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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This comprehensive text examines existing and emerging electrical drive technologies. The authors clearly define the most basic electrical drive concepts and go on to explain the most important details while maintaining a solid connection to the theory and design of the associated electrical machines. Also including links to a number of industrial applications, the authors take their investigation of electrical drives beyond theory to examine a number of practical aspects of electrical drive control and application.
Key features:
* Provides a comprehensive summary of all aspects of controlled-speed electrical drive technology including control and operation.
* Handling of electrical drives is solidly linked to the theory and design of the associated electrical machines. Added insight into problems and functions are illustrated with clearly understandable figures.
* Offers an understanding of the main phenomena associated with electrical machine drives.
* Considers the problem of bearing currents and voltage stresses of an electrical drive.
* Includes up-to-date theory and design guidelines, taking into account the most recent advances.
This book’s rigorous coverage of theoretical principles and techniques makes for an excellent introduction to controlled-speed electrical drive technologies for Electrical Engineering MSc or PhD students studying electrical drives. It also serves as an excellent reference for practicing electrical engineers looking to carry out design, analyses, and development of controlled-speed electrical drives.
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CONTENTS
Cover
Title Page
Copyright
Preface
Abbreviations and Symbols
Chapter 1: Introduction to Electrical Machine Drives Control
1.1 What is an Electrical Machine Drive?
1.2 Controlled Variable Speed Drives
1.3 Electrical Machine Drive Implementation
1.4 Controlled Electrical Drives and Energy Efficiency
1.5 The Electrical Drive as an Element of a Controlled Industrial Process
References
Chapter 2: Aspects Common to All Controlled Electrical Machine Drive Types
2.1 Pulse Width Modulation Converter Electrical Motor Drive
2.2 Converter Interface to Power Source
2.3 Fundamental Mechanics
2.4 Basic Mechanical Load Types
2.5 Proportional-Integral-Derivative Controller in Electrical Drives
2.6 The Speed, Torque, or Position Control of an Electrical Drive
2.7 Control Time Rates and Embedded System Principles
2.8 Per-Unit Values
Chapter 3: The Fundamentals of Electric Machines
3.1 Energy Conversion in Electric Machines
3.2 Industrial Machine Windings
3.3 Effective Winding Turns and Spatial Harmonics
3.4 Induction Machine Rotors
3.5 The Damper Winding
3.6 AC Winding Systems
3.7 DC Machine Windings
3.8 The Brushless DC Machine
3.9 The Magnetic Circuit of an Electric Machine
3.10 Motor Voltage, Flux Linkage, Flux, Field Weakening, and Voltage Reserve
3.11 Motors in Power-Electronic Electrical Drives
References
Chapter 4: The Fundamentals of Space-Vector Theory
4.1 Introduction to the Space Vector for Current Linkage
4.2 Space-Vector Equivalent Circuits and the Voltage-Vector Equations
4.3 Space-Vector Model in the General Reference Frame
4.4 The Two-Axis Model
4.5 Application of Space-Vector Theory
References
Chapter 5: Torque and Force Production and Power
5.1 The Lorentz Force
5.2 The General Equation for Torque
5.3 Power
5.4 Reluctance Torque and Co-Energy
5.5 Reluctance Torque and the Cross-Field Principle in a Rotating Field Machine
5.6 Maxwell's Stress Tensor in the Definition of Torque
References
Chapter 6: Basic Control Principles for Electric Machines
6.1 The Control of a DC Machine
6.2 AC Machine Control Basics
6.3 Vector Control of AC Motors
6.4 Direct Flux-Linkage Control and Direct Torque Control
6.5 Improving DFLC to Achieve DTC
6.6 Other Control Principles
References
Chapter 7: DC and AC Power Electronic Topologies – Modulation for the Control of Rotating-Field Motors
7.1 The Thyristor Bridge as a Power-Electronic Drive Component
7.2 The Cycloconverter
7.3 The Load Commutated Inverter Drive
7.4 Voltage Source Inverter Power Stages
7.5 The Matrix Converter
7.6 Multilevel Inverters
7.7 The Structure and Interfaces of a Frequency Converter
References
Chapter 8: Synchronous Electrical Machine Drives
8.1 Synchronous Machine Drives for Power Generation
8.2 Synchronous Motor Drives
8.3 Synchronous Machine Models
8.4 Equivalent Circuits and Machine Parameters for a Synchronous Machine
8.5 Measuring Motor Parameters Using a Frequency Converter
8.6 Finite Element Analysis (FEA) for Determining the Synchronous Machine Inductances
8.7 The Relationship between the Stator and Rotor Excitations for a Synchronous Machine
8.8 The Vector Diagram for a Synchronous Machine
8.9 Torque Production for a Synchronous Machine
8.10 Simulating an Electrically Excited Salient-Pole Machine via Constant Parameters
8.11 The Current Equations for a Synchronous Machine
8.12 Simulating a Synchronous Machine in a Discrete-Time System
8.13 The Implementation of Vector Control for a Synchronous Machine
8.14 Field-Winding Current, Reactive Power, and the Dynamics of a Synchronous Machine Drive
8.15 The DOL Synchronous Machine and Field-Winding Current Supply
References
Chapter 9: Permanent Magnet Synchronous Machine Drives
9.1 PMSM Configurations and Machine Parameters
9.2 The Equivalent Circuit and Space-Vector Diagram for a PMSM
9.3 Equations Based on the Electric Current Angle
9.4 PMSM Current Vector Control
9.5 PMSM Direct Flux Linkage and Torque Control
9.6 Torque Estimation Accuracy in a PMSM DTC Drive
9.7 Speed and Position Sensorless Control Methods for PM Machines
References
Chapter 10: Synchronous Reluctance Machine Drives
10.1 The Operating Principle and Structure of a SynRM
10.2 Model, Space-Vector Diagram, and Basic Characteristics of a SynRM
10.3 The Control of a SynRM
10.4 Further Development of SynRM Drives – PMaSynRM
References
Chapter 11: Asynchronous Electrical Machine Drives
11.1 The Working Principle of the Induction Motor – Direct Online Drives
11.2 Asynchronous Machine Structures and the Main Norms
11.3 Frequency Converter Drives – Losses in a PWM Inverter Drive
11.4 Frequency Converter Control Methods for an Induction Motor
11.5 A summary of Industrial Induction Motor Drives
11.6 Doubly Fed Induction Machine Drives
Appendix IM1
References
Chapter 12: Switched Reluctance Machine Drives
12.1 The Torque or Force of an SR Machine
12.2 Average Torque
12.3 Control Systems for a SR Machine
12.4 The General Controller Structure
12.5 The Position Sensorless Operation of an SR Machine
12.6 A Summary of SR Drives
References
Chapter 13: Other Considerations: The Motor Cable, Voltage Stresses, and Bearing Currents
13.1 Cable Modelling
13.2 Reflected Voltage at a Cable Impedance Point of Discontinuity
13.3 Continuing Voltage at a Cable Impedance Point of Discontinuity
13.4 Motor Overvoltage
13.5 Limiting Overvoltages with Impedance Matching
13.6 Motor Bearing Currents in the Inverter Drive
13.7 Reducing Bearing Currents
References
Index
End User License Agreement
List of Tables
Table 1.1
Table 1.2
Table 3.1
Table 3.2
Table 4.1
Table 6.1
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 7.5
Table 8.1
Table 8.2
Table 8.3
Table E8.1
Table E8.2
Table E8.3
Table E8.4
Table E8.5
Table 8.4
Table 8.5
Table 8.6
Table 8.7
Table 9.1
Table 9.2
Table 11.1
Table 11.2
Table 11.3
Table 11.4
Table 11.5
Table 11.6
List of Illustrations
Figure 1.1
Figure 1.2
Figure 1.3
Figure 1.4
Figure 2.1
Figure 2.2
Figure 2.3
Figure 2.4
Figure 2.5
Figure 2.6
Figure 2.7
Figure 2.8
Figure 2.9
Figure 2.10
Figure 2.11
Figure 2.12
Figure 3.1
Figure 3.2
Figure 3.3
Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 3.9
Figure 3.10
Figure 3.11
Figure 3.12
Figure 3.13
Figure 3.14
Figure 3.15
Figure 3.16
Figure 3.17
Figure 3.18
Figure 3.19
Figure 3.20
Figure 3.21
Figure 3.22
Figure 3.23
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 4.17
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12
Figure 6.13
Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17
Figure 6.18
Figure 6.19
Figure 6.20
Figure 6.21
Figure 6.22
Figure 6.23
Figure 6.24
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
Figure 7.15
Figure 7.16
Figure 7.17
Figure 7.18
Figure 7.19
Figure 7.20
Figure 7.21
Figure 7.22
Figure 7.23
Figure 7.24
Figure 7.25
Figure 7.26
Figure 7.27
Figure 7.28
Figure 7.29
Figure 7.30
Figure 7.31
Figure 7.32
Figure 7.33
Figure 7.34
Figure 7.35
Figure 7.36
Figure 7.37
Figure 7.38
Figure 7.39
Figure 7.40
Figure 7.41
Figure 7.42
Figure 7.43
Figure 7.44
Figure 7.45
Figure 7.46
Figure 7.47
Figure 7.48
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 8.19
Figure 8.20
Figure 8.21
Figure 8.22
Figure 8.23
Figure 8.24
Figure 8.25
Figure 8.26
Figure 8.27
Figure 8.28
Figure 8.29
Figure 8.30
Figure 8.31
Figure 8.32
Figure 8.33
Figure 8.34
Figure 8.35
Figure 8.36
Figure 8.37
Figure E8.1
Figure E8.2
Figure E8.3
Figure E8.4
Figure E8.5
Figure E8.6
Figure E8.7
Figure E8.8
Figure E8.9
Figure E8.10
Figure 8.38
Figure 8.39
Figure 8.40
Figure 8.41
Figure 8.42
Figure 8.43
Figure 8.44
Figure 8.45
Figure 8.46
Figure 8.47
Figure 8.48
Figure 8.49
Figure 8.50
Figure 8.51
Figure 8.52
Figure 8.53
Figure 8.54
Figure 8.55
Figure 8.56
Figure 8.57
Figure 8.58
Figure 8.59
Figure 8.60
Figure 8.61
Figure 8.62
Figure 8.63
Figure 8.64
Figure 8.65
Figure 8.66
Figure 8.67
Figure 8.68
Figure 8.69
Figure 8.70
Figure 8.71
Figure 8.72
Figure 8.73
Figure 8.74
Figure 9.1
Figure 9.2
Figure 9.3
Figure 9.4
Figure 9.5
Figure 9.6
Figure 9.7
Figure 9.8
Figure 9.9
Figure 9.10
Figure 9.11
Figure 9.12
Figure 9.13
Figure 9.14
Figure 9.15
Figure 9.16
Figure 9.17
Figure 9.18
Figure 9.19
Figure 9.20
Figure 9.21
Figure 9.22
Figure 9.23
Figure 9.24
Figure 9.25
Figure 9.26
Figure 9.27
Figure 9.28
Figure 9.29
Figure 9.30
Figure 9.31
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 10.10
Figure 10.11
Figure 10.12
Figure 10.13
Figure 10.14
Figure 10.15
Figure 10.16
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 11.5
Figure 11.6
Figure 11.7
Figure 11.8
Figure 11.9
Figure 11.10
Figure 11.11
Figure 11.12
Figure 11.13
Figure 11.14
Figure 11.15
Figure 11.16
Figure 11.17
Figure 11.18
Figure 11.19
Figure 11.20
Figure 11.21
Figure 11.22
Figure 11.23
Figure 11.24
Figure 11.25
Figure 11.26
Figure 11.27
Figure 11.28
Figure 11.29
Figure 11.30
Figure 11.31
Figure 11.32
Figure 11.33
Figure 11.34
Figure 11.35
Figure 11.36
Figure 11.37
Figure 11.38
Figure 11.39
Figure 11.40
Figure 11.41
Figure 11.42
Figure 11.43
Figure 11.44
Figure 11.45
Figure 11.46
Figure 11.47
Figure 11.48
Figure 11.49
Figure 11.50
Figure 11.51
Figure 11.52
Figure 11.53
Figure 11.54
Figure 11.55
Figure 11.56
Figure 11.57
Figure 11.58
Figure 11.59
Figure 11.60
Figure 11.61
Figure 11.62
Figure 11.63
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 12.7
Figure 12.8
Figure 12.9
Figure 12.10
Figure 12.11
Figure 12.12
Figure 12.13
Figure 12.14
Figure 12.15
Figure 13.1
Figure 13.2
Figure 13.3
Figure 13.4
Figure 13.5
Figure 13.6
Figure 13.7
Figure 13.8
Figure 13.9
Figure 13.10
Figure 13.11
Figure 13.12
Figure 13.13
Figure 13.14
Figure 13.15
Figure 13.16
Figure 13.17
Figure 13.18
Figure 13.19
Figure 13.20
Figure 13.21
Figure 13.22
Figure 13.23
Figure 13.24
Figure 13.25
Figure 13.26
Figure 13.27
Figure 13.28
Figure 13.29
Figure 13.30
Figure 13.31
Figure 13.32
Guide
Cover
Table of Contents
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Electrical Machine Drives Control
An Introduction
Juha Pyrhönen
Department of Electrical EngineeringLappeenranta University of Technology, Finland
Valéria Hrabovcová
Faculty of Electrical EngineeringUniversity of Žilina, Slovakia
R. Scott Semken
Department of Mechanical EngineeringLappeenranta University of Technology, Finland
This edition first published 2016
© 2016 John Wiley & Sons Ltd
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Library of Congress Cataloging-in-Publication Data
Names: Pyrhönen, Juha, author. | Hrabovcová, Valéria, author. | Semken, R. Scott, author.
Title: Electrical machine drives control : An introduction / Juha Pyrhönen, Valéria Hrabovcová, R. Scott Semken.
Description: Chichester, West Sussex, United Kingdom : John Wiley & Sons, Inc., [2016] | Includes bibliographical references and index.
Identifiers: LCCN 2016015388 | ISBN 9781119260455 (cloth) | ISBN 9781119260400 (epub) | ISBN 9781119260448 (epdf)
Subjects: LCSH: Electric driving. | Electric motors–Electronic control.
Classification: LCC TK4058 .P89 2016 | DDC 621.46–dc23 LC record available at https://lccn.loc.gov/2016015388
A catalogue record for this book is available from the British Library.
ISBN: 9781119260455
Preface
A basic study of electrical drives is fundamental to an electrical engineering curriculum, and, today, gaining a better academic understanding of the theory and application of controlled-velocity electrical drive technologies is increasingly important. Electrical drives provide superior control properties for a wide variety of processes, and the number of applications for precision-controlled motor drives is increasing. A modern electrical drive accurately controls motor torque and speed with relatively high electromechanical conversion efficiencies, making it possible to considerably reduce energy consumption. Because of the present pervasive use of electric machinery and the associated large energy flows, the introduction of more effective and efficient electrical drives promises significant environmental benefit, and electrical engineers are responding by introducing new and more efficient electrical drives to a myriad of industrial processes.
A controlled-velocity electrical drive combines power electronics, electric machinery, a control system, and drive mechanisms to apply force or torque to execute any number of desired functions. The term electric machinery refers primarily to the electromagnetic mechanical devices that convert electricity to mechanical power or mechanical power to electricity—that is, to electric motors or generators. The term control system refers to the control electronics, instrumentation, and coding that monitor the condition of the electric machinery and adjust operating speed and/or match force or torque to load.
With a rigorous introduction to theoretical principles and techniques, this academic reference and research book offers the master of science or doctoral student in electrical engineering a textbook that provides the background needed to carry out detailed analyses with respect to controlled-velocity electrical drives. At the same time, for engineers in general, the text can serve as a guide to understanding the main phenomena associated with electrical machine drives. The edition includes up-to-date theory and design guidelines, taking into account the most recent advances in the field. The years of scientific research activity and the extensive pedagogical skill of the authors have combined to produce this comprehensive approach to the subject matter. The considered electric machinery consists of not only classic rotating machines, such as direct current, asynchronous, and synchronous motors and generators, but also new electric machine architectures that have resulted as the controller and power electronics have continued to develop and as new materials, such as permanent magnets, have been introduced. Examples covered include permanent magnet synchronous machines, switched reluctance machines, and synchronous reluctance machines.
The text is comprehensive in its analysis of existing and emerging electrical drive technologies, and it thoroughly covers the variety of drive control methods. In comparison to other books in the field, this treatment is unique. The authors are experts in the theory and design of electric machinery. They clearly define the most basic electrical drive concepts and go on to explain the critical details while maintaining a solid connection to theory and design of the associated electric machinery. Addressing a number of industrial applications, the authors take their investigation of electrical drives beyond theory to examine a number of practical aspects of control and application. Scalar, vector, and direct torque control methods are thoroughly covered with the nonidealities of direct torque control being given particular focus.
The expert body of knowledge that makes up this book has been built up over a number of years with contributions from numerous colleagues from both the Lappeenranta University of Technology and the University of Žilina in Slovakia. The authors are grateful for their help.
In particular, the authors would like to thank Professor Tapani Jokinen for his extensive contributions in general, Professor Olli Pyrhönen for his expert guidance on the control of synchronous electrical machine drives, Dr. Pasi Peltoniemi for the detailed and valuable example on tuning the control of an electrically excited synchronous machine, and M.Sc. Juho Montonen for his permanent magnet machine analysis. The authors would also like to specifically thank Dr. Hanna Niemelä, who translated some of the included text from its original Finnish. Finally, we give our warmest thanks to our families, who accommodated our long hours of writing, editing, and manuscript preparation.
This academic reference and research book uniquely provides comprehensive materials concerning all aspects of controlled-velocity electrical drive technology including control and operation. The treatise is based on the authors' extensive expertise in the theory and design of electric machinery, and in contrast to existing publications, its handling of electrical drives is solidly linked to the theory and design of the associated electric machinery.
Abbreviations and Symbols
A
magnetic vector potential [Vs/m], linear current density [A/m]
AC
alternating current
AM
asynchronous machine
ASIC
application-specific integrated circuit
A1–A2
armature winding terminals of a DC machine
AlNiCo
aluminium nickel cobalt permanent magnet
A
transmission ratio
B
magnetic flux density, vector [T] [Vs/m
2
]
B
magnetic flux density, scalar [T] [Vs/m
2
]
BLDC
brushless DC motor
B1–B2
commutating pole winding of a DC machine
C
capacitance [F], machine constant, speed of light [m/s]
C
E
constant, function of machine construction
C
T
torque producing dimensionless factor
C1–C2
compensating winding of a DC machine
C
io,i
outer or inner capacitance between the ball and the race in the ball bearing [F]
C
g
capacitance between the races of the ball bearing [F]
C
01
, C
02
capacitance of the filter [F]
C
wf
capacitance between the stator winding and the stator frame [F]
C
wr
capacitance between the stator winding and the rotor core [F]
C
sr
capacitance between the stator and rotor cores [F]
c
experimentally determined coefficient, distributed capacitance [F/m]
c/h
duty cycles per hour
c
′
capacitance per unit length [F/m]
CENELEC
Comité Européen de Normalisation Electrotechnique
CHP
combined heat and power
CSI
current source inverter
D
diameter [m], friction coefficient, code (drive end)
D1, D2
diode 1, diode 2
DΩ
viscous friction, frictional torque
DC
direct current
DFIG
doubly fed induction generator
DFIM
doubly fed induction motor
DFLC
direct flux linkage control
DTC
direct torque control
D1–D2
series magnetizing winding terminals of a DC machine
d
thickness [m], axis
DOL
Direct On Line
DSC
Direct Self Control
E
electromotive force (emf) [V], RMS, electric field strength [V/m], scalar
E
PMph
phase value of emf induced by PM [V]
emf
electromotive force [V]
E
electric field strength, vector [V/m]
ESR
equivalent series resistance [Ω]
e
electromotive force [V], instantaneous value
e
(
t
) or per-unit value
e
s
back electromotive force vector induced by the stator flux linkage
ψ
s
[V] or per-unit value
e
m
back electromotive force induced by the air gap flux linkage
ψ
m
[V] or per-unit value
F
force [N], scalar
F
force [N], vector
F1, F2
terminals of field winding
FEA
finite element analysis
FLC
flux linkage control
FOC
field oriented control
FPGA
field programmable gate array
F
m
magnetomotive force
[A], (mmf)
FPGA
field-programmable gate array
f
frequency, characteristic oscillation frequency [Hz], or per-unit value
f
sw
switching frequency [Hz] or per-unit value
g
distributed conductance [S/m]
G
m
transfer function
G
ce
closed loop transfer function
GTO
gate turn-off thyristor
H
magnetic field strength [A/m]
h
PM
height of permanent magnet material [m]
I
electric current [A], RMS
IE1, 2, 3, 4
efficiency classes
IC
cooling methods
IGBT
insulated-gate bipolar transistor
IGCT
integrated gate-commutated thyristor, integrated gate controlled thyristor
IEC
International Electrotechnical Commission
IEEE
Institute of Electrical and Electronics Engineers
IM
induction motor
Im
imaginary part
IP
enclosure class
i
(
t
)
instantaneous value of current [A]
i
B
base value for current [A]
I
k
,
I
s
starting current [A]
I
st
locked rotor current (starting) [A]
I
ef
effective load current [A]
i
a
armature current [A]
i
com
common current linkage [A]
i
f
field current [A]
i
m
magnetizing current space vector [A] or per-unit value
i
PM
PM represented by a current source in the rotor [A] or per-unit value
i
PE
current in the protective earth wire of the motor cable [A] or per-unit value
i
mPE
earthing current [A] or per-unit value
J
moment of inertia [kgm
2
], inertia, current density [A/m
2
], magnetic polarization [Vs/m
2
]
J
m
moment of inertia of the motor [kgm
2
]
J
load
load moment of inertia [kgm
2
]
J
tot
total moment of inertia [kgm
2
]
j
imaginary unit
K
kelvin, transformation ratio, constant
K
p
amplification
k
coupling factor
k
C
Carter factor
k
d
distribution factor
k
gain
gain coefficient
k
p
pitch factor
k
ri
reduction factor (current ratio of synchronous machine)
k
riav
ratio of magnitudes of the current space vectors
k
rs
transformation ratio between stator and rotor
k
sq
,
k
sk
skewing factor
k
w
winding factor
k
w
N
effective number of turns
L
inductance [H]
L
c
choke
LCI
load commutated inverter
L
D
total inductance of the direct damper winding [H] or per-unit value
L
Dσ
leakage inductance of the direct damper winding [H] or per-unit value
L
d
direct axis synchronous inductance [H] or per-unit value
L
dD
mutual inductance between the stator equivalent winding on the d-axis and the direct equivalent damper winding [H] or per-unit value
L
dF
mutual inductance between the stator equivalent winding on the d-axis and the field winding (in practice
L
md
) [H] or per-unit value
transient inductance [H] or per-unit value
direct axis transient inductance [H] or per-unit value
direct axis subtransient inductance [H] or per-unit value
L
f
total inductance of the field winding [H] or per-unit value
L
F
inductance of the DC field winding [H] or per-unit value
L
fσ
leakage inductance of the field winding [H] or per-unit value
L
k
short-circuit inductance [H] or per-unit value
L
kσ
mutual leakage inductance between the field winding and the direct damper winding, i.e., the Canay inductance [H] or per-unit value
L
m
magnetizing inductance [H] or per-unit value
L
md
magnetizing inductance of an
m
-phase synchronous machine, in d-axis [H] or per-unit value
L
mn
mutual inductance [H] or per-unit value
L
mq
quadrature magnetizing inductance [H] or per-unit value
L
Q
total inductance of the quadrature damper winding [H] or per-unit value
L
Qσ
leakage inductance of the quadrature damper winding [H] or per-unit value
L
pd
main inductance of a single phase [H] or per-unit value
L
p
main inductance of a single phase [H] or per-unit value
L
q
quadrature axis synchronous inductance [H] or per-unit value
quadrature axis subtransient inductance [H] or per-unit value
L
mutual inductance between the stator equivalent winding on the q-axis and the quadrature equivalent damper winding (in practice
L
mq
) [H] or per-unit value
L
0
equivalent inductance [H] or per-unit value
L
m0
magnetizing inductance at no load at the rated stator flux level or per-unit value
LSRM
linear switched reluctance machine
L
s
stator synchronous inductance [H] or per-unit value
L
sσ
stator leakage inductance [H] or per-unit value
L
01
,
L
02
inductance of the filter [H] or per-unit value
L
′
transient inductance [H] or per-unit value
L
″
subtransient inductance [H] or per-unit value
L1, L2, L3
network phases
l
length [m], magnetizing route [m], distance [m], relative inductance, distributed inductance [H/m]
l
cr
critical cable length [m]
l
e
effective core length [m]
l
′
equivalent core length, effective machine length [m], inductance per unit length [H/m]
M
mutual inductance [H], or per-unit value
M
modulation index
MMF
magnetomotive force [A]
m
number of phases, mass [kg]
m
a
amplitude modulation ratio
m
f
frequency modulation ratio
m
′
phase number of the reduced system
m
0
constant
N
number of turns in a winding, magnetic north pole, code (nondrive end)
N
p
number of turns of one pole pair
NdFeB
neodymium iron boron permanent magnet
NEMA
National Electrical Manufacturers Association
NPC
neutral point clamped (inverter)
n
normal unit vector of the surface
n
number of teeth, number of units determined by the subscript
pu
per unit
P
power, losses [W] or per-unit value
P
ef
effective power [W]
P
e
electrical power [W] or per-unit value
P
el
electrical power [W] or per-unit value
P
in
input power [W] or per-unit value
P
mec
mechanical power [W] or per-unit value
PE
protective earth wire of the motor cable
PID
proportional-integrating-differentiating controller
PMSM
permanent magnet synchronous motor (or machine)
PWM
pulse-width-modulation
PM
permanent magnet
PMaSynRM
permanent magnet assisted synchronous reluctance motor
MTPV
maximum torque per volt
MTPA
maximum torque per ampere
P
ρ
friction loss [W] or per-unit value
p
number of pole pairs
Q
electric charge [C], number of slots
q
number of slots per pole and phase, instantaneous charge,
q
(
t
) [C]
R
resistance [Ω] or per-unit value
R
ball
resistance of the ball of the ball bearing [Ω]
R
ri
resistance of the inner race of the ball bearing [Ω]
R
ro
resistance of the outer race of the ball bearing [Ω]
R
D
resistance of the direct damper winding [Ω] or per-unit value
representing the part of mechanical power associated with
R
r
R
f
resistance of the field winding [Ω] or per-unit value
R
F
resistance of the field winding [Ω] or per-unit value
RM
reluctance machine
RMS
root mean square
R
s
stator resistance [Ω]
R
Q
resistance of the quadrature damper winding [Ω] or per-unit value
R
01
,
R
02
resistance of the filter [Ω] or per-unit value
r
radius [m], distributed resistance [Ω/m]
r
radius unit vector
S1–S9
duty types of electrical machines
S
apparent power [VA], or per-unit value, surface [m
2
]
S
switch, magnetic south pole
SM
synchronous motor
SR
switched reluctance
SRM
switched reluctance motor
SynRM
synchronous reluctance motor
SVM
space vector modulated inverters
S
st
maximum permitted starting apparent power [VA] or per-unit value
S
PE
power processing ability required by power electronics [VA] or per-unit value
S
U
,
S
V
,
S
W
switching function variables
SmCo
samarium cobalt permanent magnet
SynRM
synchronous reluctance machine
s
,
slip, Laplace domains operator
s
b
slip at
T
b
s
0
base slip value
T
temperature [K] [°C], duration [s], torque [Nm], cycle time of the oscillation [s]
T1, T2
transistor 1, transistor 2
TEFC
totally enclosed fan cooled
T
sub
duration of the subsequent of the modulation [s]
ΔT
temperature rise [K] [°C]
T
torque space vector [Nm] or per-unit value
T
b
pull out torque, breakdown torque [Nm] or per-unit value
T
em
electromagnetic torque [Nm] or per-unit value
T
e
electromagnetic torque [Nm] or per-unit value
T
L
load torque [Nm] or per-unit value
T
max
maximal torque [Nm] or per-unit value
T
N
nominal, rated torque [Nm] or per-unit value
T
pull-in
synchronizing torque [Nm] or per-unit value
T
s
starting torque [Nm] or per-unit value
T
wL
working torque of the load [Nm] or per-unit value
t
0
operating period [s]
t
c
commutation period [s]
t
cef
effective cooling period [s]
T
1
starting torque, locked rotor torque [Nm] or per-unit value
T
u
minimum torque [Nm] or per-unit value
T
I
integrating time constant [s]
T
D
differentiating time constant [s]
t
time [s]
t
tangential unit vector
t
j
cycle time [s]
t
p
time of pulse propagation (wave propagation time) [s]
t
r
rise time, duration of converter pulse [s]
U
voltage [V], RMS
U
d
supply voltage [V]
U
DC,meas
measured intermediate voltage [V]
U
depiction of a phase
u
voltage, instantaneous value
u
(
t
), incoming voltage [V] or per-unit value
u
cm
common mode voltage (star point voltage) [V] or per-unit value
u
r
reflected voltage [V] or per-unit value
u
drop
voltage drop estimation error [V] or per-unit value
u
2
forward travelling voltage [V] or per-unit value
u
DCmE
voltage from DC link midpoint to PE [V] or per-unit value
Δ
u
voltage drop [V] or per-unit value
Δ
U
DC,offs
offset voltage [V] or per-unit value
V
depiction of a phase
VDE
Verband Deutscher Elektroingenieure
VRM
variable reluctance motor
VSI
voltage source inverter
v
speed, velocity, wave velocity, propagation speed of the voltage pulse [m/s]
v
vector
W
energy [J], coil span (width) [m]
W
depiction of a phase
W
*
,
W
x
magnetic co-energy [J]
W
e
magnetic energy (energy stored in magnetic field) [J]
W
mec
mechanical work [J]
W
mt
energy converted into mechanical work when the transistor is conducting [J]
W
md
mechanical work when the diode is conducting [J]
W
fc
energy stored in the magnetic field [J]
W
R
energy returning to the voltage source [J]
W
d
energy returned through the diode to the voltage source [J]
w
ins
thickness of the insulation layer,[m]
w
Fe
thickness of the iron layer,[m]
X
reactance [Ω]
x
coordinate, axis
Y
admittance [S]
y
axis
Z
impedance, nonlinear impedance of the ball bearing [Ω]
Z
m
characteristic impedance of the motor cable [Ω]
Z
s
characteristic impedance of the filter [Ω]
Z
s01
,
Z
s02
impedance of the filter [Ω]
Z
0
characteristic impedance [Ω]
z
coordinate, length [m]
z
Q
number of conductors in a slot
α
angle [rad] [°], coefficient, temperature coefficient, relative pole width of the pole shoe
α
i
factor of the arithmetical average of the flux density
α
PM
relative permanent magnet width
α
SM
relative pole width coefficient for synchronous machines
β
angle [rad] [°]
Γ
energy ratio, cylinder that confines the rotor, integration route
γ
angle, rotor angle [rad] [°], coefficient
γ
c
commutation angle [rad] [°]
γ
D
switch conducting angle, dwelling angle [rad] [°]
γ
0
turn on switching angle [rad] [°]
δ
air gap (length) [m], load angle [rad] [°]
δ
de
equivalent air gap (slotting taken into account) in the d-axis [m]
δ
e
equivalent air gap (slotting taken into account) [m]
δ
ef
effective air gap (influence of iron taken into account) [m]
δ
′,
δ
0
minimum air gap, (air gap in the middle of the pole shoe) [m]
minimum air gap, influence of slotting is taken into account [m]
equivalent direct axis air gap [m]
equivalent quadrature axis air gap [m]
δ
s
load angle [rad] [°]
δ
m
load angle [rad] [°]
Δ
δ
ef
additional effective air gap caused by PM [m]
ɛ
permittivity [F/m], stroke angle [rad] [°], angle, correction term
ɛ
r
relative permittivity
ɛ
0
permittivity of vacuum 8.854·10
−12
[F/m]
η
efficiency
Θ
current linkage vector [A] or per-unit value
Θ
current linkage [A], angle [rad] [°]
θ
angle [rad] [°]
ϑ
angle [rad] [°]
κ
angle, current angle [rad] [°], vector position in a sector
λ
angle [rad] [°],
μ
permeability [Vs/Am],
μ
r
relative permeability
μ
0
permeability of vacuum, 4 · π · 10
–7
[Vs/Am] [H/m]
ν
pulse velocity [m/s], ordinal of harmonic
П
surface [m
2
]
ρ
resistivity [Ωm], reflection factor (coefficient)
ρ
ν
transformation ratio for IM impedance, resistance, inductance
σ
leakage factor, ratio of the leakage flux to the main flux, Maxwell stress [N/m
2
]
σ
F
tension, tension force [Pa]
σ
F
n
normal tension [Pa]
σ
F
tan
tangential tension [Pa]
σ
mec
mechanical stress [Pa]
τ
relative time, transmission coefficient, control bit (torque or flux linkage)
direct axis transient time constant with an open-circuit stator winding [s]
direct axis transient time constant [s]
direct axis subtransient time constant [s]
quadrature axis subtransient time constant [s]
quadrature axis subtransient time constant with open-circuit stator winding [s]
τ
p
pole pitch [m]
τ
v
phase zone distribution
τ
A
armature time constant [s]
τ
mec
mechanical time constant [s]
Φ
magnetic flux space vector [Wb] [Vs] or per-unit value
Φ
magnetic flux [Wb] [Vs]
Φ
δ
air gap flux [Wb] [Vs]
Φ
h
main magnetic flux [Wb] [Vs]
ϕ
magnetic flux, instantaneous value
ϕ
(
t
) [Wb] [Vs],
φ
phase shift angle, power factor angle [rad] [°]
ψ
magnetic flux linkage [Vs] or per-unit value
ψ
h
flux linkage of a single phase [Vs] or per-unit value
ψ
m
air-gap flux linkage [Vs] or per-unit value
ψ
s,u
stator flux linkage integrated from the converter voltages [Vs] or per-unit value
ψ
s,i
stator flux linkage calculated from the current model [Vs] or per-unit value
ψ
s0
initial flux linkage (∼
ψ
PM
) [Vs] or per-unit value
ψ
A
armature reaction flux linkage [Vs] or per-unit value
ψ
C
compensating winding flux linkage [Vs] or per-unit value
ψ
B
commutating pole winding flux linkage [Vs] or per-unit value
ψ
F
field winding flux linkage [Vs] or per-unit value
ψ
PM
permanent magnet flux linkage [Vs] or per-unit value
ψ
tot
total flux linkage of the machine [Vs] or per-unit value
Ω
mechanical angular speed [rad/s] or per-unit value
Ω
hs
speed of high speed area starts at
Ω
hs
or per-unit value
ω
electric angular velocity [rad/s], angular frequency [rad/s] or per-unit value
Subscripts
0
section
1
primary, fundamental component, beginning of a phase, locked rotor torque, phase number
2
secondary, end of a phase, phase number
3
phase number
a
armature, shaft
A
armature
arm
armouring
ad
additional
av
average
act
actual
b
base value, peak value of torque, blocking
bar
concerning bar
bearing
concerning bearing
C
capacitor
c
conductor, commutation
cp
constant power
calc
calculated
corr
correction
cr, crit
critical
D
direct, damper
d
direct, direct axis, distribution
DC
direct current
E
back emf (electromotive force)
e
electrical, electric
eff
effective
el
electric, electrical
em
electromagnetic
err
error
est
estimate
ext
external
f,
field, filter
filt
filtered
F
force, field
Fe
iron
grid
concerning a grid
i
internal
k
short circuit, ordinal
L
load
LL
line to line
m
mutual, main, motor, mechanical
M
motor
mag
magnetizing, magnetic
max
maximum
mec
mechanical
meas
measured
min
minimum
N
rated
n
nominal, normal, normalized, normalization, orthogonal component
non-sal
nonsaliency
new
new value
old
old value
p
pole, pitch
ph
phase
pu
per unit value
PM
permanent magnet
q
quadrature, quadrature axis, zone
r
rotor, rotor reference frame
ref
reference
res
reserve
s
stator
sal
saliency
sk
skewing
slipring
concerning a slip ring
sub
subtransient
sum
vector sum of currents
syn
synchronous
sw
switching
t
tangential
tan
tangential
tot
total
tr
transient
triangle
triangle waveform
u
pull-up torque
v
zone, coil
w
end winding leakage flux
x
x-direction, axis
y
y-
direction, axis
z
z
-direction, phasor of voltage phasor graph
δ
air gap
Φ
flux
ν
harmonic
σ
leakage
Superscripts
^,
peak/maximum value, amplitude
′
imaginary, apparent, reduced, referred, virtual, transient
*
base winding, complex conjugate
s
stator reference frame
r
rotor reference frame
g
general reference frame
Boldface symbols are used for space vectors
i
current space vector,
i
=
i
x
+ j
i
y
,
i
=
i
e
j
θ
[A] or per-unit value
i
absolute or per-unit value of current space vector
I
complex RMS phasor of the current
1Introduction to Electrical Machine Drives Control
Few technologies are more important to our collective quality of life than electrical drive technology. One could say that electric motors drive and electric generators power the world. Further, power electronics offers an indefatigable tool for accurate power conversion. And it seems the importance of the technology is poised to rise to even greater heights in the course of the next few decades as more reliable, more cost effective, and more flexible electrical drive systems become available.
For more than a century, electrical machine drives have been powering production processes for numerous industries. Applications include pumping, ventilation, compression, milling, crushing, grinding, conveying, and transporting. In modern robot-dependent manufacturing systems, electrical drives are responsible for precise position control of various robot arms and end effectors.
Concerns about air quality in cities and the increasing demand for improvements in energy efficiency favour using even more electric or hybrid vehicles for transportation needs. The current rate of change toward even more electromobility is limited only by today's high price of electric storage technology. The electrical drives themselves, that is, the motors and converters, are more than sufficient to serve as a replacement for the existing internal combustion engines in cars and buses.
Today, more than 50% of the world population lives in urban areas, and that percentage is growing. This growth in population powers increasing demand for more and better methods of moving people, materials, and things. Electrical machine drives are becoming an increasingly essential element of these transportation applications. Globalization, the accelerating process of international integration, puts added demand on sea and air transport, and ships and even aircraft are relying more and more on the most up-to-date electrical drive systems.
In addition, the average age of the world population is advancing at a rate unparalleled in human history. By 2050, the elderly will account for 16% of the global population. Caring for these 1.5 billion senior citizens over the age of 65 will strain the world's existing healthcare infrastructure. Fortunately, intelligent machinery has the potential to address the needs of the ageing population and to ease this demographic challenge. As the sinew of intelligent machinery, the increasing importance of electrical machines drives again seems to be clear.
Climate change is also bringing about ever more troubling environmental challenges. Permafrost in Siberia is melting and releasing methane into the atmosphere, there are stronger and increasingly damaging storms, and many drought areas are experiencing unprecedented levels of dryness. The burning of carbon-based fossil fuels to produce both electrical and motive power has been identified as a major contributor to climate change, and moving toward electrical power production technologies that do not burn fuels is a possible solution. Electrical generator drives are essential components of several of the more climate-friendly power production options currently available such as hydro, wind, and geothermal. Moreover, electric vehicles, a green alternative to fuel-burning cars, buses, and trucks, also rely on electrical motor drives.
At present, electric motors are the world's single biggest consumer of electricity, accounting for about 70% of industrial power consumption and nearly 45% of total global electricity consumption. Most in service are polyphase current (AC) induction motors, which are inexpensive and easy to maintain and can be directly connected to an AC power source. However, the majority of these AC induction motors lack flexible speed control, so they are not being used as efficiently as possible. Modern electrical drive technology is beginning to offer more cost-effective solutions with excellent speed control, making it possible to significantly improve efficiencies and minimize power consumption. These developments will encourage the replacement of AC motor systems in existing applications and the implementation of modern electrical drives for any new ones.
1.1 What is an Electrical Machine Drive?
The word drive comes from the Anglo-Saxon word dríf-an, which was a verb meaning to urge (an animal or person) to move. It is used as a noun here that can be defined as the means for giving motion to a machine or machine part. Therefore, an electrical drive can be defined as an electrical means of imparting motion. When an electrical drive is operated in reverse, it becomes a means of harnessing motion to generate electricity. To be more specific, when an electrical drive is driving, it can be referred to as an electrical motor drive. When it is driven, it can be referred to as an electrical generator drive.
Depending on the application, electric machines often operate in both motoring and generating modes. And, often, there is no technology difference between an electrical motor drive and an electrical generator drive. For example, the electric drive motor that propels an electric train or automobile—referred to as a traction motor—must run forward and backward and brake in both directions.
Electrical machine drives can be categorized as either noncontrolled or controlled motor or generator drives. Most motor drives working in industrial applications are noncontrolled. Almost exclusively, these are three-phase AC induction motors with direct on line (DOL) or across the line starting. Large-scale power generation mostly uses DOL drives based on synchronous generator drives.
To improve performance and efficiency, many applications are making use of controlled electrical drives. Controlled electrical motor drives are starting to become more popular in cases where the drives are tied into an industrial automation system. Distributed generation is driving demand in electrical power industries for speed-controlled electrical generator drives. In wind power, for example, so-called full power converters are becoming more common where both the generator and the network connection are fully controlled via power electronics.
1.2 Controlled Variable Speed Drives
The primary function of any variable speed drive is to control speed, force production, acceleration, deceleration, and direction of movement, whether it be rotary or linear. Unlike constant speed electric machines, variable speed drives can smoothly change speed to anywhere within their design operating range, and this adjustability makes it possible to optimize production processes for improved product quality, production speed, or safety.
Electrical variable speed drives are offered in a number of basic types, but the two most versatile for general purpose applications, and therefore the most common, are direct current (DC) drives and adjustable frequency AC drives. An electrical variable speed drive typically includes the following three principle elements.
The high-level controller enables (a) the operator to start, stop, and change speed via a human-machine interface (HMI) using buttons, switches, and potentiometers or (b) a plant control and set point master computer to send similar commands.
The drive controller converts the fixed voltage and frequency of an AC power source into adjustable power output to control the electric drive motor over its range of speeds.
The drive motor transforms electrical energy into motor movement. Shaft rotation or linear actuator movement speed varies with power applied by the drive controller.
1.2.1 DC Variable Speed Drives
DC drives are motor speed control systems based on DC motors or generators.
In a traditional rotary DC motor, the rotor (armature) spins inside a magnetic field that is initially produced either electromagnetically or via attached permanent magnets (PMs). The most common electromagnetic approach is to supply the field and armature windings separately. The result is referred to as a separately excited DC motor. If, instead, the no-load magnetic field is produced using PMs, the result is referred to as a PMDC motor. Separately excited and PMDC represent two of the more important and commonly used DC motor types.
In a separately excited and compensated DC motor, speed is directly proportional to the voltage applied to the armature and inversely proportional to motor flux, which is a function of field current. As a result, speed can be controlled via either armature voltage or field current. In a PMDC motor, speed is also directly proportional to the applied voltage. However, since the PMDC magnetic field remains constant, PMDC motor speed cannot be increased beyond the rated speed by reducing armature field current.
DC Drive Control
The speed and torque of a DC motor are independent. Speed is proportional to the applied voltage, and torque is proportional to the applied current.
As in all drives, power varies in direct proportion to speed. That is, 100% rated power is developed only at 100% rated motor speed with rated torque. Constant power over a specified speed range is needed for some applications. An armature-controlled DC drive can deliver less-than-maximum nearly constant power over a portion of its operating speed range. Because it is a function of speed, the level of power available depends on where in the speed range it is needed. For example, a particular drive might be capable of delivering 50% of its maximum power from 50% to 100% of its rated speed, so if 4 kW was needed over the upper half of the drives speed range, an armature-voltage–controlled drive rated for 8 kW would be required.
In addition to being armature-voltage controllable, the performance of separately excited DC drives can be influenced by changes in field current. Normally, they operate using a constant field excitation, but they can be pushed over their rated speed by reducing field flux beyond the rated speed point. This is called field weakening.
The Advantages of the DC Drive
Brushed DC motors are more complicated than AC motors and require more maintenance. Their most vulnerable component is the mechanical commutator, which acts as a mechanical inverter in a motor or a mechanical rectifier in a generator. The maximum speed of a DC motor depends on its mechanical endurance, which may be limited because of the commutator and brushes. Some of the disadvantages of the traditional DC motor can be overcome with a brushless DC motor architecture. The brushless DC motor moves the armature to the stator side and uses power-electronic commutation. Its architecture is similar to that of a PM synchronous AC motor.
The primary advantages can be summarized as follows.
DC drives can be less complex and less expensive for most power ratings.
DC drives can provide starting and accelerating torques exceeding 400% of rated (Sowmya, 2014).
DC drives are able to control speed over a wide range (above and below rated speed).
DC drives can be quick starting, stopping, reversing, and accelerating.
DC drives offer accurate speed control and a linear speed-torque curve.
DC drives dominate in sub-kilowatt power applications.
DC drives are easier to understand for maintenance and operations personnel.
1.2.2 AC Variable Speed Drives
AC drives are machine speed control systems based on AC motors or generators. AC motors typically operate using three-phase AC. Single-phase supplied AC induction motors are also widely used for lighter duty applications. The motors can be rotary or linear. In general, the controller characteristics are the same for either. For clarity, the following discussion focuses on rotary AC motor drives.
A rotary AC motor has a stationary stator and a spinning rotor. The stator is wound with a circular array of conductor coils (the windings) that produces static lines of current and a rotating magnetic field. The rotor carries lines of current that also produce a magnetic field. Both rotate as the rotor spins. The interaction between the rotor or stator currents and the common rotating magnetic field is responsible for the force production (torque) of the motor. Depending on motor type, the rotor currents may be produced via electromagnetic induction or via an active set of rotor windings. In a PM machine, the function of the stator is the same. However, the PM rotor lacks the lines of current and only contributes a spinning magnetic field. In analysis, the PM can be replaced by an equivalent current, if needed. The stator currents and the common rotating magnetic field are responsible for force production in a PM machine.
The two most common AC motor types are induction motors and synchronous motors, each with a number of variations.
The Induction Motor
An induction motor (also called an asynchronous motor) relies on a slight difference in speed between the rotating magnetic field of the stator and the rotating speed of the rotor to induce current in the rotor's AC windings or integral conductive squirrel cage. This difference in speed is referred to as slip.
