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MEE 20 / PRINCIPLE OF ELECTRICAL MACHINES / FEBRUARY 2008 SUL 1 1 To Be A World Class Maritime Academy To Be A World Class Maritime Academy Principle of Electrical Machines Energy and Power Systems
72

Principle of Electrical Machine

Apr 10, 2015

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Page 1: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 11

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Prin

cipl

e of

Ele

ctri

cal M

achi

nes

Ene

rgy

and

Pow

er S

yste

ms

Page 2: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 22

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

�B

uild

stro

ng fo

unda

tion

in th

e ba

sic

prin

cipl

es

of m

agne

tic c

ircu

its a

nd e

lect

rom

agne

tic

ener

gy c

onve

rsio

n.

Intro

duct

ion

At t

he c

ompl

etio

n of

this

cha

pter

, you

sho

uld

be a

ble

to

�A

cqui

re a

nd a

pply

fund

amen

tal p

rinc

iple

s of

scie

nce

and

engi

neer

ing.

�Id

entif

y, fo

rmul

ate

and

mod

el p

robl

ems a

nd fi

nd

engi

neer

ing

solu

tions

bas

ed o

n a

syst

ems a

ppro

ach.

�W

ork

inde

pend

ently

as w

ell a

s with

oth

ers i

n a

team

.�

Com

mun

icat

e ef

fect

ivel

y.

Page 3: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 33

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Spec

ific

Topi

cs�

Pow

er g

ener

atio

n-Tr

ansf

orm

atio

n an

d D

istri

butio

n�

Pow

er sy

stem

on

land

and

ship

Intro

duct

ion

to m

achi

ne p

rinci

ple

�Pr

inci

ple

of e

lect

rom

agne

tic e

nerg

y co

nver

sion

�D

efin

ition

of m

agne

tic q

uant

ities

�In

duct

ion

�Lo

sses

�3

phas

e ci

rcui

t�

Act

ive

and

reac

tive

pow

er

Page 4: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 44

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Pow

er g

ener

atio

n-Tr

ansf

orm

atio

n an

d D

istri

butio

n�

1. M

echa

nica

l ene

rgy

(mov

emen

t)�

2.R

otat

iona

l ene

rgy

(mov

emen

t abo

ut a

n ax

is-c

ircul

ar)

�3.

Elec

trica

l ene

rgy

(ele

ctro

n flo

w)

�4.

Wor

k (a

pplic

atio

n of

forc

e th

roug

h a

dist

ance

)�

5.Po

wer

(rat

e of

doi

ng w

ork)

�6.

Effic

ienc

y (o

utpu

t / in

put )

Page 5: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 55

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Uni

t Con

vers

ions

& D

imen

sion

al A

naly

sis

*Po

wer

(Wat

ts)

*

A

ltern

ativ

e un

its th

at m

ay b

e us

edhp

(hor

sepo

wer

)=74

5.7

W*

Ele

ctri

c Po

tent

ial(V

olts

)*

Cur

rent

(Am

pere

s), A

*R

esis

tanc

e(O

hms)

*SI

uni

ts(V

olts

, Am

pere

s, O

hms,

Wat

ts)

*E

nglis

h un

its(in

ches

, fee

t, po

unds

etc

.).

Page 6: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 66

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Intro

duct

ion

to M

achi

nery

Prin

cipl

esA

n el

ectr

ic m

achi

ne:

is a

dev

ice

that

can

con

vert

eith

er m

echa

nica

l ene

rgy

to

elec

tric

ene

rgy

or v

ice

vers

a.

A g

ener

ator

:co

nver

ts m

echa

nica

l ene

rgy

to e

lect

rica

l ene

rgy.

A m

otor

:co

nver

ts e

lect

rica

l ene

rgy

to m

echa

nica

l ene

rgy.

Alm

ost

all p

ract

ical

mot

ors

and

gene

rato

rs c

onve

rt e

nerg

y fr

om

one

form

to a

noth

er th

roug

h th

e ac

tion

of a

mag

netic

fiel

d.

Ano

ther

clo

sely

rel

ated

dev

ice

is th

e tr

ansf

orm

er.

Page 7: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 77

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

A tr

ansf

orm

er:

is a

dev

ice

that

con

vert

s ac

ele

ctri

cal

ener

gy a

t on

e vo

ltage

leve

l to

ac e

lect

rica

l ene

rgy

at a

noth

er v

olta

ge le

vel,

but

with

the

sam

e fr

eque

ncy.

In g

ener

al,

tran

sfor

mer

s op

erat

e on

the

sam

e pr

inci

ples

as

gene

rato

rs a

nd m

otor

s, a

nd a

re u

sual

ly s

tudi

ed t

oget

her

with

ge

nera

tors

and

mot

ors.

The

se 3

type

s of d

evic

es a

re in

evita

ble

in m

oder

n da

ily li

fe.

*Mot

ors f

ind

appl

icat

ions

in se

vera

l hom

e ap

plia

nces

.*I

n th

e w

ork

plac

e, m

otor

s pro

vide

the

mot

ive

pow

er fo

r

alm

ost a

ll to

ols.

*Gen

erat

ors a

re e

ssen

tial t

o su

pply

the

pow

er u

sed

by a

ll th

ese

mot

ors.

Intr

oduc

tion

to M

achi

nery

Prin

cipl

es .

. . .

.

Page 8: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 88

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Mec

hani

cal E

nerg

y

Elec

trica

l Ene

rgy

Mot

orG

ener

ator

Tra

nsfo

rmer

Intr

oduc

tion

to M

achi

nery

Prin

cipl

es .

. . .

.

Elec

trica

l Ene

rgy

Page 9: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 99

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

INTR

OD

UC

TIO

N

The

elec

trom

agne

tic s

yste

m is

a n

eces

sary

ele

men

t of a

ll ro

tatin

g an

d st

atic

ele

ctric

mac

hine

ry a

nd e

lect

rom

echa

nica

l dev

ices

.

The

role

of

elec

trom

agne

tic s

yste

m i

s to

est

ablis

h an

d co

ntro

l el

ectro

mag

netic

fiel

ds fo

r car

ryin

g ou

t con

vers

ion

of e

nerg

y, a

nd

trans

fer.

Prac

tical

ly a

ll m

otor

s an

d ge

nera

tors

, dep

end

upon

the

mag

netic

fie

ld a

s th

e co

uplin

g m

ediu

m a

llow

ing

inte

rcha

nge

of e

nerg

y in

ei

ther

dire

ctio

n be

twee

n el

ectri

cal a

nd m

echa

nica

l sys

tem

s.

A

trans

form

er

thou

gh

not

an

elec

trom

echa

nica

l co

nver

sion

de

vice

, pr

ovid

es

a m

eans

of

tra

nsfe

rrin

g el

ectri

cal

ener

gy

betw

een

two

elec

trica

l por

ts v

ia th

e m

ediu

m o

f a m

agne

tic fi

eld.

Page 10: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1010

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

It is

, th

eref

ore,

se

en

that

al

l el

ectri

c m

achi

nes

incl

udin

g tra

nsfo

rmer

s us

e th

e m

ediu

m

of

mag

netic

fie

ld

for

ener

gy

conv

ersi

on a

nd tr

ansf

er.

INTR

OD

UC

TIO

N .

. . .

.

τ,ω

Blo

ck d

iagr

am r

epre

sent

atio

n of

ele

ctro

mec

hani

cal e

nerg

y co

nver

sion

e, I

Ele

ctri

cal

Syst

emC

oupl

ing

Syst

emM

echa

nica

lSy

stem

Page 11: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1111

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRIN

CIP

LE O

F EL

ECTR

O-M

ECH

AN

ICA

L EN

ERG

Y C

ON

VER

SIO

N

The

elec

trom

agne

tic s

yste

m is

a n

eces

sary

ele

men

t of a

ll ro

tatin

g an

d st

atic

ele

ctric

mac

hine

ry a

nd e

lect

rom

echa

nica

l dev

ices

.

The

role

of

elec

trom

agne

tic s

yste

m i

s to

est

ablis

h an

d co

ntro

l el

ectro

mag

netic

fie

lds

for

carr

ying

out

con

vers

ion

of e

nerg

y, i

ts

proc

essi

ng a

nd tr

ansf

er.

It is

, th

eref

ore,

se

en

that

al

l el

ectri

c m

achi

nes

incl

udin

g tra

nsfo

rmer

s us

e th

e m

ediu

m

of

mag

netic

fie

ld

for

ener

gy

conv

ersi

on a

nd tr

ansf

er.

Sinc

e el

ectro

mec

hani

cal e

nerg

y co

nver

sion

invo

lves

the

inte

rcha

nge

of

ener

gy b

etw

een

an e

lect

rical

and

a m

echa

nica

l sy

stem

, th

e pr

imar

y qu

antit

ies

invo

lved

in

the

mec

hani

cal

syst

em a

re t

orqu

e an

d sp

eed,

w

hile

the

anal

ogou

s qu

antit

ies

in th

e el

ectri

cal s

yste

m a

re c

urre

nt a

nd

volta

ge re

spec

tivel

y.

Page 12: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1212

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRIN

CIP

LE O

F EL

ECTR

O-M

ECH

AN

ICA

L EN

ERG

Y C

ON

VER

SIO

N .

. .

τ,ω

Blo

ck d

iagr

am r

epre

sent

atio

n of

ele

ctro

mec

hani

cal e

nerg

y co

nver

sion

e, I

Ele

ctri

cal

Syst

emC

oupl

ing

Syst

emM

echa

nica

lSy

stem

Page 13: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1313

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRIN

CIP

LE O

F EL

ECTR

O-M

ECH

AN

ICA

L EN

ERG

Y C

ON

VER

SIO

N .

. .

Mot

or a

ctio

n re

sults

whe

n th

e el

ectri

cal s

yste

m c

ause

s a

curr

enti

to fl

ow th

roug

h co

nduc

tors

that

are

pla

ced

in a

mag

netic

fiel

d.

A m

agne

tic f

orce

is

prod

uced

on

each

con

duct

or s

o th

at i

f th

e co

nduc

tors

are

loc

ated

on

a st

ruct

ure

that

is

free

to

rota

te,

anel

ectro

mag

netic

torq

ue T

resu

lts.

Mor

eove

r, w

ith

the

deve

lopm

ent

of

this

m

otor

ac

tion

the

revo

lvin

g co

nduc

tors

cut

thro

ugh

the

mag

netic

fie

ld a

nd t

here

by

unde

rgo

an e

.m.f.

ew

hich

is re

ally

a re

actio

n vo

ltage

ana

logo

us to

th

e in

duce

d e.

m.f

in th

e pr

imar

y w

indi

ng o

f a tr

ansf

orm

er.

Page 14: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1414

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

DEF

INIT

ION

OF

MAG

NET

IC Q

UA

NTI

TIES

Mag

net:

It is

a s

ubst

ance

hav

ing

the

prop

ertie

s of

attr

actin

g iro

n an

d its

allo

ys.

Mag

netic

fiel

d:

It is

def

ined

as

the

regi

on o

f sp

ace

arou

nd a

mag

net

in

whi

ch

ther

e ex

ists

a

mag

netic

fo

rce

(eith

er

forc

e of

at

tract

ion

or fo

rce

of re

puls

ion)

. M

agne

tic li

nes

of fo

rce:

Thes

e ar

e th

e im

agin

ary

lines

of

forc

e in

a m

agne

tic f

ield

w

hich

st

art

from

th

e N

orth

po

le,

pass

th

roug

h ai

r or

m

agne

tic m

ediu

m, a

nd e

nd a

t Sou

th p

ole.

Page 15: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1515

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Mag

netic

circ

uit:

DEF

INIT

ION

OF

MAG

NET

IC Q

UA

NTI

TIES

. . .

. .

It is

a c

ontin

uous

pat

h oc

cupi

ed b

y m

agne

tic li

nes o

f for

ce.

Mag

netic

flux

: It

is th

e nu

mbe

r of l

ines

of m

agne

tic fo

rce

cros

sing

the

spac

e oc

cupi

ed b

y a

mag

netic

fiel

d(φ)

.M

agne

to-m

otiv

e-fo

rce

(m.m

.f):

It dr

ives

or

tries

to

driv

e m

agne

tic f

lux

to f

low

thr

ough

m

agne

tic c

ircui

t and

is th

e an

alog

y to

e.m

.f. in

ele

ctric

circ

uit.

It is

equ

al to

the

effe

ctiv

e cu

rren

t flo

w a

pplie

d to

the

core

(Ni).

Its

unit

is A

mpe

re-tu

rn.

Page 16: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1616

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

DEF

INIT

ION

OF

MAG

NET

IC Q

UA

NTI

TIES

. . .

. .

Am

pere

-turn

(AT)

:It

is th

e un

it fo

r m

mf

and

is g

iven

by

the

prod

uct o

f nu

mbe

r of

tur

ns o

f m

agne

tic c

ircui

t an

d th

e cu

rren

t flo

win

g in

the

tu

rns (

Ni )

. R

eluc

tanc

e (S

or ℜ

) :Th

is is

the

term

giv

en to

the

mat

eria

l cha

ract

eris

tics

that

resi

st

the

gene

ratio

n of

mag

netic

flux

insi

de it

. It

is t

he o

ppos

ition

off

ered

by

a m

agne

tic p

ath

to t

he

esta

blis

hmen

t of

a m

agne

tic f

lux

and

is t

he a

nalo

gy t

o re

sist

ance

in e

lect

ric c

ircui

t. (A

T/W

b)

Rel

ucta

nce,

S =

Al µA

lAl

=

ρ

ρ1

Res

ista

nce

R =

()

0A

lAl

rµµ

µ×

==

Page 17: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1717

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

DEF

INIT

ION

OF

MAG

NET

IC Q

UA

NTI

TIES

. . .

. .

Perm

eanc

e:

Perm

eanc

eis

reci

proc

al to

relu

ctan

ce. I

t is

also

the

anal

ogy

to

cond

ucta

nce

in e

lect

ric c

ircui

t.

Res

idua

l mag

netis

m:

It is

the

mag

netis

m w

hich

rem

ains

in

a m

ater

ial

even

the

ef

fect

ive

mag

netiz

ing

forc

e ha

s bee

n re

duce

d to

zer

o.

Page 18: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1818

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

MAG

NET

IC F

IELD

The

mag

netic

fie

ld in

a m

achi

ne f

orm

s th

e en

ergy

link

bet

wee

n th

e el

ectri

cal a

nd m

echa

nica

l sys

tem

s.

It is

pro

duce

d by

cur

rent

s flo

win

g in

coi

ls o

f w

ire i

nsid

e th

e m

achi

ne, o

r by

a co

mbi

natio

n of

coi

ls a

nd p

erm

anen

t mag

nets

.

It is

def

ined

as

the

regi

on o

f sp

ace

arou

nd a

mag

net

in w

hich

th

ere

exis

ts a

mag

netic

forc

e (e

ither

forc

e of

attr

actio

n or

forc

e of

re

puls

ion)

.

1.A

cu

rren

t-car

ryin

g w

ire

(con

duct

or)

prod

uces

a

mag

netic

fiel

d in

the

area

aro

und

it.

Page 19: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 1919

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

3.A

cur

rent

-car

ryin

g w

ire in

the

pres

ence

of a

mag

netic

fie

ld h

as a

forc

e in

duce

d on

it. T

his i

s the

ba

sis

of

mot

or a

ctio

n.

4.A

mov

ing

wire

in th

e pr

esen

ce o

f a m

agne

tic fi

eld

has

a vo

ltage

indu

ced

in it

. Thi

s is t

he b

asis

of t

he g

ener

ator

ac

tion.

2.A

tim

e-ch

angi

ng m

agne

tic f

ield

ind

uces

a v

olta

ge i

n a

coil

of w

ire i

f it

pass

es t

hrou

gh t

hat

coil.

Thi

s is

the

ba

sis o

f tra

nsfo

rmer

act

ion.

MAG

NET

IC F

IELD

. . .

.

Page 20: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2020

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRO

DU

CTI

ON

OF

MA

GN

ETIC

FIE

LD

Figu

re

show

s a

rect

angu

lar

core

with

a

win

ding

of

N t

urns

of

wire

w

rapp

ed

arou

nd

one

leg

of th

e co

re.

If t

he c

ore

is c

ompo

sed

of i

ron

or c

erta

in o

ther

sim

ilar

met

als,

esse

ntia

lly a

ll th

e m

agne

tic f

ield

pro

duce

d by

the

cur

rent

will

rem

ain

insi

de th

e co

re

Page 21: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2121

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Acc

ordi

ng t

o A

mpe

re�s

Law

for

the

pro

duct

ion

of a

mag

netic

fie

ld b

y a

curr

ent:

∫=

•ne

tI

dIH

Whe

re H

is

the

mag

netic

fiel

d in

tens

ity p

rodu

ced

by th

e cu

rren

t I ne

t.

PRO

DU

CTI

ON

OF

MA

GN

ETIC

FIE

LD .

. . .

So t

he p

ath

of i

nteg

ratio

n in

Am

pere

�s l

aw i

s th

e m

ean

path

le

ngth

of t

he c

ore

l c.

The

curr

ent p

assi

ng w

ithin

the

path

of

inte

grat

ion

I net

is th

en N

i, si

nce

the

coil

of w

ire c

uts

the

path

of

inte

grat

ion

N ti

mes

whi

le

carr

ying

cur

rent

i.

Page 22: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2222

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRO

DU

CTI

ON

OF

MA

GN

ETIC

FIE

LD .

. . .

Am

pere

�s la

w th

us b

ecom

es

Ther

efor

e, t

he m

agni

tude

of

the

mag

netic

fie

ld i

nten

sity

in

the

core

due

to th

e ap

plie

d cu

rren

t is

clNi

H=

The

stre

ngth

of

the

mag

netic

fie

ld f

lux

prod

uced

in th

e co

re(H

) al

so d

epen

ds o

n th

e m

ater

ial o

f the

cor

e.

HB

µ=Th

e re

latio

nshi

p be

twee

n th

e m

agne

tic fi

eld

inte

nsity

(H) a

nd th

e re

sulti

ng m

agne

tic f

lux

dens

ity B

pro

duce

d w

ithin

a m

ater

ial

is

give

n by

µ=

mag

netic

per

mea

bilit

yof

mat

eria

lB

= re

sulti

ng m

agne

tic fl

ux d

ensi

ty p

rodu

ced.

iN

lH

rµµ

µ×

=0

Page 23: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2323

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

PRO

DU

CTI

ON

OF

MA

GN

ETIC

FIE

LD .

. . .

The

perm

eabi

lity

of fr

ee sp

ace

is c

alle

d µ

0, an

d is

giv

en b

y

H/m

10

47

0−

×=

πµ

Rel

ativ

e pe

rmea

bilit

y (µ

r)is

a c

onve

nien

t w

ay t

o co

mpa

re t

he

perm

eabi

lity

of m

ater

ials

.

The

mag

nitu

de o

f the

flux

den

sity

is g

iven

by

clNi

HB

µµ

==

The

equa

tion

for t

otal

flux

isBA

Thus

, the

tota

l flu

x in

the

core

due

to th

e cu

rren

t iin

the

win

ding

is

whe

re A

is th

e cr

oss-

sect

iona

l are

a of

the

core

.clNiA

BAµ

φ=

=

Page 24: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2424

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

MA

GN

ET

IC C

IRC

UIT

S

It is

a c

ontin

uous

pat

h oc

cupi

ed b

y m

agne

tic li

nes o

f for

ce.

Mag

netic

circ

uit

is a

nalo

gous

to a

n el

ectri

c ci

rcui

t.

In a

sim

ple

elec

tric

circ

uit,

the

volta

ge s

ourc

e V

driv

es a

cur

rent

I

acro

ss a

resi

stan

ce R

. In

the

ele

ctric

circ

uit,

it is

the

vol

tage

or

elec

trom

otiv

e fo

rce

that

dr

ives

the

curr

ent f

low

.

Page 25: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2525

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

By

anal

ogy,

the

corr

espo

ndin

g qu

antit

y in

the

mag

netic

circ

uit i

s ca

lled

the

mag

neto

mot

ive

forc

e (m

mf).

MA

GN

ET

IC C

IRC

UIT

S . .

. . .

The

pola

rity

of th

e m

mff

rom

a c

oil o

f wire

can

be

dete

rmin

ed a

s fo

llow

s:

If

the

finge

rs

of

the

right

han

d cu

rl in

the

di

rect

ion

of t

he c

urre

nt

flow

in

a co

il of

wire

, th

en t

hum

b w

ill p

oint

in

the

dire

ctio

n of

the

po

sitiv

e m

mf.

Page 26: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2626

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

mm

fof t

he m

agne

tic c

ircui

t is

equa

l to

the

effe

ctiv

e cu

rren

t flo

w a

pplie

d to

the

core

, or

MA

GN

ET

IC C

IRC

UIT

S . .

. . .

F= φ

Whe

re F

= m

agne

tom

otiv

efo

rce

of th

e ci

rcui

tφ=

flux

of t

he c

ircui

tℜ

= re

luct

ance

of t

he c

ircui

t

We

see

that

the

relu

ctan

ce o

f the

cor

e is

Al c µ=

Rel

ucta

nces

in

a

mag

netic

ci

rcui

t ob

ey

the

sam

e ru

les

as

resi

stan

ces i

n an

ele

ctric

circ

uit.

Page 27: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2727

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

...5

43

21

+ℜ

+ℜ

+ℜ

+ℜ

+ℜ

=ℜ

eq

MA

GN

ET

IC C

IRC

UIT

S . .

. . .

The

equi

vale

nt re

luct

ance

of a

num

ber o

f rel

ucta

nces

in

serie

s is

ju

st th

e su

m o

f the

indi

vidu

al re

luct

ance

s:

Sim

ilarly

, re

luct

ance

s in

pa

ralle

l co

mbi

ne

acco

rdin

g to

th

e eq

uatio

n

...1

11

11

1

54

32

1ℜ

+ℜ

+ℜ

+ℜ

+ℜ

=ℜ

eq

Page 28: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2828

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

LE

AK

AG

EFL

UX

In a

ll pr

actic

al m

agne

tic c

ircui

ts, m

ost o

f th

e flu

x is

con

fined

to

the

inte

nded

pat

h by

use

of m

agne

tic c

ores

but

a s

mal

l am

ount

of

flux

alw

ays l

eaks

thro

ugh

the

surr

ound

ing

air.

This

stra

y flu

x is

cal

led

the

leak

age

flux.

i P(t

)

v P(t

)+ -

+ -

v S(t

)~

Lea

kag

e fl

ux,

φL

PM

utu

al f

lux,

φM

Lea

kag

e fl

ux,

φL

S

Page 29: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 2929

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Leak

age

is c

hara

cter

istic

of a

ll m

agne

tic c

ircui

ts a

nd c

an n

ever

be

fully

elim

inat

ed.

Cal

cula

tions

con

cern

ing

the

mai

n m

agne

tic c

ircui

t ar

e us

ually

ca

rrie

d ou

t w

ith t

he e

ffec

t of

lea

kage

flu

x ei

ther

ign

ored

or

empi

rical

ly a

ccou

nted

for.

Spec

ial

stud

ies

of l

eaka

ge m

ust

be m

ade

for

ac m

achi

nes

and

trans

form

ers s

ince

thei

r per

form

ance

is a

ffec

ted

by it

.

LE

AK

AG

EFL

UX

. . .

.

Page 30: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3030

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

FRIN

GIN

G

At

an a

ir-ga

p in

a m

agne

tic c

ore,

the

flu

x fr

inge

s ou

t in

to

neig

hbor

ing

air p

aths

as s

how

n in

Fig

ure

belo

w.

The

resu

lt is

non

-uni

form

flu

x de

nsity

in

the

air-

gap

(dec

reas

ing

outw

ard)

, enl

arge

men

t of

the

effe

ctiv

e ai

r-ga

p ar

ea a

nd a

dec

reas

e in

th

e av

erag

e ga

p flu

x de

nsity

.

Page 31: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3131

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

effe

ct o

f frin

ging

incr

ease

s with

the

air-

gap

leng

th.

FRIN

GIN

G .

. . .

g

gg

Al 0µ=

ℜTh

e ga

p re

luct

ance

wou

ld n

ow b

e gi

ven

by

A g>

A

Frin

ging

incr

ease

s the

cro

ss se

ctio

nal a

rea

of th

e ai

r gap

.

Page 32: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3232

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

IND

UC

TIO

N

Self

indu

ctio

nSe

lf-in

duct

ion

is th

e ph

enom

enon

whe

reby

a c

hang

e in

the

curr

ent

in a

con

duct

or in

duce

s an

emfi

n th

e co

nduc

tor i

tsel

f.i.e

., w

hen

a co

nduc

tor

is g

iven

a c

urre

nt, f

lux

will

be

prod

uced

, an

d if

the

curr

ent i

s cha

nged

the

flux

also

cha

nges

.

Va

ria

ble

ac

sup

ply

~

Cu

rre

nt,

iS

Ma

gne

tic li

ne

s o

f fo

rce

Page 33: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3333

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

SEL

F IN

DU

CT

ION

. . .

.

As

per F

arad

ay�s

Law

whe

n th

ere

is a

cha

nge

of fl

ux, a

n em

fwill

be

indu

ced.

This

is c

alle

d se

lf in

duct

ion.

The

indu

ced

emf

will

be

alw

ays

oppo

site

in

dire

ctio

n to

the

ap

plie

d em

f.

The

oppo

sing

em

fthu

s pr

oduc

ed is

cal

led

the

coun

ter e

mfo

f sel

f in

duct

ion.

Page 34: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3434

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

It is

the

elec

trom

agne

tic in

duct

ion

prod

uced

by

one

circ

uit i

n th

e ne

arby

circ

uit

due

to t

he v

aria

ble

flux

of th

e fir

st c

ircui

t cu

tting

th

e co

nduc

tor o

f the

nea

rby

circ

uit.

MU

TU

AL

IN

DU

CT

ION

Whe

n tw

o co

ils a

re k

ept n

ear

to e

ach

othe

r an

d if

a va

riabl

e cu

rren

t is

give

n to

one

coi

l, th

e flu

x pr

oduc

ed d

ue t

o th

at v

aria

ble

curr

ent

cuts

bo

th th

e co

ils, a

nd a

n em

fwill

be

indu

ced

in b

oth

the

coils

.

Page 35: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3535

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

phen

omen

on b

y w

hich

em

fis

indu

ced

in th

e se

cond

coi

l due

to

the

varia

tion

of c

urre

nt in

firs

t coi

l is c

alle

d m

utua

l ind

uctio

n.

Bot

h th

e ci

rcui

ts h

ave

no e

lect

rical

con

tact

s w

ith e

ach

othe

r bu

t m

agne

tic li

nkag

es.

This

prin

cipl

e is

app

lied

in tr

ansf

orm

ers,

indu

ctio

n co

ils, e

tc.

MU

TU

AL

IN

DU

CT

ION

. . .

. .

Page 36: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3636

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

MA

GN

ET

IC C

IRC

UIT

CA

LC

UL

AT

ION

S

Nor

mal

ly m

agne

tic c

ircui

t ca

lcul

atio

ns i

nvol

ve t

wo

type

s of

pr

oble

ms.

In t

he f

irst

type

of

prob

lem

it

is r

equi

red

to d

eter

min

e th

e ex

cita

tion

(mm

f) n

eede

d to

est

ablis

h a

desi

red

flux

orflu

x de

nsity

at

a g

iven

poi

nt in

a m

agne

tic c

ircui

t.

In th

e se

cond

cat

egor

y th

e flu

x (o

r flu

x de

nsity

) is

unk

now

n an

dis

requ

ired

to b

e de

term

ined

for a

giv

en g

eom

etry

of t

he m

agne

tic

circ

uit a

nd sp

ecifi

ed m

mf.

Page 37: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3737

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

MA

GN

ET

IC C

IRC

UIT

CA

LC

UL

AT

ION

S . .

. . .

CO

RE

WIT

H A

IR-G

AP

Tran

sfor

mer

s are

wou

nd o

n cl

osed

cor

es.

Rot

atin

g m

achi

nes

have

a m

ovin

g el

emen

t an

d m

ust

ther

efor

e ha

ve a

ir-ga

ps in

the

core

s out

of n

eces

sity

. A

typ

ical

mag

netic

circ

uit

with

an

air-

gap

is s

how

n in

Fig

ure

belo

w.

Page 38: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3838

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

It is

ass

umed

that

the

air-

gap

is n

arro

w a

nd th

e flu

x co

min

g ou

t of

the

core

pas

ses s

traig

ht d

own

the

air-

gap

such

that

the

flux

dens

ity

in th

e ai

r-ga

p is

the

sam

e as

in th

e co

re.

Act

ually

the

flux

in th

e ga

p fr

inge

s out

so th

at th

e ga

p flu

x de

nsity

is

som

ewha

t les

s tha

n th

at o

f the

cor

e.

MA

GN

ET

IC C

IRC

UIT

CA

LC

UL

AT

ION

S . .

. . .

CO

RE

WIT

H A

IR-G

AP.

. . .

.

The

mm

fNi i

s now

con

sum

ed in

the

core

plu

s the

air-

gap.

Fr

om th

e Fi

gure

, N

i = H

cl c+

Hgl g

gg

ccc

lB

lB

Ni

0µµ

+=

Ass

umin

g th

at a

ll th

e co

re fl

ux p

asse

s stra

ight

dow

n th

e ai

r-ga

p , i

.e.,

no

frin

ging

eff

ect,

Bg

= B

cA

BA

Bg

c=

Page 39: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 3939

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

gg

ccc

il

Bl

BN

0µµ

+=

MA

GN

ET

IC C

IRC

UIT

CA

LC

UL

AT

ION

S . .

. . .

CO

RE

WIT

H A

IR-G

AP.

. . .

.

Bg

= B

c

AB

AB

gc

==

φ

+

=A

lA

lN

g

cci

0µφ

µφ

()

eqg

cℜ

=ℜ

+ℜ

φF

==

ℜA

l cc

0µco

re re

luct

ance

==

ℜA

l gg

0µai

r-ga

p re

luct

ance

Whi

ch m

eans

tha

t in

a m

agne

tic c

ircui

t w

ith a

ir-ga

p, c

ore

relu

ctan

ce

may

be

negl

ecte

d w

ith n

o si

gnifi

cant

loss

of a

ccur

acy.

This

ass

umpt

ion

will

be

gene

rally

mad

e in

mod

elin

g ro

tatin

g m

achi

nes.

Page 40: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4040

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

MA

GN

ET

IC B

EH

AV

IOR

OF

FER

RO

MA

GN

ET

IC M

AT

ER

IAL

S

To

illus

trate

th

e be

havi

or

of

mag

netic

pe

rmea

bilit

y in

a

ferr

omag

netic

mat

eria

l, ap

ply

a di

rect

cur

rent

to th

e co

re, s

tarti

ng

with

0 A

and

slo

wly

wor

king

up

to t

he m

axim

um p

erm

issi

ble

curr

ent.

Whe

n th

e flu

x pr

oduc

ed i

n th

e co

re i

s pl

otte

d ve

rsus

the

mm

fpr

oduc

ing

it, th

e re

sulti

ng p

lot l

ooks

like

figu

re b

elow

.

Page 41: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4141

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

This

type

of

plot

is c

alle

d a

satu

ratio

n cu

rve

or a

mag

netiz

atio

n cu

rve.

MA

GN

ET

IC B

EH

AV

IOR

OF

FER

RO

MA

GN

ET

IC M

AT

ER

IAL

S. .

. .

At f

irst,

a sm

all i

ncre

ase

in th

e m

mf

prod

uces

a h

uge

incr

ease

in

the

resu

lting

flux

. A

fter

a ce

rtain

poi

nt,

thou

gh,

the

mm

fin

crea

ses

ther

e is

a

rela

tivel

y sm

alle

r inc

reas

e in

the

flux.

Fina

lly, a

n in

crea

se in

the

mag

neto

mot

ive

forc

e pr

oduc

es a

lmos

t no

cha

nge

at a

ll.

The

regi

on in

whi

ch th

e cu

rve

flatte

ns o

ut is

cal

led

the

satu

ratio

n re

gion

, and

the

core

is sa

id to

be

satu

rate

d.

Page 42: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4242

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

In c

ontra

st,

the

regi

on w

here

the

flu

x ch

ange

s ve

ry r

apid

ly i

s ca

lled

the

unsa

tura

ted

regi

onof

the

curv

e, a

nd th

e co

re is

sai

d to

be

uns

atur

ated

. Th

e tra

nsiti

on r

egio

n be

twee

n th

e un

satu

rate

d re

gion

and

the

sa

tura

ted

regi

on is

som

etim

es c

alle

d th

e kn

eeof

the

curv

e.

Not

e th

at th

e flu

x pr

oduc

ed i

n th

e co

re i

s lin

early

rel

ated

to

the

appl

ied

mm

fin

the

unsa

tura

ted

regi

on.

MA

GN

ET

IC B

EH

AV

IOR

OF

FER

RO

MA

GN

ET

IC M

AT

ER

IAL

S. .

. .

From

the

figur

e, it

is s

een

that

the

rela

tions

hip

betw

een

B a

nd H

ha

s the

sam

e sh

ape

as th

e re

latio

nshi

p be

twee

n flu

x an

d m

mf.

Page 43: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4343

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

EN

ER

GY

LO

SSE

S IN

A F

ER

RO

MA

GN

ET

IC C

OR

EM

AG

NE

TIC

BE

HA

VIO

R O

F FE

RR

OM

AG

NE

TIC

MA

TE

RIA

LS.

.

Inst

ead

of a

pply

ing

a di

rect

cur

rent

to

the

core

, le

ts a

pply

an

alte

rnat

ing

curr

ent.

Ass

ume

that

the

flux

in th

e co

re is

initi

ally

zer

o.

As

the

curr

ent

incr

ease

s fo

r th

e fir

st t

ime,

the

flu

x in

the

cor

e tra

ces o

ut p

ath

abin

figu

re.

This

is b

asic

ally

the

satu

ratio

n cu

rve

expl

aine

d ab

ove.

H

owev

er,

whe

n th

e cu

rren

t fa

lls a

gain

, th

e flu

x tr

aces

out

a

diffe

rent

pat

h fr

om t

he o

ne i

t fo

llow

ed w

hen

the

curr

ent

was

in

crea

sed.

As

the

curr

ent d

ecre

ases

, the

flux

in th

e co

re tr

aces

out

pat

hbc

d,

and

late

r whe

n th

e cu

rren

t inc

reas

es a

gain

, the

flux

trac

es o

ut p

ath

deb.

Page 44: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4444

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

EN

ER

GY

LO

SSE

S IN

A F

ER

RO

MA

GN

ET

IC C

OR

E .

. . .

MA

GN

ET

IC B

EH

AV

IOR

OF

FE

RR

OM

AG

NE

TIC

MA

TE

RIA

LS.

Page 45: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4545

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Not

ice

that

the

am

ount

of

flux

pres

ent

in t

he c

ore

depe

nds

not

only

on

the

amou

nt o

f cur

rent

app

lied

to th

e w

indi

ngs

of th

e co

re,

but a

lso

on th

e pr

evio

us h

isto

ry o

f the

flux

in th

e co

re.

This

dep

ende

nce

on t

he p

rece

ding

flu

x hi

stor

y an

d th

e re

sulti

ng

failu

re to

retra

ce fl

ux p

ath

is c

alle

d hy

ster

isis

.

Path

bcd

ebtra

ced

out i

n th

e fig

ure

is c

alle

d a

hyst

eris

islo

op.

EN

ER

GY

LO

SSE

S IN

A F

ER

RO

MA

GN

ET

IC C

OR

E .

. . .

MA

GN

ET

IC B

EH

AV

IOR

OF

FER

RO

MA

GN

ET

IC M

AT

ER

IAL

S. .

. .

Page 46: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4646

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

HY

STE

RIS

IS L

OSS

Ene

rgy

loss

es in

a fe

rrom

agne

tic c

ore

. . .

.M

agne

tic b

ehav

ior

of F

erro

mag

netic

mat

eria

ls. .

.

Whe

n th

e m

agne

to-m

otiv

e fo

rce

is r

emov

ed, t

he f

lux

in t

he c

ore

does

not

go

to z

ero.

In

stea

d, so

me

mag

netic

flux

is le

ft in

the

core

.

This

mag

netic

flux

is c

alle

d th

e re

sidu

al fl

uxin

the

core

.

It is

pre

cise

ly th

e m

anne

r tha

t per

man

ent m

agne

ts a

re p

rodu

ced.

To fo

rce

the

flux

to z

ero,

an

amou

nt o

f mm

fkno

wn

as th

e C

oerc

ive

mag

neto

-mot

ive

forc

em

ust b

e ap

plie

d to

the

core

in th

e op

posi

te

dire

ctio

n.

Page 47: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4747

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

HY

STE

RIS

IS L

OSS

. . .

.E

nerg

y lo

sses

in a

ferr

omag

netic

cor

e . .

. .

Mag

netic

beh

avio

r of

Fer

rom

agne

tic m

ater

ials

. . .

To u

nder

stan

d th

e be

havi

our

of f

erro

mag

netic

mat

eria

ls,

it is

ne

cess

ary

to k

now

abo

ut th

eir s

truct

ure.

With

in th

e m

etal

, the

re a

re m

any

smal

l reg

ions

cal

led

dom

ains

.

In e

ach

dom

ain,

all

the

atom

s ar

e al

igne

d w

ith t

heir

mag

netic

fie

lds

poin

ting

in th

e sa

me

dire

ctio

n, s

o ea

ch d

omai

n w

ithin

the

mat

eria

l act

s as a

smal

l per

man

ent m

agne

t.

The

reas

on th

at a

who

le b

lock

of

iron

can

appe

ar t

o ha

ve n

o flu

xis

th

at t

hese

num

erou

s tin

y do

mai

ns a

re o

rient

ed r

ando

mly

with

in t

he

mat

eria

l as s

how

n in

figu

re.

Page 48: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4848

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

HY

STE

RIS

IS L

OSS

. . .

.E

nerg

y lo

sses

in a

ferr

omag

netic

cor

e . .

. .

Mag

netic

beh

avio

r of

Fer

rom

agne

tic m

ater

ials

. . .

Fig.

b

Fig.

a :

Mag

netic

dom

ains

orie

nted

rand

omly

.Fi

g. b

: M

agne

tic d

omai

ns li

ned

up in

the

pres

ence

of a

n ex

tern

al

mag

netic

fiel

d.

Fig.

a

Page 49: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 4949

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Whe

n an

ext

erna

l mag

netic

fiel

d is

app

lied

to th

is b

lock

of i

ron,

it

caus

es d

omai

ns te

nd to

alig

n th

emse

lves

in a

n or

derly

fas

hion

inth

e di

rect

ion

of a

pplie

d m

agne

tic fi

eld.

As

the

stre

ngth

of

the

exte

rnal

mag

netic

fie

ld c

ontin

ues

to

incr

ease

, who

le d

omai

ns t

hat

are

alig

ned

in t

he w

rong

dire

ctio

n re

-orie

nt th

emse

lves

as a

uni

t to

line

up w

ith th

e ex

tern

al fi

eld.

HY

STE

RIS

IS L

OSS

. . .

.E

nerg

y lo

sses

in a

ferr

omag

netic

cor

e . .

. .

Mag

netic

beh

avio

r of

Fer

rom

agne

tic m

ater

ials

. . .

The

key

to h

yste

resi

sis

that

whe

n th

e ex

tern

al m

agne

tic f

ield

is

rem

oved

, the

dom

ains

do

not c

ompl

etel

y ra

ndom

ize

agai

n.W

hy d

o th

e do

mai

ns re

mai

n lin

ed u

p?B

ecau

se tu

rnin

g th

e at

oms i

n th

em re

quire

s ene

rgy.

Orig

inal

ly,

ener

gy w

as p

rovi

ded

by t

he e

xter

nal

mag

netic

fie

ld t

o ac

com

plis

h th

e al

ignm

ent;

whe

n th

e fie

ld i

s re

mov

ed,

ther

e is

no

sour

ce o

f ene

rgy

to c

ause

all

the

dom

ains

to ro

tate

bac

k.

Page 50: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5050

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Hys

tere

sisL

oss:

The

hyst

eres

islo

ss i

n an

iro

n co

re i

s th

e en

ergy

req

uire

d to

ac

com

plis

h th

e re

-orie

ntat

ion

of d

omai

ns d

urin

g ea

ch c

ycle

of t

he

ac a

pplie

d to

the

core

.

HY

STE

RIS

IS L

OSS

. . .

.E

nerg

y lo

sses

in a

ferr

omag

netic

cor

e . .

. .

Mag

netic

beh

avio

r of

Fer

rom

agne

tic m

ater

ials

. . .

The

piec

e of

iron

is n

ow a

per

man

ent m

agne

t.O

nce

the

dom

ains

are

alig

ned,

som

e of

them

will

rem

ain

alig

ned

until

a so

urce

of e

xter

nal e

nerg

y is

supp

lied

to c

hang

e th

em.

Exam

ples

of

exte

rnal

sou

rces

of

ener

gy t

hat

can

chan

ge t

he

alig

nmen

t are

: a la

rge

mec

hani

cal s

hock

, hea

ting,

etc

.

Page 51: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5151

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

HY

STE

RIS

IS L

OSS

. . .

.E

nerg

y lo

sses

in a

ferr

omag

netic

cor

e . .

. .

Mag

netic

beh

avio

r of

Fer

rom

agne

tic m

ater

ials

. . .

If th

e m

agne

tizin

g fo

rce

appl

ied

to a

mag

netic

mat

eria

l is

carr

ied

thro

ugh

a co

mpl

ete

cycl

e fr

om +

Hm

axto

�H

max

and

back

to

+Hm

ax, t

he B

-H c

hara

cter

istic

is d

escr

ibed

by

a hy

ster

isis

loop

as

show

n in

figu

re.

The

area

of

the

loop

rep

rese

nts

the

ener

gy lo

ss in

a u

nit c

ube

of

the

core

mat

eria

l dur

ing

one

cycl

e.Th

e hy

ster

isis

loss

is e

xpre

ssed

em

piric

ally

as

Whe

re t

he v

alue

of

n de

pend

s on

the

nat

ure

of

the

core

mat

eria

l. n

may

var

y be

twee

n 1.

5 an

d 2.

5 fo

r di

ffer

ent

mat

eria

ls.

How

ever

, th

e hy

ster

isis

loss

var

ies

dire

ctly

as

the

freq

uenc

y fo

r a g

iven

Bm

ax.

nh

Bf

Pm

ax∝

Page 52: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5252

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

ED

DY

CU

RR

EN

T L

OSS

Ene

rgy

loss

es in

a fe

rrom

agne

tic c

ore

. . .

.M

agne

tic b

ehav

ior

of F

erro

mag

netic

mat

eria

ls. .

.

A t

ime-

chan

ging

flu

x in

duce

s vo

ltage

with

in a

fer

rom

agne

tic

core

in

just

the

sam

e m

anne

r as

it

wou

ld i

n a

wire

wra

pped

ar

ound

that

cor

e.

Thes

e vo

ltage

s cau

se sw

irls o

f cur

rent

to fl

ow w

ithin

the

core

It is

the

sha

pe o

f th

ese

curr

ents

tha

t gi

ves

rise

to t

he n

ame

eddy

cu

rren

ts.

Thes

e ed

dy c

urre

nts

are

flow

ing

in a

res

istiv

e m

ater

ial (

the

iron

of

the

core

), so

ene

rgy

is d

issi

pate

d by

them

.

The

lost

ene

rgy

goes

into

hea

ting

the

iron

core

.

Page 53: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5353

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

amou

nt o

f ene

rgy

lost

due

to e

ddy

curr

ents

(edd

y cu

rren

t los

s)is

pro

porti

onal

to th

e si

ze o

f the

pat

hs th

ey fo

llow

with

in th

e co

re.

ED

DY

CU

RR

EN

T L

OSS

. . .

. .

Ene

rgy

loss

es in

a fe

rrom

agne

tic c

ore

. . .

.M

agne

tic b

ehav

ior

of F

erro

mag

netic

mat

eria

ls. .

.

For t

his

reas

on, i

t is

cust

omar

y to

bre

ak u

p an

y fe

rrom

agne

tic c

ore

into

man

y sm

all s

trips

or laminations,a

nd to

bui

ld th

e co

re u

p ou

t of

thes

e st

rips.

An

insu

latin

g re

sin

is u

sed

betw

een

the

strip

s, so

tha

t th

e cu

rren

t pa

ths f

or e

ddy

curr

ents

are

lim

ited

to v

ery

smal

l are

as.

Bec

ause

the

insu

latin

g la

yers

are

ext

rem

ely

thin

, thi

s act

ion

redu

ces

eddy

cur

rent

los

ses

with

ver

y lit

tle e

ffec

t on

the

cor

e�s

mag

netic

pr

oper

ties.

The

iron

in th

e m

agne

tic c

ircui

ts is

lam

inat

ed to

pre

vent

exc

essi

ve

eddy

cur

rent

s.

Page 54: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5454

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

eddy

cur

rent

loss

can

als

o be

exp

ress

ed in

term

s of

the

appl

ied

volta

ge a

nd th

e nu

mbe

r of

turn

s in

the

exci

ting

win

ding

whe

n th

ere

sist

ance

of t

he w

indi

ng is

neg

ligib

le.

ED

DY

CU

RR

EN

T L

OSS

. . .

. .

Ene

rgy

loss

es in

a fe

rrom

agne

tic c

ore

. . .

.M

agne

tic b

ehav

ior

of F

erro

mag

netic

mat

eria

ls. .

.

The

expr

essi

on is

2 max

2B

fP e

Page 55: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5555

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

THR

EE �

PHA

SE C

IRC

UIT

SA

t the

com

plet

ion

of th

is c

hapt

er, y

ou s

houl

d be

abl

e to

: D

emon

stra

te in

dep

th u

nder

stan

ding

of t

he c

once

pts

of b

asic

thre

e-ph

ase

circ

uits

.

Dis

cuss

the

diffe

renc

es b

etw

een

thre

e-ph

ase

and

sing

le-p

hase

vo

ltage

s.D

iscu

ss th

e ch

arac

teris

tics

of d

elta

and

wye

conn

ectio

ns.

Com

pute

the

volta

ge a

nd c

urre

nt v

alue

s fo

r del

ta a

nd w

yeci

rcui

ts.

Con

nect

del

ta a

nd w

yeci

rcui

ts a

nd m

ake

mea

sure

men

ts w

ith

mea

surin

g in

stru

men

ts.

Acq

uire

and

app

ly fu

ndam

enta

l prin

cipl

es o

f sci

ence

and

eng

inee

ring.

Com

mun

icat

e ef

fect

ivel

y.A

cqui

re te

chni

cal c

ompe

tenc

e in

spe

cial

ized

are

a (th

ree-

phas

e ci

rcui

ts) o

f eng

inee

ring.

Wor

k in

depe

nden

tly a

s w

ell a

s w

ith o

ther

s in

a te

am

Page 56: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5656

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

THR

EE �

PHA

SE C

IRC

UIT

SIn

trod

ucti

onTh

ree-

phas

e sy

stem

s di

ffer

from

sin

gle-

phas

e sy

stem

s in

th

at th

ey u

se a

set

of t

hree

vol

tage

sin

stea

d of

one

.

In g

ener

al, a

thre

e-ph

ase

syst

em is

mer

ely

a co

mbi

natio

n of

thre

e si

ngle

pha

se s

yste

ms

of w

hich

the

thre

e vo

ltage

s di

ffer

in p

hase

by

120

elec

tric

al d

egre

esfr

om e

ach

othe

r in

a p

artic

ular

seq

uenc

e.

Ther

e ar

e tw

o ba

sic

thre

e-ph

ase

conn

ectio

ns,

the

wye

(sta

r) a

nd th

e de

ltaco

nnec

tions

.

Page 57: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5757

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Arm

atur

e w

ith c

oils

Fig.

2.1

Sch

emat

ic d

iagr

am o

f a th

ree-

phas

e ge

nera

tor

Φ

ω

Rot

or w

ith

field

win

ding

Coi

l A

Coi

l BC

oil C

Phas

e se

quen

ceis

the

ord

er

in w

hich

the

var

ious

pha

ses

reac

h th

e m

axim

um v

alue

.A

BC

AC

B

EMFs

indu

ced

in

the

thre

e id

entic

al w

indi

ngs

A, B

and

Car

e el

ectr

ical

ly d

istr

ibut

ed b

y 12

0oan

d m

ay b

e ex

pres

sed

as b

elow

:

e B(t)

=EM

sin

(ωt -

120

o )

e C(t)

=EM

sin (ωt-

240o )

e A(t

)=E

M s

in (ωt -

0o ),

Thre

e-ph

ase

syst

ems

may

be

bala

nced

or u

nbal

ance

d.

Page 58: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5858

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Bal

ance

d an

d un

bala

nced

syst

ems

A

thre

eA

th

ree --

phas

e po

wer

sy

stem

in

w

hich

th

e th

ree

phas

e po

wer

sy

stem

in

w

hich

th

e th

ree

gene

rato

rs

have

ge

nera

tors

ha

ve

volta

ges

volta

ges

that

ar

e ex

actly

th

at

are

exac

tly

equa

leq

ual

in

in

mag

nitu

de a

ndm

agni

tude

and

120

deg

120

deg

diffe

rent

in p

hase

, and

in w

hich

di

ffere

nt in

pha

se, a

nd in

whi

ch

all

all

thre

e lo

ads

are

iden

tical

thre

e lo

ads

are

iden

tical

is c

alle

d a

bala

nced

thr

eeis

cal

led

a ba

lanc

ed t

hree

--ph

ase

syst

em.

phas

e sy

stem

.

Bal

ance

d sy

stem

Un-

bala

nced

sys

tem

A

thre

eA

th

ree --

phas

e po

wer

sy

stem

in

w

hich

th

e th

ree

phas

e po

wer

sy

stem

in

w

hich

th

e th

ree

gene

rato

rs h

ave

gene

rato

rs h

ave

volta

ges

volta

ges

that

are

th

at a

re u

nequ

alun

equa

l in in

mag

nitu

dem

agni

tude

and/

or

and/

or d

o no

t diff

er b

y 12

0 de

g in

pha

sedo

not

diff

er b

y 12

0 de

g in

pha

se, a

nd/o

r in

whi

ch

, and

/or i

n w

hich

al

l al

l th

ree

load

s ar

e no

t id

entic

alth

ree

load

s ar

e no

t id

entic

alis

cal

led

a ba

lanc

ed

is c

alle

d a

bala

nced

th

ree

thre

e --ph

ase

syst

em.

phas

e sy

stem

.

Page 59: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 5959

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Req

uire

men

ts o

f a b

alan

ced

syst

em

!!A

ll th

ree

varia

bles

hav

e th

e A

ll th

ree

varia

bles

hav

e th

e sa

me

ampl

itude

.sa

me

ampl

itude

.

!!A

ll th

ree

varia

bles

hav

e th

e A

ll th

ree

varia

bles

hav

e th

e sa

me

freq

uenc

y.sa

me

freq

uenc

y.

!!A

ll th

ree

varia

bles

are

A

ll th

ree

varia

bles

are

120

deg

. in

phas

e.12

0 de

g. in

pha

se.

120

240

0

Page 60: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6060

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

pow

erde

liver

ed b

y a

sing

le-p

hase

syst

em p

ulsa

tes.

Ang

le

+ -0

1

20

2

40

36

0A

ngle

13

2

+ -

In 3

-pha

se sy

stem

, the

ave

rage

pow

erde

liver

ed to

load

is

con

stan

tra

ther

than

pul

satin

g

Adv

anta

ges o

f thr

ee-p

hase

circ

uits

In a

bal

ance

d 3-

phas

e sy

stem

, con

duct

ors

need

be

only

abo

ut 7

5%th

e si

ze o

f co

nduc

tors

for

a s

ingl

e-ph

ase

syst

em o

f th

e sa

me

kVA

ratin

g.

Page 61: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6161

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Ana

lysi

s of t

hree

-pha

se b

alan

ced

circ

uits

In t

his

conn

ectio

n, s

imila

r en

ds (

star

t or

fin

ish)

of e

ach

of t

he t

hree

-ph

ase

win

ding

s ar

e jo

ined

toge

ther

.

s f

s f

s f

I PH

I PH

I PH

I L

I L

I L

V ab

V bc

V ca

N

The

com

mon

term

inal

is re

ferr

ed to

as

the

neut

ral p

oint

(N).

a cb

The

othe

r th

ree

term

inal

s ar

e co

nnec

ted

to 3

term

inal

s a,

b, a

ndc

(line

te

rmin

als)

.

Star

-con

nect

ed c

ircu

its

Page 62: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6262

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

The

sour

ce is

sai

d to

be

bala

nced

if th

e vo

ltage

s V a

n, V b

nan

d V c

n(c

alle

d ph

ase

volta

ges)

, hav

e th

e sa

me

mag

nitu

de a

nd s

um to

zer

o, i.

e.,

Line

and

pha

se v

olta

ges

are

diffe

rent

in

a w

ye(s

tar)

co

nnec

tion.

Line

and

pha

se c

urre

nts

are

the

sam

ein

a

wye

(sta

r)

conn

ectio

n.

I PH

I PH

I PHI L

I L I L

Na cb

Vab

Vbc

Vca

Ana

lysi

s of 3

-pha

se st

ar c

onne

cted

cir

cuits

. . .

.

Page 63: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6363

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Ana

lysi

s of 3

-pha

se st

ar c

onne

cted

cir

cuits

. . .

.

Neu

tral

vol

tage

Con

side

r the

thre

e-ph

ase

bala

nced

wye

conn

ecte

d sy

stem

sho

wn

in F

ig.

N

Z L

Z L

Z L

I A

I B I C

E∠0o E∠

-120

oE∠

-240

o

Z G

Z G

Z G

A B C

N

LG

NA

ZZ

VE

I+−

∠=

o 0

LG

NB

ZZ

VE

I+

−−

∠=

o12

0

LG

NC

ZZ

VE

I+

−−

∠=

o24

0

Acc

ordi

ng t

o K

ircho

ff�s

curr

ent

law

,I A

+ I B

+ I C

= 0

024

012

00

=+

−−

∠+

+−

−∠

++−

∠⇒

LG

N

LG

N

LG

N

ZZ

VE

ZZ

VE

ZZ

VE

oo

o

LG

N

LG

ZZ

VZ

ZE

EE

+=

+−

∠+

−∠

+∠

⇒3

240

120

0o

oo

Sinc

e,

,024

012

00

=−

∠+

−∠

+∠

oo

oE

EE

V N=

0.

The

curr

ent i

n th

e th

ree

lines

are

:

Page 64: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6464

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Sing

le P

hase

Equ

ival

ent o

f a B

alan

ced

Thre

e Ph

ase

Syst

em

The

exp

ress

ion

for A

-pha

se c

urre

nt is

I A =

LZ

Z+

∠ G

No

V - 0

E=

LG

ZZ

+∠o 0

E.

The

circ

uit

diag

ram

th

at

repr

esen

ts

the

sing

le-p

hase

eq

uiva

lent

of

a

bala

nced

thre

e-ph

ase

syst

em is

Fig.

Sin

gle-

phas

e eq

uiva

lent

of a

thre

e-ph

ase

bala

nced

syst

em

I A

Z LV A

N

Z G

E∠0o

This

vi

ew

sim

plifi

es

com

puta

tion

of

a ba

lanc

ed

thre

e-ph

ase

pow

er s

yste

m.

The

resu

lts fo

r one

pha

se

can

be a

pplie

d to

all

the

thre

e ph

ases

.

Ana

lysi

s of 3

-pha

se st

ar c

onne

cted

cir

cuits

. . .

.

Page 65: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6565

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Ana

lysi

s of 3

-pha

se st

ar c

onne

cted

cir

cuits

. . .

.V

olta

ges a

nd c

urre

nts

By

Kirc

hoff�

svo

ltage

law

, lin

e vo

ltage

(VA

B=

V L) i

s gi

ven

by

BA

BNAN

NB

ANL

VV

VV

VV

V−

=−

=+

=N

egle

ctin

g th

e so

urce

impe

danc

e (Z

G),

N

Z L

Z L

Z L

I A

I B I C

E∠0o E∠

-120

oE∠

-240

o

Z G

Z G

Z G

A B C

N

oo

120

0−

∠−

∠=

EE

V L[

])12

0si

n()

120

cos(

jE

E−

−=

Ej

Ej

EE

2323

2321

+=

−−

−=

()

oo

o30

330

sin

30co

s3

2123

3∠

=+

=

+=

Ej

Ej

E

Ther

efor

e, t

he r

elat

ions

hip

betw

een

the

mag

nitu

des

of t

he l

ine

volta

ge a

nd

phas

e vo

ltage

in a

wye

conn

ecte

d ge

nera

tor o

r loa

d is

o

303

∠=

PhL

VV Th

us, t

he li

ne-to

-line

vol

tage

has

a m

agni

tude

equ

al to

√3

times

the

mag

nitu

de

of th

e ph

ase

volta

gean

d it

lead

s th

e co

rres

pond

ing

phas

e vo

ltage

by

30°.

It ca

n be

obs

erve

d th

at th

e lin

e cu

rren

ts a

re id

entic

al to

the

corr

espo

ndin

g ph

ase

curr

ents

. Ph

LI

I=

Page 66: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6666

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Ana

lysi

s of 3

-pha

se d

elta

con

nect

ed c

ircu

itsIn

thi

s co

nnec

tion,

diff

eren

t en

ds (

star

t &

fin

ish)

of t

he t

hree

-pha

ses

are

join

ed to

geth

er. T

here

is n

o ne

utra

l poi

nt (N

)in

delta

con

nect

ion.

s f

s f

s f

I ph

I ph

I ph

BA C

a

bc

I L

I L I L

Line

and

pha

se c

urre

nts

are

diffe

rent

in a

de

lta c

onne

ctio

n.

Line

and

pha

se v

olta

ges

are

the

sam

ein

a

delta

con

nect

ion.

Page 67: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6767

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Ana

lysi

s of 3

-pha

se d

elta

con

nect

ed c

ircu

its .

. . .

.V

olta

ges a

nd c

urre

nts

Con

side

r the

thre

e-ph

ase

bala

nced

del

ta s

yste

m s

how

n in

Fig

.

R LR L

R L

I CA

I AB

I BC

V AB

V CA

B

A C

A

BC

V BC

I A

I B I C

G

ener

ator

Load

o 0∠

=Ph

ABV

Vo

120

−∠

=Ph

BCV

Vo

240

−∠

=Ph

CA

VV

Bec

ause

the

load

is re

sist

ive,

the

phas

e cu

rren

tsar

e gi

ven

by:

o 0∠

=Ph

ABI

Io

120

−∠

=Ph

BCI

Io

240

−∠

=Ph

CA

II

In a

del

ta c

onne

ctio

n, th

e lin

e-to

-line

vol

tage

betw

een

any

two

lines

will

be

the

sam

eas

th

e vo

ltage

in

th

e co

rres

pond

ing

phas

e.

App

lyin

g K

CL

to n

ode

A y

ield

s,C

AAB

AI

II

−=

oo

240

0−

∠−

∠=

PhPh

II

[])

240

sin(

)24

0co

s(j

II

PhPh

−−

=

PhPh

PhPh

Ij

Ij

II

2323

2321

−=

+−

−=

()

oo

o30

330

sin

30co

s3

2123

3−

∠=

−=

−=

PhPh

PhI

jI

jI

o30

3−

∠=

PhL

IITh

e ph

ase

volta

ges

in th

e ge

nera

tor a

re g

iven

by

Page 68: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6868

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

I Ale

ads I

AB

by

30ο

VA

Bla

gs V

Aby

30

οA

CB

pha

se

sequ

ence

I Ala

gs I A

Bby

30

οV

AB

lead

s V

Aby

30

οA

BC

pha

se

sequ

ence

Cur

rent

m

agni

tude

s

Vol

tage

m

agni

tude

s

Del

ta c

onne

ctio

nW

yeco

nnec

tion

PhL

II

3=

PhL

II

=

PhLL

VV

=Ph

LLV

V3

=

Ana

lysi

s of t

hree

-pha

se b

alan

ced

circ

uits

. . .

.

Page 69: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 6969

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

DE

LT

A T

O S

TA

R T

RA

NSF

OR

MA

TIO

N

z CZ B

z A

CB

AA

CB

Fig.

Del

ta to

Sta

r tr

ansf

orm

atio

n.

The

val

ue o

f im

peda

nce

betw

een

any

two

ends

of

the

star

or

delta

mus

t be

eq

ual w

hen

the

two

circ

uits

are

equ

al.

Z A +

ZB

=

CA

BC

AB

CA

BC

AB

)(

ZZ

ZZ

ZZ

++

+(1

)Z B

+ Z

C =

C

AB

CA

B

AB

CA

BC

)(

ZZ

ZZ

ZZ

++

+(2

)

Z C +

ZA

=

CA

BC

AB

BC

AB

CA

)(

ZZ

ZZ

ZZ

++

+(3

)Eq

uatio

ns (1

) + (3

) -(2

)

z AB

z CA

z BC

Page 70: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 7070

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Z A =

C

AB

CA

B

CA

AB

ZZ

ZZ.

Z+

+

z Cz B

z A

CB

A

z AB

zCA

z BC

Z B =

C

AB

CA

B

AB

BC

ZZ

ZZ.

Z+

+

Z C =

C

AB

CA

B

BC

CA

ZZ

ZZ.

Z+

+

Del

ta to

sta

r tra

nsfo

rmat

ion

. . .

.

Page 71: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 7171

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

STA

R T

O D

EL

TA

TR

AN

SFO

RM

AT

ION

CB

AA

CB

Fig.

Sta

r to

Del

ta tr

ansf

orm

atio

n.

The

val

ue o

f adm

ittan

cebe

twee

n an

y tw

o en

ds o

f the

star

or

delta

mus

t be

equa

l w

hen

the

two

circ

uits

are

equ

al.

Y AB

= C

BA

BA

YY

YY.

Y+

+Y B

C=

CB

A

CB

YY

YY.

Y+

+Y C

A=

CB

A

AC

YY

YY.

Y+

+

Y CY B

Y AY A

BY C

A

Y BC

Page 72: Principle of Electrical Machine

MEE

20

/ PR

INCI

PLE

OF

ELEC

TRIC

AL M

ACH

INES

/ FE

BR

UAR

Y 20

08SU

L 7272

To

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

yTo

Be A

Wo

rld

Cla

ss M

ari

tim

e A

cad

em

y

Act

ive

pow

er a

nd re

activ

e po

wer

cal

cula

tions

The

tota

l ave

rage

pow

er a

bsor

bed

by a

thre

e ph

ase

bala

nced

load

del

iver

ed

by a

thre

e-ph

ase

gene

rato

r, is

equ

alto

the

sum

of t

he p

ower

s in

eac

h ph

ase.

Th

e vo

ltage

and

cur

rent

in e

ach

phas

e ar

e eq

ual.

The

tota

l 3-p

hase

real

pow

eris

θco

s3

cos

33

××

×=

××

==

LLL

PhPh

PhT

IV

IV

PP

whe

re, θ

is th

e ph

ase

angl

e be

twee

n th

e vo

ltage

and

the

curr

ent o

r,

PhPhPh

PhT

RVR

IP

22

33

=

Sim

ilarly

, the

tota

l rea

ctiv

e po

wer

is,

θθ

sin

3si

n3

××

×=

=L

LLPh

PhPh

TI

VI

VQ

Q

or

PhPhPh

PhT

XVX

IQ

22

33

=

or,

Tota

l app

aren

t pow

eris

,

PhPh

LLL

PhPh

TT

T

ZI

IV

IV

jQP

S

××

=

××

=

×=

±=

2

*

*

3

3

3

PhPhT

ZVS

2

3=

P 1 P 2

P 1 P 3

P 2

PT

= P

1+

P2

+ P

3P

T=

P1

+ P

2