TechRef_SeriesReactance

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DIgSILENT PowerFactory

Technical Reference Documentation

Series Reactor

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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.

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1 General Description

A B C Rrea Xrea A B C Rrea Rrea Xrea Xrea Terminal i Terminal j Rrea Xrea Terminal i Terminal j I:bus1 I:bus2 U:bus2 U:bus2

Figure 1.1: Three Phase Model

A B C Rrea Xrea A B C Rrea Rrea Xrea Xrea Terminal i Terminal j Rrea Xrea Terminal i Terminal j I:bus1 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

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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 Zrearelation

For a three phase reactor:

Zrea= uk 100%· U2 n Sn in Ohm

For a single phase reactor:

Zrea= uk 100%· U2 n 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

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1.1.3 Copper Losses PCU <=> Short-circuit voltage ukr, real part relation

ukr = PCU Sn· 1000

· 100 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 Lrearelation

Lrea=

Xrea

2 · π · fnom

· 1000 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

Rrea= ukr 100%· U2 nom Snom = PCU 1000· U2 nom S2 nom in Ohm

Rrea= ukr 100%· Unom2 3 · Snom = PCU 1000· Unom2 3 · S2 nom 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

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1.1.6 Reactance Xrea<=>short-circuit voltage, uk and ukr, Impedance Zrea

Xrea= √ uk2_{− ukr}2 100% · U2 nom Snom =pZ2

rea− R2rea in Ohm

Xrea= √ uk2_{− ukr}2 100% · U2 nom 3 · Snom =pZ2

rea− R2rea 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)

In · 100 in %

• loading : Loading in %

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• 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 RMS Model

1.4.1 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 EMT Model

1.5.1 AC-Model without Saturation

The series reactor is modelled by the differential equation of a resistance in series with an inductance:

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Ubus1:A(t) − Ubus2:A(t) = Rrea:r· Ibus1:A(t) + Lrea:r·

d(Ibus1:A(t))

dt Ubus1:B(t) − Ubus2:B(t) = Rrea:s· Ibus1:B(t) + Lrea:s·

d(Ibus1:B(t))

dt Ubus1:C(t) − Ubus2:C(t) = Rrea:t· Ibus1:C(t) + Lrea:t·

d(Ibus1:C(t))

dt Ibus1:A(t) + Ibus2:A(t) = 0

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 se-lects 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:

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• 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 char-acteristics. 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

psi0 Knee-point Flux of asymptotic piece-wise linear characteristic. Typical value around 1.1 to 1.2 times the rated flux.

p.u. ψknee

p.u. lunsat

xmair Magnetizing reactance for saturated conditions.

p.u. lsat

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.

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iM = ψM lunsat for ψM ≤ ψknee iM = 1 lsat

(ψM− ψknee) + iknee for ψM > ψknee

iknee=

ψknee

lunsat

Where

• iM is the magnetizing current in p.u.

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

psi0 Knee-point Flux of asymptotic piece-wise linear characteristic. Typical value around 1.1 to 1.2 times the rated flux.

p.u. ψknee

p.u. lunsat

xmair Magnetizing reactance for saturated conditions.

p.u. lsat

ksat Saturation exponent of polynomial representation. Typical values are 9,13,15. The higher the exponent the sharper the saturation curve.

- 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.

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iM = ψM lunsat · ( 1 + ψM ψ0 ksat) for ψM ≤ ψsat iM = 1 lsat

(ψM− ψsat) + iknee for ψM > ψsat

ψsat= ksat+ 1 ksat · ψknee iknee= ψknee lunsat Where

• iM is the magnetizing current 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 char-acteristic 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.

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.

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:

• Ubaseis the Rated Voltage of the series reactor (ucn) in kV

• Sbaseis the Rated Power of the series reactor (Sn) in M V A

• Ibase[A] = √ 2 ·√Sbase[M V A] 3 · Ubase[kV ] · 1000 • Ψbase[V · s] = √ 2 ·Ubase[kV ]/ √ 3 2πf [Hz] · 1000 • Lbase[H] = U_base2 [kV ] Sbase[M V A] · 1 2πf [Hz]

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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 (ψ0is ignored in the

transformation):    ψM :A ψM :B ψM :C   =       1 0 1 −1 2 √ 3 2 1 −1 2 − √ 3 2 1       ×    ψd ψq 0   

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:

   ψM :A ψM :B ψM :C   =       1 0 1 −1 2 √ 3 2 1 −1 2 − √ 3 2 1       ×    ψd ψq ψ0   

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)

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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

Ubus1:A(t) − Ubus2:A(t) = Rrea:r· Ibus1:A(t) +

1 2πf ·

d(Ψbus1:A(t))

dt Ubus1:B(t) − Ubus2:B(t) = Rrea:s· Ibus1:B(t) +

1 2πf ·

d(Ψbus1:B(t))

dt Ubus1:C(t) − Ubus2:C(t) = Rrea:t· Ibus1:C(t) +

1 2πf · d(Ψbus1:C(t)) dt Ibus1:A(t) + Ibus2:A(t) = 0 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)

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2 Dynamic Simulation

2.1 RMS and EMT Simulation

2.1.1 AC-Model

Rin

Xin

AC Model

Rin

Lin

DC Model

Figure 2.1: Input/Output Definition of AC Series Reactor Model (RMS-Simulation)

2.1.2 DC-Model

Rin

Xin

AC Model

Rin

Lin

DC Model

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A

Parameter Definitions

Table A.1: Series Reactor Parameters

Parameter Description Unit

loc name Name

outserv Out of Service

ucn Rated voltage kV

Sn Rated power MVA

Curn Rated current kA

pRating Thermal rating systp System type nphases Phases

uk Short-circuit voltage %

Zd Absolute impedance Ohm

lrea Inductance mH

xrea Reactance Ohm

Pcu Copper losses kW

ukr Short-circuit voltage %

rrea Resistance Ohm

maxLoad Thermal load limit % iAstabint A-stable integration algorithm

psi0 Knee flux p.u.

xmair Saturated reactance p.u. ksat Saturation exponent

satcur Current (peak) p.u.

satflux Flux (peak) p.u.

iInterPol Interpolation

smoothfac Smoothing factor %

Inom Rated current kA

xreapu Linear reactance p.u.

B

Signal Definitions

Table B.1: Input/Output signals

Name Description Unit Type Model

Rin Resistance Input Ohm IN AC, DC (RMS, EMT) Xin Reactance Input Ohm IN AC (RMS, EMT) Lin Inductance Input Ohm IN DC (RMS, EMT)

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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

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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

TechRef_SeriesReactance

DIgSILENT PowerFactory

Technical Reference Documentation

Series Reactor

Contents

1

General Description

1.1

Input Parameter

1.2

Load flow model

1.3

Short-circuit model

1.4

RMS Model

1.5

EMT Model

1.6

Harmonics/Power Quality Model

2

Dynamic Simulation

2.1

RMS and EMT Simulation

Rin

Xin

AC Model

Rin

Lin

DC Model

Rin

Xin

AC Model

Rin

Lin

DC Model

A

Parameter Definitions

B

Signal Definitions

List of Figures

List of Tables