Principles of Operation of Syncronous Machines

8/20/2019 Principles of Operation of Syncronous Machines

1/18

ppendix

Principles

of

Operation

of

Synchronous

achines

A GENERAL DISCUSSION

The commercial birth of the alternator synchronous generator)can be dated back

to August 24, 1891. On that day, the first large-scale demonstration of transmis

sion of AC power was carried out. The transmission was from Lauffen,

Germany

to Frankfurt, about 110 miles away. The occasion was an international electrical

exhibition in Frankfurt. This demonstration was so convincing as to the feasibil

ity of the utilization of AC systems for transmission of power over long distances

that the city of Frankfurt adopted it for their first power plant, commissioned in

1894 exactly one hundred years before the writing of this book see Fig. A-I).

The Lauffen-Frankfurt demonstration, and the consequent decision by the

city of Frankfurtto use alternatingpower delivery, were instrumental in the adop

tion by New York s Niagara Falls power plant of the same technology. The Nia

gara Falls powerplant becameoperational in 1895. For all practicalpurposes,the

great DC versusAC duel was over. SouthernCaliforniaEdison s history book re

ports its Mill Creek hydro plant is the oldest active polyphase 3-phase)plant in

the United States. Located in San Bernardino County California, its first units

went into operation on September 7, 1893, placing it almost two years ahead of

the Niagara Falls project. One of those earlier units is still preserved and dis

played at the plant.

It is interesting to note that, although tremendous development in machine

ratings, insulation components, and design procedures has occurred over the last

100 years, the basicconstituents of the machine have remainedthe same.

153


2/18


3/18

Principles

of Operation of Synchronous

Machines

ISS

The stationary field synchronous

machine

has salientpoles

mounted

on the

stator-the stationary member. The poles are magnetized either by permanent

magnets or by a DCcurrent. The

armature,

normally

containing a 3-phase wind

ing,is

mounted

on the shaft. The armature

winding

is fed through threeslip-rings

collectors anda set of

brushes

sliding on

them.

This arrangement can be found

in

machines

up to about5

kVA

in

rating.

For largermachines-all those

covered

in this book-the

typical

arrangement usedis the rotating

magnetic

field.

The

rotating

magneticfield also

known

as revolving field synchronous ma

chinehasthefield

winding

wound on therotating

member

the rotor andthear

mature

wound on the stationary

member

the stator . The rotating winding is

energized by a DCcurrent, creating a

magnetic

field thatmustbe rotated at syn

chronous speed.

Therotating field

winding

canbeenergized

through

a set of slip

rings and

brushes

external excitation , or from a diode

bridge

mounted on the

rotor self-excited . The rectifier bridge is fed from a shaft-mounted alternator,

which is itselfexcited by the pilotexciter. In externally fed fields, the source can

bea shaft-driven DC

generator,

a separately excited DC

generator,

or a solid-state

rectifier. Several

variations to these

arrangements exist.

The statorcore is madeof insulated steel laminations. The thickness of the

laminations and the typeof steel are chosen to minimize eddycurrent and hys

teresis losses.The core is mounteddirectlyonto the frame or in large 2-pole

machines through spring bars. The core is slotted normally open slots , and

the coils

making

the winding are placed in the slots.There are several types of

armature windings; e.g., concentric windings of several types, cranked coils,

split windings of various types, wave windings, and lap windings of

various

types.

Modern

largemachines typically arewoundwithdouble-layer lapwind

ings.

The rotor field is eitherof salient pole Fig. A-2a or non salient pole con

struction,

alsoknown as roundrotoror cylindrical rotor

Fig. A-2b .

Non-salient-pole

rotors

are utilized in 2- or 4-pole

machines,

and occasion

ally

in 6-pole

machines.

Theseare typically

driven

by

steam-

or gas-turbine prime

movers.

The vastmajority of salient-pole machines havesixormorepoles. They

include all

synchronous hydrogenerators, almost all synchronous condensers, and

the

overwhelming majority

of

synchronous motors.

Non-salient-pole

rotors

are typically

machined

out of a solid steel

forging.

Thewinding isplacedinslots

machined

outof therotorbodyandretained against

the largecentrifugal forces by metallic wedges, normally madeof

aluminum

or

steel.

Theendpartof the windings is retained by theso-called retaining rings. In

the caseof largemachines, thesearemadeoutof steel.

Largesalient-pole

rotors

aremadeof laminated polesretaining the

winding

underthepole

head.

Thepolesarekeyed ontotheshaftor spider-and-wheel struc

ture.

Salient-pole

machines

have an additional

winding

in the

rotating

member.

This

winding,

madeof copperbars short-circuited at both ends, is imbedded in

the headof the pole,close to the faceof the pole.The purpose of this

winding

is


4/18

156

Stator

slots

Poleface

Appendix

Stator

core

a)

Rotor

winding

b)

Fig.A-2 Schematic

cross

section

of a

synchronous

machine a)Salientpole;

b)

Round

rotor

to start the motoror condenser under its own power as an induction

motor

and

takeit unloaded to almost

synchronous

speed

when

the rotoris pulledin bythe

synchronous

torque

Thewinding also servestodamptheoscillations of therotor

aroundthe synchronous speed andis therefore namedthe

damping winding

also

known as

amortisseurs .

A OP R TION

It is convenient to introduce the

fundamental

principles describing the operation

of a synchronous machine in terms of an

ideal

cylindrical-rotor machine con

nected to an

infinite

bus.The infinitebus represents a busbarof constantvoltage

which

can deliver or

absorb

active and reactive powerwithout any limitations.

The idealmachine has zero resistance and

leakage

reactance, infinitepermeabil

ity,andno saturation, as well as zeroreluctance torque

The production of torque in the

synchronous

machine results from the nat

ural tendency of twomagnetic fields to alignthemselves. Themagnetic fieldpro

ducedby the stationary

armature

is

denoted

as

t s

The

magnetic

field produced

by the rotating field is

>r

The resultant

magnetic

fieldis

< >

< >s

+ >

The flux t>

r

is established in the airgapof themachine

Bold symbols indicate

vectorquantities.


5/18

Principles of peration of Synchronous achines

157

Whenthe torqueapplied to the shaft is zero, the magnetic fields of the rotor

and stator completely align themselves. The instant torque is introduced to the

shaft,eitherin a generating modeor in a motoring mode, and a small angle is cre

ated

between

the stator and rotor fields. This angle

A)

is called the

torque angle

of the machine.

A.3.1 No oad Operation

Whenthe ideal

machine

is connected to the infinite bus, a 3-phase balanced

voltage

V) is applied to the stator

winding

withinthe context of this

work,

3

phase

systems

and

machines

are assumed . It can be shown that a 3-phase bal

ancedvoltage applied to a 3-phasewinding evenly distributed around the core of

an armature will produce a rotating revolving) magnetomotive force mmf) of

constant

magnitude

F

8

) . This rnmf, actingupon the reluctance encountered along

its path, results in the magnetic flux 4),) previously introduced. The speed at

which

this field revolves around the centerof the machine is related to the supply

frequency and the numberof poles, by the following expression:

f

n

s

=

12

p

where

f

=

electrical frequency in Hz

p = numberof poles of the

machine

n

s

=

speedof the revolving field in revolutions per

minute

rpm .

If no current is supplied to the DC field winding, no torque is generated, and

the resultant flux

4),),

which in this case equals the stator flux

4 ,, ,

magnetizes

the core to the extent the applied voltage

VI)

is exactly opposed by a counter

electromotive force cemt) E

1

) .

If the rotor s excitation is slightly increased, and

no torque applied to the shaft, the rotor provides some of the excitation required

to produce E

1)

causing an equivalent reduction of

s .

This situation represents

the underexcited condition shown in condition

no-load

a) in Figure A-3.When

operating under this condition, the

machine

is said to behave as a lagging con

denser; i.e., it absorbs reactive power from the

network.

If the field excitation is

increased over the value required to produce E

1

) ,

the stator currents generate a

flux that counteracts the field-generated flux. Underthiscondition, themachine is

said to be overexcited, shown as condition no-load b) in Figure A-3. The ma

chine is behaving as a leading condenser; i.e., it is delivering reactive power to

the

network.

Underno-load condition, boththe torque angle

A)

andtheloadangle

0)

are

zero.The load angle is defined as the angle between the rotor s mmf F

f

or flux

4 / and the resultant mmf F,) or flux ,). The load angle 0) is the most com

monly

used because it establishes the torque limits the

machine

can attain in a

simplemanner discussed later). Onemustbe awarethat, in manytexts, the name


6/18

158

ppendix

agging

eading

~ s

,

eading

,

,

~ - - - ~ ~ et>R

,

o \

\

\

\

\

\

\

,

\

\

\

\

\

,

VI

E

I

VI

E

I

agging


7/18

Principles Operation

Synchronous Machines

159

0 and the angle between ~ and

E

J

are very similar. In this book, the more

commonnamepower angle is usedfor the angle between V

J

and (Ej . In Figure

A-3,the powerangle is alwaysshownas zerobecausethe leakage impedance has

been neglected in the idealmachine.

It is importantat this stage to introducethedistinction betweenelectricaland

mechanical angles. In studyingthe performance of the synchronous machine,all

the electromagnetic calculationsare carriedout based on electric quantities; i.e.,

all angles are electricalangles.Toconvert the electrical anglesused in the calcu

lations to the physicalmechanical angles we observe, the following relationship

applies:

mechanical angle

= electrical

angle

A.3.2 Motor Operation

If a breakingtorque is applied to the shaft, the rotor starts fallingbehindthe

revolving-armature-induced mmf

F

s

) In order to maintain the requiredmagne-

tizing mmf (F,), the armature current changes. If the machine is in the under

excited mode, the conditionmotor (a) in FigureA-3 represents the new phasor

diagram. On the other hand,

if

the machine is overexcited, the new phasor dia

gram

is

represented bymotor (b)

in

FigureA-3. The activepowerconsumedfrom

the networkunder theseconditionsis givenby:

Active power

= t

•

/1 •

cos PI

(per phase)

If the torqueis increased, a limit is reachedinwhichtherotorcannotkeepup

with the revolving field. The machinethenstalls.This is knownas fallingout of

step, or pullingout of step, or slippingpoles. The maximum torque limit is

reachedwhen the angle 0 equals

rt/2

electrical. The convention is to define 0 as

negative for motor operation and positive for generator operation. The torque

is also a function of the magnitude of > and

< >f

Whenoverexcited, the valueof

f fis largerthanin the underexcited condition. Therefore, synchronous motorsare

capable of greatermechanical output when overexcited. Likewise, underexcited

operation is moreprone to result in an out-of-step situation.

A.3.3 Generator Operation

Let s assumethat the machine is running at no-loadand a positivetorque is

applied to the shaft; Le. the rotor flux angle is advancedahead of the stator flux

angle.As in the case of motor operation,the statorcurrentswill change to create

the new conditionsof equilibrium shown in Figure

A-3,

under gener tor If the

machine is initiallyunderexcited, condition(a) in FigureA-3 results.On the other

hand, if themachineis overexcited, condition(b) in Figure

A-3

results.


8/18

160

ppendix

It is important to notethatwhen seen from the terminals, withthemachine

operating

in underexcited mode, the power

factor

angle


9/18

ppendix Principles

of

Operation

of

Synchronous Machines

161

In FigureA-4, the reactanceX

a

representsthemagnetizingor demagnetizing

effect of the stator windings on the rotor. It is also called the m gn tizing

reac-

tance R, represents the effective resistanceof the stator. The reactance X repre

sents the stator leakage reactance.The sum of

X

a

and

X

is used to represent

the

total reactanceof the machine,and is called the synchronous

reactance

X

s .

Zs is

the

synchronous impedance

of the machine. It is important to remember that the

equivalent circuit described in Figure A 4 represents the machine only under

steady-statecondition.

The simpleequivalentcircuitof FigureA-5a seep. 62 suffices to determine

the steady-state performance parameters of the synchronous machineconnected to

a powergrid. These parameters include voltages, currents, power

factor

and load

angle see Fig.

A-5b .

The regulation of the machine can be easily found from the

equivalent circuitfor different loadconditions by usingthe regulation

formula:

9t( ) = 100· Vno IOad - Ioad)/ Ioad

A 3 5 Performance Characteristics: V Curves

and Rating Curves

If

the activepower flowof the synchronousmachine is keptconstant, a fam

ily of curves can be obtained relating the magnitude of the armature current to

that of the field current.The curves, shapedas

V

see Fig.

A-6

are drawn for var

ious load conditions. In the graph, the lagging and leading operating regions can

be discerned.

Physical considerations define the limits of operation of synchronous ma

chines.These limitsare expressedas a familyof concentriccapabilitycurves see

Fig.A-7 .

• The top part of the rating curves is defined by the field winding heating

and insulation system.

• The right side of the curves is limited by the heating of the armature and

the typeof armature insulation.

• The bottompart of the curves is limited by the heating of the core-end re

gion.

Ratingcurves are normallydrawn for a numberof hydrogenpressures in hydro

gen-cooledmachines ,or for ambient temperatures in air-cooledmachines .

Both the ratingcurves and the

V-curves

can be combined in one graph.This

graph is used

by

the machine operators and protectionengineers to set the limits

of safe operationon the machine.


10/18

162

ppen ix

E IZ V

IZ

Lagging power factor overexcited

Leading power

factor underexcited

a Generator operation

v

IZ

I E

Leading

power

factor overexcited

Lagging

power

factor underexcited

b Motor operation

Fig.A-5 Steady-state equivalentcircuitand vectordiagram.


11/18

Principles

peration

Synchronous achines

163

1 6 w r ~ ~ _ _ r _ ~ _ _ _ r _ _ _ r _ _ ~

1.5 J - - - + - - - - + - - - J - - - - I - - - - - 1 ~ - + _ - _ + _ - _ + _ - _ + - _ _ i - - i _ _ _ i

1.4 L - - - - L - - - + - - ~ - - - . - - ~ - + _ _ - _ + _ - _ _ . . _ - _ _ _ t _ - _ _ _ 4 ~ - + _ _ _ i

1.0 PF . . --- ---

1 3

J - - - - I - - - - + - - ~ - - - - - _ I _ _ - ~ _ + _ _ I _ _ - ~ - _ + - ~ : - - + _ _ _ 4

0.95 PF

~ . . . . 0 . 9 5 P F

1.2 J - - - ~ - - + - - ~ - - - - - - I _ _ I _ _ ~ _ + _ _ I _ _ 4 ~ - _ _ _ + _ - ~ - - + _ _ _ 4

9 PF

0.85 PF

One per unit

~ t o I 6 147.059MVA

~ f

or

5487

A

00 100 200 300 400 500 600 700 800 900 1000 1tOO 1200

Fieldcurrent(A)

1 ...-...--1----...-.-

0.2

. . . . . . ~ ~ . .

C

1.1

::s

u

1.0

E

0.9

~

0.80 PF

~

8

0.8

. .

0

0.7

«I

bO

Q)

e

0.6

2

::I

~

0.5

Fig.A·6 Typical

V curves

for generatoroperation. (Copyright

©

1987.ElectricPower

ResearchInstitute.)


12/18

164

ppendix

Limited

by stator core

heating and field heating

0.95 PF

6

0.90PF

0.85 PF

0.80PF

0.70PF

imited

by

core end heating

statorend winding

heating and

minimum

excitation

1------ ---- ---I----I----4----1-t----6-- --I--..- ---... Megawatts

80

I I I ~ ~ . ~ I t . . . . f _ _ _ _ _ _ _ t

Stability limit for

4 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ v o k a g e ~ g u l a t o r

1 ~ _ _ _ _ f ~ ~ ~ _ _ _ _ _ _ _ _ _ l

120

c:

1

~

-

80

QJ

60

0

~

40

/

20

s

~

~

-0

0

60

80

20 40

1

t O

~

~

20

Fig. A-7 Typical capability curves for a synchronous generator. Copyright Q 1987.

Electric Power Research Institute. EPRI EL-5036. PowerPlant lectrical

eference

Series Volumes 1-16. Reprinted withPennission.


13/18

Principles

of peration of Synchronous achines

A.4 OPER TING ONSTR INTS

165

In addition to the rating curves described in SectionA.3.5, design characteristics

of the machine impose additional limits to its range of allowed .operation. The

items described in the next few sections represent some of the most important

constraints imposed on the machine. ANSI and IEEE standards in the United

States and other standards abroadprovide in manycases typical ranges for those

values.Also, typical valuescan be found in technicalpapers, books, and bulletins

publishedby themachinemanufacturers.

It is interesting tonote that in certaincases suchasmaximum-allowed over

and under-frequency operation of turbine-driven generators), the prime mover

steam or gas-turbine) may impose stricter limitations on the operation of the

unit than the generator.

Reference [1] is an excellent source of information on the operational re

quirementsof largesynchronous machines.

A.4.1 Volts per Hertz V/Hz

The term volts per hertz has been borrowed from the operation of trans

formers. In transformers,

thefund ment l volt ge equ tion

is given by:

v=4.44 • f • B

max

• area of core • number of turns

whereBmax is the vector magnitudeof the flux density

in

the core of the trans

form r

By rearrangingthe variables, the followingexpressionis obtained:

V/f [V/

] = 4.44 • B

max

•

area

of ore

number

of

turns

or alternatively,

B

max

[Tesla] = constant> V/f

or,

in

another annotation,

B

max

x V/Hz

This last equation indicates that the maximum flux density in the core of a

transformeris proportionalto the terminalvoltagedividedby the frequencyof the

supply voltage. This ratio is known as

V/Hz.

A set of equations very similar to the ones above can be written for the ar

mature of an alternate-current machine. In this case, the constant includeswind

ing parameterssuch as winding

pitch

and

distri ution

factors. However, the end

result is the same; i.e., in the armatureof an electrical alternate current machine,

the maximumcore flux density is proportionalto the terminalvoltagedivided by

the supplyfrequency orVlHz).


14/18

166

ppen ix

The importance of thisratioresides in thefactthatinmachines, as

well

asin

transformers,

the

operating

point of the

voltage

is such that, for the given rated

frequency, theflux

density

isjust below thekneeof thesaturation point.

Increasing

the

volts

per tum in the

machine

or

transformer raises

the

flux

density

above

thekneeof the saturation curve seeFig.

A-8 .

Consequently, large

magnetization currents

are

produced,

as well as large

increases

in the core loss

due to the bigger hysteresis loopcreated see Fig. A 9 . Bothof these result in

substantial increases incoreandcopperlosses andexcessive temperature risesin

bothcoreand

windings.

If not

controlled,

this

condition

can result in lossof the

core interlaminar

insulation,

aswellas lossof lifeof thewinding insulation.

TheANSI C50.30-1972/1EEE Std67-1972

standard

state

generators

arenor

mally

designed

to

operate

at rated output of up to 105 of rated

voltage

[1].

ANSIIIEEE

C57 standards for transformers state the same

percentage

for rated

loads andupto 110 of ratedvoltage at no-load. In

practice,

the operator should

make surethemachine remains below

limits

thatmay

affect

the

integrity

of both

the

generator

and the unit transformer. The

aforementioned standards

state that

synchronous

motors, likemotors in

general,

are

typically designed

forratedoper

ation under voltages ofupto 110 ofratedvoltage. For

operation

of

synchronous

machines at otherthanrated

frequencies,

refertoANSI

C50.30-1972

[1].

B

max

max

- - t - - - - . - - -+ -

rated

mag

rated

Magnetizing

currrent

Fig.A 8 Typical saturation curvefor transformers andmachines.


15/18

rinciples of

Operation

of Synchronous

Machines

B T

Areaof

additional

hysteresis losses

H Nm

Hysteresis

loop

for

rated

V/HZ

Hysteresis loop

for

increased V/HZ

Fig.A-9 Hysteresis lossesunder

normal

and

abnormal

conditions.

A 4 Negative Sequence Currents and

/2 2t

167

A 3-phase balanced supplyvoltage applied to a symmetrical 3-phase wind-

ing generates a constant-magnitude flux in the airgapof the machine which ro

tatesat synchronous speedaroundthe circumference of themachine. In addition,

the slots and other asymmetries

within

the magnetic pathof the fluxcreate low

magnitude spaceharmonics; i.e.,

fluxes

that rotatein both directions, of multiple

frequencies of the fundamental supply frequency. In a synchronous machine the

main fundamental flux rotatesin thesamedirection and speedas the rotor.

It happens thatwhenthe supplyvoltage or currents areunbalanced, an addi

tionalfluxof fundamental frequency appears in the airgapof themachine.

How-

ever, this flux rotatesin theopposite direction fromthe

rotor.

This flux induces in

the rotor windings and body voltages and currents with twice the fundamental

frequency. Thesearecallednegative-sequence currents nd voltages.

There are

several abnormal

operating conditions that give rise to large cur

rents flowing in the

forging

of the rotor rotorwedges teeth,end rings, and field

windings of synchronous machines. These conditions include unbalanced

arma-

turecurrent producing negative-sequence currents as wellas asynchronous mo

toringor generation operation with loss of field producing alternate strayrotor

currents. The resultant strayrotorcurrents tendto flowon thesurfaceof the rotor

generating /2 2 losseswith rapid overheating of critical rotor components. If


16/18

168

Appendix

notproperly controlled, serious.damage to therotorwillensue.Of particularcon

cernis damageto the end rings and

wedges

of round rotors(seeFig.A-I0).

For all practical purposes, all large synchronous machines have installed

protective relays that will

remove

the machine from operation under excessive

negative sequence current operation. To properly set the protective relays, the

operatorshould obtain

maximum

allowable negative sequence

/2

values from

the machine s manufacturer. The values shown in Table A-I are contained in

ANSIIIEEE C50.13-1977 [2] as valuesof continuous 1

2

current to be withstood

by a generator without

injury,

while exceeding neither rated

kVA

nor 105 of

ratedvoltage.

TABLE A-I.

Values

of Permissible /2Currentin a Generator

yp ofGenerator

Salient-pole:

Withconnected amortisseur winding

Without

connected

amortisseur

winding

Cylindrical rotor.

Indirectly cooled

Directlycooledup to 950 MVA

951-1,200MVA

1,200-1,500 MVA

Permissible /2 as

of RatedStatorCurrent

10

5

10

8

6

5

Whenunbalanced fault currentsoccur in the vicinity of a generator, the 1

2

valuesof TableA-I will probably beexceeded. In order to set the protection re

lays to remove the machine from the network before damage is incurred, but

avoiding unnecessary relay misoperation, manufacturers have developed the so

called

2

2

t

values.

These valuesrepresent the

maximum

time in secondsa ma

chinecanbesubjected to a negative-sequence current. In the

/2 2

t expression, the

current is given as per unit of rated stator current. These values shouldbe ob

tained from the manufacturer.

Table

A 2

shows typical valuesgiven in the stan

dard [2].

TABLEA-2. Values of Permissible 12ft in a Generator

TypeofMachine

Salient-pole generator

Salient-pole condenser

Cylindrical-rotor

generator:

Indirectly cooled

Directly cooled,0-800 MVA

Directlycooled,

801-1,600

MVA

Permissible (/2

Y

40

30

30

30

10-5/800) MVA-800)


17/18

Principles peration

Synchronous achines

169

40

- . t s

0

20 t - - - - - - - + ~ ~ - , . - - - - - _ + _ ~ . . . . .

80 __

r r

60

J ~ _ _ _ I : . _ ~ _ t

t

t - - - - - - - - - - l ~ ~ _ _ _ _ 4 ~ ~ ~ ~ - _ _ t

f

Fig.

A tO Temperature

rise

measured

at the end of the

rotor body

duringshort-term

unbalanced load operation Reproduced with permission from Design

andPerformance of LargeSteamTurbineGenerators, 1974,ABB.


18/18

170

A 4 3 Overspeed

Appendix

Manufacturers of large rotating machines normally test their products to

withstand speedsof up to 20 over rated

speed

Nevertheless, agingof the ma

chine

may to some extent, encroach on the originaldesign

margins

Therefore,

overspeed is a seriousconditionthatmustbeavoidedby propersettingof thepro

tectiveinstrumentation. In steam-turbine generators, the turbine is often the item

most sensitive to overspeed operation of the unit, and protection is set accord

ingly

Hydrogenerators tendto overspeed for longerperiodsduringa suddenloss

of load, due to the slowerwater

valves

Manyold salient-pole hydrogenerators still in operation, whichwere origi

nallydesigned for 50-Hzoperation, wereconverted yearsago to 60-Hzoperation

(a 2 speed increase), in addition to large up-rating of delivered load. The

changewaspredicated on the largedesign

margins

of theseold machines. How

ever, inmostcasesit is difficult toknowtheremaining overspeed

margin

of these

machines Detailed mechanical calculations are required.

R F R N S

[1] ANSI C50.30-1972/IEEE Std 67-1972, IEEE Guide for Operation and

Maintenance of Turbine Generators.

[2] ANSIIIEEE C50.13-1977, Requirements for Cylindrical-RotorSynchronous

Generators.

ITION L RE ING

A

wealthof literature exists for the reader interested in a more in-depth un

derstanding of synchronous machine theory The following is only a very short

listof textbooks readily available describing theoperation anddesignof synchro

nous

machines in

a manneraccessible to theuninitiated.

DinoZorbas,

ElectricMachines Principles Applications and Control Schemat

ics.

West Publishing

Company 1989

M

G. Say Alternating

Current Machines. Pitman

Publishing Limited, 1978

Theodore

Wildi Electrical Machines DrivesandPower Systems.

Prentice Hall.

Vincent

del

Toro ElectricMachines and PowerSystems.

Prentice Hall,

1985

M. Liwschitz-Garik andC. C.Whipple, ElectricMachinery Vols. 2. D. Van

Nostrand Co., Inc.

A.

E. Fitzgerald andC.

Kingsley ElectricMachinery.

McGraw-Hill.

Principles of Operation of Syncronous Machines

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