DIgSILENT PowerFactory. Technical Reference Documentation. Series Reactor - the resistance and the reactance of the reac...
DIgSILENT PowerFactory Technical Reference Documentation
Series Reactor ElmSind
DIgSILENT GmbH Heinrich-Hertz-Str. 9 72810 - Gomaringen Germany T: +49 7072 9168 0 F: +49 7072 9168 88 http://www.digsilent.de
[email protected] Version: 2016 Edition: 1
Copyright © 2016, 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. Series Reactor (ElmSind)
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Contents
Contents 1 General Description 1.1 Input Parameter
4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.1.1 Input mode of the rating parameter . . . . . . . . . . . . . . . . . . . . . .
4
1.1.2 Short-circuit voltage uk Impedance Zrea relation . . . . . . . . . . .
5
1.1.3 Copper Losses PCU Short-circuit voltage ukr, real part relation . . .
6
1.1.4 Reactance Xrea Inductance Lrea relation . . . . . . . . . . . . . . .
6
1.1.5 Resistance Rrea Copper Losses PCU , Short-circuit voltage ukr, real part relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.1.6 Reactance Xrea short-circuit voltage, uk and ukr, Impedance Zrea .
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1.2 Load flow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2.1 AC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.2.2 DC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.3 Short-circuit model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.4 RMS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.4.1 AC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.4.2 DC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5 EMT Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5.1 AC-Model without Saturation . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5.2 AC-Model with Saturation . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.5.3 DC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1.6 Harmonics/Power Quality Model . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Dynamic Simulation
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2.1 RMS and EMT Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.1.1 AC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2.1.2 DC-Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A Parameter Definitions
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B Signal Definitions
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List of Figures
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Series Reactor (ElmSind)
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Contents
List of Tables
Series Reactor (ElmSind)
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1
General Description
1
General Description
Terminal i Terminal i A
B
C
A
Terminal j Terminal j Rrea Rrea
Xrea Xrea A
B
C
Rrea Rrea
Xrea Xrea B
Rrea Rrea
Xrea Xrea C
A
B
C
Figure 1.1: Three Phase Model Terminal i Terminal i I:bus1 I:bus1
Rrea Rrea
Xrea Xrea
U:bus2 U:bus2
Terminal j Terminal j I:bus2 I:bus2
U:bus2 U:bus2
Figure 1.2: Single Phase Model The series reactor can be used to limit the short-circuit current. A three phase and single phase model is available.
1.1
Input Parameter
The resistance and the reactance of the reactor can be entered at different input options: • Short-circuit voltage uk in % and copper losses in kW or real part of the short-circuit voltage in % • Impedance (magnitude) in Ohm and copper losses in kW or real part of the short-circuit voltage in % • Reactance X and Resistance R in Ohm • Inductance L in mH and Resistance in Ohm
1.1.1
Input mode of the rating parameter
For the definition of the rating parameter they are two different input modes available: Series Reactor (ElmSind)
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1
General Description
a) Rated Voltage in kV and Rated Power in MVA b) Rated Voltage in kV and Rated Current in kA For a three phase reactor is the rated current calculated as:
In = √
Sn 3 · Un
in kA
for a single phase reactor: √ In =
3 · Sn Un
in kA
and for a DC single phase reactor:
In =
Sn Un
in kA
where, • In : Rated Current in kA • Un : Rated Voltage (Line-Line) of the reactor in kV • Sn : Rated Power of the reactor in MVA
1.1.2
Short-circuit voltage uk Impedance Zrea relation
For a three phase reactor:
Zrea =
uk U2 · n 100% Sn
in Ohm
For a single phase reactor:
Zrea =
uk Un2 · 100% 3 · Sn
in Ohm
• Zrea : Impedance magnitude of the reactor in Ohm • uk : Short-circuit voltage in % • Un : Rated Voltage (Line-Line) of the reactor in kV • Sn : Rated Power of the reactor in MVA Series Reactor (ElmSind)
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1
General Description
1.1.3
Copper Losses PCU Short-circuit voltage ukr, real part relation
ukr =
PCU · 100 Sn · 1000
in %
• ukr : Short-circuit voltage, real part in % • PCU : Copper Losses in kW • Sn : Rated Power of the reactor in MVA
1.1.4
Reactance Xrea Inductance Lrea relation
Lrea =
Xrea · 1000 2 · π · fnom
in mH
• Lrea : Inductance of the reactor in mH • Xrea : Reactance of the reactor in Ohm • fnom : Nominal frequency of the grid in Hz
1.1.5
Resistance Rrea Copper Losses PCU , Short-circuit voltage ukr, real part relation
For a three phase reactor:
Rrea =
2 2 ukr Unom PCU Unom · = · 2 100% Snom 1000 Snom
in Ohm
For a single phase reactor:
Rrea =
2 2 Unom PCU Unom ukr · = · 2 100% 3 · Snom 1000 3 · Snom
in Ohm
• Rrea : Resistance of the reactor in Ohm • PCU : Copper Losses in kW • Unom : Rated Voltage (Line-Line) of the reactor in kV • Snom : Rated Power of the reactor in MVA • ukr : Short-circuit voltage, real part in %
Series Reactor (ElmSind)
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1
General Description
1.1.6
Reactance Xrea short-circuit voltage, uk and ukr, Impedance Zrea
For a three phase reactor: √ Xrea =
2 p uk 2 − ukr2 Unom 2 − R2 · = Zrea rea 100% Snom
in Ohm
For a single phase reactor: √ Xrea =
2 p uk 2 − ukr2 Unom 2 − R2 · = Zrea rea 100% 3 · Snom
in Ohm
• Xrea : Reactance of the reactor in Ohm • Unom : Rated Voltage (Line-Line) of the reactor in kV • Snom : Rated Power of the reactor in MVA • uk : Short-circuit voltage, magnitude in % • ukr : Short-circuit voltage, real part in % • Zrea : Impedance magnitude of the reactor in Ohm
1.2
Load flow model
The series reactor is completely considered in the Load Flow calculation. A warning message will be printed on the output window if the rated voltage differs more than 10% as the nominal voltage of the bus bars. An error message will be printed on the output window if the rated voltages differs more than 50%.
1.2.1
AC-Model
For the Load Flow calculation is the reactor modelled by it’s nominal frequency behaviour:
Ubus1 − Ubus2 = Ibus1 · (Rrea + jω · Lrea) Ibus1 + Ibus2 = 0 The loading of the reactor is calculated as follow:
loading =
max(Ibus1 , Ibus2 ) · 100 In
in %
• loading : Loading in % • In : Rated current of the reactor in kA Series Reactor (ElmSind)
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1
General Description
• Ibus1 : Magnitude of the current at terminal i • Ibus2 : Magnitude of the current at terminal j For an unbalanced load flow calculation is the highest current of all phases used.
1.2.2
DC-Model
Under DC-conditions, a reactor is a closed circuit, hence only the resistance is considered:
Ubus1 − Ubus2 = Ibus1 · Rrea Ibus1 + Ibus1 = 0
1.3
Short-circuit model
For the Short-Circuit calculation is the reactor modelled by it’s nominal frequency behaviour:
Ubus1 − Ubus2 = Ibus1 · (Rrea + jω · Lrea) Ibus1 + Ibus2 = 0
1.4 1.4.1
RMS Model AC-Model
The RMS-simulation model of the series capacitance is fully compatible to the load flow model.
1.4.2
DC-Model
In DC circuits, network transients are considered as well. The series reactor is hence modelled by the differential equation of a resistance in series with a inductance:
Ubus1 (t) − Ubus2 (t) = Rrea · Ibus1 (t) + Lrea ·
d(Ibus1 (t)) dt
Ibus1 + Ibus2 = 0
1.5 1.5.1
EMT Model AC-Model without Saturation
The series reactor is modelled by the differential equation of a resistance in series with an inductance: Series Reactor (ElmSind)
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1
General Description
d(Ibus1:A (t)) dt d(Ibus1:B (t)) Ubus1:B (t) − Ubus2:B (t) = Rrea:s · Ibus1:B (t) + Lrea:s · dt d(Ibus1:C (t)) Ubus1:C (t) − Ubus2:C (t) = Rrea:t · Ibus1:C (t) + Lrea:t · dt Ibus1:A (t) + Ibus2:A (t) = 0 Ubus1:A (t) − Ubus2:A (t) = Rrea:r · Ibus1:A (t) + Lrea:r ·
Ibus1:B (t) + Ibus2:B (t) = 0 Ibus1:C (t) + Ibus2:C (t) = 0
1.5.2
AC-Model with Saturation
The saturation of the reactance can be simulated in the EMT model. 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.
Linear The input parameters are listed in Table 1.1. Table 1.1: Basic data of the linear characteristic Parameter
Description
Unit
Symbol
xreapu
Magnetizing reactance for unsaturated conditions. In p.u. values, the linear reactance is equal to the reciprocal of the magnetizing current (reactive part of the exciting current).
p.u.
lunsat
No saturation is considered. In this case, the current is proportional to the flux:
iM =
ψM lunsat
Where: • iM is the magnetizing current in p.u. Series Reactor (ElmSind)
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1
General Description
• ψM is the magnetizing flux in p.u. The p.u. values used for the definition of the saturation characteristic of the positive sequence model are referred to the same base quantities mentioned in 1.5.2.
Two slope Figure 1.3 shows the magnetizing current-flux curves for the two slope and polynomial characteristics. The input parameters of the two slope saturation characteristic are listed in Table 1.2.
Figure 1.3: Two slope and polynomial saturation curves
Table 1.2: Basic data of the two-slope saturation characteristic Parameter
Description
Unit
Symbol
psi0
Knee-point Flux of asymptotic piece-wise linear characteristic. Typical value around 1.1 to 1.2 times the rated flux. Magnetizing reactance for unsaturated conditions. 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.
p.u.
ψknee
p.u.
lunsat
p.u.
lsat
xreapu
xmair
In the case of the two slope curve, the series reactor saturation is approximated by two linear slopes, which are separated by the value of the knee flux. The first slope is given by the linear reactance, while the second is given by the saturated reactance. The saturated reactance value is fairly low compared with the unsaturated reactance. Series Reactor (ElmSind)
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1
General Description
ψM lunsat 1 (ψM − ψknee ) + iknee = lsat ψknee = lunsat
iM =
for ψM ≤ ψknee
iM
for ψM > ψknee
iknee
Where • iM is the magnetizing current in p.u. • ψM is the magnetizing flux in p.u. The p.u. values used for the definition of the saturation characteristic of the positive sequence model are referred to the same base quantities mentioned in 1.5.2.
Polynomial Figure 1.3 shows the magnetizing current-flux curves for the polynomial characteristic. The input parameters are listed in Table 1.3. Table 1.3: Basic data of the polynomial saturation characteristic Parameter
Description
Unit
Symbol
psi0
Knee-point Flux of asymptotic piece-wise linear characteristic. Typical value around 1.1 to 1.2 times the rated flux. Magnetizing reactance for unsaturated conditions. 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. Saturation exponent of polynomial representation. Typical values are 9,13,15. The higher the exponent the sharper the saturation curve.
p.u.
ψknee
p.u.
lunsat
p.u.
lsat
-
ksat
xreapu
xmair ksat
In the polynomial type, the saturation is also represented by two linear slopes, but smoothed by a polynomial function, in which the higher the exponent is, the sharper the saturation becomes.
Series Reactor (ElmSind)
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1
General Description
iM =
ψM lunsat
( ·
1+
ψM ψ0
ksat )
1 (ψM − ψsat ) + iknee lsat ksat + 1 = · ψknee ksat ψknee = lunsat
iM = ψsat iknee
for ψM ≤ ψsat for ψM > ψsat
Where • iM is the magnetizing current in p.u. • ψM is the magnetizing flux in p.u. • ψ0 is a parameter 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, in 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 derivative (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 same base quantities mentioned in 1.5.2.
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. The p.u. values used for the definition of the saturation characteristic of the positive sequence model are referred to the same base quantities mentioned in 1.5.2.
Base Quantities 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 is the Rated Voltage of the series reactor (ucn) in kV • Sbase is the Rated Power of the series reactor (Sn) in M V A √
Sbase [M V A] 2· √ · 1000 3 · Ubase [kV ] √ √ Ubase [kV ]/ 3 • Ψbase [V · s] = 2 · · 1000 2πf [Hz] 2 Ubase [kV ] 1 • Lbase [H] = · Sbase [M V A] 2πf [Hz] • Ibase [A] =
Series Reactor (ElmSind)
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1
General Description
Ignoring the Saturation The saturation is ignored when any of the following conditions are met: • The reactance xrea is zero • It is a DC reactor • The input signal Xin is connected
Considerations for 3-Limb Core The ABC per unit flux values are calculated from the dq flux components (ψ0 is ignored in the transformation):
1 ψM :A 1 − ψM :B = 2 1 ψM :C − 2
√0 3 2 √ 3 − 2
1
ψd 1 × ψq 0 1
The zero-sequence current in p.u. is given by:
i0 =
ψ0 2πf · lunsat:r
Considerations for 5-Limb Core The ABC per unit flux values are calculated from the dq0 flux components:
1 ψM :A 1 − ψM :B = 2 1 ψM :C − 2
√0 3 2 √ 3 − 2
1
ψd 1 × ψq ψ0 1
The zero-sequence current in p.u. is given by:
i0 = 0
Equations The magnetizing currents in p.u. are calculated according to the type of saturation selected:
iM :A (t) = f (ψM :A ) iM :B (t) = f (ψM :B ) iM :C (t) = f (ψM :C )
Series Reactor (ElmSind)
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1
General Description
The equations for voltage and current per phase in actual values are given by: Ibus1:A (t) = (iM :A + i0 ) · Ibase Ibus1:B (t) = (iM :B + i0 ) · Ibase Ibus1:C (t) = (iM :C + i0 ) · Ibase 1 2πf 1 Ubus1:B (t) − Ubus2:B (t) = Rrea:s · Ibus1:B (t) + 2πf 1 Ubus1:C (t) − Ubus2:C (t) = Rrea:t · Ibus1:C (t) + 2πf Ibus1:A (t) + Ibus2:A (t) = 0 Ubus1:A (t) − Ubus2:A (t) = Rrea:r · Ibus1:A (t) +
d(Ψbus1:A (t)) dt d(Ψbus1:B (t)) · dt d(Ψbus1:C (t)) · dt ·
Ibus1:B (t) + Ibus2:B (t) = 0 Ibus1:C (t) + Ibus2:C (t) = 0
1.5.3
DC-Model
The series reactor is modelled by the differential equation of a resistance in series with an inductance:
Ubus1 (t) − Ubus2 (t) = Rrea · Ibus1 (t) + Lrea ·
d(Ibus1 (t)) dt
Ibus1 (t) + Ibus2 (t) = 0
1.6
Harmonics/Power Quality Model
Frequency-dependent characteristics may be defined for the following parameters (parameter names follow in parentheses): R (rrea) and L (lrea). Note: For absolute characteristics, the values defined in the element (not in the characteristic) will be used at the fundamental frequency.
Series Reactor (ElmSind)
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2
Dynamic Simulation
2 2.1 2.1.1
Dynamic Simulation RMS and EMT Simulation AC-Model
Rin Xin
AC Model
Figure 2.1: Input/OutputRin Definition of AC Series Reactor Model (RMS-Simulation)
2.1.2
DC-Model
Rin Xin Lin
AC Model DC Model
Rin Lin
DC Model
Figure 2.2: Input/Output Definition of DC Series Reactor Model (RMS-Simulation)
Series Reactor (ElmSind)
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B
A
Signal Definitions
Parameter Definitions Table A.1: Series Reactor Parameters
B
Parameter
Description
Unit
loc name outserv ucn Sn Curn pRating systp nphases uk Zd lrea xrea Pcu ukr rrea maxLoad iAstabint psi0 xmair ksat satcur satflux iInterPol smoothfac Inom xreapu
Name Out of Service Rated voltage Rated power Rated current Thermal rating System type Phases Short-circuit voltage Absolute impedance Inductance Reactance Copper losses Short-circuit voltage Resistance Thermal load limit A-stable integration algorithm Knee flux Saturated reactance Saturation exponent Current (peak) Flux (peak) Interpolation Smoothing factor Rated current Linear reactance
kV MVA kA
% Ohm mH Ohm kW % Ohm % p.u. p.u. p.u. p.u. % kA p.u.
Signal Definitions Table B.1: Input/Output signals Name
Description
Unit
Type
Model
Rin Xin Lin
Resistance Input Reactance Input Inductance Input
Ohm Ohm Ohm
IN IN IN
AC, DC (RMS, EMT) AC (RMS, EMT) DC (RMS, EMT)
Series Reactor (ElmSind)
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List of Figures
List of Figures 1.1 Three Phase Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2 Single Phase Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3 Two slope and polynomial saturation curves
. . . . . . . . . . . . . . . . . . . .
10
2.1 Input/Output Definition of AC Series Reactor Model (RMS-Simulation) . . . . . .
15
2.2 Input/Output Definition of DC Series Reactor Model (RMS-Simulation) . . . . . .
15
Series Reactor (ElmSind)
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List of Tables
List of Tables 1.1 Basic data of the linear characteristic . . . . . . . . . . . . . . . . . . . . . . . . .
9
1.2 Basic data of the two-slope saturation characteristic . . . . . . . . . . . . . . . .
10
1.3 Basic data of the polynomial saturation characteristic . . . . . . . . . . . . . . . .
11
A.1 Series Reactor Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
B.1 Input/Output signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
Series Reactor (ElmSind)
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