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DEVELOPMENT OF HIGH PERFORMANCE INDUCTION
MOTOR DRIVES
by
GOLAM RASUL CHOWDHURY, B.S.E.E., M.S.E.E.
A THESIS
IN
ELECTRICAL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
IN
ELECTRICAL ENGINEERING
Approved
Accepted
May, 1994
f"t'G
Bos ACKNOWLEDGMENTS
7/ ~ql( JVo. ,//I would like to express my respect and gratitude to Dr. M. Giesselmann for his
'~ 'Ji(J, 2--constant guidance, continuous encouragement, and valuable suggestions and supervision,
throughout the entire progress of this work. I would also like to thank Dr. John Craig and
Dr. William Marcy for serving on my thesis committee. Appreciation goes to the staff of
the Pulsed Power Laboratory of Texas Tech University, for their friendly cooperation .
.. 11
CONTENTS
ACKNOWLEDGMENTS .. 11
ABSTRACT Vlll
LIST OFT ABLES IX
LIST OF FIGURES X
LIST OF ABBREVIATIONS xu
CHAPTER
I. INTRODUCTION 1
Adjustable Speed AC Motors Drives 1
Brief Review of Existing Technology 3
Scope of the Thesis 5
Organization of the Thesis 7
ll. POLYPHASE INDUCTION MOTOR 8
Introduction 8
The Polyphase Induction Motor 8
Basic Principle of Operation of Induction Motor 9
Torque in an Induction Motor 11
The Concept of Rotor Slip 11
Frequency of Rotor Circuit 12
Induction Motor Equivalent Circuit 13
111
ill. SPEED CONTROL OF INDUCTION MOTORS 22
Introduction 22
Methods of Speed Control for Polyphase Induction Motors 22
Speed Control by Pole Changing 23
Speed Control by Changing the Line Frequency 24
Speed Control by Changing the Line Voltage 25
Speed Control by Changing the Rotor Resistance 26
Selecting an Adjustable Speed Drive 26
Control System for Adjustable Frequency Drive 27
Sinusoidal Pulse Width Modulation (PWM) Switching Scheme 27
Square Wave Modulation Scheme 28
Space Vector Pulse Width Modulation 29
Advantages of Space Vector PWM Over Sinusoidal PWM 33
IV. FUNDAMENTALS OF ADJUSTABLE SPEED INDUCTION MOTOR DRNES 41
Introduction 41
Basic Block Diagram of Induction Motor Drive 41
AC to DC Converter 42
Static Frequency Converter: Generation of Adjustable Frequency AC Power 43
Safety Circuit and High Voltage Isolation 44
PWM Generation 45
IV
V. DEVELOPMENT OF INDUCTION MOTOR DRIVES WITH REAL TIME PWM CONTROL
Introduction
Z180 Microprocessor Based Real Time Drive
Experimental Results
51
51
51
53
Design using a PWM Coprocessor and a Digital Signal Processor 53
Basic Block Diagram of the Drive 54
Texas Instrument's TMS320C26 Based KIT 54
TMS320C26 Digital Signal Processor 55
DSK Assembler 56
DSK Debugger 56
Hanning TC 11 OG 17 AP PWM Chip 56
Pin Description of the PWM Chip 57
PWM Chip Structure 57
Hardware Interface 58
Data and Control Buses 59
Writing the Control Word 60
Reading the Status Word 60
Writing Data 60
Reading Data 61
Modulation Strategy 61
v
Calculating the Phase Voltages 62
Transformation of Input Voltages 63
Angle Incrementing 63
Enabling Pulse Generation 64
Normalizing the Parameter Values 64
Managing the Modulator 67
Polling Mode 68
Interrupt Mode 68
Hardware and Software Test Tools 69
Experimental Results 71
VI. DYNAMIC MODELING OF VECTOR DRIVE 88
Introduction 88
Space Phasor of Rotor Current 89
The Stator and Rotor Flux-Linkage Space Phasors in Their Own Reference Frames 91
The Rotor Flux-Linkage Space Phasor in the Stationary Reference Frame 92
Electromagnetic Torque Production in an Induction Motor 92
Electromagnetic Torque in Reference Frame Fixed to the Rotor Flux-Linkage Space Phasor' 93
Stator Voltage Equations inn the Rotor-Flux Oriented Reference Frame 95
Simulation of Vector Drive 96
Performance Analysis of the Vector Drive 98
VI
Vll. CONCLUSIONS 107
REFERENCES 108
APPENDIX
A. DYNAMIC C PROGRAM TO GENERATE PWM SIGNALS 110
B. ASSEMBLY PROGRAM TO INITIALIZE THE HANNING 116 PWMCHIP
Vll
ABSTRACT
Two microprocessor-based compact drives for three-phase induction motors were
built and tested. Real time pulse width modulated waveforms were generated to drive the
inverters using a microprocessor and a PWM modulator chip. This dissertation discusses
the design, implementation, and testing of the drives and gives experimental results.
Dynamic modeling of a vector controlled drive was also undertaken. The
performance analysis of the complete closed loop system incorporating the vector
controlled drive and the three-phase induction motor was carried out using Microsims'
Design Center Version 6.0. The results of the simulation are also presented.
Vlll
LIST OF TABLES
5 .1. Overview of Pins List of the Hanning PWM Chip
5.2. The Operation of the 8-bit Bus Mode
5.3. The Operation of the 16-bit Bus Mode
5.4. The Functions of the 16 Control Bits of the Status Word
5.5. The Functions of the 16 Status Bits of the Status Word
5.6. Write Address (WAD) for the Parameter Values
5. 7. Read Address (RAD) of the Parameter Values
IX
72
73
74
75
76
77
78
LIST OF FIGURES
2.1. Sketch of Squirrel-Cage Rotor
2.2. Cutaway View of Wound-Rotor Motor
2.3. Transformer Model of the Induction Motor
2.4. Resulting Rotor Equivalent Circuit
2.5. Final Per-Phase Rotor Equivalent Circuit
2.6. Per-Phase Equivalent Circuit for the Induction Motor
3.1. Torque-Speed Characteristics of a Wound-Rotor Induction Motor
3 .2. Simplified Three-Phase Inverter Bridge
3.3. Three-Phase Sinusoidal PWM Waveforms
3 .4. Square-Wave Modulation Scheme
3.5. Space Vector Diagram
3.6. Reference Voltage and Inverter States Representation
3.7. Mean Inverter Output Voltages by Space Vector PWM
4.1. Induction Motor Controller Basic Block Diagram
4.2. High Voltage DC Supply
4.3. Simplified Diagram of IR-2130 Demo Board
4.4. PCB for High Voltage Isolation
5.1. Basic Block Diagram of the Prototype Controller Incorporating the Little Giant
5.2. Measured Line-to-Line Voltage and Line Current of the Motor Driven by the Z 180 Based Controller
X
16
17
18
19
20
21
34
35
36
37
38
39
40
47
48
49
50
79
80
5.3. Basic Block Diagram of the Prototype Controller Incorporating the Hanning PWM Chip and TI DSP 81
5.4. The Pin Configuration of the Hanning PWM Chip 82
5.5. PWM Modulator Structure 83
5.6. External Connections for 8-Bit Bus Operation 84
5.7. The Switching Times Around a Switching Period 85
5.8. The Overall System Hardware Configuration using the Hanning PWM Chip and TI DSP 86
5.9. Measured Line-to-Line Voltage and Line Current of the Motor Driven by the Controller Based on the Hanning PWM Chip and TI DSP 87
6.1. Cross-Section of an Elementary Symmetrical Three-Phase Machine 99
6.2. The Relationship Between the Stationary and Rotating Reference Frames I 00
6.3. Schematic of the Rotor-Flux Oriented Control of an Induction Motor Drive 10 I
6.4. Block Diagram of the System Incorporating the Vector Controlled Drive and a Three-Phase Induction Motor 102
6.5 Block Diagram of the Motor Model and Dynamic Model of Induction Motor in the General Reference Frame 103
6.6 Mechanical Model of the Motor and Model for 3-to-2 Phase Transformation 104
6.7 Mechanical Model of the Load 105
6.8. Results of Simulation of the Complete System Incorporating the Dynamic Models of the Vector Controlled Drive and a Three-Phase Induction Motor 106
Xl
LIST OF ABBREVIATIONS
V a.b,c - Three-Phase Stator Voltages (120° phase shift)
- Synchronous Speed in rad/s
Bs - Stator Magnetic Flux Density
Br - Rotor Magnetic Flux Density
s - Slip of the Motor
- Amplitude Modulation Ratio
vd - DC Bus Voltage
-V,.q - Reference Voltage Vector
a. - Angle Around the Periphery With Respect to the Rotor Winding
9r - Rotor Angle
- Speed of the rotor reference frame ( COr = d9/dt )
- Stator Flux-Linkage Space Phasor "'"
-
- Rotor Flux-Linkage Space Phasor "'' -
Te - Electromagnetic Torque Production in the Motor
- Stator Voltage Space Phasor in the Rotor Flux-Oriented Space Phasor utvfr -
Rs - Resistance of a Stator Phase Winding
Lm - Magnetizing Inductance
Ls, Lsi - Self- and Leakage Inductances of the Stator, Respectively
Lr, Lri - Self- and Leakage Inductances of the Rotor, Respectively
Xll
Plfll -
DPlfll=
PlflO =
DPHIO=
PHIADD=
TAUS
TTOT
TMIN
Voltage component Ua
Voltage component Ub
Phase angle, upper half
Frequency, upper half
Phase angle, lower half
Frequency, lower half
Difference phase angle, Upper half
Tum-off time
Blanking time
Tum-on time
VORTL - Switching frequency scale value
TST ART = Start of processing cycle
Xlll
CHAPTER I
INTRODUCTION
Adjustable-Speed AC Motor Drives
An electric motor is an electromagnetic conversion device that translates its input
electrical energy into output mechanical motion. In motion control applications, the prime
competitive candidates in electrical machines are de machines, induction machines,
synchronous machines, stepper motors, and switched reluctance motors. To a unified
machine analyst, the generic behavior of all the machines is the same. A de machine is
essentially an ac machine internally, where commutators and brushes function as
elements of a position-sensitive mechanical inverter. Here, the orthogonal disposition of
field mmf and armature mmf is the prime reason for enhanced speed of response. This
type of machine has been traditionally favored in electric motion control applications.
Induction motors are widely used in industry because of their low cost, high reliability,
and rugged construction. When operated directly from supply line voltages (60Hz utility
input at essentially a constant voltage), an induction motor operates at a nearly constant
speed. But, in industry, there has long been a demand for control of speed, torque, or
position with long-term stability. The de motor has satisfied some of these requirements.
In particular, the separately excited de motor has been used mainly for applications where
there was a requirement of fast response with high performance. However, de motors
have certain disadvantages, which are due to the existence of the commutator and the
brushes. That is, they require periodic maintenance; they cannot be used in explosive or
1
corrosive environments and they have limited commutator capability under high-speed.
high-voltage operating conditions. AC motors such as the squirrel-cage induction motors
are brushless and have a robust construction, which permits reliable maintenance free
operation at high speed. Their simple rotor construction and small dimension compared
with de motors result in a lower cost motor and a higher power/weight ratio.
Unfortunately, the induction motors are inflexible in speed when operated on a
standard constant-frequency ac supply. The synchronous speed of an induction motor is
determined by the supply frequency and the number of poles for which the stator is
wound. The induction motor, under normal operating conditions, runs slightly below
synchronous speed. For intermittent operation at reduced speeds and light loads, stator
voltage control of the induction motor is satisfactory. However, efficient wide-range
speed control of the cage-rotor induction motor is only possible when an adjustable
frequency ac supply is available. Consequently, in this thesis, attention is mainly
concentrated on the adjustable-frequency method of variable-speed ac drives. One
important application of these drives is in the process control by controlling the speed of
fans, compressors, pumps, blowers, and the like. The ultimate goal of this research
project was to develop real time pulse width modulation, PWM, based high performance
drives by using the advances of microcomputer technology. The EPROM based drive
previously developed was not based on real time PWM technique. This thesis includes a
detailed description of the design, hardware implementation, and test of the drive
performance. To test the performance of the drive, a three-phase 1/3 hp 4-pole induction
motor was used.
2
Brief Review of Existing Technology
Although the induction motor is superior to the de machine with respect to size.
weight, efficiency, maximum speed, reliability, cost, etc., because of its highly non-linear
dynamic structure with high dynamic interactions, it requires more complex control
schemes than, say, a separately excited de machine. In the past, the various technologies
for speed control of ac machines often required the use of auxiliary rotating mechanical
devices such as clutches, gears, and pulleys. Speed control using mechanical devices was
reasonably effective, but presented some major problems. These mechanical devices
required constant maintenance, adjustments, and replacements, which in turn increased
the cost of the control system. Moreover, the overall system efficiency was reduced due
to heat and friction losses associated with the mechanical drives. So, using mechanical
drives was not the most desirable and cost effective method of speed control.
Due to the inherent problems of using mechanical devices, it was necessary to
fmd a way to control the input of the motor rather than the output. In recent years, the
development of power electronic systems has opened many doors in the arena of motor
control. Thus, the auxiliary mechanical devices have now been replaced by solid-state ac
drive systems using various types of power semiconductors operating as electrically
controllable switches. High efficiency is attained because of the low "on-state"
conduction losses when the power semiconductor is conducting the load current and the
low "off-state" leakage losses when the power semiconductor is blocking the source, or
load, voltage. The transition time between the blocking and the conduction states, and
vice versa, depend on the type of power semiconductor used; but times range from 150 JlS
3
for a large thyristor to 50 ns for a field-effect transistor [1]. Recently, manufacturers have
assembled more than one power semiconductor in a single package, or module. The use
of such a module reduces the number of necessary heat sinks and electrical
interconnections. Various combinations of devices, for example, thyristors and diodes,
IGBTs and diodes are assembled in a common package. For low currents, complete
power circuits, made-up of, for example, six transistors and six feedback diodes, have
been arranged into a three-phase bridge circuit. The selling price of these modules and of
the basic power semiconductors themselves has been declining as the market expands.
Another major factor in the ac drive technology is the availability of
microprocessors for the control of ac drive systems. Microprocessors, specifically Digital
Signal Processors (DSPs), operate at an adequately high clock frequency to complete
their calculations in sufficient time to directly control the gating of the power
semiconductor switches in a three-phase bridge circuit operating from an intermediate
DC voltage derived from the utility supply.
These rapid technological advancements and declining pnces for power
semiconductor devices and microprocessors, coupled with a demand for a high
efficiency, adjustable speed control for both existing and newly installed equipment, have
led to the world-wide application of adjustable-frequency controllers for ac motors.
4
Scope of the Thesis
The research conducted at Texas Tech University was to develop motor drives
for three-phase induction motors that can ultimately be integrated into intelligent power
modules. The main function of these power modules was to control the switching of the
power semiconductor devices used as switches in the three-phase inverter circuits. The
power modules are constructed in hybrid technology. The frrst-generation devices
contained a six-pulse, three-phase bridge that consists of either six BIT's, MOSFET's, or
IGBT' s. Also included in the first-generation devices were integrated drive circuits and
current-limiting circuitry, as well as an over-temperature alarm output.
The second-generation devices used advanced power semiconductors like the
power MOSFET and IGBT. The second-generation devices also contained drive logic
and isolated power supplies. Additional circuitry provided protection for over-current and
over-temperature conditions as well as blanking time of the semiconductor switches.
The third-generation devices used EPROMs as the central part to generate PWM
signals. Here, space vector modulation technique was used to create PWM signals. The
EPROM is programmed with a ftxed set of PWM data. Thus the EPROM based drive was
not based on real time PWM generation.
The main objective of this work was to design and implement three-phase
induction motor drives with real time PWM control by using the advances in
microcomputer technology. As a frrst part of the project, a prototype controller
incorporating a Z 180 microprocessor was developed. The microprocessor was
' programmed using a host computer downloaded via an RS-232 interface to generate real
5
time PWM signals to control the gating of IGBT switches. The space vector modulation
technique was used to generate PWM signals.
A second prototype controller incorporating a general purpose microprocessor
(TMS320C26) in combination with a special "PWM-coprocessor'' (HANNING
TCIIOG17AP) was built and tested. The "PWM coprocessor" is capable of operating in a
quasi standalone mode or in close contact with the controlling microprocessor for real
time PWM generation and field oriented control. The operating principle of the PWM
generator chip is also based on the above mentioned principle.
Dynamic modeling of drive performance was performed using the evaluation
version of MicroSim's Design Center System 3, release 6.0 software package. This
provides a new structured, multilevel approach to dynamic drive modeling using a
graphical user interface.
Prime areas of improvements due the application of microprocessor or digital
technique are:
a. Cost reduction in control electronics,
b. Real time PWM scheme,
c. Optimized PWM scheme and improved performance,
d. Improved reliability due to the reduction of the number of components,
e. Standard universal hardware is required and the only changes are to the
software, which is very flexible and can be easily modified,
f. Digital transmission require a minimal amount of cabling and is very tolerant to
noise; it eliminates drift and electromagnetic interference problems,
6
g. Centralized operator communications, monitoring, and diagnostics.
Organization of the Thesis
The thesis is divided into seven chapters. Chapter I introduces the general theory
and background of adjustable speed control of induction motors. It also gives a brief
review of existing technology of speed control. Chapter ll introduces the induction motor
and the underlying principles of operation of the induction motor. Chapter III discusses
about the various methods of speed control of a three-phase induction motor and various
modulation techniques. Fundamentals of adjustable speed induction motor drives are
focused on in Chapter IV. This chapter discusses the various components of an induction
motor controller. The design and testing of the controllers are discussed in Chapter V.
Chapter VI discusses about the dynamic modeling of a vector controlled drive. The
results of the simulation of a complete closed loop system incorporating the vector
controlled drive and a three-phase induction motor are presented in this chapter.
Conclusions and some suggestions for future research are presented in Chapter VII.
7
CHAPTERll
POLYPHASE INDUCTION MOTOR
Introduction
The emphasis in this chapter is on understanding the theory and principle of
operation of the induction motor, and methods of speed control. The theory and principle
of operation will aid in deriving the equivalent circuit for the induction motor. The
equivalent circuit, in tum, is helpful in deriving the dynamic model of the induction
motor and the complete motor drive. There are a number of ways in which the speed of
an induction motor can be controlled. The objective is to choose the best suitable one.
The Polyphase Induction Motor
An induction motor has two main parts: a stator and a rotor. The rotor is separated
from the stator by a small air gap. The rotor voltage, which produces the rotor current and
rotor magnetic field, is induced in the rotor windings instead of being physically
connected by wires. The stator of a three-phase induction motor consists of three-phase
windings which are distributed in the stator slots displaced by 120 electrical degrees, with
respect to each other. Polyphase induction motors fall into two categories, depending on
the rotor construction. They are the wound rotor and the squirrel-cage rotor types. The
squirrel-cage rotor consists of a stack of laminations. It has electrically conducting bars
inserted through it, close to the periphery in the axial direction, which are electrically
shorted at each end of the rotor by end rings, thus producing a cagelike structure. This
also illustrates the simple, low-cost, and rugged nature of the rotor. Figure 2.1 shows a
sketch of a squirrel-cage rotor [2].
The wound rotor has a three-phase winding similar to that in the stator and is
wound for the same number of poles as the stator winding. The rotor winding on the
8
wound-rotor terminates in slip rings mounted on the rotor shaft. The rotor winding is
normally shorted through brushes riding on the slip rings. Therefore, wound rotor
induction motors have their rotor currents accessible at the stator brushes. Figure 2.2
shows a cutaway view of a complete wound rotor induction motor [2].
Basic Principle of Operation of Induction Motor
The operation of a three-phase induction motor is based on the principle of
Faraday's law of electromagnetic induction and the Lorentz force on a conductor. If a
balanced set of three-phase sinusoidal voltages at a frequency f = ro /27t is applied to the
stator, it results in a balanced set of currents, which establishes a flux density distribution,
Bag in the air gap with the following properties:
1. it has a constant amplitude, and
2. it rotates at a constant speed, also called the synchronous speed, of Clls radians
per second.
The synchronous speed in a p-pole motor, supplied by frequency f, can be obtained as 2ro
ro =- rad/s (2.1) s p
which is synchronized to the frequency f of the applied voltages and currents to the stator
windings. In terms of revolutions per minute (rpm), the synchronous speed is
n =60~= 1201. (2.2)
s 21t p
The air-gap flux Cl>ag' due to flux density Bag• rotates at a synchronous speed relative to
the stationary stator. The rotating magnetic field passes over the rotor bars (which are
also stationary initially), and according to Faraday's law of induction, induces a voltage in
them. The relative motion of the rotor compared to the stator magnetic field produces the
voltage in the rotor bar. Mathematically, Faraday's law is given below [3]. dcp
eiNJ = -N dt . (2.3)
9
Equation 2.3 states that if a flux passes through a coil with N turns, a voltage will be
induced in the coil that is directly proportional to the rate of change of flux with respect
to time. The negative sign is the result of Lenz's law, which states that the induced current
is always in a direction to oppose the action that produces it.
The second principle of operation is based upon the Lorentz force [3]. The
Lorentz force states that, if a current carrying conductor is placed under the influence of a
magnetic field, then a mechanical force is induced on the conductor. The induced force is
given by
F =i(lxB} (2.4)
where i is the magnitude of current in the conductor, 1 is the length of the conductor, and
B is the magnetic flux density vector. Equation 2.4 can also be expressed in the following
form
F = ilBsin9 (2.5)
where 9 is the angle between the conductor and the flux density vector. So, a torque is
produced, due to interaction of the air-gap flux and the rotor current, and the rotor starts
running. In this case, it is the rotating air-gap flux which ultimately produces the rotation
of the rotor, and hence the rotor starts running in the same direction of the rotating air-gap
flux and tries to catch up. But the speed of an induction motor can never be the same as
the synchronous speed of the rotating air-gap flux. Because, if it were the case, then there
would be no relative motion between the rotating rotor and the air-gap flux. With no
relative motion, the induced voltage on the rotor bars would be zero, which in turn means,
there would not be any rotor currents. Consequently, there would not be any torque
produced and the motor would ultimately stop. So, the maximum speed of an induction
motor can be very close to the synchronous speed, but it can never reach exactly the
synchronous speed.
10
Torque in an Induction Motor
The torque in an induction motor is produced by the interaction of air-gap flux
and rotor current. The induced rotor voltage produces a rotor current in the rotor bars.
Since the rotor assembly is inductive, the rotor current lags behind the rotor voltage. The
current flowing in the rotor circuit produces a rotating magnetic field Br. The induced
torque in the motor is defined as [2]:
t,_~ = kB xB .,., , s (2.6)
where Bs and Br are the stator and rotor magnetic flux density, respectively.
If the rotor were turning at synchronous speed, then the rotor bars would be
stationary relative to the magnetic field and there would be no induced voltage. Hence,
with no rotor induced voltage, there would be no rotor current and consequently, no rotor
magnetic field. With no rotor magnetic field, the induced torque would be zero, and the
rotor would slow down as a result of friction losses. An induction motor can thus speed
up to near synchronous speed, but it can never exactly reach synchronous speed.
The Concept of Rotor Slip
The voltage induced in a rotor bar of an induction motor depends on the speed of
the rotor relative to the rotating magnetic field. Two terms are commonly used to defme
the relative motion of the rotor and the magnetic fields. One is slip speed, defined as the
difference between synchronous speed and rotor speed [2].
nslip = nsync - n,. (2.7)
where
nslip = slip speed of the motor,
nsync = speed of magnetic field (synchronous speed),
nm = mechanical shaft speed of rotor.
11
The other term used to describe the relative motion is slip, which is the relative speed
expressed on a per unit or a percentage basis. That is, slip is defined as [2] n,up
s= (xlOO%), (2.8) nJYnC nnnc -n,.
s = · (xlOO%). (2.9) nsync
So, at synchronous speed of the rotor s = 0, while s = 1 if the rotor is stationary. All
normal motor speeds fall somewhere between these two limits. The mechanical speed of
the rotor shaft in terms of synchronous speed and slip can be expressed as
n,. = (1- s )nJY"C (2.10)
Frequency of Rotor Circuit
The voltage and frequency in the rotor of an induction motor depend upon the
slip. If the rotor is at standstill, then the rotor currents will have the same frequency as the
stator currents. However, if the motor runs at synchronous speed, the frequency of the
rotor currents will be zero. For speeds between the synchronous speed and standstill, the
frequency of the rotor currents is directly proportional to the difference between the
synchronous speed and the speed of the motor. Therefore, the rotor frequency can be
expressed as [2]:
/,=sf (2.11)
where f is the stator supply frequency and s is the slip. Remembering the defmition for
synchronous speed, equation 2.11 can be expressed as
f _ _L(n -n ) r - 120 sync "' •
(2.12)
12
Induction Motor Equivalent Circuit
The equivalent circuit of the polyphase induction motor is very similar to the
usual transformer equivalent circuit, because the induction motor is essentially a
transformer with a rotating secondary winding. As in a static transformer, the primary or
stator current establishes a mutual flux that links the secondary or rotor windings, and
also a leakage flux that links only the primary winding. This leakage flux induces a
primary emf which is proportional to the rate of change of primary current. Its effect may
be represented, in the usual manner, by a series leakage reactance, X 1, in each stator
phase as shown in Figure 2.3 [2]. R 1 is the stator resistance per phase and (R 1 + jX 1) is
the stator leakage impedance per phase. The mutual flux in the air gap induces slip
frequency emfs in the rotor. The voltage drop across the stator leakage impedance causes
the air gap emf per phase Et, and the mutual flux per pole to decrease slightly as the load
is applied to the motor. The resultant stator current, I 1, is composed of the magnetizing
current, Im, and the load component of the stator current I2. which cancels the
magnetomotive force (mmf) due to the rotor current.
As in a transformer the mutual flux in an induction motor links both the stator and
the rotor. This is represented by the magnetizing reactance Xm. In addition, the leakage
fluxes are represented by leakage reactances. Core losses are represented by the core
resistance Rc. Xm and Rc together form the magnetizing circuit.
In deriving the rotor equivalent circuit, the actual squirrel-cage rotor winding is
considered to be replaced by an equivalent short-circuited rotor winding. Then it is
referred to the primary according to the usual transformer procedure of referring
secondary quantities. However, some changes are necessary to account for the fact that
the secondary winding is rotating. This is being derived in the following.
13
At standstill, the induced emf per phase in the equivalent rotor is equal to f:r1, and
the rotor frequency equals the supply frequency to the stator. If the rotor slip is s, the
rotor emf is
E2 = sE,
and the rotor frequency and rotor reactance per phase are
where L2 is per-phase rotor inductance.
At standstill;
Where E; and x; are the rotor emf and rotor reactance, respectively, at standstill.
(2.13)
(2.14)
(2.15)
If R2 is the equivalent rotor resistance per phase and X2 is the equivalent rotor
leakage reactance per phase, then the rotor current is given by [2]:
For a slips;
E2 12=--
R2 + jX2 .
- R2 .. -+jX., s •
(2.16)
(2.17)
Equation 2.16 implies that at low slip the rotor resistance predominates and the
rotor current varies linearly with slip. At high slip, the rotor reactance predominates and
the rotor current approaches a steady value. Figure 2.4 shows the resulting rotor
equivalent circuit, and Figure 2.5 shows the fmal per phase rotor equivalent circuit.
One last transformation is required to produce the final equivalent circuit for an
induction motor. In a transformer, the currents, voltages, and impedance on the secondary
side can be referred to the primary side by a transformation using the turns ratio. The
14
same type of transformation can be perfonned on the induction motor's rotor equivalent
circuit. using the effective turns ratio ae, the transformed rotor quantities are listed below:
(2.18)
(2.19)
(2.20)
Finally, the complete per-phase equivalent circuit for the induction motor is shown in
. 2 ' 2 Ftgure 2.6 where X2 = ae X2 and ~ = ae ~.
15
Figure 2.1. Sketch of Squirrel-Cage Rotor
16
Figure 2.2. Cutaway View of Wound-Rotor Motor
17
Xl
+
El
Rl=p,.ll'la.,.y w1nc11ng ,.•s•sta.nce R,.=seconcla.,.y wlncl;ng ,..s.sta.nce Xl=p,.II'IG.'"Y Lea.ka.ge ,.ea.c:ta.nce X2=sec:oncla.,.y lea.ka.ge ,.ea.cta.nce Xl'l=l'la.gnetlzJng ,.ea.cta.nce Rc=,.esu;;ta.nce a.ccount1ng for co,.e losses
Figure 2.3. Transformer Model of the Induction Motor
18
rc___. Jrffi._x_r_' ___
Rr r=sEr'
Figure 2.4. Resulting rotor equivalent circuit
19
jXr'
Rr/s
Er=sEr'
Figure 2.5. Final per-phase Rotor Equivalent Circuit
20
11 R1 -+
E1 ! Vo
Rc r2/s fr---------------~--------'
Figure 2.6. Per-phase equivalent circuit for the induction motor
21
CHAPTER Ill
SPEED CONTROL OF INDUCTION MOTORS
Introduction
Recently there has been a tremendous surge in the application of induction motors
In motion control systems. Historically, ac machines, such as the induction and
synchronous types, have been favored for constant speed applications. In the last two
decades, ac motion control technology has grown with the advent of modem solid-state
drives. In this chapter various methods of controlling speed of induction motors are
discussed, and fmally an attempt is made to select the best one suitable for an adjustable
speed drive. Control systems for adjustable speed drive are also discussed in this chapter.
Methods of Speed Control for Polyphase Induction Motors
The normal operating range of a typical induction motor is confmed to less than 5
percent slip, and the speed variation over that range is more or less directly proportional
to the load on the shaft of the motor. Even if the slip could be made larger, the efficiency
of the motor would become very poor, since the copper losses are directly proportional to
the slip of the motor [2].
There are two possible ways by which the speed of an induction motor can be
controlled. One way is to vary the synchronous speed keeping the slip constant. The other
technique is to vary the slip of the motor for a given load. Each of these approaches will
be taken up in more detail below.
The synchronous speed of an induction motor is given by 120/
n = . sync p
So the only ways in which the synchronous speed of the motor can be varied are
1. by changing the electrical frequency and
22
(3.1)
2. by changing the number of poles on the machine.
Slip control may be accomplished by varying either the rotor resistance or the terminal
voltage of the motor. Each of these techniques are discussed below in brief.
Speed Control by Pole Changing
There are three major approaches to changing the number of poles in an induction
motor [2]:
1. the Method of Consequent Poles,
b. Multiple Stator Windings, and
c. Pole Amplitude Modulation (PAM).
The method of consequent poles relies on the fact that, the number of poles in the stator
winding of an induction motor can easily be changed by a factor of 2:1 with changes in
the coil connections. So, with this method the speed change is in the ratio of 2:1. The
traditional approach to overcoming this limitation is to employ multiple stator windings
with different number of poles and to energize only one set at a time. It is clearly
understood that multiple stator windings increase the expense of the motor. Also
energizing only part of the stator results in a poor weight to power ratio.
In PAM, a multiple set of poles is achieved in a single stator winding where the
resulting number of poles can be in the ratios other than 2:1. The number of poles in a
winding can be switched simply by changing the connections at the six terminals, in the
same manner as in the method of consequent poles.
23
Speed Control by Changing the Line Frequency
According to the relationship, n'1'1C = 120// p, the rate of rotation of the stator
magnetic field (synchronous speed) of an induction motor will change in direct
proportion to the change in electrical frequency applied to the stator. The synchronous
speed of the motor at rated conditions is called base speed. By changing the electrical
frequency applied to the stator of an induction motor, it is possible to adjust the speed
either above or below the base speed. However, to ensure safe operation, it is important to
maintain certain voltage limits as frequency changes. This is discussed below.
A static converter (inverter) which delivers a voltage with adjustable frequency to
a motor must also vary the terminal voltage as a function of frequency in order to
maintain proper magnetic conditions in the core. In practice, magnetic devices usually
operate near saturation in order to give maximum utilization of the core material. The
magnitude of the voltage applied to the motor plays an important role in utilizing the core
as the frequency changes. When running at speeds below the base speed of the motor, the
terminal voltage applied to the stator should be decreased linearly with decreasing stator
frequency. If it is not done, the steel in the core of the motor will saturate resulting in
excessive magnetization currents and iron losses.
To understand the necessity for voltage reduction, recall that an induction motor is
essentially a transformer with a rotating secondary rotor. As with any transformer, flux in
the core of an induction motor cab be found from Faraday's law as [2]:
v( t) = - N dcp . dt
Solving for the flux cp gives
ell=-~ J v(t }dt =- ~ J vm sine«dt
v cp = _....!!!,_ cos rot
CJlN
Where v m is the peak amplitude of the supply voltage.
24
(3.2)
(3.3)
(3.4)
Note that the electrical frequency (oo) appears in the denominator of the above
expression. Therefore, if for example, the electrical frequency applied to the stator
decreases by 10 percent while the magnitude of the voltage applied to the motor remains
constant, the flux in the core of the motor will increase by about 10 percent and the
magnetization current of the motor will increase. In the unsaturated region of the motor's
magnetization curve, the increase of magnetization current will also be about 10 percent.
However, in the saturated region of the motor's magnetization curve a 10 percent increase
in flux requires a much larger increase in magnetization current. Induction motors are
normally designed to operate near the saturation point on their magnetization curves, so
the increase in flux due to a decrease in frequency will cause excessive magnetization
current to flow in the motor.
So, whenever the frequency falls below the rated frequency of the motor, it is
customary to decrease the applied stator voltage in direct proportion to the decrease in
frequency and thus the applied voltage/frequency ratio must be held constant. This mode
of operation is known as constant volts/hertz ratio or simply "volts/cycle." The
magnetization current will then be unaffected and will not reach excessive levels.
When the frequency applied to the motor exceeds the rated frequency, care should
be taken in increasing the voltage level. Otherwise, if the applied voltage is too high,
--there might be insulation breakdown in the stator windings.
Speed Control by Changing the Line Voltage
The torque developed by an induction motor is proportional to the square of the
applied voltage. The voltage applied can not be increased too far beyond the rated value,
otherwise it will cause insulation breakdown. So, though this method is simple, the speed
of the motor may be controlled over a limited range by varying the line voltage. This
method of speed control is sometimes used on small motors driving fans.
25
Speed Control by Changing the Rotor Resistance
In wound rotor induction motors, it is possible to control the speed by inserrting
extra resistances into the rotor circuit of the motor. This will change the torque-speed
chracteristics, since the ratio ~ determines the steady-state behavior. A typical torques
speed chracteristics curve for a wound rotor motor is shown in Figure 3 .1.
In industry applications, squirrel-cage type of induction motors are commonly
used. Therefore, only squirrel-cage induction motors are considered only for this research
project.
Selecting an Adjustable Speed Drive
The problem in selecting an adjustable speed drive IS to choose the
system/method that can most economically provide the required range of speed with the
desired accuracy and speed of response. The adjustable frequency supply by static
frequency converters can provide the best adjustable speed drive for the following
reasons:
1. It is possible to adjust the speed of the motor either above or below the base
speed.
2. A properly designed adjustable frequency drive can be simple and flexible.
3. It is particularly attractive in multimotor systems when large number of small
ac motors are supplied simultaneously with the same frequency and voltage.
The advent of modem solid-state technology and VLSIIULSI circuits, and sophisticated
computer-aided design techniques have added new dimensions to the design and
implementation of reliable, low cost, and simple adjustable frequency drives. For these
reasons, the adjustable frequency method of speed control has been selected to control the
speed of an ac motor.
26
Control Systems for Adjustable Frequency Drive
Modem methods of static frequency conversion have liberated the induction
motor from its historical role as a fixed speed machine, but the inherent advantages of
adjustable frequency operation cannot be fully realized unless a suitable control
technique is employed. The choice of control strategy is vital in determining the overall
characteristics and performance of the drive system. However, it is to be noted that, in
order to vary the speed of the motor, it is necessary to control both the frequency and
voltage applied to the motor.
The most common way is to use an inverter bridge, shown in Figure 3.2[4], that
consists of six switches that connect each motor tenninal to either the positive or the
negative rail of a constant de voltage source. Some basic considerations related to
different possible modulation techniques, to control the switching, are summarized and
investigations are made to select the best suitable one.
Sinusoidal Pulse Width Modulation (SPWM) Switching Scheme
The pulse width modulation technique is quite simple and is illustrated in Figure
3.3[5]. The objective of SPWM three-phase inverters is to shape and control the three
phase output voltages in magnitude and frequency with an essentially constant input de
voltage V d· To obtain balanced three-phase output voltages in a three-phase SPWM
inverter, a triangular voltage waveform is compared with three sinusoidal control voltages
that are 120 degrees out of phase as shown in Figure 3.3a. It can be seen in Figure 3.3b
that the pulses in the output waveforms have a sine weighting equivalent to the reference
waveform. That is, for each phase, if the respective control signal is high compared to the
triangular wave, the top switch of the phase is closed. On the other hand, if the signal is
low, the bottom switch is closed instead. For each phase, the fundamental component of
the output voltage is of the same frequency of the respective sinusoidal control voltage.
27
Thus, in order to produce a sinusoidal output voltage waveform at a desired frequency, a
sinusoidal control signal of the same frequency is compared with the triangular wave.
The frequency of the triangular wave establishes the switching frequency of the inverter.
The peak value of the phase to neutral voltage, Van (of the fundamental
frequency) of a SPWM inverter varies linearly with the amplitude modulation ratio rna as v
VG/1 = m, f , (rna< 1). (3.5)
Therefore, the line-to-line nns voltage at fundamental frequency can be written as
.J3 Vu = T2 VG/1 (3.6)
.J3 = 2Jim,Vd (3.7)
= 0.6123m,Vd (3.8)
Where the amplitude modulation ratio is defined as the ratio between the peak value of
the controlling sinusoidal voltage to the peak value of triangular wave v
m = control G •
V,,.;g (3.9)
Square Wave Modulation Scheme
In the square wave switching scheme, each switch of the inverter legs is ON for
one half cycle ( 1800) of the desired output frequency. This results in an output voltage
waveform as shown in Figure 3.4[5]. From Fourier analysis, the peak value of the voltage
of the fundamental frequency of a phase can be obtained for a given input V d as [5]:
v = ~ vd . (3 .1 O) Gil 1t 2
So, the fundamental frequency line-to-line rms voltage component in the output can be
obtained as .J3 4 vd
v ----u- J21t 2
(3.11)
= 0.18Vd. (3.12)
28
In all these equations vd is the de bus voltage.
In the square wave mode of operation, the inverter itself cannot control the
magnitude of the output ac voltages. The applied voltage must be of the correct value in
relation to the output frequency (constant v/f ratio), and in this case must be controlled by
varying the de bus. This requires a voltage regulating stage prior to the inverter bridge.
From the above discussion, the SPWM technique of variable frequency drive
seems to be more attractive and has been taken into consideration in implementing a
variable frequency drive. Previously, at Texas Tech University, a complete variable
frequency drive has been designed and implemented employing SPWM technique. An
improved version of the SPWM technique, is the Space Vector Pulse Width Modulation
which is discussed below.
Space Vector Pulse Width Modulation
Recent developments in the PWM inverter technology have primarily been in the
area of digital control circuitry and real time microprocessor based waveform generation.
For digital and microprocessor based systems, a modified strategy (of classical SPWM)
known as space vector PWM has certain advantages. In this section some basic features
of space vector PWM are discussed.
The three-phase inverter is constituted by six switches and there are eight possible
inverter states: six active states and two zero or idle states. In correspondence to each
configuration, the six switches have a well defined state: on or off. So, all the possible
inverter configurations can be identified by three bits, one for each inverter leg. For each
leg the bit is "1" when the upper switch is closed and "0" when the lower switch is closed
instead. The states-bits representation is shown below.
29
STATE (a) (b) (c)
state 0 0 0 0
state 1 1 0 0
state 2 1 1 0
state 3 0 1 0
state 4 0 1 1
state 5 0 0 1
state 6 1 0 1
state 7 1 1 1
The principle of space vector modulation is based on a two-dimensional (a, ~)
representation of the voltages. The vector corresponding to the eight states can be placed
in the a, ~axes as shown in Figure 3.5[6]. The states as shown above defme six sectors
which are of use in locating the voltage vector. The three machine voltages are
represented by a voltage reference vector V ~ . There are eight possible states available for
this vector according to eight switching positions of the inverter, which are depicted in
Figure 3.6 [4].
The eight inverter states of table 3-1, can be written as the following:
2 {j(k -1)7t ) - -
3vd ex
3 k = 1,2 ... 6.
v* = (3.13)
O,k = 0,7
-Thus, the voltage reference vector V ~ can be synthesized solely by a combination of
these eight states. For a sufficiently high switching frequency, the reference voltage
vector V ~ is assumed to be constant during one switching period. As a consequence, in a
time average sense, the voltage reference vector V ~ in a switching period T s' can be
approximated by two non-zero voltage inverter states, each for a certain amount of time:
v ~·r; = v*.~ + V:+l.~+t· 30
(3.14)
In other words, the reference voltage vector V ~ is realized, in an average sense. by
computing the duty ratio for the two voltage vectors ¥: and V'=+t which are adjacent to
V n1. Let, ~ and ~.1 be the amount of time spent on V'= and VA:+t• respectively, that can be
calculated as follow.
For switching period T, and for a reference voltage vector in sector I, it follows
that [6]
Jr t 1i+T2 r
vn~.dt = J ~.dt+ J~.dt+ ]Yo.dt (3.15) 0 0 7j 7j+7i
- ~ - -Where V0 corresponds to V7 or V8 which are null voltage vectors. If V1 and V2 are
constant, it follows that
- - -v ret·~=~ .J"; + v2.7; (3.16)
which is same as equation 3.14 for k = 1. In a, ~ axes the above equation becomes
r;v ~[c~sy] = ~ f2v11[1] + 7; f2vd[c~s60:] smy V3 0 V3 stn60
(3.17)
0< 'Y < 60°.
Hence,
sin( 60° - 'Y) ~=a . o 7;
Sln60 (3.18)
siny T;=a. o~·
sm60 (3.19)
In order to keep the switching frequency constant, the remainder of the switching period
is spent on the zero states
T.,+Tg=To=~-r;-7; (3.20)
and
(3.20)
In Figure 3.6a, the inverter states are shown, and in Figure 3.6b the reference voltage
vector synthesis is depicted.
31
For the sectors 11-VI, the same rules apply. This results in a definite switching
order according to Figure 3.6c. To obtain the minimum switching frequency of each
inverter leg, it is necessary to arrange the switching sequence in such a way that the
transition from one state to the next is performed by switching only one inverter leg. If,
for example, the reference vector sits in sector I, the switching sequence has to be
... 0127210127 .... This results in a definite switching order according to Figure 3 .6c.
To compare the results of the space vector PWM with the sinusoidal PWM
concepts, the mean values of the line to neutral voltages over one switching cycle are
evaluated. For sector I, the three mean values can found as [7]
v. = vd (T. + T.. _ To + To ) 1 T 1 2 2 2
s
= ]Ja~sin(y+60°)
v. = vd (r.. _ T. _ To + To ) 2 T 2 1 2 2
s
= 2a V, sin( y - 30°)
- vd ( To To) v. =- -T.-T,--+-3 T 1
- 2 2 s
=-~.
(3.21)
(3.22)
(3.23)
(3.24)
(3.25)
(3.26)
Taking into account the necessary changes in the other sectors, for the fundamental
period
~(t) = a"Y, sin cot 0~00
= A sin( rot+ 30°) 3o0ScJXS9oO
~(t) = v;(t- T I 3) = ~(t+ T I 3).
Hence, the line-to-line voltages are
~2(t) = ~(t)-V2 (t) =*Vdsin(ov+30°)
~2 ( t) = v;3 ( t - T I 3) = V31 ( t + T I 3).
32
(3.27)
(3.28)
(3.29)
(3.30)
(3.31)
Both the line-to-neutral voltage and the line-to-line voltages are shown in Figure 3.7[4]. It
turns out that, with space vector PWM, the line-to-line voltage seen by the machine is
sinusoidal, as expected. However, the phase-to-neutral voltage is not sinusoidal.
In a symmetrical three-phase inverter involving sinusoidal PWM, the peak value
of line-to-line voltage is
J3 V,I =-mvd.
2 (3.32)
Comparing the line-to-line voltages according to the SPWM and space vector PWM[7] 4
m =-a. (3.33) 3
The maximum value for a sinusoidal PWM is a = J3. This leads to the maximum 2
modulation index in the case of space vector PWM 2
mmu = J3 = 1.15.
This is approximately 15 percent more than with SPWM.
Advantages of Space Vector PWM Over Sinusoidal PWM
(3.34)
1. It was shown in the previous discussion that with space vector modulation a
modulation index of 1.15 can be reached without any constraints, whereas in sinusoidal
PWM, notches are suppressed and low-order harmonics occur in the range of
overmodulation m> 1. In addition, the harmonic content of the inverter output voltages
and currents is less for space vector modulation method than for its counterpart.
2. Space vector modulation is quite useful in digital systems because the
microprocessor can calculate on line the times Tk, Tk+1' and To and transfer them to a
hardware modulator.
33
!Torque-Speed Diagam ~+Pole lnductioo Motor as a fln:tioo of R rotl
250.-----------------------------------------~
200
150 'E' z -i ~ 100
50
0~--------~--------~----------~----~--~ 0 500 1000
Spat [RPM]
1500
1- R_ra.0.10 - R_ra.o.:~> - R_ra.o.so I
2000
Figure 3.1. Torque-Speed Characteristics Curve of a Wound-Rotor Induction Motor
34
+Y ---------------~----------------~-----------------&----------
Phose A Phose 8 Phose C
Induction Motor
Figure 3.2. Simplified Three-Phase Inverter Bridge
35
+Y
0 1
f•J "AN
~- T v.,
o~~~~~~~~-L~~u_~l_, 11BN
~T v.,
o~~~~~~~~~~~~r~,
0
,. ,. ,.
~ .... ..,funct.mental "U.l
r.: ~.__ l"'
~
(bJ
"'• - 0.8, "'' - 15
• t.Ll!C,. ,.,, ,,., + 2)
I.~ ... 2M • f (21nf + 1)
Harmonics of (1
(cJ
~
Figure 3.3. Three-Phase Sinusoidal PWM Waveforms
36
I ~ v.,
r t
;, - II AN +
J DA+ o •• De ... rA+ v~J I [·~· TA-v, I· tao• ~
rA-uBN
DA- D•- De-
J I' tao•
"I ,.._
r •• N liA r._
• tl]f
A B c IICN
f•l
Jrc•l A I rc. Vu.. Tc-v, • tl]l
uu 1 1
' .-,,
hlnnonics 0 1 fA fa (Ill
(cJ
Figure 3.4. Square-Wave Modulation Scheme
37
Scaarl )
Figure 3.5. Space Vector Diagram
38
b)
b.
u I
I ._
: • J I . I I • I T
• I I •
0 1 ~ 7
Figure 3.6. Reference Voltage and Inverter States Representation a) Inverter Configuration b) Voltage Vector Reference Synthesis in a Switching Period c) Optimum Pulse Pattern of Space Vector
39
Line-to-line Voltage
Phase Voltage Fundamental phase voltage
!! • JV Sectors
Figure 3.7. Mean Inverter Output Voltages by Space Vector PWM
40
CHAPrERIV
FUNDAMENTALS OF ADJUSTABLE-SPEED
INDUCTION MOTOR DRIVES
Introduction
The emphasis of this chapter is on understanding the fundamentals of a three
phase induction motor drive implemented at Texas Tech University as a part of this
research project. This will help in understanding the drive at the block diagram and
subsystem level. In most applications, squirrel-cage induction motors are commonly
used. So, the drive implemented is for a squirrel-cage induction motor.
Basic Block Diagram of Induction Motor Drive
The basic block diagram of an open-loop induction motor drive is shown in
Figure 4.1. An adjustable-speed drive system basically consists of an adjustable
frequency converter, control circuitry to control the converter, and an electric motor
which drives a mechanical load at an adjustable speed. The system block diagram shows
all the subsystems and how they interact with each other. The frequency converter
supplies an adjustable-frequency three-phase voltage to the motor. It operates by
switching between the positive and negative sides of a high voltage de bus system. The
de bus voltage is generated by a ac to de converter. The switching of the frequency
converter is controlled by PWM signals. To ensure safety and high voltage isolation the
driver includes an International Rectifier driver chip and opto-isolators. The subsystems
of the driver are discussed below.
41
AC to DC converter
To power the induction motor, a relatively large de voltage was created from a
three-phase 208V utility supply. Figure 4.2 shows the schematic of the ac to de converter
used. This high voltage de voltage is connected to the power semiconductor devices of
the frequency converter. This voltage is also referred to as the bus voltage. In most acto
de converters the input stage converts the input ac voltage into an unregulated de bus
voltage. A full bridge rectifier in combination with a capacitor was used to generate the
high voltage de. The bridge rectifier is a modular one incorporating six rectifier diodes.
The six diodes are arranged to form a simple three-phase rectifier.
The equations used to design the de power supply are given below
J3 Vu(rms) =~Vd (4.1) 2-v 2
2J2 vd = T3~1(rms) (4.2)
Where ~1 and Vd are the line-to-line supply voltage and de bus voltage, respectively. The
de power supply was designed so that no voltage regulation was required. By using a
three-phase rectifier, it was possible to keep the filter capacitor at a reasonable size as
compared to a single-phase rectifier. This type of configuration proved to be cheap,
rugged, and inexpensive.
Since, the power supply is transformerless, care should be taken when switching
on the main power supply. Otherwise, the initial high inrush current may cause serious
damage to the rectifier. For this reason, an auto transformer was used to gradually
increase the voltage to its rated value eliminating the possibility of initial inrush current.
However, in the case where an auto transformer is not available, it is recommended to use
variable series resistance with each of the main utility supply phase to limit the initial
inrush current.
42
Static Frequency Converter:Generation of Adjustable Frequency AC Power
The function of the frequency converter is to generate adjustable frequency ac
power for the motor. The frequency converter synthesizes a sinusoidal output voltage for
the motor by alternately switching the output to either side of the high voltage de bus.
Previously, rotating frequency converters were used for many years. Now-a-days
rotating converters have been replaced by solid-state static frequency converters. In order
to obtain high efficiency in a static frequency converter, it is essential to use solid-state
switching devices which are either on or off. In the on-state, the switching device
approximates an ideal closed switch having zero voltage drop across it and a current that
is determined by the external circuit. If the solid-state switch can be triggered from the
off-state into the on-state by a low power control signal, the device can be used in the
converter circuit for the generation of adjustable-frequency voltage and current. The
MOS bipolar devices, which include the Insulated Gate Bipolar Transistor (IGBT), and
MOS-controlled Thyristor (MCT), can be turned on and off with a MOS gate and have
excellent switching characteristics. An electrical signal applied to their gates control their
switching. This feature allows these devices to be used readily in circuits supplied from a
de source. They do not require any auxiliary components, like inductors, capacitors, and
sometimes auxiliary thyristors, that are required by thyristor inverters, because thyristors
cannot be turned off on command.
An international Rectifier IR 2130 demo board was used to build a static
frequency converter. A simplified diagram of the converter is shown in Figure 4.3. The
board contains six IGBT switches which constitute the three-phase converter and an
International Rectifier's IR-2130 driver chip.
43
Each phase of the induction motor is connected to either side of the de bus via the
IGBT switching devices. By applying a control voltage to the gate of the IGBTs in a
specific pattern, a sinusoidal output voltage can be synthesized as each phase of the
motor is switched to either side of the de bus. The output frequency is determined by the
rate at which the converter switches are gated.
Safety Circuit and High Voltage Isolation
It has been mentioned that, the IGBT switches operate between the positive and
the negative sides of the high voltage de bus supply. On the other hand, the control
circuitry of the drive is fully digital and requires only a 5V de supply. So, to ensure
safety, the high voltage part of the drive requires isolation from the low voltage part.
Also, the induction motor is inherently inductive. So, the currents flowing in the motor
cannot change instantaneously. This requires a safety measure to be taken while
switching the motor phases between either sides of the high voltage de bus system. The
safety measures taken in implementing the drive are discussed below.
Anti-Parallel Diodes. Since the induction motor in inherently inductive, an
alternate path must be provided for the motor current when the switch is turned off. The
path is provided by connecting a diode in anti-parallel to each of the IGBT switches as
shown in Figure 4.3. However, when regeneration occurs, the roles of the switch and the
return current diodes are reversed. The diodes now return the regenerated power to the de
bus and the switching devices carry the magnetizing current. The power return to the de
bus will increase the de voltage above its normal value. Therefore, precaution must be
taken to consume this regenerated power to prevent excessive voltage from building up
and damaging the circuit. It should be noted that no power can flow back to the utility
across the three-phase rectifier.
44
Blanking Time. The two IGBT switches in each phase of the frequency converter
are switched in such a way that, they are never on simultaneously to avoid short
circuiting of the high voltage de bus. So, for a particular time interval, when the upper
switch of a phase is on, then in the next switching interval, the tum-on signal of the other
(lower) switch of the same phase is delayed until the upper switch is turned back to off
state. Thus, in practice the two switches of the same phase are both off for a short time
interval, known as blanking time. This blanking time is provided by the International
Rectifier IR-2130 driver chip. The chip has a built in blanking time of 2 J.lS [9].
High-Voltage Isolation. The isolation between the high voltage and low voltage
de is required to keep the system electrically separate while allowing functional
interconnections of the system. Six HCPL-2200 optocouplers were used for this purpose.
An optocoupler is an optically coupled logic gate that combines a GaAsP LED and an
integrated high gain photon detector. One feature of the particular detector used here is a
three-state output stage and built in schmitt trigger with hysteres. The three-state output
eliminates the need for a pull-up resistor and allows for direct drive of the data buses. The
actual mask used to make the printed circuit board (PCB) for the high voltage isolation is
shown in Figure 4.4.
PWM Generation
The function of pulse width modulation is to shape and control the three-phase
output voltages in magnitude and frequency with an essentially constant input voltage. It
has already been mentioned in the previous chapter that among the various possible
PWM techniques space vector PWM was selected for our project. The basic features of
the PWM techniques have also been discussed in the previous chapter.
45
Employing the technique of space vector PWM, two prototype real time based
motor controllers have been developed and tested. These are discussed in the following
chapter.
46
High Voltage DC Supply
Keypad
1------~
Frequency Converter
SPWM Generation
Microcontroller
3-pnase Induction Moto!'"
Liauia Crysta l Display
Figure 4.1. Induction motor controller basic block diagram
47
8A/250V
1 .......
1500uF n 450V 680k 280-340V DC
T -T
1' I
l 8A/250V -• • • ~
Figure 4.2. High voltage de supply
48
~~~· ______,, I ----4~~~---~ ___,! I !'
I I
~ 11:---c_;-?RD~- i ! f-M-lO-~D 2 27 ~ II
I I
H~n-a> D 3 26---~-+-.
Hin-)J ~ 4 0 25!11 Lin-to ~5 ~ 24.._......_.
Lin-a> a; 6 ,.- 23:
FUJI 6M8175L -060
Lin-)> a 7 '---+--.;
l-out ~ 8 N +-+-~~--+--.~ ~--~a1 9 ~~==J=~==~-4--====r~:
I a i1o
' .....__-~~11 _L 12
I L.....-----4 -----13
Figure 4.3. Simplified Diagram of IR-2130 Demo Board
49
.:~r· .:Jr· .:Jr .:Jr .:1r .:11· .................. ~ Figure 4.4. PCB for High Voltage Isolation
50
CHAPTERV
DEVELOPMENT OF INDUCTION MOTOR DRIVES
WITH REAL TIME PWM CONTROL
Introduction
In recent years, there has been increasing emphasis on the use of digital and
microprocessor-based techniques for the generation of PWM waveforms. Among the
several possible methods, such as dedicated analog/digital, dedicated signal processor or
microprocessor methods of implementation, the last one offers several advantages. A
microcomputer-based modulator, if judiciously designed, can provide considerable
simplification of hardware with significant improvement in performance. The hardware
simplification also adds to the reliability improvement. As a result of the research
involving the development of microprocessor-based real time three-phase drives, two
prototype drives were built and tested. This chapter discusses these two drives and shows
experimental results.
Z180 Microprocessor-Based Real Time Drive
A prototype drive using a Z 180 microprocessor-based controller was built and
tested. The Little Giant, a Z180 microprocessor-based miniature control computer made
by Z-World Engineering has the following principal features [ 1 0].
It is a compact (5.6x4.8 inches) single board miniature control computer with:
a. Z180 Microprocessor running at 9.216 MHz clock speed;
b. Power fail detect and warning;
c. Watchdog timer system. The watchdog, if enabled, automatically resets the
board;
d. Up to 256K bytes of EPROM;
51
e. Up to 512K bytes of battery backed RAM;
f. 512 bytes (not K bytes) of EEPROM;
g. Four serial ports;
h. 16-bit parallel port. This can be directly interfaced to many devices;
i. 8-bit high voltage and high current port;
j. Liquid crystal display interface;
k. Eight channel AID converter with configurable input amplifiers;
1. 12-bit DAC with output in the range 0-2.5 volts.
The Little Giant was programmed using the Dynamic C programming language. Dynamic
C allows the user to quickly write, download, and test software for the Little Giant. The
dynamic C runs on an mM-PC or compatible computer and creates a program that is sent
to the target system (down-loaded) through a serial communication link (RS-232). This
program is then tested by executing it on the target system while under the supervision of
the Dynamic C monitor. The complete drive system using the Little Giant is shown in
Figure 5.1. The drive system used the IGBT based static inverter, the IR-2130 driver chip,
and optoisolators as discussed previously in Chapter IV.
A C program was written in dynamic C to generate real time PWM signals using
space vector modulation technique. The function of the program was to digitally control
the six IGBT switches of the inverter. The basic feature of the digital control scheme of
the IGBT switches using 3-bits was discussed in Chapter III. The main features of the C
program are
a. It calculates the switching times Tk, Tk+l' and T0 required to generate
PWM signal;
b. The value of the switching time period T s can be changed on screen; and
c. Using commands from Dynamic C library, the program defines the mode of the
16-bit parallel interface port on the Little Giant.
52
According to the calculated time intervals Tk, Tk+1, and To, the microprocessor
generates the PWM signal. The actual Dynamic C program that generates the PWM
signals is listed in Appendix A.
The switching frequency of the IGBTs can be changed by changing the value of
the switching time period T s· The PWM signal generated by the microprocessor was sent
to the gates of the IGBT switches via the IR-2130 driver chip which provided a built in
blanking time of 2 fJ.S.
Experimental Results
The prototype controller incorporating the Z 180 microprocessor was tested on a
three-phase 1/3 hp 4-pole induction motor. The measured line-to-line voltage and line
current of the motor are shown in Figure 5.2.
Design using a PWM Coprocessor and a Digital Signal Processor
A second prototype controller incorporating a digital signal processor tn
combination with a special "PWM-Coprocessor" was built and tested. The "PWM-Co
processor" is a Hanning TC 11 OG 17 AP chip, which is capable of operating in a quasi
standalone mode or in close contact with the controlling microprocessor for real-time
PWM generation. The operating principle of the PWM chip is space vector modulation.
The objective was to develop an easy to build high performance drive by using the
advances of microcomputer technology. A detailed description of the design,
implementation, and testing of the prototype motor drive is given in the following
sections.
53
Basic Block Diagram of the Drive
The basic block diagram of the prototype motor controller design incorporating
the Hanning PWM chip and a Texas Instrument's Digital Signal Processor (DSP),
TMS320C26 is shown in Figure 5.3. A combination of the same International Rectifier
IR-2130 driver chip with the same IGBT based inverter demo board provides the static
frequency converter. The same six opto-isolators provide total electrical isolation
between the high voltage power electronic stage and the controller.
Texas Instrument's TMS320C26 based KIT
The Texas Instrument's TMS320C26 DSP starter Kit (DSK) was used to control
the PWM Coprocessor in order to generate real time PWM signals. The DSK assembler
and debugger are software interfaces that help to develop, test, and refine DSK assembly
language programs. The DSP starter Kit was programmed using TMS320C26 assembly
language. The assembly program was developed at a host computer, which in turn created
a DSK assembler source file, and then executed by invoking the DSK debugger. An RS-
232 serial communication cable provided the link between the DSK and the host
computer. The main features of the DSK are:
a. TMS320C26 DSP running at 40 MHz,
b. On board system clock generating a 40 MHz clock signal,
c. Analog interface circuit, and
d. On board regulated power supply to generate 5V de from 9V ac.
The DSK is very compact (2.5 x 3.5 inches) and can be easily interfaced with other
circuits. All the data, address, and other control pins of the DSP are readily available to
be interfaced with the outside world.
54
TMS320C26 Digital Signal Processor
Digital signal processors are high speed microcomputers than generally act as
peripheral components to a central processor and help in processing 1/0 signals. A very
dominant member in this family is the Texas Instrument's TMS320C2X series. The key
features of an advanced version of the aforementioned series, the 68-pin TMS320C26
DSP, are [11]:
- 100 ns instruction cycle,
- 544-word programmable on-chip data RAM,
- 1568-word configurable program/data RAM,
- 128K-word total data/program memory space,
- 32-bit ALU/accumulator,
- 16x16-bit parallel multiplier with a 32-bit product,
- Single-cycle multiply/accumulate instructions,
- Repeat instructions for efficient use of program space and enhanced execution,
- Block moves for data/program management,
- On-chip timer for control operations,
- Up to eight auxiliary registers with dedicated arithmetic unit,
-Up to eight-level hardware stack,
- 16 input and 16 output channels,
- 16-bit parallel shifter,
-Wait states for communication to slower off-chip memories/peripherals,
- Serial port for direct codec interface,
- On-chip clock generator,
- Single 5V supply.
55
Faster program execution has been possible in the TMS320 family by using what is
called a modified Harvard architecture, which permits overlap of instruction fetch and
execution of consecutive instructions.
DSK Assembler
The DSK assembler is a simple and easy to interface. The key features of the DSK
assembler are [12]:
Quick: The DSK assembler differs from many other assemblers in that it does not
go through a linker phase to create an output fue. Instead, the DSK uses special
directives to assemble code at an absolute address during the assembly phase. As
a result small programs can be created quickly and easily.
Easy-to-use: Larger programs can be created by simply chaining flies together.
DSK Debugger
The debugger is easy to learn. Its user friendly window and menu-oriented
interface reduces learning time and eliminates the need to memorize complex commands.
The debugger is capable of loading and executing code with single-step, breakpoint, and
run-time halt capabilities [12].
Hanning TC110G17AP PWM Chip
The Hanning TC 11 OG 17 AP is a "quasi space vector modulator" to control three
phase inverters. The key features of the chip are [13]:
a. Three-phase pulse width modulator for ac motors,
b. Pulse pattern generation for a three-phase sinusoidal supply at the required
voltage, frequency, and phase angle,
c. Switching frequencies up to 18 KHz ,
d. Uses space vector modulation,
56
e. Presetable blanking, tum-on, and turn-off times,
f. Transform input voltages from cartesian into polar form, and
g. 8/16-bit bus interface compatible with a range of 8-bit single-chip
microprocessors and digital signal processors.
The Hanning PWM chip is a slave peripheral for generating the PWM control signals for
a three-phase inverter used to supply an induction motor. Besides being closely linked
with the host processor, it can also generate the entire pulse pattern independently,
thereby relieving the host processor from intensive processing and time critical
calculations. The Hanning TC 11 OG 17 AP is manufactured in 2 J.lm-CMOS Gate Array
Technology and is available in a 40-pins plastic DIL or 48-pins PLCC package.
Pin Description of the PWM Chip
The PWM chip used in this project was a 40-pin plastic DIP. The p1n
configuration is shown in Figure 5.4[4] and an overview of the pins list is summarized in
Table 5.1[13].
PWM Chip Structure
In this paragraph, the modulator structure is presented. The simplified block
diagram is shown in Figure 5.5[4] and the following blocks can be identified [13].
Bus Interface
The modulator is connected to the microprocessor (DSP) by the bus interface. It
consists of 16-bit bi-directional data/control buses. The read/write data are temporarily
stored by the bus interface. The temporary register is read or written to by the register
bank through an internal bus. The internal bus interface is able to work in 8 or 16-bit
mode.
57
Register Bank
The parameters used to produce the required pulse pattern (voltage, phase angle,
frequency, etc.) are stored in the register bank.
Calculator Unit
The switching points are calculated by the calculator unit which is an internal processor.
A special algorithm runs two times during each switching period to determine the pulse
width according to the parameters stored in the register bank.
Pulse Logic Unit
The switching times are converted into PWM signals by the pulse logic unit.
Control Unit
The control unit produces the control signals for the remaining parts of the circuits.
Hardware Interface
In order to connect the chip to the DSP, a set of hardware interface signals are
provided. The hardware interface signals are described below.
Reset
The modulator needs a minimum 50 ns reset signal. After resetting, all the internal
registers are in the initial status: the output signals Ul-U3, 01-03 are inhibited, the
calculator is switched off (EIN = 0), the bus interface is set into the 8-bit mode (BUS 16 =
0) and all the registers are cleared.
58
Clock
The chip is equipped with an internal quartz oscillator. If an external clock is
used, then it is connected to the CLK pin of the chip. The maximum clock frequency is
18 MHz. All the output signals (U1-U3, 01-03, INT) are synchronized to the rising edge
of the clock signal.
Data and Control Buses
The interface consists of 16-bit bi-directional data buses (DBO-DB 15), 2 address
bits (AO and AI), and three control input signals ( RD, WR, and CE). The 8-bit and 16-bit
operation mode can be selected by setting the appropriate bit in the control register
(BUS16 = 0 for 8-bit, BUS16 = 1 for 16-bit).
8-bit Bus Mode
After reset the bus mode defaults to 8-bit bus mode. In this mode address bit AO
controls the multiplexing of the lower (DBO-DB7, AO =)and upper (DB8-DB15, AO = 1)
data bytes of the data word. Both bytes may be connected to the 8 data lines of the
modulator chip. When a byte is placed on the bus the remaining byte is automatically
placed in the high Z (impedance) mode. Figure 5.6 shows the external connections for
the 8-bit data bus mode. While transferring data the lower byte (AO = 0) must be written
frrst followed by the upper byte ( AO = 1). The operation of the 8-bit bus mode is shown
in Table 5.2[13].
16-bit Bus Mode
The 16-bit bus mode is selected when bit BUS16 (bit 7 of the status register
discussed later) is set high (1). During 16-bit bus mode all 16 data bits DBO-DB15 are
59
written or read simultaneously. The operation of the 16-bit bus mode is shown in Table
5.3[13].
Interrupt Output
The INT output signal is the chip calculation ready signal, which can be used to
generate the interrupt signal for the DSP.
Power Switches Control Signals
The U1-U3 and 01-03 output signals control the inverter legs power switches.
The U1-U3 control the lower switches and 01-03 control the upper switches.
Current Sign Input Signals
These input signals can be used for compensating the power switches tum off
delay. These signals have to be connected to the 11-13 input pins.
Writing the Control Word
When the control word is written it contains control bits which are used to set
internal functions. The functions of the 16 control bits of the status word are shown in
Table 5.4[13].
Reading the Status Word
Reading the status word enables the internal status to be checked. The 16-bits of
the status word have the functions shown in Table 5.5[13].
60
Writing Data
The parameter values required to generate a specific pulse pattern are written
sequentially according to the write address WAD. Therefore, the write address WAD
must be defmed first. The data bytes or word is then stored in the bus interface register
(A 1 = 0) and an internal write cycle transfers the data to the internal register bank. A
write cycle (internal) may only be executed outside a processing cycle. If the write
register is being used then the WRFLAG bit of the status word is set to high ( 1) and new
values may not be written. WRFLAG must be low (0) before data can be written. After
each write the write address (WAD) is automatically incremented so that the WAD bits
need not be set if consecutive data values are sent. The parameter values are written using
the write address (WAD) as shown in Table 5.6[13]. The normalization of the data
values are shown later.
Reading Data
Internal data may be read after an internal cycle is initiated by setting the read
address RAD and RDSTART bits causing the RDFLAG bit to be immediately set to low
(0). Upon completion of the read cycle data is stored in the internal read register. The
modulator can then read the data via the internal bus interface. The read cycle can only be
executed provided processing or write cycle are not active. The internal values may be
read by means of the RAD address as shown in Table 5.7[13].
Modulation Strategy
The Hanning modulator chip implements space vector modulation with the
switching times positioned symmetrically around a switching period as shown in the
modulation timing diagram of Figure 5.7[4]. The timing diagram shown does not include
61
blanking time. H a phase voltage Un is normalized to ±1, then the times shown in Figure
5. 7 may be calculated as follows [ 13]:
T0 = T/2(1 +Un)
Tu = T/2(1-Un)
T1 = T/4(1-Un)
T2 = T/4(1+Un)
T = 1/fswitch
On time of upper switch,
On time of lower switch,
Time at which the upper switch is turned on during the first
half of a switching period,
Time at which the upper switch is turned off during the
second half of a switching period,
Where fswitch = switching frequency.
The above calculations are done considering the power switches as ideal. In the real life,
some non idealities have to considered, due to blanking time, motor current direction, and
the power switches characteristics.
Calculating the Phase Voltages
The modulator chip produces six PWM control signals to switch the six inverter
power switches. Internally on and off, the modulator is capable of producing the
reference voltage U 1, U2, and U3 with a quasi space vector strategy. As an example, the
complete procedure for the Ut voltage is shown below [13].
U1 (cp) = 2U(sin(cp+ 30°)-1) 0< cp S60 O
Ut =U
U1 ( cp) = 2U (sin( cp - 30°) - 1)
U1(cp) = 2U(sin(cp+ 30°)+ 1)
Ut =-U
60° < cp <120 °
120° < «<> < 180°
0 0 180 < cp < 240
0 0 240 < «<> < 300
62
The other two phase voltages U2 and U3 are derived from U I as:
u2(q,) = ut(«P-1200) U3(cp) = u
1(q,-240°).
The voltage U is calculated by the Ua and Ub values stored in the register bank, as:
U=~U:+Ut.
The value of the phase angle, q,, is also stored in the register bank.
Transformation of Input Voltages
The output voltage vector U may be entered in cartesian form as components U a
and Ub. The internal values the algorithm uses are calculated as follows [I3]:
if U> I then U = I (circle limit)
phi= phi+ arctan(Ub/Ua), phase angle (q,).
If new values of Ua and Ub are not provided then next processing cycle uses the
following values
These values correspond to the last values input so that both U and phi remain the same.
Angle Incrementing
After each processing cycle, that means at twice the switching frequency or twice
every switching period, the internally stored angle phi (cl>) is incremented by the angle
dphi. The derived switching frequency is calculated as follows [I3]:
phi = phi + dphi
f = (2fswitcb)( dphi)/360° or dphi = 360f/(2fswitch)·
It can be advantageous while implementing some control processes to alter the phase
angle by means of stepping it. In order to do this a data value PHIADD (WAD= 6) may
be used to add an angle to phi (phi = phi + phiadd).
63
Enabling Pulse Generation
Pulse generation is enabled, by setting bit EIN to high ( 1) in the control register.
Prior to setting bit EIN all internal data must have already been written. Pulse generation
is disabled by setting bit EIN to low (0) [13].
Normalizing the Parameter Values
Voltage Components <Ua and Ub)
The voltage components Ua (WAD= 0) and Ub (WAD= 1) must be written in 2's
complement format using bit 15 as the sign bit. They are normalized as follows [13]:
U = Uats_o Or U = UalS..O a 215 a 8QOOH
Examples:
Ua Ua
OOOOH 0.0
4000H 0.5
7FFFH 0.99997
8000H -1.0
COOOH -0.5
FFFFH -0.0
Ub is normalized in the same way.
Phase Angle (PHil, PHIO, and PHIADD)
The phase angle phi can be defined by means of the values PHil (WAD= 2) and
PHIO (WAD= 4) and PHIADD (WAD= 6). These values are normalized as follows [13]:
phi= {PHI1t4 .. o*212 + PHI015 .. o}*3600!(6*224) OH <PHil< 6000H.
PHIADD is normalized in the same way as PHI 1.
64
Examples:
PHil PHIO phi
OOOOH OOOOH 00
OOOOH OOlOH 0.000003576°
OOOlH OOOOH 0.01465 0
0800H OOOOH 0
30
OCOOH OOOOH 0
45
1000H OOOOH 0
60
1800H OOOOH 0
90
30000H OOOOH 0
180
6000H OOOOH 360°·
Output Frequency
The fundamental output frequency can be output either as a difference angle or it
may be added to the phase angle phi each processing cycle. In order to obtain a high
output frequency resolution two words DPHII (WAD = 3), and DPHIO (WAD = 5) are
used to determine the difference angle. The difference angle is represented as 2's
complement with bit DPHII12 serving as the sign bit. The normalization is shown below
[13].
f = output frequency (fundamental)
fclk = clock frequency
Nscale = prescaling factor= VORTL + 1.
65
Examples:
With a prescaling factor Nscale of 1 and a clock frequency of 18MHz the
following normalization will result
DPHI1tt..o*212 + DPHI015 .. 4 = f /0.0003492
f = 50Hz => DPHil = 0022H, DPHIO => E3COH
f =-50Hz=> DPifll = lFDDh, DPHIO => 1C40H.
Turn-off (TAUS), Blanking (TIOT), and Minimum Tum-on (TMIN) Times
Only the lower 6-bits (DB5 .. 0) of TAUS (WAD = 8), TIOT (WAD = 9), and
TMIN (WAD = 1 0) are stored and processed by the modulator to calculate the times.
These values are related to the resolution of switching signals [13]
TAUS= TAUS5 .. 0* N ~ea~e/ leUr.
TTOT = TTOT5 .. 0* N ~ea~e/ leUr.
TMIN = 2*TMIN5 .. o* N .ca~el leUr.·
Examples:
fclk = 18MHz, Nscale = 1
TAUS =0010H
TTOT=003FH
TMIN=0030H
=>TAUS= 0.889 J.ls
=> TTOT = 3.5 JJ.S
=> TMIN = 5.33 JJ.S.
Pre-Scaling the Switching Frequency (VORTL)
The inverter switching frequency can be set by dividing the CLK input by means
of a programmable prescaler. The prescale value is VORTL (WAD= 11) and consists of
5 bits (VORTL4 .. Q). The prescaler may be used as follows [13]:
Nscale = VORTL4 .. 0 + 1 fswitch = leUr./(Nscak *1024).
66
Examples: At a clock frequency of 18 MHz the following values results:
VORTI...
OOOOH
OOOlH
OOIOH
OOlFH
Nscale
I
2
3
32
fswitch
17.85 KHz
8.789 KHz
1.034 KHz
549.3 KHz.
The maximum allowable value of VORTI... is 31.
Start Time for a Calculation cycle (TST ART)
Tstart is dependent upon the scaling factor VORTL and must be changed as follows [13]:
TSTART = INT( 512- (322/(VORTL + 1))).
Examples:
VORTL
OOOOH
OOOIH
OOIFH
TSTART
190 = OOBEH
351 = 015FH
501 = OIF5H.
Managing the Modulator
Since the modulator has been designed for different applications, it will be
explained below how to manage it in constant Vlf applications. In addition the two
operation modes: Polling mode and Interrupt mode will be focused on. For a constant
V / f inverter, the voltage-frequency control is obtained by giving to the modulator the
Ua component (Ub = 0) and the output frequency using the differential angle DPHI.
67
Polling Mode
The polling mode is used to write the modulator parameters into the register bank
separately during different switching periods. In this mode, the microprocessor (DSP)
waits for the WRFLAG bit of the status word to be set to low (0). The next parameter
cannot be written until WRFLAG goes to low (0) again. The WAD auto increment mode
can be used and seems to be quite efficient during each register bank write. The register is
incremented after each write automatically, so the next parameter can be written into the
next register address without setting the new address [13].
Interrupt Mode
In interrupt mode, the calculation (processing) cycle and the processor interrupt
signals must be synchronized. This can be achieved, if the processor interrupt signal is
started by the modulator INT signal rising edge. The sequence of operations are the
following [13]:
1. After receiving the interrupt, the program JUmps to the Interrupt Service
Routine (ISR).
2. The microprocessor (DSP) writes the register bank address into the control
register.
3. The frrst parameter is written into the register bank without waiting for the
WRFLAG.
4. After 8-clock pulses, the next parameter can be written into the modulator.
The interrupt service routine has to execute all the necessary instructions between two
calculation cycles.
The simplest running mode is the polling mode. It is a typical asynchronous
communication mode between the modulator and the DSP. The modulator is programmed
in polling mode.
68
Hardware and Software Test Tools
The actual digital control circuitry, incorporating the Hanning modulator chip and
the TI DSP, used for the test and a software program example are presented here. The
DSP works with 40 a MHz clock signal. The overall system hardware configuration is
shown in Figure 5.8. The hardware configuration is constituted by the following main
blocks:
1. TMS320C26 Based Starter Kit,
2. Hanning PWM Modulator,
3. 74LS374 Latches,
4. 74LS04 HEX-Inverter,
5. Inverter Demo Board ( IR 2130 Demo Board),
6. Opto-isolators.
Software
The software interface between the modulator and the DSP is rather simple. The
modulator works with its own algorithm, and needs only the updated parameters and
start/stop signals to be written to it. The parameters can be written into the modulator in
two stages:
Initial Loading Mode
The voltage components, frequency, timing values, etc. (all as initial values) are
written into the register bank.
69
Running Mode
The new values are calculated by the external control algorithm and. thus written
into the modulator in order to achieve the required performance.
Control and data are written into the control and data register respectively. All the
control commands ( like 8-bit/16-bit mode select, start/stop command, etc.) and the data
register bank addresses are written into the control register. The modulator controVstatus
word is written through the parallel port PA6 and the data word is written through the
parallel port PA4. The selection between the controVstatus and data word is achieved by
connecting together the AI address bit of the DSP and the AI input pin of the modulator.
The program was written in TMS320C26 assembly language.
Initial Loading
The initialization procedure is shown in the assembly program listed in Appendix
B. After the reset (hardware), the modulator is in the initial status. The initial loading was
started by setting the 16-bit operation mode and was finished by setting the start
modulator bit (EIN bit) to 1. The write address register was used in the auto increment
mode. Instead of checking the WRFLAG, the DSP enters into a delay loop after writing
each of the parameters into the modulator. The delay loop causes the DSP to enter into a
NOP (no operation) mode.
First, it was necessary to set the WAD register in the control word according to
the frrst parameter address. Second, the frrst parameter value was written into the register
bank. Other parameters were written following the sequence shown in Table 5.6. It is not
necessary to set the WAD register for the other parameters. Only the parameter values
were written into the register bank.
70
Experimental Results
The prototype controller was tested on a three-phase 1/3 hp 4-pole induction
motor. The measured line-to-line voltage and the line current of the motor are shown in
Figure 5.9.
71
Table 5.1. Overview of Pins List of the Hanning PWM Chip
PIN NUMBER NAME FUNCTION PINTYPE
21,40 Vee Supply Voltage Input
1, 10, 20, 31 GND Ground Input
2-18 DBO-DB15 Data bus bit 0 .. 15 Input/output
19 RST Reset Input
22 CLK Clock signal Input
23 CLKO Clock output Output
24 INT Interrupt signal Output
32,28,25 11-13 Current direction Input
33,29,26 U1-U3 Lower transistors control signal Output
34,30,27 01-03 Upper transistors control signal Output
72
Table 5.2. The Operation of the 8-bit Bus Mode
RD WR CE AO AI FUNCTION
X X 1 X X High Z, write disabled
1 1 0 X X High Z, write disabled
0 1 0 0 0 DBO-DB7 =data byte, D88-D8 15 = high Z
0 1 0 1 0 DBO-DB7 =high Z, D88-D815 =data byte
0 1 0 0 1 DBO-OB7 =status byte, 088-0815 =high Z
0 1 0 1 1 OBO-OB7 =high Z, 088-0B 15 =status byte
1 0 0 0 0 Write OB0-087 to data register
1 0 0 1 0 Write 088-0815 to data register
1 0 0 0 1 Write 080-087 to status register
1 0 0 1 1 Write 088-0B 15 to status register
0 0 0 X X Not allowed
73
Table 5.3. The Operation of the 16-bit Bus Mode
RD WR CE AO AI
X X 1 X X
1 1 0 X X
0 1 0 X 0
0 1 0 X 1
1 0 0 X 0
1 0 0 X 1
0 0 0 X X
FUNCTION
High Z, write disabled
High Z write disabled
DBO-DB 15 =data word
DBO-Db15 =status word
Write DBO-DB15 to data register
Write DBO-DB 15 to status register
Not allowed
74
Table 5.4. The Functions of the 16 Control Bits of the Status Word
BIT NAME FUNCTION
0 EIN EIN enables ( 1) and disables (0) pulse calculation and output
I liNT Determines whether the current polarity is controlled externally by
pins 11-13 (0), or internally by control bits IINTl-IINT3 (I)
2 liNT I Current polarity of inverter leg 1, I = positive current
3 IINT2 Current polarity of inverter leg 2
4 IINT3 Current polarity of inverter leg 3
5 Not used
6 TESTFL Testflag must be zero during normal operation
7 BUS16 Used to select 8-bit (0) or 16-bit (1) bus mode
8 WADO Write address bit 0. Bits W AD0-3 determine which data value is to
be written next. THE WRITE ADDRESS IS AUTOMATICALLY
INCREMENTED AT THE END OF EACH WRITE
9 WADI Write address bit 1
IO WAD2 Write address bit 2
II WAD3 Write address bit 3
I2 RADO Read address bit 0. The read address determines which internal
data value is to be read next
13 RADl Read address bit 1
14 RDSTART Start read cycle. A high (I) enables the read function
15 Not used
75
Table 5.5. The Functions of the 16 Bits of the Status Word
BIT NAME
0 WRFLAG
1 RDFLAG
FUNCTION
Write flag indicates whether the write register is clear (0) or
whether it contains data (1). Data may only be written if WRFLAG
is low (0)
Read flag indicates whether a read cycle is complete (0) or
incomplete (1). After flag RDSTART (bit 14 of the control word)
is written RDFLAG must be low (0) before reading the data value
2 CALCFLAG Processing flag indicates whether an internal processing cycle is in
progress ( 1) or whether a read can be executed (0)
3-15 Used for testing purpose only (not specified)
76
Table 5.6. Write Address (WAD) for the Parameter V aloes
WAD3-0 NAME FUNCTION
0000 (0) Ua Voltage component Ua
0001 (1) ub Voltage component Ub
0010 (2) PHil Phase angle, upper half
0011 (3) DPHil FfeQuency,upperhaJf
0100 (4) PHIO Phase angle, lower haJf
0101 (5) DPHIO Frequency, lower half
0110 (6) PHIADD Difference phase angle, Upper half
0111 (7) Not used
1000 (8) TAUS Tum-off time
1001 (9) ITOT Blanking time
1010 (10) TMIN Tum-on time
1011 (11) VORTL Switching frequency scale value
1100 (12) TSTART Start of processing cycle
1101 (13) Not used
1110 (14) Not used
1111 (15) Not used
77
Table 5.7. Read Address (RAD) of the Parameter Values
RADI-O NAME FUNCTION
00 (0) PIDO Phase angle, lower half
01 (1) Plfll Phase angle, upper half
10 (2) u Voltage value
11 (3) Not used
78
HOST PC
LITILE ~ GIANT
TARGET
SYSTEM
I I ~ l
RS-232 COMUNICATION LINK ,, DATA PORT {EXTERNAL)
~ ~
.
-IR.-2130 -OPTO- _., TO
DEMO -- -ISOLATORS MOTOR BOARD --
Figure 5.1 Basic Block diagram of the Prototype Controller Incotporating the Little Giant
79
211U---------------------------------------------------------------------
•
LINE~TO-LINE .VOLTAGE .OF THE MOTOR
I I I
I • : I 1 I I
-2·-~-----------------------------------------------------------------------------------------1 D U(3)
1-IA------------------------------------------------------------------------------------------
lA
I I I I I I I I
LlNE CURRENT OF THE MOTOR '
SEL>>: -1-IA+--------r--------r--------r--------r--------r--------r--------r--------r--------r--------l
Is 5115 11115 15115 21115 25115 31115 35115 -Ills .. 5115 51115 D I ( 11)
Figure 5.2. Measured Line-to-Line Voltage and Line current of the Motor Driven Driven by the Z180 Based Controller
80
HOST PC
I I ..,__..,
RS-232 COMUNICATION LINK=:;
DSK ITARGET SYSTEM
DATA/CONTROL BUS (EXTERNAL)
,, .
PWM
CHIP .... OPTO- ..... .,... ISOLATORS ...
IR.-2130
DEMO BOARD
--_ TO t---~
-MOTOR ..-----~ -
Figure 5.3 Basic Block Diagrani of the Prototype Controller Incorporating the Hanning PWM Chip and TI DSP
81
, e
PWM
Figure 5.4. The Pin Configuration of the Hanning PWM Chip
82
PROCESSOR
INTERFACE
REGISTER BANK
BUS INTERFACE
CALCULATOR
UNIT
PULSE LOGIC UNIT
CONTROL UNIT
Figure 5.5. PWM Modulator Structure
83
INVERTER
INTERFACE
U.l .... ·-··-··············-··-········1
• 1 4(~ PINS 2-9 ARE 080-087 OF' lHE PWt\A CHIP
DSP 080 087
--------------4-_.~, j•:~t :; -:O.l
················································-···············-···-~··· ····-··~ ,') ,Xf!
--------------------~~=~--•4 37e 5 ~c.l. ······························································--r··· ···t··· ........ - ~~
------------------~~~+-..... 6 ~~ _________ _.,_.-+-t-+-+-+-_.7 3~·
----------~~:~~:~~~~--•8 3~ ............................................... ···-~·-· .... L_. ··-i-. - 9 3 -,e
i ! i ! .I r 1 ~ ~~ t ! l l I ---···1··; p 3<:~ : : l : .12 W~ CHIP ~·c.t
l ~ ········-······~ 1 ··~ 2~ i : 14 27. : 1 ,. 2. l:;.;,.· : : ······--·-·-·······-·~ ~.... l ...
: 16 2~ ,___ ____ _...,, "J
~----------._.18 24+ :·Jt '"'"; .. ~L..
?1; PINS 11-18 ARE 080-08.15 OF lHE PWU CHIP • 19
Figure 5.6. External Connections for 8-Bit Bus Operation
84
CAI..CUlAT10N WRITE
INT
01
U1
FIRST HALF PERIOD
T
SECON:> HALF PERIOD
Figure 5.7. The Switching Times Around a Switching Period
85
7
D5P DO-O 7
D5P IV'fo -c>= UJA
7 .q,~
D5P AI_ AO_
7.q,SJ74 ~us -Q.K tO en 20 ... lO""' ~ -;;;. so&ft lOu; 70 .....
II II 10,;.;;; -t= ~ IJ.q,':,,.
10 I" 20.-;; 30'-' ~:;;;
~~ : !~ '---
IOK ~~~~
rf Ill br~ .. r.-+ 010 ...;;;.
~
II II ,,.
W{"C ....._I
I 2 ~; l 3 :; ~
7 -.-.....
-~il ~ c::::::liD
- ___..., 10 f.- .............. II ____.., 12 ll r- f.-
.............. .. ~
IS 2 ---.....
16 ~~ f.- L-<un 17
~~ >---II! f.-
"" 19 2 o- ..-.ot I - 20 21 u- l(JII('II
I II II I _.,....,~~~I
7C.Sl74 doo~ooooo U4 _..,. •-'• .... .,
Yl IIIII I
Figure 5.8. Overall System Hardware Configuration Using the Hanning PWM Chip and TI DSP
86
211U------------------------------------------------------------------------------------------
lool~ ........ - ....
0 0
LINE-TO-LIN~ I( ~~ ~F THE MOTOR -211U•-----------------------------------------------------------------------------------------a U(l)
1-IA------------------------------------------------------------------------------------------o
I I I I I I I
sEL>>: LINE ·cURRENT ·oF THE MoToR , -1-IA+--------~--------~--------~--------~--------~--------~--------~--------~--------~--------I
Is 5115 11115 15115 21115 25115 11115 35115 ~tillS lt5115 51115 a 1(12)
Figure 5.9. Measured Line-to-Line Voltage and Line Current of the Motor Driven by the Controller Based on the Hanning PWM Chip and TI DSP.
87
CHAPTER VI
DYNAMIC MODELING OF VECTOR DRIVE
Introduction
Vector control techniques incorporating fast microprocessors have made possible
the application of induction motor drives for high performance applications where
traditionally only de drives were applied. Torque control of both ac and de machines is
achieved by controlling the motor currents. However, in contrast to a de machine, in an ac
machine both the magnitude and the phase angle of the current has to be controlled. This
means the current vector has to controlled in an ac machine. This is the reason for the
terminology "vector control." In a de machine, commutator and brushes play an
important role in fixing the orientation of the field flux and armature mmf. On the other
hand, in an ac machine the field flux and spatial angle of armature mmf require external
control. In the absence of such an external control, the spatial angles between the various
fields in an ac machine vary with the load and yield unwanted oscillating dynamic
response. The underlying principle of vector control is that, the torque and flux producing
current components are decoupled and the transient response characteristics are similar to
those of a separately excited de machines. Another salient point regarding vector control
is, that the system will adapt to any load disturbances as fast as a de machine. The aim of
this chapter is to derive a dynamic model of the vector controlled drive. To achieve the
total dynamic model, the controller is coupled with a dynamic model of a three-phase
induction motor. The modeling of the system was carried out using Microsim's Design
Center Version 6.0. The dynamic model of the induction motor was developed by Dr.
Giesselmann [ 14].
88
Space Phasor of Rotor Current
The space phasor quantities of an induction motor expressed in different reference
frames will aid in understanding the development of torque in the machine. The torque
equation will form the basis for vector control.
For a three-phase smooth air-gap induction motor, if it is assumed that [15]:
1. rotor windings have an effective turns ratio Nre and
2. there is no zero-sequence rotor current,
then the resultant rotor mmf distribution fr(8, t) produced by the rotor windings carrying
currents ira(t), im(t), and irc(t) can be expressed as follows[15]:
/,.(9,t) = N n![i,..(t )cosa+im(t )cos{ a- 21t/3)+irr(t )cos( a -41t/3)] (6.1)
where a is the angle around the periphery with respect to the axis of the rotor winding ra
as shown in Figure 6.1 [15]. By introducing complex notation, it is possible to express the
above equation as follows:
f, (a ,t) = ~ N .. Re ~ [li .. (t)+ai,. (t)+a\., (t)]e-;a (6.2)
In equation 6.2 the complex quantity multiplied by the e-ja is the rotor space phase
current~'
~ = ~ [i .. (t )+ai,.(t )+ a\,(t )] =~~;a, (6.3)
expressed in the reference frame fiXed to the rotor. The relationship between the
stationary and rotating reference frames is shown in Figure 6.2[15]. In equation 6.2 1, a,
and a 2 are spatial operators, a= ei2"'
3 and a 2 = ei4"
13• The speed of the rotor reference
frame is ro,. = d9,. / dt, where 8r is the rotor angle.
89
The rotor current has two components: direct- and quadrature -axis components.
These two components of rotor current are related to the instantaneous values of the
actual three-phase rotor currents by[ 15]
. {· 1 . 1 . J l = l --l --l ra. "' 2"' 2rc (6.4)
. {3(. . ) ~~ = CV2 lm -Ire (6.5)
2 where c = 3 for the non-power invariant, classical form of the transformation. Thus the
defmition of the space phasor of the rotor currents in the reference frame ftxed to the
rotor is as follows
-ir =ira.+ ji~. (6.6)
For a machine with quadrature-phase rotor windings, ira and ir~ are non-transformed,
actual rotor currents which flow in the rotor windings ra and r~, respectively.
From Figure 6.1, it follows that a= 9-9r, where 9 is the angle around the
periphery with reference to the axis SD. Thus equation 6.2 can be simplified as
follows [IS]
-~" (9 9 t) = ~ N Re[T e-j(e-e.>] = ~ N Re[te-je] (6.7) Jr ' r' 2 re r 2 re r
where (6.8)
is the space phasor of the rotor current expressed in the stationary reference frame fixed
to the stator.
90
The Stator and Rotor Flux -Linkage Space Phasors in their Own Reference Frames
The space phasor of the stator flux-linkages W, can be defmed in terms of the
instantaneous values of the flux linkages of the three stator windings. The total stator
flux-linkages space phasor can be expressed as follows[15]
- _2( 2 ) 'If s - J 'If sA + tl\lf .rB +a 'If 1c (6.9)
where the instantaneous values of the phase-variable flux linkage components are
'V .sA = lilA + M,i,8 + M ),c + M,, cos9,i"'
+M,,cos(9, +2n/3)in, + M,cos(9, +4n/3)irr (6.10)
'11,8 = Lj,8 + M)IA + M),c + Ms, cos(9, +4n/3}i,a
+ M,, cos9,in, + M, cos( 9, + 2x/3)irr (6.11)
"'sC = Lise+ M ),s + M )lA + M, cos( 9, + 2rt/3)i"'
+ M sr cos( 9, + 4x/ 3 ); '*' + M, cos 9 ,i rr. < 6.12)
In these equations, is is the self-inductance of a stator phase winding, M, is the mutual
inductance between the stator windings, and M, is the stator-rotor mutual inductance.
Substituting equations 6.10, 6.11, and 6.12 into equation 6.9 and simplifying the
following space-phasor equation for the stator flux linkages in the stationary reference
frame is obtained[15].
~ - .... - - .i8 'V s = L), + L,i, = L,is + L,i,e ' (6.13)
where L, = l,- M, is the total three-phase stator inductance and Lm is the three-phase
magnetizing inductance, L,. = ~ M,. The stator flux-linkage space phasor describes the
magnitude and phase angle of the peak of the sinusoidal flux distribution in the air-gap.
Following the same procedure for the rotor flux-linkage space phasor ('fl,) in the
reference frame fiXed to the rotor, the following equation results[ IS]
(6.14)
91
where 4 = L, - M, is the total three-phase rotor inductance and ~· is the space phasor of
the stator current expressed in the reference frame fiXed to the rotor.
The Rotor-Flux Linkage Space Phasor in the Stationary Reference Frame
The rotor flux -linkage space phasor in the reference frame fiXed to the rotor is
composed of two components: direct- and quadrature-axis components ('fl ra, 'V tiS). The
rotor flux-linkage space phasor in the rotor reference frame is related to the rotor flux
linkage space phasor in the stationary reference frame ( 'V rd, 'V ) by the same "
transformation e18' as given in equation 6.8 for the rotor current. Thus the following
equation for the rotor flux-linkage space phasor in the stationary reference frame
results[15]
-· • ( • ) j9 "'r = "'rd + l'V rq = "'IQ + l'V tiS e r • (6.15)
By substituting equation 6.14 into 6.15
\ii ~ = ( L,~ + Lm~· }ei9r = L, ( i,ei8r) + L, ( ~'ej9,}
(6.16)
Electromagnetic Torque Production in an Induction Motor
The developed electromagnetic torque in an induction motor can be expressed in
the following vectorial form[ 15]:
~ = C\ii, x~· (6.17)
where under linear magnetic condition C is a constant and \f1, and ~· are the space
phasors of the stator flux-linkages and rotor currents, respectively, both expressed in the
stationary reference frame. Equation 6.17 can also be written in the following form
r; = qv,l~lsinr (6.18)
where l'ii ,j and ~~ are the magnitudes of the stator flux-linkage and rotor current space
phasors respectively and 'Y is the torque angle. When 'Y = 90°, the developed
92
electromagnetic torque in the induction motor becomes similar to the electromagnetic
torque in a de machine. However, in a de motor, the armature current and main flux
distribution are ftxed in space-the former is due to the action of the commutator and
brushes. Thus torque control in de machine can be established independently controlling
the excitation flux and armature current. In an ac machine, it is much more difficult to
realize this principle, because these quantities are coupled. They also depend on the
magnitude, frequency, and phase angles of the stator currents. In addition, it is very
difficult to monitor the rotor current of a squirrel-cage induction motor. These points
have to taken into consideration to develop vector control drive for an induction motor.
Electromagnetic Torque in the Reference Frame Fixed to the Rotor Flux-Linkage Space Phasor
The rotor flux-linkage space phasor in the stationary reference frame flXed to the
stator can be expressed as[15]
'fl~ = lV rej9• = 'f1 rd + j'fl rq = l'fl rlejp, (6.19)
where llfl rl and Pr are the magnitude and phase angle of the rotor flux-linkage space
phasor in the stationary reference frame. The stator current space phasor in the special
reference frame fixed to the rotor flux-linkage is[15]
r = r e- jp, = i + j'i l'lfr s u sy
(6.20)
where~ is the space phasor of the stator currents in the stationary reference frame. In the
special reference frame the rotor flux-linkage space phasor is coaxial with the direct-axis
(x-axis) and thus has only direct-axis component
(6.21)
For a machine with P pole-pairs, the electromagnetic torque in a general reference
frame can be expressed as[15]
T 3PL,.- ~ =- -lit Xl e 2 L T '! sg
r
(6.22)
93
where Lm is the total three-phase magnetizing inductance and Lr is the total three-phase
rotor inductance. In tenns of the direct- and quadrature-axis components of the general
reference frame[ IS]
-i,g = i.u + ji,.
Substituting equation 6.23 in 6.22
T. = ~ P? (w,.;., -w .;u). ,
Substituting equation 6.21 into 6.24
T 3PL,. . =- -\11 I • e 2 L T rr, ,
(6.23)
(6.24)
(6.25)
In the special reference frame under consideration, the rotor flux-linkage space phasor
can be expressed as[ 15]
(6.26)
The rotor magnetizing current <Z:.,) in the reference frame under consideration can be
expressed as[15]
~ v ""' 4 ~ -:- ~ ( )~ 11ft,=-= -l,'lf, +l,\V, = l,\V, + l+a, 1,., Lift Lm
(6.27)
where a,= t is the rotor leakage factor. Lrl and Lr are the rotor leakage inductance and
self-inductance, respectively. The rotor magnetizing current in the special reference frame
has a component only in the real-axis of the special reference frame[15]
~ . .. . 1!J 11ft, = lmrx + Jlmry = 1mrx = '
Lm (6.28)
From equations 6.28 and 6.25
T 3 p I!.n ~~ I; e =- _,lft,r'Y.
2 L, (6.29)
The very important feature of equation 6.29 is that, the electromagnetic torque can be
controlled by independently controlling the flux -producing current component jl,., I and
the torque producing current component isy· The tenns Lm and Lr are constants under
94
linear magnetic conditions. Thus the expression for torque of an induction motor as
shown in equation 6.29 is similar to that of a separately excited de motor.
Stator Voltage Equations in the Rotor-Flux Oriented Reference Frame
In the reference frame fiXed to the rotor flux-linkage space phasor the stator space
phasor voltage can be expressed as[15]
- - ';" df,., dl,., . -:- . -:-u,., - R1l,., + L1 -d + L,. -+ JOl,, L1l,., + JOl,., L,1,.,. (6.30) t dt
From equation 6.27,
(6.31)
Substituting equation 6.31 into 6.30
T. df,., ';" - u,., . ·-=- ( ")( . lr I dll,.,l) I dt +,,.,-If- Jm,.,T,,,.,- T,- T, Jm,.,r,., + dt (6.32)
Where R5 is the resistance of a stator phase winding, r,· is the stator transient time
constant of the machine, r;· = L, , where L, is the stator transient inductance, R,
L, = (L,- L~/ L,), Ts is the stator time constan~ T, = L1 / R,. By resolving equation 6.32
into its real (x) and imaginary axis (y) components, the following two-axis differential
equations are obtained[ 15]
'dill: . - ~ ·. - ( - ') dll,.,l T, + 'v: - + m,,T,,., T, T, dt R, dt
(6.33)
. di usy . ( ') lr I T, _2!.. + i sy = --(J) ,., T, i v: - T, - T, (J) "'' r'mr • dt R,
(6.34)
When the rotor flux {w,) is constant and since w, = L,i,.,, thus under linear magnetic
conditions the rotor magnetizing current ji,, I is also constant. Under these conditions
di
lr I = i and if the term L ~ is neglected, then the above equations can be simplified mr SJ: ' I dt
as follows [ 15]
(6.35)
95
(6.36)
It follows from the above two equations tha~ in the direct-axis voltage (usx> equation. the
rotational voltage is affected by the quadrature-axis stator current (isy) and in the
quadrature-axis voltage equation, the rotational tenn is influenced by the direct-axis
stator current (isx>· Thus the rotor flux (or isx) is not solely controlled by the direct-axis
stator voltage, but also influenced by the quadrature-axis stator current (isy>· Similarly,
the torque producing stator current component is controlled not only by the quadrature
axis stator voltage but also dependent on the direct-axis stator current. This unwanted
coupling is canceled by using a decoupling circuit and thus, the rotor flux is controlled by
Usx and electromagnetic torque is controlled by Usy' which are independent of each other.
This concept is utilized in implementation of the rotor flux-oriented control of the
voltage-source inverter-fed induction motor drive described in the following section.
Simulation of Vector Drive
The schematic of the rotor-flux oriented control of a voltage-source inverter-fed
induction motor utilizing the concepts described above is shown in Figure 6.3[15]. In this
figure, the reference value of the rotor flux is lw ~1 and when it is divided by the
magnetizing inductance, the rotor magnetizing current is obtained, which is equal to the
direct-axis stator current reference isxref· The reference value of the rotor speed ( CJl ~) is
compared with its actual value (roJ and the error serves as input to the speed controller.
The output of the speed controller is the torque reference, which is, however, proportional
to the quadrature-axis stator current reference (;,.q).
The direct- and quadrature axis stator current references are used in the
decoupling circuit. Stator reference current isxref is frrst multiplied by the stator
resistance <Rs) before it reaches a summing node. At the summing node ro,.rL),~ is
subtracted from Ria~. Thus at the ouput side of the summing node the direct-axis stator
96
reference voltage component in the rotor flux-oriented reference frame is obtained.
Similarly, the quadrature-axis stator current reference ts multiplied by the stator
resistance and the rotational voltage component m,.,Lisur~ is added to it to get the
quadrature-axis stator reference voltage component in the rotor flux-oriented reference
frame. The voltage references "un~ and u,q are transformed into the two-axis voltage
components of the stationary reference frame ( uiD~, ".an~), by using the transformation
eiP,, where Pr is the space angle of the rotor flux-linkage space phasor with respect to the
real axis of the stationary reference frame. This transformation is shown below[ 15].
• ( • ) jp UIDnf + )UIQ~ = Uunf + JU~ e '.
By resolving into real and complex parts
(6.37)
(6.38)
(6.39)
These two-axis voltage references are then transformed into their three-phase
reference values by using two-phase to three-phase transformation. Two-phase to three
phase transformation is based on the principle that, in the absence of zero sequence
voltages, the projections of the voltage space phasor on the corresponding axis yield the
instantaneous values of the phase voltages[l5]
usA.nf = Re(u_,n/) = Re(u,Dnof + jurQ~) = u,0~ (6.40)
where ii is the reference value of the stator-voltage space phasor in the stationary .rnf
reference frame[l5],
(6.41)
and (6.42)
97
Performance Analysis of the Vector Drive
To test the performance of the vector drive, it was connected to a three-phase
induction motor and the complete system was simulated using the Design Center
software. The complete block diagram of the system incorporating the vector controlled
drive and the motor used for simulation in the Design Center is shown in Figure 6.4. The
block diagram of the motor model and the dynamic model of the induction motor general
reference frame is shown in Figure 6.5. Figure 6.6 shows the mechanical model and 3-to-
2 phase transformation block model. The mechanical model of the load is shown in
Figure 6. 7. The dynamic model of the induction motor was developed by Dr.
Giesselmann [14]. The results of the simulation are shown in Figure 6.8.
98
Im
Figure 6.1. Cross-Section of an Elementary Symmetrical Three-phase Machine
99
rfJ ~ \ \ \ \ \
\ \ \
\ \ \ \
\ \ \
\
sQ
,,, l,,
\ \ --------------------------•50
Figure 6.2. The Relationship Between the Stationary and Rotating Reference Frames
100
Speed 01111trollcr
Us.rrd
Usyref
i•,nl /( T ritner)
-
Figure 6.3. Schematic of the Rotor-Flux Oriented Control of an Induction Motor
101
Psi_n/Lm3
oraue Command:
V_l_ref 0 ch
PARAt.t E1 [ RS:
Pi 3.14159265 lr 75.0'"5
V~----~2=-~ Vb lnduction..Wotor
V~-----~:5 Vc "-'-C'I! frame .-d:
Om ref 4
PARAt.t[T[RS: PARAUE1ERS: F"rea_n 60 LS-t JLsl+lrll
V..ll 480
F"AN
Psi_n tv4>h.J)e(]lc/Orneoo_nl Orneoo_n f2+Pi+F"rea_nl l~ tL~/Rsl V4>h~lc t~rt(2)+V..Ll/sart(3)l
Vector Controller with Voltoge Output: Ref_F'rome_Tron9form
Vf"IN1~,._ fpov-,J_lj V..!J
-V"IN2 I ---4~ V("IN)•P --I Rho - (l"V("IN3)) v 9'1C vVg'lf~ ...a
t.tech - '> Elec OeQr~
F'lu'IC Reference: - V("IN1)•R9-<:;.!.!JL.. R~u 1.0 V("IN2)• LU V..!J'Il_ref
YTY l V("IN3)
Toraue Command: Jlul I cd
- V{"IN1)•R9• V..!Jy_ref I<:L:!_. ....__ V("IN2)• L~
V("IN3)
Rotor Flu'JC Oriented Control:
Figure 6.4. Block Diagram of the System Incorporating the Vector Controlled Drive and a Three-Phase Induction Motor.
102
2 .. 3
V...c:A -~ V.JP> V_bl ~ V-5>> V_c4 ~v~
Block Diaqrom of Motor Model: General Reference Frome:
V_o v V..sd Ls Lsd Tor au
l_s Lsa V_b Om ref IJ l_rd
V_c v V_sq IJ l_rq
0 _e O~_e
480 V, 60 Hz, 15 hp, 3-phose, induciion moior:
PARAMETERS: PARAMETERS: PARAMETERS: Lm3 BOm Rs 0.25 Ls JLm3+Lslt Lsi 3.2m Rr 0.30 Lr JLm3+Lrl[ Lrl 4.0m J 0.1 P 2
~~--i -V(~IN1)+( +V(~IN2)+L5
-......!::!~...-~1 + V(~IN :3)+ Lm:3 1
Lrl.d
1Lm:3l
Lm:3...d
Lrla
Rr...d H
Rotational Voltaoe:
Rr..a H
Rotational VoltaQe:
Figure 6.5. Block Diagram of the Motor Model and Dynamic Model of Induction Motor in the General Reference Frame
103
Mechanical Model:
Toroue
1k RJood
Tor ue
Load
H_Tsense
V(~IN)/J V(~IN) • P
Angular Acceleration: Omego_mech Omego_elec
1G 1G 1G R_tc R_tb R-lo
3 - > 2 Block with current throuqhput:
No zero seQuence voltoQes:
H
- -:-(V(%1N1)
-V(%1N2)) /SOR1(3) H_Q H
- -:-
-V(%1N1~/2 -+sQrl(3
- -:-•V(%1N2)/2
-V(%1N1)/2 -sQrt(3) •V(~IN2)/2
Figure 6.6. Mechanical Model of the Motor and Model for 3-to-2 Phase Transformation
104
\J), 20 Nm at 1800 RPM
V %IN •V %IN .....___,__...,
F AN_T o rq u e ~----~ /FAN_RPM /FAN_RPM
PARAMETERS: FAN_Torque 20 FAN_RPM 1 800
Figure 6. 7. Mechanical Model of the Load
RPM
105
51U~-----------------------------------------------------------------------------------------~
.. -----------~~~:~~-~--=~:~~--------~==------......L~~--------------------------.1 ~ U(Uector_control:T_ref) • U(U1.Mech•nic•l.Torque)
311U ~-----------------------------------------------------------------------------------------~ I I
I I I I I I I I
Voltage, ·Phase a I
SEL>> : -311U ~-----------------------------r-----------------------------T-----------------------------~
Is 1.55 1.15 1.55 ~ U(U1:0 .. ch) o U(U1:U•)
Figure 6.8. Results of Simulation of the Complete System Incorporating the Vector Controlled Drive and a Three-Phase Induction Motor
106
CHAPrER VII
CONCLUSIONS
Microprocessor-based prototype controllers have been designed which provide
real time control of the PWM signals to drive an ac motor. The real time based
adjustable-frequency drives allow an efficient, wide-range speed control of the motor.
They also allow the motor to transition from one speed to another very smoothly. The
previously designed EPROM based controller did not perform real time PWM
generation. The EPROM was programmed with a fiXed set of data corresponding to a
fixed set of desired output voltages.
Further research in the area of microprocessor-based real time control of ac
motors can be performed. A complete closed loop system can be developed incorporating
a microprocessor and the Hanning PWM chip. The speed of the motor (taken as a de
voltage by using a Tachometer) or the line current of the motor (taken by using a Hall
effect sensor) can be used as feedback parameters.
As a precursor to future hardware implementation, the dynamic model of a vector
controlled drive was derived using Microsim's Design Center Version 6.0. The
performance analysis of the complete closed loop system incorporating the vector
controlled drive and a three-phase induction motor was carried out. The dynamic
modeling of the vector drive gives a direction to design a complete high perfonnance
drive system for ac motors.
107
REFERENCES
[ 1] JMD Murphy, FG Turnbull, Power Electronic Control of AC Motors, Pergamon Press plc, Headington Hill Hall, Oxford, England, 1989.
[2] S. J. Chapman, Electric Machinery Fundamentals (2nd ed.), McGraw-Hill, New York. 1991.
[3] V. DelToro, Electrical Enginering Fundamentals, Prentice Hall, New Jersey, 1972.
[ 4] F. Profumo, " Pulse Width Modulation Control," IEEE Industry Applications Societty, Annual Meeting on " Microprocessor Control of Motor Drives and Power Converters," pp. 3.1-3.35, Houston, Texas, October, 1992.
[5] N. Mohan, T. Underland, W. Robbins, Power Electronics: Converters. Applications. and Design, John Wiley & Sons Inc., New York, 1989.
[6] C. Lott, J. H. Xu, S. Saadate, B. Davat," A New Approach of Control by Model of a Voltage Source GTO Active Power Filter," The 4th International IMACS-TCl Conference on " Computational Aspects of Electromechanical Energy Converters and Drives," pp. 555-559, 7-8 July 1993.
[7] H. W. VanDer Broeck, H. C. Skudelny, G. V. Stanke," Analysis and Realization of a Pulse-Width Modulator Based on Voltage Space Vectors, " IEEE Transaction on Industry Applications, pp. 142-149, Vol. 24, No.1, January/February, 1988.
[8] C. E. Eldred," Development of Intelligent Power Modules for Induction Motor Controllers," Master's Thesis, Department of Electrical Engineering, Texas Tech University, December 1993.
[9] International Rectifier Preliminary Data Sheet, No. PD 6.019, 1990, California.
[10] z World Engineering, Little Giant Miniature Controller Technical Manual, Board Revision E, Dynamic C Version 2, Davis, California, 1992.
[11] Texas Instruments TMS320C2x User's Guide, Digital Signal Processing Products, No. 1604907-9271,, Revision C, January, 1993.
108
[12] Texas Instruments TMS320C2x DSP Starter KIT User's Guide, Microprocessor development Systems, No. 2617630-9741, March, 1993.
[13] Hanning- PBM 1/87 Data Manual, 3-phase-Pulsbreitenmodulator, Vl.2, 1989.
[14] M. Giesselmann, "Advanced Modeling of Adjustable Speed AC-Motor Drives using PSPICE," in Proc. 4th International Conference on " Computational Aspects of Electromechanical Energy Converters and Drives," Montreal, Canada. July 7-9, 1993.
[15] P. Vas, Vector Control of AC Machines, Oxford University Press, Oxford, 1990.
109
APPENDIX A
DYNAMIC C PROGRAM TO GENERATE PWM SIGNALS
110
***********************************************************************
DYNAMIC C CODES TO GENERATE REAL TIME PWM SIGNALS
***********************************************************************
main()
{
int delay, ts, i, oldst, newst, oldcycle, new cycle, zerocycle, oldstate, new state, outer;
float pi, deg, rad, oldcyclef, newcyclef, zerocyclef, amp, time;
int olddelay[6], newdelay[6], zerodelay1[6], zerodelay2[6], old[6], new[6];
I* SETTING THE PORT MODE*/
outport (PIOCA, Oxcf);
outport (PIOCA, OxOO);
I* DEFINING THE STATES OF THE SWITCHES *I
old[O] = Ox73;
old[l] = Ox3B;
old[2] = OxAB;
old[3] = Ox8F;
old[4] = OxC7;
old[5] = Ox57;
new[O] = Ox3B;
new[l] = OxAB;
new[2] = Ox8F;
new[3] = OxC7;
new[4] = Ox57;
111
new[5] = Ox73;
time= 10.0;
ts = 256;
pi = 22.on .o;
amp= 1.0;
deg = 0.0;
for ( i = 0; i<6; i++)
{
rad = deg * pi/180.0;
oldst = (int) ((deg - 0.1)/60.0);
if ( oldst < 0) oldst = 0;
newst = oldst + 1;
if ( oldst = = 5 ) newst = 0;
oldcycle = (int) ( ts *amp* sin ( newst * pi/3- rad ));
newcycle = (int) ( ts *amp* sin( rad- oldst * pi/3 ));
if ( oldcycle = = 128 && newcycle = = 128) zerocycle = 0;
zerocycle = (int) ( ts - oldcycle - newcycle + 0.5);
oldcycle = (int) ( oldcycle * 0.5 );
newcycle = (int) ( newcycle * 0.5 );
zerocycle = (int) (zerocycle * 0.25 + 0.5 );
oldcyclef =(float) ((time/( 36.0 * 256.0 )) * oldcycle );
newcyclef =(float) (( time/36.0 * 256.0 )) * newcycle );
112
zerocyclef =(float) (( time/36.0 * 256.0 )) * zerocycle );
olddelay [i] = (int) ( 0.5 + oldcyclef * ( 5000.0n5.0 ));
newdelay [i] = (int) ( 0.5 + newcyclef * ( 5000.0n5.0 ));
zerodelay1 [i] = (int) ( 0.5 + zerocyclef * ( 5000.0n5.0 ));
zerodelay2 [i] = (int) ( 0.5 + zerocyclef * ( 5000.0n5.0 ));
deg = deg + 360.0/36.0;
}
while (1)
{
for ( outer = 0; outer < 6; outer ++ )
{
oldstatae = old[ outer];
newstate = new[ outer];
for ( i = 0; i < 6; i++ )
{
for ( delay = 0; delay< zerodelay1 [i] ; delay ++ )
outport (PIODA, OxE3);
for (delay= 0; delay< olddelay[i] ; delay++)
outport (PIODA, oldstate );
for (delay= 0; delay< newdelay[i] ; delay++)
outport (PIODA, newstate);
for ( delay = 0; delay < zerodelay2[i] ; delay ++ )
113
outport (PlOD A, Ox IF );
for ( delay = 0; delay < newdelay[i] ; delay ++ )
outport (PIODA, newstate);
for (delay= 0; delay< olddelay[i] ; delay++)
outport (PlOD A, oldstate );
for (delay= 0; delay< zerodelayl [i] ; delay++)
outport (PIODA, OxE3);
}
oldstate =old[ outer- 1];
newstate =new[ outer- 1];
for ( i = 0; i < 6; i++ );
{
for (delay= 0; delay< zerodelayl [i] ; delay ++ )
outport (PIODA, OxE3);
for ( delay = 0; delay < newdelay[i] ; delay ++ )
outport (PIODA, newstate );
for (delay= 0; delay< olddelay[i] ; delay++)
outport (PlOD A, oldstate );
for ( delay = 0; delay < zerodelay2[i] ; delay ++ )
outport (PlOD A, Ox IF );
for ( delay = 0; delay < olddelay[i] ; delay ++ )
outport (PlOD A, oldstate );
114
}
}
for ( delay = 0; delay < newdelay[i] ; delay ++ )
outport (PIODA, newstate );
for (delay= 0; delay< zerodelayl[i]; delay++)
outport (PIODA, OxE3);
}
}
115
APPENDIXB
ASSEMBLY PROGRAM TO INITIALIZE
THE HANNING PWM CHIP
116
SOURCE CODES FOR THE ASSE:MBL Y PROGRAM USED
TO GENERATE REAL TWE PWM SIGNALS USING THE TI-DSP
AND A HANNING PWM CIUP
***********************************************************************
ALLOCATING :MEMORY LOCATIONS FOR THE PARAMElERS TO BE
WRI'rl'EN INTO THE PWM CHIP (POLLING MODE)
***********************************************************************
.PS OFBOOH ; PROGRAM CODES STARTS HERE
.ENTRY ; PROGRAM ENTRY POINT
UA .SET 5 ;VOLTAGECO~ONENTUA
PHil .SET 10 ; PHASE ANGLE, UPPER HALF
DPHil .SET 20 ; FREQUENCY, UPPER HALF
EMPTY .SET 30 ; TO DEFINE SOME PARAMETERS AS 0000
TAUS .SET 40 ; TURN-OFF TIME
TIOT .SET 50 ; BLANKING TIME
TMIN .SET 60 ; TURN-ON TIME
VORTL .SET 70 ; SWITCHING FREQUENCY SCALER
TSTART .SET 80 ; START OF PROCESSING CYCLE
CONTROL .SET 90 ; CONTROL WORD
117
***********************************************************************
THE PARAMETERS NECESSARY TO INITIALIZE THE PWM CHIP ARE LOADED
IN THEIR CORRESPONDING ADDRESSES
***********************************************************************
ZAC
SACL
LALK
SACL
LALK
SACL
LALK
SACL
LACK
SACL
LACK
SACL
LACK
SACL
LACK
SACL
LALK
SACL
EMPTY
UA
0200H
PHil
0189
DPHil
63
TAUS
35
TTOT
255
TMIN
09
VORTL
480
TSTART
; ZERO THE ACCUMULATOR
118
***********************************************************************
CONTROL WORD SETS 16-BIT BUS MODE AND ADDRESS OF VOLTAGE
COMPONENT UA. PULSE CALCULATION IS DISABLED. CONTROL WORD IS
SENT THROUGH PORT PA6
***********************************************************************
LALK
SACL
OUT
CALL
0000000010010110B,O
CONTROL
CONTROL,6
DELAY
***********************************************************************
REPEAT THE ABOVE PROCESS
***********************************************************************
LALK
SACL
OUT
CALL
0000000010010110B,O
CONTROL
CONTROL,6
DELAY
119
***********************************************************************
SEND ALL THE PARAMETERS TO INITIALIZE THE PWM CHIP, THE
PARAMETERS ARE SENT THROUGH PORT PA4
***********************************************************************
OUT UA,4 ; SEND VOLTAGE COMPONENT UA
CALL DELAY
OUT EMPfY,4 ; SEND VOLTAGE COMPONENT UB
CALL DELAY
OUT Plll1,4 ; SEND PHASE ANGLE, UPPER HALF
CALL DELAY
OUT DPHil, 4 ; SEND FREQUENCY, UPPER HALF
CALL DELAY
OUT EMPfY,4 ; SEND PHASE ANGLE, LOWER HALF
CALL DELAY
OUT EMPTY,4 ; SEND FREQUENCY, LOWER HALF
CALL DELAY
OUT EMPTY,4 ; SEND DIFFERENCE PHASE ANGLE
CALL DELAY
OUT EMPfY,4 ; ADDRESS NOT USED
CALL DELAY
OUT TAUS, 4 ; SEND TURN-OFF TIME
CALL DELAY
OUT TIOT,4 ; SEND BLANKING TIME
CALL DELAY
120
OUT
CALL
OUT
CALL
OUT
CALL
TMIN,4
DELAY
VORn,4
DELAY
TSTART, 4
DELAY
; SEND TURN-ON TIME
; SEND SWITCHING FREQUENCY SCALER
; SEND STARTING TIME
***********************************************************************
CONTROL WORD ENABLES PULSE CALCULATION AND OUTPUT
***********************************************************************
LALK
SACL
OUT
CALL
0000000010010111B,O
CONTROL
CONTROL,6
DELAY
***********************************************************************
REPEAT THE ABOVE PROCESS
***********************************************************************
LALK
SACL
OUT
CALL
B
0000000010010111B,O
CONTROL
CONTROL,6
DELAY
TERMINATE
121
DELAY:
RPT 7FH
NOP
RPT 7FH
NOP
RPT 7FH
NOP
RET
TERMINATE:
.END
122
