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Copyright © 2017 Hassan Sowidan
ECE 330
POWER CIRCUITS AND ELECTROMECHANICS
LECTURES 4 AND 5
THREE-PHASE CONNECTIONS (1)
Acknowledgment-These handouts and lecture notes given in class are based on material from Prof. Peter
Sauer’s ECE 330 lecture notes. Some slides are taken from Ali Bazi’s presentations
Disclaimer- These handouts only provide highlights and should not be used to replace the course textbook.
9/4/2017
Copyright © 2017 Hassan Sowidan
WHY THREE-PHASE?
• Most effective in terms of equipment and wires.
• Produces smooth rotating magnetic field.
• Constant instantaneous power.
9/4/2017 2
Copyright © 2017 Hassan Sowidan
THREE-PHASE VOLTAGES
• The three phases are usually referred to as abc.
• Another standard notation is RYB (Red-Yellow-Blue).
• Voltages:
– Same magnitude.
– Same frequency.
– Out of phase by 120o.
9/4/2017 3
a
a'
+
-
b
b'
+
-
c
c'
+
-
Copyright © 2017 Hassan Sowidan
THREE-PHASE VOLTAGES
• Positive-sequence voltages are most common (abc).
• Negative-sequence voltages, flip b and c (acb).
9/4/2017 4
'
'
'
( ) cos ( )
( ) cos ( 120 )
( ) cos ( 120 )
aa m
o
bb m
o
cc m
v t V t
v t V t
v t V t
'
'
'
02
1202
1202
omaa
ombb
omcc
VV
VV
VV
'
'
'
( ) cos( )
( ) cos( 120 )
( ) cos( 120 )
aa m
o
bb m
o
cc m
v t V t
v t V t
v t V t
'
'
'
02
1202
1202
omaa
ombb
omcc
VV
VV
VV
Copyright © 2017 Hassan Sowidan
THREE-PHASE VOLTAGES
• If phase a has angle θv , the positive sequence is (you
practice the negative sequence):
• Phasor representation:
9/4/2017 5
'
'
'
( ) cos( )
( ) cos( 120 )
( ) cos( 120 )
aa m v
o
bb m v
o
cc m v
v t V t
v t V t
v t V t
'
'
'
2
1202
1202
maa v
ombb v
omcc v
VV
VV
VV
Vaa’
Vbb’
Vcc’
-120o
+120o
+θv
Positive
Sequence
Vaa’
Vcc’
Vbb’
-120o
+120o
+θv
Negative
Sequence
Copyright © 2017 Hassan Sowidan
THREE-PHASE CONNECTIONS
• In general, positive sequence is used unless
otherwise specified.
• Two main connections:
– Wye (Y)
– Delta (Δ)
9/4/2017 6
a
a’
+-
b’ b
+-
c’
c
+
-
Delta
Connection
b
-+
c +-
a
n
+
- Y
Connection
Copyright © 2017 Hassan Sowidan
PHASE AND LINE
• Phase voltage (Vø) and phase current (Iø) are
defined across an element:
• Line-to-line (or line) voltage (Vll) and line current
(Il) are defined on the line:
9/4/2017 7
+
Vφ
-
Iφ
Load
Iφ
Source
+
Vφ
-
+
-
Il+
Vll
-
+
Vll
-
+
Vll
-
Il
Il
a
b
c
Copyright © 2017 Hassan Sowidan
THREE-PHASE CONNECTION
WYE CONNECTION:
The three windings are represented by coils. In the wye
connection, terminals , , and are joined and
labeled as terminal , also called the neutral terminal
9/4/2017 8
a b c
n
Copyright © 2017 Hassan Sowidan
THREE-PHASE CONNECTION
DELTA CONNECTION:
In the delta connection, terminal is connected to , and
to Finally, can be connected to terminal .
The voltage across and is
identically equal to zero
9/4/2017 9
a
= ( ) ( ) ( )ac aa bb ccv v t v t v t
c
b
c
b
a
Copyright © 2017 Hassan Sowidan
Y-CONNECTION
• Voltages can be line-to-line (Vll) or line-to-neutral (Vln).
• Currents can be line (Il) or phase (Iø).
• Line-to-line voltages can be referred to as line
voltages (Vl).
• Line-to-neutral voltages can be referred to as phase
voltages (Vø).
9/4/2017 10
Copyright © 2017 Hassan Sowidan
Y-CONNECTION
• Line-to-line voltages are vab , vbc , and vca .
• Line-to-neutral voltages are van , vbn , and vcn which
are also
• Example: and so on.
9/4/2017 11
0 , 120 , 120 .o o o
an bn cnV V V V V V
b
-+
c +-
a
n
+
-
ia
in
ibic
van
vbn
vcn
ab an bnV V V
bc bn cnV V V
c a cn anV V V
Copyright © 2017 Hassan Sowidan
Y-CONNECTION
• Thus:
9/4/2017 12
0 120
120 120
120 0
o o
ab
o o
bc
o o
ca
V V V
V V V
V V V
Vab
Vbc
Vca
+30o
Vbn
Van
Vcn
| | 3 | |ll
l
V V
I I
3 30
3 90
3 150
o
ab
o
bc
o
ca
V V
V V
V V
Copyright © 2017 Hassan Sowidan
Y OR ∆ CONNECTION?
In distribution, the secondary winding is often in wye,
as it provides a neutral for single or three phase loads.
The primary is often in delta, as it allows 3rd
harmonics to flow within the transformer and prevent
it flowing into the supply.
9/4/2017 14
Copyright © 2017 Hassan Sowidan
Y OR ∆ CONNECTION?
• In Y connection, voltage across each coil is smaller than the
line voltage, so it is preferable where high line voltage are
used as in high voltage power systems, to protect coils from
high voltage.
• In delta connection current passing through coils are smaller
than line currents, therefore coils can be rated for smaller
current.
9/4/2017 15
Copyright © 2017 Hassan Sowidan
Y-SOURCE, Y-LOAD
9/4/2017 16
: 0 3
an a n n
bn b n n
cn c n n
a b c n n
V I Z I Z
V I Z I Z
V I Z I Z
add I I I Z I Z
-++
-
+
-
nL
Z
Z Z
Zn
Ia
IbIc
In
+
Van
--
Vbn+ -
V cn
+
n
,
3 0
0
, ,
a b c n
n n
n
an bn cna b c
but by KCL I I I I
I Z Z
I
V V VI I I
Z Z Z
Copyright © 2017 Hassan Sowidan
Y-SOURCE, Y-LOAD
• For a load impedance
9/4/2017 17
,Z Z
0
120120 120
120120 120
ana l
o
o obnb l
o
o ocnc l
VVI I I
Z Z
VVI I I
Z Z
VVI I I
Z Z
Copyright © 2017 Hassan Sowidan
Y-SOURCE, Y-LOAD
9/4/2017 18
3
* * *
* * * *
* *
* *
, 0 . .
( )
a b c n n
an a bn b cn c
an a bn b cn a b
an cn a bn cn b
bc b ca a
S S S S S if S i e balanced load
V I V I V I
V I V I V I I
V V I V V I
V I V I
Copyright © 2017 Hassan Sowidan
Y-SOURCE, Y-LOAD
9/4/2017 19
3
3
3
3 90 120 3 150
3 1 30 1 150
3 3 cos 3 sin
3
3
o o o
o o
ll l
S V I V I
V I
V I j
S V I
S V I
Copyright © 2017 Hassan Sowidan
Y-SOURCE, Y-LOAD
• Therefore,
• Note that (Vll) can also be written as (Vl).
9/4/2017 20
3
3
3
3
3 cos( )
3 sin( )
ll l
ll l
ll l
S V I
P V I
Q V I