Balanced Three Phase System
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Transcript of Balanced Three Phase System
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Balanced Three-Phase System
EE 103 CIRCUITS 3
by:Cesar G. Manalo, Jr.
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Objectives
Construct the circuit and phasor diagram of a three-
phase system with a balanced wye- and/or delta-
connected load.
Solve for the phase and line current/voltage of a three-phase system with balanced wye- and/or delta-
connected load.
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Balanced Three-Phase Load
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Balanced 3-Phase Loads
A 3-phase load is said to bebalanced, if all phase impedances
(load) are equal, otherwise, they
are unbalanced.
In a Y-connected load, the phaseimpedances or loads are
connected to a common point.
Za
Zc
Zb
3-phase Y-connected
Balanced Load, ZA= ZB= ZC
3-phaserectifier
3-phase induction motor
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Balanced 3-Phase Loads
Za
Zc
Zb
3-phase Y-connectedBalanced Load, Za= Zb= Zc
Va
VbVc
A
B
C
VAB
VBC
VCAn
3-phase Y-connected sourceor generator
Balanced 3-phase 3-wire Y-Y Circuit with Balanced 3-phase source
ZT
ZT
ZT
Transmission line
Za
Zc
Zb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
Va
VbVc
A
B
C
VAB
VBC
VCAn
3-phase Y-connected source
or generatorTransmission line
+-
+
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Balanced 3-Phase Loads
Za
Zc
Zb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
Va=VAn
Vb=VBnVc=VCn
A
B
C
VAB
VBCVCA
n
3-phase Y-connected source
or generatorTransmission line
Ia
IbIc
IA
IB
IC
IN Ia
IbIc
Va
Vb Vc
Balanced 3-phase 4-wire Y-Y Circuit with Balanced 3-phase source
+
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Illustrative Problem 1
A 3-phase Y-connected load with phase impedance Z = 150 + j270
is connected to the secondary of a Y-connected transformer with a110-V phase voltage. Find,
a) The line voltages
b) Line currents IA, IB, ICassuming V2a= 110
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Illustrative Problem 1
a) Repeat a) if neutral of load is connected to neutral of source.
Za
Zc
Zb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
A
B
C
VAB
VBC
VCA
IA
IB
IC
Ia
Ib Ic
Va
Vb Vc
3-phase transformer
IN
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Per Phase Analysis
Za
ZcZb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
IA
IB
IC
IN = 0 Ia
IbIc
Va
Vb Vc
VAB
VBC
VCA
A
B
C
NZ
a
IA
IN = 0Ia Va
Va=VAB/1.73
A
NPer phase analysis using phase A
Zb
IB Vb
IN = 0
B
N
Vb=VBC/1.73
Ib
Per phase analysis using phase
B
Zc
C
N
VC=VCA/1.73IC
Ic
Vc
Per phase analysis using phase C
n
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Per Phase Analysis
Za
ZcZb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
IA
IB
IC
IN = 0 Ia
IbIc
Va
Vb Vc
VAB
VBC
VCA
A
B
C
N
Za
IA
IN = 0Ia Va
Va=VAB/1.73
A
N
Per phase analysis using phase A
Zb
IB Vb
IN = 0
B
N
Vb=VBC/1.73
Ib
Per phase analysis using phase B
Zc
C
N
VC=VCA/1.73IC
Ic
Vc
Per phase analysis using phase C
n
A per phase analysis can be done on a balanced 3-phase system.
In a balance 3-phase 4-wire system, the magnitude of the current
on the neutral line is zero.
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Illustrative Problem 2
Repeat Illustrative problem # 1 using per phase analysis.
Za
Zc
Zb
3-phase Y-connected
Balanced Load, Za= Zb= Zc
A
B
C
VAB
VBC
VCA
IA
IB
IC
Ia
Ib Ic
Va
Vb Vc
3-phase transformer
impedance Z = 150 + j270
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Illustrative Problem No. 3
a
bc
A
B
C
230 V
N
IA
IB
IC
Ia
IbIc
Z
Z
Z
230 V 230 V
3-phase Alternator
Balance3-phase load,Z : R = 75, XL= 50
A balance 3-phase load is connected to a 3-phase alternator with
line-to-line voltage of 230 volts. Find:a) Load phase currents
b) Load line currents
c) Phasor diagram of phase and line currents.
+
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Balanced 3-Phase Loads
A
B
C
230 V
IA
IB
IC
Z
230 V
230 V
Balance3-phase
load,
Z : R = 75, XL= 50
Z
Z
IAB
IBC
ICA
Let:
VAB= 230 30o
VBC= 230 -90oVCA= 230 150
o
14.90)50()75( 22 Z
69.33
75
50tan 1
AIII CABCAB 55.214.90
230
for balance 3-phase load
Since Z is inductive, the load phase currents
will lag the line voltages by 33.69o. Hence,
69.355.2)69.3330(55.2AB
I
69.12355.2)69.3390(55.2BCI
116.3155.2)69.33150(55.2CA
I
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Balanced 3-Phase Loads
69.355.269.333055.2AB
I
69.12355.2)69.3390(55.2BCI
116.3155.2)69.33150(55.2CA
I
33.69o
33.69o
IAB
IBC
ICA
)(CAABCAABA
IIIII
)(ABBCABBCB
IIIII
)(BCCABCCAC
IIIII
IA
IB
IC
33.69o
86.31o
153.69o AI
III
AB
CBA
41.4)55.2(73.173.1
VABVCA120o
120o 120o
VBC
30o
(equal in RMS value but not
in phase)
IA
IB
IC
Z
Balance3-phase load, Z : R = 75, XL= 50
Z
Z
IAB
IBC
ICA
69.33
Vector calculator
http://www.1728.org/vectors.htmhttp://www.1728.org/vectors.htm -
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Assignment 1
a
bc
A
B
C
230 V
N
IA
IB
IC
Ia
IbIc
Z
Z
Z
230 V 230 V
3-phase Alternator
Balance3-phase load,
Z = 75+j 50 ZT= 0.3 + j0.4
A balance Y-connected 3-phase load is connected to a 3-phase alternator withline-to-line voltage of 230 volts. Using mesh and per phase methods, find:
a) Load phase currents
b) Load line currents
c) Phasor diagram of phase voltage and phase currents and line currents
Let:
VAB= 230 30o
VBC
= 230 -90o
VCA= 230 150o
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ZT
ZT
ZT
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Power and Power Measurement in
Balanced Three-Phase Load