Balanced 3-phase systems
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Transcript 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
3
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 !
4
Balanced 3-phase systems
Generation of 3-phase voltage: Generator
SEE VIDEO
5
Balanced 3-phase systems
Generation, Transmission and Distribution
6
Balanced 3-phase systems
Generation, Transmission and Distribution
7
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
-
8
Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection
a
Van
v an ( t )
+
n
Vcn
b
Vbn
o
Van Vp 0
2 Vp cos( t )
v bn ( t )
2 Vp cos( t 120 )
V bn Vp 120
v cn ( t )
2 Vp cos( t 120 )
Vcn Vp 120
o
o
o
RMS phasors !
c
240o
120o
Van
o
Vbn
Vcn
9
Balanced 3-phase systems
Source : Y connection
Vcn Vp 120
a
Van
SOURCE CONNECTIONS
+
o
120o
n
Vcn
Vbn
V an Vp 0
120o
120o
b
c
V bn Vp 120
o
Phase sequence : Van leads Vbn by 120o and Vbn leads Vcn by 120o
This is a known as abc sequence or positive sequence
10
o
Balanced 3-phase systems
SOURCE CONNECTIONS
Source : Y connection
a
Van
v an ( t )
+
v cn ( t )
o
Van Vp 0
2 Vp cos( t )
2 Vp cos( t 120 )
o
Vcn Vp 120
o
n
Vcn
v bn ( t )
o
2 Vp cos( t 120 ) V bn Vp 120
b
Vbn
RMS phasors !
c
120o
Van
o
240o
Vcn
Vbn
11
Balanced 3-phase systems
Source : Y connection
V bn Vp 120
a
Van
SOURCE CONNECTIONS
+
o
120o
n
Vcn
Vbn
V an Vp 0
120o
b
c
120o
Vcn Vp 120
o
Phase sequence : Van leads Vcn by 120o and Vcn leads Vbn by 120o
This is a known as acb sequence or negative sequence
12
o
Balanced 3-phase systems
SOURCE CONNECTIONS
Source : connection
a
v bc ( t )
Vab
Vca
v ab ( t )
+
b
v ca ( t )
o
Vab Vp 0
2 Vp cos( t )
o
2 Vp cos( t 120 ) Vbc Vp 120
2 Vp cos( t 120 )
o
Vca Vp 120
o
o
Vbc
RMS phasors !
c
120o
240o
Vab
Vbc
Vca
13
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.
14
Balanced 3-phase systems
Ia
A
a
Van
Vcn
V an Vp 0
+
In
N
n
V cn V p 120
c
Vbn
Ib
Ic
o
V bn V p 120
ZY
Ib
Ia
Balanced Y-Y Connection
Vp 0
b Ic
ZY
o
C
V ab V an V nb
ZY
V p 0 V p 60
o
V p 120
o
ZY
V p 120
Phase
voltages
ZY
B
o
o
line
currents
o
3 V p 30
o
Vbc Vbn Vnc
3 Vp 90
ZY
Ia Ib Ic In 0
The wire connecting n and N can be removed !
V ca V cn Vna
o
3 Vp 150
o
o
line-line
voltages
OR
Line
voltages
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Balanced 3-phase systems
Balanced Y-Y Connection
V ab V an V nb
V p 0 V p 60
o
3 V p 30
o
o
16
Balanced 3-phase systems
Balanced Y-Y Connection
V ab V an V nb
V p 0 V p 60
o
3 V p 30
o
V cn
V an
o
Vbn
17
Balanced 3-phase systems
Balanced Y-Y Connection
V ab V an V nb
V p 0 V p 60
o
3 V p 30
o
o
V an
Vnb
18
Balanced 3-phase systems
Balanced Y-Y Connection
V ab V an V nb
V p 0 V p 60
o
3 V p 30
o
V an
o
Vnb
Vbn
Vbc Vbn Vnc
3 Vp 90
o
Vnc
19
Balanced 3-phase systems
Balanced Y-Y Connection
Vna
V ab V an V nb
V p 0 V p 60
o
3 V p 30
V cn
o
V an
o
Vnb
Vbn
Vbc Vbn Vnc
3 Vp 90
o
Vnc
V ca V cn Vna
3 Vp 150
o
20
Balanced 3-phase systems
V ca
V ab V an V nb
V p 0 V p 60
o
3 V p 30
Balanced Y-Y Connection
o
V ab
30
o
V cn
o
30
V an
Vbn
Vbc Vbn Vnc
30
3 Vp 90
3 Vp 150
o
o
Vbc
V ca V cn Vna
o
o
VL
where
VL V ab V bc V ca
3 Vp
and V p V an Vbn V cn
Line voltage LEADS phase voltage by 30o
21
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
22
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
V an
ZY
Based on the sequence, the other line currents can be
obtained from:
I b I a 120
o
I c I a 120
o
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Balanced 3-phase systems
Balanced Y- Connection
Ia
a
Van
A
+
Z
n
Vcn
Ib
c
Vbn
V ab
3 V p 30
o
B
b Ic
I AB
3 Vp 90
3 Vp 150
V CA
C
I CA
V cn V p 120
V AB
Using KCL,
o
o
o
o
Ia I AB ICA
I AB (1 1 120 )
o
Z
I AB
I BC
VBC
V ca
V bn V p 120
Z
I AB Z
o
IBC
V AB
Vbc
V an Vp 0
ICA
V BC
Z
V CA
Z
Phase
currents
3 30
o
Ib IBC I AB
IBC (1 1 120 )
o
IBC
3 30
o
Ic ICA
3 30
o
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Balanced 3-phase systems
Balanced Y- Connection
Ic
ICA
30
o
I AB
30
Ib
Ia I AB ICA
o
30
o
I AB (1 1 120 )
o
I AB
IBC
Ib IBC
IL
IL I a I b I c
o
IBC (1 1 120 )
o
3 Ip
IBC
where
3 30
Ia
I AB
and
3 30
o
Ip I AB I BC I CA o
Ic ICA 3 30
Phase current LEADS line current by 30o
25
Balanced 3-phase systems
Balanced - Connection
Ia
a
V ab V p 0
A
Vca
Vab
Ib
+
c
Vbc
V ab V AB
Z
B
b Ic
I AB
V bc V p 120
Z
I AB Z
C
I CA
Vbc VBC
V ca V CA
ICA
V cn V p 120
o
o
IBC
V AB
Using KCL,
Ia I AB ICA
I AB (1 1 120 )
o
Z
I AB
I BC
o
V BC
Z
V CA
Z
Phase
currents
3 30
o
line
currents
Ib IBC I AB
IBC (1 1 120 )
o
IBC
3 30
o
Ic ICA
3 30
o
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Balanced 3-phase systems
Balanced - Connection
Ia
a
V ab V p 0
A
Vca
Z
Ib
+
c
Vab
Vbc
b Ic
B
V bc V p 120
Z
I AB Z
o
C
I CA
V cn V p 120
o
o
IBC
Alternatively, by transforming the connections to the equivalent Y
connections per phase equivalent circuit analysis can be performed.
27
Balanced -Y Connection
Balanced 3-phase systems
Ia
A
a
V ab V p 0
Vca
N
Ib
Vbc
V bc V p 120
ZY
Loop1
+
c
Vab
ZY
V ca V p 120
ZY
B
b Ic
o
o
o
C
How to find Ia ?
Ia Ib
Loop1 - V ab Z Y I a Z Y I b 0
Since circuit is balanced, Ib = Ia-120o
V ab
ZY
I a I b I a (1 1 ( 120 ))
o
Ia
Therefore
Ia
Vp
3
30
3 30
o
o
ZY
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Balanced -Y Connection
Balanced 3-phase systems
Ia
A
a
V ab V p 0
Vca
N
Ib
+
c
Vbc
V bc V p 120
ZY
Vab
b Ic
ZY
B
o
V ca V p 120
ZY
o
o
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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