Techref_2-w-transformer_3phase.pdf

DIgSILENT PowerFactory Technical Reference Documentation

Two-Winding Transformer (3-Phase) ElmTr2

DIgSILENT GmbH Heinrich-Hertz-Str. 9 72810 - Gomaringen Germany T: +49 7072 9168 00 F: +49 7072 9168 88 http://www.digsilent.de [email protected] r1010

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 means electronic or mechanical, without the prior written permission of DIgSILENT GmbH. Two-Winding Transformer (3-Phase) (ElmTr2)

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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Modelling Details and Application Hints

23

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

23

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

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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

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

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Contents

3 Input/Output Definitions of Dynamic Models

29

4 Input Parameter Definitions

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

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

32

5 References

35

List of Figures

36

List of Tables

37

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General Description

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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, block transformers, phase shifters or MV-voltage regulators. The model makes special consideration for auto-transformers. This first section describes the general model and is valid for all PowerFactory calculation functions. Particular aspects, such as saturation or capacitive effects, which are only relevant for some calculation functions are described in the following sections. Section 2. provides useful hints for special applications of the 2-winding transformer model.

1.1 1.1.1

Model Diagrams Positive and Negative sequence models

The detailed positive-sequence model with absolute impedances (in Ohm) is shown in Figure 1.1. It contains the leakage reactances and the winding resistances of the HV and LV side and 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 of the per-unitized model has a complex winding ratio with a magnitude of 1:1 and models the phase 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 type and element dialogs are described as follows:

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2 Ur,HV Sr 2 Ur,LV Zr,LV = Sr zsc = Usc /100

Zr,HV =

PCu /1000 Sr p 2 − r2 = zsc sc

rsc = xsc

(1) (2) (3) (4) (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 1 ZM = i0 /100 Sr rF e = PF e /1000 1 xM = q 1 − r21 z2

(9)

M

(10) (11) (12)

Fe

where, Zr,HV Zr,LV Ur,HV , Ur,LV Sr PCu uSC zSC rSC xSC γX,HV,1

Ω Ω kV MVA kW % p.u. p.u. p.u. p.u.

γR,HV,1

p.u.

rCu,HV , rCu,LV xσ,HV , xσ,LV

p.u. p.u.

I0 PF e xM rF e

% kW p.u. p.u.

Nominal impedance, HV side Nominal impedance, LV side Rated voltages on HV/LV side Rated power Copper losses Relative short-circuit voltage Short-circuit impedance Short-circuit resistance Short-circuit reactance Share of transformer shortcircuit reactance on HV side in the positive-sequence system Share of transformer shortcircuit resistance on HV side in the positive-sequence system Resistances on HV/LV sides Leakage reactances on HV/LV side no-load current No-load losses Magnetizing impedance Shunt resistance

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General Description

1.1.2

Tap changer

The tap changer is represented by an additional, ideal transformer connected to either the HV or the LV side (see Figure 1.3 and Figure 1.4). In most application, the winding ratio of this transformer is real and is defined by the actual tap position (in number of steps) times the additional 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 to Figure 1.5. There are two possibilities of specifying a phase shifting transformer. Either by entering magniTwo-Winding Transformer (3-Phase) (ElmTr2)

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General Description

tude and angle (dutap and ϕtap ) of the additional voltage per tap step or by defining magnitude and angle at each individual tap-step (|U + dutap |, ϕu ). The latter is supported by the measurement 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 including a 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)

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General Description

1.2

Load-Flow Analysis

The load flow ComLdf calculation uses the detailed model for the transformer, that is all shunt and 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 type data section it is modelled using its constructive properties, in the element data section it is defined 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 tap changer is connected physically) Additional voltage per tap.

-

Constant phase between fix voltage and additional voltage of the winding (parameter φt in Figure 1.5) Range of possible positions for the tap changer. At the neutral position, the winding ratio corresponds to the ratio of the rated voltages

degree (◦ )

Additional voltage ∆u per tap Phase of ∆u

Neutral/min./max. position

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-

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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 circuit impedances and copper losses (short circuit resistance) in the positive- and zero-sequence systems. For tap positions between min. and neutral and between neutral and max. tap dependent parameters 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, all tap-dependent parameters can be entered per tap step. If the option According to measurement report is enabled the corresponding type-parameters are overwritten by the respective element parameters. The corresponding input dialogue is shown in Figure 1.8 with a brief parameter description in Table 1.2.

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Table 1.2: Data of measurement protocol for transformer elements Parameter

Description

Unit

Voltage Angle

Voltage at tap position i. Absolute tap-angle (parameter φu in Figure 1.5) S/C voltage of the transformer Copper losses Rating factor for considering tap-dependent transformer rating. The additional rating factor is multiplied by the general rating factor (Rating Factor on the Basic Data page).

kV degree (◦ )

uk PCu Add. rating Factor

% kW (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 flow page of the transformer element. Additionally, automatic tap adjustment can be globally enabled or disabled by the load flow command. The information required for tap changer control is shown in Figure 1.9 and described in Table 1.3.

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General Description

Figure 1.9: Data for automatic tap changer control

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Table 1.3: Dialog fields for the automatic tap changer control Parameter

Description

According to Measurement report Tap position

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

Automatic tap changing Tap changer

Controlled node

Setpoint

Control mode

Tap position used during the load flow calculation. If Automatic Tap Changing is activated this value corresponds to the initial tap position. Activating automatic tap adjustment in load flow analysis. continuous An idealized, continuous tap changer is assumed. As a result, the tap controller can ideally comply with the specified control condition This option is useful for voltage regulators in distribution systems having a very large number of tap steps or for thyristor controlled tap changers. discrete Standard option. Only integer tap positions are considered. HV Tap controls the HV-side. LV Tap controls the LV-side EXT Slave mode. The tap changer just follows the tap position of the selected Master -transformer. Only for V control mode: local the voltage setpoint and voltage range settings (max./min. voltage) must be enter in the transformer dialog bus target voltage the voltage setpoint and voltage range settings (max./min. voltage) are taken from the controlled busbar (topological search) V Voltage control. For unbalanced load flow analysis, the controlled phase needs to be defined additionally. Q Reactive power control (see also Figure 1.10) P Active power control (only applicable to phase shifters, see also Figure 1.10)

Figure 1.10: Orientation of Power values counted positive

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Table 1.4: Additional data for tap changer control Parameter

Description

Set Point Lower/Upper bound

V-/Q-/P- reference (depending on selected control mode) Lower and upper boundary of the controlled variable. In case of discrete tap changers, the tap control can drive the controlled variable just into a permitted band. In case of continuous tap changers the tap controller can ideally regulate to the reference point. Allows for the selection of a bus bar different from the transformer terminals (V-control). In case of P-or Q-control the flow through any cubicle can be controlled.

Remote Control

Voltage control includes optional line drop compensation. This function controls the voltage at a remote busbar without measuring the voltage at that bus-bar. Instead, the actual value is estimated by measuring the voltage at the HV or LV side of the transformer and simulating the voltage drop across the line. The principle of the line drop compensation is shown in Figure 1.11, the corresponding parameters are explained in Table 1.5.

Figure 1.11: Principle of line drop compensation

Table 1.5: Line drop compensation (for voltage control) Parameter

Description

Unit

Current transformer rating Voltage transformer ratio RSet, XSet

Primary CT-current-rating.

A

Ratio of the voltage transformer

-

LDC-impedance, defined as voltage drop at rated current. It corresponds to the LDC-impedance in Ohm times the secondary CT current rating.

V

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General Description

Generally, there is more than just one possible solution to a load flow problem considering automatic tap changer control. Especially in meshed networks, several transformers can control the voltage in certain areas. In case of parallel transformers, the problem can usually be solved by operating the two parallel transformers in a master slave mode. In a general configuration however, especially when parallel transformer have different short circuit impedances or different tap steps, the steady state network solution cannot be obtained that easily. PowerFactory addresses the mentioned problem by allowing the user to enter a controller time constant, specifying the speed of control actions and hence the participation of several transformers regulating the voltage of the same bus bar. The approach is based on controller block diagrams according to Figure 1.12. In case of flowcontrollers (P-/Q-control) the controller sensitivity translating a power mismatch into an equivalent turns-ratio percentage can be entered additionally. In the actual load flow algorithm, which just looks at steady state conditions, controller time constants 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

1.3 1.3.1

Parameter

Description

Unit

Controller time constant Controller sensitivity dv/dP Controller sensitivity dv/dQ

Time constant of the controller

s

Estimated sensitivity of active power flow towards tap changer variations Estimated sensitivity of reactive power flow towards tap changer variations

%/MW %/Mvar

Short-Circuit Analysis Type data for IEC S/C calculations

Short-Circuit calculations according to IEC assume that the shunt impedances in positive- and negative-sequence (magnetizing reactance, iron losses) are neglected. The shunt impedances Two-Winding Transformer (3-Phase) (ElmTr2)

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General Description

in the zero-sequence system however must be considered. These parameters are shown in the dialog of IEC S/C calculation. Another detail specific to IEC calculation is the distinction between no-load and on-load tap changers. Different impedance correction factors apply for each group. The property of on-load variation 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 correction factor 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 generator. Network transformers are individually. Two different calculation procedures can be applied. The first is a general correction independent of the actual operating conditions of a selected transformer. The second is more specific and may lead to more precise calculation results. The selection of the correction method along with 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 tap controller definitions are not considered here. For the simulation of tap controllers, a separate dynamic model needs to be defined that can be interfaced with the transformer using the input variable nntapin (tap-input).

1.5

Harmonic Simulation

For accurately modelling high frequency effects of transformers, additional capacitances need to be considered, as shown in Figure 1.14. These capacitances are equivalent capacitances of the model and not the actual winding capacitances. For obtaining equivalent capacitances from winding capacitances, the winding connection (D/Y) must be considered additionally. The high frequency model according to Figure 1.14 provides an accurate frequency response

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General Description

with respect to voltages and currents at the transformer terminals. However, it is not possible to simulate 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 zerosequence system (b)

1.6

EMT Simulation

For simulating nonlinear, electromagnetic transient such as transformer inrush currents or ferroresonance, core saturation needs to be included into the transformer model. Furthermore, depending on the frequencies involved in the transient simulation, the transformer model has to account 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 sequence. For simplicity, the tap changer has been left aside in the figure; however it is considered in the model according to Figure 1.3, Figure 1.4 and Figure 1.5 as described in previous chapters. The exciting current of a transformer (no-load test) consist of an imaginary part, which is the magnetizing current flowing through the non-linear reactance XM in Figure 1.15, and a smaller real part flowing through the resistance RF e , which accounts for the excitation losses.

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General Description

The non-linear magnetizing reactance XM represents the saturation characteristic of the transformer and it is defined in the transformer type (TypTr2\EMT simulation page). The model supports 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. The polynom fits asymptotically into the piecewise linear definition. Current/Flux values: the user inputs current-flux values as a sequence of points and selects among 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 terms of the distribution of the leakage reactance and resistance (TypTr2\EMT-Simulation page). Default value is 0.5 which means that the total leakage impedance of the transformer (short-circuit impedance) equally distributes between the HV and the LV winding. The user can modify the position 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 characteristics. 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

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

Description

Unit

Knee Flux

Knee-point of asymptotic piece-wise linear characteristic. Typical value around 1.1 to 1.2 times the rated flux. Magnetizing reactance for unsaturated conditions Lunsat . In p.u. values, the linear reactance is equal to the reciprocal of the magnetizing current (reactive part of the exciting current). Magnetizing reactance for saturated conditions Lsat . Exponent of polynomial representation (ksat ). Typical values are 9,13,15. The higher the exponent the sharper the saturation curve.

p.u.

Linear (unsaturated) reactance

Saturated reactance Saturation exponent

p.u.

p.u. -

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 adjusts the unsaturated reactance based on the no-load current and no-load losses entered in the load flow page (TypTr2\Load Flow) and vice-versa:

1 = XM

s

2

IM Irated

 −

Pexc Srated

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 with the unsaturated reactance. Typical values for two-winding transformers are 1 to 2 times the short-circuit inductance and 3 to 4 times for autotransformes [1]. The polynomial characteristic uses expression 14 to fit the curve asymptotically into the piecewise linear definition. The higher the exponent, the sharper the saturation curve:

iM

ΨM = · LM

! ΨM ksat 1 + Ψ0

(14)

Where,

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General Description

iM ΨM LM Ψ0

ksat

Magnetizing current Magnetizing flux Linear reactance This parameter is automatically calculated so that the polynomial characteristic fits the saturated reactance in full saturation and transits steadily into the piece-wise linear characteristic at the knee flux point. Saturation exponent, i.e. polynome degree

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

-

This polynomial characteristic is always inside the corresponding linear representation. In full saturation the polynomial characteristic is extended linearly. Compared to the two-slope curve, it does 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 sequence model are referred to the following bases quantities: • Ubase [kV]: nominal voltage of the (energizing) winding, i.e. the winding used for the no load test • Sbase [MVA]: nominal power of the (energizing) winding Sbase [M V A] × 1000 • Ibase [A] = √ 3 · Ubase [kV ] √ Ubase [kV ]/ 3 • ψbase [V · s] = × 1000 2πf [Hz]   2 Ubase [kV ] 1 • Lbase [H] = · Sbase [M V A] 2πf [Hz] Current-Flux values The user can also define the saturation curve in terms of measured current-flux values and select 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 impressed voltage, the magnetizing flux in p.u. is equal to the magnetizing voltage in p.u., thus flux and voltage are interchangeable and the p.u. current-flux curve represents a p.u. currentvoltage curve as well. Furthermore, it can be assumed that the applied voltage remains fairly linear during the non-load tests and hence the ration between RMS and peak values of the √ voltage is given by 2. On the contrary, the magnetizing current is distorted (non-sinusoidal) because of the saturation curve. As a consequence of that, the ratio between the RMS and peak value of the magnetizing √ current 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 peak values of the corresponding nominal variables:

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√

Sbase [M V A] 2× √ × 1000 3 · Ubase [kV ] √ √ Ubase [KV ]/ 3 Ψbase [V · s] = 2 × × 1000 2πf [kHz] Ibase [A] =

1.6.2

Zero Sequence magnetizing reactance

The zero sequence magnetizing current strongly depends on the construction characteristic of the transformer core (three-legged, five-legged, shell-type, etc.) and its vector group. Figure 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 approximates a zero-sequence short-circuit, as the delta-connected winding short-circuits the zerosequence 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 excitation current results generally higher than the positive-sequence excitation current and strongly depends on the core type. To account for the higher zero-sequence linear exciting current when no delta-connected winding is available, PowerFactory allows for the definition of a linear (unsaturated) zero-sequence magnetizing impedance. This zero-sequence magnetizing impedance and its R/X ratio is defined in the load flow page (TypTr2\Load flow); the parameters are made available depending on 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, the transformer 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 are roughly equal in the three legs and must therefore return outside the core through the airgap and the tank. Because of the fact that the air-gap and the tanks are no-magnetic, the zero-sequence magnetizing current is nearly linear and therefore the model uses the linear zero-sequence magnetizing impedance defined in the load flow page. In other words, it does not consider zero-sequence saturation effects. 5 Limbs core: use this option for five-legged and shell-type cores. As the zero-sequence fluxes return inside the core, the model uses the saturation characteristic (of the positive sequence) in the zero-sequence magnetizing reactance as well. Two-Winding Transformer (3-Phase) (ElmTr2)

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1.6.3

Residual flux

The residual flux is the magnetizing flux which remains in the core after the transformer has been switched off. A residual flux, other than a remanent 1 flux, implies then the circulation of a magnetizing current (ΨM = LM · IM ). Once the transformer has been switched off, this magnetizing current circulates through the noload losses resistance Rm and de-magnetizes the core. The flux decays then exponentially with a time constant Lm /Rm with Lm the linear magnetizing inductance. To simulate the decaying magnetizing current and hence the decaying residual flux it is necessary to define the no-load losses. Otherwise, if Rm =0, the magnetizing current cannot circulate and PowerFactory will automatically 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. For simplicity, 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 components) as follows:

2   3 ψd     ψq  =  0  1 ψ0 3

1 − 3 1 √ 3 1 3

1    3  ψa 1    − √  ×  ψb   3 1 ψc 3

The inverse transformation is given by:

   1  ψa    − 1  ψb  =  2  1 ψc − 2

√0 3 2 √ 3 − 2

1



   ψd   1 ×   ψq    ψ0 1

The calculation parameters c:psim c, c:psim b and c:psim c give the resulting flux (simulation result) 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. However as the residual flux has a major impact on the amplitude of inrush currents, it has to be considered 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 capacitances have to be considered. 1 The

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

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

21

1

General Description

The stray capacitances of a transformer do not only depend on its construction characteristics of 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, proximity to other grounded components, walls, etc.). For that reason, the stay capacitances are not part of 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 the stray capacitances in the model by ticking the Consider Capacitances option. The model account 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].

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

22

2

Modelling Details and Application Hints

2 2.1

Modelling Details and Application Hints Reference Values

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

2.2 2.2.1

Zero Sequence Models of Common Vector Groups Yd-transformer

This model is described in detail in section 1.1.3 as a general example for the zero-sequence system modelling. Please refer to that section for further explanation. If no accurate data are available from the manufacturer, the following estimations can be used for the zero-sequence impedance voltages as seen from the grounded side: Core-type transformer (3-limb) usc,0 = 0.85 · Usc,1 , Shell-type transformer (4/5-limb) usc,0 = 1.0 · Usc,1 ,

uRr,0 = 0 uRr,0 = 0

where usc,0 is the positive sequence impedance voltage. Concerning the model for the magnetic flux saturation characteristics the transformer types with 3 or 4/5 limbs behave differently in general. In the 3-limb design, the zero-sequence flux defined by 15 is not guided via the transformer limbs but uses parallel paths (e.g. through the transformer vessel, oil, ) and thus can be modelled as linear without saturation effects.

Ψ0 =

2.2.2

1 · (ΨA + ΨB + ΨC ) 3

(15)

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 be derived from this equivalent circuit by assuming infinite grounding impedances at the respective side.

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

23

2

Modelling Details and Application Hints

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 the magnetic circuit of the transformers. Typical ranges are: Core-type transformer (3-limb)

zM 0 zsc,0

Shell-type transformer (4/5-limb)

2.2.3

= 3 . . . 10

zM 0 zsc,0

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

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

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

zM 0 = 1..2.4 zsc,0

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

24

2

Modelling Details and Application Hints

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 sequence system, as shown in Figure 2.3.

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

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

25

2

Modelling Details and Application Hints

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 (Autotransformer) can be checked on the Basic Data page of the element (see Figure 21). This activates the interpretation as an autotransformer. This option only is shown when the type selected for the transformer is of vector group YY. The effect of this connection can be seen in Figure 22. Besides the additional connection between the star points, only one grounding impedance can be entered.

Figure 2.4: Auto-transformer option

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

26

2

Modelling Details and Application Hints

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

For the YY autotransformer the currents of HV side and LV side both flow through the same grounding impedance ZE = RE + jXE . The voltage over this grounding impedance ZE thus affects the zero-sequence system voltages on both sides. This makes it necessary to consider the 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 impedance of auto-transformers. The approach for modeling this is equivalent to the internal delta tertiary winding modeling of Yy-transformers.

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

27

2

Modelling Details and Application Hints

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

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

28

3

3

Input/Output Definitions of Dynamic Models

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 Parameter

Description

Unit

nntapin

Tap position (input)

-

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

Description

Unit

psimd psimq psim0

Magnetizing flux, d-component Magnetizing flux, q-component Magnetizing flux, 0-component

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

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

Description

Unit

psim a psim b psim c im a im b im c

Magnetizing flux, phase A Magnetizing flux, phase B Magnetizing flux, phase C Magnetizing current, phase A Magnetizing current, phase B Magnetizing current, phase C

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

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

29

4

Input Parameter Definitions

4 4.1

Input Parameter Definitions 2-Winding-Transformer Type Parameter

Description

loc name nt2ph strn frnom utrn h utrn l uktr

Name Technology Rated Power Nominal Frequency Rated Voltage: HV-Side Rated Voltage: LV-Side Positive Sequence Impedance: Short-Circuit Voltage uk Positive Sequence Impedance: Copper Losses Positive Sequence Impedance: SHC-Voltage (Re(uk)) ukr Positive Sequence Impedance: Ratio X/R Vector Group: HV-Side Vector Group: LV-Side Vector Group: Phase Shift Vector Group: Name Zero Sequ. Impedance, Short-Circuit Voltage: Absolute uk0 Zero Sequ. Impedance, Short-Circuit Voltage: Resistive Part ukr0 Tap Changer: at Side Tap Changer: Additional Voltage per Tap Tap Changer: Phase of du Tap Changer: Neutral Position Tap Changer: Minimum Position Tap Changer: Maximum Position Magnetizing Impedance: No Load Current Magnetizing Impedance: No Load Losses Zero Sequence Magnetizing Impedance: Mag. Impedance / uk0 Zero Sequence Magnetizing R/X ratio: Mag. R/X Distribution of Zero Sequ. Leakage-Impedances: z, Zero Sequ. HV-Side

pcutr uktrr xtor tr2cn h tr2cn l nt2ag vecgrp uk0tr ur0tr tap side dutap phitr nntap0 ntpmn ntpmx curmg pfe zx0hl n

rtox0 n zx0hl h

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

Unit

MVA Hz kV kV % kW %

*30deg % %

% deg

% kW

30

4

Input Parameter Definitions

Parameter

Description

zx0hl l

Distribution of Zero Sequ. Leakage-Impedances: z, Zero Sequ. LV-Side Tap dependent impedance Tap dependent impedance: uk (min. tap) Tap dependent impedance: uk (max. tap) Tap dependent impedance: Pcu (min. tap) Tap dependent impedance: Re(uk) (min. tap) Tap dependent impedance: X/R (min. tap) Tap dependent impedance: Pcu (max. tap) Tap dependent impedance: Re(uk) (max. tap) Tap dependent impedance: X/R (max. tap) Tap dependent impedance: uk0 (min. tap) Tap dependent impedance: uk0 (max. tap) Tap dependent impedance: Re(uk0) (min. tap) Tap dependent impedance: Re(uk0) (max. tap) Distribution of Leakage Reactances (p.u.): x,Pos.Seq. HV-Side Distribution of Leakage Reactances (p.u.): x,Pos.Seq. LV-Side Distribution of Leakage Resistances (p.u.): r,Pos.Seq. HV-Side Distribution of Leakage Resistances (p.u.): r,Pos.Seq. LV-Side On-load Tap Changer Tap Changer: Voltage Range Class Inrush Peak Current: Ratio Ip/In Inrush Peak Current: Max. Time Magnetizing Reactance: Type Magnetizing Reactance: Knee Flux Magnetizing Reactance: Linear Reactance Magnetizing Reactance: Saturated Reactance

itapzdep uktmn uktmx pcutmn ukrtmn xtortmn pcutmx ukrtmx xtortmx uk0tmn uk0tmx uk0rtmn uk0rtmx itrdl itrdl lv itrdr itrdr lv oltc pT ansiclass pict2 pitt2 itrmt psi0 xmlin xmair

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

Unit

% % kW %

kW %

% % % %

% p.u. s p.u. p.u. p.u.

31

4

Input Parameter Definitions

Parameter

Description

Unit

ksat it0mt

Saturation Exponent Zero Sequence Magnetizing Reactance: Type Zero Sequence Stochastic model

StoTyptrf

pStoch

4.2

2-Winding-Transformer Element Parameter

Description

loc name typ id bushv bushv bar buslv buslv bar iZoneBus outserv ntnum ratfac Snom i auto

Name Type (TypTr2) HV-Side (StaCubic) HV-Side LV-Side (StaCubic) LV-Side Zone Out of Service Number of: parallel Transformers Rating Factor Rated Power Connected Star Points (Auto Transformer) HV-side, phase 2 internally grounded Grounding Impedance, HV Side: Neutral Point Grounding Impedance, HV Side: Re Grounding Impedance, HV Side: Xe LV-side, phase 2 internally grounded Grounding Impedance, LV Side: Neutral Point Grounding Impedance, LV Side: Re Grounding Impedance, LV Side: Xe r (Sbase) x (Sbase) r0 (Sbase) x0 (Sbase) HV-Side, Rated Current LV-Side, Rated Current According to Measurement Report Tap: Tap Position Tap: Automatic Tap Changing Tap: Tap Changer Tap: Controlled Node Tap: Phase

i eahv ignd h re0tr h xe0tr h i ealv ignd l re0tr l xe0tr l rSbasepu xSbasepu r0Sbasepu x0Sbasepu Inom h Inom l iTaps nntap ntrcn i cont t2ldc ilcph

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

Unit

MVA

Ohm Ohm

Ohm Ohm p.u./Sbase p.u./Sbase p.u./Sbase p.u./Sbase kA kA

32

4

Input Parameter Definitions

Parameter

Description

imldc i rem p rem

Tap: Control Mode Tap: Remote Control Tap: Controlled Node (StaBar,ElmTerm) Tap: Controlled Branch (Cubicle) (StaCubic) Tap: Voltage Setpoint Tap: Lower Voltage Bound Tap: Upper Voltage Bound Tap: Active Power Setpoint Tap: Lower Active Power Bound Tap: Upper Active Power Bound Tap: Reactive Power Setpoint Tap: Lower Reactive Power Bound Tap: Upper Reactive Power Bound Tap: Controller Time Constant Tap: Line Drop Compensation Tap: Current Transformer Rating Tap: Voltage Transformer Ratio Tap: Rset V Tap: Xset V Tap Controller (ElmTr2) Measured at Measurement Report Unit Transformer Long-term operating condition before short-circuit are known Values for LV-Side: Highest Operating Voltage Values for LV-Side: Highest Operating Current Values for LV-Side: Power factor Values for HV-Side (only for Unit Transformer): Minimum Operating Voltage Frequent Fault ( >10(5)/lifetime, Category II(III) ) Consider HF-Parameter HF-Parameter: Capacitance HV-Ground HF-Parameter: Capacitance LV-Ground HF-Parameter: Capacitance HV-LV, 1-Sequence HF-Parameter: Capacitance HV-LV, 0-Sequence

p cub usetp usp low usp up psetp psp low psp up qsetp qsp low qsp up Tctrl ildc ldcct ldcpt ldcrs ldcxs tapctrl iMeasLoc mTaps iblock ilt op Ub lv Ib lv cosphib lv Ubqmin hv

ifrqft iopt hf Cg h Cg l Cc1 hl Cc0 hl

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

Unit

p.u. p.u. p.u. MW MW MW Mvar Mvar Mvar s A

kV kA

kV

myF myF myF myF

33

4

Input Parameter Definitions

Parameter

Description

Unit

FOR1 FOE FOD iperfect pTypStoch pStoch i uopt maxload

Forced Outage Rate Forced Outage Expectancy Forced Outage Duration Ideal component Type model Element model OPF-Controls: Tap Position OPF-Constraints: Max. Loading

1/a h/a h

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

StoTyptrf %

34

5

5

References

References

[1] Guidelines for representation of network elements when calculating transients. Technical report, Cigre Working Group 33.02, 1990. [2] Allan Greenwood. Electrical Transients in Power Systems. John Wiley & Sons, 1991.

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

35

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 in detailed (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 zerosequence 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 detailed representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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

36

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 parameter) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

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

37

List of Tables

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

38