Vector Group

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.



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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.



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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-zagEach 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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• 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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• 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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• 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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• 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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• 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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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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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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• 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.



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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.



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A) Three phase banks of 3 single phase 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.



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A) Three phase banks of 3 single phase 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.



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A) Three phase banks of 3 single phase transformer:4) Star-star connection with neutral: The presence of neutral connection provides path for 3rd harmonic compensating currents.



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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.



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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.



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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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Paralleling of a transformer of group 3 with transformer of group 4

• 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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Paralleling of a transformer of group 1

with transformer of group 2

• 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.

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