1337683699.3104Lecture 07 - Synchronous Machines

7/18/2019 1337683699.3104Lecture 07 - Synchronous Machines

1/98

ELEN 3441 Fundamentals of Power Engineering Spring 2008

1

Instructor:

Dr. Gleb V. Tcheslavski

Contact:

[email protected]

Office Hours:

TBD; Room 2030

Class web site:

http://ee.laar.e!u/"leb/In!e#.ht

$ecture %: &'nchronous achines
mailto:[email protected]:[email protected]


2/98


2

Construction of s'nchronous

achines

Sn!"ronous ma!"ines are #$ ma!"ines t"at "a%e a field

!ir!uit supplied & an e'ternal ($ sour!e)

*n a sn!"ronous generator+ a ($ !urrent is applied to t"e rotor winding

produ!ing a rotor magneti! field) ,"e rotor is t"en turned & e'ternal means

produ!ing a rotating magneti! field+ w"i!" indu!es a 3-p"ase %oltage wit"in

t"e stator winding)

*n a sn!"ronous motor+ a 3-p"ase set of stator !urrents produ!es a

rotating magneti! field !ausing t"e rotor magneti! field to align wit" it) ,"e

rotor magneti! field is produ!ed & a ($ !urrent applied to t"e rotorwinding)

Field windings are t"e windings produ!ing t"e main magneti! field .rotor

windings for sn!"ronous ma!"ines/; armature windings are t"e windings

w"ere t"e main %oltage is indu!ed .statorwindings for sn!"ronous

ma!"ines/)


3/98


3


achines

,"e rotor of a sn!"ronous ma!"ine is a large ele!tromagnet) ,"e magneti! poles

!an &e eit"er salient .sti!ing out of rotor surfa!e/ or non-salient !onstru!tion)

Non-salient-pole rotor usuall two- and four-pole rotors) Salient-pole rotor four

and more poles)

Rotors are made laminated to redu!e edd !urrent losses)


4/98


4


achines

Salient pole wit" field

windings

Salient pole wit"out

field windings

o&ser%e laminations

# sn!"ronous rotor wit" 8 salient poles


5/98



achines

,wo !ommon approa!"es are used to suppl a ($ !urrent to t"e field !ir!uits on

t"e rotating rotor

1) Suppl t"e ($ power from an e'ternal

($ sour!e to t"e rotor & means of

slip rings and &rus"es;

2) Suppl t"e ($ power from a spe!ial

($ power sour!e mounted dire!tl on

t"e s"aft of t"e ma!"ine)

Slip rings are metal rings !ompletel en!ir!ling t"e s"aft of a ma!"ine &ut insulated

from it) ne end of a ($ rotor winding is !onne!ted to ea!" of t"e two slip rings on

t"e ma!"ine5s s"aft) 6rap"ite-lie !ar&on &rus"es!onne!ted to ($ terminals ride on

ea!" slip ring suppling ($ %oltage to field windings regardless t"e position or speed

of t"e rotor)


6/98


7


achines

Slip rings

rus"


7/98ELEN 3441 Fundamentals of Power Engineering Spring 2008

9


achines

Slip rings and &rus"es "a%e !ertain disad%antages in!reased fri!tion and wear

.t"erefore+ needed maintenan!e/+ &rus" %oltage drop !an introdu!e signifi!ant

power losses) Still t"is approa!" is used in most smallsn!"ronous ma!"ines)

n large generators and motors+ &rus"less e'!iters are used)

# &rus"less e'!iter is a small #$ generator w"ose field !ir!uits aremounted on t"e stator and armature !ir!uits are mounted on t"e rotor

s"aft) ,"e e'!iter generator5s 3-p"ase output is re!tified to ($ & a 3-

p"ase re!tifier .mounted on t"e s"aft/ and fed into t"e main ($ field

!ir!uit) *t is possi&le to ad:ust t"e field !urrent on t"e main ma!"ine &

!ontrolling t"e small ($ field !urrent of t"e e'!iter generator .lo!ated on

t"e stator/)

Sin!e no me!"ani!al !onta!t o!!urs &etween t"e rotor and t"e stator+ e'!iters of

t"is tpe reuire mu!" less maintenan!e)



8


achines

# &rus"less e'!iter a

low 3-p"ase !urrent is

re!tified and used to

suppl t"e field !ir!uit

of t"e e'!iter .lo!atedon t"e stator/) ,"e

output of t"e e'!iter5s

armature !ir!uit .on t"e

rotor/ is re!tified and

used as t"e field

!urrent of t"e main

ma!"ine)



ed wit" t"e me!"ani!al rotational speed)

120

me

n Pf = .9)11)1/

?"ere feis t"e ele!tri!al freuen!+ @>;

nmis me!"ani!al speed of magneti! field .rotor speed for sn!"ronous

ma!"ine/+ rpm;

Pis t"e num&er of poles)

Steam tur&ines are most effi!ient w"en rotating at "ig" speed; t"erefore+to generate 70 @>+ t"e are usuall rotating at 3700 rpm and turn 2-pole

generators)

?ater tur&ines are most effi!ient w"en rotating at low speeds .200-300

rpm/; t"erefore+ t"e usuall turn generators wit" man poles)



13

Internal "enerate! volta"e of a

s'nchronous "enerator

,"e magnitude of internal generated %oltage indu!ed in a gi%en stator is

2A CE N f K = =

w"ere Kis a !onstant representing t"e !onstru!tion of t"e ma!"ine+ is flu' in it

andis its rotation speed)

Sin!e flu' in t"e

ma!"ine depends

on t"e field !urrent

t"roug" it+ t"einternal generated

%oltage is a

fun!tion of t"e

rotor field !urrent)

=agneti>ation !ur%e .open-!ir!uit !"ara!teristi!/ of a

sn!"ronous ma!"ine

14



14

)*uivalent circuit of a s'nchronous

"enerator

,"e internall generated %oltage in a single p"ase of a

sn!"ronous ma!"ine EAis notusuall t"e %oltage appearing

at its terminals) *t euals to t"e output %oltage Vonl w"en

t"ere is no armature !urrent in t"e ma!"ine) ,"e reasonst"at t"e armature %oltage EAis not eual to t"e output

%oltage Vare

1) (istortion of t"e air-gap magneti! field !aused & t"e

!urrent flowing in t"e stator .armature rea!tion/;2) Self-indu!tan!eof t"e armature !oils;

3) Resistan!eof t"e armature !oils;

4) Effe!t of salient-polerotor s"apes)

1



1


"enerator

#rmature rea!tion .t"e

largest effe!t/

?"en t"e rotor of a sn!"ronous

generator is spinning+ a %oltage

EAis indu!ed in its stator) ?"ena load is !onne!ted+ a !urrent

starts flowing !reating a

magneti! field in ma!"ine5s

stator) ,"is stator magneti! field

BSadds to t"e rotor .main/

magneti! field BRaffe!ting t"e

total magneti! field and+

t"erefore+ t"e p"ase %oltage)

Lagging

load

17



17


"enerator

#ssuming t"at t"e generator is !onne!ted to a lagging load+ t"e load !urrent IAwill

!reate a stator magneti! field BS+ w"i!" will produ!e t"e armature rea!tion %oltage

Estat) ,"erefore+ t"e p"ase %oltage will &e

A statV E E = + .9)17)1/

,"e net magneti! flu' will &e

net R S B B B= + .9)17)2/Rotor field Stator field

Note t"at t"e dire!tions of t"e net magneti! flu' and t"e p"ase %oltage are t"e

same)

19



19


"enerator

#ssuming t"at t"e load rea!tan!e isX+ t"e armature rea!tion %oltage is

stat AE jXI= .9)19)1/

,"e p"ase %oltage is t"enA AV E jXI = .9)19)2/

#rmature rea!tan!e !an &e modeled & t"e following

!ir!uitA

@owe%er+ in addition to armature rea!tan!e effe!t+

t"e stator !oil "as a self-indu!tan!e LA.XAis t"e

!orresponding rea!tan!e/ and t"e stator "asresistan!e RA) ,"e p"ase %oltage is t"us

A A A A AV E jXI jX I RI = .9)19)3/

18



18


"enerator

ften+ armature rea!tan!e and self-indu!tan!e are !om&ined into t"e sn!"ronous

rea!tan!eof t"e ma!"ine

S AX X X= + .9)18)1/

A S A AV E jX I RI =

,"erefore+ t"e p"ase %oltage is

.9)18)2/

,"e eui%alent !ir!uit of a 3-p"ase

sn!"ronous generator is s"own)

,"e ad:usta&le resistor Radj!ontrols t"e

field !urrent and+ t"erefore+ t"e rotor

magneti! field)

1



1e+ t"e

armature resistan!e R#


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24

+ower an! tor*ue in s'nchronous

"enerators

,"en t"e real output power of t"e sn!"ronous generator !an &e appro'imated as

3 sinAout

S

V EP

X

.9)24)1/

?e o&ser%e t"at ele!tri!al losses are assumed to &e >ero sin!e t"e resistan!e is

negle!ted) ,"erefore

conv out P P .9)24)2/

@ere is t"e torue angleof t"e ma!"ine t"e angle &etween Vand EA)

,"e ma'imum power !an &e supplied & t"e generator w"en D


25/98


2

+ower an! tor*ue in s'nchronous

"enerators

,"e ma'imum power spe!ified & .9)24)3/ is !alled t"e stati! sta&ilit limit

of t"e generator) Normall+ real generators do not approa!" t"is limit full-

load torue angles are usuall &etween 10and 200)

,"e indu!ed torue is

sinind R S R net R net !B B !B B !B B = = = .9)2)1/

Noti!e t"at t"e torue angle is also t"e angle &etween t"e rotor magneti! fieldBR and t"e net magneti! field Bnet)

#lternati%el+ t"e indu!ed torue is

3 sinAind

m S

V E

X

= .9)2)2/

27


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27

,easurin" paraeters of

s'nchronous "enerator o!el

,"e t"ree uantities must &e determined in order to des!ri&e t"e generator model

1),"e relations"ip &etween field !urrent and flu' .and t"erefore &etween t"e field

!urrent IFand t"e internal generated %oltage EA/;

2),"e sn!"ronous rea!tan!e;

3),"e armature resistan!e)

?e !ondu!t first t"e open-!ir!uit teston t"e sn!"ronous generator t"e generator

is rotated at t"e rated speed+ all t"e terminals are dis!onne!ted from loads+ t"e

field !urrent is set to >ero first) Ne't+ t"e field !urrent is in!reased in steps and t"e

p"ase %oltage .w"is" is eual to t"e internal generated %oltage EAsin!e t"e

armature !urrent is >ero/ is measured)

,"erefore+ it is possi&le to plot t"e dependen!e of t"e internal generated %oltage

on t"e field !urrent t"e open-!ir!uit !"ara!teristi! .$$/ of t"e generator)

29


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29



Sin!e t"e unsaturated !ore of t"e ma!"ine "as a

relu!tan!e t"ousands times lower t"an t"e

relu!tan!e of t"e air-gap+ t"e resulting flu'

in!reases linearl first) ?"en t"e saturation is

rea!"ed+ t"e !ore relu!tan!e greatl in!reases

!ausing t"e flu' to in!rease mu!" slower wit"t"e in!rease of t"e mmf)

?e !ondu!t ne't t"e s"ort-!ir!uit teston t"e sn!"ronous generator t"e generator

is rotated at t"e rated speed+ all t"e terminals are s"ort-!ir!uited t"roug"

ammeters+ t"e field !urrent is set to >ero first) Ne't+ t"e field !urrent is in!reased in

steps and t"e armature !urrent IAis measured as t"e field !urrent is in!reased)

,"e plot of armature !urrent .or line !urrent/ %s) t"e field !urrent is t"e s"ort-!ir!uit

!"ara!teristi! .S$$/ of t"e generator)

28


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28



,"e S$$ is a straig"t line sin!e+ for t"e

s"ort-!ir!uited terminals+ t"e magnitude of

t"e armature !urrent is

2 2

AA

A S

EI

R X

=

+

.9)28)1/

,"e eui%alent generator5s !ir!uit during S$

,"e resulting

p"asor diagram

,"e magneti!

fields during s"ort-

!ir!uit testSin!e BSalmost !an!els BR+ t"e

net field Bnetis %er small)

2


29/98




#n appro'imate met"od to determine t"e sn!"ronous rea!tan!eXSat a gi%en

field !urrent

1)6et t"e internal generated %oltage EAfrom t"e $$ at t"at field !urrent)

2)6et t"e s"ort-!ir!uit !urrent IA,SCat t"at field !urrent from t"e S$$)

3)FindXSfrom

,

AS

A SC

EX

I

Sin!e t"e internal ma!"ine impedan!e is

{ }2 2

,

sinceA

S A S S S A

A SC

E" R X X X R

I= + = ?

.9)2


30/98




# draw&a! of t"is met"od is t"at t"e internal generated %oltage EAis measured

during t"e $$+ w"ere t"e ma!"ine !an &e saturated for large field !urrents+ w"ile

t"e armature !urrent is measured in S$$+ w"ere t"e !ore is unsaturated)

,"erefore+ t"is approa!" is a!!urate for unsaturated !ores onl)

,"e appro'imate %alue of sn!"ronous

rea!tan!e %aries wit" t"e degree ofsaturation of t"e $$)

,"erefore+ t"e %alue of t"e sn!"ronous

rea!tan!e for a gi%en pro&lem s"ould &e

estimated at t"e appro'imate load of t"e

ma!"ine)

,"e winding5s resistan!e !an &e

appro'imated & appling a ($ %oltage

to a stationar ma!"ine5s winding and

measuring t"e !urrent) @owe%er+ #$

resistan!e is slig"tl larger t"an ($

resistan!e .sin effe!t/)

31


31/98



s'nchronous "enerator o!el: )#

E'ample 9)1 # 200 #+ 480 + 0 @>+ B-!onne!ted sn!"ronous generator wit" arated field !urrent of # was tested and t"e following data were o&tained

1) VT,OCD 40 at t"e rated IF)

2) IL,SCD 300 # at t"e rated IF)

3) ?"en a ($ %oltage of 10 was applied to two of t"e terminals+ a !urrent of 2 #

was measured)

Find t"e generator5s model at t"e rated !onditions .i)e)+ t"e armature resistan!e and

t"e appro'imate sn!"ronous rea!tan!e/)

Sin!e t"e generator is B-!onne!ted+ a ($

%oltage was applied &etween its twop"ases)

,"erefore

2

100.2

2 2 25

#CA

#C

#CA

#C

VR

I

VR

I

=

= = =

32


32/98



s'nchronous "enerator o!el: )#

,"e internal generated %oltage at t"e rated field !urrent is

,

540311.8

3 3

TA $C

VE V V= = = =

,"e sn!"ronous rea!tan!e at t"e rated field !urrent is pre!isel

2 22 2 2 2

2 2

,

311.80.2 1.02

300

AS S A A

A SC

EX " R R

I= = = =

?e o&ser%e t"at ifXSwas estimated %ia t"e appro'imate formula+ t"e result would

&e

,

311.8 1.04300

AS

A SC

EXI

= =

?"i!" is !lose to t"e pre%ious result)

,"e error ignoring RAis mu!" smaller

t"an t"e error due to !ore saturation)

,"e eui%alent !ir!uit

33


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The &'nchronous "enerator

operatin" alone

,"e &e"a%ior of a sn!"ronous generator %aries greatl under

load depending on t"e power fa!tor of t"e load and on

w"et"er t"e generator is woring alone or in parallel wit" ot"er

sn!"ronous generators)

#lt"oug" most of t"e sn!"ronous generators in t"e world

operate as parts of large power sstems+ we start our

dis!ussion assuming t"at t"e sn!"ronous generator wors

alone)

nless ot"erwise stated+ t"e speed of t"e generator is

assumed !onstant)

34


34/98



operatin" alone

Effe!ts of load !"anges

# in!rease in t"e load is an

in!rease in t"e real andGor

rea!ti%e power drawn from t"e

generator)

Sin!e t"e field resistor is unaffe!ted+ t"e field !urrent is !onstant and+ t"erefore+ t"e

flu' is !onstant too) Sin!e t"e speed is assumed as !onstant+ t"e magnitude oft"e internal generated %oltage is !onstant also)

#ssuming t"e same power fa!tor of t"e load+ !"ange in load will !"ange t"e

magnitude of t"e armature !urrent IA

) @owe%er+ t"e angle will &e t"e same .for a

!onstant PF/) ,"us+ t"e armature rea!tion %oltagejXSIAwill &e larger for t"e

in!reased load) Sin!e t"e magnitude of t"e internal generated %oltage is !onstant

A S AE V jX I= + .9)34)1/

#rmature rea!tion %oltage %e!tor will Hmo%e parallelI to its initial position)

3


35/98



operatin" alone

*n!rease load effe!t on generators wit"

Lagging PF

Leading PF

nit PF

37


36/98



operatin" alone

1) For lagging.indu!ti%e/ loads+ t"e p"ase .and terminal/ %oltage

de!reases signifi!antl)

2) For unit power fa!tor .purel resisti%e/ loads+ t"e p"ase .and

terminal/ %oltage de!reases slig"tl)

3) For leading.!apa!iti%e/ loads+ t"e p"ase .and terminal/ %oltage rises)

6enerall+ w"en a load on a sn!"ronous generator is added+ t"e following!"anges !an &e o&ser%ed

Effe!ts of adding loads !an &e des!ri&ed & t"e %oltage regulation

100%n% f%

f%

V VVRV

= .9)37)1/

?"ere Vnlis t"e no-load %oltage of t"e generator and Vflis its full-load %oltage)

39


37/98



operatin" alone

# sn!"ronous generator operating at a lagging power fa!tor "as a fairl large

positi%e%oltage regulation) # sn!"ronous generator operating at a unit power

fa!tor "as a smallpositi%e%oltage regulation) # sn!"ronous generator operating

at a leading power fa!tor often "as a negati%e%oltage regulation)

Normall+ a !onstant terminal %oltage supplied & a generator is desired) Sin!e t"e

armature rea!tan!e !annot &e !ontrolled+ an o&%ious approa!" to ad:ust t"eterminal %oltage is & !ontrolling t"e internal generated %oltage EA= K) ,"is

ma &e done & !"anging flu' in t"e ma!"ine w"ile %aring t"e %alue of t"e field

resistan!e RF+ w"i!" is summari>ed

1) (e!reasing t"e field resistan!e in!reases t"e field !urrent in t"e generator)

2) #n in!rease in t"e field !urrent in!reases t"e flu' in t"e ma!"ine)3) #n in!reased flu' leads to t"e in!rease in t"e internal generated %oltage)

4) #n in!rease in t"e internal generated %oltage in!reases t"e terminal %oltage of

t"e generator)

,"erefore+ t"e terminal %oltage of t"e generator !an &e !"anged & ad:usting t"e

field resistan!e)

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38/98



operatin" alone: )#aple

E'ample 9)2 # 480 + 70 @>+ B-!onne!ted si'-pole sn!"ronous generator "as aper-p"ase sn!"ronous rea!tan!e of 1)0 ) *ts full-load armature !urrent is 70 # at0)8 PF lagging) *ts fri!tion and windage losses are 1) ? and !ore losses are 1)0

? at 70 @> at full load) #ssume t"at t"e armature resistan!e .and+ t"erefore+ t"e I2R

losses/ !an &e ignored) ,"e field !urrent "as &een ad:usted su!" t"at t"e no-load

terminal %oltage is 480 )

a) ?"at is t"e speed of rotation of t"is generatorJ

&) ?"at is t"e terminal %oltage of t"e generator if

1) *t is loaded wit" t"e rated !urrent at 0)8 PF lagging;

2) *t is loaded wit" t"e rated !urrent at 1)0 PF;

3) *t is loaded wit" t"e rated !urrent at 0)8 PF leading)

!) ?"at is t"e effi!ien! of t"is generator .ignoring t"e unnown ele!tri!al

losses/ w"en it is operating at t"e rated !urrent and 0)8 PF laggingJ

d) @ow mu!" s"aft torue must &e applied & t"e prime mo%er at t"e full loadJ

"ow large is t"e indu!ed !ountertorueJ

e) ?"at is t"e %oltage regulation of t"is generator at 0)8 PF laggingJ at 1)0

PFJ at 0)8 PF leadingJ

3


39/98




Sin!e t"e generator is B-!onne!ted+ its p"ase %oltage is

3 277TV V V = =#t no load+ t"e armature !urrent IAD 0 and t"e internal generated %oltage is EAD

299 and it is !onstant sin!e t"e field !urrent was initiall ad:usted t"at wa)

a) ,"e speed of rotation of a sn!"ronous generator is

120 12060 1200

6m en f rpm

P= = =

w"i!" is

12002 125.7

60m rad s = =&)1) For t"e generator at t"e rated !urrent and t"e 0)8

PF lagging+ t"e p"asor diagram is s"own) ,"e p"ase

%oltage is at 00+ t"e magnitude of EAis 299 +

40


40/98




1 60 36.87 60 53.13S AjX I j= = and t"at

,wo unnown uantities are t"e magnitude of Vand t"e angle of EA.From t"e

p"asor diagram

( ) ( )2 2

2 sin cosA S A S AE V X I X I = + +

( )22

cos sin 236.8A S A S AV E X I X I V = =,"en

Sin!e t"e generator is B-!onne!ted+

3 410TV V V= =

41

Th & h


41/98




&)2) For t"e generator at t"e rated !urrent andt"e 1)0 PF+ t"e p"asor diagram is s"own)

,"en

( )22

cos sin 270.4A S A S AV E X I X I V = =

3 468.4TV V V= =and

&)3) For t"e generator at t"e rated !urrent and t"e

0)8 PF leading+ t"e p"asor diagram is s"own)

,"en

( )22

cos sin 308.8A S A S AV E X I X I V = =

3 535TV V V= =and

42

Th & h t


42/98




!) ,"e output power of t"e generator at 70 # and 0)8 PF lagging is

3 cos 3 236.8 60 0.8 34.1out AP V I !& = = =

,"e me!"ani!al input power is gi%en &

34.1 0 1.0 1.5 36.6in out e%ec %oss core %oss mec' %ossP P P P P !&= + + + = + + + =,"e effi!ien! is

34.1100 % 100% 93.2%

36.6

out

in

P

P = = =

d) ,"e input torue of t"e generator is

36.6291.2

125.7

inapp

m

PN m

= = = -

43

Th & h t


43/98




,"e indu!ed !ountertorue of t"e generator is

e) ,"e %oltage regulation of t"e generator is

34.1271.3

125.7

convapp

m

PN m

= = = -

Lagging PF480 410

100% 17.1%410

VR= =

nit PF

Lagging PF

480 468100% 2.6%

468

VR

= =

480 535100% 10.3%

535VR

= =

44

T i l h t i ti f


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Terinal characteristics of

s'nchronous "enerators

#ll generators are dri%en & a prime mo%er+ su!" as a steam+ gas+ water+ wind

tur&ines+ diesel engines+ et!) Regardless t"e power sour!e+ most of prime mo%ers

tend to slow down wit" in!reasing t"e load) ,"is de!rease in speed is usuall

nonlinear &ut go%ernor me!"anisms of some tpe ma &e in!luded to lineari>e t"is

dependen!e)

,"e speed drop .S(/ of a prime mo%er is defined as

100%n% f%

f%

n nS#

n

=

=ost prime mo%ers "a%e a speed drop from 2K to 4K) =ost go%ernors "a%e a

me!"anism to ad:ust t"e tur&ine5s no-load speed .set-point ad:ustment/)

.9)44)1/

4

T i l h t i ti f


45/98




# tpi!al speed

%s) power plot

Sin!e t"e s"aft speed is lined to t"e ele!tri!al freuen! as

120

me

n Pf = .9)4)1/

t"e power output from t"e generator is related to its freuen!

# tpi!al

freuen! %s)

power plot

( )p n% s(sP s f f= .9)4)2/

perating freuen! of t"e sstemSlope of !ur%e+ ?G@>

47

T i l h t i ti f


46/98




# similar relations"ip !an &e deri%ed for t"e rea!ti%e power and terminal %oltageVT) ?"en adding a lagging load to a sn!"ronous generator+ its terminal %oltage

de!reases) ?"en adding a leading load to a sn!"ronous generator+ its terminal

%oltage in!reases)

,"e plot of terminal %oltage %s)

rea!ti%e power is not ne!essarillinear)

ot" t"e freuen!-power and

terminal %oltage %s) rea!ti%e power

!"ara!teristi!s are important for

parallel operations of generators)

?"en a generator is operating alone suppling t"e load

1),"e real and rea!ti%e powers are t"e amounts demanded & t"e load)

2),"e go%ernor of t"e prime mo%er !ontrols t"e operating freuen! of t"e sstem)

3),"e field !urrent !ontrols t"e terminal %oltage of t"e power sstem)

49

T i l h t i ti f


47/98



s'nchronous "enerators: )#aple

E'ample 9)3 # generator wit" no-load freuen!of 71)0 @> and a slope s!of 1 =?G@> is

!onne!ted to Load 1 !onsuming 1 =? of real

power at 0)8 PF lagging) Load 2 .t"at is to &e

!onne!ted to t"e generator/ !onsumes a real

power of 0)8 =? at 0)909 PF lagging)

a) Find t"e operating freuen! of t"e sstem &efore t"e swit!" is !losed)

&) Find t"e operating freuen! of t"e sstem after t"e swit!" is !losed)

!) ?"at a!tion !ould an operator tae to restore t"e sstem freuen! to 70 @>

after &ot" loads are !onne!ted to t"e generatorJ

,"e power produ!ed & t"e generator is

( )p n% s(sP s f f=

,"erefores(s n%

p

Pf f

s=

48

T i l h t i ti f


48/98



s'nchronous "enerators: )#aple

a) ,"e freuen! of t"e sstem wit" one load is

161 60

1s(s n%

p

Pf f )*

s= = =

&) ,"e freuen! of t"e sstem wit" two loads is1.8

61 59.21

s(s n%

p

Pf f )*

s= = =

!) ,o restore t"e sstem to t"e proper operating freuen!+ t"e operator s"ould

in!rease t"e go%ernor no-load set point & 0)8 @>+ to 71)8 @>) ,"is will restoret"e sstem freuen! of 70 @>)

4e at a !ommon freuen!) ,"e freuen!ies of two

ma!"ines must &e %er !lose to ea!" ot"er &ut not e'a!tl eual) *f freuen!ies

differ & a small amount+ t"e p"ase angles of t"e on!oming generator will !"ange

slowl wit" respe!t to t"e p"ase angles of t"e running sstem)

*f t"e angles &etween t"e %oltages !an &e o&ser%ed+ it is possi&le to !lose t"e

swit!" S"w"en t"e ma!"ines are in p"ase)

2

General proce!ure for parallelin"


52/98



"enerators

?"en !onne!ting t"e generator %2to t"e running sstem+ t"e following stepss"ould &e taen

1)#d:ust t"e field !urrent of t"e on!oming generator to mae its terminal %oltage

eual to t"e line %oltage of t"e sstem .use a %oltmeter/)

2)$ompare t"e p"ase seuen!es of t"e on!oming generator and t"e running

sstem) ,"is !an &e done & different was1/ $onne!t a small indu!tion motor to t"e terminals of t"e on!oming generator

and t"en to t"e terminals of t"e running sstem) *f t"e motor rotates in t"e

same dire!tion+ t"e p"ase seuen!e is t"e same;

2/ $onne!t t"ree lig"t &ul&s a!ross t"e

open terminals of t"e swit!") #s t"e p"ase

!"anges &etween t"e two generators+ lig"t&ul&s get &rig"ter .large p"ase differen!e/

or dimmer .small p"ase differen!e/) *f all

t"ree &ul&s get &rig"t and dar toget"er+

&ot" generators "a%e t"e same p"ase

seuen!es)

3



53/98



"enerators

If phase sequences are different, two of the conductors on the oncominggenerator must be reversed.

3) ,"e freuen! of t"e on!oming generator is ad:usted to &e slig"tl "ig"er t"an

t"e sstem5s freuen!)

4) ,urn on t"e swit!" !onne!ting %2to t"e sstem w"en p"ase angles are eual)

,"e simplest wa to determine t"e moment w"en two generators are in p"ase is &o&ser%ing t"e same t"ree lig"t &ul&s) ?"en all t"ree lig"ts go out+ t"e %oltage

a!ross t"em is >ero and+ t"erefore+ ma!"ines are in p"ase)

# more a!!urate wa is to use a sn!"ros!ope a meter

measuring t"e differen!e in p"ase angles &etween two a

p"ases) @owe%er+ a sn!"ros!ope does not !"e! t"ep"ase seuen!e sin!e it onl measures t"e p"ase

differen!e in one p"ase)

,"e w"ole pro!ess is usuall automatedA

4

Operation of "enerators in parallel


54/98



with lar"e power s'stes

ften+ w"en a sn!"ronous generator is added to a power sstem+ t"at sstem is

so large t"at one additional generator does not !ause o&ser%a&le !"anges to t"e

sstem) # !on!ept of an infinite &us is used to !"ara!teri>e su!" power sstems)

#n infinite &usis a power sstem t"at is so large t"at its %oltage and freuen! do

not %ar regardless of "ow mu!" real and rea!ti%e power is drawn from or supplied

to it) ,"e power-freuen! and rea!ti%e power-%oltage !"ara!teristi!s are



55/98




$onsider adding a generator to an

infinite &us suppling a load)

,"e freuen! and terminal %oltage of all

ma!"ines must &e t"e same) ,"erefore+

t"eir power-freuen! and rea!ti%epower-%oltage !"ara!teristi!s !an &e

plotted wit" a !ommon %erti!al a'is)

Su!" plots are !alled sometimes as "ouse

diagrams)

7



56/98




*f t"e no-load freuen! of t"e on!oming

generator is slig"tl "ig"ert"an t"e

sstem5s freuen!+ t"e generator will &e

HfloatingI on t"e line suppling a small

amount of real power and little or no

rea!ti%e power)

*f t"e no-load freuen! of t"e on!oming

generator is slig"tl lowert"an t"e

sstem5s freuen!+ t"e generator will

suppl a negati%e power to t"e sstem t"egenerator a!tuall !onsumes energ

a!ting as a motorC

=an generators "a%e !ir!uitr

automati!all dis!onne!ting t"em from t"e

line w"en t"e start !onsuming energ)

9



57/98




*f t"e freuen! of t"e generator isin!reased after it is !onne!ted to t"e

infinite &us+ t"e sstem freuen!

!annot !"ange and t"e power supplied

& t"e generator in!reases)

Noti!e t"at w"en EAstas !onstant .field

!urrent and speed are t"e same/+ EAsin.w"i!" is proportional to t"e output power

if VTis !onstant/ in!reases)

*f t"e freuen! of t"e generator is furt"er in!reased+ power output from t"e

generator will &e in!reased and at some point it ma e'!eed t"e power !onsumed &

t"e load) ,"is e'tra power will &e !onsumed & t"e load)

8



58/98




#fter t"e real power of t"e generator is ad:usted to t"e desired %alue+ t"e generatorwill &e operating at a slig"tl leading PF a!ting as a !apa!itor t"at !onsumes rea!ti%e

power) #d:usting t"e field !urrent of t"e ma!"ine+ it is possi&le to mae it to suppl

rea!ti%e power to t"e sstem)

Summari>ing+ w"en t"e generator is operating in parallel to an infinite &us

1),"e freuen! and terminal %oltage of t"e generator are !ontrolled & t"e

sstem to w"i!" it is !onne!ted)

2),"e go%ernor set points of t"e generator !ontrol t"e real power supplied

& t"e generator to t"e sstem)

3),"e generator5s field !urrent !ontrols t"e rea!ti%e power supplied & t"egenerator to t"e sstem)

) 6enerator 2 "as a no-load freuen!

of 71)0 @> and a slope s!2of 1 =?G@>) ,"e two

generators are suppling a real load of 2) =?

at 0)8 PF lagging)

a) Find t"e sstem freuen! and power supplied & ea!" generator)

&) #ssuming t"at an additional 1 =? load is atta!"ed to t"e power sstem+ find t"e

new sstem freuen! and powers supplied & ea!" generator)

!) ?it" t"e additional load atta!"ed .total load of 3) =?/+ find t"e sstem

freuen! and t"e generator powers+ if t"e no-load freuen! of %2is in!reased& 0) @>)

,"e power produ!ed & a sn!"ronous generator wit" a gi%en slope and a no-load

freuen! is

( )p n% s(sP s f f=

73

Generators in parallel with other


63/98



"enerators of the sae si-e: )#

,"e total power supplied & t"e generators euals to t"e power !onsumed & t"eload

1 2%oadP P P= +

a) ,"e sstem freuen! !an &e found from

( ) ( )1 2 1 ,1 2 ,2%oad p n% s(s p n% s(sP P P s f f s f f= + = +

as 1 ,1 2 ,2

1 2

1 61.5 1 61.0 2.560.0

1 1

p n% p n% %oad

s(s

p p

s f s f Pf )*

s s

+ + = = =

+ +

( ) ( )

( ) ( )

1 1 ,1

2 2 ,2

1 61.5 60 1.5

1 61.0 60 1

p n% s(s

p n% s(s

P s f f ,&

P s f f ,&

= = =

= = =

,"e powers supplied & ea!" generator are

74



64/98



"enerators of the sae si-e: )#

&) For t"e new load of 3) =?+ t"e sstem freuen! is

1 ,1 2 ,2

1 2

1 61.5 1 61.0 3.559.5

1 1

p n% p n% %oad

s(s

p p

s f s f Pf )*

s s

+ + = = =

+ +

( ) ( )

( ) ( )

1 1 ,1

2 2 ,2

1 61.5 59.5 2.0

1 61.0 59.5 1.5

p n% s(s

p n% s(s

P s f f ,&

P s f f ,&

= = =

= = =,"e powers are

!) *f t"e no-load freuen! of 62in!reases+ t"e sstem freuen! is

1 ,1 2 ,2

1 2

1 61.5 1 61.5 3.5

59.751 1

p n% p n% %oad

s(sp p

s f s f P

f )*s s

+ +

= = =+ +

( ) ( )1 2 1 ,1 1 61.5 59.75 1.75p n% s(sP P s f f ,&= = = =

,"e powers are

7



65/98



"enerators of the sae si-e

?"en two generators of t"e same si>e are woring in parallel+ a !"ange infreuen! .go%ernor set points/ of one of t"em !"anges &ot" t"e sstem freuen!

and power supplied & ea!" generator)

,o ad:ust power s"aring wit"out !"anging

t"e sstem freuen!+ we need to in!rease

t"e freuen! .go%ernor set points/ of onegenerator and simultaneousl de!rease t"e

freuen! of t"e ot"er generator)

,o ad:ust t"e sstem freuen! wit"out!"anging power s"aring+ we need to

simultaneousl in!rease or de!rease t"e

freuen! .go%ernor set points/ of &ot"

generators)

77



66/98




Similarl+ to ad:ust t"e rea!ti%e power

s"aring wit"out !"anging t"e terminal

%oltage+ we need to in!rease

simultaneousl t"e field !urrent of one

generator and de!rease t"e field !urrent of

t"e ot"er generator)

,o ad:ust t"e terminal %oltage wit"out

!"anging t"e rea!ti%e power s"aring+ we

need to simultaneousl in!rease or

de!rease t"e field !urrents of &ot"

generators)

79



67/98




*t is important t"at &ot" generators &eing paralleled "a%e dropping

freuen!-power !"ara!teristi!s)

*f two generators "a%e flat or almostflat freuen!-power !"ara!teristi!s+

t"e power s"aring &etween t"em !an

%ar widel wit" onl finest !"anges in

no-load speed) For good of power

s"aring &etween generators+ t"e

s"ould "a%e speed drops of 2K to K)

78

& h t


68/98


&'nchronous otors

,"e field !urrent IFof t"e motor

produ!es a stead-state rotor

magneti! field BR) # 3-p"ase set of

%oltages applied to t"e stator produ!es

a 3-p"ase !urrent flow in t"e windings)

# 3-p"ase set of !urrents in an

armature winding produ!es a uniform

rotating magneti! field Bs.

,wo magneti! fields are present in t"e ma!"ine+ and t"e rotor field tends to alignwit" t"e stator magneti! field) Sin!e t"e stator magneti! field is rotating+ t"e rotor

magneti! field will tr to !at!" up pulling t"e rotor)

,"e larger t"e angle &etween two magneti! fields .up to a !ertain ma'imum/+ t"e

greater t"e torue on t"e rotor of t"e ma!"ine)

7ero) ,"e

motor will %i&rate "ea%il and finall o%er"eatsC

87

&tartin" s'nchronous otors


86/98


&tartin" s'nchronous otors

,"ree &asi! approa!"es !an &e used to safel start a sn!"ronous motor

1)Redu!e t"e speed of t"e stator magneti! field to a low enoug" %alue

t"at t"e rotor !an a!!elerate and two magneti! fields lo! in during one

"alf-!!le of field rotation) ,"is !an &e a!"ie%ed & redu!ing t"e freuen!

of t"e applied ele!tri! power .w"i!" used to &e diffi!ult &ut !an &e donenow/)

2)se an e'ternal prime mo%er to a!!elerate t"e sn!"ronous motor up to

sn!"ronous speed+ go t"roug" t"e paralleling pro!edure+ and &ring t"e

ma!"ine on t"e line as a generator) Ne't+ turning off t"e prime mo%er will

mae t"e sn!"ronous ma!"ine a motor)

3)se damper windings or amortisseur windings t"e most popular)

89

,otor startin" b' aortisseur or


87/98


" '

!aper win!in"s

#mortisseur .damper/ windings are spe!ial &arslaid into not!"es !ar%ed in t"e rotor fa!e and t"en

s"orted out on ea!" end & a large s"orting ring)

88

,otor startin" b' aortisseur or


88/98


" '

!aper win!in"s

# diagram of a salient 2-pole rotor wit" anamortisseur winding+ wit" t"e s"orting &ars on t"e

ends of t"e two rotor pole fa!es !onne!ted & wires

.not uite t"e design of a!tual ma!"ines/)

?e assume initiall t"at t"e

rotor windings aredis!onne!ted and onl a 3-

p"ase set of %oltages are

applied to t"e stator)

#s BSsweeps along in s !ounter-!lo!wise dire!tion+ it

indu!es a %oltage in &ars of t"e amortisseur winding

#t tD 0+ assume t"at BS

.stator field/ is %erti!al)

( )inde v B % = .9)88)1/

8ero+ t"e motor will speed up)

@owe%er+ t"e rotor will ne%er rea!" t"e sn!"ronous speedC *f a rotor was running

at t"e sn!"ronous speed+ t"e speed of stator magneti! field BSwould &e t"e same

as t"e speed of t"e rotor and+ t"erefore+ no relati%e motion &etween t"e rotor and

t"e stator magneti! field) *f t"ere is no relati%e motion+ no %oltage is indu!ed and+t"erefore+ t"e torue will &e >ero)

*nstead+ w"en t"e rotor5s speed is !lose to sn!"ronous+ t"e regular field !urrent

!an &e turned on and t"e motor will operate normall) *n real ma!"ines+ field !ir!uit

are s"orted during starting) ,"erefore+ if a ma!"ine "as damper winding

1)(is!onne!t t"e field windings from t"eir ($ power sour!e and s"ort t"em out;

2)#ppl a 3-p"ase %oltage to t"e stator and let t"e rotor to a!!elerate up to near-

sn!"ronous speed) ,"e motor s"ould "a%e no load on its s"aft to ena&le motor

speed to approa!" t"e sn!"ronous speed as !losel as possi

3)$onne!t t"e ($ field !ir!uit to its power sour!e t"e motor will lo! at

sn!"ronous speed and loads ma &e added to t"e s"aft)


92/98


"enerators an! otors

Sn!"ronous generator and sn!"ronousmotor are p"si!all t"e same ma!"inesC

# sn!"ronous ma!"ine !an suppl real

power to .generator/ or !onsume real

power .motor/ from a power sstem) *t

!an also eit"er !onsume or suppl

rea!ti%e power to t"e sstem)1) ,"e distinguis"ing !"ara!teristi! of a

sn!"ronous generator .suppling P/

is t"at EAlies a"ead of Vw"ile for a

motor EAlies &e"ind V)

2) ,"e distinguis"ing !"ara!teristi! of ama!"ine suppling rea!ti%e power is

t"at Ea'(s V.regardless w"et"er it

is a motor or generator/) ,"e ma!"ine

!onsuming rea!ti%e power "as

Ea'(s< V)


93/98


&'nchronous achine ratin"s

,"e speed and power t"at !an &e o&tained from a sn!"ronous motor or generatorare limited) ,"ese limited %alues are !alled ratingsof t"e ma!"ine) ,"e purpose of

ratings is to prote!t t"e ma!"ine from damage) ,pi!al ratings of sn!"ronous

ma!"ines are %oltage+ speed+ apparent power .#/+ power fa!tor+ field !urrent and

ser%i!e fa!tor)

1) oltage+ Speed+ and Freuen!,"e rated freuen! of a sn!"ronous ma!"ine depends on t"e power sstem to

w"i!" it is !onne!ted) ,"e !ommonl used freuen!ies are 0 @> .Europe+ #sia/+

70 @> .#meri!as/+ and 400 @> .spe!ial appli!ations air!raft+ spa!e!raft+ et!)/) n!e

t"e operation freuen! is determined+ onl one rotational speed in possi&le for t"e

gi%en num&er of poles120 e

m

fn

P= .9)


94/98



# generator5s %oltage depends on t"e flu'+ t"e rotational speed+ and t"eme!"ani!al !onstru!tion of t"e ma!"ine) For a gi%en design and speed+ t"e "ig"er

t"e desired %oltage+ t"e "ig"er t"e flu' s"ould &e) @owe%er+ t"e flu' is limited & t"e

field !urrent)

,"e rated %oltage is also limited & t"e windings insulation &readown limit+ w"i!"

s"ould not &e approa!"ed !losel)

*s it possi&le to operate a sn!"ronous ma!"ine at a freuen! ot"er t"an t"e

ma!"ine is rated forJ For instan!e+ !an a 70 @> generator operate at 0 @>J

,"e !"ange in freuen! would !"ange t"e speed) Sin!e EA= K+ t"e

ma'imum allowed armature %oltage !"anges w"en freuen! !"anges)Spe!ifi!all+ if a 70 @> generator will &e operating at 0 @>+ its operating

%oltage must &e deratedto 0G70 or 83)3 K)


95/98



2) #pparent power and Power fa!tor,wo fa!tors limiting t"e power of ele!tri! ma!"ines are

1/=e!"ani!al torue on its s"aft .usuall+ s"aft !an "andle mu!" more torue/

2/@eating of t"e ma!"ine5s winding

,"e pra!ti!al stead-state limits are set & "eating in t"e windings)

,"e ma'imum a!!epta&le armature !urrent sets t"e apparent power rating for a

generator

3 AS V I=

*f t"e rated %oltage is nown+ t"e ma'imum a!!epted armature !urrent determines

t"e apparent power rating of t"e generator

, ,max , ,max3 3rated A L rated LS V I V I = =

.9)


96/98



,"e stator !upper losses also do not depend on t"e !urrent angle2

3SCL A AP I R= .9)


97/98



*f t"e armature %oltage e'!eeds its ma'imum allowed %alue+ t"e windings !ould &edamaged) ,"e angle of IAt"at reuires ma'imum possi&le EAspe!ifies t"e rated

power fa!tor of t"e generator) *t is possi&le to operate t"e generator at a lower

.more lagging/ PF t"an t"e rated %alue+ &ut onl'& de!reasing t"e apparent power

supplied & t"e generator)

Sn!"ronous motors are usuall rated in terms of real output power and t"e lowestPF at full-load !onditions)

3) S"ort-time operation and ser%i!e fa!tor

# tpi!al sn!"ronous ma!"ine is often a&le to suppl up to 300K of its rated power

for a w"ile .until its windings &urn up/) ,"is a&ilit to suppl power a&o%e t"e rated

%alues is used to suppl momentar power surges during motor starts)*t is also possi&le to use sn!"ronous ma!"ine at powers e'!eeding t"e rated

%alues for longer periods of time+ as long as windings do not "a%e time to "it up too

mu!" &efore t"e e'!ess load is remo%ed) For instan!e+ a generator t"at !ould

suppl 1 =? indefinitel+ would &e a&le to suppl 1) =? for 1 minute wit"out

serious "arm and for longer periods at lower power le%els)


98/98


,"e ma'imum temperature rise t"at a ma!"ine !an stand depends on t"einsulation !lass of its windings) ,"e four standard insulation !lasses wit" t"e

temperature ratings are

# 700$ a&o%e t"e am&ient temperature

800$ a&o%e t"e am&ient temperature

F 100$ a&o%e t"e am&ient temperature

@ 120$ a&o%e t"e am&ient temperature,"e "ig"er t"e insulation !lass of a gi%en ma!"ine+ t"e greater t"e power t"at !an

&e drawn out of it wit"out o%er"eating its windings)

,"e o%er"eating is a serious pro&lem and sn!"ronous ma!"ines s"ould not &e

o%er"eated unless a&solutel ne!essar) @owe%er+ power reuirements of t"e

ma!"ine not alwas nown e'a!tl prior its installation) e!ause of t"is+ general-purpose ma!"ines usuall "a%e t"eir ser%i!e fa!tor defined as t"e ratio of t"e

a!tual ma'imum power of t"e ma!"ine to t"e rating on its plate)

For instan!e+ a ma!"ine wit" a ser%i!e fa!tor of 1)1 !an a!tuall &e operated at

11K of t"e rated load indefinitel wit"out "arm

Documents

1337683699.3104Lecture 07 - Synchronous Machines