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Lesson 11:
Three Phase Transformers
A set of three similar single phase transformers may be connected to form a three-phasetransformer (three-phase transformer bank). The primary and secondary windings may be
connected in either star or delta configurations
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Three Phase TransformersThree Similar Single-phase Transformers
Connected to form a three phase TransformerFour possible connections/, /, , and /
Step up
Step down
One can be removed
Seldom used
Figure 11.2.1 a, b, c and d for 3 phase transformers connections
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Three Phase Transformer Bank
1.Three single-phase transformers connected in a three-phase bank.
2. Three sets of windings wrapped on a common core.
Ease of transportationInefficient magnetic circuit, less efficient
Higher capital cost than a single one
1-phase of the transformer at fault, the other two are not affected
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Figure 11.2.2 three-phase transformer structure
Usually 3-limb core structure
5-limb core may be used to reduce the overall height of a 3-limb coreMagnetic flux shares the magnetic circuit
Fault on one-phase very likely affects the other two
3-phase Transformer
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Tertiary Winding
A third set of windings usually exists in 3-phase transformer and used to:
Providing voltage to auxiliary power purposes in the substation or to supply localdistribution system
Power factor correction
Delta connected tertiary windings will provide a circuit for the third harmonics of theexciting current
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Wye / Wye connection
N n
A
B
C
a
b
c
IA
Ia
VAN
VAB
VCN
VBN Vbn
Van
Vcn
Vab
Figure 11.2.3
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Single Phase Diagram of 3 phase transformers
L o a dS u p p l y
N e t w o r k
T r a n s fo rm e r
Y -Y
Three-phase network supplies a load
through a transformer.
Transformer LoadSupply Network
Xtr_s
Van
Vload_an
VAN
Vnet_AN
Xnet
IA
Ia
N
n
A
a
Xtr_s
Van
Vload_an
VAN
IA
IaV
net_AN
Xnet
Equivalent circuit of the wye-wye
Single-phase equivalent circuit for phase
A of the three-phase wye-wye
transformer system
Figure 11.2.4 Single Phase Diagram of 3 phase transformers
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Wye / Delta connection
A
B
C
N
VAN
VAB
VBN
VBC
VCN
IA
Iba
Icb
VCA
a
b
c
a
b
c
Ia
Ic
Ib
Vab
Vbc
Vca
Iac
Figure 11.2.5
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Physical connections of 3 phase Transformers
Ia
Ib
Ic
Vab
Vbc
Vca
VCN
VBN
VAN
A
B
C
a
b
c
Icb
Iba
Iac
Transformer
AC
AC
AC
IC
IB
IA
VAN
VBN
VCN
Supply
Iab
Ibc
Ica
Load
VAB
VBC
VCA
Iac
Vca
Vbc
Vab
N
Figure 11.2.6 Wye-delta connected transformer
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Figure 11.2.7 Single-phase equivalent circuit of a wye-delta transformer
Xtr_s
Van Vs_an
VAN
IA Ia
Vp_AN
Xtr_p
Rtr_p
Rtr_s
Xm
Rc
Tspe
Y-
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Delta / Wye connection
A
B
C
n
a
b
c
VBC
IaIA
Ib
Ic
VAB
VCA Vca
Vab
Vbc
Van
Vbn
Vcn
IC
IB
ICA
IAB
IBC
Figure 11.2.8
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Delta / Delta connection
A
B
C
a
b
c
VAB
Ia
Iba
Iac
IA
IAB
ICA
Vab
Figure 11.2.9
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* 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.
AB and abZeroVAB
is in phase with Vab
Delta-Delta
AB and a30VAB
is in phase with Van
Delta-Wye
A and ab30VAN
is in phase with Vab
Wye-Delta
A and aZeroVAN
is in phase with Van
Wye-Wye
Windings Placed on the Same LegPhase Shift*Primary and Secondary Voltage Phase
RelationTransformer Connection
Table 11.2.1Three-phase Transformer Relations
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Three-phase transformer - Phase shift
Y-
VAB // Va
VAB
leads Vab
by 30o
-Y also provides line-to-line phaseshift
Y-Y and - connections have nophase shift
Figure 11.2.10
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Three-phase transformer - single-phase equivalent circuit
Validity conditions:
Identical transformers balancedsource and load
Only one phase variables are used, the other phases are similar.
equivalent Y-representation
line-to-neutral = phase voltage
-Y transformation
Figure 11.2.11 a, b, c, and d
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Three-phase transformer - open delta connection
One phase can be removed
Operation at reduced load
Possible only in
-
connection
Figure 11.2.12 a, and b
58.03
30cos2
3
)30cos(2
)30cos(
)30cos(
==
=
=+=
=
+=
P
P
VIP
VIPPP
IVP
IVP
V
bcabV
cbcab
aabab
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Three-phase transformer unit
Balanced three-phase voltage
Balanced three-phase flux
Return leg can be removed
In-plan construction easy to
manufacture
Same operation as transformer bank
Figure 11.2.13 a, b, c, and d
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Example 11-1
Three-single phase transformers are connected grounded Y-Y to two three
phase loads connected in and Y
a) Draw single-line diagram.
b) The single-phase equivalent circuit with transformer referred to HV side.
Solution:
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240 120
VLS
VS
240120
120240
VLP
VP
a
b
c
100kVA5%
100kVA
5%
100kVA
5%SL1 = 75kVA
Pf = 0.9 lagging
SL2 = 24kVA
Pf = 0.9 leading
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VLP = 240x = 415.2V
VLS = 120x = 207.6V
300KVA
415/207.65%
Y-Y
SS1 SL2
~
a)
3
3
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kVA
S 251 = =KVA
S 82
240 120
100KVA
S1 S2
(J.05) ZbHV
b)
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c)
Sb=100KVA
S1p.u. S2p.u.
J.05Vb=240 Vb=120
Y-Y
1. Y-Y 2. Y- 3. -Y 4. -
aV
V
LS
LP ==S
P
V3
V3
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VLP
NP3
NP2
NP1
VP
a
b
c
Y-
NS2
NS3
NS1
a
b
cVLSVS
b
a
c
V L P
N P 1
N P 2
N P 3
N S 1
N S 2
N S 3
b
a
c
V SV P
PLPVV= 3 SLS
VV=
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aV
V
S
P =
aV
V
V
V
S
P
Ls
LP
3
3
==
LS
LP
V
Va
3=
The voltage ratio of each phase
The line voltage ratio
LS
P
LS
V
LS
LP
V
V
VV
Va
LP
=== 3
3
From the above
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Y-. The secondary voltage is shifted 30 relative to the primary voltage.
c
b
a H
HVVan LV
30
Vca
Vab
Vbc
a
c
b
LV
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Because of the phase shift. transformers can not be connected in
parallel unless they have proper phase sequence. (i.e. They are in
phase with each other).
Y Y parallel Y- ? NO
Y- parallel Y- ? Yes. However, you must identify the correctphase sequence.
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+
-V PV L P
V L S
V S
a
b
c
PLPVV = SLS VV = 3
LS
LP
s
P
LS
LP
V
Va
a
V
V
V
V 3
33===
S
P
LS
LP
LS
LP
V
V
V
V
V
Va
===
3
3From above we have
-Y
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For-Y connection, the secondary Voltage Lags the primary Voltage by30
V L S
+
-V L P
+
-
V P
a
b
c
N P 1V S
N S 3
N S 2
N S 1
a
b
c
-
PLPVV = SLS VV
=
aV
V
V
V
S
P
LS
LP ==
-for
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3- Phase Real Power Transformer
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Appliances Transformer
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Harmonics in Transformer
Harmonics in transformer occur due to the effect of saturation and Hysteresis which areto produce non-sinusoidal current if the applied voltage is sinusoidal.
Upon saturation, the flux waveform is flat topped and contains mainly 3rd harmonic
component.
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Effects of harmonic currents
(i) Additional I2R losses due to circulating currents .
(ii) Increased iron loss in core.
(iii) Magnetic interference with protective gear and communication circuits.
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Effects of harmonic voltages
(i) Increased dielectric stress.
(ii) Electric field interference with communication circuit.
(ii) Harmonic resonance may occur between the inductance of
transformer windings and the capacitance of a feeder to which it is
connected.
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In 3-ph Supply System (1/2)
Star-connected with isolated neutral the line voltage contains no 3rd
harmonic component and 3rd harmonic current is precluded.
Star connected with neutral wire, the 3rd harmonic currents can flow andstill no 3rd harmonic line voltages.
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In 3-ph Supply System (2/2)
Delta Connected, the 3rd harmonic emfs around the 3-phase windings aresummed, which causes a circulating 3rd harmonic current around the 3-phase
windings.
But the line voltages across any two lines contain no 3rd harmonic component,
since they are short circuited by the windings.
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