Principles of Operation of Syncronous Machines
Transcript of Principles of Operation of Syncronous Machines
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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
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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
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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.
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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
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158
ppendix
agging
eading
~ s
,
eading
,
,
~ - - - ~ ~ et>R
,
o \
\
\
\
\
\
\
,
\
\
\
\
\
,
VI
E
I
VI
E
I
agging
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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.
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160
ppendix
It is important to notethatwhen seen from the terminals, withthemachine
operating
in underexcited mode, the power
factor
angle
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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.
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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.
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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.)
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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.
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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).
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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.
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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
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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)
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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.
-
8/20/2019 Principles of Operation of Syncronous Machines
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.