syn mc phasor diagram-part 1
TRANSCRIPT
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Flux and MMF PhasorsThe flux produced by field winding
1 1
2 2
3 3
4 4No of
conductors
MMF
MMF is sinusoidal
Flux is sinusoidal
Therefore, nduced
ar!ature "oltage is
sinusoidal#
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Flux and MMF Phasors$onsider cylindrical rotoralternator operation#
%lternator is rotated at syn speed by pri!e !o"er
Field wdg is excited
%r!ature "oltage is induced which is gi"en by
$ase 1& No 'oad (peration
Va0=Vt0=Ef=4.44 f TphfKw
Ef= No load voltage, Excitation voltage or Excitation emf.
Tph= Turns per phase of arm wdg.
f= Flux per pole produced by field winding
Kw= Winding Factor
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)enerated e!f lags the flux by *++#
%xis of Field
fFf
Ef
%lternator phasor diagra! at no load
900
f
Ef
No Load Voltage,
Excitation Voltage
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%xis of Field
f
$ase 2& nity Power Factor 'oad
N -.1 .2
/1
/2 01
02
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%xis of Field
$ase 2& nity Power Factor 'oad
-.1 .2
/1
/2 01
02
N
f
%xis of ar!ature
winding .1.2
N pole rotate anticlocwise
$onductor .1 !o"es clocwise#
N
-
!f is induced with dot polarity in .1 ..5
n .2 cross polarity
aFa
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%xis of Field
$ase 2& nity Power Factor 'oad
-.1 .2
/1
/2 01
02
N
f
%xis of ar!ature
winding .1.2
N pole rotate anticlocwise
$onductor .1 !o"es clocwise#
N
-
!f is induced with dot polarity in .1 ..5
n .2 cross polarity
ar%xis of Field
.esultant air gap flux
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%xis of Field
$ase 2& nity Power Factor 'oad
f
%xis of ar!ature
winding .1.2
ar%xis of Field
.esultant air gap flux
-pace6phasor diagra! of !!f and flux
Fa
Ff
Fr
Ef
Ia
Ti!e6phasor
diagra! of Ef
and Iaat upf
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$ase 2& nity Power Factor 'oad
f
ar
$o!bined -pace and Ti!e phasor diagra! at upf
Fa
Ff
Fr
Ef
Ia
-N
N
-
.epultion
%ttraction
Te
t is a .otorwhich
has to !o"e
clocwise
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$ase 2& nity Power Factor 'oad
f
ar
$o!bined -pace and Ti!e phasor diagra! at upf
Fa
Ff
Fr
Ef
Ia
-N
N
-
.epultion
%ttraction
Te
Teand are inopposite
direction
Field polesare leading
to ar! poles%r! reaction
!!f is cross6!agneti7ing at
upf#
lectro!agnetic
tor8ueTeis towardsresultant !!f or flux#
t is a .otorwhich
has to !o"e
clocwise
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$ase 3& 9ero Power Factor 'agging 'oad
f a
r
$o!bined -pace and Ti!e phasor diagra! at 7ero
pf lagging
FaFf Fr
Ef
Te
%r! reaction !!f
is de6!agneti7ing
at 7ero pf lagging#
Ia
Ff -Fa=Fr
f - a= r
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$ase 4& 9ero Power Factor 'eading 'oad
f
ar
$o!bined -pace and Ti!e phasor diagra! at 7ero
pf leading
Fa
FfFr
Ef
Te
%r! reaction !!f
is !agneti7ing at
7ero pf leading#
Ia
Ff +Fa=Fr
f + a= r
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$ase :& 'aggingPower Factor 'oad
f
a
r
$o!bined -pace and Ti!e Phasor ;iagra!
at 'agging Power Factor load
Fa
Ff
Fr
Ef
Te
'oad with lagging pf
is co!!onload
Ia
Ff +Fa=Fr
f + a= r
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$ase :& 'aggingPower Factor 'oad
f
aFa
Ff
Ia
f
=90+
a
Two !!fsare sinusoidaly distributed along
the air gap periphery#
The relati"e "elocity between the two !!fs
is 7ero#
r
r
;ue to unifor! air gap
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$ase :& 'aggingPower Factor 'oad
f
aFa
Ff
Ia
=90+
r
Er
Ef
r
Er= ir ga! "oltage
Er
900
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$ase :& 'aggingPower Factor 'oad
f
aFa
Ff
Ia
=90+
r
Er
Ef Fro# air ga! "oltage,$%&tract lea'agei#!edance dro!
(Iaxland Iara
(IaxlEr= ir ga! "oltage
IaraTer#inal "oltageor &%$ "oltage i$o&tainedVt
In air ga! "oltage, add)%t%al Ind%ctancedro!, (Ia*#
(Ia*#
No load "oltage Efi$ o&tained
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$ase :& 'aggingPower Factor 'oad
Ia
Er
Ef
(Iaxl
Iara
Vt
(Ia*#*#+xl =*$(Ia*$
=90+
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$ase :& 'aggingPower Factor 'oad
Ia
Ef
Iara
Vt
*#+xl =*$(Ia*$
T%$ "oltage e%ation ofcl. rotorgenerator i$
Ef=Vt+Iara+(Ia*$
Te angle &et/een Vt
and Iai$ , !o/er factor
angle
Te angle &et/een Vtand Efi$ , !o/er angle,
tor%e angle or loadan le
Te angle &et/een Ef andIai$ =+, internal
di$!lace#ent angle orinternal !o/er factorangle
For generator Ef lead$ Vt
=90+
=90+ +for generator
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$ase :& 'aggingPower Factor 'oad
Ia
Ef
Iara
Vt
(Ia*$
Ef=Vt+Iara+(Ia*$=90+
=90+ +for generator
Eflead$ to Vt
for 1enerator
saaatf XIjrIVE ++=
ct%al "aria&le$ are
!a$or$
22
2
2
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$ase :& 'aggingPower Factor 'oad
Ia
Ef
Vt
(Ia*
$
Ef=Vt+Iara+(Ia*$
If re$i$tance i$
neglected
Ef=Vt+(Ia*$
=90+
=390+ +4 5670for generator
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nity Power Factor
Ia
Ef Vt
(Ia*$
Ef=Vt+Iara+(Ia*$
If re$i$tance i$
neglected
Ef=Vt+(Ia*$
=90+
=90+ +for generator
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'eading Power Factor
Ia
Ef
Vt(Ia*$
Ef=Vt+Iara+(Ia*$
If re$i$tance i$
neglected
Ef=Vt+(Ia*$
=90+
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$ylindrical .otor -ynchronous Motor
%xis of Field
-.1 .2
/1
/2 01
02
Nf
%xis of ar!ature
winding .1.2
For !otor ar! current is
opposite wrt generator
-
N
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$ylindrical .otor -ynchronous Motor
%xis of Field
-Nf
%xis of ar!ature
winding .1.2
-
N
Ia
-Iar
.epultion
%ttraction
t is a .otorwhich
has to !o"e
anticlocwise
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$ylindrical .otor -ynchronous Motor
%xis of Field
-Nf
%xis of ar!ature
winding .1.2
-
N
Ia
-Iar
.epultion
%ttraction
Te
This is a !otoroperation
Field poles are;.%));behind
the resultant air gap
flux or by ar! poles#
Teand are insamedirection
lectro!agnetic
tor8ueTeis towardsresultant !!f or flux#
t is a .otorwhich
has to !o"e
anticlocwise
Teis fro! N offieldpole to -
of ar!pole
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T%$ "oltage e%ation ofcl. rotor#otor i$
Vt=Ef+Iara+(Ia*$
Te angle &et/een Vt
and Iai$ , !o/er factor
angleTe angle &et/een Vtand Efi$ , !o/er angle,
tor%e angle or loadan le
Te angle &et/een Ef andIai$ =-, internal
di$!lace#ent angle orinternal !o/er factorangle
For #otor Vt
lead$ to Ef
$ylindrical .otor -ynchronous Motor
Ia
Vt
Iara
Ef
(Ia*$
=90+
=90+ -for #otor
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Ia
Vt
Ef
(Ia*
$
If re$i$tance i$
neglected
Vt=Ef+(Ia*$
$ylindrical .otor -ynchronous Motor
Vt=Ef+Iara+(Ia*$
Ia
Vt
Ef
(Ia*
$
a$or :iagra# at Lagging o/er Factor
=390+ ; 4 5670for #otor
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nity Power Factor
Ia
EfVt
(Ia*$
$ylindrical .otor -ynchronous Motor
If re$i$tance i$
neglected
Vt=Ef+(Ia*$
Vt=Ef+Iara+(Ia*$
=390+ ; 4 5670for #otor
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'eading Power Factor
If re$i$tance i$
neglected
Vt=Ef+(Ia*$
Vt=Ef+Iara+(Ia*$
$ylindrical .otor -ynchronous Motor
Ia
Ef
Vt
(Ia*$
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-alient Pole-ynchronous )eneratorn cyl rotor, air gap is unifor!#
The ar! flux is independent of spatial orientation
wrt field poles#
n salient pole, air gap is not unifor!#
The reluctancealong d axis is !uch s!allerthan
8 axis#
The ar! flux is greateralong d axis than along 8
axis#
.esol"e ar! !!f along d axis and along 8 axis#
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%.M%T. MMF
; 6 %xis
%.M%T.
F';
= 6 %xis
%r! wdg along =6axis
%r! wdg along ;6axis
-alient Pole-ynchronous )enerator
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n cyl rotor, air gap is unifor!#
The ar! flux is independent of spatial orientation
wrt field poles#
n salient pole, air gap is not unifor!#
The reluctancealong d axis is !uch s!allerthan
8 axis#
The ar! flux is greateralong d axis than along 8
axis#
.esol"e ar! !!f along d axis and along 8 axis#
-o two !!falong d axis and one !!falong 8
axis
-alient Pole-ynchronous )enerator
- li P l - h )
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$onsider ar! current Ialagging to Efby *++#
-alient Pole-ynchronous )enerator
f
a
r
$o!bined -pace and
Ti!e phasor diagra!
Fa
Ff Fr
Ef
Te
Ia
Ff -Fa=Fr
f - a= r
: :ing action
?e$%ltant fl%x decrea$e$.
r
- li t P l - h ) t
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$onsider ar! current Ialeading to Efby *++#
-alient Pole-ynchronous )enerator
f
ar
$o!bined -pace and
Ti!e phasor diagra!
Fa
Ff
Fr
Ef
TeIa
Ff +Fa=Fr
f + a= r
: :ing action
?e$%ltant fl%x increa$e$.
r
- li t P l - h ) t
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$onsider ar! current Iais in phase with Ef.
-alient Pole-ynchronous )enerator
f
a
$o!bined -pace and
Ti!e phasor diagra!
Fa
Ff
Ef
Te
Ia
Ff +Fa=Fr
f +a= r
: : Bf Phasor diagra! is correct#
4A3...43 q**qaaatf XXIXjIrIVE =
e
Ef=Ef !1 b
Now consider the phasor diagra! of salient
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+
p g
pole syn M(T(. at leadingpower factor#
Vt
Iara
Ia
(Id*d(I*
Id
I
Ef
First draw a perpendicular line
fro! base of Iara for )BTB?.
EfG
o
a&
cd
bc is perpendicular to Ia, so
!ust be reacti"e drop Ia*
(Ia*and extend Ia line
Fro! base of Iara,draw
perpendicular line on od
eaG
$onsider A bce and oac
cb =+
b=bc cos(+)bc=IaX3 =IaX cos(+)
=IqXIqXq
=X2222()Xq
Now consider the phasor diagra! of salient
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+
p g
pole syn M(T(. at leadingpower factor#
Vt
Iara
Ia
(Id*d(I*
Id
I
Ef
EfG
o
a&
cd
(Ia*
eaG
Ef!= Vt1 Iara1 jIaXq
="#a$%
Th&s 's cac&at*
Th ca aso b cac&at* fro, -oac
=
oa
ac
HH aaoa
bcab
+
4I.3..........aat
qat
rIcosV
XIs'+V
+=
( ) =+ta
Now consider the phasor diagra! of salient
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+
p g
pole syn M(T(. at leadingpower factor#
Vt
Iara
Ia
(Id*d(I*
Id
I
Ef
EfG
o
a&
cd
(Ia*
eaG
Now obtainEf 1 Ef!=c* c)*)
4+= s'+(XIXI qa**
q*** XIXI =
43 q** XXI = ?Positi"e
EfEf> Phasor diagra! is correct#
4A3...43 q**qaaatf XXIXjIrIVE +=Ef=Ef !+c*
xa!ple
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p
% salient pole synchronous generator has the
following per unit para!eters&X*=.3 Xq=0.53 ra=0.06
$o!pute the excitation "oltage Efon a per unit basis,
when the generator is deli"ering rated
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The "oltage e8uation for salient pole syn
generator is&
Ef
IaraVt
Ia
(Id*d
(I*
Id
I
Ef=Vt +Iara +(Id*d +(I* Efi$ al/a$along axi$
3a4 Kit Vta$ a reference !a$or,
Vt=6.00+(0.00Vt=?ated "oltage
For rated 'V, Ia= ?ated "al%e
Ia=6.00 178.9 For 0.7 !f lagging=0.7 - (0.
Fir$t calc%late EfG=Vt +Iara +(Ia*
Iara=30.7 - (0.430.M4
=30.0 - (0.06M4
-olution
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Ef
IaraVt
Ia
(Id*d
(I*
Id
I
EfG=Vt +Iara +(Ia*
(Ia*=
= 30.7 +(0.4
(30.7 - (0.430.74
=36.00+(0.004+30.0 - (0.06M4+
30.7 +(0.4
= 6. M +(0.M
= 6. M .8
=.0 and +=.+A.9=M9.M
Id = Ias'3+4 = 6.00s'3M9.M4
=0.7
I = Iacos3+4 =0.M0O
Ef= EfG +Id3*d-*4
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f f d d
3&4 a$or diagra# for leading !f
.8= 6.997
Ef
IaraVtIa
(Id*d
(I*
Id
I
=+A.9Ia=0.7 + (0. Iara=0.0 + (0.06M
(Ia*,
(Ia*=-0.7+ (0.
EfG
EfG=Vt +Iara +(Ia*=0.M9+(0.MM=0.79 60.60
0
60.600=
-=6A.Id=0.AM
Ef= EfG+Id3*d-*4
= 0 9A 60 600