22893773 36 2 field orientated control of a multi level pwm inverter fed induction motor
TRANSCRIPT
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
1/123
School of Electrical and Computer Engineering
Department of Electrical Engineering
Final Year Thesis
Semester 1, 2002
Field Orientated Control
of a Multi-Level PWM Inverter Fed Induction Motor
Student Jason Monzu
I.D: 09711107
Supervisor: Dr. W. W. L. Keerthipala
Co-Supervisor: Dr. W. Lawrance
Due date: 31ST
May 2002
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
2/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
TITLE: FIELD ORIENTED CONTROL OF A MULTILEVEL PWM
INVERTER FED INDUCTION MOTOR.
AUTHOR:
FAMILY NAME: MONZU
GIVEN NAME: JASON CARMELO
DATE: SUPERVISOR:
31ST
MAY 2002 DR W.W.L KEERTHIPALA
DEGREE: OPTION:
BACHELOR OF ENGINEERING ELECTRICAL
ABSTRACT:
This thesis presents the simulation of a Field Orientated Control of a Multi level PWM
Inverter fed induction motor system and its implementation in terms of programming and
code in a real time operating system. Field Orientated Control allows precise
controllability and excellent transient behaviour when used to control an induction motor
by manipulating the angle and amplitude of the torque and speed producing current
vectors. A closed loop feedback control system is employed to give the system stability
and rapid response. The implementation of software code for the vector algorithms
through a rapid phototyping interface will also be investigated in this project.
INDEXING TERMS:
Field Orientated Control, Vector Control, Direct axis, Quadrature axis, Park
transformation, Clarke Transformation, Beta estimation, DSP, Rapid prototyping.
GOOD AVERAGE POOR
TECHINICAL WORK
REPORT PRESENTATION
EXAMINER:CO-EXAMINER:
Jason C Monzu Page I
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
3/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Mr Jason Carmelo Monzu
78 Lesouef Drive
Kardinya
Perth W.A. 6163
31st
May 2002
Prof. A Zoubir
Head of School
Electrical and Computer Engineering
Curtin University
P.O. Box U1987
Perth WA 6000
Dear Professor Zoubir,
Please find attached the project thesis titled Field Oriented Control of a multi-level PWM
Inverter Fed Induction Motor for the partial completion of the Bachelor Degree of
Electrical Engineering.
Yours Faithfully
Jason Monzu
09711107
Jason C Monzu Page II
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
4/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Table of Contents
LIST OF FIGURES ...........................................................................................................VI
LIST OF TABLES ..........................................................................................................VIII
NOMENCLATURE........................................................................................................... IX
CHAPTER 1 ..........................................................................................................................1
1 INTRODUCTION.........................................................................................................1
1.1 BACKGROUND..........................................................................................................11.2 PROJECT OBJECTIVE .................................................................................................2
1.3 PAST INVESTIGATIONS .............................................................................................3
CHAPTER 2 ..........................................................................................................................5
2 THEORY REVIEW......................................................................................................5
2.1 THREE PHASE INDUCTION MOTOR.............................................................................5
2.2 FIELD ORIENTATED CONTROL................................................................................12
2.2.1 Field Orientated Control overview..................................................................12
2.2.2 Motor Transformation Algorithms...................................................................162.2.2.1 Clarke Transformation .............................................................................16
2.2.2.2 Park Transformation ................................................................................17
2.2.2.3 Beta Estimation ........................................................................................20
2.2.3 Field Oriented Control Principal.....................................................................21
2.3 CURRENT FEEDBACK IN AC VARIABLE SPEED DRIVES ...........................................24
2.3.1 Methods of measuring current .........................................................................24
2.3.2 Current feedback in high performance Vector Drives.....................................25
2.4 SPEED FEEDBACK IN AC VARIABLE SPEED DRIVES ................................................26
2.4.1 Analogue Speed Transducer ............................................................................26
2.4.2 Digital Speed Transducer ................................................................................26
2.4.3 Digital Position Transducers ...........................................................................27
2.5 DIGITAL SIGNAL PROCESSORS IN AC VARIABLE SPEED DRIVES .............................28
2.6 PWM 5 LEVEL INVERTER .....................................................................................30
2.6.1 Full Bridge PWM Inverter Topology ...............................................................31
2.6.2 PWM Control ...................................................................................................33
2.6.3 Five Level PWM Inverter .................................................................................34
CHAPTER 3 ........................................................................................................................37
3 TECHNICAL REVIEW.............................................................................................37
Jason C Monzu Page III
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
5/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
3.1 COMPARATIVE ANALYSIS OF TORQUE-CONTROLLED IM DRIVES WITH
APPLICATIONS IN ELECTRIC AND HYBRID VEHICLES..........................................................37
3.1.1 Integration of the stator voltage equation........................................................39
3.1.2 Calculation of the rotation angle .....................................................................42
3.1.3 Flux control loop..............................................................................................433.1.4 Torque control Strategies.................................................................................43
3.1.5 PI versus fuzzy control in the torque control loop ...........................................47
3.2 REVIEW CONCLUSION.............................................................................................48
CHAPTER 4 ........................................................................................................................50
4 VECTOR DRIVE CONTROL FEEDBACK LOOPS.............................................50
4.1 SPEED CONTROL LOOP ...........................................................................................54
4.2 TORQUE CONTROL LOOP STAGE 1 ..........................................................................55
4.3 TORQUE CONTROL LOOP STAGE 2 ..........................................................................564.4 TORQUE AND SPEED ERROR SIGNALS......................................................................57
4.5 INVERTER INPUT LOOP............................................................................................60
CHAPTER 5 ........................................................................................................................62
5 PHYSICAL IMPLEMENTATION...........................................................................62
5.1.1 Current Sensing................................................................................................62
5.1.1.1 HCPL-788J Optocoupler..........................................................................63
5.1.2 Speed sensor.....................................................................................................65
CHAPTER 6 ........................................................................................................................66
6 PROGRAMMING AND LOGIC IMPLEMENTATION .......................................66
6.1 RTAI REAL TIME SYSTEM OPERATION...................................................................67
6.2 HARDWARE............................................................................................................67
6.2.1 The parallel bus ...............................................................................................68
6.2.2 The interface board..........................................................................................68
6.3 SOFTWARE .............................................................................................................69
6.3.1 Prototype software code...................................................................................70
CHAPTER 7 ........................................................................................................................72
7 SIMULATION RESULTS .........................................................................................72
7.1 INDUCTION MOTOR MODEL.....................................................................................72
7.1.1 Induction motor simulation results ..................................................................74
7.2 FREQUENCY MAP....................................................................................................75
7.2.1 Frequency map simulation results ...................................................................76
7.3 3S 2R TRANSFORMATION ...................................................................................77
7.3.1 3S to 2R simulation results...............................................................................80
7.4 ROTOR FLUX GENERATION.....................................................................................83
7.4.1 Rotor flux estimation simulation results ..........................................................85
Jason C Monzu Page IV
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
6/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
7.5 TORQUE MAP..........................................................................................................87
7.5.1 Torque map simulation results.........................................................................88
7.5.2 Speed and Torque Error signals ......................................................................89
7.5.2.1 Speed error signal.....................................................................................89
7.5.2.2 Torque error signal...................................................................................907.5.2.3 Torque reference map ..............................................................................91
7.5.2.4 Speed and torque error results..................................................................93
CHAPTER 8 ........................................................................................................................94
8 CONCLUSION............................................................................................................94
8.1.1 Summary...........................................................................................................94
8.1.2 Recommendations for future work ...................................................................95
9 REFERENCES............................................................................................................97
10 APPENDICES .......................................................................................................102
10.1 APPENDIX A - PSCAD SYSTEM BLOCK DIAGRAMS .............................................103
10.2 APPENDIX B - PSCAD OUTPUT WAVEFORMS ......................................................104
10.3 APPENDIX C -AUTOCAD SYSTEM PLOTS ............................................................105
10.4 APPENDIX D - TEXAS INSTRUMENTS TMS320C55 DATA SHEETS........................106
10.5 APPENDIX E - C PROGRAM CODE ........................................................................107
10.5.1 PI controller...............................................................................................108
10.5.2 System routine ............................................................................................108
10.5.3 Convert phase current into i_alpha and i_Beta.........................................109
10.5.4 Transformation into rotating reference frame...........................................10910.5.5 rotor model in rotor flux coordinates ........................................................109
10.5.6 calculation of flux.......................................................................................109
10.5.7 Slip .............................................................................................................109
10.5.8 Angle of flux ...............................................................................................110
10.5.9 Speed control..............................................................................................110
10.5.10 Current control ..........................................................................................111
10.5.11 Back transformation into stator coordinates .............................................111
10.5.12 Calculation of u_alpha and u_Beta ...........................................................112
10.5.13 Calculation of times for space vector modulation .....................................112
10.5.14 Transfer data to modulator ........................................................................112
10.6 APPENDIX F - TYPICAL TORQUE CHARACTERISTICS FOR INDUSTRIAL MACHINERY112
Jason C Monzu Page V
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
7/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
List of Figures
Figure 2-1: Equivalent Circuit of an AC Induction Motor ....................................................9
Figure 2-2: Torque Vs. Speed characteristics .....................................................................11
Figure 2-3: Typical Vector Transformation ........................................................................12
Figure 2-4: Phasor representation of a typical Vector Transformation..............................13
Figure 2-5: 3-Phase current space vector ...........................................................................15
Figure 2-6: Clarke space vector Transformation................................................................16
Figure 2-7: 2 variable Stationary space vector at o degrees ..............................................18
Figure 2-8: 2 variable rotating space vector at 60 degrees in the excitation frame ...........18
Figure 2-9: Beta estimation .................................................................................................20
Figure 2-10: FOC scheme for an AC-motor showing Park and Clarke Transformations ..22
Figure 2-11: Current load vectors in an AC induction motor.............................................24
Figure 2-12: Circuit Diagram of a Full Bridge PWM Inverter...........................................31
Figure 2-13: Diagram of PWM Output [10] .......................................................................32
Figure 2-14: Triangle comparison PWM implementation [10] ..........................................33
Figure 2-15: Five level staircase output voltage. [1]..........................................................34
Figure 2-16: Five Level PWM Control ................................................................................35
Figure 2-17: Five level PWM generation ............................................................................36
Figure 3-1: Step response (10-25Nm) of torque control loop with idsas reference at 2100
RPM [18] .............................................................................................................................45
Figure 3-2: Step response (0.34-0.2 Wb) of flux control loop with idsas reference at 2100
RPM [18] .............................................................................................................................45
Jason C Monzu Page VI
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
8/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 3-3: Step response (0.34-0.2 Wb) of the flux loop for torque and flux loops at 2100
RPM [18] .............................................................................................................................46
Figure 3-4: Step response (10-25Nm) of the flux loop for torque and flux loops at 2100
RPM [18] .............................................................................................................................46
Figure 3-5: Step torque modification for both PI and FL controllers. [18]........................48
Figure 5-1: Speed sensor from a shaft mounted transducer................................................54
Figure 5-2: Torque control loop -Rotor Flux and Beta estimations....................................55
Figure 5-3: Torque estimation algorithm ............................................................................56
Figure 5-4: Torque and speed error algorithm ...................................................................58
Figure 5-5: Inverter input algorithm ...................................................................................61
Figure 6-1: HCPL-788J Typical System Diagram .............................................................64
Figure 7-1: Interface structure of parallel bus. ...................................................................69
Figure 8-1: Induction motor simulation model(Appendix A) .............................................72
Figure 8-2: Voltage and Current inputs into the IM ..........................................................74
Figure 8-3: Frequency map simulation block diagram(Appendix A).................................75
Figure 8-4: Frequency Ramp over one second (Appendix B)..............................................76
Figure 8-5: abc to d-q voltage transformation block diagram (Appendix A).....................77
Figure 8-6: abc to d-q current transformation block diagram (Appendix A)......................78
Figure 8-7: d-q to D-Q current transformation block diagram (Appendix A) ....................79
Figure 8-8: IDSe
and IQSe
in the excitation frame (Appendix B) .......................................80
Figure 8-9: Dot product of IDSe
and IQSe
equals zero. (Appendix B) ..................................81
Figure 8-10: Rotor flux estimation block diagram (Appendix A)........................................83
Figure 8-11: Rotor flux calculated waveform (Appendix B) ..............................................85
Figure 8-12: Original Beta estimation(Appendix B) ...........................................................85
Jason C Monzu Page VII
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
9/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 8-13: New Beta estimation including Theta measurement (Appendix B) ................86
Figure 8-14: Torque map block diagram (Appendix A) ......................................................87
Figure 8-15: Comparison between calculated torque Vs. measure torque over 1 sec
(Appendix B). .......................................................................................................................88
Figure 8-16: Speed error schematic ....................................................................................89
Figure 8-17: Torque Error schematic .................................................................................90
Figure 8-18: Torque reference map.....................................................................................91
Figure 8-19: New loop current IDSenew .................................................................................93
List of Tables
Table 1: Induction motor parameters ..................................................................................73
Jason C Monzu Page VIII
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
10/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
NOMENCLATURE
ia, ib, ic - Stator phase currents
i, i - Stator current components
id, iq - Stator current flux and torque components
id ref, iq ref - Stator current flux and torque reference vectors
e - Excitation frame
- Rotor Flux Angle
imR - Rotor Magnetizing Current
J - Moment of Inertia
K1, k2 - Proportional constant and integration constant of
PI controller respectively
Lm - Mutual Inductance between stator and rotor
N - Speed of Induction Motor in rpm
P - Output power of induction motor
DSP - Digital Signal Processor
r - Rotor Angular Speed
- Motor Speed
LR - Rotor Inductance
LS - Stator Inductance
RR - Rotor Resistance
RS - Stator Resistance
TR - Rotor Time Constant
TS - Stator Time Constant
Jason C Monzu Page IX
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
11/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
CHAPTER 1
1 Introduction
1.1 Background
The control of a DC or AC induction motor involves a manipulation of the vector
relationship in space of the air gap magnetic flux to the rotor current. From fundamental
mathematics, a vector represents both the magnitude and direction of a variable, such as
voltage or current. This type of AC variable speed drive gets it name from the fact that the
system attempts to separately measure and control the two vector components that make up
the overall stator current of the motor. Specifically, it attempts to measure and control the
torque-producing current in an AC motor. In a DC motor the switching action of the
commutator determines the position of the armature current in relation to the flux giving
control over the torque of the motor. It is this aspect of the DC motor that makes precise
control a relatively simple and effective procedure.
In an induction motor the rotating flux is responsible for setting up the rotor current and the
relationship between them is a function of the slip and certain other variables. This makes
controllability a more delicate process that requires some form of closed loop control
system to modify the field vectors of the motor. This closed loop system that modifies
vector components of the motor is what is known as Vector Control. Due to the vast
popularity of AC induction motors in industry this type of delicate control is used
frequently to control the speed and the torque of the induction motor.
Jason C Monzu Page 1
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
12/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
In applications with high dynamic requirements, where speed or load change rapidly, a
better form of control is necessary. The dynamic response has to be at least 10 times better
than that provided by standard variable voltage variable frequency drives. In the past, DC
drives have been effectively used for these difficult applications because of their inherent
ability to separately and directly control speed and torque. However, the high maintenance
requirements of DC drives has encouraged the development of alternate solutions. Vector
Control has evolved to provide a level of dynamic performance for AC drives which is
equivalent to or better than DC drives. Thanks to ever advancing technological
developments particularly in the area of semiconductor science and microprocessor and
DSP refinement the capabilities and knowledge are now accessible to allow greater control
over AC motor drives.
1.2 Project objective
The primary objective of this thesis was to simulate and test a Vector Control system with
the intent to produce some physical implementation. This thesis is based on the
continuation of past Field Orientated Control projects and provides corrections and
advancements made in the simulation and implementation.
Implementation initially consists of the hardware component specifications and
information of all sensors and equipment along with a complete blueprint of the Control
System. This blueprint was constructed in such a way that it allows for the progression of
this project in years to come. A large component of the implementation is the code
associated with the algorithms and the control system. A detailed prototype design of a
Jason C Monzu Page 2
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
13/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Field Orientated Control system was produced in the C programming language but has not
been tested. As a secondary objective the project will also cover areas of Vector Control
code for real time operating using a PC in a Linux environment.
1.3 Past Investigations
This section discusses the problems encountered with precious project and the limitations
of the current project.
Initially the project required a great deal of refinement in terms of motor parameter values
and general system simulation setup. The values of inductance and resistances were
determined based on comparison to other similar models as the values obtained from
previous work were inconclusive. This led to the induction motor model and all
transformations being reconstructed to allow for the desired change to generate the
expected phase voltage and current waveforms.
Problems were also encountered in the Beta estimation schematic from the previous
project. A solution to this was the construction of a new rotor flux estimation to conform
with the new design and the respective changes. The value of rotor position angle theta was
discovered to be incorrect also due to the induction motor setup. This problem generated
incorrect values of current and voltage as the value Beta is used in many of the torque and
current estimation algorithms.
Considerable consideration into choice of Digital Signal Processors concluded that the use
of the TMS320C40 DSP was not financially viable. The actual DSP chip was but the
Jason C Monzu Page 3
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
14/123
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
15/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
CHAPTER 2
2 Theory Review
2.1 Three phase induction motor
For industrial and mining applications the 3-phase AC induction motor is the prime mover
for the vast majority of machines and processes. The beauty of such a device is that it can
be operated directly from the mains or controlled by adjustable frequency drives such as
PWM inverters. The importance of the AC induction motor to the economy is paramount
as they are used in more than 90% of all motor applications for example driving pumps,
fans, compressors, mixers, mills, conveyors and crushers. The popularity of such a motor
stems to its simplicity, reliability and low cost making it a very economically viable
choice. To clearly understand how a Vector Control system works it is essential to firstly
understand the principal operation of the squirrel cage induction motor.
The AC induction Motor is comprised of two electromagnetic parts:
1) Stator which is stationary
2) Rotor which rotates about the ends supported by bearings
The stator and rotor are each comprised of an electrical circuit made of insulated copper or
aluminium to carry current and a magnetic circuit usually made of laminated steel to carry
magnetic flux.
Jason C Monzu Page 5
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
16/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The stator the outer stationary part of the motor consists of an outer cylindrical frame, a
magnetic path and insulated electrical windings. The outer cylindrical frame is made of
some metal alloy which incorporates and mountings or support brackets. The magnetic
path is comprised of a set of slotted steel laminations pressed into the cylindrical space
inside the outer frame which is laminated to reduce eddy currents and hence reduce losses.
The insulated electrical windings are placed inside the slots of the laminated magnetic path
and in the case of a 3-phase motor 3 sets of windings are required.
The rotor or rotating part of the motor consists of a set of slotted steel laminations pressed
together in the form of a cylindrical magnetic path and the electrical circuit. In the case of
this project specifically the squirrel cage induction motor is used as opposed to the wound
rotor type. This type of AC induction motor is comprised of a set of copper or aluminium
bars installed into the slots which are connected to an end ring at each end of the rotor.
Thus the construction of this type of motor resembles a cage hence the name squirrel
cage motor. The aluminium rotor bars are in direct contact with the steel laminations but
the rotor current tends to flow through the aluminium bars not the laminations.
The connection of the stator terminals of an AC induction motor to a 3-Phase AC power
supply induces a 3-Phase alternating current to flow in the stator windings. The presence
of these currents establishes a fluctuating magnetic flux that rotates around inside the
stator. This speed of rotation in synchronization with the frequency is named the
synchronous speed. In its simplest form the induction motor consists of 3 fixed stator
windings spaced 120 degrees apart. The flux completes one rotation for every cycle of the
Jason C Monzu Page 6
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
17/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
supply voltage and so on a 50Hz power supply the stator flux rotates at a speed of 50
revolutions per second or equivalently 3000 RPM. Therefore the number of poles of the
motor is inversely proportional to its operating speed. The synchronous speed is a function
of the number of poles of the motor and the supply frequency as shown in the relationship
below,
pf
n120
0
=
Where n0 Synchronous rotating speed in rev/min
f Power supply frequency in hertz
p Number of poles
Initially the voltage supplied from the magnetic field created by the stator current induces a
current flow in the rotor bars. The rotating stator magnetic flux passes from the stator iron
path, across the air-gap between the stator and rotor and penetrates the rotor iron path.
Therefore as the magnetic field rotates the lines of flux cut the rotor conductors and
consistent with Faradays law induces a voltage in the rotor windings which is relative to
the rate of change of flux. A magnetic field is set up by the current flow through the rotor
bars which is attributed to the short circuiting of the rotor bars by the end rings. It is this
magnetic field that interacts with the rotating stator flux to produce the rotational force and
in accordance with Lenzs law the rotor will accelerate to flow in the direction of rotating
flux.
Jason C Monzu Page 7
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
18/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
In the case of starting, the rotor is stationary and the magnetic flux cuts the rotor at
synchronous speed therefore inducing the highest rotor voltage and rotor current. As the
motor builds up speed the rate at which the magnetic flux cuts the rotor winding reduces
and therefore the induced rotor voltage decreases proportionally along with the frequency
of the voltage and current. Generally as the rotor speed becomes closer to the synchronous
speed the magnitude and frequency of the rotor voltage decreases showing a directly
proportional relationship. Therefore the closer the relationship between the synchronous
speed and the rotor speed the lesser the induced voltage and current in the rotor would be
and consequently the lower the rotor current the less torque produced by the motor.
Therefore for the motor to produce torque it must rotate at a speed slower or faster than the
synchronous speed. The speed of the rotor is called the slip speed and the difference in the
speed between the synchronous speed and the rotor speed is called the slip. Based on this
information the torque of an AC induction motor is a function of the slip and the amount of
slip is determined by the load torque which is the torque required to turn the rotor shaft.
As the shaft torque increases, the slip increases and more flux lines cut the rotor windings,
which in turn increases the rotor current and consequently the rotor magnetic field and
ultimately the rotor torque. A typical percentage variation for slip is approximately 1% of
the synchronous speed at no-load and 6% at full load.
The relationship for slip in per unit is as follows:
pf
n
nnn
sslip
120
)(
0
0
0
=
==
Jason C Monzu Page 8
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
19/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Where n0 = Synchronous rotating speed in rev/min
n = Actual rotational speed in rev/min
s = Slip in per-unit
f = Frequency
p = Number of poles in the motor
To understand the performance of an ac induction motor it is useful to represent it in such a
manner that simplifies the system for calculations and observations, hence the equivalent
circuit model was constructed. The model varies in complexity and construction
depending on the type of induction motor and the range of parameters involved.
Figure 2-1 [2] below is a diagrammatic representation of the AC equivalent circuit,
Figure 2-1: Equivalent Circuit of an AC Induction Motor
Where V1 = Stator terminal voltage per phase
I1 = Stator current
I2 = Stator current
R1 = Stator winding resistance
X1 = Stator leakage reactance
Jason C Monzu Page 9
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
20/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
X2 = Rotor leakage reactance
R2 = Rotor resistance
Xm = Magnetizing inductance
Rc = Core losses
Pag = Air gap power
When choosing a motor to suit a certain application or load the primary considerations are
with respect to the torque and speed of the motor. The torque speed curve of an AC
induction motor can be determined using the equivalent circuit model and various
equations.
The following relationship for torque is:
602 n
PT
=
=
Where T = Torque
P = Mechanical Power
n = speed of shaft
Figure 2-2 [2] is a typical example of a torque Vs. speed curve for an induction motor:
Jason C Monzu Page 10
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
21/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-2: Torque Vs. Speed characteristics
On starting the torque must exceed the load breakaway torque for the induction motor to
pull away and thereafter the motor accelerates providing the motor torque always exceeds
the load torque. As the speed increases the torque will approach maximum level as seen in
the above characteristics then passing this point the torque is reduced as the speed
increases until the motor stalls. In reference to the torque-speed curve the final drive
speed stabilizes at the point where the load torque exactly equals the motor output torque.
In the instance where the load torque was to increase, the motor speed would in turn
decrease creating an increase in slip and stator current, hence the motor torque would
increase to match the load requirements.
Jason C Monzu Page 11
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
22/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.2 Field Orientated Control
2.2.1 Field Orientated Control overview
Field orientated control is the process of obtaining precise controllability over an induction
motor fed by a multilevel PWM inverter by manipulating the angle and amplitude
components of the stator field. The actual process involves a number of detailed
transformations to obtain a simplified model of an induction motor from a 3-phase time
and speed dependent system into a two co-ordinate time invariant system. Basically it
allows an induction motor to be controlled in a similar fashion to a dc motor by isolating
and simplifying the necessary variables for torque and speed control. The basis of the
control system is that stator current is referenced with respect to a synchronously rotating
frame and the torque (q) and flux components (d) aligned respectively to give
instantaneous controllability. Below depicts a ideal vector system for Field Orientated
Control [19],
Figure 2-3: Typical Vector Transformation
Jason C Monzu Page 12
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
23/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-4: Phasor representation of a typical Vector Transformation
The previous figures display the vector diagrams associated with the division of the stator
current in accordance with the d and q axis. Therefore this approach allows simple and
Jason C Monzu Page 13
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
24/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
accurate acquisition of constant reference values of torque and flux components to
maintain direct torque control. This is achieved in accordance to the following relationship
of torque in the (d,q) excitation reference frame [15],
SqRim
Where m = Torque
R = Rotor flux
iSq = Stator current vector
In essence the above relationship states that m and R iSq are directly proportional to each
other. Consequently maintaining a constant value of rotor flux will give a direct linear
relationship between the torque and torque component (iSq) allowing precise control by
governing the torque component of the stator current vector.
Vector analysis plays a major role in analysing the three-phase components of an AC
motor, namely the voltage currents and fluxes. Each phase of the stator current is
separated into it relative vector of the form ia, ib and ic. The complex stator current vector
is then determined using these three instantaneous stator currents and is represented as
follows [15],
Where
cbas iiii2 ++=
32
j
e=
34
2j
e=
Jason C Monzu Page 14
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
25/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The following diagram shows the stator current complex space vector [15],
Figure 2-5: 3-Phase current space vector
The system now has to be transformed from the 3-phase rotating current state into a 2-
variable time invariant co-ordinate system, which are equivalent to the armature and field
currents of a DC motor. The transformation from this state is performed using the Clarke
and Park transformations with each step being performed independently with the intention
of reversibility.
Jason C Monzu Page 15
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
26/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.2.2 Motor Transformation Algorithms
2.2.2.1 Clarke Transformation
The intention of the Clarke Transform is to perform the first phase of the 2-variable
transformation by converting the 3-phase currents ia, ib and ic into an orthogonal reference
frame iqss
and idss
[15], These components are the in reference to the stator frame. The
diagram is as follows,
Figure 2-6: Clarke space vector Transformation
Jason C Monzu Page 16
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
27/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
This vector can now be represented in terms of a matrix equation to obtain a value for is
and is in terms of the 3-phase phasor currents, this relationship is as follows,
=
cs
bs
as
s
qs
s
ds
i
i
i
I
I
1112
3
2
30
2
1
2
11
This matrix is used as an algorithm to produce a 2-variable co-ordinate system that is
dependent on time and speed.
2.2.2.2 Park Transformation
The Park transformation is the most integral part of the control algorithm. It is the process
of converting the 2-variable iqss
and idss
system into another 2-variable D and Q rotating
reference frame. The vector diagram displays the d axis aligned with the motor flux and
representing the motor rotor flux angle. The Park transformation system is illustrated on
the following page.
Jason C Monzu Page 17
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
28/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-7: 2 variable Stationary space vector at o degrees
From the 2 variable stationary frame it is then the responsibility of the Park transformation
to convert the signal into a rotating excitation co ordinate system. A vector diagram of the
Park transformation is shown below,
Figure 2-8: 2 variable rotating space vector at 60 degrees in the excitation frame
Jason C Monzu Page 18
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
29/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
This allows the construction of the torque and flux components of the stator current and the
ability to manipulate these vectors to achieve direct torque control. These torque and flux
components of the stator current can be determined according to the following vector
matrix,
=
s
qs
s
ds
e
QS
e
DS
I
I
I
I
cossin
sincos
Using the above transformation the stator currents are now in the reference D-Q excitation
frame. These currents are used to control motors torque and flux independently. Similarly
the voltage matrix is as follows,
=
s
qs
s
ds
e
QS
e
DS
V
V
V
V
cossin
sincos
Jason C Monzu Page 19
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
30/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.2.2.3 Beta Estimation
Beta is the angle between the stationary reference frame to the rotating excitation frame. It
is essential in the Park transformation to transfer the signal into a rotational co ordinate
system. The angle Beta is derived as follows,
=
=
=
d
e
q
e
QS
e
QS
e
DS
e
DS
F
F
F
F
111 tantantan
Figure 2-9: Beta estimation
Jason C Monzu Page 20
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
31/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.2.3 Field Oriented Control Principal
The power circuit for a vector converter consists of firstly a diode rectifier to convert 3-
phase AC to a DC voltage with a DC link capacitor filter to provide a smooth and steady
DC voltage. Secondly a gate controlled semi-conductor inverter bridge to convert DC to a
PWM variable voltage variable frequency output suitable for a AC induction motor.
Finally and most importantly a microprocessor based digital control circuit to control the
switching and provide protection and a user interface. This type of Field Orientated
Control uses essentially a cascaded closed loop system with two separate control loops one
for speed and the second for current. The control strategy is similar to that used for the
control of a DC drive where the speed loop controls the output frequency proportional to
the speed and the torque loop controls the motor in-phase current proportional to the
torque. Following is a basic overview of the Field Orientated Control process including
the Park and Clarke transformations discussed previously [9],
Jason C Monzu Page 21
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
32/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-10: FOC scheme for an AC-motor showing Park and Clarke Transformations
Initially the loop begins with the measured values of current from the motor which are fed
into the primary Clarke transformation system converting the 3-phase currents into a 2-
variable stationary reference frame. The currents idsS
and iqsS
are then transferred into the
secondary Park transform [9] where they are transformed from a stationary system into the
d-q rotating reference frame [9] with rotation angle Beta. The currents iDSe
and iQSein the
excitation frame are then compared to referenced values of torque and flux needed to
produce the required values. The errors are processed and the resulting components
undergo the Inverse Park and Clarke Transformation to be reconverted to a 3-phase voltage
signal that is sent to the Inverter Bridge. The Inverter controls the switching in such a way
Jason C Monzu Page 22
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
33/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
that the desired voltage and frequency are generated at the output according to the PWM
algorithm.
From the previously discussed AC motor characteristics the stator current is comprised of
two components, the Magnetizing current and the load current [25]. The magnetizing
current (IM) is approximately constant over speed and lags the voltage by 90 degrees. The
load current is in phase with the voltage and is directly proportional to the torque over all
changes in load. Therefore the major objective of the Vector Controller is to continuously
calculate the value of the torque producing current.
Under no-load conditions, almost all the no load stator current (IS) comprises the
magnetizing current. Any torque producing current is only required to overcome the
windage and friction losses in the motor [21]. Slip is almost zero, stator current lags the
voltage by 90 degrees resulting in a power factor that is close to zero.
At low motor loads, the stator current (IS) is the vector sum of the magnetizing current (IM)
with a slightly increased active torque producing current. Stator current lags the voltage
hence power factor and slip is poor [23].
At high motor loads, the stator current is the vector sum of the magnetizing current with a
greatly increased active torque producing current, which increases in proportion to the
increase in load torque. Stator current lags the voltage by the angle , so power factor has
improved to be close to full load power factor. Below shows the relationship between the
vector diagrams of the system at low and high loads [27],
Jason C Monzu Page 23
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
34/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-11: Current load vectors in an AC induction motor
The central part of the Vector Control system is the Active motor model that continuously
models the conditions inside the motor in order to calculate the active torque producing
current, slip and magnetic flux.
2.3 Current Feedback in AC variable speed drives
2.3.1 Methods of measuring current
Current feedback is required in AC variable speed drives for a number of purposes [28],
Protection - Short circuit, earth fault and thermal overload in motor circuits
Metering - Metering and indication of the process control system
Control - Current limit and current loop control.
Jason C Monzu Page 24
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
35/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Over the years several different methods have been developed to measure current and
convert it into an electronic form suitable for the drive controller. The method chosen
depends on the required accuracy of measurement and cost of implementation. The two
main methods of control are Current Shunt and the Hall effect sensor.
The Current Shunt principal is based on the current flowing through a link of pre-calibrated
resistance. The voltage measured across the link is directly proportional to the current
passing through it therefore according to the relationship V=IR the current can be
determined.
The Hall Effect sensor relies on the output voltage being DC which is directly proportional
to the current flowing through the sensor. High accuracy and stability over a wide current
and frequency range are amongst the main advantages of this device. This device is
commonly used with modern digital control circuits.
2.3.2 Current feedback in high performance Vector Drives
High performance drives that employ Field Oriented Control required some kind of current
feedback for the control loop to function correctly. In such cases the motor current varies
according to the load applied to the motor and the torque produced. The stator current for
each phase is used to construct a vector diagram from which requires the current
magnitude of all three phases. This can be achieved preferably with one Hall Effect CT in
each output phase or alternatively two in the output phases and one on the DC bus [29]. In
reality only two phases need to be measured as the final phase can be deduced from the
Jason C Monzu Page 25
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
36/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
relationship between the other current readings, however the DC bus current sensor is still
required for device protection.
2.4 Speed Feedback in AC variable speed drives
In closed loop speed control of electric motors and positioning systems, the speed and
position feedback from the rotating system is provided by transducers, which convert
mechanical speed into an electrical quantity compatible with the control system [7]. Some
of the more common techniques used today are Analogue speed Transducers, Digital
Speed Transducers and Digital Position Transducers.
2.4.1 Analogue Speed Transducer
Analogue Speed Transducer such as a Tachometer Generator which converts rotation
speed into an electrical voltage, which is proportional to the speed, and transferred to the
control system over a pair of screened wires.
2.4.2 Digital Speed Transducer
Digital Speed Transducers such as Rotary Incremental Encoders [17] that convert speed
into a series of pulses. The pulses are transferred to the control system over one or more
pairs of screened wires.
Jason C Monzu Page 26
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
37/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.4.3 Digital Position Transducers
Digital Position Transducers such as Rotary Absolute Encoder [17] that converts position
into a bit code whose value represents an angular position. The code is transferred
digitally to the control system over a screened parallel or serial communications link.
Jason C Monzu Page 27
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
38/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.5 Digital Signal Processors in AC variable speed drives
With the advances in microprocessor technology and DSP controllers there has been a host
of commercially available microprocessors that provide PWM module for control of
inverters. Typically the signals and algorithms associated with such a system can be very
complex and lengthy to compute. However through the use of DSP and the digitization of
the signal, calculation of the output, and the output to the D/A converter all must be
completed within the sample clock period. The speed at which this can be done determines
the maximum bandwidth that can be achieved with the system. For adequate dynamic
response or a Vector Control system the calculations associated with Field Orientated
Control completed around 2000 times per second which is less than 1ms [22]. The ability
to continuously model the induction motor at this speed only became viable recently the
development of the 16 bit microprocessor. Initially sufficient processing power was quite
expensive, but over a period of time, the cost of the processors have reduced and
processing speed has increased significantly.
Many different types of microprocessors have been utilized in the implementation of Field
Orientated Control. The MC68040 has been utilized in both field-orientated control and in
the implementation of ANN observer estimation of the rotor flux angle. The system also
includes 4 Mbytes of RAM, two 32-pin EPROM sockets, dual port MC68681 I.C. for
serial port communication, Local Resource Controller (LRC), VSB and VME bus
interfaces. One port of the MC68681 is connected to the 486 PC. The MC68040 operates
at 27.6 MIPS with a clock frequency of 33 MHz and 32-bit address/data bus [16].
Jason C Monzu Page 28
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
39/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The TMS320 is a DSP from Texas instruments that has been specifically designed for
Field Orientated Control. The TMS320's high level of throughput results from the chip's
comprehensive instruction set and highly pipelined architecture. Based on a modified
Harvard Architecture, the TMS320 allows transfer between program and data spaces for
increased device flexibility. Constants can be stored in program memory, and program
branches based on data computations can be performed. Thus, parallel operations can
execute a complex instruction in one 200-nanosecond (ns) cycle. Competing chips
typically execute instructions in 250-, 300- or 400-ns cycles [16].
The TMS320's speed in enhanced by the arithmetic logic unit's (ALU's) 16 x 16-bit
multiplier that uses 16-bit, signed 2's complement numbers to form a 32-bit product in 200
ns. Although the TMS320 accepts 16-bit inputs and has a 16-bit output, it features a 32-bit
ALU/accumulator that carries out all arithmetic operations to 32 places for greater numeric
precision [16].
Jason C Monzu Page 29
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
40/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.6 PWM 5 level Inverter
Early forms of DC to AC conversion are derived from the basic buck converter, where a
power semiconductor is used to switch a DC signal into a square wave (Square Wave
Inverter). With the introduction of power storage components, such as inductors and
capacitors, this square wave will resemble a rough sinusoidal wave. The desired sinusoidal
output can be further refined with the use of logic control on the semiconductors, enabling
the positive and negative peaks of the square wave to be delayed (Phase Shifted Square
Wave inverters), creating a zero level. All these adjustment were made in the aid of
producing a perfect sinusoidal output or in other words decreasing the Total Harmonic
Distortion (THD) [28].
PWM inverters further refine the conversion of the DC input to an AC output. This
advancement in inverters was not possible until recent semiconductor technology
advancements, in this particular project the semiconductors must have a high power rating
combined with a high switching frequency. PWM inverters use high-speed semiconductor
switches to switch the DC signal at varied time intervals, this will create varied pulse
widths, hence the name Pulse Width Modulator.
Jason C Monzu Page 30
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
41/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.6.1 Full Bridge PWM Inverter Topology
The basic construction of a PWM inverter can be understood by using the single-phase full
bridge model depicted in the figure below.
Figure 2-12: Circuit Diagram of a Full Bridge PWM Inverter [Constructed using PSIM demo]
As you can see the DC input signal is feed into the two legs of the full bridge inverter and
with the aid of the high-speed semiconductor switches converted in to an ac signal. The
semiconductor switches are controlled but he PWM control logic, which switch the DC
input at varied time intervals, creating varied pulse widths. The adjustment function is
called a Modulation function, M(t). The Modulation function is defined as follows [28],
Jason C Monzu Page 31
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
42/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
carriertheofmagnatudewhereA
signalmodulatingtheofmagnatudeAwhere
2/)1()(
c
m
=
=
= cm
ANAtM
The Modulation function is used to determine the output, as shown in the equation below.
VintMtVd )()( =
The desired output is no longer the dc average value, but is a unique wanted component.
This should be a moving average to denote the variation of the average output with time.
The moving average can be defined by the integral.[10]
=
t
Tt dssfTtV )(
1
)(
The figure below depicts the PWM output and the moving average created by the output.
Figure 2-13: Diagram of PWM Output [10]
Jason C Monzu Page 32
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
43/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.6.2 PWM Control
In order to control the semiconductors of the PWM inverter, a triangular reference signal
along with a sinusoidal reference signal are used to determine the switching times for the
semiconductors. These inputs are compared and will control the ON/OFF states of the
semiconductors. The following diagram depicts the two inputs of the comparator.
Figure 2-14: Triangle comparison PWM implementation [10]
The PWM logic is created by comparison of the sinusoidal signal to the triangular signal.
When the reference sinusoidal signal is above the triangular sawtooth signal the PWM
logic is switched on and when the sinusoidal signal falls below the triangular sawtooth
signal the PWM logic switches off. The duration of this switching is dependent on the
length of time from when the sinusoidal signal remains above or below the triangular
sawtooth signal. This process is displayed in the above figure 2-14 [28].
Jason C Monzu Page 33
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
44/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
2.6.3 Five Level PWM Inverter
The intent of using the Five Level PWM Inverter is to reduce the THD of the output ac
signal. The Five Level PWM signal involves constructing the ac output with five discrete
voltage levels. However when doing this the design and operation of the inverter will
change. The figure below depicts the desired output of such an inverter, which the five
discrete voltage levels clearly show. It is important to point out that the pulse modulations
have been exaggerated to give a better understanding.
Figure 2-15: Five level staircase output voltage. [1]
Like the progression of the multilevel PWM inverter suggest a five level PWM is
controlled by four triangular reference signals and one sinusoidal reference signal, shown
in the figure below. It can be seen below that the four different triangular references, or
bands, have differing offsets with the same amplitude, this essential for the inverters
operation
Jason C Monzu Page 34
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
45/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-16: Five Level PWM Control
The basic circuit design is depicted in the PSCAD diagram below, which clearly shows the
importance of the offset carriers, which control the PWM inverter. This system is not
useful for driving an induction motor as the output will have voltage spikes due to the
inductive currents not being permitted to flow when the IGBT interrupts the current to the
mid levels.
Jason C Monzu Page 35
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
46/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 2-17: Five level PWM generation
Once the circuitry for a single-phase five level PWM inverter is fully understood, little
effort is needed to expand the circuit into the required three phase five level PWM inverter.
This was easily implemented by duplicating the single-phase inverter three times and
modifying the modulating phase of each respective modulating sine wave signal for each
phase [10]. Although the above circuit is a five level PWM inverter, this circuit is not
possible to be used in the implementation of this project as the predominately inductive
load of the motor, causes KCL violations as there is no current path for the reverse current
from the inductive load.
Jason C Monzu Page 36
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
47/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
CHAPTER 3
3 Technical Review
3.1 Comparative Analysis of Torque-Controlled IM Drives with
Applications in electric and Hybrid Vehicles.
This review presents torque-controlled drives control based on machine flux and torque
estimation. The theory surrounding this review has been credited to the IEEE paper on
Analysis of Torque-Controlled IM Drives with Applications in electric and Hybrid
Vehicles [18]. The theoretical aspects of the methods are discussed and a comparative
analysis is provided with emphasis on DSP Implementation and experimental results.
Problems in the application of these techniques to propulsion systems are also discussed
and possible solutions are presented.
An electric propulsion system is generally based on a torque-controlled electrical drive.
Many of the methods of Vector Control published require a torque feedback signal.
In this review a comparative analysis of the torque-controlled methods with current
controllers is presented. For the purpose of comparison, torque controlled methods based
on stator voltage orientation are being studied. The dependence of the system based on
implementation methods, calculation the phase angle and the effects of obtaining the d-q
Jason C Monzu Page 37
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
48/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
current references using open loop and closed loop flux and torque observers are
compared.
The topics that this paper focuses on are as follows:
1) Digital integration methods for obtaining the flux from
the stator voltages:
a) saturation of each flux component feedback.
b) low pass filter without any feedback.
c) saturated magnitude on the feedback path.
2) Open loop or closed loop torque controller:
a) calculation ofiqs current from the torque reference.
b) calculation ofiqs current from the closed loop torque PI controller.
c) calculation ofiqs current from the closed loop torque fuzzy logic based controller.
3) Open loop or closed loop flux controller:
a) ids reference without control of flux.
b) ids reference current from flux PI controller.
4) Calculation of the angle for Vector Control from:
a) flux coordinates.
b) estimated electrical frequency.
Jason C Monzu Page 38
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
49/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The different combinations of the above control techniques influence the performance of
the system. The above techniques are discussed in detail in the following sections.
3.1.1 Integration of the stator voltage equation
Different techniques for the estimation of the torque produced by the induction motor are
presented in the literature. Among these, the torque estimation using the integration of
stator voltages depends less on the machine parameter variations. First, the flux
components are computed by integration of the voltages in the stationary reference frame
(,) using the following equations[18]:
dtiRv
dtiRv
ssss
sss
s
)(
)(
=
=
The accuracy of this calculation depends on the accurate value of the stator resistance as
well as on the integration method. Another aspect of the control is the electromagnetic
torque (Te) which is estimated using the following eqn. [18]:
[ ] ssss iiPp
Te =22
3
This estimated value of torque can be used for the torque control loop even if the induction
machine control method is based on rotor flux orientation.
Jason C Monzu Page 39
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
50/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
In the above flux equations the currents are obtained using current sensors, and the
voltages are the outputs of the PI controllers after d-q to a-transformation. This method
though quite reliable introduces errors in flux estimation, these are as follows,
1) A delay between the reference voltages used in estimation and the actual fundamental
components of the phase voltages.
2) Measured currents are passed through the A-to-D converter at a given sampling
frequency.
3) Flux integration by a digital low-pass filter introduces errors in phase and gain.
The common solution consists in the use of a low-pass filter that has the input-output
relation given by [18]
xs
yc
+
=
1
where c is chosen so that "s +c" ~ "s" for all the operating frequencies. If the lowest
stator frequency that should pass properly through filter is 8 Hz, then c
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
51/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The output can be further improved by re-writing the transfer function to introduce a
variable feedback within the low pass filter . This implementation leads to behaviour closer
to l/.s. Also, by saturating the feedback component (y), the dc bias component can be
limited.
xs
ys
yxs
ys
sx
ss
ys
xs
y
ccc
cc
c
+
++
=+
=
++
+
=
+
=
11
11
11
][1
]1[1
1][
]1[1
]1[1
1][
][][][
22
11
21
kxT
Tky
Tky
kyT
Tky
Tky
kykyky
sc
s
sc
sat
sc
sc
sc
+
++
=
+
+
+=
+=
Where ysat represents the saturated feedback.
Several digital integration methods have been tested in and a comparison of the current and
flux waveforms are presented further in the report (limitation of both flux components on
the feedback path, low-pass filter without any feedback and limitation of the flux
magnitude on the flux feedback). Experimental results have shown that the integration
method with limitation of the flux magnitude leads to reduced ripple.
Jason C Monzu Page 41
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
52/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
3.1.2 Calculation of the rotation angle
In any Vector Control method, an important item is the calculation or estimation of the
rotational angle or the SIN/COS function corresponding to this angle. The current
measurement resolution influences the angle estimation.
To obtain an estimate of stator flux orientation the following calculations can be used:
Electrical frequency [18],
=
=
dt
RivRiv
e
ss
ssssssss
e
22
)()(
Estimated flux components [18],
22
22
cos
sin
ss
s
ss
s
+=
+=
Precision ofdepends on the accuracy ofe that is a small dc value in low speeds (low
frequencies), obtained through a relationship in between small values (i or ). Accordingly,
at low speeds, accuracy of calculation is jeopardized by the large percentage of ripple in
e. For this reason, using the definition of SIN/COS based on the estimated flux
components in low speeds leads to better results than the calculation of electrical frequency
Jason C Monzu Page 42
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
53/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
(e). Using electrical frequency estimation at high speeds is better since it is essentially a
dc component that can be easily filtered to remove the inherent noise. Both methods were
implemented and tested and the experimental results confirmed the above statement.
3.1.3 Flux control loop
Since the dynamics of the flux regulator is not very important, the flux control loop is a
typical PI control loop based on the estimated flux magnitude signal. A Fuzzy Logic
controller would not introduce any major improvement for the performance of the overall
system. However, the output of the PI controller can be limited to different values. In order
to improve the flux loop dynamics, a negative ids current has been allowed during the
transients. The level of the positive limit at the controller output is a function of the
inverter output phase current ratings.
When the flux orientation is perfect, qs= 0 and , ds = | |. There are two possibilities of
developing the control based on ds or | |. The flux magnitude has been calculated and
used as the feedback signal in this control approach
3.1.4 Torque control Strategies
This review presents three different methods of torque control based on stator or rotor flux
orientation, these are as follows,
1) Open-loop torque control loop with closed loop stator flux control.
2) PI/Fuzzy torque control loop with closed loop stator flux
control based on rotor flux orientation.
Jason C Monzu Page 43
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
54/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
3) PI/Fuzzy torque control loop with closed loop stator flux control based on stator
flux orientation.
The influence of each control loop on the overall system performance is next discussed. In
this study, the current control loop sampling time was at 100 s, and the outer control
loops (torque and flux) are sampled at 300 s and, 600 s, respectively. In this particular
report to achieve better results special caution has been taken in software such that to do
not modify both flux and torque at the same time.
In the open-loop torque control, iqs reference is calculated by [18],
eqs
TKi =
The dynamic results will be affected whether iqsis calculated based upon flux reference or
estimated flux magnitude seen in the figures below. Figures 3-1 to 3-4 are presenting step
modification in flux or torque for the same base system, for different control structures.
Fig. 3-1 presents a control system containing a torque control loop while idsis introduced
as reference without any flux control loop. Fig. 3-2 presents a flux control loop with iqs
command without a torque control loop. Figs. 3-3 and 3-4 are introducing the full system
with both torque and flux control loops for step modification in either flux or torque. It can
also be seen the improved performance of the system containing both torque and flux
control loops.
Jason C Monzu Page 44
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
55/123
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
56/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 3-3: Step response (0.34-0.2 Wb) of the flux loop for torque and flux loops at 2100 RPM [18]
Figure 3-4: Step response (10-25Nm) of the flux loop for torque and flux loops at 2100 RPM [18]
Jason C Monzu Page 46
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
57/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
3.1.5 PI versus fuzzy control in the torque control loop
In propulsion systems, the torque control loop response is important. In order to decrease
the response time of the torque control loop and to minimize the influence of the induction
machine speed on the torque loop transients, a fuzzy logic control loop instead of the
conventional PI controller has been investigated. Fig. 3-5 [18] presents the torque control
loop responses at different speeds (500 RPM, 5000 RPM, and 7500 RPM) for both control
methods. The fuzzy logic controller has been developed in software using a simple
structure with two inputs, with seven triangular membership functions for each input,
linear de-fuzzification (Sugeno controller) [34] and triangular membership functions for
the iqs current (output of the FLC controller). The results are demonstrating that the FLC
has the same transient response at each speed. Measurement of the system efficiency has
been performed for different methods under study. The differences between these methods
at nominal speed are less than 2% for different torque levels.
Jason C Monzu Page 47
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
58/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
Figure 3-5: Step torque modification for both PI and FL controllers. [18]
3.2 Review conclusion
This paper presents a review of the torque-controlled IM drives based on the current-
controlled PWM voltage source converters and flux control loop. This review was found
to be quite relevant to the underlining themes of Field Orientated Control particularly as
they are directed at a propulsion system such as a hybrid vehicle. The review presents
Jason C Monzu Page 48
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
59/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
different integration methods of the stator voltage equation and compares them based on
the type of control method and the response of the system to these changes.
The advantages of stator flux control over rotor flux control are reviewed and the results
demonstrate the advantage of a system with two control loops (torque and flux) in terms of
stability and variable ripple despite the higher complexity. The report covers both PI
controllers and Fuzzy logic and focuses on the benefits of each. Essentially the Fuzzy
logic controller is more complex, but is less influenced by the parameter variations and less
dependent on speed.
This review concentrates on the most appropriate methods of control for application in a
hybrid and electric vehicle. The results obtained allow further insight into Field Orientated
Control and allow a greater depth of understanding into the control methods with respect to
a direct propulsion system.
Jason C Monzu Page 49
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
60/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
CHAPTER 4
4 Vector Drive Control Feedback loops
The term closed loop feedback control emphasizes the nature of the control system, where
feedback is provided from the output back to the input of the controller. A perfect example
of a closed loop feedback control system is a driver in a motor car. The speed of the car is
assessed by the drivers eye looking at the speedometer (speed transducer). This measured
speed is mentally compared to the desired speed (speed reference), which may be the set
limit for that stretch of road. Depending on the error, the driver (controller) may decide to
increase speed by further depressing the accelerator to adjust the speed reference. The
driver continually measures and re-evaluates the error between measured and desired speed
and adjusts the accelerator accordingly. At the same time the driver might be
simultaneously engaged in several other feedback control closed loop tasks such as
steering the car.
In the Vector Control system employs the use of an AC frequency converter to control the
voltage and frequency fed to the motor to suit the load characteristics . For example when
an operator selects a speed setting on a potentiometer, the system implements this selection
this selection by adjusting the output frequency and voltage to ensure that the motor runs at
its set speed. The accuracy of the control system and its response to the operators
command is determined by the type of control system employed.
Jason C Monzu Page 50
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
61/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The levels of control are:
Simple open-loop control No feedback from the process
Closed-loop control Feedback of a process variable
Cascade closed-loop control Feedback from more than one variable
When load torque and load position have to be continuously and accurately controlled the
closed loop control method is the most effective means of control feedback and will be the
method used in this project. The best compromise for accuracy and efficiency is the use
two feedback loops, these being the Speed and Torque control loops.
The first feedback loop controller is know as the speed control loop and uses the speed
error from a speed sensor to calculate the desired current. The primary objective being to
either increase speed or decrease speed. The speed loop therefore controls the output
frequency proportional to speed. The system was based on the knowledge that the speed
was recorded from a speed transducer positioned at the shaft of the motor. Therefore this
reduces the need for complicated calculations used to estimate speed. This is not always a
desirable alternative as in many cases the installation of a speed transducer is difficult or
economically unjustified. The speed error signal becomes the set point for the torque
regulator and is processed by a PID algorithm. This signal is compared to the in-phase
current feedback from the motor circuit and the error signal determines whether the motor
needs to accelerate or decelerate.
Jason C Monzu Page 51
-
8/7/2019 22893773 36 2 Field Orientated Control of a Multi Level PWM Inverter Fed Induction Motor
62/123
Field Orientated Control of a Multi-Level PWM Inverter Fed Induction Motor
The speed reference signal is derived from the inputs of the controller for the specific
Vector Control application. For example a conveyor is needed to be driven at 0.5m/s, that
speed can then be translated into a shaft speed in RPM depending on the appropriate gear
ratios.
The second feedback loop controller is known as the torque control loop. The loop
compares the set torque with the output of the torque estimation algorithm, with the new
error current calculates the desired output voltages. The measured process variable in this
case is the measured motor current which is proportional to the motor torque. Therefore
this control loop is often called the current loop.
In the design of the torque control loop it is assumed that the rate of change of current is
higher than the rate of change of speed or essentially saying that the motor is operating at a
constant speed. The current loop must allow for a time delay between output frequency
and the current. It then determines the desired inverter output frequency and voltage which
is used by the PWM to determine switching logic. The torque estimation algorithm can be
seen in the simulation chapter.
The main functions of the Field Orientated Control sequence are:
To continuously calculate the value of the torque producing current. This is
achieved by implementing the following actions:
Continuously mod