• Author / Uploaded
• VladimirCoello

Citation preview

DIgSILENT PowerFactory Technical Reference Documentation

Three-Winding Transformer ElmTr3,TypTr3

DIgSILENT GmbH Heinrich-Hertz-Str. 9 72810 - Gomaringen Germany T: +49 7072 9168 0 F: +49 7072 9168 88 http://www.digsilent.de [email protected] Version: 15.2 Edition: 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 means electronic or mechanical, without the prior written permission of DIgSILENT GmbH. Three-Winding Transformer (ElmTr3,TypTr3)

1

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 transformer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 PowerFactory Handling

14

4 Application in Power Systems

15

5 Input/Output Definitions of Dynamic Models

17

List of Figures

19

List of Tables

20

Three-Winding Transformer (ElmTr3,TypTr3)

2

2

Model Diagrams and Input Parameters

1

General Description

The 3-winding transformer is a 3-port element connecting 3 cubicles in the network. PowerFactory comes with a built-in model for three-winding transformers explained in this document. Section 2 presents the sequence equivalent models of the three-winding transformer including generalized tap-changers (for phase and magnitude). The input parameters are also covered in this section. More Specific PowerFactory handling issues are explained in Section 3. Section 4 discusses typical applications of three-winding transformers in power systems.

2 2.1

Model Diagrams and Input Parameters Positive and Negative sequence models

The detailed positive-sequence models with impedances in per unit are shown in Figure 2.1 and Figure 2.2. 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 designated by rCu and Xσ together with the corresponding winding initials. An ideal transformer with a 1:1 turns ratio links the three windings at the magnetic star point. The models also include a magnetisation reactance and an iron loss resistance designated respectively by xM and rF e . 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 changed from the star point (Figure 2.1) to the terminal sides (Figure 2.2) with the default position being the star point.

Figure 2.1: PowerFactory positive-sequence model of the 3-winding transformer, taps modelled at star point

Three-Winding Transformer (ElmTr3,TypTr3)

3

2

Model Diagrams and Input Parameters

Figure 2.2: PowerFactory positive-sequence model of the 3-winding transformer, taps modelled at terminals

2.2

Positive sequence input parameters

Ur,T,HV , Ur,T,M V , Ur,T,LV SrT,HV , SrT,M V , SrT,LV usc,HV −M V , usc,M V −LV , usc,LV −HV PCu,HV −M V , PCu,M V −LV , PCu,LV −HV ur,sc,HV −M V , ur,sc,M V −LV , ur,sc,LV −HV X/RHV −M V , X/RM V −LV , X/RLV −HV i0 PF e

kV

Rated voltages on HV/MV/LV side

MVA

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

%

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

kW

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

%

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

% kW

No-load current, related to rated current at HV side No-load losses

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

Three-Winding Transformer (ElmTr3,TypTr3)

4

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,M V =

M in(SrT,HV , SrT,M V ) √ 3 · UrT,M V

in kA

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

usc,HV −M V =

Usc,HV · 100% UrT,HV

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 corresponding input field • Real part of short-circuit voltage in %: ur,sc,HV −M V =

PCu,HV −M V · 100% M in(SrT,HV , SrT,M V ) · 1000

with PCu in kW. • X/R ratio: Imaginary part of the short-circuit voltage HV-MV: q 2 2 ui,HV −M V = Usc,HV −M V − Ur,sc,HV −M V X/R ratio for HV-MV: X/RHV −M V =

Three-Winding Transformer (ElmTr3,TypTr3)

Ui,HV −M V Ur,HV −M V

5

2

Model Diagrams and Input Parameters

The short-circuit voltage and impedance are referred to the minimum of the HV-side and MVside rated powers. ur,sc,HV −M V = rCu,HV + rCu,M V 100% ui,sc,HV −M V xσ,HV −M V = = xσ,HV + xσ,LV 100%

rCu,HV −M V =

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 =

M in(SrT,M V , SrT,LV ) √ 3 · UrT,LV

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

usc,M V −LV =

Usc,M V · 100% UrT,M V

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 corresponding input field • Real part of short-circuit voltage in %: ur,sc,M V −LV =

PCu,M V −LV · 100% M in(SrT,M V , SrT,LV ) · 1000

with PCu in kW.

Three-Winding Transformer (ElmTr3,TypTr3)

6

2

Model Diagrams and Input Parameters

• X/R ratio: Imaginary part of the short-circuit voltage HV-MV: q 2 2 ui,M V −LV = Usc,M V −LV − Ur,sc,M V −LV X/R ratio for HV-MV: X/RM V −LV =

Ui,M V −LV Ur,M V −LV

The short-circuit voltage and impedance are referred to the minimum of the MV-side and LV-side rated powers. rCu,M V −LV = xσ,M V −LV

2.2.3

ur,sc,M V −LV = rCu,M V + rCu,LV 100% ui,sc,M V −LV = = xσ,M V + xσ,LV 100%

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 =

M in(SrT,HV , SrT,LV ) √ 3 · UrT,LV

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

usc,LV −HV =

Usc,HV · 100% UrT,HV

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 corresponding input field Three-Winding Transformer (ElmTr3,TypTr3)

7

2

Model Diagrams and Input Parameters

• Real part of short-circuit voltage in %: ur,sc,LV −HV =

PCu,LV −HV · 100% M in(SrT,HV , SrT,LV ) · 1000

with PCu in kW. • X/R ratio: Imaginary part of the short-circuit voltage LV-HV: q 2 2 ui,LV −HV = Usc,LV −HV − Ur,sc,LV −HV X/R ratio for LV-HV: X/RLV −HV =

Ui,LV −HV Ur,LV −HV

The short-circuit voltage and impedance are referred to the minimum of the LV-side and HV-side rated powers. rCu,LV −HV = xσ,LV −HV

2.2.4

ur,sc,LV −HV = rCu,LV + rCu,HV 100% ui,sc,LV −HV = = xσ,LV + xσ,HV 100%

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 the following equation:: i0 =

I0 Ir,LV

·

SrT ,LV Sref

× 100% with

Ir,LV =

√

SrT ,LV 3·UrT ,LV

in kA

I0 measured no load current in kA PF e measured iron losses in kW Three-Winding Transformer (ElmTr3,TypTr3)

8

2

Model Diagrams and Input Parameters

Sref = Sr,HV in MVA → reference power in PowerFactoryis equal to HV-side rated power The measured active power PF e in kW is entered directly into the corresponding PowerFactory input field.

xM =

rF e =

2.2.5

Sref PF e · 1000

100% i0

PF e in kW and Sref in M V A

Relation between input parameters and absolute impedances

The relation between the input parameters in the type and element dialogs and the absolute impedances are described in the following: Impedance ZHV −M V seen from the HV-side:

usc,HV −M V = ZHV,M V ·

M in(SrT ,HV ,SrT ,M V ) 2 UrT ,HV

× 100%

with ZHV −M V in Ohm referred to UrT,HV

× 100%

with ZM V −LV in Ohm referred to UrT,M V

× 100%

with ZLV −HV in Ohm referred to UrT,LV

Impedance ZM V −LV seen from the MV-side:

usc,M V −LV = ZM V,LV ·

M in(SrT ,M V ,SrT ,LV ) 2 UrT ,M V

Impedance ZLV −HV seen from the LV-side:

usc,LV −HV = ZLV,HV ·

2.3

M in(SrT ,LV ,SrT ,HV ) 2 UrT ,LV

Zero sequence models

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

Three-Winding Transformer (ElmTr3,TypTr3)

9

2

Model Diagrams and Input Parameters

2.3.1

Zero-sequence Input parameters

u0sc,HV −M V , u0sc,M V −LV , u0sc,LV −HV ur,sc,HV −M V , ur,sc,M V −LV , ur,sc,LV −HV X/RHV −M V , X/RM V −LV , X/RLV −HV i0M

2.3.2

%

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

%

Relative zero-sequence short-circuit voltage, resistive part of paths HV-MV, MV-LV, LV-HV Relative short-circuit voltage, X/R ratio of path HV-MV, MV-LV, LV-HV

%

Zero-sequence magnetizing reactance, no load current

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-sequence voltage. It is recommended for a D-d-d transformer to set the zero-sequence short-circuit voltage equal to the positive sequence short-circuit voltage.

Three-Winding Transformer (ElmTr3,TypTr3)

10

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

Figure 2.8 shows that the LV-side and the MV-side have no zero-sequence connection to the terminals. 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

Three-Winding Transformer (ElmTr3,TypTr3)

11

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

Three-Winding Transformer (ElmTr3,TypTr3)

12

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

Three-Winding Transformer (ElmTr3,TypTr3)

13

3

3

PowerFactory Handling

PowerFactory Handling

In PowerFactory each 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 changers for each winding is done in the load-flow page of the transformer type. Then, in the load-flow page of the element a tap changer is specified for automatic control. Note that in order to have the load-flow algorithm adjust the taps while trying to find a solution, in the load-flow command ”Basic Options” page, the option Automatic Tap Adjust of Transformers must be enabled. In entering positive and zero sequence voltages for a three-winding transformer, one must note that they are referred to the minimum rated power of the two windings. For example, for a 60/60/10 MVA, 132/22/11 kV transformer, a value of 10% is specified both for the HV-MV and LV-HV positive-sequence short-circuit voltages. The impedance value (referred to HV-side) of the impedance between the HV and MV terminals is

0.1 ×

(132kV )2 = 29.04 primary Ω 60M V A

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

0.1 ×

(132kV )2 = 174.24 primary Ω 10M V A

It is possible to use manufacturers or any other available measurement data for load-flow calculation. By clicking on the right-arrow in the load-flow specification page of a transformer element, the user goes to a new window where the option According to Measurement Report is displayed. Checking this option shows a table where data from measurements can be directly entered (Figure 3.1).

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

Three-Winding Transformer (ElmTr3,TypTr3)

14

4

4

Application in Power Systems

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 winding. The effect can be explained using the zero-sequence diagrams in Figure 2.9 and Figure 2.11. 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 resistances and leakage reactances are referred to the HV side, the circuit in Figure 4.1 is obtained. The impedance of the middle leg is normally much less than that of the right leg which is why the third-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 can also be used to connect shunt reactors, capacitors, or SVCs (Figure 4.2). In Figure 4.2, the star-connected windings are shown as separate windings; however, this application is common also 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 where there is one high-voltage side, and two low-voltage sides with the same voltage rating. This is cost-effective because then only one switchgear is needed for the high-voltage side (Figure 4.3). The same argument goes for network transformers for example in distribution networks.

Three-Winding Transformer (ElmTr3,TypTr3)

15

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 three different 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 a 12-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 for 30◦ phase shift

Three-Winding Transformer (ElmTr3,TypTr3)

16

5

5

Input/Output Definitions of Dynamic Models

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

nntapin nntapin nntapin

Tap position (HV), controller input Tap position (MV), controller input Tap position (LV), controller input

Unit

Table 5.2: Signals of RMS transformer model Parameter

Description

Unit

I0rDelta h

Circulating Current in HV-Delta-Winding, Real Part Circulating Current in MV-Delta-Winding, Real Part Circulating Current in LV-Delta-Winding, Real Part Circulating Current in HV-Delta-Winding, Imaginary Part Circulating Current in MV-Delta-Winding, Imaginary Part Circulating Current in LV-Delta-Winding, Imaginary Part

kA.

I0rDelta m I0rDelta l I0iDelta h I0iDelta m I0iDelta l

kA. kA. kA. kA. kA.

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

Description

Unit

psim r psim i psim 0

Magnetizing flux (Real Part) Magnetizing flux (Imaginary Part) Magnetizing flux (Zero-Sequence)

p.u. p.u. p.u.

Three-Winding Transformer (ElmTr3,TypTr3)

17

5

Input/Output Definitions of Dynamic Models

Table 5.4: Signals of EMT transformer model Parameter

Description

Unit

I0Delta h

Circulating Current in HV-Delta-Winding Circulating Current in MV-Delta-Winding Circulating Current in LV-Delta-Winding Zero-Sequence Current in HV-Delta-Winding Zero-Sequence Current in MV-Delta-Winding Zero-Sequence Current in LV-Delta-Winding

kA

I0Delta m I0Delta l i0 h i0 m i0 l

Three-Winding Transformer (ElmTr3,TypTr3)

kA kA kA kA kA

18

List of Figures

List of Figures 2.1 PowerFactory positive-sequence model of the 3-winding transformer, taps modelled at star point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.2 PowerFactory positive-sequence model of the 3-winding transformer, taps modelled 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 for 30◦ phase shift . . . . . . . . . . . . . . . . . . . . . . . . . .

16

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

Three-Winding Transformer (ElmTr3,TypTr3)

19

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

Three-Winding Transformer (ElmTr3,TypTr3)

20