1-sistem tiga fasa
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Three Phase Circuits
Overview• Perusahaan Listrik memasok
konsumen dalam bentuk tegangan dan arus sinusoidal
• Terdapat keuntungan secara teknis dan ekonomis pembangkitan dan penyaluran tenaga listrik menggunakan sistem tiga fasa
• Beberapa peralatan listrik seperti motor-motor besar membutuhkan suplai tiga fasa untuk pengoperasiannya
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 ).
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