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, reproduced, copied, or transmitte transmitted d 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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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, reproduced, copied, or transmitte transmitted d 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 Genera Generall Des Descri cripti ption on
4
1.1 Mod Model el Diagr Diagrams ams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.1.1 Positiv Positive e and Negativ Negative e sequence sequence models models . . . . . . . . . . . . . . . . . . .
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1.1.2 1.1 .2 Tap change changerr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.1.3 1.1 .3 Zero sequen sequence ce mod models els . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2 Load-Flow Load-Flow Analysis Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2.1 Tap changer changer basic basic data . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2.2 Tap dependent dependent impedance impedance . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2.3 Measurement Measurement protocol protocol (element-spe (element-specific) cific) . . . . . . . . . . . . . . . . . .
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1.2.4 Automatic Automatic tap changer changer control control . . . . . . . . . . . . . . . . . . . . . . . .
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1.3 Short-Circuit Short-Circuit Analysis Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.3.1 Type data data for IEC S/C S/C calculat calculations ions . . . . . . . . . . . . . . . . . . . . . .
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1.3.2 Element Element dat data a for for IEC S/C calculations calculations . . . . . . . . . . . . . . . . . . . .
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1.4 RMS Simula Simulatio tion n
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5 Harmonic Harmonic Simulatio Simulation n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.6 EMT Simula Simulatio tion n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.6.1 Saturation Saturation characteris characteristic tic . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.6.2 Zero Sequence Sequence magnetizing magnetizing reactance reactance . . . . . . . . . . . . . . . . . . .
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1.6.3 1.6 .3 Residu Residual al flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.6.4 Stray Stray capacitance capacitances s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Modelling Modelling Details Details and and Applicat Application ion Hints
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2.1 Ref Reference erence Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2 Zero Sequence Sequence Models Models of of Common Common Vector Vector Groups Groups . . . . . . . . . . . . . . . . .
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2.2.1 2.2 .1 Yd-tra Yd-transf nsforme ormerr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2.2 YNyn/YNy YNyn/YNy /Yyn -transforme -transformerr . . . . . . . . . . . . . . . . . . . . . . . . .
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2.2.3 Model of YNyn/YN YNyn/YNy/Yyn y/Yyn-tran -transforme sformerr with closed closed tertiary delta delta winding winding . .
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2.2.4 Model of YNzn/YNz/ YNzn/YNz/Zyn-tr Zyn-transf ansformer ormer . . . . . . . . . . . . . . . . . . . . .
25
2.3 Auto-tra Auto-transfo nsformer rmer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Two-Winding Transformer (3-Phase) (ElmTr2)
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Contents
3 Input/Output Definitions of Dynamic Models
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4 Input Parameter Definitions
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4.1 2-Winding-Transformer Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4.2 2-Winding-Transformer Element . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 References
35
List of Figures
36
List of Tables
37
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
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 Model Diagrams 1.1.1 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:
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
2 U r,HV S r 2 U r,LV Z r,LV = S r zsc = U sc /100
Z r,HV =
rsc = xsc =
(1) (2) (3)
P Cu /1000 S r
− 2 zsc
(4)
2 rsc
rCu,HV = γ R,HV,1 rCu,LV = (1 γ R,LV,1 ) xσ,HV = γ X,HV,1 xσ,LV = (1 γ X,LV,1 )
(5)
· r ·r · x ·x
−
−
sc
(6)
sc
(7)
sc
(8)
sc
(9)
1 i0 /100 S r rF e = P F e /1000 1 xM = Z M =
1 2
zM
−
(10)
(11)
1
(12)
2
rF e
where,
Z r,HV Z r,LV U r,HV , U r,LV S r P Cu uSC zSC rSC xSC γ X,HV,1
Ω Ω kV MVA kW % p.u. p.u. p.u. p.u.
γ R,HV,1
p.u.
Share of transformer shortcircuit resistance on HV side in the positive-sequence system
rCu,HV , r Cu,LV xσ,HV , x σ,LV
p.u.
Resistances on HV/LV sides
p.u.
Leakage reactances on HV/LV side
I 0 P F e xM rF e
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
%
no-load current
kW
No-load losses
p.u.
Magnetizing impedance
p.u.
Shunt resistance
Two-Winding Transformer (3-Phase) (ElmTr2)
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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 ϕ tap ) of the additional voltage per tap step or by defining magnitude and angle at each individual tap-step ( U + dutap , ϕ u ). 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 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)
Two-Winding Transformer (3-Phase) (ElmTr2)
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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 ∆u per tap
Additional voltage per tap.
%
Phase of ∆ u
Constant phase between fix voltage and additional voltage of the winding (parameter φt in Figure 1.5)
degree ( )
Neutral/min./max. position
Range of possible positions for the tap changer. At the neutral position, the winding ratio corresponds to the ratio of the rated voltages
-
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
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.
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
Table 1.2: Data of measurement protocol for transformer elements Parameter
Description
Unit
Voltage
Voltage at tap position i.
kV
Angle
Absolute tap-angle (parameter φu in Figure 1.5)
degree ( )
uk
S/C voltage of the transformer
%
PCu
Copper losses
kW
Add. rating Factor
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).
(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.
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
Figure 1.9: Data for automatic tap changer control
Two-Winding Transformer (3-Phase) (ElmTr2)
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General Description
Table 1.3: Dialog fields for the automatic tap changer control Parameter
Description
According to Measurement report
Instead of the type data for the tap-dependent transformer values the element-specific measurement report is used
Tap position
Tap position used during the load flow calculation. If Automatic Tap Changing is activated this value corresponds to the initial tap position.
Automatic tap changing
Activating automatic tap adjustment in load flow analysis.
Tap changer
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.
Controlled node
Setpoint
Control mode
HV LV
Tap controls the HV-side. 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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General Description
Table 1.4: Additional data for tap changer control Parameter
Description
Set Point
V-/Q-/P- reference (depending on selected control mode)
Lower/Upper bound
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.
Remote Control
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.
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
Primary CT-current-rating.
A
Voltage transformer ratio
Ratio of the voltage transformer
-
RSet, XSet
LDC-impedance, defined as voltage drop at rated current. It corresponds to the LDC-impedance in Ohm times the secondary CT current rating.
V
Two-Winding Transformer (3-Phase) (ElmTr2)
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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 Parameter
Description
Unit
Controller time constant
Time constant of the controller
s
Controller sensitivity dv/dP
Estimated sensitivity of active power flow towards tap changer variations
%/MW
Controller sensitivity dv/dQ
Estimated sensitivity of reactive power flow 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- 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
Two-Winding Transformer (3-Phase) (ElmTr2)
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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 X M in Figure 1.15, and a smaller real part flowing through the resistance R F e , which accounts for the excitation losses.
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General Description
The non-linear magnetizing reactance X M 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.
p.u.
Linear (unsaturated) reactance
Magnetizing reactance for unsaturated conditions L unsat. In p.u. values, the linear reactance is equal to the reciprocal of the magnetizing current (reactive part of the exciting current).
p.u.
Saturated reactance
Magnetizing reactance for saturated conditions L sat .
p.u.
Saturation exponent
Exponent of polynomial representation (ksat). Typical values are 9,13,15. The higher the exponent the sharper the saturation 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 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 = X M
− I M I rated
2
P exc S rated
2
(13)
where,
I M : Magnitude of the exciting current in the no-load test P exc : Excitation losses in the no-load test I R , S R : 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:
ΨM iM = LM Where,
·
Two-Winding Transformer (3-Phase) (ElmTr2)
ΨM 1+ Ψ0
ksat
(14)
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General Description
iM ΨM LM Ψ0
Magnetizing current
p.u.
Magnetizing flux
p.u.
Linear reactance
p.u.
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.
p.u.
ksat
Saturation exponent, i.e. polynome degree
-
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: • U base[kV]: nominal voltage of the (energizing) winding, i.e. the winding used for the no load test • S base[MVA]: nominal power of the (energizing) winding
A] √ S 3 · U [M V[kV ] × 1000 √ U [kV ]/ 3 [V · s] = × 1000 2πf [Hz] base
• I base [A] =
base
• ψbase
• Lbase [H ] =
base
2 U base [kV ] S base[M V A]
·
1 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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√ √ S [MV A] 2× × 1000 3 · U [kV ] √ U [KV ]/√ 3 [V · s] = 2 × × 1000 2πf [kH z] base
I base[A] =
base
Ψbase
base
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 = L M I M ).
·
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 L m / 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:
ψd ψq = ψ0
2 3 0
− 13 13 √ 13 − √ 13 ×
1 3
1 3
1 3
ψa ψb ψc
The inverse transformation is given by:
− − ψa ψb = ψc
1 1 2 1 2
√ 03 2 √ − 23
×
1 1 1
ψd ψq ψ0
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
2
Modelling Details and Application Hints
Modelling Details and Application Hints
2.1 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 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-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 U sc,1 , Shell-type transformer (4/5-limb) usc,0
· = 1.0 · U
sc,1 ,
uRr,0 = 0 uRr,0 = 0
where u sc,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 =
1 (ΨA + Ψ B + ΨC ) 3
·
(15)
2.2.2 YNyn/YNy /Yyn -transformer The zero sequence equivalent circuit diagram of the YNyn transformers is depicted in Figure2.1. 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 = r Cu, 0,HV + x σ,0,HV S/C impedance LV-side zsc,0,LV = r Cu,0,LV + x σ,0,LV S/C impedance both sides zsc,0 = z sc,0,HV + z sc,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)
= 3 . .. 10
zM 0 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-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 (Autotrans- former) 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 Z E = RE + jX E . The voltage over this grounding impedance Z E 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
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) Parameter
Description
Unit
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.
Two-Winding Transformer (3-Phase) (ElmTr2)
29
4
4
Input Parameter Definitions
Input Parameter Definitions
4.1 2-Winding-Transformer Type Parameter
Description
loc name
Name
nt2ph
Technology
strn
Rated Power
MVA
frnom
Nominal Frequency
Hz
utrn h
Rated Voltage: HV-Side
kV
utrn l
Rated Voltage: LV-Side
kV
uktr
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: Ratio X/R
tr2cn h
Vector Group: HV-Side
tr2cn l
Vector Group: LV-Side
nt2ag
Vector Group: Phase Shift
vecgrp
Vector Group: Name
uk0tr
Zero Sequ. Impedance, Shor t-Circuit Voltage: Absolute uk0
%
ur0tr
Zero Sequ. Impedance, Shor t-Circuit Voltage: Resistive Part ukr0
%
tap side
Tap Changer: at Side
dutap
Tap Changer: Additional Voltage per Tap
%
phitr
Tap Changer: Phase of du
deg
nntap0
Tap Changer: Neutral Position
ntpmn
Tap Changer: Minimum Position
ntpmx
Tap Changer: Maximum Position
curmg
Magnetizing Impedance: No Load Current
%
pfe
Magnetizing Impedance: No Load Losses
kW
zx0hl n
Zero Sequence Magnetizing Impedance: 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
Two-Winding Transformer (3-Phase) (ElmTr2)
Unit
*30deg
30
4
Input Parameter Definitions
Parameter
Description
zx0hl l
Distribution of Zero Sequ. Leakage-Impedances: z, Zero Sequ. LV-Side
itapzdep
Tap dependent impedance
uktmn
Tap dependent impedance: uk (min. tap)
%
uktmx
Tap dependent impedance: uk (max. tap)
%
pcutmn
Tap dependent impedance: Pcu (min. tap)
kW
ukr tmn
Tap dependent impedance: Re(uk) (min. tap)
%
xtortmn
Tap dependent impedance: X/R (min. tap)
pcutmx
Tap dependent impedance: Pcu (max. tap)
kW
ukr tmx
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 Changer
pT
Tap Changer: Voltage Range
ansiclass
Class
pict2
Inrush Peak Current: Ratio Ip/In
p.u.
pitt2
Inrush Peak Current: Max. Time
s
itrmt
Magnetizing Reactance: Type
psi0
Magnetizing Reactance: Knee Flux
p.u.
xmlin
Magnetizing Reactance: Linear Reactance
p.u.
xmair
Magnetizing Reactance: Saturated Reactance
p.u.
Two-Winding Transformer (3-Phase) (ElmTr2)
Unit
%
31
4
Input Parameter Definitions
Parameter
Description
ksat
Saturation Exponent
it0mt
Zero Sequence Magnetizing Reactance: Type Zero Sequence
pStoch
Stochastic model
Unit
StoTyptrf
4.2 2-Winding-Transformer Element Parameter
Description
loc name
Name
typ id
Type (TypTr2 )
bushv
HV-Side (StaCubic)
bushv bar
HV-Side
buslv
LV-Side (StaCubic)
buslv bar
LV-Side
iZoneBus
Zone
outserv
Out of Service
ntnum
Number of: parallel Transformers
ratfac
Rating Factor
Snom
Rated Power
i auto
Connected Star Points (Auto Transformer)
i eahv
HV-side, phase 2 internally grounded
ignd h
Grounding Impedance, HV Side: Neutral Point
re0tr h
Grounding Impedance, HV Side: Re
Ohm
xe0tr h
Grounding Impedance, HV Side: Xe
Ohm
i ealv
LV-side, phase 2 internally grounded
ignd l
Grounding Impedance, LV Side: Neutral Point
re0tr l
Grounding Impedance, LV Side: Re
Ohm
xe0tr l
Grounding Impedance, LV Side: Xe
Ohm
rSbasepu
r (Sbase)
p.u./Sbase
xSbasepu
x (Sbase)
p.u./Sbase
r0Sbasepu
r0 (Sbase)
p.u./Sbase
x0Sbasepu
x0 (Sbase)
p.u./Sbase
Inom h
HV-Side, Rated Current
kA
Inom l
LV-Side, Rated Current
kA
iTaps
According to Measurement Repor t
nntap
Tap: Tap Position
ntrcn
Tap: Automatic Tap Changing
i cont
Tap: Tap Changer
t2ldc
Tap: Controlled Node
ilcph
Tap: Phase
Two-Winding Transformer (3-Phase) (ElmTr2)
Unit
MVA
32
4
Input Parameter Definitions
Parameter
Description
imldc
Tap: Control Mode
i rem
Tap: Remote Control
p 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
MW
psp low
Tap: Lower Active Power Bound
MW
psp up
Tap: Upper Active Power Bound
MW
qsetp
Tap: Reactive Power Setpoint
Mvar
qsp low
Tap: Lower Reactive Power Bound
Mvar
qsp up
Tap: Upper Reactive Power Bound
Mvar
Tctrl
Tap: Controller Time Constant
s
ildc
Tap: Line Drop Compensation
ldcct
Tap: Current Transformer Rating
ldcpt
Tap: Voltage Transformer Ratio
ldcrs
Tap: Rset V
ldcxs
Tap: Xset V
tapctrl
Tap Controller (ElmTr2)
iMeasLoc
Measured at
mTaps
Measurement Report
iblock
Unit Transformer
ilt op
Long-term operating condition before short-circuit are known
Ub lv
Values for LV-Side: Highest Operating Voltage
kV
Ib lv
Values for LV-Side: Highest Operating Current
kA
cosphib lv
Values for LV-Side: Power factor
Ubqmin hv
Values for HV-Side (only for Unit Transformer): Minimum Operating Voltage
ifrqft
Frequent Fault ( > 10(5)/lifetime, Category II(III) )
iopt hf
Consider HF-Parameter
Cg h
HF-Parameter: Capacitance HV-Ground
myF
Cg l
HF-Parameter: Capacitance LV-Ground
myF
Cc1 hl
HF-Parameter: Capacitance HV-LV, 1-Sequence
myF
Cc0 hl
HF-Parameter: Capacitance HV-LV, 0-Sequence
myF
Two-Winding Transformer (3-Phase) (ElmTr2)
Unit
A
kV
33
4
Input Parameter Definitions
Parameter
Description
Unit
FOR1
Forced Outage Rate
1/a
FOE
Forced Outage Expectancy
h/a
FOD
Forced Outage Duration
h
iperfect
Ideal component
pTypStoch
Type model
pStoch
Element model
i uopt
OPF-Controls: Tap Position
maxload
OPF-Constraints: Max. Loading
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
