TechRef 2 W Transformer 3Phase

DIgSILENT PowerFactoryTechnical Reference Documentation

Two-Winding Transformer (3-Phase)ElmTr2

DIgSILENT GmbH

Heinrich-Hertz-Str. 972810 - Gomaringen

Germany

T: +49 7072 9168 00F: +49 7072 9168 88

http://[email protected]

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Copyright ©2011, 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.

Two-Winding Transformer (3-Phase) (ElmTr2) 1

http://www.digsilent.de

mailto:[email protected]

Contents

Contents

1 General Description 4

1.1 Model Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1.1 Positive and Negative sequence models . . . . . . . . . . . . . . . . . . . 4

1.1.2 Tap changer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.3 Zero sequence models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Load-Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.1 Tap changer basic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.2 Tap dependent impedance . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Measurement protocol (element-specific) . . . . . . . . . . . . . . . . . . 9

1.2.4 Automatic tap changer control . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Short-Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.1 Type data for IEC S/C calculations . . . . . . . . . . . . . . . . . . . . . . 14

1.3.2 Element data for IEC S/C calculations . . . . . . . . . . . . . . . . . . . . 15

1.4 RMS Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.5 Harmonic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 EMT Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6.1 Saturation characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6.2 Zero Sequence magnetizing reactance . . . . . . . . . . . . . . . . . . . 20

1.6.3 Residual flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.6.4 Stray capacitances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2 Modelling Details and Application Hints 23

2.1 Reference Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Zero Sequence Models of Common Vector Groups . . . . . . . . . . . . . . . . . 23

2.2.1 Yd-transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.2 YNyn/YNy /Yyn -transformer . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2.3 Model of YNyn/YNy/Yyn-transformer with closed tertiary delta winding . . 24

2.2.4 Model of YNzn/YNz/Zyn-transformer . . . . . . . . . . . . . . . . . . . . . 25

2.3 Auto-transformer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26


Contents

3 Input/Output Definitions of Dynamic Models 29

4 Input Parameter Definitions 30

4.1 2-Winding-Transformer Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 2-Winding-Transformer Element . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5 References 35

List of Figures 36

List of Tables 37


1 General Description


The two-winding transformer model is a very detailed model for various kinds of three-phase,two-winding transformers in power systems. It can represent e.g. network transformers, blocktransformers, phase shifters or MV-voltage regulators. The model makes special considerationfor auto-transformers.

This first section describes the general model and is valid for all PowerFactory calculation func-tions.

Particular aspects, such as saturation or capacitive effects, which are only relevant for somecalculation functions are described in the following sections.

Section 2. provides useful hints for special applications of the 2-winding transformer model.

1.1 Model Diagrams

1.1.1 Positive and Negative sequence models

The detailed positive-sequence model with absolute impedances (in Ohm) is shown in Fig-ure 1.1. It contains the leakage reactances and the winding resistances of the HV and LV sideand the magnetization reactance and the iron loss admittance close to the ideal transformer.

The model with relative impedances (in p.u.) is shown in Figure 1.2. The ideal transformer ofthe per-unitized model has a complex winding ratio with a magnitude of 1:1 and models thephase shift representing the vector groups of the two windings

Figure 1.1: Positive sequence model of the 2-winding transformer (in Ohms)

Figure 1.2: Positive sequence model of the 2-winding transformer (in p.u.)

The relation between the mathematical parameters in the model and the parameters in the typeand element dialogs are described as follows:



Zr,HV =U2r,HV

Sr(1)

Zr,LV =U2r,LV

Sr(2)

zsc = Usc/100 (3)

rsc =PCu/1000

Sr(4)

xsc =√z2sc − r2sc (5)

rCu,HV = γR,HV,1 · rsc (6)rCu,LV = (1− γR,LV,1) · rsc (7)

xσ,HV = γX,HV,1 · xsc (8)xσ,LV = (1− γX,LV,1) · xsc (9)

ZM =1

i0/100(10)

rFe =Sr

PFe/1000(11)

xM =1√

1z2M− 1

r2Fe

(12)

where,

Zr,HV Ω Nominal impedance, HV sideZr,LV Ω Nominal impedance, LV sideUr,HV , Ur,LV kV Rated voltages on HV/LV sideSr MVA Rated powerPCu kW Copper lossesuSC % Relative short-circuit voltagezSC p.u. Short-circuit impedancerSC p.u. Short-circuit resistancexSC p.u. Short-circuit reactanceγX,HV,1 p.u. Share of transformer short-

circuit reactance on HV side inthe positive-sequence system

γR,HV,1 p.u. Share of transformer short-circuit resistance on HV side inthe positive-sequence system

rCu,HV , rCu,LV p.u. Resistances on HV/LV sidesxσ,HV , xσ,LV p.u. Leakage reactances on HV/LV

sideI0 % no-load currentPFe kW No-load lossesxM p.u. Magnetizing impedancerFe p.u. Shunt resistance



1.1.2 Tap changer

The tap changer is represented by an additional, ideal transformer connected to either the HVor the LV side (see Figure 1.3 and Figure 1.4). In most application, the winding ratio of thistransformer is real and is defined by the actual tap position (in number of steps) times theadditional voltage per steps.

Figure 1.3: Transformer model with tap changer modelled at HV - side

Figure 1.4: Transformer model with tap changer modelled at LV - side

Figure 1.5: Complex tap changer model in PowerFactory

Phase shifters are modelled by a complex ratio using a complex value of dutap according toFigure 1.5.

There are two possibilities of specifying a phase shifting transformer. Either by entering magni-



tude and angle (dutap and ϕtap) of the additional voltage per tap step or by defining magnitudeand angle at each individual tap-step (|U + dutap|, ϕu). The latter is supported by the measure-ment report in the transformer element (see also section 1.2.3).

1.1.3 Zero sequence models

The zero sequence equivalent model of a Yd-transformer as a typical representation includinga tap changer at the HV side is shown in Figure 1.6.

More transformer models for further configurations are shown in section 2.2.

(a)

(b)

Figure 1.6: Yd transformer (a) in the zero-sequence system with HV side tap changer in detailed(a) and simplified representation (b)



1.2 Load-Flow Analysis

The load flow ComLdf calculation uses the detailed model for the transformer, that is all shuntand branch impedances for positive- and zero-sequence system.

A component that is of special interest for load flow calculations is the tap changer. In the typedata section it is modelled using its constructive properties, in the element data section it isdefined in its control behaviour for steady-state simulation.

There are 3 areas where the tap changer is referenced:

1. Basic data of the tap changer;

2. Tap dependent impedance for a transformer type;

3. Measurement protocol specific for a transformer element.

1.2.1 Tap changer basic data

The basic data of the tap changer are listed in the following Table 1.1.

Table 1.1: Basic data of tap changers

Parameter Description Unit

At side Side at which the tap changer is modelled(not necessarily the side to which the tapchanger is connected physically)

-

Additional voltage∆u per tap

Additional voltage per tap. %

Phase of ∆u Constant phase between fix voltage and ad-ditional voltage of the winding (parameter φtin Figure 1.5)

degree ()

Neutral/min./max.position

Range of possible positions for the tapchanger. At the neutral position, the wind-ing ratio corresponds to the ratio of the ratedvoltages

-



Figure 1.7: Type options for tap changers

1.2.2 Tap dependent impedance

The parameter section for the tap-dependent impedance appears when this option is activated(see Figure 1.7). Parameters that can be considered to be tap-dependent are the short circuitimpedances and copper losses (short circuit resistance) in the positive- and zero-sequencesystems.

For tap positions between min. and neutral and between neutral and max. tap dependentparameters are interpolated using splines.

1.2.3 Measurement protocol (element-specific)

A very precise method tap-changer description is the so-called measurement report. Here, alltap-dependent parameters can be entered per tap step.

If the option According to measurement report is enabled the corresponding type-parametersare overwritten by the respective element parameters. The corresponding input dialogue isshown in Figure 1.8 with a brief parameter description in Table 1.2.



Table 1.2: Data of measurement protocol for transformer elements


Voltage Voltage at tap position i. kVAngle Absolute tap-angle (parameter φu in Fig-

ure 1.5)degree ()

uk S/C voltage of the transformer %PCu Copper losses kWAdd. rating Factor Rating factor for considering tap-dependent

transformer rating. The additional rating fac-tor is multiplied by the general rating factor(Rating Factor on the Basic Data page).

(p.u.)

Figure 1.8: Element-specific measurement protocol

1.2.4 Automatic tap changer control

Automatic tap changer control is activated by setting the corresponding option on the load flowpage of the transformer element. Additionally, automatic tap adjustment can be globally enabledor disabled by the load flow command. The information required for tap changer control is shownin Figure 1.9 and described in Table 1.3.



Figure 1.9: Data for automatic tap changer control



Table 1.3: Dialog fields for the automatic tap changer control

Parameter Description

According toMeasurementreport

Instead of the type data for the tap-dependent transformervalues the element-specific measurement report is used

Tap position Tap position used during the load flow calculation. If AutomaticTap Changing is activated this value corresponds to the initialtap position.

Automatic tapchanging

Activating automatic tap adjustment in load flow analysis.

Tapchanger

continuous An idealized, continuous tap changer isassumed. As a result, the tap controller can ideally comply withthe specified control conditionThis option is useful for voltage regulators in distributionsystems having a very large number of tap steps or for thyristorcontrolled tap changers.discrete Standard option. Only integer tap positions areconsidered.

Controllednode

HV Tap controls the HV-side.LV Tap controls the LV-sideEXT Slave mode. The tap changer just follows the tapposition of the selected Master -transformer.

SetpointOnly for V control mode:local the voltage setpoint and voltage range settings(max./min. voltage) must be enter in the transformer dialogbus target voltage the voltage setpoint and voltage rangesettings (max./min. voltage) are taken from the controlledbusbar (topological search)

Controlmode

V Voltage control. For unbalanced load flow analysis, thecontrolled phase needs to be defined additionally.Q Reactive power control (see also Figure 1.10)P Active power control (only applicable to phase shifters, seealso Figure 1.10)

Figure 1.10: Orientation of Power values counted positive



Table 1.4: Additional data for tap changer control

Parameter Description

Set Point V-/Q-/P- reference (depending on selected control mode)Lower/Upperbound

Lower and upper boundary of the controlled variable. In case ofdiscrete tap changers, the tap control can drive the controlledvariable just into a permitted band. In case of continuous tapchangers the tap controller can ideally regulate to the referencepoint.

Remote Control Allows for the selection of a bus bar different from thetransformer terminals (V-control). In case of P-or Q-control theflow through any cubicle can be controlled.

Voltage control includes optional line drop compensation. This function controls the voltage ata remote busbar without measuring the voltage at that bus-bar. Instead, the actual value isestimated by measuring the voltage at the HV or LV side of the transformer and simulating thevoltage drop across the line.

The principle of the line drop compensation is shown in Figure 1.11, the corresponding param-eters are explained in Table 1.5.

Figure 1.11: Principle of line drop compensation

Table 1.5: Line drop compensation (for voltage control)


Currenttransformer rating

Primary CT-current-rating. A

Voltagetransformer ratio

Ratio of the voltage transformer -

RSet, XSet LDC-impedance, defined as voltagedrop at rated current. It corresponds tothe LDC-impedance in Ohm times thesecondary CT current rating.

V



Generally, there is more than just one possible solution to a load flow problem consideringautomatic tap changer control. Especially in meshed networks, several transformers can controlthe voltage in certain areas. In case of parallel transformers, the problem can usually be solvedby operating the two parallel transformers in a master slave mode.

In a general configuration however, especially when parallel transformer have different shortcircuit impedances or different tap steps, the steady state network solution cannot be obtainedthat easily.

PowerFactory addresses the mentioned problem by allowing the user to enter a controller timeconstant, specifying the speed of control actions and hence the participation of several trans-formers regulating the voltage of the same bus bar.

The approach is based on controller block diagrams according to Figure 1.12. In case of flow-controllers (P-/Q-control) the controller sensitivity translating a power mismatch into an equiva-lent turns-ratio percentage can be entered additionally.

In the actual load flow algorithm, which just looks at steady state conditions, controller timeconstants and sensitivities are translated into equivalent participation factors.

(a) (b)

Figure 1.12: Principle of simulated dynamic control for V and P/Q

The parameters offered by PowerFactory are explained in Table 1.6.

Table 1.6: Dynamic and static control parameters


Controller timeconstant

Time constant of the controller s

Controllersensitivity dv/dP

Estimated sensitivity of active powerflow towards tap changer variations

%/MW

Controllersensitivity dv/dQ

Estimated sensitivity of reactive powerflow towards tap changer variations

%/Mvar

1.3 Short-Circuit Analysis

1.3.1 Type data for IEC S/C calculations

Short-Circuit calculations according to IEC assume that the shunt impedances in positive- andnegative-sequence (magnetizing reactance, iron losses) are neglected. The shunt impedances



in the zero-sequence system however must be considered. These parameters are shown in thedialog of IEC S/C calculation.

Another detail specific to IEC calculation is the distinction between no-load and on-load tapchangers. Different impedance correction factors apply for each group. The property of on-loadvariation of the tap changer therefore can be enabled in the IEC S/C calculation dialog.

1.3.2 Element data for IEC S/C calculations

This page contains additional information which is used to calculate the impedance correctionfactor of the transformer.

The first criterion defines whether the transformer is a unit transformer or a network transformer.In case of unit transformers, one common correction factor is applied to transformer and gener-ator. Network transformers are individually.

Two different calculation procedures can be applied. The first is a general correction indepen-dent of the actual operating conditions of a selected transformer. The second is more specificand may lead to more precise calculation results. The selection of the correction method alongwith the additional data required are shown on the S/C page, as can be seen in Figure 1.13.

Figure 1.13: Type specific data for IEC short-circuit calculations

1.4 RMS Simulation

The model used by the RMS simulation is identical to the load flow model. However, the tapcontroller definitions are not considered here. For the simulation of tap controllers, a separatedynamic model needs to be defined that can be interfaced with the transformer using the inputvariable nntapin (tap-input).

1.5 Harmonic Simulation

For accurately modelling high frequency effects of transformers, additional capacitances needto be considered, as shown in Figure 1.14.

These capacitances are equivalent capacitances of the model and not the actual winding ca-pacitances. For obtaining equivalent capacitances from winding capacitances, the winding con-nection (D/Y) must be considered additionally.

The high frequency model according to Figure 1.14 provides an accurate frequency response



with respect to voltages and currents at the transformer terminals. However, it is not possible tosimulate effects internal to the transformer, such as internal voltage stress.

(a)

(b)

Figure 1.14: HF Model for the external capacitances in positive sequence system (a) and zero-sequence system (b)

1.6 EMT Simulation

For simulating nonlinear, electromagnetic transient such as transformer inrush currents or ferro-resonance, core saturation needs to be included into the transformer model. Furthermore,depending on the frequencies involved in the transient simulation, the transformer model has toaccount for the stray capacitances between windings and winding to ground.

1.6.1 Saturation characteristic

Figure 1.15 shows the equivalent model of 2 winding 3-phase transformer for the positive se-quence. For simplicity, the tap changer has been left aside in the figure; however it is consideredin the model according to Figure 1.3, Figure 1.4 and Figure 1.5 as described in previous chap-ters.

The exciting current of a transformer (no-load test) consist of an imaginary part, which is themagnetizing current flowing through the non-linear reactance XM in Figure 1.15, and a smallerreal part flowing through the resistance RFe, which accounts for the excitation losses.



The non-linear magnetizing reactance XM represents the saturation characteristic of the trans-former and it is defined in the transformer type (TypTr2\EMT simulation page). The modelsupports the following options:

Linear: no saturation considered

Two slope: the saturation curve is approximated by a two linear slopes

Polynomial: the saturation curve is approximated by a polynom of user-defined order. Thepolynom fits asymptotically into the piecewise linear definition.

Current/Flux values: the user inputs current-flux values as a sequence of points and selectsamong a piecewise-linear or spline interpolation.

Figure 1.15: Equivalent circuit of the 2 winding 3-phase transformer for the positive sequence

The position of the magnetizing branch in the equivalent model of Figure 1.15 is defined in termsof the distribution of the leakage reactance and resistance (TypTr2\EMT-Simulation page). De-fault value is 0.5 which means that the total leakage impedance of the transformer (short-circuitimpedance) equally distributes between the HV and the LV winding. The user can modify theposition of the magnetizing branch in the transformer model by modifying these factors.

Two slope and polynomial characteristic

Figure 16 shows the magnetizing current-flux curves for the two slope and polynomial charac-teristics. The input parameters of both curves are the same except for the saturation exponent,which only applies to the polynomial characteristic. The input parameters are listed in Table 7.

Figure 1.16: Two slope and polynomial saturation curves



Table 1.7: Basic data of the two-slope and polynomial saturation characteristics


Knee Flux Knee-point of asymptotic piece-wiselinear characteristic. Typical valuearound 1.1 to 1.2 times the rated flux.

p.u.

Linear(unsaturated)reactance

Magnetizing reactance for unsaturatedconditions Lunsat.In p.u. values, the linear reactance isequal to the reciprocal of themagnetizing current (reactive part ofthe exciting current).

p.u.

Saturatedreactance

Magnetizing reactance for saturatedconditions Lsat.

p.u.

Saturationexponent

Exponent of polynomial representation(ksat). Typical values are 9,13,15. Thehigher the exponent the sharper thesaturation curve.

-

The reciprocal of the p.u. unsaturated reactance is equal to the the p.u. magnetizing current(i.e. the imaginary part of the exciting current). Therefore, the program automatically adjuststhe unsaturated reactance based on the no-load current and no-load losses entered in the loadflow page (TypTr2\Load Flow) and vice-versa:

1

XM=

√(IMIrated

)2

−(PexcSrated

)2

(13)

where,

IM : Magnitude of the exciting current in the no-load test

Pexc: Excitation losses in the no-load test

IR,SR: Are the rated current and apparent power of the transformer respectively

The saturated reactance is also referred as the air-core reactance; it is fairly low compared withthe unsaturated reactance. Typical values for two-winding transformers are 1 to 2 times theshort-circuit inductance and 3 to 4 times for autotransformes [1].

The polynomial characteristic uses expression 14 to fit the curve asymptotically into the piece-wise linear definition. The higher the exponent, the sharper the saturation curve:

iM =ΨM

LM·

(1 +

∣∣∣∣ΨM

Ψ0

∣∣∣∣ksat)

(14)

Where,



iM Magnetizing current p.u.ΨM Magnetizing flux p.u.LM Linear reactance p.u.Ψ0 This parameter is automatically calculated so that the

polynomial characteristic fits the saturated reactance in fullsaturation and transits steadily into the piece-wise linearcharacteristic at the knee flux point.

p.u.

ksat Saturation exponent, i.e. polynome degree -

This polynomial characteristic is always inside the corresponding linear representation. In fullsaturation the polynomial characteristic is extended linearly. Compared to the two-slope curve, itdoes not contain a singular point at the knee flux and therefore its derivate (magnetizing voltage)is continuously defined.

The p.u. values used for the definition of the saturation characteristic of the positive sequencemodel are referred to the following bases quantities:

• Ubase[kV]: nominal voltage of the (energizing) winding, i.e. the winding used for the noload test

• Sbase[MVA]: nominal power of the (energizing) winding

• Ibase[A] =Sbase[MVA]√3 · Ubase[kV ]

× 1000

• ψbase[V · s] =Ubase[kV ]/

√3

2πf [Hz]× 1000

• Lbase[H] =

(U2base[kV ]

Sbase[MVA]

)· 1

2πf [Hz]

Current-Flux values

The user can also define the saturation curve in terms of measured current-flux values andselect between a piecewise linear or spline interpolation.

The current-flux values in the table are peak values in p.u.. In a power transformer with im-pressed voltage, the magnetizing flux in p.u. is equal to the magnetizing voltage in p.u., thusflux and voltage are interchangeable and the p.u. current-flux curve represents a p.u. current-voltage curve as well. Furthermore, it can be assumed that the applied voltage remains fairlylinear during the non-load tests and hence the ration between RMS and peak values of thevoltage is given by

√2.

On the contrary, the magnetizing current is distorted (non-sinusoidal) because of the saturationcurve. As a consequence of that, the ratio between the RMS and peak value of the magnetizingcurrent is not longer

√2 and the user has to enter truly peak values in the table.

The base quantities of the p.u. values in the current-flux table are also referred to the peakvalues of the corresponding nominal variables:



Ibase[A] =√

2× Sbase[MVA]√3 · Ubase[kV ]

× 1000

Ψbase[V · s] =√

2× Ubase[KV ]/√

3

2πf [kHz]× 1000

1.6.2 Zero Sequence magnetizing reactance

The zero sequence magnetizing current strongly depends on the construction characteristicof the transformer core (three-legged, five-legged, shell-type, etc.) and its vector group. Fig-ure 1.17 shows the equivalent circuit for the zero sequence.

Figure 1.17: Equivalent circuit of the 2 winding 3-phase transformer for the zero-sequence

Transformer with delta-connected windings

If the transformer has delta-connected windings, then any zero sequence excitation approx-imates a zero-sequence short-circuit, as the delta-connected winding short-circuits the zero-sequence current. In that cases there is no need to represent zero sequence saturation.

Transformer without delta-connected windings

If the transformer type does not have delta-connected windings, then the zero-sequence excita-tion current results generally higher than the positive-sequence excitation current and stronglydepends on the core type.

To account for the higher zero-sequence linear exciting current when no delta-connected wind-ing is available, PowerFactory allows for the definition of a linear (unsaturated) zero-sequencemagnetizing impedance. This zero-sequence magnetizing impedance and its R/X ratio is de-fined in the load flow page (TypTr2\Load flow); the parameters are made available dependingon the vector group (i.e. hidden in case of delta-connected winding).

To account for the core type dependency of the the zero-sequence saturation characteristic, thetransformer model supports the following two options in the EMT-simulation page (TypTrf ):

3 Limbs core: use this option for three-legged core designs. In this core type, the fluxes areroughly equal in the three legs and must therefore return outside the core through the air-gap and the tank. Because of the fact that the air-gap and the tanks are no-magnetic, thezero-sequence magnetizing current is nearly linear and therefore the model uses the linearzero-sequence magnetizing impedance defined in the load flow page. In other words, itdoes not consider zero-sequence saturation effects.

5 Limbs core: use this option for five-legged and shell-type cores. As the zero-sequencefluxes return inside the core, the model uses the saturation characteristic (of the positivesequence) in the zero-sequence magnetizing reactance as well.



1.6.3 Residual flux

The residual flux is the magnetizing flux which remains in the core after the transformer hasbeen switched off. A residual flux, other than a remanent 1 flux, implies then the circulation of amagnetizing current (ΨM = LM · IM ).

Once the transformer has been switched off, this magnetizing current circulates through the no-load losses resistance Rm and de-magnetizes the core. The flux decays then exponentially witha time constant Lm/Rm with Lm the linear magnetizing inductance. To simulate the decayingmagnetizing current and hence the decaying residual flux it is necessary to define the no-loadlosses. Otherwise, if Rm=0, the magnetizing current cannot circulate and PowerFactory willautomatically set the residual flux to 0 as soon as the transformer has been switched off.

The user can also define the residual flux in the EMT simulation by a parameter event. Forsimplicity, the residual flux is entered in dq0-components using the following signals:

psimd: residual flux, d-component in p.u.

psimq: residual flux, q-component in p.u.

psim0: residual flux, zero-sequence component in p.u.

The dq0-transformation relates the dq0-fluxes with the abc-fluxes (phase or natural compo-nents) as follows:

ψdψqψ0

=

2

3−1

3

1

3

01√3− 1√

31

3

1

3

1

3

×ψaψbψc

The inverse transformation is given by:

ψaψbψc

=

1 0 1

−1

2

√3

21

−1

2−√

3

21

×ψdψqψ0

The calculation parameters c:psim c, c:psim b and c:psim c give the resulting flux (simulationresult) in natural components for the phases a, b and c respectively.

It is in general quite difficult to predict the residual flux of a transformer in a reliably way. How-ever as the residual flux has a major impact on the amplitude of inrush currents, it has to beconsidered in the model. If it is not known, typical maximum values between 0.8 and 0.9 p.u.can be assumed for worst-case conditions.

1.6.4 Stray capacitances

In high frequency EMT-applications, e.g. switching or lightning studies, transformer capaci-tances have to be considered.

1The remanent flux is the flux at i=0 in the hysteresis curve



The stray capacitances of a transformer do not only depend on its construction characteristicsof the transformer (like for instance length of the windings, insulating material, core dimensions,etc.) but also on its installation characteristics as well (indoor or outdoor transformer, proximityto other grounded components, walls, etc.). For that reason, the stay capacitances are not partof the transformer type data but defined in the element (ElmTr2).

On the EMT-Simulation page of the element (ElmTr2\EMT-Simulation) the user can enable thestray capacitances in the model by ticking the Consider Capacitances option. The model ac-count for the following capacitances:

Capacitance HV to ground: applies both for the positive and zero-sequence

Capacitanve LV to ground: applies both for the positive and zero-sequence

Capacitance HV-LV, positive sequence:

Capacitance HV-LV, zero sequence:

For typical values the reader is referred to [2].


2 Modelling Details and Application Hints


2.1 Reference Values

All transformer parameters entered in p.u. or % are referred to the transformer ratings. Trans-former rated voltages different from nominal bus bar voltages are correctly considered.

2.2 Zero Sequence Models of Common Vector Groups

2.2.1 Yd-transformer

This model is described in detail in section 1.1.3 as a general example for the zero-sequencesystem modelling. Please refer to that section for further explanation.

If no accurate data are available from the manufacturer, the following estimations can be usedfor the zero-sequence impedance voltages as seen from the grounded side:

Core-type transformer (3-limb) usc,0 = 0.85 · Usc,1, uRr,0 = 0

Shell-type transformer (4/5-limb) usc,0 = 1.0 · Usc,1, uRr,0 = 0

where usc,0 is the positive sequence impedance voltage.

Concerning the model for the magnetic flux saturation characteristics the transformer typeswith 3 or 4/5 limbs behave differently in general. In the 3-limb design, the zero-sequence fluxdefined by 15 is not guided via the transformer limbs but uses parallel paths (e.g. through thetransformer vessel, oil, ) and thus can be modelled as linear without saturation effects.

Ψ0 =1

3· (ΨA + ΨB + ΨC) (15)

2.2.2 YNyn/YNy /Yyn -transformer

The zero sequence equivalent circuit diagram of the YNyn transformers is depicted in Figure 2.1.The equivalent circuit diagram of star connected transformers with isolated star point can bederived from this equivalent circuit by assuming infinite grounding impedances at the respectiveside.



Figure 2.1: YNyn transformer (zero-sequence system)

S/C impedance HV-side zsc,0,HV = rCu,0,HV + xσ,0,HV

S/C impedance LV-side zsc,0,LV = rCu,0,LV + xσ,0,LV

S/C impedance both sides zsc,0 = zsc,0,HV + zsc,0,LV

The zero-sequence magnetizing impedance ratio depends strongly on the construction of themagnetic circuit of the transformers. Typical ranges are:

Core-type transformer (3-limb) zM0

zsc,0= 3 . . . 10

Shell-type transformer (4/5-limb) zM0

zsc,0= 10 . . . 100 (or bank of 3 single phase units)

2.2.3 Model of YNyn/YNy/Yyn-transformer with closed tertiary delta winding

An internal tertiary delta winding can be considered either using the PowerFactory three-windingmodel or, in a simplified way, by considering that the short circuit impedance of the internal deltawinding can be modeled by an impedance parallel to the zero sequence magnetizing impedanceof Figure 19. Hence, an internal delta winding can be modeled by simply assuming a very lowzero-sequence magnetizing reactance.

Typical values are:

zM0

zsc,0= 1..2.4



The short circuit resistance of the delta-tertiary winding can be entered as R/X ratio in the Mag.R/X field.

Figure 2.2: Zero sequence model of YNYnd-Transformer

2.2.4 Model of YNzn/YNz/Zyn-transformer

A zig-zag winding completely uncouples primary and secondary side of the zero sequencesystem, as shown in Figure 2.3.

Figure 2.3: YNzn transformer (zero-sequence system) with HV side tap changer in detailedrepresentation



2.3 Auto-transformer Model

The PowerFactory model for the auto-transformer is a special case of the 2-winding star/star(YY)-Transformer.

As soon as an auto-transformer symbol is entered, the option Connected Star Points (Autotrans-former) can be checked on the Basic Data page of the element (see Figure 21). This activatesthe interpretation as an autotransformer. This option only is shown when the type selected forthe transformer is of vector group YY.

The effect of this connection can be seen in Figure 22. Besides the additional connectionbetween the star points, only one grounding impedance can be entered.

Figure 2.4: Auto-transformer option



Figure 2.5: YY transformer (zero-sequence system) in auto-transformer configuration (incl. tapchanger on the HV side)

For the YY autotransformer the currents of HV side and LV side both flow through the samegrounding impedance ZE = RE + jXE . The voltage over this grounding impedance ZE thusaffects the zero-sequence system voltages on both sides. This makes it necessary to considerthe absolute value of the impedances, currents and voltages and not the p.u.-values.

Very often, an additional delta tertiary winding is used to reduce the zero-sequence impedanceof auto-transformers. The approach for modeling this is equivalent to the internal delta tertiarywinding modeling of Yy-transformers.



Figure 2.6: YYd transformer (zero-sequence system) in auto-transformer configuration


3 Input/Output Definitions of Dynamic Models

3 Input/Output Definitions of Dynamic Models

Figure 3.1: Input/Output Definition of 2-winding transformer model for RMS and EMT simulation

Table 3.1: Input Variables of RMS and EMT transformer model


nntapin Tap position (input) -

Table 3.2: State Variables of transformer model for EMT-simulation


psimd Magnetizing flux, d-component p.u.psimq Magnetizing flux, q-component p.u.psim0 Magnetizing flux, 0-component p.u.

Table 3.3: Additional parameters and signals of EMT transformer model (calculation parameter)


psim a Magnetizing flux, phase A p.u.psim b Magnetizing flux, phase B p.u.psim c Magnetizing flux, phase C p.u.im a Magnetizing current, phase A p.u.im b Magnetizing current, phase B p.u.im c Magnetizing current, phase C p.u.


4 Input Parameter Definitions


4.1 2-Winding-Transformer Type


loc name Nament2ph Technologystrn Rated Power MVAfrnom Nominal Frequency Hzutrn h Rated Voltage: HV-Side kVutrn l Rated Voltage: LV-Side kVuktr Positive Sequence Impedance:

Short-Circuit Voltage uk%

pcutr Positive Sequence Impedance:Copper Losses

kW

uktrr Positive Sequence Impedance:SHC-Voltage (Re(uk)) ukr

%

xtor Positive Sequence Impedance: RatioX/R

tr2cn h Vector Group: HV-Sidetr2cn l Vector Group: LV-Sident2ag Vector Group: Phase Shift *30degvecgrp Vector Group: Nameuk0tr Zero Sequ. Impedance, Short-Circuit

Voltage: Absolute uk0%

ur0tr Zero Sequ. Impedance, Short-CircuitVoltage: Resistive Part ukr0

%

tap side Tap Changer: at Sidedutap Tap Changer: Additional Voltage per

Tap%

phitr Tap Changer: Phase of du degnntap0 Tap Changer: Neutral Positionntpmn Tap Changer: Minimum Positionntpmx Tap Changer: Maximum Positioncurmg Magnetizing Impedance: No Load

Current%

pfe Magnetizing Impedance: No LoadLosses

kW

zx0hl n Zero Sequence MagnetizingImpedance:Mag. Impedance / uk0

rtox0 n Zero Sequence Magnetizing R/X ratio:Mag. R/X

zx0hl h Distribution of Zero Sequ.Leakage-Impedances: z, Zero Sequ.HV-Side




zx0hl l Distribution of Zero Sequ.Leakage-Impedances: z, Zero Sequ.LV-Side

itapzdep Tap dependent impedanceuktmn Tap dependent impedance: uk (min.

tap)%

uktmx Tap dependent impedance: uk (max.tap)

%

pcutmn Tap dependent impedance: Pcu (min.tap)

kW

ukrtmn Tap dependent impedance: Re(uk)(min. tap)

%

xtortmn Tap dependent impedance: X/R (min.tap)

pcutmx Tap dependent impedance: Pcu (max.tap)

kW

ukrtmx Tap dependent impedance: Re(uk)(max. tap)

%

xtortmx Tap dependent impedance: X/R (max.tap)

uk0tmn Tap dependent impedance: uk0 (min.tap)

%

uk0tmx Tap dependent impedance: uk0 (max.tap)

%

uk0rtmn Tap dependent impedance: Re(uk0)(min. tap)

%

uk0rtmx Tap dependent impedance: Re(uk0)(max. tap)

%

itrdl Distribution of Leakage Reactances(p.u.): x,Pos.Seq. HV-Side

itrdl lv Distribution of Leakage Reactances(p.u.): x,Pos.Seq. LV-Side

itrdr Distribution of Leakage Resistances(p.u.): r,Pos.Seq. HV-Side

itrdr lv Distribution of Leakage Resistances(p.u.): r,Pos.Seq. LV-Side

oltc On-load Tap ChangerpT Tap Changer: Voltage Range %ansiclass Classpict2 Inrush Peak Current: Ratio Ip/In p.u.pitt2 Inrush Peak Current: Max. Time sitrmt Magnetizing Reactance: Typepsi0 Magnetizing Reactance: Knee Flux p.u.xmlin Magnetizing Reactance: Linear

Reactancep.u.

xmair Magnetizing Reactance: SaturatedReactance

p.u.




ksat Saturation Exponentit0mt Zero Sequence Magnetizing

Reactance: Type Zero SequencepStoch Stochastic model StoTyptrf

4.2 2-Winding-Transformer Element


loc name Nametyp id Type (TypTr2)bushv HV-Side (StaCubic)bushv bar HV-Sidebuslv LV-Side (StaCubic)buslv bar LV-SideiZoneBus Zoneoutserv Out of Servicentnum Number of: parallel Transformersratfac Rating FactorSnom Rated Power MVAi auto Connected Star Points (Auto

Transformer)i eahv HV-side, phase 2 internally groundedignd h Grounding Impedance, HV Side:

Neutral Pointre0tr h Grounding Impedance, HV Side: Re Ohmxe0tr h Grounding Impedance, HV Side: Xe Ohmi ealv LV-side, phase 2 internally groundedignd l Grounding Impedance, LV Side:

Neutral Pointre0tr l Grounding Impedance, LV Side: Re Ohmxe0tr l Grounding Impedance, LV Side: Xe OhmrSbasepu r (Sbase) p.u./SbasexSbasepu x (Sbase) p.u./Sbaser0Sbasepu r0 (Sbase) p.u./Sbasex0Sbasepu x0 (Sbase) p.u./SbaseInom h HV-Side, Rated Current kAInom l LV-Side, Rated Current kAiTaps According to Measurement Reportnntap Tap: Tap Positionntrcn Tap: Automatic Tap Changingi cont Tap: Tap Changert2ldc Tap: Controlled Nodeilcph Tap: Phase




imldc Tap: Control Modei rem Tap: Remote Controlp rem Tap: Controlled Node

(StaBar,ElmTerm)p cub Tap: Controlled Branch (Cubicle)

(StaCubic)usetp Tap: Voltage Setpoint p.u.usp low Tap: Lower Voltage Bound p.u.usp up Tap: Upper Voltage Bound p.u.psetp Tap: Active Power Setpoint MWpsp low Tap: Lower Active Power Bound MWpsp up Tap: Upper Active Power Bound MWqsetp Tap: Reactive Power Setpoint Mvarqsp low Tap: Lower Reactive Power Bound Mvarqsp up Tap: Upper Reactive Power Bound MvarTctrl Tap: Controller Time Constant sildc Tap: Line Drop Compensationldcct Tap: Current Transformer Rating Aldcpt Tap: Voltage Transformer Ratioldcrs Tap: Rset Vldcxs Tap: Xset Vtapctrl Tap Controller (ElmTr2)iMeasLoc Measured atmTaps Measurement Reportiblock Unit Transformerilt op Long-term operating condition before

short-circuit are knownUb lv Values for LV-Side: Highest Operating

VoltagekV

Ib lv Values for LV-Side: Highest OperatingCurrent

kA

cosphib lv Values for LV-Side: Power factorUbqmin hv Values for HV-Side (only for Unit

Transformer): Minimum OperatingVoltage

kV

ifrqft Frequent Fault ( >10(5)/lifetime,Category II(III) )

iopt hf Consider HF-ParameterCg h HF-Parameter: Capacitance

HV-GroundmyF

Cg l HF-Parameter: CapacitanceLV-Ground

myF

Cc1 hl HF-Parameter: Capacitance HV-LV,1-Sequence

myF

Cc0 hl HF-Parameter: Capacitance HV-LV,0-Sequence

myF




FOR1 Forced Outage Rate 1/aFOE Forced Outage Expectancy h/aFOD Forced Outage Duration hiperfect Ideal componentpTypStoch Type modelpStoch Element model StoTyptrfi uopt OPF-Controls: Tap Positionmaxload OPF-Constraints: Max. Loading %


5 References

5 References

[1] Guidelines for representation of network elements when calculating transients. Technicalreport, Cigre Working Group 33.02, 1990.

[2] Allan Greenwood. Electrical Transients in Power Systems. John Wiley & Sons, 1991.


List of Figures

List of Figures

1.1 Positive sequence model of the 2-winding transformer (in Ohms) . . . . . . . . . 4

1.2 Positive sequence model of the 2-winding transformer (in p.u.) . . . . . . . . . . 4

1.3 Transformer model with tap changer modelled at HV - side . . . . . . . . . . . . . 6

1.4 Transformer model with tap changer modelled at LV - side . . . . . . . . . . . . . 6

1.5 Complex tap changer model in PowerFactory . . . . . . . . . . . . . . . . . . . . 6

1.6 Yd transformer (a) in the zero-sequence system with HV side tap changer indetailed (a) and simplified representation (b) . . . . . . . . . . . . . . . . . . . . 7

1.7 Type options for tap changers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.8 Element-specific measurement protocol . . . . . . . . . . . . . . . . . . . . . . . 10

1.9 Data for automatic tap changer control . . . . . . . . . . . . . . . . . . . . . . . . 11

1.10 Orientation of Power values counted positive . . . . . . . . . . . . . . . . . . . . 12

1.11 Principle of line drop compensation . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.12 Principle of simulated dynamic control for V and P/Q . . . . . . . . . . . . . . . . 14

1.13 Type specific data for IEC short-circuit calculations . . . . . . . . . . . . . . . . . 15

1.14 HF Model for the external capacitances in positive sequence system (a) and zero-sequence system (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.15 Equivalent circuit of the 2 winding 3-phase transformer for the positive sequence 17

1.16 Two slope and polynomial saturation curves . . . . . . . . . . . . . . . . . . . . 17

1.17 Equivalent circuit of the 2 winding 3-phase transformer for the zero-sequence . . 20

2.1 YNyn transformer (zero-sequence system) . . . . . . . . . . . . . . . . . . . . . 24

2.2 Zero sequence model of YNYnd-Transformer . . . . . . . . . . . . . . . . . . . . 25

2.3 YNzn transformer (zero-sequence system) with HV side tap changer in detailedrepresentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Auto-transformer option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 YY transformer (zero-sequence system) in auto-transformer configuration (incl.tap changer on the HV side) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.6 YYd transformer (zero-sequence system) in auto-transformer configuration . . . 28

3.1 Input/Output Definition of 2-winding transformer model for RMS and EMT simulation 29


List of Tables

List of Tables

1.1 Basic data of tap changers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Data of measurement protocol for transformer elements . . . . . . . . . . . . . . 10

1.3 Dialog fields for the automatic tap changer control . . . . . . . . . . . . . . . . . 12

1.4 Additional data for tap changer control . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Line drop compensation (for voltage control) . . . . . . . . . . . . . . . . . . . . . 13

1.6 Dynamic and static control parameters . . . . . . . . . . . . . . . . . . . . . . . . 14

1.7 Basic data of the two-slope and polynomial saturation characteristics . . . . . . . 18

3.1 Input Variables of RMS and EMT transformer model . . . . . . . . . . . . . . . . 29

3.2 State Variables of transformer model for EMT-simulation . . . . . . . . . . . . . . 29

3.3 Additional parameters and signals of EMT transformer model (calculation param-eter) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29


List of Tables


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