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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
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.
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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 Model Diagrams and Input Parameters
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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2 Model Diagrams and Input Parameters
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 Model Diagrams and Input Parameters
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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2 Model Diagrams and Input Parameters
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%
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,MVLV = PCu,MVLV
M in(SrT,MV, SrT,LV) 1000 100%
withPCu
in kW.
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2 Model Diagrams and Input Parameters
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%
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
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2 Model Diagrams and Input Parameters
Real part of short-circuit voltage in %:
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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2 Model Diagrams and Input Parameters
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 Model Diagrams and Input Parameters
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 Model Diagrams and Input Parameters
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 Model Diagrams and Input Parameters
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 Model Diagrams and Input Parameters
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
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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4 Application in Power Systems
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
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
Parameter Description Unit
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
Parameter Description Unit
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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5 Input/Output Definitions of Dynamic Models
Table 5.4: Signals of EMT transformer model
Parameter Description Unit
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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