NAME-PARMAR RAHUL S.BRANCH-ELECTRICALROLL NO-131080109020(313)

A.C.E.T-SANAND

POLYPHASE CIRCUITS

LEARNING GOALS

Three Phase CircuitsAdvantages of polyphase circuits

Three Phase ConnectionsBasic configurations for three phase circuits

Source/Load ConnectionsDelta-Wye connections

THREE PHASE CIRCUITS

))(240cos()(

))(120cos()(

))(cos()(

VtVtv

VtVtv

VtVtv

mc

mbn

man

VoltagesPhase ousInstantane

ai

bi

ci

)240cos()(

)120cos()(

)cos()(

tIti

tIti

tIti

mc

mb

ma

Currents Phase Balanced

2120mV

)()()()()()()( titvtitvtitvtp ccnbbnaan power ousInstantane

TheoremFor a balanced three phase circuit the instantaneous power is constant

)(cos2

3)( WIV

tp mm

THREE-PHASE CONNECTIONS

Positive sequencea-b-c

Y-connectedloads Delta connected loads

SOURCE/LOAD CONNECTIONS

BALANCED Y-Y CONNECTION

120||

120||

0||

pcn

pbn

pan

VV

VV

VV

Positive sequencephase voltages

abV

bcV

caV

Line voltages

| | 0 | | 120

| | 1 (cos120 sin120)

1 3| | | |

2 2

3 | | 30

ab an bn

p p

p

p p

p

V V V

V V

V j

V V j

V

210||3

90||3

pca

pbc

VV

VV

VoltageLine ||3 pL VVY

cnc

Y

bnb

Y

ana Z

VI

Z

VI

Z

VI ;;

120||;120||;|| LcLbLa IIIIII

0 ncba IIII For this balanced circuit it is enough to analyze one phase

Relationship betweenphase and line voltages

LEARNING EXAMPLEFor an abc sequence, balanced Y - Y three phase circuit

30208abV

Determine the phase voltages

Balanced Y - Y

Positive sequencea-b-c

30||3 pab VV

120||

120||

0||

pcn

pbn

pan

VV

VV

VV

Positive sequencephase voltages

)3030(3

|| ab

anV

V

30by lags aban VV

30208abV

60120

180120

60120

an

bn

an

V

V

V

The phasor diagram could be rotated by any angle

DELTA CONNECTED SOURCES

Relationship betweenphase and line voltages

30||3 pab VV

30by lags aban VV

120

120

0

Lca

Lbc

Lab

VV

VV

VV

903

1503

303

Lcn

Lbn

Lan

VV

VV

VV

150120

90120

30120

cn

bn

an

V

V

V

180208

60208

60208

ca

bc

ab

V

V

VExample

Convert to an equivalent Y connection

30

||3||

lineline II

Line-phase currentrelationship

iprelationsh

voltagephase-Line

30

||3||

phase

phaseVV

LEARNING EXTENSION

currents phase the Find

.4012 aAI

19093.6

5093.6

7093.6

CA

BC

AB

I

I

I

Y

Y baab RRR

)(|| 312 RRRRab

321

312 )(

RRR

RRRRR ba

321

213 )(

RRR

RRRRR cb

321

321 )(

RRR

RRRRR ac

SUBTRACT THE FIRST TWO THEN ADDTO THE THIRD TO GET Ra

a

b

b

a

R

RRR

R

R

R

R 13

3

1 c

b

c

b

R

RRR

R

R

R

R 12

1

2

REPLACE IN THE THIRD AND SOLVE FOR R1

Y

RRR

RRR

RRR

RRR

RRR

RRR

c

b

a

321

13

321

32

321

21

Y

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

a

accbba

c

accbba

b

accbba

3

2

1

tionsTransforma

Y

OF REVIEW

3321

R

RRRRR Y

THANK YOU…….