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List of contents

Chapter0: Introduction

Chapter 1: 3-Phase AC Motors

Chapter 2: Frequency converters

Chapter 3: Frequency converters and Motors

Chapter 4: Protection and Safety

Appendix I: General Mechanical Theory

Appendix II: General AC TheoryAppendix III: Generally used Abbreviations

Literature reference

Index


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4 LI ST OF CONTENTS

List of contents

CHAPTER 0: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Advan ta ges of infinitely var iable speed r egulat ion . . . . . . . . .10

Cont rol or regu lat ion? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

CHAPTER 1: 3-P HASE AC MOTORS . . . . . . . . . . . . . . . . . . . . . .13

Asynchronous m otors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

St a tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15

Magnet ic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16

Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Slip, t orqu e and speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

Efficiency and losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Magnet ic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25

Equivalen t circuit d iagr am . . . . . . . . . . . . . . . . . . . . . . . . . .25

Speed cha nge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29

Cha nging t he n um ber of poles . . . . . . . . . . . . . . . . . . . . . . .29

Slip control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Frequ ency regu lat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

Motor da ta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35

Types of load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44

Synchronous m otors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47Relucta nce motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49

CHAPTER 2: FREQUENCY CONVERTERS . . . . . . . . . . . . . . . . . . .52

The rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Uncontrolled r ectifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54

Cont rolled r ectifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56

The int ermedia te circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

The inver ter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Transist ors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Pulse-Amplitu de-Modu lat ion (PAM) . . . . . . . . . . . . . . . . . . 68

Pulse-Width-Modu lat ion (PWM) . . . . . . . . . . . . . . . . . . . . . 70

Sin us-cont rolled P WM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71

Synchronous P WM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

Asynchronous PWM . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .75

Cont rol circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81

Danfoss cont rol prin ciple . . . . . . . . . . . . . . . . . . . . . . . . . . . .82

VVC control prin ciple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84

VVCplus

control principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86


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LI ST OF CONTENTS 5

Field-or ient ed (Vector) control . . . . . . . . . . . . . . . . . . . . . . .91

V/f character ist ic and flux vector cont rol . . . . . . . . . . . . . .93

VVCplus slip compen sa t ion . . . . . . . . . . . . . . . . . . . . . . . . . . .94

Automat ic Motor Adapta t ion (AMA) . . . . . . . . . . . . . . . . . .95

Automat ic Energy Optim isat ion (AEO) . . . . . . . . . . . . . . . .95

Opera ting at th e cur ren t limit . . . . . . . . . . . . . . . . . . . . . . .96

Protect ive functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98

The microchip in general . . . . . . . . . . . . . . . . . . . . . . . . . . .101

Computer s for frequ ency conver ter s . . . . . . . . . . . . . . . . .102

Comm unicat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104

Ser ial communicat ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106

Man ufactu rer -indepen dent comm un icat ion . . . . . . . . . . . .111

CHAPTER 3: FREQUENCY CONVERTERS AND MOTORS . . . . . .113

Oper a tiona l condit ions of the motor . . . . . . . . . . . . . . . . . . . .115Compensa t ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Load-dependen t an d load-independen t compen sat ion

pa rameter s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Slip compensa t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116

Motor t orque cha racter ist ics . . . . . . . . . . . . . . . . . . . . . . . . . .117

Curr ent limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117

Requirem ent s from advan ced digita l frequen cy

conver ter s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120

Sizing a frequency convert er . . . . . . . . . . . . . . . . . . . . . . . . .121Load cha racter ist ics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121

Curr ent distribut ion in t he frequency convert er

(cos of the motor ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125Dyna mic brake opera t ion . . . . . . . . . . . . . . . . . . . . . . . . . .128

Rever sing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130

Ramps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131

Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132

Motor load a nd motor h eat ing . . . . . . . . . . . . . . . . . . . . . . . .134

Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136

CHAPTER 4: PROTECTION AND SAFETY . . . . . . . . . . . . . . . . . .139

Extra pr otect ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139

Reset to zero (TN syst em) . . . . . . . . . . . . . . . . . . . . . . . . . . . .140

Ear thing (TT system ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140

Protect ive relay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141

Elect romagnet ic compa t ibility . . . . . . . . . . . . . . . . . . . . . . . .143

Basic Sta nda rd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144

Gen er ic Sta nda rd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144


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6 LI ST OF CONTENTS

Product St anda rd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144

Disper sa l of inter feren ce . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146

Couplin g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146

Hard-wired d ispersa l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148

Mains supply int er ference . . . . . . . . . . . . . . . . . . . . . . . . . . .148

Transien ts/over-voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149

Radio-frequency int er ference . . . . . . . . . . . . . . . . . . . . . . . . .151

Screen ed/ar moured cables . . . . . . . . . . . . . . . . . . . . . . . . . . .153

Power Factor compensa tion un its . . . . . . . . . . . . . . . . . . . . .154

Selection of a frequency convert er for

variable speed dr ives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155

APPENDIX I: GENERAL MECHANICAL THEORY . . . . . . . . . . . .159

St ra ight -line m ot ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159

Rota t ing motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159Work and power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161

APPENDIX II: GENERAL AC THEORY . . . . . . . . . . . . . . . . . . . .162

Power factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165

3-phase AC cur ren t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166

Star or delt a connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167

APPENDIX III: GENERALLY USED ABBREVIATIONS . . . . . . . . . .168

LITERATURE REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . .169

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170


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CHAPTER 0: I NTRODUCTION 7

0. Int roduct ionA stat ic frequ ency conver ter is an electr onic un it which p rovides

infinit ely variable cont rol of the speed of th ree-pha se AC motors

by converting fixed mains voltage and frequency into variable

quan tities. Whilst t he pr inciple has a lways rema ined the sa me,

there have been many changes from the first frequency con-

vert ers, wh ich feat ur ed t hyr istors, to todays m icroprocessor-

cont rolled, digita l un its.

Becau se of th e ever-increas ing degree of aut oma tion in indu str y,

there is a constant need for more automatic controls, and a

stea dy increase in pr oduction speeds and bett er m ethods to fur -

th er impr ove th e efficiency of production plant s a re being devel-

oped all the time.

Today electric motors are an important standard industrial

product. These motors a re designed t o ru n a t a fixed speed and

work has been going on for many years to optimise the control

of th eir ru nn ing speed.

Fig. 0.01


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8 CHAPTER 0: I NTRODUCTION

It was not until the static frequency converter was introduced

th at th ree-pha se AC motors with infinitely variable speed could

be u sed effectively.

The vast majority of the static frequency converters used by

industry today to control or regulate the speed of three-phase

AC motors are designed according to two different principles

(Fig. 0.02):

frequency converters with out an intermediate circuit (also

kn own as direct convert ers), an d

frequency converters with a variable or consta nt int ermediate

circuit.

Fr equency convert ers with an int erm ediat e circuit h ave eith er a

direct curr ent inter mediat e circuit or a direct voltage inter me-

diate current and are called current-source inverters and volt-

age-source inverters.

Intermediate circuit inverters offer a number of advantages

over th e direct inverter, such a s:

better reactive current control

reduction of har monics

no limita tions with respect to out put frequency (but t here is a

limita tion to th e cont rol and pr opert ies of th e electr onic com-

ponen ts u sed. Frequency convert ers for high outpu t frequen -

cies ar e mostly inter mediat e circuit inverters.)

Frequency converters

Frequency convertersw/o inter mediat e circuit

Direct current

inter med. circuit

Fr equency convertersw/ int erm ediate circuit

Variable Constant

Direct voltage

inter med. circuit

Direct voltage

inter med. circuit

Current-source Voltage-source Voltage-sourcefreq. conver ters freq. conver ters freq. conver tersCSI-converters VSI-converter s VSI-converter s

Fig. 0.02 Converter principles


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Direct inverters tend to be slightly cheaper than intermediate

circuit inver ter s, though th ey typically suffer from poorer reduc-

tion of ha rm onics.

As most frequ ency conver ter s use a DC voltage int erm ediat e cir-

cuit , th is book will focus ma inly on th is group of conver ter s.



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Adva ntag es of inf initely variablespee d adjustme nt

Today, the frequency converter controlled, three-phase AC

motor is a standard element in all automated process plants.

Apart from its ability to use the good properties of three-phase

AC motors, infinitely variable speed regulation is often a basic

requirement because of the design of the plant. In addition, it

offers a nu mber of fur th er a dvant ages:

Energy savings

Energy can be saved if the motor speed matches requirements

at an y given m omen t in t ime. This applies in pa rt icular to cen-

trifugal pumps and fan drives where the energy consumed is

reduced by the cube of th e speed. A drive run ning a t ha lf speed

th us only takes 12.5% of th e ra ted power.

Process optimisation

Adjust ing th e speed to th e production pr ocess offers a nu mber ofadvantages. These include increasing production, while reduc-

ing rejection rates and decreasing material consumption and

wear.

S m ooth m achin e operation

The number of starts and stops with full speed change can be

dramatically reduced. Using soft start-up and stop ramps,

shocks a nd impacts on th e ma chine component s can be avoided.


Fig. 0 .03 Energy savings


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Less m ain tenance

A frequen cy convert er r equires no ma inten an ce. When used t o

control motor s, th e life-time of plants can be increased. For

example, in water supply systems, the water hammer that

occurs with direct mains connection of the pump motors disap-

pear s, an d dam age to th e water pipes is avoided.

Im proved work in g environm ent

The speed of conveyor belts can be matched exactly to the

required working speed. For example, bottles on the conveyor

belt in a bott le filling line m ake much less noise if th e belt speed

can be reduced when t he bott les ar e queuing.

If the speed of a fan is adjustable, unnecessary noise near the

fan can be reduced, as can t he dra ught.


Fig. 0.04 Improved working environm ent


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Con trol or regu lat ion ?

Many people use th e ter ms control and regula t ion int er -

cha ngeably. However, th ey do ha ve precise definitions lar gely

as a resu lt of developmen ts in t he field of au tomat ion.

The terms control and regulation depend on the type of

plan t. With speed cont rol a signa l which is expected t o pro-

duce the r equired speed is sent to th e motor. With speed regu-

lat ion a feedback signa l is given from the pr ocess. If th e speeddoes not corr espond to the requirem ent s, the signa l to the m otor

is regulated a ut oma tically un til the m otor speed is as it sh ould

be.


Fig. 0.05 Distinction between control and regulation

Control

Regulation

Actu al value

Process


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1. Three-phase AC motorsThe first electr ic motor, a DC un it, was bu ilt in 1833. The speed

regu lat ion of th is motor is simple and fulfils th e requ irement s of

th e ma ny different applicat ions a nd systems.

In 1889, the first AC motor was designed. More simple and

robust than the DC motor, the three-phase AC unit suffered

from fixed speed values and torque characteristics, which is

why, for many years, AC motors could not be used in special-

dut y applicat ions.

Three-phase AC motors are electromagnetic energy converters,

converting electrical energy into mechanical energy (motor

operation) and vice versa (generating operation) by means of

electromagnetic induction.

The principle of electromagnetic induction is that if a wire is

moved th rough a ma gnet ic field (B), a volta ge is indu ced. If th e

wire is in a closed circuit , a cur rent (I) will flow. When the wire

is moved, a force (F), which is vert ical to th e magnet ic field, will

act on t he wire.

a) Generatin g principle (indu ction by mea ns of movement ).

In th e genera ting pr inciple, moving a wire in th e ma gnetic fields

genera tes a voltage (Fig. 1.01a).

b) Motor prin ciple

In motors, th e induction principle is r eversed a nd a cur ren t-con-

ducting wire is positioned in a ma gnet ic field.

The wire is then influenced by a force (F) that moves the wire

out of th e magn etic field.

CHAPTER 1: THREE-PHASE AC MOTORS 13

N

S

N I

I

I FF I

F

B B

F

S

Fig. 1.01 Principle for electrom agnetic indu ction

a) Generator principle b) Motor principle


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In the motor principle, the magnetic field and current-distrib-

ut ed wire genera te th e movemen t (Fig. 1.01b).

The magnetic field in the motor is generated in the stationary

par t (the st at or) and th e wires, which a re influenced by the elec-

tr oma gnetic forces, are in th e rotat ing par t (the r otor).

Three-phase AC motors can be divided into two main groups:

asynchronous an d synchronous motors.

The stators basically work in the same way in both types, but

th e design and r otor movement in relat ion t o th e ma gnetic field

differs. In synchronous (which means simultaneous or the

sam e) th e speed of rotor a nd m agnet ic field ar e th e sam e an d in

asynchronous t he speeds a re different .

Three-pha se AC motors

synchronous asynchronous

Rotor with sa lient poles Slip r ing rotorFull pole rotor Short-circuit rotor

14 CHAPTER 1: THREE-PHASE AC MOTORS

Fig. 1.02 Types of three-phase AC m otors


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Asyn chronou s motors

Asynchronous motors are the most widely used and require

pra ctically no ma inten an ce. In mechan ical term s, th ey ar e vir-

tually standard units, so suitable suppliers are always nearby.

There are several types of asynchronous motors, all of which

work on t he sa me ba sic prin ciple.

The two main component s of an asynchronous m otor ar e th e sta -

tor (sta tiona ry elemen t) and t he r otor (rotat ing elemen t).

Stator

The st a tor is a fixed par t of th e sta tionary motor. It cons ists of a

stator housing (1), ball-bearings (2) that support the rotor (9),

bear ing blocks (3) for positioning of the bea rings an d a s a finishfor th e st at or housing, fan (4) for motor cooling an d va lve casing

(5) as protection against the rotating fan. A box for electrical

conn ections (6) is locat ed on t he side of the s ta tor h ous ing.

In th e sta tor housing is an iron core (7) ma de from thin (0.3 to

0.5 mm) iron sheets. These iron sheets have punched-out sec-

tions for t he t hr ee phase windings.


5 4 3 2 10 9 2 1

6 7 3

Fig. 1.03 Build-up of an asynchronous m otor


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The pha se windings and t he sta tor core generate t he m agnetic

field. The number of pairs of poles (or poles) determines the

speed a t wh ich t he m agn etic field rota tes. If a m otor is conn ect-

ed t o its r at ed frequen cy, the speed of th e magn etic field is called

th e synchronous speed of th e motor (n 0).

Magne tic f ie ld

The magnetic field rotates in the air gap between stator and

rotor. After conn ectin g a phase winding to a ph ase of th e supply

voltage, a magnet ic field is indu ced.

The position of th is ma gnet ic field in th e st a tor core is fixed, but

its direction cha nges. The speed at which th e direction cha nges

is determined by the frequency of the supply voltage. At a fre-quen cy of 50 Hz the alter na ting field cha nges direction 50 times

per second .

If two pha se windings ar e conn ected t o each pha se at t he same

time, two magnetic fields are induced in the stator core. In a

two-pole motor, ther e is a 120 degree displacemen t between t he

two fields. The m aximu m values of the fields a re a lso displaced

in time.


t

0

N S N

S N S

360180

I11

IL1

I10 V

Fig 1.04 One phase results in an alternating field

Pole pair s (p) 1 2 3 4 6

Number of poles 2 4 6 8 12

n 0 [1/min] 3000 1500 1000 750 500

Table 1.01 Pole pairs (p), pole nu m ber

and syn chronous m otor speed


15/161


This results in t he creation of a m agnet ic field th at rotat es in t he

sta tor. However, th e field is h ighly asymm etr ical u nt il the t hird

phase is conn ected .

The th ree pha ses generat e th ree ma gnetic fields in th e stat or

core wh ich a re displaced 120 degrees in rela tion to each oth er.

The st at or is now conn ected t o th e th ree-pha se supply voltagean d t he m agnet ic fields of th e individual ph ase windings bu ild

a symmet rical, rota ting magnet ic field called th e motor rotat ing

field. The am plitude of th e rota ting field is const an t at 1.5 times

th e ma ximu m value of th e alter na ting fields. Rota tion is at :

(f 60)n 0 = [1/min]p

t

0 36018012060 300240

I11 I22 I33

I

N

S

N

S

N

S

N

S

S

N

S

N

S

N

f = fr equ en cyn0 = synchronous speedp = no. of pole pa irs

t

0 360180120 300

I11I22

I

N

S

S

N

S

N

N

S

N

S

Fig. 1.05 Two phases result in an asymm etrical rotating field

L1

I1

L2

I2

0 V

0 V

L1

I1

L2

L3I2

I3

Fig. 1.06 Th ree phases result in a symm etrical rotating field


16/161

The speed t her efore depen ds on th e nu mber of pa irs of poles (p)

and the frequency (f) of the supply voltage. The illustration

below sh ows t he size of the ma gnet ic fields (F) in t hr ee differen t

periods.

The visualisation of the r ota ting field with a vector a nd a corr e-

sponding angular velocity makes up a circle. As a function of

time in a system of co-ordina tes, th e rotat ing field ma kes u p a

sinu soidal curve. The rota ting field becomes elliptic if the am pli-

tu de cha nges during a rotation.

Rotor

The rotor (9) is moun ted on th e motor sha ft (10) (see F ig. 1.03).

Like th e sta tor, the r otor is made of th in iron sh eets with gaps

pun ched t hr ough t hem . Ther e ar e two main t ypes of rotor: slip

ring motors and short-circuit motors the difference being

determ ined by cha nging the windings in t he gaps.

Slip ring rotors, like the stator, have wound coils placed in the

gaps a nd th ere a re coils for ea ch pha se coming t o th e slip rings.

After a short -circuit of th e slip rings, th e rotor will fun ction a s a

short -circuit rotor.

Short-circuit rotors have cast-in aluminium rods in the gaps.

An a luminium ring is used a t ea ch en d of th e rotor t o short-cir-

cuit t he r ods.

The short-circuit rotor is the more frequently used of the two.

Since the two rotors pr incipa lly work in t he sa me wa y, only th e

short -circuit rotor will be described.


3 =1/2max.

1 = max.

3 = max.

2 =1/2max.

1 =1/2max.

2 =1/2max.

= 3/2max.

= 3/2max.

= 3/2max.3 =

32max.

1 =32max.

Fig. 1.07 Th e size of the m agnetic fields is constant


17/161


When a rotor bar is placed in t he r ota ting field, a ma gnetic pole

ru ns th rough t he r od. The ma gnetic field of th e pole indu ces a

cur ren t (IW) in t he r otor ba r wh ich is only influen ced by force (F)

(Figs. 1.08 and 1.09a).

This force is determ ined by th e flux dens ity (B), the indu ced cur -

rent (IW), the lengt h (l) of th e rotor an d the a ngle (q) between th e

force and th e flux density

If is assum ed t o be = 90, th e force is

The next pole that goes through the rotor bar has the opposite

pola rity. This induces a cur ren t in th e opposite dir ection. Since

the direction of the magnetic field has also changed, the force

acts in t he same direction as before (Fig. 1.09b).

When th e full rotor is placed in th e rota ting field (see Fig. 1.09c),

the rotor bars are affected by forces that turn the rotor. The

speed (2) of th e rotor does not r each t ha t of th e rota ting field (1),since at the same speed no currents are induced in the rotor

bars.

I W

lS

N

N

F

S

B

a) b) c)

S

F

N

1 N

2

S

B

Magnetic flux ()

Rotating field

Force

(F)

Leve

r (r)

Fig. 1.08 Rotating field and short-circuit rotor

Fig. 1.09 Induction in the rotor bars

F = B IW l sin

F = B IW l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.01


18/161

Slip, torque an d spee d

Under n orm al circumst an ces, the speed of th e rotor, n n, is lower

th an th e speed of th e rotat ing field, n0. The slip, s, is the differ -

ence between t he speed of th e rotat ing field an d t he speed of th e

rotor:

The slip is often expressed as a percentage of the synchronous

speed an d is norma lly between 4 an d 11 percent of ra ted speed:

The flux density (B) is defined as t he flux () per cross-section-al a rea (A). Fr om equa tion 1.01 th e following force can th erefore

be calculat ed:

The force at which the cur ren t-conducting wire is moved is pro-

portional to the magnetic flux () and the current (Iw) in thewire.

In the rotor bars, a voltage is induced via the magnetic field.

This voltage allows a cur ren t (Iw) to flow thr ough th e short -cir-

cuit ed rotor bar s. The individual forces in t he r otor bars combine

to set up a t orque, T, on th e motor sh aft.


Fig. 1.10 Th e motor torque is force mu ltiplied by lever arm

r

F

n 0 n ns = 100[%]n 0

IW lF = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.02A

(f 60)n 0 = [1/min]pp = no. of pole pairs

s = n 0 n n

F ~ IW

M

0 1n0

n

s0

s


19/161

The relat ionsh ip between motor t orque and speed ha s a cha ra c-

ter istic sequen ce which varies with th e form of th e rotor. The

motor t orque results in a force which t ur ns t he m otor sha ft.

The force a rises, for example, in t he circumference of a flywheel

fitt ed to th e sha ft. With th e force (F) an d th e ra dius (r) of th e fly-

wheel, th e motor t orque

W = F r can be calculat ed.

The work done by th e motor expressed as : W F d where d isth e distan ce that a m otor pulls for a given load, n is th e number

of revolut ions:

d = n 2 p r

Work can also be described as power multiplied by the time in

which this power is active: W = P x t.

The torque is th us:

This formula shows the relationship between the speed, n, the

torqu e T [Nm ] an d th e motor power P [kW].

The form ula provides a qu ick overview when looking at n , T an d

P in relation to the corresponding values at a given operating

point (nr, Tr and P r). The opera ting point is norm ally th e ra ted

opera ting point of th e motor a nd th e form ula can be modified a s

follows:

In this proportional calculation, the constant 9550 is not

applied.

T P nin which Tr = , P r = and n r = Tn P n n n


W (P t r) = F r = r =d n 2 r

P 9550T = (t = 60 sec.)

n

P rTr = an d for P r = T r n r ,n r


20/161

Exam ple:

Load = 15% of th e ra ted va lue, speed = 50% of th e ra ted va lue.

The power genera ted is 7.5% of th e ra ted power gener at ed, since

P r = 0.15 0.50 = 0.075.

In a ddition t o th e norma l opera ting ra nge of th e motor, th ere ar e

two brak e ra nges.

In th e ra nge where th e motor is pulled above th e syn-

chronous speed and acts as a generator creating an opposite

torque, while at the same time giving an output back into themains supply.

In th e ra nge of , bra king is ter med regenera tive braking.

If two phases of a motor are suddenly swapped, the rotating

field chan ges direction. Imm ediately after th is, th e speed ra tio

will be


nK, TK

nN , TN

n N, I N

T0, I 0

0, Ta

0, Ia

0

1

I

T

1

0

0

1

1

0

n0, 0

n0

ns0

s

n0

ns0

s

8 In

Fig. 1.11 Current and load characteristics of the m otor

n> 1,

n 0

n< 0

n 0

n= 1.

n 0

(Break-down t orque)

(Rated torque)


21/161


The m otor, previous ly loaded with th e torque T, now bra kes with

a br aking t orqu e. If th e motor is not switched off a t n = 0, it will

cont inue r un ning, but in t he n ew direction of th e rotat ing field.

The motor works in its norma l ra nge between .

The m otor s work ing ra nge can be divided into two area s: star t-

up ra nge an d operating ra nge .

There are some important points in the working range of the

motor:

Ta is the sta rt ing torque of th e motor the torque th at builds up

the motor power when rated voltage and rated frequency are

being fed while at sta ndst ill.

Tk is th e sta lling torque of th e motor. This is the largest t orque

th e motor is able to gener at e while ra ted voltage an d ra ted fre-

quen cy ar e being fed.

Tn is the ra ted t orque of th e motor. The r at ed values of th e motor

are the mechanical and electrical values for which the motor

was designed in accordance with the IEC 34 standard. These

can be seen from the motor nameplate and are also referred to

as na me-plat e values. The r at ed values indicat e th e motor soptimal operating point for direct connection to the mains sup-

ply.

Efficien cy and losses

The motor t ak es up electr ical power from th e ma in supply. At a

constant load, the input is larger than the mechanical output

th a t th e motor is a ble to provide du e to losses or inefficiencies

in the motor. The relation between output and input is themotor efficiency, .

The typical efficiency of a m otor is bet ween 0.7 and 0.9, depen d-

ing on t he size of th e motor an d th e nu mber of poles.

n k n< < 1n 0 n 0

n0 < < 1

n 0

n n k0

facts worth knowing vf d

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