Three Phase Circuits

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SISTEM INSTALASI LISTRIK KONSUMEN

APP - TM

KUBIKEL TM KUBIKEL TRTRAFO

PANEL HUBUNG BAGI CABANG

PERUSAHAANPENYEDIA

TENAGA LISTRIK(PLN)

INSTALASI LISTRIK KONSUMEN

Single Phase Three-Wire Systems

Z1

Z1

a A

n

bB

N

V1

V1

Z1

Z1

a A

n

bB

N

V1

V1

1

1 1

anaA

V VIZ Z

1

1 1

bnbB aA

V VI IZ Z

0nN aA bBI I I

Z1

Z1

aA

n

b B

N

V1

V1

Z3

Z2

Z2

Z4

IaA

IbB

I3

1 2 3 3 1 3 1aA bBZ Z Z I Z I Z I V

3 1 2 3 1 3 1aA bBZ I Z Z Z I Z I V + 1 2 3 3 0aA bB aA bBZ Z Z I I Z I I

0aA bBI I or

115Ð0

115Ð0

39 W

1 W

1 W

47 W

j W

j W

2 W

a A

n

b B

N

I1

I2

Example

Find I1, I2 and InN !

1

2

42 2 115 02 50 115 0

o

o

IjIj

Ð Ð

42 50 4 2097 2,51oj j Ð

1

2

50 2 1 2,85 1, 41115 02 42 1 2, 41 1, 21

oo

o

I jI j

Ð Ð Ð

The determinant is

Solving by matrix inversion

SISTEM TIGA FASA

N

C

B

A

a

bc

n

FASOR SISTEM 3 FASA

V a n

V bn

V cn - V bn

V ab

V ab = V an - V b n

V ab = 3 V an Ð3 0 o

3 0 o

0

120

120

oan p

obn p

ocn p

V V

V V

V V

Ð

Ð

Ð

0

120

120

oan p

obn p

ocn p

V V

V V

V V

Ð

Ð

Ð

Positive or abc sequence

Negative or acb sequence

0an bn cnV V V

100 0anV Ð

100 120bnV Ð

a

bn

Vbn

Vnb

Van

Vab

Three-Phase Wye-Wye Systems

Zl

Zl

Zl

ZL

ZL ZL

a

n

bc

A

B C

N

Van

Vbn

Vcn

n N

o o

o

o

o

o

a A

b B

c C

ZPZL

ZL

ZL

ZP

ZP

ZN

120 120

120 120

anaA

P

oobn an

bB aAP P

oocn an

cC aAP P

VIZ

V VI IZ Z

V VI IZ Z

Ð Ð

Ð Ð

0nN aA bB cCI I I I

120 120

120 120

aA L P

o obB L P

o ocC L P

I I I

I I I

I I I

Ð Ð

Ð Ð

Ð Ð

cosp p pP V I 3 pP P

| | 0 | | 120

| | 1 (cos120 sin120)

1 3| | | |2 2

3 | | 30

ab an bn

p p

p

p p

p

V V VV V

V j

V V j

V

Ð Ð

Ð

Ð

Ð

210||3

90||3

pca

pbc

VV

VV

VoltageLine ||3 pL VV

Delta ConnectionZl

Zl

Zl

a

bc

A

B CZL

ZLZ L

+

+

+

_

_

_

L PV V 3 L PI I

3 cosL LP V I

Wye-Delta Transformations

YRRR

RRR

RRRRRR

RRRRRR

c

b

a

321

13

321

32

321

21

YR

RRRRRRR

RRRRRRRR

RRRRRRRR

a

accbba

c

accbba

b

accbba

3

2

1

230Ð0

230Ð0

21 W

3 W

3 W

21 W

3 W

a A

n

b B

N

-j4 W

-j4 W

Find the currents IaA, IbB, and InN in this symetric single phase three wire systems. Sketch in phasor diagram !

Van

Vbn

Vcn

n

o

o

o

a A

bB

c

C

ZP

ZP

ZP

o

o

o

In the Wye-Delta system shown, the source is positive sequence with Van = 100 Ð0 Vrms and the phase impedance is Zp = 3 – j4 W. Find the line voltage VL, the line current IL and the power delivered to the load !

• A balanced three-phase, positive sequence source with Vab = 200Ð0 V rms is supplying a ∆-connected load, ZAB = 50 Ω, ZBC = 20 + j20 Ω, ZCA = 30 – j40 Ω. Find the line current (IaA , IbB , IcC ).