332038674-Vector-Group-of-Transformers.ppt

Electrical and I&C Dept., Steag
Encotec India
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Presented By: Vinod J. Patel
To
Vector groups of Transformer
Training on

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Introduction to Vector Group
• The vector group marks the circuitry of
windings and their phase position to each
other. It consists of a capital and small
letter plus a code number. The capital
letter A, B, C refers to the HV winding
and the lower case a, b, c to the LV
winding with (A), (B), (C) for a tertiary
winding, where provided. Neutral
terminals precede line terminals.

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Introduction to Vector Group
• Each winding has two ends designated by
the subscript numbers 1, 2, or if there are
intermediary tapings (or there are
sections of the same winding) these are
numbered in order to their separation
from end 1. The most common vector
groups are summarized alongside, input
left-hand, output right-hand. Unless
otherwise requested.

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Requirement of Vector Group
• In 3 phase transformers polarity alone is
insufficient to represent the relation between
HV and LV windings. In addition to the
terminal marking on HV and LV side voltage
vector diagram are required to show the
angular displacement between HV and LV
winding. Vector group is necessary to indicate
the terminal marking and the phase
displacement between primary and secondary
voltages or currents.

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Under normal condition the line to line
voltages on HV side are displaced from
corresponding voltages on LV sides. Also
line to neutral voltage on HV side are
displaced from corresponding voltages on
LV side. The displacement depend upon the
transformer connections. As per IS 2026-
1972, there are four vector groups of
standard connections
Requirement of Vector Group

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Phase shifts in Star Delta
Transformers
• Positive & Negative phase sequence voltages
and currents undergo a phase shift in passing
through a star-delta transformer which
depends on labeling of terminals.
• Before considering the phase shift, we need to
discuss the standard polarity marking of a
single phase transformer as shown in the
figure-1. The transformer ends marked with a
dot have the same polarity. Therefore, voltage
VHH' is in phase with voltage VLL'.

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VHH'
H
H'
VLL'
L
L'
I1 I2
Figure-1
Polarity Marking of a single phase
transformer

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• Consider now a star/delta transformer
with terminal labeling as indicated in
Figure-2. Windings shown parallel to
each other are magnetically coupled.
Assume that the transformer is excited
with positive sequence voltages and
carries positive sequence currents. With
the polarity mark shown, we can
immediately draw the phasor diagram of
Figure-3.
Transformers

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• The following relatdionship between the
voltages on two sides of the transformer
is observed from the phasor diagram.
Positive sequence line voltages on star
side lead the corresponding voltages on
the delta side by 30 deg. The same also
applies for the line currents.
Transformers

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A
B
C
N
a
c
b
Star side quantities lead delta side quantity by 30 deg.
Figure-2
Star Delta Transformation

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VAB1
VBC1
VCA1
VCN1
VAN1
VBN1
Vab1
Vca1
Vbc1
30 deg.
Positive Sequence Voltage on a Star / Dleta Transformer
Figure-3
Phasor diagram of star-delta Transformer

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• If the delta side is connected as shown in Figure-4
the phase shift reverses; the delta side quantities
lead the star side quantity by 30 deg.
A
B
C
N
c
b
a
Delta side quantities lead Star side quantity by 30 deg.
Figure-4

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• Instead if the transformer of Figure-2 is now
excited by negative phase sequence voltages &
currents, the voltage phasor diagram will be as
shown in Figure-5.
VAB2
VCA2
VBC2
VBN2
VAN2
VCN2
Vab2
Vbc2
Vca2
30 deg.
Negative Sequence Voltage on a Star / Dleta Transformer
Figure-5

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• The phase shift in comparison to
positive sequence case now reverses,
i.e. the star side quantities lag the
delta side quantities by 30 deg. The
result for figure- 4 also
correspondingly reverses.

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• It is assumed that a star/delta
transformer is so labeled that the positive
sequence quantities on the HV side lead
their corresponding positive sequence
quantities on the LV side by 30 deg. The
reverse is the case of negative sequence
quantities wherein HV quantities lag the
corresponding LV quantities by 30 deg.

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• The interconnection of the phase windings to give
a three phase, three-or four wire supply provides
three alternative modes of connection
(1) Mesh or Delta
(2) Star
(3) Zig-zag
Each of these can be achieved in two ways.
For Example a star Connection may be had by
joining together A1, B1 and C1, to form the
neutral and using A2, B2 and C2 as line terminals.
Alternatively A2, B2 and C2 may be joined to give
neutral and A1, B1 and C1 may be used as line
terminals.

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• Since primary and secondary can be
treated in either of these ways, at least
twelve methods of connection are
possible. These are arranged in four main
groups, as given below, according to the
phase displacement which exists between
the line voltages on the two sides of the
transformer.

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Vector Groups (Group-1)
• Group 1: Zero phase displacement
(Yy0, Dd0, Dz0)
1) Yy0: Star – Star Connection
2) Dd0: Delta – Delta Connection
3) Dz0: Delta – Zig-zag Connection

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Yy0: Star – Star Connection

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Dd0: Delta – Delta Connection

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Dz0: Delta – Zig-zag Connection

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• Group 2: 180 degree phase
displacement (Yy6, Dd6, Dz6)
1) Yy6: Star – Star Connection
2) Dd6: Delta – Delta Connection
3) Dz6: Delta – Zig-zag Connection

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Yy6: Star – Star Connection

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Dd6: Delta – Delta Connection

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Dz6: Delta – Zig-zag Connection

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• Group 3: 30 degree lag phase
displacement (Dy1, Yd1, Yz1)
1) Dy1: Delta – Star Connection
2) Yd1: Star – Delta Connection
3) Yz1: Star – Zig-zag Connection

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Dy1: Delta – Star Connection

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Yd1: Star – Delta Connection

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Yz1: Star – Zig-zag Connection

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• Group 4: 30 degree lead phase
displacement (Dy11, Yd11, Yz11)
1) Dy11: Delta – Star Connection
2) Yd11: Star – Delta Connection
3) Yz11: Star – Zig-zag Connection

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Dy11: Delta – Star Connection

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Yd11: Star – Delta Connection

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Yz11: Star – Zig-zag Connection

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Symbol Description
• Phase displacement zero = 0
• Phase displacement 180 degree = 6
• Phase displacement 30 degree lag = 1
• Phase displacement 30 degree lead = 11
• Letter Y represents star connected HV
• Letter y represents star connected LV
• Letter D represents delta connected HV
• Letter d represents delta connected LV
• Letter Z represents star connected zig-zag

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• The most popular method of connecting
transformer is the delta-star connections
(4, Dy11). The connection diagram
illustrates the relative position of the
terminals in the terminal box and the
internal connections that are made. The
HV winding is connected to a 3-wire
supply, of phase sequence A, B, C, and at
the instant chosen the potential of A is at
its maximum positive value. Thus the line
voltages on the HV side will form an
equilateral triangle.
Description of Dy11

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• The line terminals are A2, B2 and C2 and
the corners of the triangles are so
marked. It is to be noted that phase A of
the transformer lies between A2 and B2,
Phase B between B2 and C2 and phase C
between C2 and A2 owing to internal
connections used.
Description of Dy11

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• From the phasor diagrams of induced
voltages for HV and LV sides it is
observed that the voltage of the HV line
A2 is at the maximum value, the LV line
a2 has been advanced 30 degree. In fact
the transformer connections have
produced this displacement of 30 degree
for all lines.
Description of Dy11

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• All the other methods of connections in the
same main group no. 4 gives a similar 30 degree
advance which is the basis of classification.
• With group no. 1 there is no phase
displacement but the group no. 2 gives the
phase displacement of 180 degree. Group no. 3
cause the LV line voltage to lag by 30 degree.
• For parallel operation of transformers the
essential requirement is that the transformer
connections belong to the same main group.
Description of Vector Groups

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• It is possible to obtain any desired phase
shift with a three phase transformer if the
primary and / secondary windings are
divided into a sufficient number of
sections. The Zig-Zag connection is one
example of a sectionalized winding.

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• 15 percent more turns are required for a given
total voltage per phase compared with a
normal phase connection in Zig-zag winding,
which may increase in the frame size for the
given rating.
• Nevertheless, the advantages of zig-zag
arrangement may offset the cost; unbalanced
loads on the secondary side are distributed
better on the primary side.
• The zig-zag / star connection has been
employed where delta connections were
mechanically weak (on account of large
number of turns and small copper sections) in
HV transformers.

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• In star connection with earthed neutral the
maximum voltage of the phase winding to
ground is 1/V3 (or 57.7%) of the line voltage,
while in delta connection this is equal to the line
voltage in case of earthing of one of the line
during a fault. Therefore, Phase voltage, turns
and insulation are less in star connection than
those in delta connection and for very high
voltage transformers the star connection on HV
side is about 10% cheaper than delta
connection.
Choice between Star and Delta connection

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• A delta connected primary is necessary for a
star connected LV secondary feeding mixed
three phase and single phase loads. In case of
unbalanced single phase loads on secondary,
delta connected primary is necessitated to
permit the flow of zero sequence current I0=
In/3 = 1/3 (IA + IB + IC) so that IA + IB + IC =
0.
• This means that only positive and negative
sequence current flows in the lines on the delta
side.

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• This could also be achieved by star
connected primary provided the primary
and secondary star points are earthed,
but this is not recommended because of
flow of ground current for unbalanced
secondary loads.

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Choice of Transformer
connections:
(A) Star-Star (Yy0 or Yy6) connections:
This type of transformer is most
economical for small current and high
voltage transformers. The advantages
and disadvantages of such arrangement
are as under.

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Star-Star (Yy0 or Yy6)
connections
• Advantages:
• The number of turns per phase and the amount
of insulation is minimum because phase voltage
= 1/V3 of line voltage.
• There is no phase displacement between
primary and secondary voltages.
• With star point available on both sides it is
possible to provide neutral connection.
• Economical for small HV transformer.

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connections
• Disadvantages:
• If the load on secondary side of transformer is
unbalanced, the phase voltages of load side change
unless the load star point is earthed. The difficulty of
shifting neutral can be overcome by connecting the
primary star point to the star point of the Generator.
• The primary of the transformer draws a magnetizing
current which has third and fifth harmonics. If neutral
of primary is not connected to neutral of Generator, the
third and fifth harmonics current can not flow hence
the flux in the core can not be sinusoidal wave and,
therefore, the voltages will be distorted. By connecting
the primary neutral to Generator neutral, the path for
return of these third and fifth harmonics current is
provided and, therefore, the trouble of distortion of
voltage is overcome.

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connections
• Disadvantages:
• Even if neutral of primary is connected to
neutral of Generator or earthed, still the third
harmonic is present in the alternator voltage
form, it will appear on secondary side. Though
the secondary line voltages do not contain third
harmonic voltage; but third harmonic voltages
are additive in the neutral and cause the
current in the neutral of triple frequency ( 3rd
harmonic) which will cause interference to the
nearby communication system.
• Third harmonic voltages may be high in shell
type 3 phase transformers.

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Delta-Delta (Dd0 or Dd6)
connections
• This arrangement is generally used in system
which carry large current or low voltages and
especially when continuity of service must be
maintained even though one of the phase
develops fault. When one of the phase is
removed in delta-delta connected
transformers, operation continues on what is
known as open delta. By being operated in
this way , the transformer delivers three
phase currents and voltages in their correct
phase relationship but the capacity of the
transformer is reduced to 57.7% of what it
was all three phase winding sound.

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connections
• Advantages:
• There is no phase displacement between
the primary and secondary voltages.
• There is no distortion of flux, because the
third harmonic component of
magnetizing current can flow in delta
connected primary winding without
flowing in the line wires.

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connections
• Advantages:
• The cross section of conductor is reduced
because the phase currents is 1/V3 times
of the line current.
• No difficulty is experienced due to
unbalancing of loads on secondary side.
• Suitable for large HV transformers
• Large load unbalance can be tolerated,
3rd harmonic voltages are damped out.

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connections
• Disadvantages:
• More insulation is required in
comparison to star-star connections.
• The absence of star point may be
disadvantageous. If one line gets earthed
due to fault, maximum voltage between
windings and core will be full line
voltage.

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Star-Delta (Yd1 or Yd11)
connections
This type of transformer connection is
used principally where the voltage is to be
stepped down as, for example, at the end
of a transmission line. In this type of
connection of transformers the neutral of
the primary winding is earthed. In this
system line voltage ratio is 1/V3 times of
transformer turn ratio and secondary line
voltages have a phase shift of +/- 30
degree with respect to primary line
voltages.

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Star-Delta (Yd1 or Yd11)
connections
On the HV side of the transformer,
insulation is stressed only to the extent of
57.7% of the line voltage and, therefore,
there is some saving in the cost of
insulation. Very common for supply
networks. One star point for a neutral to
serve mixed 1 phase and 3 phase loads.

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Delta-Star (Dy1 or Dy11)
connections
This scheme of connection is generally used
where it is necessary to step up the voltage as
for example, at the beginning of a HT
transmission system. On the high voltage side
of the transformer, insulation is stressed only
to the extent of 57.7% of line to line voltage.
Another advantage is that the neutral point is
stable and will not float when load is
unbalanced. There is no distortion of flux
because the existence of a delta connection
allows a path for the 3rd harmonic currents.

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connections
In this scheme of connection the line
voltage ratio is V3 times of transformer
turn ratio and the secondary line voltage
have a phase shit of +/- 30 degree with
respect to primary line voltages.

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connections
The neutral of the secondary is grounded to
provide 3-phase, 4-wire system and this scheme
of connection is widely used in distribution
system because it can be used to serve both the
three phase power equipment and single phase
lighting circuits. In such case the 11,000 / 400 V
transformer connections provide a four wire
secondary, with neutral supplying the 4th wire.
The three phase equipment is connected to the
line wires to operate at 400V while the lighting
equipment is connected between one of the line
wires and neutral to operate at 230 Volts.

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connections
• Used for distribution transformer. Star
side is used on load side.
• Star-Delta or Delta-Star connected
transformers can not be operated in
parallel with star-star or delta-delta
connected transformer even though the
voltage ratio are correctly adjusted as
there will be a 30 degree phase difference
between corresponding voltages on the
secondary sides.

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Interconnected star/star (Zig-Zag)
• Reduces 3rd harmonic voltages and not
sensitive to condition of unbalanced
loading.
• Restricted to low voltage windings.
• Phase voltages are composed of half
voltages with 60 degree displacement,
15% more turns are required.
• Some times used in rectifier supply.

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• A three phase transformer is either in the form
of a three phase unit or in the form of a bank of
three single phase units.
• A single three phase unit is less costly (cost less
by 15%) than a bank of 3 single phase unit.
• Star-Star connection is used for connecting
together two high voltage transmission system
of unequal voltage. In this case it is necessary
that the connection used to be such as not to
cause a shift in phase form primary to
secondary. Therefore only two connections are
applicable, namely, Star – Star and Delta –
Delta.
Arrangements of 3 phase Transformer and
connections

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• For high voltage Star – Star connection is
preferred because the voltage stresses of the
winding to the ground with neutral grounded
are only 58% of the voltage stress to ground of
similar units connected delta to delta. When the
star to star connection is used for this purpose a
tertiary winding is provided to suppress the
third harmonic voltages which would otherwise
appear on the system.
Arrangements of 3 phase
Transformer and connections

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• The tertiary is a third winding and is often used
in power transformers to provide station power
requirements or tie with synchronous
condenser.
• The disturbances from harmonic voltages and
currents constitute one of the objections to this
use of Star-Star connected transformer.
Another objection in its use is that unbalanced
loads can not be carried on the secondary side
unless the primary neutral or fourth wire is
provided.

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• Another objection is that it is practically
impossible to construct 3-single phase
units, or even a three phase unit, in which
the magnetizing currents of each of the
three windings are exactly identical. This
makes it impossible to have perfectly
balanced voltages in each of the three
windings of the star – star connection.

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Harmonics:
• A sinusoidal wave form of current or voltage
consists of only one frequency component
called fundamental. Such a sinusoidal
waveform does not contain harmonics of other
frequencies.
• A non sinusoidal periodic waveform can be
considered to be composed of several sinusoidal
waveforms of fundamental frequencies and
other harmonic frequencies.
• Harmonic currents cause additional I2R loss,
core loss, magnetic interference with protective
relays and interference in communication
circuits. Thus the harmonics should be avoided.

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Harmonics:
• Harmonics are caused by high flux densities in
the core of power transformers. If the cross
section of core is insufficient, the core gets
saturated. The operating point is on the non
linear region of the B/H curve. Even if primary
voltage have sinusoidal waveform, the
secondary waveform may be non sinusoidal
because of magnetic core. If the core cross
section is inadequate, core gets saturated and
3rd harmonics are generally present in the
secondary waveform.
• Harmonics are caused by operation of thyristor
controlled devices.

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Effect of Transformer connection
on harmonics
• Single phase transformer:
• If core is not saturated, i.e. if operating
point of magnetizing current is in the line
portion of B/H curve, harmonics are not
present. If core saturates, 3rd harmonic
e.m.fs and 3rd harmonic currents
induced on the secondary side.

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A) Three phase banks of 3 single phase
transformer:
• The method of connection decides the
harmonic generation
1)Delta-delta connection: Delta connection
provides closed path to 3rd harmonic e.m.f
which circulate 3rd harmonic currents in
closed delta. The 3rd harmonic voltage drop
within the closed delta. As a result on 3rd
harmonic voltages appear at line terminals.
Similar behaviors occur in the Delta-delta
connection for 5th and 7th harmonics.
on harmonics

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transformer:
2) Stat-delta connection and Delta-star
connection without neutral wire or neutral
grounding:
3rd harmonic voltages and currents circulate
in closed delta and are absent on line terminal
on delta side however the waveform departs
from true sinusoidal waveform as 3rd
harmonic currents can not circulate on star
side.
on harmonics

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transformer:
3) Star-star connection without neutral
earthing:
There is no path for circulation of 3rd
harmonic current the neutral point oscillates.
The line to neutral point voltages of all the 3
phases fluctuate.
on harmonics

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transformer:
4) Star-star connection with neutral:
The presence of neutral connection
provides path for 3rd harmonic
compensating currents.
on harmonics

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B) Three phase transformer units:
• It is desirable to distinguish between the cases
where the phases are magnetically separate,
and those where they are magnetically (as
well as electrically) interlinked. In 3-phase
shell types transformer the magnetic circuit
are separate and do not interact and the
discussion for the 3 bank of 1 phase
transformer will apply.
on harmonics

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B) Three phase transformer units:
• In the more common 3 phase 3 limb core type unit,
however, this is not so, any 3rd harmonics are all
upward or downward at a given instant in the limbs,
and their return path must be external (i.e. in the air,
oil or the wall of tank). These paths have a high
reluctance and there is a strong tendency to suppress
3rd harmonic core fluxes. The residuals may cause
eddy current loss in the tank, an effect cancelled it a
copper band is fitted around the inside perimeter of the
tank.
• In five limbed cores, the end limbs provide a
magnetic path for third harmonic fluxes.
on harmonics

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Paralleling of a transformer of group 3
with transformer of group 4
• Group 3 has phase displacement of 30
degree lag, i.e. -30 degree. Group 4 has
phase displacement of 30 degree lead, i.e.
+30 degree. A transformer of group 3 can
be connected in parallel with that of
group 4 by cross connecting any two of
the three external connections on HV
side, without any other changes.

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• Alternatively any two LV connections may be
cross connected without other change.
• Thus connect A, B, C of transformer X to
busbars r,y,b and a,b,c of transformer Y to bus
bar R,Y,B.
• Connect a, c, b of transformer X to bus bar
r,y,b and a,b,c of transformer to busbar r,y,b to
adjust the phase displacement difference
between group 3 and group 4.

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• Group 1 has zero displacement and
group 2 has 180 degree phase
displacement. For parallel operations,
one of the internal connections of all the
three winding of one of the transformers
on one side only (either HV or LV) is
necessary to be changed. Thus bringing
same phase shift, i.e. zero degrees or 180
degree in both transformers.

332038674-Vector-Group-of-Transformers.ppt

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332038674-Vector-Group-of-Transformers.ppt