syn mc phasor diagram-part 1

7/25/2019 Syn Mc Phasor Diagram-Part 1

1/67

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#


2/67

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


3/67

)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


4/67

%xis of Field

f

$ase 2& nity Power Factor 'oad

N -.1 .2

/1

/2 01

02


5/67

%xis of Field


-.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


6/67

%xis of Field


-.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


7/67

%xis of Field


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


8/67


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


9/67


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


10/67

$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


11/67

$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


12/67

$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


13/67


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


14/67


f

aFa

Ff

Ia

=90+

r

Er

Ef

r

Er= ir ga! "oltage

Er

900


15/67


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


16/67


Ia

Er

Ef

(Iaxl

Iara

Vt

(Ia*#*#+xl =*$(Ia*$

=90+


17/67


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


18/67


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


19/67


Ia

Ef

Vt

(Ia*

$

Ef=Vt+Iara+(Ia*$

If re$i$tance i$

neglected

Ef=Vt+(Ia*$

=90+

=390+ +4 5670for generator


20/67

nity Power Factor

Ia

Ef Vt

(Ia*$

Ef=Vt+Iara+(Ia*$

If re$i$tance i$

neglected

Ef=Vt+(Ia*$

=90+

=90+ +for generator


21/67

'eading Power Factor

Ia

Ef

Vt(Ia*$

Ef=Vt+Iara+(Ia*$

If re$i$tance i$

neglected

Ef=Vt+(Ia*$

=90+


22/67

$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


23/67


%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


24/67


%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


25/67

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


Ia

Vt

Iara

Ef

(Ia*$

=90+

=90+ -for #otor


26/67

Ia

Vt

Ef

(Ia*

$

If re$i$tance i$

neglected

Vt=Ef+(Ia*$


Vt=Ef+Iara+(Ia*$

Ia

Vt

Ef

(Ia*

$

a$or :iagra# at Lagging o/er Factor

=390+ ; 4 5670for #otor


27/67

nity Power Factor

Ia

EfVt

(Ia*$


If re$i$tance i$

neglected

Vt=Ef+(Ia*$

Vt=Ef+Iara+(Ia*$

=390+ ; 4 5670for #otor


28/67

'eading Power Factor

If re$i$tance i$

neglected

Vt=Ef+(Ia*$

Vt=Ef+Iara+(Ia*$


Ia

Ef

Vt

(Ia*$


29/67

-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#


30/67

%.M%T. MMF

; 6 %xis

%.M%T.

F';

= 6 %xis

%r! wdg along =6axis

%r! wdg along ;6axis

-alient Pole-ynchronous )enerator


31/67

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


- li P l - h )


32/67

$onsider ar! current Ialagging to Efby *++#


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


33/67

$onsider ar! current Ialeading to Efby *++#


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


34/67

$onsider ar! current Iais in phase with Ef.


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


61/67

+

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



62/67

+

p g


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



63/67

+

p g


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


64/67

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


65/67

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


66/67

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


67/67

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

syn mc phasor diagram-part 1

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