TechRef 3 W Transformer

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DIgSILENTPowerFactory

Technical Reference Documentation

Three-Winding Transformer

ElmTr3,TypTr3


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DIgSILENT GmbH

Heinrich-Hertz-Str. 972810 - Gomaringen

Germany

T: +49 7072 9168 0F: +49 7072 9168 88

http://www.digsilent.de

[email protected]

Version: 15.2Edition: 1

Copyright 2014, DIgSILENT GmbH. Copyright of this document belongs to DIgSILENT GmbH.No part of this document may be reproduced, copied, or transmitted in any form, by any meanselectronic or mechanical, without the prior written permission of DIgSILENT GmbH.

Three-Winding Transformer (ElmTr3,TypTr3) 1
http://www.digsilent.de/mailto:[email protected]:[email protected]://www.digsilent.de/


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Contents

Contents

1 General Description 3

2 Model Diagrams and Input Parameters 3

2.1 Positive and Negative sequence models . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Positive sequence input parameters . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 HV-MV Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 MV-LV Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.3 LV-HV Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.4 Magnetizing impedance measurement . . . . . . . . . . . . . . . . . . . . 8

2.2.5 Relation between input parameters and absolute impedances. . . . . . . 9

2.3 Zero sequence models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Zero-sequence Input parameters . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 D-d-d connection (Delta-delta-delta) . . . . . . . . . . . . . . . . . . . . . 10

2.3.3 YN-d-d connection (Grounded wye-delta-delta) . . . . . . . . . . . . . . . 11

2.3.4 YN-yn-d connection (Grounded wye-grounded wye-delta) . . . . . . . . . 11

2.3.5 YN-yn-yn connection (Grounded wye-grounded wye-grounded wye) . . . 12

2.3.6 YN-yn-d auto-transformer (Grounded wye-grounded wye-delta auto trans-former) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.7 YN-d-zn (Grounded wye-delta-grounded Z) . . . . . . . . . . . . . . . . . 13

2.3.8 YN-d-y(Grounded wye-delta-wye) . . . . . . . . . . . . . . . . . . . . . . 13

3 PowerFactoryHandling 14

4 Application in Power Systems 15

5 Input/Output Definitions of Dynamic Models 17

List of Figures 19

List of Tables 20



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2 Model Diagrams and Input Parameters

1 General Description

The 3-winding transformer is a 3-port element connecting 3 cubicles in the network. PowerFac-

torycomes with a built-in model for three-winding transformers explained in this document.

Section2 presents the sequence equivalent models of the three-winding transformer includinggeneralized tap-changers (for phase and magnitude). The input parameters are also covered inthis section. More SpecificPowerFactoryhandling issues are explained in Section3. Section4discusses typical applications of three-winding transformers in power systems.


2.1 Positive and Negative sequence models

The detailed positive-sequence models with impedances in per unit are shown in Figure 2.1and Figure2.2. The negative-sequence models are identical to the positive-sequence models.Each of the HV, MV, and LV windings has a resistance and a leakage reactance designatedby rCu and X together with the corresponding winding initials. An ideal transformer with a1:1 turns ratio links the three windings at the magnetic star point. The models also include amagnetisation reactance and an iron loss resistance designated respectively by xM and rFe.The magnetisation reactance and the iron loss resistance can be modelled at different positions(default: star point, HV-Side, MV-Side or LV-Side). Also the position of the taps can be changedfrom the star point (Figure2.1)to the terminal sides (Figure2.2)with the default position beingthe star point.

Figure 2.1: PowerFactorypositive-sequence model of the 3-winding transformer, taps modelledat star point



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Figure 2.2: PowerFactorypositive-sequence model of the 3-winding transformer, taps modelled

at terminals

2.2 Positive sequence input parameters

Ur,T,HV,Ur,T,MV,Ur,T,LV

kV Rated voltages on HV/MV/LV side

SrT,HV,

SrT,MV,SrT,LV

MVA Rated power for the windings on HV/MV/LV side

usc,HVMV,usc,MVLV,usc,LVHV

% Relative short-circuit voltage of paths HV-MV, MV-LV,LV-HV

PCu,HVMV,PCu,MVLV,PCu,LVHV

kW Copper losses of path HV-MV, MV-LV, LV-HV

ur,sc,HVMV,ur,sc,MVLV,ur,sc,LVHV

% Relative short-circuit voltage, resistive part of pathsHV-MV, MV-LV, LV-HV

X/RHVMV,

X/RMVLV,X/RLVHV

Relative short-circuit voltage, X/R ratio of path HV-MV,

MV-LV, LV-HV

i0 % No-load current, related to rated current at HV side

PFe kW No-load losses

The following sections briefly describe the measurements performed in order to determine theparameters of a three-winding transformer.



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2.2.1 HV-MV Measurement

Figure 2.3: Short-circuit on MV-side, open-circuit on LV-side

The short-circuited winding (MV-side) should carry the nominal current according to:

IN,MV = Min(SrT,HV, SrT,MV)

3 UrT,MVin kA

The positive-sequence short-circuit voltage HV-MV can be calculated from the measured volt-age on the HV-side:

usc,HVMV = Usc,HVUrT,HV

100%

The real part of the short-circuit voltage can be specified in different ways:

Copper Losses in kW:The measured active power flow in kW can be directly entered into the correspondinginput field

Real part of short-circuit voltage in %:

ur,sc,HVMV = P

Cu,HVMVM in(SrT,HV, SrT,MV) 1000

100%

withPCu in kW.

X/R ratio:Imaginary part of the short-circuit voltage HV-MV:

ui,HVMV =

U2sc,HVMV U2r,sc,HVMV

X/R ratio for HV-MV:

X/RHVMV = Ui,HVMVUr,HV

MV



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The short-circuit voltage and impedance are referred to the minimum of the HV-side and MV-side rated powers.

rCu,HVMV =

ur,sc,HVMV

100%

=rCu,HV + rCu,MV

x,HVMV = ui,sc,HVMV

100% =x,HV + x,LV

2.2.2 MV-LV Measurement

Figure 2.4: Short-circuit on LV-side, open-circuit on HV-side

The short-circuited winding (LV-side) should carry the nominal current calculated as:

IN,LV = Min(SrT,MV, SrT,LV)

3 UrT,LV

The positive-sequence short-circuit voltage MV-LV can be calculated from the measured voltageon the MV-side as:

usc,MVLV = Usc,MVUrT,MV

100%




ur,sc,MVLV = PCu,MVLV

M in(SrT,MV, SrT,LV) 1000 100%

withPCu

in kW.



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X/R ratio:Imaginary part of the short-circuit voltage HV-MV:

ui,MVLV = U2sc,MVLV

U2r,sc,MVLV

X/R ratio for HV-MV:

X/RMVLV = Ui,MVLVUr,MVLV

The short-circuit voltage and impedance are referred to the minimum of the MV-side and LV-siderated powers.

rCu,MVLV = ur,sc,MVLV

100% =rCu,MV + rCu,LV

x,MVLV = ui,sc,MVLV

100% =x,MV + x,LV

2.2.3 LV-HV Measurement

Figure 2.5: Short-circuit on LV-side, open-circuit on MV-side

The short-circuited winding (LV-side) should carry the nominal current calculated as:

IN,LV = Min(SrT,HV, SrT,LV)

3

UrT,LV

The positive-sequence short-circuit voltage LV-HV can be calculated from the measured voltageon the HV-side as:

usc,LVHV = Usc,HVUrT,HV

100%





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ur,sc,LVHV = PCu,LVHV

M in(SrT,HV, SrT,LV)

1000

100%

withPCu in kW.

X/R ratio:Imaginary part of the short-circuit voltage LV-HV:

ui,LVHV =

U2sc,LVHV U2r,sc,LVHV

X/R ratio for LV-HV:

X/RLVHV = Ui,LVHVUr,LVHV

The short-circuit voltage and impedance are referred to the minimum of the LV-side and HV-siderated powers.

rCu,LVHV = ur,sc,LVHV

100% =rCu,LV + rCu,HV

x,LVHV = ui,sc,LVHV

100% =x,LV + x,HV

2.2.4 Magnetizing impedance measurement

Figure 2.6: Measurement of iron losses and no load current on LV-side

The no-load current in % referred to the HV-side rated power is calculated according to thefollowing equation::

i0= I0Ir,LV

SrT,LVSref

100% with I r,LV = SrT,LV3UrT,LV inkA

I0 measured no load current in kA

PFe measured iron losses in kW



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Sref =Sr,HV in MVA reference power inPowerFactory is equal to HV-side rated power

The measured active powerPFe in kW is entered directly into the correspondingPowerFactory

input field.

xM =100%

i0

rFe = Sref

PFe 1000 PFe inkW andSrefin M V A

2.2.5 Relation between input parameters and absolute impedances

The relation between the input parameters in the type and element dialogs and the absoluteimpedances are described in the following:

ImpedanceZHVMVseen from the HV-side:

usc,HVMV =ZHV,MV Min(SrT,HV,SrT,MV)U2rT,HV 100% with ZHVMVin Ohm referred to UrT,HV

ImpedanceZMVLVseen from the MV-side:

usc,MVLV =ZMV,LV Min(SrT,MV,SrT,LV)U2rT,MV

100% with ZMVLVin Ohm referred to UrT,MV

ImpedanceZLVHVseen from the LV-side:

usc,LVHV =ZLV,HV Min(SrT,LV,SrT,HV)U2rT,LV

100% with ZLVHVin Ohm referred to UrT,LV

2.3 Zero sequence models

The zero-sequence model of a three-winding transformer depends on the vector group of eachwinding. The following sections describe the different vector groups, the measurement of thezero-sequence data and the input parameters. Please note that the dashed connections tothe neutral terminals exist only if the option External Star Point is enabled (see transformerdialogue). The option is only possible if one side (HV, MV or LV) is on grounded star (groundedwye) or grounded Z connection.



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2.3.1 Zero-sequence Input parameters

u0sc,HVMV,u0sc,MVLV,u0sc,LVHV

% Relative zero-sequence short-circuit voltage of pathsHV-MV, MV-LV, LV-HV

ur,sc,HVMV,ur,sc,MVLV,ur,sc,LVHV

% Relative zero-sequence short-circuit voltage, resistive partof paths HV-MV, MV-LV, LV-HV

X/RHVMV,X/RMVLV,X/RLVHV

Relative short-circuit voltage, X/R ratio of path HV-MV,MV-LV, LV-HV

i0M % Zero-sequence magnetizing reactance, no load current

2.3.2 D-d-d connection (Delta-delta-delta)

Figure 2.7: Zero-sequence model of D-d-d transformer

According to Figure 2.7 the zero-sequence impedances have no influence on the zero-sequencevoltage. It is recommended for a D-d-d transformer to set the zero-sequence short-circuit volt-age equal to the positive sequence short-circuit voltage.



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2.3.3 YN-d-d connection (Grounded wye-delta-delta)

Figure 2.8: Zero-sequence model of YN-d-d transformer

Figure2.8shows that the LV-side and the MV-side have no zero-sequence connection to theterminals. Both delta windings are short-circuited in the zero-sequence system.

2.3.4 YN-yn-d connection (Grounded wye-grounded wye-delta)

Figure 2.9: Zero-sequence model of YN-yn-d transformer



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2.3.5 YN-yn-yn connection (Grounded wye-grounded wye-grounded wye)

Figure 2.10: Zero-sequence model of YN-yn-yn transformer

2.3.6 YN-yn-d auto-transformer (Grounded wye-grounded wye-delta auto transformer)

Figure 2.11: Zero-sequence model of YN-yn-d auto transformer



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2.3.7 YN-d-zn (Grounded wye-delta-grounded Z)

Figure 2.12: Zero-sequence model of YN-d-zn transformer

2.3.8 YN-d-y(Grounded wye-delta-wye)

Figure 2.13: Zero-sequence model of YN-d-y transformer



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3 PowerFactoryHandling

3 PowerFactoryHandling

In PowerFactoryeach winding of a transformer can have taps, however only one of the tap

changers can be controlled in the load-flow calculation. The specification of the tap changersfor each winding is done in the load-flow page of the transformer type. Then, in the load-flowpage of the element a tap changer is specified for automatic control. Note that in order to havethe load-flow algorithm adjust the taps while trying to find a solution, in the load-flow commandBasic Options page, the optionAutomatic Tap Adjust of Transformersmust be enabled.

In entering positive and zero sequence voltages for a three-winding transformer, one must notethat they are referred to the minimum rated power of the two windings. For example, for a60/60/10 MVA, 132/22/11 kV transformer, a value of 10% is specified both for the HV-MV andLV-HV positive-sequence short-circuit voltages. The impedance value (referred to HV-side) ofthe impedance between the HV and MV terminals is

0.1 (132kV)2

60MV A = 29.04primary

while the impedance value (referred to HV-side) of the impedance between HV and LV terminalsis

0.1 (132kV)2

10M V A = 174.24primary

It is possible to use manufacturers or any other available measurement data for load-flow cal-

culation. By clicking on the right-arrow in the load-flow specification page of a transformerelement, the user goes to a new window where the option According to Measurement Reportisdisplayed. Checking this option shows a table where data from measurements can be directlyentered (Figure3.1).

Figure 3.1: Measurement data input page for three-winding transformer



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4 Application in Power Systems


the impact of third-harmonic currents from one star-connected side to the other star-connected

side is reduced because these currents see the delta-connected side as a short-circuited wind-ing. The effect can be explained using the zero-sequence diagrams in Figure 2.9 and Fig-ure2.11.

Let us assume a third-harmonic source at the HV side and a load at the MV side. For simplicity,the magnetizing and grounding impedances are ignored. If the MV and LV winding resistancesand leakage reactances are referred to the HV side, the circuit in Figure 4.1 is obtained. Theimpedance of the middle leg is normally much less than that of the right leg which is why thethird-harmonic current content of the load is reduced.

In this application the tertiary winding can be internal with no terminals provided for connection.However, if the terminals are brought out of the transformer tank, then the tertiary winding canalso be used to connect shunt reactors, capacitors, or SVCs (Figure4.2). In Figure4.2, thestar-connected windings are shown as separate windings; however, this application is commonalso in case of autotransformer.

Figure 4.1: Zero-sequence load connected to the secondary of YN-yn-d transformer

Figure 4.2: Small tertiary winding for zero-sequence and reactive compensation

Step-up transformers especially for hydro power plants can be three-winding transformers wherethere is one high-voltage side, and two low-voltage sides with the same voltage rating. This iscost-effective because then only one switchgear is needed for the high-voltage side (Figure4.3).The same argument goes for network transformers for example in distribution networks.



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Figure 4.3: Tertiary winding to save on the high-voltage switchgear

Another application of three-winding transformers is when at some location in the network threedifferent voltage levels for example 132kV, 22kV, and 11kV are to be connected together.

In HVDC systems, three winding transformers are used to combine two 6-pulse rectifiers into a12-pulse one to give a smoother dc voltage. In this application, the 30 phase shift between a

star-connected winding and a delta-connected winding is employed (Figure 4.4).

Figure 4.4: Tertiary winding for30 phase shift



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5 Input/Output Definitions of Dynamic Models


Figure 5.1: Input/Output Definition of 3-winding transformer model for RMS and EMT simulation

Table 5.1: Input Variables of RMS and EMT transformer model

Parameter Description Unit

nntapin Tap position (HV), controller input

nntapin Tap position (MV), controller input

nntapin Tap position (LV), controller input

Table 5.2: Signals of RMS transformer model


I0rDelta h Circulating Current inHV-Delta-Winding, Real Part

kA.

I0rDelta m Circulating Current inMV-Delta-Winding, Real Part

kA.

I0rDelta l Circulating Current inLV-Delta-Winding, Real Part

kA.

I0iDelta h Circulating Current inHV-Delta-Winding, Imaginary Part

kA.

I0iDelta m Circulating Current inMV-Delta-Winding, Imaginary Part

kA.

I0iDelta l Circulating Current in

LV-Delta-Winding, Imaginary Part

kA.

Table 5.3: State Variables of transformer model for EMT-simulation


psim r Magnetizing flux (Real Part) p.u.

psim i Magnetizing flux (Imaginary Part) p.u.

psim 0 Magnetizing flux (Zero-Sequence) p.u.



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Table 5.4: Signals of EMT transformer model


I0Delta h Circulating Current inHV-Delta-Winding kA

I0Delta m Circulating Current inMV-Delta-Winding

kA

I0Delta l Circulating Current inLV-Delta-Winding

kA

i0 h Zero-Sequence Current inHV-Delta-Winding

kA

i0 m Zero-Sequence Current inMV-Delta-Winding

kA

i0 l Zero-Sequence Current inLV-Delta-Winding

kA



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List of Figures

List of Figures

2.1 PowerFactorypositive-sequence model of the 3-winding transformer, taps mod-

elled at star point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 PowerFactorypositive-sequence model of the 3-winding transformer, taps mod-elled at terminals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Short-circuit on MV-side, open-circuit on LV-side . . . . . . . . . . . . . . . . . . 5

2.4 Short-circuit on LV-side, open-circuit on HV-side. . . . . . . . . . . . . . . . . . . 6

2.5 Short-circuit on LV-side, open-circuit on MV-side . . . . . . . . . . . . . . . . . . 7

2.6 Measurement of iron losses and no load current on LV-side . . . . . . . . . . . . 8

2.7 Zero-sequence model of D-d-d transformer . . . . . . . . . . . . . . . . . . . . . 10

2.8 Zero-sequence model of YN-d-d transformer . . . . . . . . . . . . . . . . . . . . 11

2.9 Zero-sequence model of YN-yn-d transformer . . . . . . . . . . . . . . . . . . . . 11

2.10 Zero-sequence model of YN-yn-yn transformer . . . . . . . . . . . . . . . . . . . 12

2.11 Zero-sequence model of YN-yn-d auto transformer . . . . . . . . . . . . . . . . . 12

2.12 Zero-sequence model of YN-d-zn transformer . . . . . . . . . . . . . . . . . . . . 13

2.13 Zero-sequence model of YN-d-y transformer . . . . . . . . . . . . . . . . . . . . 13

3.1 Measurement data input page for three-winding transformer . . . . . . . . . . . . 14

4.1 Zero-sequence load connected to the secondary of YN-yn-d transformer. . . . . 15

4.2 Small tertiary winding for zero-sequence and reactive compensation . . . . . . . 15

4.3 Tertiary winding to save on the high-voltage switchgear . . . . . . . . . . . . . . 16

4.4 Tertiary winding for30 phase shift . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5.1 Input/Output Definition of 3-winding transformer model for RMS and EMT simulation 17



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List of Tables

List of Tables

5.1 Input Variables of RMS and EMT transformer model . . . . . . . . . . . . . . . . 17

5.2 Signals of RMS transformer model . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.3 State Variables of transformer model for EMT-simulation . . . . . . . . . . . . . . 17

5.4 Signals of EMT transformer model . . . . . . . . . . . . . . . . . . . . . . . . . . 18

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