balanced poly phase circuits. two and four phase systems a two phase system is an electrical system...

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Balanced poly phase circuits

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Page 1: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Balanced poly phase circuits

Page 2: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Two and four phase systems

A two phase system is an electrical system in which the voltages of the phases are 90 degree out of time phase.

The emf’s Eac and Ebd are 90 degree out of time phase. A two phase system is the equivalent of two separate single-phase systems

that are separated 90 degree in time phase.

If the connection is made between the two windings at n and n`, the system would be called a four-phase system.

The voltages Eda, Eab, Ebc and Ecd are called the line voltages, while voltages E0a, E0b, E0c and E0d are called the phase voltages or voltages to neutral.

Eda=Ed0+E0a. Thus, the line voltages= times the phase voltages in the four phase star.

2

Page 3: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Two and four phase systems

The line voltages are 45 degree or 135 degree out of time phase from the phase voltages.

For four-phase mesh, the aa` line current is Iaa`=Ida+Iba. Thus, the line currents= times the phase currents degree out of time

phase in the four phase mesh2

Page 4: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three phase four wire systems

The line voltages are 45 degree or 135 degree out of time phase from the phase voltages.

For four-phase mesh, the aa` line current is Iaa`=Ida+Iba. Thus, the line currents= times the phase currents degree out of time

phase in the four phase mesh2

Page 5: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three phase four wire system

V a n

V bn

V cn- V bn

V ab

V ab = V an - V b n

V ab = 3 V an 3 0 o

3 0 o

N is the neutral wire.Lighting loads are placed from line to neutral. Motors and other three phase power loads are connected between the three lines.

Page 6: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three phase four wire system

30||3

2

3

2

1||||

)120sin120(cos1||

120||0||

p

pp

p

pp

bnanab

V

jVV

jV

VV

VVV

210||3

90||3

pca

pbc

VV

VV

VoltageLine ||3 pL VV

Page 7: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three phase four wire system

The current in any line is the same as the current in the corresponding phase.

Current in the neutral wire is obtained through the application of KCL.

These currents are equal in magnitude and displaced from one another in time phase by 120 degree.Thus the current in the neutral wire is 0 since

IIL

0 ncnbnann IIII

ncnbnann IIII

Page 8: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three phase three wire system

VVL

0 0

0

1 30 240

2 2

3 3 3 13

2 2 2 23 30

ab caa I I I I I II

I

j I

I j I I j

Page 9: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Balanced Wye loadsGiven the line voltages as 220 volts balanced three phase and R and X of each phase 6 ohms resistance and 8 ohms inductive reactance. Find the line current, power per phase and total power.Draw the vector diagram

ivviP

I

I

Z

VI

voltsjVVV

voltsjV

voltsjjV

voltsjV

wattspowertotal

wattsRIphaseperpower

amperesII

voltsV

V

na

nc

nb

na

nana

nabnba

nc

nb

na

PP

pL

LP

87.667.12

13.1737.12

13.537.12

1105.190

1105.63120127

1105.63120sin120cos127120127

0127

29049683

968

7.1286

127

1273

2

22

Page 10: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Balanced Delta loadsGiven the line voltages as 220 volts balanced three phase and R and X of each phase 6 ohms resistance and 8 ohms inductive reactance. Find the line current, power per phase and total power.Draw the vector diagram

self

Page 11: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Power calculation in balanced systems

PLLPL

LPPpt

PLLPLL

PPpt

PPpPt

PPpp

IVI

VIVP

IVIV

IVP

InVnPP

IVP

cos3cos3

3cos3

cos3cos3

3cos3

cos

cos

Wye connection

Dealta connection

Page 12: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Volt-Amperes

LLL

L

LLLL

Pppt

IVI

V

IVIV

IVvava

33

3

33

3

33

Wye connection

Dealta connection

Reactive Volt-Amperes

PLLPL

LX

PLLPLL

X

PPpX

IVI

VP

IVIV

P

IVP

sin3sin3

3

sin3sin3

3

sin3

Wye connection

Dealta connection

Page 13: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Single phase and balanced three phase power

cos5.1

240sin240sin120sin120sinsinsin

240sin240sin

120sin120sin

sinsin

3

mm

mmmmmm

aba

mma

mmb

mma

IV

ttIVttIVttIV

PPPP

ttIVP

ttIVP

ttIVP

For any phase a

tIVIV

ttIVP

mmmm

mm

2cos2

cos2

sinsin1

Page 14: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three wattmeter method

Page 15: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Two wattmeter method

Page 16: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Two wattmeter method

Page 17: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Copper required to transmit power under fixed conditions

4

3

1

3

1

3

2

1

2

3

32

3

cos3cos

cos3

cos

3

1

21

23

3

1

32

312

1

31

31

31

33

11

R

R

wiresofnumber

wiresofnumber

copper

copper

I

I

R

R

RIRI

II

VIVI

PP

VIP

VIP

Page 18: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Copper required to transmit power under fixed conditions

4

3

1

3

1

3

2

1

2

3

32

3

cos3cos

cos3

cos

3

1

21

23

3

1

32

312

1

31

31

31

33

11

R

R

wiresofnumber

wiresofnumber

copper

copper

I

I

R

R

RIRI

II

VIVI

PP

VIP

VIP

Page 19: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Harmonics in balanced three phase wye loads

240sin120sinsin240sin

120sin240sinsin120sin

740sin600sin360sin120sin

sinsinsinsin

7755331

7755331

7755331

7755331

tetetetee

tetetete

tetetetee

tetetetee

mmmmnb

mmmm

mmmmnb

mmmmna

harmonics 1 3 5 7 9 11 13

Phase A 0 0 0 0 0 0 0

Phase B 120 0 240 0 0 240 120

Phase C 240 0 120 0 0 120 240

Page 20: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Harmonics in balanced three phase wye loadsThe fundamental and all harmonics that obtained by adding a multiple of 6 to the fundamental will have the same sequence. These are first, seventh, thirteenth, nineteenth, twenty-fifth and so on.The fifth, elevenths, seventeenths, twenty-thirds have the same sequences but opposite to that of fundamentals.The third, ninth and all multiples of the third will be found to be in phase.

Eba is 30 degree ahead of ena. For the third harmonic, eba3=0. fifth, eba5 lags ena5 by 30 degree.

nabnba eee

907sin3

905sin390sin3

1507sin3

1505sin3150sin3

307sin3

305sin330sin3

77

551

77

551

77

551

tE

tEtEe

tE

tEtEe

tE

tEtEe

m

mmba

m

mmac

m

mmba

Page 21: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Harmonics in balanced three phase wye loads

23

22

72

52

1

27

25

23

21

mmmba

mmmmna

EEEE

EEEEE

Page 22: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Unbalanced system

Page 23: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

An unbalanced system is due to unbalanced voltage sources or unbalanced load. In a unbalanced system the neutral current is NOT zero.

Unbalanced three phase Y connected load.

Line currents DO NOT add up to zero.

In= -(Ia+ Ib+ Ic) ≠ 0

Page 24: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree
Page 25: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

4.2326.9

1205

9.15620

1.5310

6.8650120100

6.8650120100

0100

acabaa

ca

caca

bc

bcbc

ab

abab

bc

bc

ab

III

Z

VI

Z

VI

Z

VI

jV

jV

jVExam-1

Page 26: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

5029

21

82

249

21

82

1819

21

82

2401000866500

1201000866500

0100001000

jZ

jZ

ohmsjZ

jZ

jZ

ohmsjZ

jZ

jZ

ohmsjZ

voltsjE

jE

jE

nc

cc

nc

nb

bb

nb

na

aa

na

nc

nb

na

nbnabnnaba

naaana

bb

ncnb

cnnbbbc

nbna

bnnabba

c

b

a

VVVVV

ZIV

III

EE

EEIZIZZ

EE

EEIZIZZ

Z

Z

j

jjjZ

21

12

21

9.610.68

8.86.52

8.516.352822

18192182

Exam-3

Page 27: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

The Wye-Wye system with neutral connection

cnlg

nnncncc

bnlg

nnnbnbb

anlg

nnnanaa

ZZZ

ZIEI

ZZZ

ZIEI

ZZZ

ZIEI

nnc

nnncn

b

nnnbn

a

nnnan

nnccbbaa

IZ

ZIE

Z

ZIE

Z

ZIE

IIII

Page 28: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Methods of checking voltage phase sequence

bcbncnbnancn

bccncnbnbn

abbnbnanan

cnbnan

VIZZIZ

VIZIZ

VIZIZ

III

0

The voltage across a lamp

cnbncnbnan

bnbccnbnabananan ZZZZZ

ZVZZVZIZ

|

The voltage across “c” lamp

anancacncn IZVIZ

Page 29: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Example:5

volts

IZ

volts

IZ

V

V

V

cncn

anan

ca

bc

ab

55.712.23

45.483.86240100

45.484.86

45.6322380

90100120100454.14101000100

240100

120100

0100

Page 30: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Two wattmeter method

W1 reads cosaab IV

W2 reads coscbc IV

Page 31: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Three Phase Power Measurement Three-wattmeter method for measuring three-phase power

dtivivivT

P

dtiiivT

dtivivivT

P

vvv

vvv

vvv

dtivivivT

P

dtivivivT

P

T

cccnbbbnaaanmeter

T

ccbbaan

T

cccnbbbnaaanmeter

ncnc

nbnb

nana

T

cccbbbaaameter

T

cccnbbbnaaanabc

0

0 0

0

00

00

00

0 000

0

1

1

1

1

1

Page 32: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Power factor in unbalanced three phase system

coscos

coscos

sintancos

cossin

..........sinsinsinsin

..........coscoscoscos

cossin

cos

1

22

22

VIofmagnitude

VIfactorpowerVector

VI

VIfactorpowerVector

IVIVIVVI

VIVIVI

IVIVIVVI

IVIVIVVI

VIVI

VIfactorpowerVector

cccbbbaaa

cccbbbaaa

cccbbbaaa283vars

283 watts

Phase a

a

-433vars

250 watts

Phase c

c

200 watts

Phase b0b

cosVI

sinVIVI

Page 33: Balanced poly phase circuits. Two and four phase systems  A two phase system is an electrical system in which the voltages of the phases are 90 degree

Example:11

ampII

ohmsZZ

ohmsZ

ohmsZ

EEEIZIZ

EEEIZIZ

E

E

Egiven

an

bnnc

annb

cn

bn

an

45.48864.0

454.141

90100

90100

454.141

454.141

90100

120100

0100

90100

454.141010090100

454.141901000100

120100

0100

907.57

1507.57

307.57

1

2112

22

11

2222121

1212111