Download Balanced 3-phase systems

Three-phase Circuits
Balanced 3-phase systems
Unbalanced 3-phase systems
SKEE 1043 Circuit Theory
Dr. Nik Rumzi Nik Idris
1
Balanced 3-phase systems
Single-phase two-wire system:
•
Single source connected to a
load using two-wire system
Single-phase three-wire system:
•
•
Two sources connected to two
loads using three-wire system
Sources have EQUAL
magnitude and are IN PHASE
2
Balanced 3-phase systems
Balanced Two-phase three-wire system:
•
•
Two sources connected to two
loads using three-wire system
Sources have EQUAL
frequency but DIFFFERENT
phases
Balanced Three-phase four-wire system:
•
•
Three sources connected to 3
loads using four-wire system
Sources have EQUAL
frequency but DIFFFERENT
phases
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Balanced 3-phase systems
WHY THREE PHASE SYSTEM ?
•
ALL electric power system in the world used 3-phase system to
GENERATE, TRANSMIT and DISTRIBUTE
•
Instantaneous power is constant – thus smoother rotation of
electrical machines
•
More economical than single phase – less wire for the same power
transfer
•
To pass SKEE 1043 – to be able to graduate !
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Balanced 3-phase systems
Generation of 3-phase voltage: Generator
SEE VIDEO
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Balanced 3-phase systems
Generation, Transmission and Distribution
6
Balanced 3-phase systems
Generation, Transmission and Distribution
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Balanced 3-phase systems
Y and  connections
Balanced 3-phase systems can be considered as 3 equal single phase
voltage sources connected either as Y or Delta () to 3 single three loads
connected as either Y or 
SOURCE CONNECTIONS
LOAD CONNECTIONS
Y connected source
Y connected load
 connected source
 connected load
Y-Y
Y-
-Y
-
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Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection
a
Van
v an(t)  2Vp cos(t)
+

o
vbn(t)  2Vp cos(t  120o ) Vbn  Vp  120
n
Vcn
b
Vbn
o
 Van  Vp0
v cn(t)  2Vp cos(t  120o ) Vcn  Vp120o
RMS phasors !
c
240o
120o
Van
Vbn
Vcn
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Balanced 3-phase systems
Source : Y connection
Vcn  Vp120o
a
Van
SOURCE CONNECTIONS
+

120o
n
Vcn
Vbn
Van  Vp0o
120o
120o
b
c
Vbn  Vp  120o
Phase sequence : Van leads Vbn by 120o and Vbn leads Vcn by 120o
This is a known as abc sequence or positive sequence
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Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection
a
Van
v an(t)  2Vp cos(t)
+

o
 Van  Vp0
o
v cn(t)  2Vp cos(t  120o ) Vcn  Vp  120
n
Vcn
vbn(t)  2Vp cos(t  120o ) Vbn  Vp120o
b
Vbn
RMS phasors !
c
120o
Van
240o
Vcn
Vbn
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Balanced 3-phase systems
Source : Y connection
Vbn  Vp120o
a
Van
SOURCE CONNECTIONS
+

120o
n
Vcn
Vbn
Van  Vp0o
120o
b
c
120o
Vcn  Vp  120o
Phase sequence : Van leads Vcn by 120o and Vcn leads Vbn by 120o
This is a known as acb sequence or negative sequence
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Balanced 3-phase systems
SOURCE CONNECTIONS
Source :  connection
a
o
 Vab  Vp0
o
vbc (t)  2Vp cos(t  120o ) Vbc  Vp  120
Vab
Vca
v ab (t)  2Vp cos(t)
+

b
v ca(t)  2Vp cos(t  120o ) Vca  Vp120o
Vbc
RMS phasors !
c
120o
240o
Vab
Vbc
Vca
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Balanced 3-phase systems
LOAD CONNECTIONS
 connection
Y connection
a
a
Z1
Zb
Zc
n
b
Z2
b
Z3
Za
c
c
Balanced load:
Z 1 = Z 2 = Z3 = ZY
Z a = Z b = Zc = Z
ZY 
Z
3
Unbalanced load: each phase load may not be the same.
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Balanced 3-phase systems
Ia
A
a
Van
Vcn
+

In
Ia 
Ib 
Ic 
b Ic
ZY
B
Vp0o
ZY
Phase
voltages
Vcn  Vp120o
ZY
C
Vab  Van  Vnb
 Vp 0o  Vp 60o
ZY
Vp  120o
Vbn  Vp  120o
N
Ib
Vbn
Van  Vp0o
ZY
n
c
Balanced Y-Y Connection
line
currents
Vp120o
ZY
Ia  Ib  Ic  In  0
The wire connecting n and N can be removed !
 3 Vp 30o
Vbc  Vbn  Vnc
 3 Vp  90o
Vca  Vcn  Vna
 3 Vp150o
line-line
voltages
OR
Line
voltages
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Balanced 3-phase systems
Balanced Y-Y Connection
Vab  Van  Vnb
 Vp 0o  Vp 60o
 3 Vp 30o
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Balanced 3-phase systems
Vab  Van  Vnb
 Vp 0o  Vp 60o
Balanced Y-Y Connection
Vcn
Van
 3 Vp 30o
Vbn
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Balanced 3-phase systems
Balanced Y-Y Connection
Vab  Van  Vnb
 Vp 0o  Vp 60o
 3 Vp 30
o
Van
Vnb
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Balanced 3-phase systems
Balanced Y-Y Connection
Vab  Van  Vnb
 Vp 0o  Vp 60o
 3 Vp 30
Van
o
Vnb
Vbn
Vbc  Vbn  Vnc
 3 Vp  90o
Vnc
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Balanced 3-phase systems
Balanced Y-Y Connection
Vna
Vab  Van  Vnb
Vcn
 Vp 0o  Vp 60o
 3 Vp 30
Van
o
Vnb
Vbn
Vbc  Vbn  Vnc
 3 Vp  90o
Vnc
Vca  Vcn  Vna
 3 Vp150o
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Balanced 3-phase systems
Balanced Y-Y Connection
Vca
Vab  Van  Vnb
 Vp 0o  Vp 60o
Vab
30o Vcn
30o
Van
 3 Vp 30o
Vbn
Vbc  Vbn  Vnc
30o
 3 Vp  90o
Vbc
Vca  Vcn  Vna
 3 Vp150o
VL  3 Vp
where
VL  Vab  Vbc  Vca
and Vp  Van  Vbn  Vcn
Line voltage LEADS phase voltage by 30o
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Balanced 3-phase systems
Balanced Y-Y Connection
For a balanced Y-Y connection, analysis can be performed using an
equivalent per-phase circuit: e.g. for phase A:
Ia
A
a
Van
Vcn
+

ZY
In=0
N
n
Ib
c
Vbn
b Ic
ZY
B
ZY
C
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Balanced 3-phase systems
Balanced Y-Y Connection
For a balanced Y-Y connection, analysis can be performed using an
equivalent per-phase circuit: e.g. for phase A:
Ia
A
a
Van
+

ZY
N
n
Ia 
Van
ZY
Based on the sequence, the other line currents can be
obtained from:
Ib  Ia   120o
Ic  Ia120o
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Balanced 3-phase systems
Balanced Y- Connection
Ia
a
Van
Vcn
A
+

Z
n
Ib
c
Vbn
 VAB
Vbc  3 Vp  90
B
o
IBC 
 VBC
Vca  3 Vp150o
ICA 
VBC
Z
VCA
Z
Vbn  Vp  120o
Z
IAB Z
IBC
b Ic
V
IAB  AB
Z
Vab  3 Vp30o
 VCA
Van  Vp0o
C
ICA
Using KCL,
Vcn  Vp120o
Ia  IAB  ICA
 IAB(1  1120o )
 IAB 3  30o
Phase
currents
Ib  IBC  IAB
 IBC (1  1120o )
 IBC 3  30o
Ic  ICA 3  30o
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Balanced 3-phase systems
Balanced Y- Connection
Ic
ICA
30o
30o
IBC
Ib
IL  3Ip
IAB
Ia  IAB  ICA
30o
 IAB(1  1120o )
 IAB 3  30o
Ia
Ib  IBC  IAB
 IBC (1  1120o )
 IBC 3  30o
and Ip  IAB  IBC  ICA o
where IL  Ia  Ib  Ic
Ic  ICA 3  30
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Phase current LEADS line current by 30o
Balanced 3-phase systems
Balanced - Connection
Ia
a
Vab  Vp0o
A
Vca
Vab
Ib
+

c
Vbc
Vab  VAB
Vbc  VBC
Vca  VCA
Z
B
Z
IAB Z
IBC
b Ic
V
IAB  AB
Z
IBC 
ICA 
VBC
Z
VCA
Z
Vbc  Vp  120o
Using KCL,
C
ICA
Vcn  Vp120o
Ia  IAB  ICA
 IAB(1  1120o )
 IAB 3  30o
Phase
currents
Ib  IBC  IAB
line
currents
 IBC (1  1120o )
 IBC 3  30o
Ic  ICA 3  30o
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Balanced 3-phase systems
Balanced - Connection
Ia
a
Vab  Vp0o
A
Vca
Z
Ib
+

c
Vab
Vbc
b Ic
B
Vbc  Vp  120o
Z
IAB Z
IBC
C
ICA
Vcn  Vp120o
Alternatively, by transforming the  connections to the equivalent Y
connections per phase equivalent circuit analysis can be performed.
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Balanced -Y Connection
Balanced 3-phase systems
Ia
A
a
Vca
N
Ib
Vbc
ZY
 I a  Ib 
Vab
ZY
B
b Ic
Loop1 - Vab  Z YIa  Z YIb  0
Since circuit is balanced, Ib = Ia-120o
Ia 
Vp
ZY
3
Vca  Vp120o
ZY
How to find Ia ?
Therefore
Vbc  Vp  120o
ZY
Loop1
+

c
Vab
Vab  Vp0o
C
 Ia  Ib  Ia (1  1( 120o ))
 Ia 330o
  30o
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Balanced -Y Connection
Balanced 3-phase systems
Ia
A
a
Vca
N
Ib
Vbc
Vbc  Vp  120o
ZY
Vab
+

c
Vab  Vp0o
b Ic
ZY
B
Vca  Vp120o
ZY
C
How to find Ia ? (Alternative)
Transform the delta source connection to an equivalent Y and then
perform the per phase circuit analysis
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