIC MODEL OF INDUCTION MOTOR
..........................................................................................................................
26
2.3 INDUCTION MOTOR INDUCTANCE MATRIX CALCULATION
..........................................................................................
27
2.4 PARKS
TRANSFORMATION........................................................................................................................................................
30
2.5 INDUCTION MOTOR TORQUE CALCULATION
......................................................................................................................
30
2.6 INDUCTION MOTOR CURRENT CALCULATION
...................................................................................................................
31
2.7 INDUCTION MOTOR ROTOR SPEED
..........................................................................................................................................
33
2.8 SIMULATION OF A THREE-PHASE INDUCTION MOTOR USING
MATLAB-SIMULINK ..............................................
33
2.8.1 AC SOURCE
..................................................................................................................................................................................
35
2.8.2 ABC TO DQ0 PARKS TRANSFORMATION
..........................................................................................................................
36
2.8.3 INDUCTION MOTOR IN D-Q MODEL
....................................................................................................................................
37
2.8.4 STATOR FLUX LINKAGE CALCULATION IN Q-AXIS
.......................................................................................................
37
2.8.5 ROTOR FLUX LINKAGE CALCULATION IN Q-AXIS
........................................................................................................
38
2.8.6 STATOR FLUX LINKAGE CALCULATION IN D-AXIS
.......................................................................................................
38
2.8.7 ROTOR FLUX LINKAGE CALCULATION IN D-AXIS
........................................................................................................
39
2.8.8 STATOR CURRENT CALCULATION IN
Q-AXIS.................................................................................................................
39
2.8.9 ROTOR CURRENT CALCULATION IN Q-AXIS
..................................................................................................................
40
2.8.10 MUTUAL FLUX LINKAGE CALCULATION IN Q-AXIS
..................................................................................................
40
2.8.11 ROTOR CURRENT CALCULATION IN D-AXIS
..................................................................................................................
41
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
6/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 6
2.8.12 STATOR CURRENT CALCULATION IN D-AXIS
...............................................................................................................
41
2.8.13 MUTUAL FLUX LINKAGE CALCULATION IN D-AXIS
..................................................................................................
42
2.8.14 ELECTRICAL TORQUE CALCULATION
............................................................................................................................
42
2.8.15 ROTOR SPEED CALCULATION
............................................................................................................................................
43
2.8.16 INVERSE PARKS TRANSFORMATION
..............................................................................................................................
43
2.9 DISCUSSION AND SIMULATION RESULTS
...........................................................................................................................
44
CHAPTER THREE
..................................................................................................................................................
46
SPEEDCONTROLLEROFINDUCTIONMOTORUSINGARTIFICIALINTELLIGENCETECHNIQUES
.............46
3.1 INTRODUCTION
.............................................................................................................................................................................
47
3.2 FUZZY LOGIC CONTROLLER IN SIMULINK
..........................................................................................................................
47
3.3 SPEED CONTROLLER
....................................................................................................................................................................
50
3.4 PWM INVERTER
.............................................................................................................................................................................
51
3.5 PWM OUTPUTS
................................................................................................................................................................................
52
3.6 FLOW CHART OF FUZZY CONTROLLER
.................................................................................................................................
533.7 SIMULATION RESULTS AND DISCUSSIONS
..........................................................................................................................
543.8 INTRODUCTION TO ANFIS
..........................................................................................................................................................
55
3.9 OVERVIEW OF ANFIS
....................................................................................................................................................................
57
3.10 SIMULATION MODEL OF ANFIS
..............................................................................................................................................
58
3.11 SIMULATION RESULTS AND DISCUSSION
...........................................................................................................................
61
CHAPTER FOUR
.....................................................................................................................................................
62
OPTIMIZATIONTECHNIQUES&GENETICALGORITHMS
........................................................................................62
4.1 OPTIMIZATION
................................................................................................................................................................................
63
4.2 TRADITIONAL METHODS OF OPTIMIZATION
.......................................................................................................................
63
4.3 NON TRADITIONAL METHODS OF OPTIMIZATION
.............................................................................................................
644.4 HISTORY OF GENETIC ALGORITHMS
......................................................................................................................................
67
4.5 FUNCTIONING OF GENETIC ALGORITHMS
............................................................................................................................
68
4.6 GENETIC PARAMETERS
...............................................................................................................................................................
71
4.7BASICOPERATIONANDSTAGESINTYPICGENETICALGORITHMS
...........................................................72
4.7.1 SELECTION
...................................................................................................................................................................................
72
4.7.2 CROSS OVER
................................................................................................................................................................................
76
4.7.3 MUTATION
....................................................................................................................................................................................
79
4.8 STAGES IN GENETIC ALGORITHMS
........................................................................................................................................
80
4.9 STEPS IN GENETIC ALGORITHMS
.............................................................................................................................................
82
4.10 WHEN IN USE GENETIC ALGORITHMS
..................................................................................................................................
83
4.11 GENETIC ALGORITHMS APPLICATIONS
...............................................................................................................................
84
4.12 ADVANTAGES OF GENETIC ALGORITHMS
..........................................................................................................................
854.13 APPLICATION OF GENETIC ALGORITHMS TO HYBRID SYSTEMS
..............................................................................
85
CHAPTER FIVE
.......................................................................................................................................................
87
GENETCALGORITHMBASEDSIMULATIONOFINDUCTIONMOTORDRIVE.....................................................87
5.1 SIMULATION OF GA BASED INDUCTION MOTOR DRIVE
................................................................................................
87
5.2 SIMULATION RESULTS AND DISCUSSION WITH GA BASED FUZZY
CONTROLLER .............................................. 89
5.3 SIMULATION RESULTS AND DISCUSSION WITH GA,ANFIS,FUZZY
.............................................................................
90
5.4 COMPARATIVE APPROACH TO DIFFERENT AI BASED SIMULATION OF
INDUCTION MOTOR ............................ 91
5.5 CONTINUOS GENETIC ALGORITHM MATLAB CODE APPIXA
.......................................................................................
95
5.6 TEST FUNCTION MATLAB CODEAPPIXB
...........................................................................................................................
97
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
7/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 7
5.7 CONCLUSION
..................................................................................................................................................................................
97
5.8 THE SCOPE OF THE FUTURE WORKS
......................................................................................................................................
97
APPENDIXC
............................................................................................................................................................................98REFERENCE..............................................................................................................................................................................99
Figures
CHAPTER ONE
........................................................................................................................................................
11
INTRODUCTIONTOINDUCTIONMOTORDRIVES
.....................................................................................................11Fig.
1.1 Conceptual diagram of an induction machine
.........................................................................................................................
13
Fig. 1.2 Conventional per-phase equivalent circuit
..............................................................................................................................
13
Fig. 1.3 Torque speed curve
.................................................................................................................................................................
15
Fig. 1.4 Static and dynamic inductance definitions
..............................................................................................................................
16
Fig. 1.5 Stator phase connections for six poles
......................................................................................................................................
18
Fig. 1.6 Speed-Torque curves
.................................................................................................................................................................
18
Fig. 1.7 Torque-speed curves at various voltages
.................................................................................................................................
19
Fig. 1.8 Torque-Speed characteristics for variable frequency
control
.................................................................................................
20
Fig. 1.9 Slip ring induction motor with external rotor resistors
............................................................................................................
21
Fig. 1.10 Torque versus speed at various rotor resistances
...................................................................................................................
22
Fig. 1.11 Static Kramer method
..............................................................................................................................................................
23
CHAPTER TWO
......................................................................................................................................................
24
DYNAMICMODELLING&SIMULATIONOFINDUCTIONMOTORDRIVE
...........................................................24
Fig. 2.1 The d-q equivalent circuit of an induction motor
.....................................................................................................................
25
Fig. 2.2 Definition of d-axis and q-axis on an arbitrary
reference frame
.............................................................................................
26
Fig. 2.3 Principle of the control system
..................................................................................................................................................
34
Fig. 2.4 Induction model with conventional controller
.........................................................................................................................
34
Fig. 2.5 AC source of main model
.........................................................................................................................................................
36
Fig. 2.6 abc to DQ0 Parks transformation model
.................................................................................................................................
36
Fig. 2.7 Induction motor in d-q model
...................................................................................................................................................
37
Fig. 2.8 Flux linkage calculation model overall view
...........................................................................................................................
37
Fig. 2.9 Stator flux linkage calculation in q-axis
..................................................................................................................................
38
Fig. 2.10 Rotor flux linkage calculation in q-axis
.................................................................................................................................
38Fig. 2.11 Stator flux linkage calculation in d-axis
.................................................................................................................................
39
Fig. 2.12 Rotor flux linkage calculation in d-axis
.................................................................................................................................
39
Fig. 2.13 Stator, rotor and mutual flux linkage calculation in
q-axes
...................................................................................................
40
Fig. 2.14 Stator current calculation in the q-axis
...................................................................................................................................
40
Fig. 2.15 Rotor current calculation in the q-axis
...................................................................................................................................
40
Fig. 2.16 Mutual flux linkage calculation in the q-axis
........................................................................................................................
41
Fig. 2.17 Stator, rotor and mutual flux linkage calculation in
the d-axis
.............................................................................................
41
Fig. 2.18 Rotor current calculation in the d-axis
...................................................................................................................................
41
Fig. 2.19 Stator current calculation in the d-axis
...................................................................................................................................
42
Fig. 2.20 Mutual flux linkage calculation in the d-axis
.........................................................................................................................
42
Fig. 2.21 Electrical Torque calculation
...................................................................................................................................................
43
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
8/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 8
Fig. 2.22 Rotor speed calculation
...........................................................................................................................................................
43
Fig. 2.23 D-Q to abc inverse Parks transformer produce rotor and
stator currents
............................................................................
44
Fig. 2.24 Torque result from conventional simulation
.........................................................................................................................
45
Fig. 2.25 Speed result from conventional simulation
...........................................................................................................................
45
Fig. 2.26 Stator current result from conventional simulation
...............................................................................................................
45
Fig. 2.27 Rotor current result from conventional simulation
...............................................................................................................
45
CHAPTER THREE
.....................................................................................................................................................
46
SPEEDCONTROLLEROFINDUCTIONMOTORUSINGARTIFICIALINTELLIGENCETECHNIQUES
.............46
Fig. 3.1 Overall view of Fuzzy-logic based controller
..........................................................................................................................
47
Fig. 3.2 The Fuzzy Controller model
......................................................................................................................................................
49
Fig. 3.3 Controllable frequency sin wave generator
.............................................................................................................................
50
Fig. 3.4 Speed control model
..................................................................................................................................................................
50
Fig. 3.5 PWM inverter circuit
................................................................................................................................................................
51
Fig. 3.6 Outage block
..............................................................................................................................................................................
52
Fig. 3.7 IGBTs gating signals
.................................................................................................................................................................
52Fig. 5.8 PWM inverter output
................................................................................................................................................................
52
Fig. 3.9 Simulation process flow chart
...................................................................................................................................................
53
Fig. 3.10 Speed response with fuzzy
......................................................................................................................................................
54
Fig. 3.11 Torque response with fuzzy
.....................................................................................................................................................
54
Fig. 3.12 Stator currents with fuzzy
........................................................................................................................................................
54
Fig. 3.13 Rotor currents with fuzzy
........................................................................................................................................................
54
Fig. 3.14 ANFIS architecture
.................................................................................................................................................................
57
Fig. 3.15 Overall Neuro-Fuzzy simulation model
................................................................................................................................
58
Fig. 3.16 Neuro-Fuzzy
.............................................................................................................................................................................
60Fig. 3.17 Speed characteristics with ANFIS
..........................................................................................................................................
61
Fig. 3.18 Torque characteristics with ANFIS
.........................................................................................................................................
61
Fig. 3.19 Stator currents with ANFIS controller
..................................................................................................................................
61
Fig. 3.20 Rotor currents with ANFIS controller
..................................................................................................................................
61
CHAPTER FOUR
........................................................................................................................................................
62
OPTIMIZATIONTECHNIQUES&GENETICALGORITHMS
........................................................................................62
Fig. 4.1 Block diagram of genetic algorithm
.........................................................................................................................................
70
Fig. 4.2 General scheme of a genetic algorithm
....................................................................................................................................
70
Fig. 4.3 Roulette- wheel selection
..........................................................................................................................................................
74
Fig. 4.4 Rank selection diargam
.............................................................................................................................................................
75
Fig. 4.5 Single point crossover
................................................................................................................................................................
77
Fig. 4.6 Two point crossover
...................................................................................................................................................................
77
Fig. 4.7 Uniform crossover
......................................................................................................................................................................
78
Fig. 4.8 Stages in a typical genetic
algorithm.........................................................................................................................................
81
Fig. 4.9 Typical genetic algorithm representation
..................................................................................................................................
83
CHAPTER FIVE
.........................................................................................................................................................
87
GENETICALGORITHMSBASEDSIMULATIONOFINDUCTIONMOTORDRIVE
................................................87
Fig. 5.1 speed controller of induction motor with genetic
algorithm
.....................................................................................................
88
Fig. 5.2 Speed characristics with GA controller
.......................................................................................................................................
89
Fig. 5.3 Torque characristics with GA controller
.....................................................................................................................................
89
Fig. 5.4 Stator currents with GA controller
.............................................................................................................................................
89
Fig. 5.5 Rotor currents with GA controller
..............................................................................................................................................
89
Fig. 5.6 GA optimization
values...............................................................................................................................................................
90
Fig. 5.7 Speed with GA controller
...........................................................................................................................................................
90
Fig. 5.8 Torque with GA
controller..........................................................................................................................................................
90
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
9/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 9
Fig. 5.9 Speed with ANFIS controller
.....................................................................................................................................................
91
Fig. 5.10 Torque with ANFIS controller
.................................................................................................................................................
91
Fig. 5.11 Stator current with ANFIS
........................................................................................................................................................
91
Fig. 5.12 Rotor currents with ANFIS
.......................................................................................................................................................
91
Fig. 5.13 Speed response of conventional controller with fuzzy
...........................................................................................................
92
Fig. 5.14 Speed response of FUZZY controller
......................................................................................................................................
92
Fig. 5.15 Speed response of ANFIS controller
........................................................................................................................................
92
Fig. 5.16 Speed with GA controller
.........................................................................................................................................................
92
Fig. 5.17 Torque with GA
controller........................................................................................................................................................
92
Fig. 5.18 Torque response of conventional controller
............................................................................................................................
93
Fig. 5.19 Torque response of ANFIS
.......................................................................................................................................................
93
Fig. 5.20 Torque response of fuzzy
controller........................................................................................................................................
93
Fig. 5.21 Speed response of GA controller
..............................................................................................................................................
94
Fig. 5.22 Torque response of GA controller
............................................................................................................................................
94
Tables
Table 4.1 Population and fitness.
............................................................................................................................................................
75
Table 7.1 Speed comparison between Conventional, Genetic
algorithm, fuzzy and ANFIS
............................................................ 93
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
10/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 10
GLOSSARY OF SYMBOLS
Rs The stator resistance
Rr The rotor resistance
Lm The magnetizing inductance of the motor
Lls The stator leakage inductance
Llr The rotor leakage inductance
r The slip frequency which is the frequency of the actual rotor
current
Llr The rotor leakage inductance referred to stator side
Rr The rotor resistance referred to stator side
qs , ds Q-axis and d-axis components of stator flux
qr , dr Q-axis and d-axis components of rotor flux
iqs , ids Q-axis and d-axis components of stator current
iqr , iqr Q-axis and d-axis components of rotor current
vqs , vds Q-axis and d-axis components of stator voltage
vqr , vqr Q-axis and d-axis components of rotor voltage
p Number of poles
The angular position of the rotor
a Reference frame rotating speed
J Moment of inertia (kg/m2)
Te Electrical torque
Tl Load torque
e (k) Control error
r (k) Reference signal
y (k) Output signal
e(k) Changed error
u(Ri) The crisp u value corresponding to the maximum membership
degree
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
11/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 11
CHAPTER ONE
INTRODUCTION TO INDUCTION MOTOR DRIVES
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
12/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 12
1.1 INTRODUCTION OF INDUCTION MOTOR DRIVE
In the industrial sector especially in the field of electric
drives & control, induction motors play a vital role.Without
proper controlling of the speed, it is virtually impossible to
achieve the desired task for a specific
application. Basically AC motors, such as Induction Motors are
of Squirrel-Cage type. They are simple,
reliable, low cost and virtually maintenance-free electrical
drives. Based on the inability of conventional control
methods like PI, PID controllers to work under wide range of
operation, artificial intelligent based controllers
are widely used in the industry like ANN, Fuzzy controller,
ANFIS, expert system, genetic algorithm. The main
problem with the conventional fuzzy controllers is that the
parameters associated with the membership
functions and the rules depend broadly on the intuition of the
experts. To overcome this problem, GA based
Adaptive Neuro-Fuzzy controller and Fuzzy Logic controller are
proposed in this dissertation .
In most of the industries, induction motors play very important
and that is the reason they are manufactured inlarge numbers. About
half of the electrical energy generated in a developed country is
ultimately consumed by
electric motors, of which over 90 % are induction motors. For a
relatively long period, induction motors have
mainly been deployed in constant-speed motor drives for general
purpose applications. The rapid development
of power electronic devices and converter technologies in the
past few decades, however, has made possible
efficient speed control by varying the supply frequency, giving
rise to various forms of adjustable-speed
induction motor drives. In about the same period, there were
also advances in control methods and Artificial
Intelligence (AI) techniques. Artificial Intelligent techniques
mean use of expert system, fuzzy logic, neural
networks and genetic algorithm. Researchers soon realized that
the performance of induction motor drives can
be enhanced by adopting artificial-intelligence-based methods.
Since the 1990s, AI-based induction motor
drives have received greater attention. Among the existing
control technologies, intelligent control methods,
such as fuzzy logic control, neural network control, genetic
algorithm, and expert system, have exhibited
particular superiorities. Artificial Intelligent Controller
(AIC) could be the best controller for Induction Motor
control. Over the last two decades, researchers have been
working to apply AIC for induction motor drives [1-
6]. This is because that AIC possesses advantages as compared to
the conventional PI, PID and their adaptive
versions. Since the unknown and unavoidable parameter
variations, due to disturbances, saturation and change
in temperature exists; it is often difficult to develop an
accurate system mathematical model. High accuracy is
not usually of high importance for most of the induction motor
drive. During the operation, even when the
parameters and load of the motor varies, a desirable control
performance in both transient and steady states must
be provided. Controllers with fixed parameters cannot provide
these requirements unless unrealistically high
gains are used. Therefore, control strategy must be robust and
adaptive. As a result, several control strategies
have been developed for induction motor drives within last two
decades. The main idea for such a hybrid
controller is that with a combination of fuzzy logic and neural
network, such as uncertainty or unknown
variations in plant parameters and structure can be dealt more
effectively. Hence, the robustness of the control
of induction motor is improved. Conventional controllers have on
their side well established theoretical
backgrounds on stability and allow different design objectives
such as steady state and transient characteristics
of the closed loop system to be specified. Much research work is
in progress in the design of such hybrid
control schemes. Fuzzy controller conventionally is totally
dependent to memberships and rules, which are
based broadly on the intuition of the designer.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
13/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 13
The induction motor, which is the most widely used motor type in
the industry, has been favored
because of its good self-starting capability, simple and rugged
structure, low cost and reliability, etc. Along with
variable frequency AC inverters, induction motors are used in
many adjustable speed applications which do not
require fast dynamic response.
In induction and synchronous motors, the stator is powered with
alternating current (poly phase
current in large machines) and designed to create a rotating
magnetic field which rotates in time with the AC
oscillations. In a synchronous motor, the rotor turns at the
same rate as the stator field. By contrast, in an
induction motor the rotor rotates at a slower speed than the
stator field. Therefore the magnetic field through the
rotor is changing (rotating). The rotor has windings in the form
of closed loops of wire. The changing magnetic
flux induces currents in the windings as in a transformer, and
these currents create their own magnetic fields.
These interact with the stator field to create torque to turn
the rotor.
For these currents to be induced, the speed of the physical
rotor must be lower than that of the stator's
rotating magnetic field (ns), or the magnetic field would not be
moving relative to the rotor conductors and no
currents would be induced. As the speed of the rotor drops below
synchronous speed, the rotation rate of the
magnetic field in the rotor increases, inducing more current in
the windings and creating more torque. The ratio
between the rotation rate of the magnetic field as seen by the
rotor (slip speed) and the rotation rate of the
stator's rotating field is called "slip". Under load, the speed
drops and the slip increases enough to create
sufficient torque to turn the load. For this reason, induction
motors are sometimes referred to as asynchronous
motors.
1.2 SYNCHRONOUS SPEED
The synchronous speedof an AC motor is the rotation rate of the
rotating magnetic field created by the
stator. It is always an integer fraction of the supply
frequency. The synchronous speed nsin revolutions per
minute (rpm) is given by:
= 60 wherefis the frequency of the AC supply current in Hz
andpis the number of magnetic pole pairs per
phase. For example, a small 3-phase motor typically has six
magnetic poles organized as three opposing pairs
120 apart, each powered by one phase of the supply current, so
there is one pole pair per phase andp= 1. For
60 Hz supply frequency, its synchronous speed is thus 3600 RPM.
Under no-load conditions, when the only
load on the motor is its friction, the speed approaches
synchronous speed.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
14/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 14
The concept of vector control has opened up a new possibility
that induction motors can be controlled to
achieve dynamic performance as good as that of DC or brushless
DC motors.
In order to understand and analyze vector control, the dynamic
model of the induction motor is
necessary. In this project as a first step, an induction motor
model is derived in relatively simple terms by using
the concept of space vectors and d-q variables.
Fig. 1.1 Conceptual diagram of an induction machine.
Traditionally in analysis and design of induction motors, the
per-phase equivalent circuit of induction
motors shown in Fig. 1.1 has been widely used. In the circuit
note that all rotor parameters and variables are not
actual quantities but are quantities referred to the stator,
parameters are defined by:
Ls Lsr Rrs
Fig. 1.2 Conventional per-phase equivalent circuit
Rs: stator resistance
Rr: rotor resistance
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
15/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 15
Lm: magnetizing inductance of the motor
Ls: stator inductance
Lr: rotor inductance
Lrs: rotor inductance referred to the stato
It is also known that induction motors do not rotate
synchronously to the excitation frequency. At rated load, the
speed of induction motors are slightly less than the synchronous
speed.
1.3 SLIP
Slip sis the ratio of the rotation rate of the rotor magnetic
field to the rotation rate of the stator magnetic
field.
= N NN Where nris the rotor rotation speed in rpm. It is zero at
synchronous speed and one (100%) when the rotor isstationary. The
slip determines the motor's torque. Since the short-circuited rotor
windings have small
resistance, a small slip induces a large current in the rotor
and produces large torque.
1.4 TORQUE CURVE
The torque exerted by the motor as a function of slip is given
by a torque curve. Over a motor's normal
load range, the torque line is close to a straight line, so the
torque is proportional to slip. As the load increases
above the rated load, increases in slip provide less additional
torque, so the torque line begins to curve over.
Finally at a slip of around 20% the motor reaches its maximum
torque, called the "breakdown torque". If the
load torque reaches this value, the motor will stall. At values
of slip above this, the torque decreases. In 3-phase
motors the torque drops but still remains high at a slip of 100%
(stationary rotor), so these motors are self-
starting. The starting torque of an induction motor is less than
other types of motor, but still around 300% of
rated torque. In 2-pole single-phase motors, the torque goes to
zero at 100% slip (zero speed), so these require
alterations to the stator such as shaded poles to provide
starting torque.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
16/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 16
Fig. 1.3 Torque speed curve1.4.1 LOCKED ROTOR TORQUE: The
minimum torque that a motor will develop at rest for all
angular
positions of the rotor is called locked rotor torque or starting
torque.
1.4.2PULL-UP TORQUE: The minimum torque delivered by an AC motor
during the period of acceleration
from zero to the speed at which breakdown occurs.
1.4.3BREAK-DOWN TORQUE: Itis the point at which an excessive
load on the motor will cause it to stop.
1.4.4FULL-LOAD TORQUE: The torque a motor produces at its rated
horsepower and full-load speed.
As I said r is called the slip frequency which is the frequency
of the actual rotor current. In the steady-
state AC circuit, current and voltage phasors are used and they
are denoted by the overline. In Fig. 1.2, power
consumption in the stator is interpreted as Is2Rs, while Ir 2Rrs
represents both power consumption in the rotor
and the mechanical output (torque). By subtracting rotor loss Ir
2Rr from Ir 2Rrs, produced torque (mechanical
power divided by the shaft speed) is given by:
= By definition, two kinds of analysis of induction motors are
considered in the literature:
1) The static inductance: that the slope of the straight line
(OA) from the origin through the actual
operating point A on the magnetizing curve Fig. 1.4. The static
inductance is therefore the division of
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
17/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 17
the flux by the magnetizing current.This value is used for
steady state condition or when operation of
the machine changes from one to another steady state situation
and the transients are not so important.
Static inductance
Fig. 1.4 static and dynamic inductance definitions
2) The dynamic inductance:that the slope of the tangent line
(AC), to the magnetizing curve at the same
operating point A, as represented in Fig. 1.4.
1.5 OBJECTIVES
Induction Motors have many applications in the industries,
because of the low maintenance and
robustness. The speed control of induction motor is more
important to achieve maximum torque and efficiency.
This thesis presents an integrated environment for speed control
of induction motor (IM) including simulation.The integrated
environment allows users to compare simulation results between
classical and genetic algorithm
controllers i.e. Fuzzy and ANFIS. It is due to its unique
characteristics like high efficiency, good power factor
and extremely rugged nature of Induction motor. The genetic
algorithm and fuzzy logic controller and artificial
neuro-fuzzy controllers are also introduced to the system for
keeping the motor speed to be constant. The
performance of genetic algorithm and fuzzy logic and artificial
neuro-fuzzy based controllers is compared with
that of the conventional proportional integral controller. The
dynamic modeling of Induction motor is done and
the performance of the Induction motor drive has been
analyzed.
1.6 CHAPER BREAK UP
In the first chapter the basic knowledge required to understand
the Induction motor operation is briefly
covered.
In the second chapter the dynamic model of Induction motor is
fully formulated and its mathematical
equations are clearly proven.
At the third chapter the different techniques to control the
induction motor speed is briefly listed and
then explained.
= Dynamic inductance
=
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
18/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 18
At the fourth chapter the dynamic simulation of induction motor
drive according to the model expressed
in chapter two is done and each and every part is separately
explained and executed.
The fifth chapter will discuss how to improve the speed control
of induction motor based on genetic
algorithm controller for taking better results compare to
dynamic model simulation.
The sixth chapter will discuss how to improve the speed control
of fuzzy controller based simulation
with replacing fuzzy controller part with genetic algorithm
controller.
At the end the seventh chapter will compare all discussed
methods, and find a technique as the best in
this project
.
1.7 SPEED CONTROL METHODSFollowing are the methods employed to
control the speed of induction motors.
A) Pole changing.
B) Stator voltage control.
C) Supply frequency control.
D) Eddy-current control.
E) Rotor resistance control.
F) Slip power recovery.
While pole changing is applicable to squirrel cage motors,
stator voltage control and supply frequency
control can be used for both squirrel cage and wound rotor
motors. Whereas rotor resistance control and slip
power recovery methods are applicable only to wound rotor motors
as they are controlled from the rotor circuit.
A) POLE CHANGING METHOD:
For a particular frequency, the synchronous speed is inversely
proportional to the number of poles.
Changing the number of poles can change synchronous speed and
therefore the motor speed. Provision for
changing the number of poles has to be incorporated at the time
of manufacturing stage and such machines are
called, pole-changing motorsor multi-speed motors.
Squirrel cage rotor is not wound for any specific number of
poles. It produces the same number of poles
as stator winding has. Therefore, in a squirrel cage motor, an
arrangement is required only for changing the
number of poles in stator. In wound rotor motor, arrangement for
changing the number of poles in rotor is also
required, which complicates the machine. Therefore, this method
of speed control is only used with squirrel
cage motors.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
19/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 19
This method is simple but expensive arrangement for changing the
number of stator poles. It uses two
separate windings, which are wound for two different pole
numbers. An economical and common alternative is
to use a single stator winding divided into few coil groups, and
by rearranging the coil groups we can obtain
different speeds, which are factor of 2. The Fig. 3.1 shows a
phase winding which consists of six coils divided
into two groups a-b consisting of odd number coils(1,3,5)
connected in series and c-d consisting of even
numbered coils(2,4,6) connected in series which are shown.
Fig. 1.5 Stator phase connections for six poles
The speed-torque curves for 6 pole and 12 pole formation can be
shown as in Fig. 3.2.
Fig. 1.6 Speed-Torque curves
In some applications, change in speed is required only by a
small amount (for example. fan and pump
drives).Such a small change in speed is possible by pole
amplitude modulation. As pole systems are not
alternating along the periphery, these motors in modified
connection suffer from harmonic currents and
voltages, and have lower power factor and efficiency than pole
changing motors.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
20/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 20
B) STATOR VOLTAGE CONTROL:
By reducing the stator voltage, speed of a high-slip induction
motor can be reduced by an amount, which
is sufficient for the speed control. While torque is
proportional to square of the voltage, the voltage if reduced
reduces the speed. So for the same current the motor develops
lower torque therefore such loads which demand
less torque with the decrease in the speeds are suitable under
this control ( fan and pump drives ).
This method of speed control is not suitable for normal mains
fed with 3-phase Induction Motor. The
portion of speed torque curve beyond the point of maximum torque
is unstable. The normal cage motor has
small resistance and therefore, the unstable portion is large.
The speed control is possible only in narrow band
of speeds. The starting current of these motors is also very
high. The equipment used to control the speed must
be able to withstand this current. The power factor is poor at
large slips. Therefore special rotor design with
high resistance is required to be able to take advantage of
speed control by voltage variation. The Fig. 3.3 shows
the Torque-Speed curves of an Induction motor at various
voltages assuming sinusoidal voltage.
This method is very simple but speed control range is very much
limited. Speed range can be made
wider if the rotor resistance is larger. The line p.f is poor.
The line and motor currents have harmonic content.
Fig. 1.7 Torque-speed curves at various voltages
Machine has poor efficiency, heating of motor is more, and
regeneration is not possible. It is used with
fan loads, blowers and pumps.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
21/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 21
C) VARIABLE FREQUENCY CONTROL(V/F):
Synchronous speed P
f
Ns 120
..(3.1)
And, motor speed, sr NsN 1 (3.2) check
eqn no
From the above it is evident that synchronous speed is directly
proportional to the supply frequency.
Therefore, by varying supply frequency we can control the speed
of the induction motor. Motor speed can be
controlled below and above the synchronous speed. Voltage
induced in stator is proportional to the product of
supply frequency and air gap flux. If stator drop is neglected,
terminal voltage can be considered proportional to
the product of frequency and flux. The equations 3.3 and 3.4
justify the above statements.
pssmw Tfk.E 444 (3.3)
pssmw Tfk.V 444 ...(3.4)
While any increase in flux beyond the rated value is undesirable
from the consideration of saturation
effects a decrease in flux is also avoided to retain the torque
capability of motor. Therefore, the variable
frequency control below the rated frequency is generally carried
out by reduced machine phase voltage along
with the frequency; the motor is operated at a constant voltage
because of limitations imposed by stator
insulation or supply voltage limitations.
The motor is always operated on the portion of the speed torque
curves with a negative slope, by
limiting either the slip speed or the current for getting the
advantages of the high torque to current ratio, high
efficiency and a good power factor.
Fig. 1.8 Torque-Speed characteristics for variable frequency
control
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
22/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 22
Variable frequency control gives larger torques with reduced
currents for the complete range of speeds. This
method provides a highly efficient variable speed drive with
excellent running and transient performance.
Regenerative braking is also possible below synchronous speed
down to zero speed.
D) EDDY CURRENT CONTROL
Drive consists of an eddy current clutch placed between an
induction motor running at a fixed speed and
the variable speed load. Speed is controlled by controlling D.C
excitation to magnetic circuit of the clutch.
Since motor runs at a fixed speed, it can be fed directly from
AC mains.
E) ROTOR RESISTANCE CONTROL
This method is suitable for wound rotor induction motor. Maximum
torque is independent of rotor
resistance, speed at which the maximum torque is produced
changes with rotor resistance. For the same torque,
speed falls with an increase in rotor resistance. Advantages of
rotor resistance control are that motor torque
capability remains unaltered even at low speeds. Only other
method, which has this advantage, is variable
frequency control. This method is used for only low speeds,
because of low cost of rotor resistance and high
torque capability at low speeds, and rotor resistance control is
employed in cranes, high load drives. A major
disadvantage is low efficiency due to additional losses in
resistor connected in the rotor circuit.
Fig. 1.9 Slip ring induction motor with external rotor
resistors
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
23/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 23
Fig. 1.10 Torque versus speed at various rotor resistances,
curves 1, rotor short-circuited; 2-4,
increasing values of external resistance
F) SLIP ENERGY RECOVERY SCHEMEThe portion of air gap power,
which is not converted into mechanical power, is called slip power.
Slip
control methods regulate the amount of slip power. The slip
power is controlled by controlling the voltage
injection into the rotor. By this method induction motor speed
can be controlled from speed zero to speed higher
than the synchronous speed. Instead of wasting power in external
resistors, it is usefully employed here.
Therefore, these methods of speed control are classified as slip
power recovery schemes. The circuital
connections for slip energy recovery scheme and torque speed
characteristics can be as shown in the next
Figures.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
24/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 24
Fig. 1.11 Static Kramer method
The main problem in providing suitable source is that the
frequency of the injected emf must match the
rotor slip frequency at all speeds. Two such schemes are: static
Scherbiusdrives and static Kramer drives which
provides speed control of wound rotor motor below and above
synchronous speed respectively.
This speed is suitable for driving high capacity centrifugal
pumps and fans. Speed control is achieved from
above synchronous speed to zero speed.
.1.8 CONCLUSION
In this chapter mathematical model of induction motor has been
developed for dynamic analysis of the
symmetrical induction machines in the arbitrary reference frame.
In chapter Four the block based simulation
will be constructed according to these equations and then will
be simulated.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
25/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 25
CHAPTER TWO
DYNAMIC MODELLING & SIMULATION OF INDUCTION MOTORDRIVE
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
26/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 26
2.1 DYNAMIC MODELLING OF INDUCTION MOTOR
The voltage and torque equations that describe the dynamic
behavior of an induction motor are time-varying. Differential
equations involve some complexity. A change of variables can be
used to reduce the
complexity of these equations by eliminating all time-varying
inductances. By this approach, a poly phase
winding can be reduced to a set of two phase windings (q-d) with
their magnetic axis formed in quadrature. In
other words, the stator and rotor variables (voltages, currents
and flux linkages) of an induction machine are
transferred to a reference frame, which may rotate at any
angular velocity or remain stationary. Such a frame of
reference is commonly known in the generalized machines analysis
as arbitrary reference frame.
Fig. 2.1: the d-q equivalent circuit of an induction motor
The dynamic analysis of the symmetrical induction machines in
the arbitrary reference frame has been
intensively used as a standard simulation approach from which
any particular mode of operation may then bedeveloped. It can be a
powerful technique in implementing the machine equations as they
are transferred to a
particular reference frame. Thus, every single equation among
the model equations can be easily implemented
in one block so that all the machine variables can be made
available for control and verification purposes[2-3].
qs (- r) qsRs RrLls= Ls+Lm L'lr= Lr+Lm
Vds Vdrds dr
ds (- r) ds Rr
Vqr
Rs Lls= Ls+Lm Llr= L'r+Lm
Vqsqs qr
Lm
Lm
ids idr
iqs iqr
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
27/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 27
2.2 DYNAMIC MODEL OF INDUCTION MOTOR
Before everything, its better to clarify some of the parameters
and concepts that are existing in thedynamic model.
Rs: the stator resistance
Rr: the rotor resistance
Lm: the magnetizing inductance of the motor
Lls: the stator leakage inductance
Llr: the rotor leakage inductance
r: the slip frequency which is the frequency of the actual rotor
current
Llr: the rotor leakage inductance referred to stator side
Rr: the rotor resistance referred to stator side
qs , ds : q-axis and d-axis components of stator flux
qr , dr: q-axis and d-axis components of rotor flux
iqs , ids: q-axis and d-axis components of stator current
iqr , iqr:q-axis and d-axis components of rotor current
vqs , vds: q-axis and d-axis components of stator voltage
vqr , vqr:q-axis and d-axis components of rotor voltage
Note that in this equivalent circuit, all rotor parameters and
variables are not actual quantities but are quantities
referred to the stator. And also we know that induction motors
do not rotate synchronously to the excitation
frequency. At rated load, the speed of induction motors are
slightly less than the synchronous speed.
Fig. 2.2: d-axis and q-axis on an arbitrary reference frame.
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
28/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 28
Let the stator to rotor winding turn ratio be n and the angular
position of the rotor be , and definethe
rotor velocity in the form of the following that p is the number
of poles.
r=p
Fig. 2.2 illustrates the relationship between d-q axis and
complex plane on a rotating frame with respect
to stationary a-b-c frame. Note that d-axes and q-axes are
defined on a rotating reference frame at the speed of
awith respect to fixed a-b-c frame.
= a=p a
The generalized equivalent circuit on an arbitrarily rotating
frame is shown in Fig. 2.1. Now, depending
on a specific choice of a, many forms of dynamic equivalent
circuit can be established. Among them, the
synchronous frame form can be obtained by choosing a= e.
2.3 INDUCTION MOTOR INDUCTANCE MATRIX CALCULATION
The sum of the stator leakage inductance and magnetizing
inductance is called the stator inductance (Ls=
Lls+ Lm), and the sum of the rotor leakage inductance and
magnetizing inductance is called the rotor inductance
(Lr=Llr+ Lm), where we have the following equations:
= = As we can see in the Fig. 2.1 the rotating emf-es are
represented by voltage sources and not by
Inductances. Consequently, rotor appears near to the natural
induced voltage, expressed by means of the rotor
speed.
Driving the model equations can be generated from the d-q
equivalent circuit of the induction machine
shown in Fig. 2.1. The voltage and current equations associated
with this circuit can be found as follows:
The flux linkages can be achieved as follows:
= + .(2.1) = + = + ..(2.2) = + ...........(2.3)
=
+
=
+
......(2.4)
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
29/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 29
The voltage equations are as following:
= +
+ .....(2.5) = + ...(2.6) = + + ( ) ....(2.7) = + ( )
..(2.8)
For obtaining the voltages the following steps have to be
done:
By placing the equation 1 and equation 2 into the equation 5,
vqs obtained as:
= + + = + + +( +)
=
+
+
+
+
..(2.9)
By placing the equation 1 and equation 2 into the equation 6,
vds obtained as:
= + = + ( + )
( +)
= + + (2.10)By placing the equation 2 and equation 3 into the
equation 7 , vqr obtained as:
= + + ( )
= + (
+
)
+ ( )( +)
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
30/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 30
= +
+
+ ( ) ( ) .(2.11)By placing the equation 1 and equation 4 into
the equation 8, vdr obtained as:
= + ( ) = + ( +) ( +)
= + + ( ) ( ).(2.12)According to calculation, for ease of
studying equations 2.9,2.10,2.11,2.12 are listed below: = + + + + =
+ + = + + + ( ) + ( )
=
+
+
(
)
(
)
Vdrand Vqrare short circuited hence they are equal to zero. The
electrical transient model in terms of voltages
and currents can be given in matrix form as:
00
= + + ( )( ) + ( )( ) +
In the above matrixprepresents the operator. For stationary
reference frame, by substituting = 0, the abovematrix equation is
reduced to:
00
= + 00 + 00 ( )( ) + ( )( ) +
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
31/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 31
Moreover, for synchronous frame, we have = 0
0 =
+
+
()( ) + ()( ) + Since actual stator variables either to be
generated or to be measured are all in stationary a-b-c frame,
frame
transform should be executed in the control. The most popular
transform is between stationary a-b-c frame
quantities to synchronously rotating d-q quantities.
2.4 PARKS TRANSFORMATION
The following equation shows how a-b-c frame can be transformed
into the q-d frame:
0 = cossin cos( 2/ 3) cos( + 2/ 3)sin( 2/ 3) sin( + 2/ 3)
0.5 0.5 0.5
And its inverse transform is given by:
=
coscos(
2
/ 3)
sin 1sin(
2
/ 3) 1
cos(
+ 2
/ 3) sin(
+ 2
/ 3) 1
0
As we have seen the voltage and current in stationary and rotor
reference frame in the form of [] = [] []isachieved, where [v] and
[i] are 4x1 column matrices of voltage and current and are given
as
[ ] and [ ]respectively.2.5 INDUCTION MOTOR TORQUE
CALCULATION
The torque equation is:
=3
2 21
(2.13) Which is in the vector form. Equation 2.13 can be
rewriten as (Bolded letters shows it is in vector space):=
3
4 1 () ...(2.14)
For calculating the electromagnetic torque, transfer [] = [][]to
the stationary reference frame so that the will be equal to
zero.then s is kept as superscript which is written as follows:
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
32/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 32
[] = [] []Where [
] and [
]are 4x1 column matrices of voltage and current in the
stationary frame and are given as
[]and [ ]respectively.So the impedance matrix will be as
follows: + 00 + 00 ( )( ) + ( )( ) +
Although the torque expression on the above is derived from
stationary reference frame, it is true for any other
reference frames such as Many other forms of torque equations
are also possible, such as:
= 322 ( ) =
3
4 ...(2.15)
We can eliminate Irso that the equation will change to:
=
3
4 .....(2.16) 2.6 INDUCTION MOTOR CURRENTS CALCULATIONAccording
to the single phase circuit of the induction motor shown in Fig.
1.4 one can write current
equations of stator and rotor in the d-q axis as follows:
=
..(2.17)
= ( ) ..(2.18) = ..(2.19) = ( ) ..(2.20)
By substituting and in the above equations we have the following
equations according to the currentflow orientation and knowing that
( = ):
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
33/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 33
=
+
..(2.21) = + ..(2.22) = .(2.23)
Referring to equations 2.5,2.6,2.7,2.8 we can write the flux
linkage equations as followings in the per unit (b
is the base value of angular frequency and suppose induction
motor is working in the synchronous speed):
1 = 1 = + .(2.24)
1
=
1 = + + ( ) .(2.25)
1 = ( ) 1
= ( )
+
.(2.26)1 = + ( )
1 = + ( ) + ( ) .(2.27)
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
34/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 34
2.7 INDUCTION MOTOR ROTOR SPEEDThe speed rin the above equations
is related to the torque by the following mechanical dynamic
equation: = + = +2 (2.28)Then we can rewrite the above equation
for as follows:
= 2 ( ) .(2.29) Where:p: number of poles
J: moment of inertia (kg/m2)
2.8 SIMULATION OF THREE-PHASE INDUCTION MOTOR USING
MATLAB/SIMULINK
SIMULINK is a powerful software package for the study of dynamic
and nonlinear systems. Using
SIMULINK, the simulation model can be built up systematically
starting from simple sub-models. The
induction motor model developed may be used alone or it can be
incorporated in an advanced motor drive
system, e.g. field oriented control.
Simulink is an environment for multidomain simulation and
Model-Based Design for dynamic and
embedded systems. It provides an interactive graphical
environment and a customizable set of block libraries
that let you design, simulate, implement, and test a variety of
time-varying systems, including communications,
controls, signal processing, video processing, and image
processing. Simulink is integrated with MATLAB,
providing immediate access to an extensive range of tools that
let you develop algorithms, analyze and visualizesimulations,
create batch processing scripts, customize the modeling
environment, and define signal, parameter,
and test data.
In this project the simulation process will be starting from
conventional modeling according to the
mathematical equations that are expressed in previous parts. The
next plan is to improve the operation of
induction motor in the sense that how speed can be increased and
in the same duration of time we take faster
rising, so two more techniques will be applied to enhance the
control system, one will be fuzzy logic controller
and second one will be Adaptive Neuro-Fuzzy Inference System
that usually is abbreviated to ANFIS. But
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
35/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 35
before getting down controlling system First will discuss on
conventional simulation. The principle of the
control system is shown in Fig. 2.3.
Fig.2.3: Principle of the control system
Over the years different mathematical models have been used to
examine different problems associated
with induction motors. These range from the simple equivalent
circuit models to more complex d,q models and
abc models which allow the inclusion of various forms of
impedance and/or voltage unbalance. In this project
for more simplicity d-q models is preferred so that it will
simplify the very complicated non-linear equations to
be solved and simulated. In Fig. 2.4 the block-diagram of
induction motor and its drive that are simulated in
MATLAB/simulink are shown.
Fig. 2.4: Induction model with Conventional controller
In the Fig. 2.4 the structure of conventional simulation of
induction motor is shown. According to the model
the AC voltage source that is the sinusdoial signal generator
predefined by MATLAB/simulink, is applied to
Parks transformation matrix, then abc system will be converted
to d-q form. In the next step the voltage sources
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
36/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 36
that are imaged into d-axis and q-axis are applied to induction
motor model. According to the previous section
and proven equations the induction motor equations are expressed
in d-q frame. The outputs after calculating
the expressed equations, will be stator and rotor currents
separately in the d-axis and q-axis, torque and rotor
speed. It can be the last stage but for more result clearance
the currents are converted to abc frame with the help
of inverse Parks transformation. So according to existance of
different parts in this model the following
headings will be discussed in details:
AC source
Abc to DQ0 Parks transformation
Induction motor in d-q model
Stator flux linkage calculation in q-axis
Rotor flux linkage calculation in q-axis
Stator flux linkage calculation in d-axis
Rotor flux linkage calculation in d-axis
Stator current calculation in the q-axis
Rotor current calculation in the q-axis
Stator current calculation in the d-axis
Rotor current calculation in the d-axis
Mutual flux linkage calculation in the q-axis
Mutual flux linkage calculation in the d-axis
Electrical Torque calculation
Rotor speed calculation
2.8.1 AC source
In the first stage balanced AC sources of sinnusdual wave forms
are provided that are predefined blocks by
simulink software, and the data related to the these three
phases like amplitude, frequency and phases are given
to the blocks through a GUI as given in Fig. 2.5: = 2 sin() = 2
sin 23 = 2 sin + 23
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
37/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 37
Fig. 2.5: AC source of main model
2.8.2 abc to DQ0 Parks transformation
As its apparent from the equation below and block diagram, with
the help of function blocks like sin,
cosin and some operational blocks like summation, multiplication
and subtraction and one constant blocks for
applying 2/ 3value, the Parks transformation is easily modeled.
The output of this block will concludes thevoltage sources in d-q
frame.
0 = cossin cos( 2/ 3) cos( + 2/ 3)sin( 2/ 3) sin( + 2/ 3)
0.5 0.5 0.5
Fig. 2.6 abc to DQ0 Parks transformation model
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
38/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 38
2.8.3 Induction motor in d-q model
In the Fig. 2.7 the overall model of IM is shown in Fig. 2.7 and
the sub-blocks will be discussed later.
Fig. 2.7: Induction motor in d-q model
2.8.4 Stator flux linkage calculation in q-axis
In Fig. 2.8 all the flux linkages of stator and rotor in d-axis
and q-axis and also mutual fluxes in d-axis and
q-axes are calculated.
Fig. 2.8: Flux linkage calculation model overall view
In Fig.2.9 the stator flux linkage in q-axis according to the
equation that earlier is proven, is constructed.
1
= +
6
Wr
5
Te
4
idr
3
iqr
2
ids
1
iqs
TL
Te
Wr
rotor speed
iqs
Fqs
Fds
ids
Te
electrical torque
Fqr
Fqs
Fmq
iqr
iqs
Subsystem4
Fds
Fdr
ids
idr
Fmd
Subsystem2
Fmq
vqs
vds
Wr
Fmd
Fqr
Fqs
Fds
Fdr
Flux linkage calculation
3TL
2
Vds
1
Vqs
-
7/13/2019 1.Modelimi i Ngasjes Dhe Motorit Asinkron- Gjithashtu
Edhe Modeli Matematik
39/103
GENETIC ALGORITHM BASED SIMULATION OF INDUCTION MOTOR DRIVE
2013
Jntuh College Of Engineering Hyderabad Page 39
Fig. 2.9: Stator flux linkage calculation in q-axis
Some variables like
and
are supplying from another blocks that are calculating these
parameters.
The constant parameters like base value of rotor speed, stator
resistance and stator leakage inductance will be
supplied through a GUI of induction motor which will modify
th