Werner Leonhard Control of Electrical Drives

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Werner Leonhard

Contrai

of

Electrical Drives

Third Edition

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Professor

WERNER

LEONHARD

Tl'

chnische Universitãt Braunschweig

IlIsti

tut für Regelungstechnik

II

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Sommer

Str.

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edition.1 Werner Leonhard. - Berlin; Heidelberg; New York;

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10

Preface

Electrical drives play

an

important

role as electromechanical energy convert-

ers

in

transportation,

material

handling and

most

production processes.

The

ease

of

controlling electrical drives is

an

important

aspect for meeting

the

in-

creasing

demands

by

the

user

with

respect

to

flexibility

and

precision, caused

by technological progress in

industry

as well as

the

need for energy conser-

vation.

At

the

sarne time,

the

control

of

electrical drives has provided

strong

incentives

to

control engineering

in

general, leading

to

the

development of

new control

structures

and

their

introduction

to

other

areas of controI.

This

is due

to

the

stringent

operating

conditions

and

widely varying specifications

- a drive

may

alternately

require control of torque, acceleration, speed or

position -

and

the

fact

that

most electric drives have -

in

contrast

to

chem-

ical

or

thermal

processes - well defined

structures

and

consistent

dynamic

characteristics.

During

the

last

years

the

field

of

controlled electrical drives has undergone

rapid

expansion due mainly

to

the

advances of semiconductors in

the

form of

power electronics as well as analogue

and

digital signal electronics, eventu-

ally

culminating

in microelectronics

and

microprocessors.

The

introduction

of electronically switched solid-state power converters has renewed

the

search

for

adjustable

speed AC

motor

drives, not

subject

to

the

limitations of

the

mechanical

commutator

of

DC

drives which

dominated

the

field for a century.

This

has

created

new and difficult control problems since

the

mechanically

simpler AC machine is a much more involved control

plant

than

a

DC

motor;

on

the

other

hand,

the

fast response of electronic power switching devices

and

their

limited overload capacity have

made

the

inclusion of protective control

functions essentiaI.

The

present phase of evolution is likely

to

continue for

some years, a new

steady-state

is

not

yet

in

sight.

This

book, originally published 1974 in

German

as "Regelung

in

der elek-

trischen Antriebstechnik", was

an

outcome of lectures

the

author

held for a

number

of

years

at

the

Technical University Braunschweig.

ln

its

updated

En-

glish version

it

characterises

the

present

state

of

the

art

without

laying claim

to

complete coverage

of

the

field. Many interesting details

had

to

be

omitted,

which

is

not

necessarily a disadvantage since details

are

often

bound

for early

obs()les(:(~Ilc(~

.

ln

selecting

and

presenting

the

material, didactic view points

ha.vc

also

hC(~1I

clllIsidcrpr].

A prerequisite for

the

reader is a basic knowledge

VI

Preface

"r

!l

0wer

electronics, electrical machines

and

control engineering, as

taught

in

1111d,

I1Ilcler-g

r

aduate

electrical engineering courses; for additional facts, re-

(11IllSC

is

made

to

specialliterature.

However,

the

text

should

be

sufficiently

::,,11'

coutained

to

be

useful also for non-experts wishing

to

extend

or refresh

Ilwir kuowledge

of

controlled electrical drives.

Tbcy

consist of several

parts,

the

electrical machine,

the

power converter,

!.II('

('oIltrol

equipment

and

the

mechanicalload,

all of which are

dealt

with

in

v:uyiJlg depths. A brief resume of mechanics

and

of

thermal

effects in electri-

()II

IIlachines is presented in Chaps,

1-4

which would

be

skipped by

the

more

1

'::

I'I

~

ri(~llCed

reáâer. Chaps.

5-9

deal

with

DC drives which have for ove r a

"'III,lIry been

the

standard

solution when

adjustable

speed was required.

This

p;\.rl.

or

the

text

also contains

an

introduction

to

line-commutated converters

,I::

IISI:<I

for

the

supply

ofDC

machines.

AC

drives

are

introduced

in Chapo

lO,

I

>l'1';iII

Jlillg

with

a general

dynamic

model of

the

symmetrical

AC motor, valid

iII

IIpC"

the

steady-state

and

transient

condition.

This

is followed in Chapo

11

II\'

ali

overview

of

static

converters

to

be

employed for

AC

drives.

The

con-

1.1'01

;1.spects

are

discussed in Chaps. 12-14

with

emphasis

on

high dynarnic

l'I'rI'Ol'lllanCe drives, where microprocessors prove invaluable in disentangling

LIli'

1I1111Civariate

interactions present in AC machines.

Chapter

15

finally de-

::nil)('s some of

the

problems connected

with

the

industrial

application of

.IriVl's, 'l'ltis

cannot

by

any

means

cover

the

wide field of special

situations

Wil.lt wllich

the

designer is confronted in

practice

but

some frequently en-

'''IIIII.I'II'd

katures

of

drive

system

applications

are

explained there.

It

will

111''''"111'

~"Ifliciently

clear

that

the

design of a controlled drive, in

particular

"I.

Iilrl','"

pow(~r

ratings,

cannot

stop

at

the

motor

shaft

but

often entails

an

;(11:0.11':"

:: ,.I'

L"(~

whole electro-mechanical system.

III

v inv

01'

Lhe

fact

that

this

book

is

an

adaptation

and

extension of

an

"111

dical.i, 'll-oricIltated

text

in

another

language,

there

are

inevitably problems

1.'

1111

1"

'I ';:

\.rd

1.0

symbols,

the

drawing

of

circuit

diagrams

etc. After

thorough

","'::lIll.a.t.iolls with

competent

advisors

and

the

publisher, a compromise so-

I"Li!)1I

was

adopted,

using symbols recommended by

IEE

wherever possible,

1.111.

rdailliug

the

authors

usage where confusion could otherwise arise with

I,i::

r(';ukrs

at

home. A list of

the

symbols is compiled following

the

table

of

,'IIIII,I'III.S,

The

underlying principIe employed is

that

time

varying

quantities

;),1'"

IISll1\.lly

dcnoted

by

lower case

latin

letters, while

capitalletters

are

ap-

pli,'"

1.11

parameters,

average quantities, phasors etc; greek

letters

are

used

pt'l'dolllÍllalltly for angles,

angular

frequencies etc. A certain

amount

of over-

1:'1

1

iH

Illl<lvoidable, since

the

number

of available symbols

is

limited. AIso

the

l.tI

dillgl'aplty still exhibits a

strong

continental bias, eventhough

an

attcmpt

III~

:

;

IH

:t!

lt

Illadc to halance

it

with

titlcs in english

la\lf(llagl

~

.

The

list

is

cer-

I.niJlJy

III'

uo

lIWilllS

('.()Inpl<!te

hut

it

contaiJlH

t.b(~

illfp\'lllnl.ioll r\,adiJy availahle

to

t.!,,

\ anl.ho!',

Dired

rdl

:

reIl('.(:~i

i1l

1.111

:

t.I'''1.

hllVI'

11"1'11

II:II'c!

:Iparillj

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''y,

wlwlI

1.1"

, Ilril':

ill

WIl,H

Lo

1)('

al'!llIowlc'dl(

nd,

l!opl'l'

IIII

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1,11

11

1

"'1

1""1

111

1.1

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w

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1.II

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,111

1111111

'"

Preface

VII

The

author

wishes

to

express his sincere

gratitude

to

two

British

col-

leagues, R. M. Davis, formerly

of

Nottingham

University

and

S. R. Bowes

of

the

University of Bristol who have given help

and

encouragement

to

start

the

work

of

updating

and

translating

the

original

German

text

and

who

have

spent

considerable

time

and

effort in reviewing

and

improving

the

ini-

tial

rough

translation;

without

their

assistance

the

work could

not

have been

completed. Anyone who has

undertaken

the

task

of

smoothing

the

transla-

tion

of a foreign

text

can

appreciate

how tedious

and

time-consuming this

can be.

Thanks

are also

due

to

the

editors

of

this Springer Series, Prof.

J.

G.

Kassakian

and

Prof.

D.

H.

Naunin,

and

the

publisher for

their

cooperation

and

continued encouragement.

Braunschweig,

October

1984 Werner Leonhard

Preface

to

the

2

nd

edition

During

the

past

10 years

the

book on Control of Electrical Drives has found

its

way

onto

many

desks in

industry

and

universities all over

the

world, as

the

author

has

noticed on

numerous

occasions. After a

reprinting

in 1990

and

1992, where errors

had

been corrected

and

a few technical

updates

made,

the

book

is now

appearing

in

a second revised edition,

again

with

the

aim

of

offer-

ing

to

the

readers

perhaps

not

the

latest

little

details

but

an

updated

general

view

at

the

field

of

controlled electrical drives, which

are

maintaining

and

extending

their

position as

the

most

ftexible source

of

controlled mechanical

energy.

The

bibliography

has

been considerably

extended

but

in view

of

the

con-

tinuous

strearn

of

high quality publications,

particularly

in

the

field

of

con-

trolled AC drives,

the

list is still far from complete.

As

those familiar

with

word processing will recognise,

the

text

and

figures

are

now

produced

as a

data

set

on

the

computer.

This

would

not

have been possible

without

the

ex-

pert

help

by

Dipl.-Ing. Hendrik Klaassen, Dipl.-Math.

Petra

Heinrich, as well

as Dr.-Ing. Rüdiger Reichow, Dipl.-Ing. Marcus Heller, Mrs.

Jutta

Stich

and

Mr. Stefan Brix,

to

whom

the

author

wishes

to

express his sincere

gratitude.

Peter

Wilson has been reading some

of

the

chapters, offering valuable sugges-

tions,

The

final layout

remained

the

task

of

the

publishers, whose patience

and

helpful

cooperation

is gratefully appreciated.

Braunschweig, May 1996

Werner Leonhard

Prefacc

to

the

3

rd

Edition

'1'1111.

(,;\.\'Iy

c\"l'ldio"

of LIli: pllblislllll's

:.;Locks

oll('I'<

,d

Hll

opportullit

,y of again

II

1''':!.I,i

"I':

I.ltc'

I

IClClI

I , IIlakil'l',

IIliJlOI'

1'01'l'I'cl.i'III:

;

:utel

I'lllal'l':illJf,

SOIlIt'

SlIh.i,'i'I

,H

I

V

III

Preface

whilc

t.hc

main

part

of

the

book was left unchanged. Tackling

this

work

1(''1uircd

the

encouragement by good friends

but

the

author

would still have

1)(

'(:11

lIu

ab

le to realise

it

alone. He expresses his sincere

gratitude

to

the

helpful

\

(':

;('

archers

at

the

Institut

für Regelungstechnik, particular1y Dipl.-Ing.

Jan

I

\\

...

kcr

and

Dipl.-Ing. Frithjof Tobaben who were always ready

to

resolve

::Illl.wilrc-related crises

on

the

computer, as well as Dipl.-Ing. Klaus Jaschke

;1.lId

C;\llél. Wirtsch.-Inform.

Danny

Wallschlager,

our

definitive

~TEX-experts

wlio

sc

participation

was essential for undertaking

the

task. Dr.-Ing. Sõnke

1\

()ck suggested a clearer definition of

the

magnetic leakage which

had

gone

II II

lIot.iccd

beforej finally, I want

to

thank

Prof.

Walter

Schumacher, now

head

(Ir

Ui(' laboratory, for his continued interest.

Werner Leonhard

1 \ r:tllllscltweig, Spring 2001

Contents

Introduction

.................................................

.

1

1.

Elementary

PrincipIes

of

Mechanics

........

.

............

.

7

1.1 Newtons Law

.........................................

.

7

1.2 Moment of

Inertia

.............

..

......................

.

9

1.3 Effect of Gearing .

.....

..........

.

..............

...

....

.

11

1.4 Power

and

Energy

.. ..

..........................

......

. .

12

1.5

Experimental

Determination

of

Inertia

...................

.

14

2.

Dynamics

of

a

Mechanical

Drive

.........................

.

17

2.1

Equations

Describing

the

Motion of a Drive with

Lumped

Inertia

..........................................

.

....

.

17

2.2

Two

Axes Drive in

Polar

Coordinates .

....

..........

.

....

.

20

2.3

Steady

State

Characteristics of Motors and Loads

.........

.

22

2.4

Stable

and

Unstable

Operating

Points

....................

.

26

3.

Integration

of

the

Simplified

Equation

of

Motion

........

.

29

3.1 Solution of

the

Linearised Equation

.............

.

........

.

29

3.1.1

Start

of a Motor with

Shunt-type

Characteristic

at

No-Ioad

........................................

.

30

3.1.2

Starting

the

Motor with a Load Torque

Proportional

to

Speed

........................

.

..............

.

32

3.1.3 Loading Transient of the Motor

Initially

Running

at

No

-Ioad Speed

..

.

..

.

..........

.

33

3.1.4

Starting

of a

DC

Motor

by Sequentially Short-circuiting

Starting

Resistors

...

.

35

3.2 Analytical Solution of Nonlinear Differential

Equation

......

.

38

3.3 Numerical

and

Graphical

Integration

.....................

.

39

4.

Thermal

Effects

in

Electrical

Machines

..................

.

43

4.1 Power Losses

and

Temperature

Restrictions

...............

. 43

4.2

Hcating

of a Homogeneous Body

.......

..

.......

.

.....

. . .

44

1.:~

Difrer('lll: Morles of

Operation

......

. .

..............

...

..

.

48

'1.:\.1

(;()ilt.illIlOIlS

Dllty

.....

'

.....

. .

..

. .

......

. . .

......

.

1K

x

Contents

4.3.2

Short

Time

Intermittent

Duty

.....................

48

4.3.3 Periodic

intermittent

duty

. . . . . . . . . . . . . . . . . . . . . . .

..

49

~

'

,.

SeparateIy

Excited

DC

Machine

. . . . . . . . .

..

. .

..

. . . . . . . . .

..

51

5.1

Introduction

....................

·.·····················

51

G.2

Mathematical

Model of

the

DC Machine

.....

........

54

G.3

Steady

State

Characteristics with

Armature

and Field Control 56

5.3.1

Armature

Control . . . . . . . . . . . . . . . . . . .

..

. . . .

..

. . .

..

57

5.3.2 Field Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..

58

5.3.3 Combined

Armature

and

Field Controlo . . . . . . . . . . .

..

61

!:iA

Dynamic Behaviour of DC Motor with

Constant

Flux

..

. . .

..

64

DC

Motor

with

Series

Field

Winding

. . . . . . . . . . . . . . . . . . .

..

69

0.1 Block

Diagram

of a Series-wound

Motor.

. . . . . . . . . . . . . . . .

..

70

O.

G.2

Steady

State

Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

"( .

ControI

of

a

Separately

Excited

DC

Machine

..

. . . . . . . . .

..

77

7.1

Introduction

....................

·······················

77

7.2 Cascade Control of

DC

Motor in

the

Armature

Control Region

79

7.:3

Cascade Control of DC Motor in

the

Field-weakening Region

90

'IA

Supplying

aDC

Motor from a

Rotating

Generator..

. . . . . .

..

93

Static

Converter

as

a

Power

Actuator

for

DC

Drives

.....

97

~u

Electronic Switching Devices . . . . . . . . . . . . . . . . . . . . . . . . . . .

..

97

K.

H.2

Line-commutated Converter

in

Single-phase Bridge Connection102

~u

Line-commutated Converter

in

Three-phase Bridge Connection119

H.tJ

Line-commutated Converters with Reduced Reactive Power

..

130

H.

:)

Control Loop Containing

an

Electronic Power Converter

....

133

n.

(;oulrol

of

Converter-supplied

DC

Drives

.................

139

~u

DC Drive with Line-commutated Converter

........

.

.......

139

~).2

DC Drives with Force-commutated Converters

.............

148

Syrnrnetrical

Three-Phase

AC

Machines

..

,

...............

163

10.1

Mathematical

Model

of

a General

AC

Machine

..........

·.·

164

10.

10.2

Induction Motor with Sinusoidal Symmetrical Voltages

in

Steady

State

........

..

............

. . .

..................

176

10.2.1

Stator

Current,

Current Locus

..................

...

176

10.2.2 Steady

State

Torque, Efficiency

..................

. . 182

10.2.3 Comparison

with

Practical

Motor Designs

..........

, 186

10.204

St.art.ing of lhe Induction Molor

.........

..

....

. 187

.Ill.

:.\

Indlld

.

ioll

Mot.()r

with

lmpr

esscd Volt.ar;c·s

or

t\

I'hit.r,\ry Wave-

rOI'lIl

:l . . '

....

. . . .

........

,

•••

. . • ,

..

. . ,

••

....

...

190

10/1

111.11\1'1.

1

011

M,J\,,!' wit.h lJn:iyllllllC't.1

i,';"

1

,11

...

VIIII

,

il.l',C·:

i

iII

S

t.c

·;\.

dy

:J.m

~;

1

11

.

1."

" . .

••

, • ,

•••

Contents

XI

1004.1

Symmetrical Components

.........................

202

10.4.2 Single-phase

Induction

Motor

........

.....

....

..

...

206

10.4.3 Single-phase Electric Brake for AC

Crane-Drives

.....

209

10.4.4 Unsymmetrical

Starting

Circuit for Induction

Motor

..

211

11.

Power

Supplies

for

Adjustable

Speed

AC

Drives

.

...

......

215

11.1

Pulse

width

modulated

(PWM) Voltage Source Transistor

Converter (IGBT)

....................

.

.................

218

11.2 Volt age Source

PWM

Thyristor

Converter

.................

225

11.3

Current

Source

Thyristor

Converters

.......

........

.....

..

232

11.4 Converter

Without

DC Link (Cycloconverter)

..............

236

12.

Control

of

Induction

Motor

Drives

.......................

241

12.1 Control

of

Induction

Motor Based on

Steady

State

Machine

Model

.................................................

242

12

.2

Rotor

Flux

Orientated

Control of Current-fed Induction Motor252

12.2.1 PrincipIe of Field

Orientation

..........

..

..........

252

12.2.2 Acquisition of

Flux

Signals

..

.....

.........

.

..

.

....

260

12.2.3 Effects of Residual Lag of

the

Current

Control Loops . 262

12.2.4 Digital Signal Processing

...

..

.....................

265

12.2

.5

Experimental

Results

.............................

268

12.2.6 Effects of a

Detuned

Flux

Model

......

. . .

..........

269

12.3 Control of Voltage-fed Induction Motor

...................

275

12.4

Field

Orientated

Control of Induction Motor with a

Current

Source Converter

.........

.

..........

......

.............

281

12.5

Control

of

an

Induction Motor

Without

a Mechanical

Sensor.

289

12.5.1 Machine Model in

Stator

Flux

Coordinates

..........

289

12.5.2

Example

of

an

"Encoderless Control"

...

.........

291

12.5.3 Simulation

and

Experimental

Results

...............

296

12.6 Control of

an

Induction Motor Using a Combined

Flux

Model 298

13.

Induction

Motor

Drive

with

Reduced

Speed

Range

.......

303

13.1 Doubly-fed Induction Machine with

Constant

Stator

Fre-

quency

and

Field-orientated

Rotor

Current

................

303

13.2 Control of a Line-side Voltage Source Converter

as a Reactive Power Compensator

......................

..

317

13.3 Wound-Rotor

Induction

with Slip-Power Recovery

..........

323

14.

Variable

Frequency

Synchronous

Motor

Drives

...........

329

14.1 Control of Synchronous Motors with

PM

Excitation

..

. .

....

331

14.2 Synchronous Motor with Field-

and

Damper-Windings

.....

. 342

14.3 Synchronous Motor

with

Load-commutated Inverter (LCI-

Driv(')

........

.

..........

....

..........

.....

.........

. 349

Werner Leonhard Control of Electrical Drives

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