Lesson 11:
Three Phase Transformers
A set of three similar single phase transformers may be connected to form a three-phase
transformer (three-phase transformer bank). The primary and secondary windings may be
connected in either star or delta configurations
Three Phase Transformers
Three Similar Single-phase Transformers
Connected to form a three phase Transformer
Four possible connections∆/λ, λ/∆, ∆, and λ/λ
Step down
Step up
One can be removed
Seldom used
Figure 11.2.1 a, b, c and d for 3 phase transformers connections
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 transportation
Inefficient magnetic circuit, less efficient
Higher capital cost than a single one
1-phase of the transformer at fault, the other two are not affected
3-phase Transformer
Usually 3-limb core structure
5-limb core may be used to reduce the overall height of a 3-limb core
Magnetic flux shares the magnetic circuit
Fault on one-phase very likely affects the other two
Figure 11.2.2 three-phase transformer structure
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 local
distribution system
Power factor correction
Delta connected tertiary windings will provide a circuit for the third harmonics of the
exciting current
Wye / Wye connection
IA
Ia
a
A
VAB
B
VBN
Van
VAN
N
VCN
Vbn
n
Vcn
Vab
b
c
C
Figure 11.2.3
Single Phase Diagram of 3 phase transformers
T ra ns form er
S u p p ly
N etw o rk
Three-phase network supplies a load
through a transformer.
L oad
Y -Y
V net_AN
X net
V AN
V an
X tr_s
A
IA
n
Ia
V load_an
a
Equivalent circuit of the wye-wye
N
Supply Network
Transformer
Xtr_s
Xnet
Vnet_AN
IA
Load
VAN
Van
Ia
Vload_an
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
Wye / Delta connection
Ia
IA
A
a
VAB VAN
VCA B
C
VBN
VBC
VCN
N
Iba
b
Figure 11.2.5
Iac
a
Ib Vab
c
b V
ca
Icb
Ic
Vbc
c
Physical connections of 3 phase Transformers
VAN
Transformer
A IA
AC
VBN
VAB
VCA
AC
VCN
Iba
VAN
B IB
VBC
C IC
AC
Supply
N
Vab
Vab
Vca
Icb
VBN
Ib
b
Iac
Vbc
Iac
VCN
Ia
a
Vbc
c
Vca
Figure 11.2.6 Wye-delta connected transformer
Iab
Ica
Ibc
Ic
Load
Rtr_p
Xtr_p
IA
Vp_AN
Rc
Tspe
Xm
Xtr_s
Van
VAN
Rtr_s
Ia
Y-∆
Figure 11.2.7 Single-phase equivalent circuit of a wye-delta transformer
Vs_an
Delta / Wye connection
A
VAB
VCA B
VBC
C
IA
Vbn
Ia
IAB
n
IB
IC
ICA V
cn
Van I
b
Ic
IBC
Figure 11.2.8
a
Vab
b
Vbc
c
Vca
Delta / Delta connection
IA
A
VAB
B
Ia
a
Iba
IAB
ICA
Iac
Vab
b
c
C
Figure 11.2.9
Table 11.2.1Three-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.
Three-phase transformer - Phase shift
•
Y-∆
•
VAB // Va
•
VAB leads Vab by 30o
•
∆-Y also provides line-to-line phase
shift
•
Y-Y and ∆-∆ connections have no
phase shift
Figure 11.2.10
Three-phase transformer - single-phase equivalent circuit
•
Validity conditions:
•
Identical transformers balanced
source 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
Three-phase transformer - open delta connection
•
One phase can be removed
•
Operation at reduced load
•
Possible only in ∆ - ∆ connection
Pab = Vab I a cos(30 + φ )
Pab = Vbc Ic cos(30 − φ )
PV = Pab + Pbc = 2VI cos(30° )
P∆ = 3VI
PV 2 cos30°
=
= 0.58
3
P∆
Figure 11.2.12 a, and b
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
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:
c
VφP
240
120
VφS
VLS
VLP
100kVA
5%
a
240
120
100kVA
5%
b
240
120
100kVA
5%
SL1 = 75kVA
Pf = 0.9 lagging
SL2 = 24kVA
Pf = 0.9 leading
a)
~
300KVA
415/207.6 SS1
5%
Y-Y
VLP = 240x
3
= 415.2V
VLS = 120x
3
= 207.6V
SL2
b)
(J.05) ZbHV
S1φ
240
S2φ
120
100KVA
S1 = 25 kVA
φ
S 2 = 8 KVA
Φ
c)
Vb=240
J.05 Vb=120
S1p.u.
S2p.u.
Sb=100KVA
1. Y-Y
Y-Y
2. Y-∆
VLP
=
VLS
3. ∆ -Y
3 Vφ P
3 Vφ S
=a
4. ∆ - ∆
Y-∆
a
b
NP1
a’
NS2
NP2
VφP
NS3
NS1
VLP
NP3
VφS
b’
VLS
c
b
b’
V
φP
N
P 1
N
S 1
V
φS
a’
V
L P
a
N
P 2
N
S 2
c’
c
N
VLP = 3VΦP
P 3
N
S 3
VLS = VΦS
c’
The voltage ratio of each phase
VΦP
VΦS
= a
The line voltage ratio
V LP
=
V Ls
3V Φ P
=
VΦS
3a
VLP
a=
3VLS
From the above
a =
V LP
V LP
VΦP
3
=
=
V LS
V LS
3V LS
„
Y-∆. The secondary voltage is shifted 30° relative to the primary voltage.
c’
c
a HV
Vb’c’
Vc’a’
30°
b
HV
Va’n LV
b’
Va’b’
LV
a’
„
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 correct
phase sequence.
∆-Y
V LP
V φS
+
-
a’
V φP
V LS
b’
c’
VLP = VΦP
VLS = 3VΦS
VLP
VΦP
a
3VLP
=
=
⇒a=
VLS
VLS
3VΦs
3
From above we have
3VLP
VLP
=
a=
VLS
VLS
3
VΦP
=
VΦS
„
For ∆-Y connection, the secondary Voltage Lags the primary Voltage by
30°
a
+
V φP
V LP
-
N S2
∆-∆
a’
+
N P1
N S3
V φS
V LS
b’
N S1
b
c’
c
VLP = VΦP
VLS = VΦS
V LP V Φ P
=
=a
V LS V Φ S
for ∆-∆
3- Phase Real Power Transformer
Appliances Transformer
Harmonics in Transformer
Harmonics in transformer occur due to the effect of saturation and Hysteresis which are
to produce non-sinusoidal current if the applied voltage is sinusoidal.
Upon saturation, the flux waveform is flat topped and contains mainly 3rd harmonic
component.
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.
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.
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 and
still no 3rd harmonic line voltages.
In 3-ph Supply System (2/2)
• Delta Connected, the 3rd harmonic emf’s around the 3-phase windings are
summed, 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.