Design and Implementation of a Three-Phase Induction Motor Control Scheme

2001 Thesis Project 1 Gareth S Roberts



Design and
Implementation of a
Three-Phase Induction
Motor Control Scheme


By
Gareth Stephen Roberts

Department of Information Technology and Electrical
Engineering,
the University of Queensland


Submitted for the degree of
Bachelor of Electrical Engineering (Honours).
October 2001



2001 Thesis Project A2 Gareth S Roberts


34 Tolaga Street,
Westlake, QLD, 4074
October 17, 2001

The Head of School,
School of Information Technology and Electrical Engineering,
University of Queensland,
St. Lucia, Qld, 4072

Dear Professor Simon Kaplan,

In accordance with the requirements of the degree of Bachelor of Engineering (Honours)
in the division of Electrical Engineering, I present the following thesis entitled “Design
and Implementation of a Three-Phase Induction Motor Control Scheme”. This thesis was
carried out under the supervision of Dr. Geoff Walker.

This thesis project has not been submitted at any other University. I declare that this
work has not been published or written by any other person, except where reference is
made by text.

Yours sincerely,



Gareth Roberts.



2001 Thesis Project A3 Gareth S Roberts
Abstract

The use of a combustion engine to motivate a car has been questioned in recent times due
to the increasing concern of “global warming”. As a result of this, the concept of driving

a car with an electric engine has become of particular interest. Dr. Geoff Walker and his
PhD students are working on the creation of the University’s own electric car.

This thesis project is focused on deriving a control scheme to drive an induction machine
that could be applied to the electric car. Induction machines are universally used in
industry because of their robustness, reliability, low price and high efficiency (up to
80%). However, until recent times, it has been hard to control the torque of the induction
motor.

By using the “TMS320F243 DSP controller,” which is embedded in an existing hardware
design and a control scheme called “Field Orientated Control,” we can control the torque
of an induction machine with a high degree of accuracy. Hence, this thesis project
demonstrates how to apply Field Orientated Control with a DSP controller. To do this,
extensive MATLAB analysis was conducted in order to optimize the control system. The
complete physical system is expected to be working on the demonstration day.
2001 Thesis Project A4 Gareth S Roberts
Acknowledgements

I wish to thank the following people:

Dr. Geoff Walker, my supervisor, for taking the time through the whole course of the
year for offering clear and enthusiastic explanations. Dr. Walker was always able to
guide the thesis along the right path.

Mr. David Finn for lending me his motor controller board. David also provided the
required information needed to operate this board.

My family, for offering support through my University years; this year in particular.

My fellow occupants in the Power Electronics labs, for putting up with my company for

days on end. To Andrew Gray and Jeffrey Jordan, thank you for the advise you offered
through the course of the year.











2001 Thesis Project A5 Gareth S Roberts
Table of Contents

Abstract………………………………………………………….. i
Acknowledgements………………………………………………. ii
List of Figures and Illustrations………………………………… iii

Chapter 1 – Need/Basis for the thesis project………………….. 1
1.1. Project Specification…………………………………. 1
1.2. Available resources…………………………………... 1
1.3. What are hyper and electric cars?……………………. 1
1.4. Why do we use an Induction motor?…………………. 3

Chapter 2 – Literature Review…………………………………... 5
2.1. The Hybrid concept…………………………………... 5
2.2. Induction Motor Theory and Practice………………… 5
2.3. Power Electronics…………………………………….. 6

2.4. Field-Orientated Control……………………………… 7
2.5. MATLAB analysis……………………………………. 8

Chapter 3 – The Hardware Design………………………………. 9
3.1. The basic control format……………………………... 9
3.2. The existing motor controller………………………... 10
3.3. Current sensing module……………………………… 11
3.4. The speed sensor……………………………………... 12

2001 Thesis Project A6 Gareth S Roberts
Chapter 4 – The Induction Motor………………………………. 14
4.1. The fundamental operating principles for an
Induction Motor……………………………………... 14
4.2. The Electrical principles of an Induction Motor…….. 14
4.3. Torque/Speed generation for an Induction Motor…… 16

Chapter 5 – Field-Orientated Control (FOC)…………………… 19
5.1. An introduction…………………………………….. 19
5.2. Transformation between reference frames…………. 20
5.3. The PI controller……………………………………. 21
5.4. PWM – Pulse-Width Modulation…………………... 22
5.5. The Overall Design…………………………………. 24
5.6. Conclusions drawn from Chapter 5………………… 26

Chapter 6 – The MATLAB design…………………………… 27
6.1. MATLAB – An introduction……………………… 27
6.2. MATLAB simulation design……………………… 27
6.2.1 Field Orientated Control using SIMULINK………... 28
6.2.2 The Current Controller……………………………… 32
6.2.3 The Motor Model…………………………………… 32

6.3. Simulation of the MATLAB design………………. 34
6.3.1. Speed response analysis……………………………. 34
6.3.2. Analysis of the Field-Orientated Section of the
Design……………………………………………….. 38
6.3.3. The significance of feedback………………………... 41
6.4. The conclusions drawn from Chapter 6……………. 42

2001 Thesis Project A7 Gareth S Roberts
Chapter 7 – The Software Design……………………………… 43
7.1. A basic overview of how the software is
organized…………………………………………… 43
7.2. The Main Program – The Field-Orientated Control
Portion of the Software Design……………………. 44
7.2.1. The torque controller & Field Weakening………….. 45
7.2.2. Calculation of iqs, ids, cos(rho) and sin(rho)………. 48
7.2.3. The Current Controller section of the software design 50
7.3. The PWM Interrupt Service Routine………………. 51
7.4. The Encoder Interrupt Service Rountine…………... 55
7.5. A/D conversion……………………………………. 57
7.6. Concluding remarks………………………………. 58

Chapter 8 – Final Project Performance and Evaluation…… 59
8.1. PWM test program………………………………... 59
8.2. Encoder test program #1…………………………... 61
8.3. Encoder test program #2…………………………... 62

Chapter 9 – Conclusion…………………………………………. 64
9.1 Summary and Conclusion…………………………... 64
9.2 Future work…………………………………………. 64

Bibliography……………………………………………………… 66
APPENDIX A – The proposed software design
APPENDIX B – PWM test program
2001 Thesis Project A8 Gareth S Roberts
APPENDIX C – Encoder detection test program #1
APPENDIX D – Encoder detection test program #2
APPENDIX E – The schematics for the Motor Controller board
2001 Thesis Project A9 Gareth S Roberts
List of Figures


Figure 1.1 – The Honda Insight
Figure 1.2 – The parallel hybrid car

Figure 3.1 – The basic physical design
Figure 3.2 – The existing motor controller board
Figure 3.3 – The current sensing module

Figure 4.1 – The per phase representation of an Induction motor in steady state
Figure 4.2 – The torque/speed curve
Figure 4.3 – Field weakening

Figure 5.1 – The transformation of the stationary reference frame to the rotating
reference frame
Figure 5.2 – The PI controller
Figure 5.3 – Leg A of the full-bridge inverter
Figure 5.4 – PWM VSI schematic and waveforms
Figure 5.5 – The complete FO controller design in a block representation

Figure 6.1 – The Look-up Table

Figure 6.2 – The complete SIMULINK design
Figure 6.3 – The FO_controller block
Figure 6.4 – The dqe2abc block
Figure 6.5 – The Inverse_Park_Transform Block
Figure 6.6 – The Inverse_Clarke_Transform Block
Figure 6.7 – The Current_controller block
Figure 6.8 – The Induction machine in stationary qd0
Figure 6.9 – The MATLAB speed simulation results
Figure 6.10 – The speed response of the control system where the proportional
gain is increased
Figure 6.11 – The speed response of the system with a proportional gain of 90
Figure 6.12 – cos(rho) and sin(rho) signals
Figure 6.13 – The ids and iqs signal curves over time
Figure 6.14 – The applied signal to phase A of the Induction motor and the drawn
current on phase A
Figure 6.15 – The speed response of the system without feedback

Figure 7.1 – The flow chart for this thesis project
Figure 7.2 – The torque controller
Figure 7.3 – Graphical representation of the trapezoidal rule
Figure 7.4 – Limiting the integration result
Figure 7.5 – Calculation of the required rotor flux: Lambdare_r
Figure 7.6 – The results of using the field-orientated technique
Figure 7.7 – Overflow prevention of the slip-angle
2001 Thesis Project A10 Gareth S Roberts
Figure 7.8 – Demonstration of the development of the slip angle over time
Figure 7.9 – Flow-chart demonstrating how the current controller section works
Figure 7.10 – PWM waveforms with dead-band
Figure 7.11 – The PWM infrastructure
Figure 7.12 – The Peripheral Interrupt Expansion Block Diagram

Figure 7.13 – The encoder detection infrastructure
Figure 7.14 – The flow-chart for Encoder detection

Figure 8.1 – Experimentally measured PWM waveforms on the CRO











2001 Thesis Project 1 Gareth S Roberts
1. Need/Basis for the thesis project

1.1. Project Specification

To design a control scheme for a three-phase induction motor drive. This induction
motor drive is proposed to be incorporated into a “hybrid car” or an “electric car”.

1.2. Available resources

•
Motor controller board. This was constructed by 1999 thesis student, Mr.
David Finn and was designed to control a brush-less DC motor. However, by
constructing a feedback loop that can detect the outputs of an induction motor, we
can use this motor controller to control an induction machine.

• TMS320F243 DSP controller. This is manufactured by the Texas Instruments
Company and is one of the major components on David Finn’s motor controller.
For this thesis project, a software control design has to be devised that will
correctly control the DSP controller to meet specifications.

• DC bus. This DC bus is made available from SUNSHARK battery packs,
12V
DC
to 140V
DC
. ~40 V
DC
is the most compatible voltage supply for the motor
controller that will be used for this thesis.

• Induction motor. Three-phase, 0.5kW, 4-pole machine. This induction motor
is only used for the prototype design presented in this thesis.

1.3. What are hybrid and electric cars?

Under the supervision of Dr. Geoff Walker, a group of Computer Science and Electrical
Engineering Ph.D. students at the University of Queensland are constructing a hybrid or
an electric car. Both of these types have been inaugurated due to the increasing concerns
of “global warming”. An electric car simply uses an electric engine as the means of
motivating the car instead of the conventional combustion engine. These cars have not
yet been released in the commercial world because the electric engine system (including
2001 Thesis Project A2 Gareth S Roberts
batteries) does not provide the same power per weight as the combustion engine from the

research to date [8].
Figure 1.1. The Honda Insight [14]


Figure 1.2. The internal infrastructure of a parallel hybrid car
[14]


A hybrid car was released commercially this year. It combines two or more sources of
power; the gasoline-electric hybrid car, for instance, does just this. The electric engine
2001 Thesis Project A3 Gareth S Roberts
boosts acceleration and reduces demand on the petrol engine, saving fuel and improving
performance in the process [14]. While cruising, power comes solely from the petrol
engine. When the vehicle is coasting downhill, or during deceleration and braking, the
electric motor recharges a nickel metal hydride battery pack. During periods when the
vehicle is stationary, the engine automatically shuts down to save fuel, and then starts up
again when the throttle is pressed. The Honda “Insight” for instance consumes less than
half the fuel of a conventional small car and harmful exhaust emissions are lowered by a
significant 90% [14]. This model features a 10kW electric motor that delivers power to
the front wheels via a five speed manual gearbox.


1.4 Why do we use an Induction motor?

For this application, the only external input for the electric motor applied by the user is
the accelerator; which is essentially a variable torque input. There are two existing
options for an electric motor: the “Direct current (DC)” type or the “Induction” type.
Induction motors are universally used in industry because of their high robustness,
reliability, low price and high efficiency (up to 80% [15]). However, the brush-less DC
motor has been, traditionally, the more attractive option for variable torque control. This

is because the torque can be controlled by varying the “armature current (i
a
)”, while the
flux can be controlled by varying the “field/exciting current (i
x
)”. These two quantities
operate in a decoupled manner, which is highly advantageous from a design perspective.
Also, an induction machine has been difficult to control due to its complex mathematical
model, its non-linear behavior during the saturation effects and the electrical parameter
oscillation that depends on the physical influence of temperature [15].

However, the recent fruition of “digital signal processors (DSPs)” has swung the
pendulum toward the induction motor for torque control. These high computational
power silicon devices have made it possible to realize far more precise digital control
algorithms. Field Orientated Control (FOC), for instance, is a vector control method that
demonstrates the capability of performing direct torque control. FOC provides an
induction motor every advantage that DC machine control can have, while freeing itself
from mechanical commutation drawbacks [9]. It is anticipated that the application of the
2001 Thesis Project A4 Gareth S Roberts
correct control algorithm combined with the inherent efficiency and power potential will
make this design very compatible for use in a hybrid car. Additionally, the induction
machine makes execution of “regenerative braking” relatively simple. Regenerative
braking is a means of using the induction machine as a brake. It is anticipated that the
outcomes from this thesis project support the claim that an induction motor is a better
means of motivating a hybrid or an electric car.

2001 Thesis Project A5 Gareth S Roberts
2 The literature review

This section of the thesis report reviews the focal sources of information that were
required to compile this thesis project.

2.1. The Hybrid car concept

Honda and Toyota only released the Hybrid car this year. Knowledge of its operational
principles is not commonly known. The web-site, “How Stuff Works”, is an educational
site that is written by Mr. Marshall Brain. It provides a basic introduction onto how a
hybrid car works. Within this article, the definition of the hybrid car and its potential
advantages are stated. The concept of the parallel hybrid car is presented. This is a car
design that simultaneously utilizes both the combustion engine and the electric engine to
turn the wheels. Mr. Brain also offers an explanation on how commercially released
hybrid cars (the Toyota “Prius” and the Honda “Insight”) work.

2.2 Induction Motor Theory and Practice

Wildi [1] is an excellent source of information on the theory behind the operation of an

induction motor. The three-phase induction machine is presented in Chapter 13. The
electromagnetic and mechanical phenomena that are responsible for the induction
motor’s many advantages are clearly explained. Wildi also presents the two types of
induction motors: “the squirrel cage induction motor” and the “wound motor”. An
explanation of the advantages and disadvantages of each is given. Essential concepts
such as “synchronous speed”, “slip”, “torque” and the rated electrical inputs are presented
and exemplified with example problems. The equivalent electrical circuit for an induction
motor is derived based on the three-phase transformer.

This book also presents the fundamentals of the induction motor from a practical
viewpoint. The small and large motor types are distinguished, where the typical electric
and mechanical characteristics of each are shown. In the later chapters (20 to 23), Wildi
takes the reader through some of the existing methods of driving an induction motor:
2001 Thesis Project A6 Gareth S Roberts
♦ Static frequency charges
♦ Static voltage controllers
♦ Rectifier-inverter systems with line commutation
♦ Rectifier-inverter systems with self-commutation
♦ Pulse-width modulation systems

Pulse-width modulation systems are the only control schemes that can be considered for
this thesis as the motor controller is specifically designed for Pulse-width modulation.

The text by Mohan, Undeland and Robbins [2] gives good explanations on the operating
principles of the induction machine. Concepts such as operating the induction motor in
the constant torque region, volts per hertz control, starting up considerations and driving
an induction machine with a three-phase bridge inverter are explained.

2.3. Power Electronics

Operation of the motor controller board requires knowledge of how the power electronic
aspects work. Mohan Undeland and Robbins [2] provides chapters of information on
power electronics; Dr. Geoff Walker utilizes this text to teach his Power Electronics
subject. In chapter two, all the current power-switching devices are presented. These
are: the Diode (the various types of diodes are presented and compared), the Bipolar
Junction Transistor (BJT), the Metal Oxide Field-Effect Transistor (MOSFET) and the
Insulated Gate Bipolar Transistor (IGBT). In this chapter, the requirements of a
switching device are also stated. The general desired characteristics of a power switching
device is to have a high blocking voltage in the reverse direction, to have minimal
switching losses (this is related to fast switching ability) and the power device is required
handle a sufficient amount of average forward current. It is found that the MOSFET
provides the minimal switching losses and is, hence, well suited for voltage switching
purposes.

2001 Thesis Project A7 Gareth S Roberts
In chapter eight, the basic switching topologies are outlined. An inverter is an electronic
configuration that transforms a DC signal into an AC signal in a controlled manner. This
is very relevant for this thesis project as we have available a DC supply and the induction
motor requires an AC supply that needs to be controlled to a certain degree of accuracy.
It compares how each topology generates harmonics. It discusses utilization of the
supply voltage. All voltage-switching designs require a modulation chip to generate
Pulse Width Modulated (PWM) signals that are applied to the gate of the power
switching devices. There are two types of PWM outlined: sinusoidal and square-wave.
While square-wave switching utilizes the supply voltage better, the harmonic content of
the output waveform is too high to really be considered an effective solution. Therefore,
sinusoidal PWM is the best option based on the literature provided in this text. Later in
the chapter, they talk about “dead-time”, which is a time delay that needs to be
introduced to the square-wave to avoid commutation of the power switching devices.

2.4. Field-Orientated Control

Bimal K. Bose’s book that he edited in 1996 [4] presents extensive explanations on FO
control. Concepts that comprise Field-Orientated (FO) control such as the rotating and
stationary reference frames, Clarke and Park transforms, PI controllers and PWM are
extensively explained. Bose also exemplifies some MATLAB models that can be used to
simulate FO control. In the later stages, “self-tuning” and “sensor-less” FO control are
investigated. Bose also offers the reader general explanations on microprocessors and
how they are the central control means of FO control.

The Texas Instruments Literature Document BPRA073 also presents theoretical and
practical clarifications on FO control. However, they present their DSP controller device,
the TMSC320C240. This device is specifically suited to motor control techniques such
as FO control. In BPRA043 [10], example assembler code used to execute FO control is
offered. Texas Instruments Technical Document BPRA076[17] provides an extensive
practical detail of how to apply FO control to an induction motor.

2001 Thesis Project A8 Gareth S Roberts
2.5. MATLAB analysis

The book, Control Systems Engineering[7] is dedicated to presenting the concepts of
generating a control design. Furthermore, MATLAB is extensively used through the
course of the book. However, “Dynamic Simulation of Electric Machinery using
MATLAB/SIMULINK”[6] is a book that specifically presents how to apply FO control
in MATLAB, how to model an induction motor in MATLAB and the control design
aspects of FO control.
2001 Thesis Project A9 Gareth S Roberts
3. The Hardware Design

3.1. The basic control format

In essence, we are endeavoring to design a controller that can vary the torque induced in
the rotor of the motor. To do this, the induction motor controller will be configured in
the following format:

Figure 3.1. The basic physical design [16]

The user applies an input signal (e.g., the throttle of the car) that will be fed into the
command generator of the DSP controller. The DSP controller will manipulate this
control signal to produce signals that the induction motor can operate off. These signals
will be converted to PWM (Pulse-Width Modulated) signals so that the Full-bridge
MOSFET (Metal-Oxide Silicon Field Effect Transistor) inverter on the motor controller
can amplify these signals to substantial voltage levels. It is anticipated that the amplified
PWM signals will then induce a torque in the rotor of the induction motor that is
proportional to the magnitude of the input signal applied by the user. The design will
utilize an encoder that sends down pulses that can be manipulated to calculate the speed
and position of the rotor. The encoder pulses and the measured currents drawn by the
induction motor form the feedback portion of the design. Hence, the major aim of this
thesis project is to develop a control strategy for the DSP controller that controls the
torque production within the induction machine. However, there is no great emphasis
placed on precise torque control.

2001 Thesis Project A10 Gareth S Roberts

3.2. The existing motor controller

David Finn’s motor controller board can be seen in figure 3.2. There are two main
features that are of particular relevance to this thesis project:

A. TMS320F243 DSP controller: provides several key functions of different nature,

in particular, signal filtering, regulation, drive signal generation, measurement,
monitoring, protection and more. The speed at which we need to execute the control
algorithms and detect signals in the control feedback loop suggests the requirement
for an advanced Digital Signal Processor. The TMS320F243 is specifically designed
for Digital Motor Control. This device combines a 16 bit fixed-point DSP core with
micro-controller peripherals in a single chip solution that is part of a new generation
of DSPs called DSP controllers[15]. This DSP controller is built with a Harvard
architecture, where the data and the instructions occupy separate memories and travel
over separate buses[16]. Because of this dual bus structure, the processor can fetch,
simultaneously, an instruction and a data operand. Pipelined operation of instructions
and data transfer is thus possible, resulting in higher instruction throughput rate[4].
This DSP controller is capable of executing 20 million instructions per second.

This DSP controller offers the following:
• 12 × PWM (Pulse Width Modulation) outputs. Six of these will be utilized to
drive the three-phase MOSFET bridge inverter on the motor controller board.
• UART (Universal Asynchronous Receiver and Transmitter), this allows for
communication to occur between the PC and the motor controller. Therefore,
data acquisition, debugging and fault logging are realized.
• 2 × fast A/D (Analogue to Digital) converters with 10-bit resolution make the
computation of accurate, real-time phase current measurements possible.
• Many more features that will be mentioned through the course of this report.
2001 Thesis Project A11 Gareth S Roberts

Figure 3.2. The existing motor controller board

B. The Power Electronics Design: three half-bridge circuits combine to form a
three-phase full-bridge inverter. The semi-conductor switches are high quality
MOSFETs that feature sufficient switching efficiency and blocking voltage for
applications of this nature. Within the DSP controller, the software generates three-

phase sinusoidal signals. These are then converted to 6 PWM signals in the DSP, one
for each MOSFET on the full-bridge inverter. Because the PWM signals are square
waves of varying duty-ratio, we can use the MOSFETs to amplify the PWM
waveform to significant voltage levels that the induction machine can operate off.
PWM generation through the software design is discussed in Chapters 5 and 7.

3.3. Current sensing module

The implemented current-sensing module consists of two current transducers. Because
the stator windings of the motor are a three-phase wye connection, we can use the
following relation to find the other unknown current magnitude:
0 = I
a
+ I
b
+ I
c
(3.1)
Where I
a
, I
b
and I
c
are the three-phase stator currents.

2001 Thesis Project A12 Gareth S Roberts
However, application of an effective current sensing module requires the designer to
consider that the DSP A/D converters operate within a voltage range of 0 to +5V. The
problem with this is that the currents sensed by the transducers are sinusoidally

oscillating between +2.5V and –2.5V. Therefore, a DC offset of +2.5V will have to be
continually added to the current signal to ensure that the current does not drop below 0.
Furthermore, the amplitudes of these signals would be greater than +2.5V.
Consequently, we would need to insert resistors on the bus to attenuate the current signal
appropriately. The existing motor controller applies all of this.

Figure 3.3. The current sensing module [17]

The added 2.5V offset is subtracted from the A/D conversion result in the PWM service
routine of the controller’s software (see Chapter 7).

3.4. The speed sensor


On the shaft of the rotor is an encoder. The encoder generates 500 pulses per revolution
in a “square-wave” format. Furthermore, the encoder generates two pulses, A and B,
which will allow the DSP controller to detect the direction of the rotor; the B pulse lags
the A pulse by 90
0
in the positive direction. The DSP controller detects rising and falling
pulses on its interrupt pins; therefore, the DSP controller is effectively detecting 2000
pulses per revolution. Based on this, the software section of the design must interrupt the
speed of the rotor based on the number of pulses it receives. The rated speed of the
induction motor used in this thesis project is 1500rpm, which is 25 rps. Therefore, the
DSP controller will receive:
2001 Thesis Project A13 Gareth S Roberts
(2000 pulses per revolution) × 25 (revolutions per second)
= 50 × 10
3
pulses per second at rated speed.

Every time a pulse is detected, the existing integer number in the free-running counter of
the DSP controller is latched into a register that the software design can read (T2CNT).
Therefore, if the software design compares a “new count”(the current value latched in the
T2CNT register) to an “old count” (the previous value), the following formula can be
applied to calculate the speed:
Speed = Clock rate ÷ (encoder rate × (“new count” – “old count”)) (3.2)
[(revolutions per second) = (counts per second) × (revolutions per pulse) × (pulse per count)]

If the induction machine was rotating constantly at the rated speed, the count difference
between consecutive encoder pulses will be (the clock speed is 20 MHz):
Count difference = 20 MHz (counts per second) ÷ (50 × 10
3
pulses per second)
= 400 counts per pulse.
If we now apply formula (3.2):
Speed = 20 MHz / (2000 × 400) = 25 rps

Also, the detection of a pulse means that the rotor has progressed by:
(360
0
per revolution) ÷ (2000 pulses per revolution) = 0.18
0
per pulse.

Considering the rate that pulses are detected, the resultant resolution of the positional
angle of the rotor seems to be more than adequate for torque control for this project. If
the resolution of the rotor angle was not satisfactory, the software design would have to
interpolate between the pulses. This is discussed in the software section (Chapter 7).

2001 Thesis Project A14 Gareth S Roberts
4. The Induction Machine

4.1 The fundamental operating principles for an induction
motor

An induction motor is an asynchronous AC (alternating current) motor. The least
expensive and most widely used induction motor is the squirrel cage motor. The major
reason why these machines are so robust and inexpensive is that no external current is
required inside the rotor to create the revolving magnetic field. An induction machine
consists fundamentally of two parts: the stator (the stationary part) and the rotor (the
moving part). For a three-phase induction machine (this will be used in this thesis
project), three-phase sinusoidal voltages are applied to the windings of the stator. This
creates a magnetic field. Because the voltages differ in phase by 120
0
with respect to
each other, a revolving magnetic field is created that rotates in synchronism with the
changing dominant poles around the cylindrical stator.

The rotor, which, for a squirrel-cage rotor consists of copper bars in a cylindrical format,
‘follows’ the created revolving magnetic field. As a consequence, a voltage is induced in
the rotor bars that is proportional to the relative angular speed of the magnetic field (this
is referenced to the angular speed of the rotor). Because a voltage is induced, magnetic
fields are created around the rotor wires. The two generated magnetic fields (in the rotor
and stator) interact to generate a force that is also proportional in magnitude to the
relative angular speed of the magnetic field. Torque is equal to force multiplied by the
radius of the cylindrical stator. Therefore, the resultant torque applied by the rotor is
proportional to the relative speed of the magnetic field with respect to the speed of the
rotor.

4.2 The Electrical principles of an Induction motor

The induction machine is an electrical device. The electrical properties that are of
particular interest to this thesis project are the stator and rotor’s resistance and
inductance, as well as the magnetizing inductance. During steady state, the induction
motor can be modeled in a per phase representation seen in figure 4.1.
2001 Thesis Project A15 Gareth S Roberts


Figure 4.1. The per phase representation of an induction motor in steady state [17]

These parameters are important for the control strategies that will be presented in chapter
5. The induction machine used in this thesis project has the following electrical
parameters:
E = rated phase voltage, 127 V
rms

P = power rating, 500W and 0.67hp
p = Pole pairs, 2
r
s
= stator resistance, 4.495 Ω
r
r
’ = rotor resistance, 5.365 Ω
x
s
= stator inductance, 16 mH
x

r
’ = rotor inductance, 13 mH
x
m
= magnetizing inductance, 149 mH
M
nom
= rated Torque, 3.41 Nm
J = rotor of inertia, 0.95 × 10
-3
kg
●
m
2


Hence, the full-load current for this three-phase motor can be calculated using the
following approximate equation:

I
FL
= 600 × P
H
/ E (4.3)
= 600 × 0.67 / 220
= 1.82 A