Transcript Lecture Notes EEE 360 - Warsaw University of Technology

EEE 360
Energy Conversion and
Transport
George G. Karady & Keith Holbert
Chapter 5
Transformers
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Lecture 12
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5.4 Three-phase transformer
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Transformers
Figure 5.46 Very large three-phase network transformer.
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Transformers
A
B
C
VBN
VCN
Vab
Vbc
Vca
a
b
c
VAN
N
Figure 5.47 A three-phase wye-delta transformer with three-legged iron core.
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Transformers
wye-wye (Y-Y)
wye-wye-delta
(Y-Y-Δ)
wye-delta (Y-Δ)
delta-delta (Δ-Δ)
delta-wye (Δ-Y)
seldom used, imbalance and 3rd harmonics
problems
frequently used to interconnect high voltage
networks (240 kV/345 kV). The delta
winding filters the 3rd harmonics, equalizes
the unbalanced current, and provides a path
for ground current
frequently used as step down (345 kV/69 kV)
used for medium voltage (15 kV), one of the
transformers can be removed (open delta)
step-up transformer in a generation station
Usual connections for three-phase transformers
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5.4.1 Wye / Wye connection
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Transformers
IA
Ia
A
a
VAB
VBN
B
Van
VAN
N
VCN
Vbn
n
Vcn
5.41.Wye/wye
Vab
b
I
c
C
Y
rate

S 3
Vrate
3

S
3 Vrate
Figure 5.48 Wye connected three-phase transformer
TYY
Np
VAN I a VBN I b VCN I c







Ns
Van I A Vbn I B Vcn I C
TYY 
Np
Ns

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VAB  3 VAN e j 30
Vab  3 Van e j 30
VAN I a

Van I A
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Transformers
Transformer
Supply
Network
Figure 5.49 Three-phase network
supplies a load through a
transformer.
Load
Y-Y
Vnet_AN
Xnet
VAN
Van
Xtr_s
A
a
Ia
IA
Vload_an
Figure 5.50 Equivalent circuit of
the wye-wye transformer system
of Figure 5.49.
n
N
Supply Network
Transformer
Xtr_s
Xnet
Vnet_AN
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IA
Load
VAN
Van
Ia
Vload_an
Figure 5.51 Single-phase equivalent
circuit for phase A of the three-phase
wye-wye transformer system of Figure
5.50.
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5.4.2 Wye / Delta connection
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Transformers
VAN
Transformer
A IA
AC
VBN
VAN
VAB
VCA
IB
B
Vab
Ia
Vab
Vca
Icb
VBN
VBC
C
AC
Supply
a
b
IC
Vbc
Iac
Ica
VCN
Vca
Vbc
c
Iab
Ib
Iac
AC
VCN
Iba
Ibc
Ic
Load
N
Figure 5.52 Wye-delta connected transformer , 5.4.2
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Transformers
Ia
IA
A
a
VAB
VCA
VAN
VBN
B
VCN
c
Iba
N
VBC
C
Iac
b
Icb
Ib
Ic
a
I
Vab
b

rate

Vca
S 3
Vrate

S
3 Vrate
Vbc
c
Figure 5.52 Wye-delta connected transformer , currents and voltages
TYΔ
Np
VAN I ba



Ns
Vab
IA
VAB  VAN  VBN  VAN  VAN e  j 120  3 VAN e j 30
I a  I ba  I ac  I ba  I ba e  j 240  3 I ba e  j 30
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Transformers
Rtr_p
Xtr_p
spe
T
IA
Vp_AN
Rc
Xm
Xtr_s
Van
VAN
Rtr_s
Ia
Vs_an
Y-
Figure 5.53 Single-phase equivalent circuit of a wye-delta transformer.
Vab  3 Van e j 30
TYspeΔ
VAB VAN 3 e j 30 VAN



Vab
Vab
Van
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TYspeΔ 
360 Chapter 5 Transformers
*
a
*
A

I
I
 ba
I
3e
I *A

 j 30 *
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5.4.3 Delta / Wye connection
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Transformers
A
VAB
VCA
B
VBC
C
IA
Ia
Vbn
a
IAB
n
IB
IC
ICA
Van
Ib
Vcn
Ic
IBC
Vab
b
Vca
Vbc
c
Figure 5.54 Delta-Wye connected transformer
I A  I AB  I CA  I AB  I AB e  j 240  3 I AB e  j 30
 j 30
spe
Δ Y
T
*
a
*
A
VAN I
VAB VAB e




Vab
Van
Van I
3
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TΔspe Y
I *a
 * 
IA
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
I *a
3 I AB e

 j 30 *
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5.4.4 Delta / Delta connection
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Transformers
IA
A
Ia
a
Iba
IAB
VAB
Vab
ICA
B
Iac
b
c
C
Figure 5.55 Delta-Delta connected transformer
TΔ-Δ
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Np
I ba
VAB I a




Ns
Vab I A I AB
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Transformers
Table 5.1 Three-phase Transformer Relations
Transformer Connection
Primary and Secondary Voltage Phase
Relation
Wye-Wye
VAN is in phase with Van
Zero
A and a
Wye-Delta
VAN is in phase with Vab
30°
A and ab
Delta-Wye
VAB is in phase with Van
–30°
AB and a
Delta-Delta
VAB is in phase with Vab
Zero
AB and ab
Phase Shift*
Windings Placed on the Same
Leg
* Note:
Phase shift lead between line-to-line voltages, VAB and Vab, and line-to-neutral voltages, VAN and Van, and
line currents, IA and Ia.
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5.4.7 Equivalent circuit
parameters
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Transformers
High
voltage
Low
voltage
A
W
C
V
AC
AC
A
AC
V
A
W
B
Full rated
voltage
Figure 5.56 Open circuit test for three-phase transformer
parameter measurement
Vo_ll 230V
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Io  13A
360 Chapter 5 Transformers
Po_3f  550W
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Transformers
Open circuit test
Vo _l n  
Po _1 f  
Vo _l l
3
Po _3 f
3
Vo _l n  1 32 .79 1V
Po _1 f  1 83 .33 3W
2
Vo_ln
Rc 
Po_1f
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Rc  96.182
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Transformers
Open circuit test
Io
Yo 
Vo_ln
Xm  
Yo  0.098S
1
2
Yo 
Rc
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Xm  1 0.2 73
1
2
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Transformers
C
High
voltage
W
Low
voltage
A
V
AC
AC
A
AC
Reduced voltage
V
B
W
A
Figure 5.56 Short circuit test for three-phase transformer
parameter measurement
Vs_ll 160V
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Is  1 6A
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Ps_3f  1200W
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Transformers
Short circuit test
Vs_ ln  
Ps_ 1f  
Rs 
Vs_ ll
3
Ps_ 3f
3
Ps_ 1f  4 00W
Ps_1f
Is
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Vs_ ln  9 2.3 76V
Rs  1.563
2
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Transformers
Short circuit test
Zs 
Vs_ln
Is
2
Xs  Zs  Rs
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Zs  5.774
2
Xs  5.558
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Exercises using MAT CAD
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Transformers
3
L23
delta-wye
P
S
Xtr
L12
1
P2
P1
wye
delta
L23
T-Y 3
AC
2
L12
2
Z23
P2
wye
1
Z12
P1
delta
Figure 5.61 One-line diagram of delta-wye connected transformer supplies
two balanced loads through a transmission line.
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