Master of Science
Thesis
Fault Current Control in the
Transmission Network
− An Electromagnetic Transient approach −
Sander A. Franke B.Sc.
Delft University of Technology
Faculty of Electrical Engineering, Mathematics
and Computer Science
June 19, 2012
Thesis committee
Prof. Ir. L. van der Sluis
Dr. Ir. M. Popov
Prof. Dr. Ir. R.P.P. Smeets
Ir. A.J.L.M. Kanters
Ir. E. Wierenga
Delft University of Technology, thesis supervisor
Delft University of Technology, daily supervisor
Eindhoven University of Technology
TenneT TSO, daily supervisor
TenneT TSO
Copyright © 2012 by S.A. Franke
Typesetting was done by LATEX
All Rights Reserved. No part of this publication may be reproduced, stored
in a retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording, scanning or otherwise, without prior permission from Delft University of Technology and the author.
Keywords: ATP-EMTP, DIgSILENT, fault current, fault current limiter, shortcircuit, superconductivity, transient recovery voltage, transmission network
Legal Notice
Neither the authors nor Delft University of Technology accept ant responsibility or liability for loss or damage occasioned to any person or property through
using the material, instructions, methods or ideas contained herein, or acting or
refraining from acting as a result of such use.
Abstract
Transmission System Operators (TSO’s) are facing an increase of fault current
levels in their networks due to the expansion of generation capacity. This thesis
investigates three possible fault current limiting measures in the Dutch transmission grid which is operated and maintained by TenneT TSO. In order to evaluate
the behavior of the fault current limiting measures, two independently operating
grid models were established and validated. The examined fault current limiters consisted of a current limiting reactor (CLR) and a superconducting fault
current limiter (SCFCL). The possibility of substation splitting was also investigated. All three measures reduced the short-circuit levels successfully to values
within the electromechanical and thermal withstand levels of the power system.
Simulation results revealed that the SCFCL has a significantly lower impact
on the rate-of-rise-of-recovery-voltage (RRRV) of the circuit breaker (CB) as
compared to the CLR. Additional measures were presented to keep the RRRV
of the CLR within the dielectric withstand levels of the CB as specified in the
IEC 62271-100.
i
Contents
Abstract
i
Preface
vii
Nomenclature
ix
1 Introduction
1.1 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
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2 Fault Currents
2.1 Basic Theory . . . . . . . . . . . . . . . .
2.1.1 Anatomy of a Short-circuit . . . .
2.1.2 The Short-circuit Characterized by
2.1.3 The Transient Recovery Voltage .
2.2 Short-circuit Calculations . . . . . . . . .
2.2.1 Analysis of Grid Faults . . . . . .
2.2.2 Symmetrical Components . . . . .
2.2.3 The Superposition Method . . . .
2.2.4 The IEC 60909 Method . . . . . .
2.3 The First Pole-to-clear Factor . . . . . . .
2.4 The IEC 62271-100 . . . . . . . . . . . . .
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the IEC
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60909
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3 The Model
3.1 Grid Model . . . . . . . . . . . . . . . . .
3.1.1 Initial study . . . . . . . . . . . . .
3.1.2 Topology of the Dutch Grid Model
3.1.3 Validation . . . . . . . . . . . . . .
3.1.4 TRV Study . . . . . . . . . . . . .
3.1.5 Limitations . . . . . . . . . . . . .
3.2 Modeling of Power System Components .
3.2.1 Circuit Breakers . . . . . . . . . .
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iii
CONTENTS
3.2.2
3.2.3
3.2.4
Generators . . . . . . . . . . . . . . . . . . . . . . . . . .
Transmission Lines . . . . . . . . . . . . . . . . . . . . . .
Transformers . . . . . . . . . . . . . . . . . . . . . . . . .
4 Fault Current Limiting Reactors
4.1 Applications of Reactors . . . . . . . . . . . . . .
4.1.1 Series Reactors . . . . . . . . . . . . . . .
4.1.2 Neutral Grounding Reactors . . . . . . .
4.2 Technical Aspects of Series Reactors . . . . . . .
4.2.1 Air-core Reactors . . . . . . . . . . . . . .
4.2.2 Oil-immersed Reactors . . . . . . . . . . .
4.3 A Practical Model . . . . . . . . . . . . . . . . .
4.3.1 Technical Parameters . . . . . . . . . . .
4.3.2 ATP-EMTP Model of the Series Reactor
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5 Superconducting Fault Current Limiters
5.1 Superconducting Materials . . . . . . . . . . . . . . . . . . . . . .
5.2 Costs of SC Materials . . . . . . . . . . . . . . . . . . . . . . . .
5.3 SCFCL Topologies . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Resistive Type . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Saturated Iron Core . . . . . . . . . . . . . . . . . . . . .
5.3.3 Magnetic Shielded Core . . . . . . . . . . . . . . . . . . .
5.3.4 Solid State FCL’s . . . . . . . . . . . . . . . . . . . . . . .
5.3.5 Overview of Different SCFCL Types . . . . . . . . . . . .
5.4 A Practical Model for a Shielded Core SCFCL . . . . . . . . . .
5.4.1 Design Aspects of a SCFCL . . . . . . . . . . . . . . . . .
5.4.2 ATP-EMTP Model of the Magnetic Shielded Core SCFCL
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6 Case Study Maasbracht 380
6.1 Splitting the Substation Into Sub Grids . . .
6.2 EMT Model of Substation Maasbracht 380 .
6.3 EMT Study Series reactor . . . . . . . . . . .
6.3.1 Results . . . . . . . . . . . . . . . . .
6.3.2 Insertion of Damping Capacitors . . .
6.4 EMT Study Magnetic Shielded Core SCFCL
6.4.1 Results . . . . . . . . . . . . . . . . .
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7 Conclusion and Recommendations
65
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . 66
Bibliography
67
Appendices
A Source Code ATP-EMTP MODELS Block Set
73
B Overview of SCFCL Projects
75
C Overview of the EMT Grid Models
81
iv
CONTENTS
D Resulting Plots TRV Study
85
D.1 Series Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
D.2 Magnetic Shielded Core SCFCL . . . . . . . . . . . . . . . . . . . 88
E Grid Parameters
91
v
Preface
This thesis describes the possible short-circuit limiting measures in the Dutch
transmission grid and is carried out as a compulsory part of my MSc study
Electrical Power Engineering at the Delft University of Technology. During my
studies I became acquainted with the field of Power System Transients through
the interesting lectures of prof. ir. L. (Lou) van der Sluis on the same topic. I
decided to fulfill my thesis within this intriguing field of research, however still
a challenging subject had to be found!
Dr. ir. M. (Marjan) Popov introduced me to the Dutch Transmission System
Operator TenneT and I was given the opportunity to work on a transient study
on fault current limiting measures in the Dutch transmission grid. During my
thesis I was given a workplace at TenneT within the business unit Grid Services.
This position gave me the chance to benefit from a tremendous amount of
technical knowledge and experience in the area of power systems, something
which I have greatly appreciated.
First of all I would like to thank ing. G.P.P. (Gert) Aanhaanen for his
technical support and interest from the side of the business unit Asset Management. I am grateful to ir. E.F. (Ernst) Wierenga who often helped me with
the DIgSILENT PowerFactory software and with whom I had many enjoyable
conversations regarding technical and non-technical subjects. I would like to
thank my daily supervisor at TenneT ir. A.J.L.M. (Jos) Kanters with whom I
had many fruitful discussions on my thesis and who guided me whenever it was
needed. I also want to thank the rest of my colleagues at TenneT who were very
interested in my work and helpful whereever they could.
Furthermore I would like to acknowledge prof. dr. ir. R.P.P. (Rene) Smeets,
who shared his expertise and was willing to take place in my thesis committee.
Dr. ir M. (Marjan) Popov I sincerely want to thank for introducing me to the
ATP-EMTP software and the subsequent support he provided in his role as my
daily supervisor at the Delft Univesity of Technology.
Ir. M.O.W. (Marinus) Grond, ing. M. (Michiel) Vis and ir. F. (Ferdinant)
Visser it was a great pleasure studying with you guys and I am sure you are
looking forward to great career (within the field of Electrical Power Engineering). Certainly someone I would like to thank is drs. J. (Jelle) Oosterhof which
provided editorial feedback and support during my thesis.
Last but definitely not least, I would like to express my gratitude to Anneloes
for her unconditional support during the period of this thesis and entire studies.
Sander Franke, Rotterdam, June 2012
vii
List of Abbreviations
AC
Aternating Current
ATP
Alternative Transients Program
BIL
Basic Impulse Level
BPA
Bonneville Power Administration
BSCCO Bismuth-strontium-calcium-copper-oxide
CT
Current transformer
CVT
Capacitive voltage transformer
DC
Direct Current
DIgSILENT Digital SImuLator for Electrical NeTwork
EM
Electromagnetic
EMT
Electromagnetic Transients
EMTP Electromagnetic Transients Program
ENTSO-E European Network of Transmission System Operators for Electricity
FCL
Fault current limiter
FORTRAN Procedural Imperative Programming Language
FPTC First pole-to-clear Factor
HTS
High Temperature Superconductor
IEC
International Electrotechnical Commission
LTS
Low Temperature Superconductor
LV
Low Voltage
ix
Nomenclature
MGb
Magnesium-diboride
ODAF Oil Directed Air Forced
ONAF Oil Natural Air Forced
ONAN Oil Natural Air Natural
p.u.
Per Unit
RE
Rare-earth
RMS
Root-mean-square
RRRV Rate of Rise of Recovery Voltage
S/N
Superconducting-to-normal transition
SC
Super conductor
SCFCL Superconducting Fault Current Limiter
SCTM Symmetrical Component Transformation Matrix
SIL
Switching Impulse Level
TACS Transient Analysis of Control Systems
TRV
Transient Recovery Voltage
TSO
Transmission System Operator
UCTE Union for the Coordination of the Transmission of Electricity
YBCO Yttrium-barium-copper-oxide
x
CHAPTER
1
Introduction
he electrical power system is probably the largest and most complex manT
made system in the world. It facilitates the transport of electrical energy
which is the most versatile and universal form of energy available. The demand
for electricity is growing continuously and is driven by technical developments
such as the introduction of digital computers in the last three decades. It is
expected that the demand for electricity will increase even more in the developed
world when electrical cars are widely introduced.
To keep a balance between the production and consumption of electricity
the generating capacities of power systems need to be expanded. Generating
capacity can be increased by installing new power plants, renewables1 or by
implementing distributed generators in the power system. As a result the transmission and distribution capacities need to be expanded as well, which leads to
the installation of additional transformers and transmission lines.
The increased production capacity and increased transmission and capacity
will also increase the prospective2 short-circuit currents in the power system.
Faults in the power system can have various causes. Such as lightning, power
system component failures or falling tree branches. It is crucial to keep the
prospective short-circuit currents within the thermal and mechanical fault current withstand levels of the power system, since fault over-currents may harm
the high-voltage equipment.
The Dutch transmission network is facing an increase in present and future short-circuit current levels as well. Until the year 2020 a large increase of
concentrated generation capacity is foreseen at the locations Eemshaven, Maasbracht and Maashaven. An overview is given in table 1.1. This thesis aims on
the “controllability” of fault currents in the Dutch transmission network that
is coordinated by the Dutch Transmission System Operator (TSO) TenneT at
1 Renewables are energy sources that comes from natural resources such as sunlight, wind,
rain, tides, and geothermal heat.
2 The prospective short-circuit current (PSCC) is the highest electric current which can
exist under short-circuit conditions.
1
Chapter 1
which this thesis is carried out. In the next section, 1.1 Research Objectives,
the objectives of this thesis will be discussed.
Location
Company
Unit
Capacity
MW
In operation
Fuel
Eemshaven
Nuon
Energie BV
RWE
Magnum
EEM-A
EEM-B
1.290
1.200
780
780
2011
2013
2013
2014
Gas
Gas
Coal
Coal
Maasbracht
Essent
Claus-C
Claus-D
1.300
1.300
2012
2018
Gas
Gas
Maasvlakte
Enecogen
Electrabel
E.On
Enecogen
CR-1
NL-MMP3
870
736
1.070
2011
2012
2013
Gas
Coal
Coal
Table 1.1: Planned construction of power plants at locations Eemshaven, Maasbracht
and Maashaven [2]
1.1
Research Objectives
The increasing fault current levels in the Dutch electrical power system will have
its impact on safety and reliability of the system. In this thesis the main goal is
to determine how fault currents can be reduced in such a way that acceptable
levels for the high-voltage equipment are achieved. This question has to be
translated into physical measures since it is the responsibility of TenneT to
facilitate electricity transmission without imposing restrictions to grid connected
parties3 . Three possible fault current limiting measures will be treated:
ˆ Fault current limiting reactors
ˆ Superconducting fault current limiters or SCFCL’s
ˆ Substation splitting
where fault current limiters based on superconducting materials have the special
interest of TenneT. These are the so called superconducting fault current limiters
or SCFCL’s.
Short-circuits are often referred to as “transients”. However transients in
power systems are far more comprehensive. A transient occurs in the power system when the network changes from one steady state into another [51]. Meaning
that the effects of switching actions by circuit breakers also need to be designated as transients. From this perspective the presence of a short-circuit current
can be seen as one steady-state situation wherein the energy is predominantly
stored in the EM field. When the short-circuit current has been interrupted
the network changes into another steady-state situation wherein the energy is
3 The Office of Energy Regulation ensures the conditions for the free market and is responsible for implementing and ensuring compliance with the 1998 Electricity Act [41]
2
Introduction
mainly in the electric field. Thus when it comes to evaluating FCL’s in the power
system, networks need to be accurately modeled and validated with respect to
voltages and currents. This is another objective of this thesis.
The investigated fault current limiting measures will be assessed on TenneT’s substation Maasbracht 380. It is expected that the substation will exceed
its maximum short-circuit withstand levels in the near future due to the construction of the Claus-D generation units connected to substation Maasbracht
380. The results will be brought together in chapter 6 Case Study Maasbracht
380.
1.2
Research Methodology
At first the relevant theory of transients in power systems will be examined.
In addition short-circuit calculations methods are discussed as they will play
an important role in the determination of equivalent sources and grid model
validation. Fault current limiting measures are studied by literature and subsequently EMT models will be established. SCFCL’s have the special interest in
this thesis, therefore multiple topologies will be treated and SC material properties examined. The behavior of several fault current limiting measures will be
tested on substation Maasbracht 380. For the Dutch electrical power system an
EMT grid model will be established, constructed out of all relevant power system components such as generator models, line models and transformer models.
Grid boundaries are replaced by equivalent sources computed by a steady-state
short-circuit calculation model which will be provided by the Asset Management
department of TenneT.
The choice of simulation software mainly depends on functionality and grade
of technical support during this thesis. At TenneT DIgSILENT PowerFactory
is a commonly used software package and support is widely available within the
business units Asset Management and Grid Services. Delft University of Technology recommends the academic ATP-EMTP software because it is supported
by the Power Systems Laboratory and through many scientific and non-scientific
experts all over the world.
DIgSILENT PowerFactory
DIgSILENT (Digital SImuLator for Electrical NeTwork) PowerFactory is a commercial simulation tool for calculations in power systems and features a broad
range of functionalities; the ones of interest in this thesis are the EMT analysis
functionality and the IEC 60909 short-circuit calculation method.
ATP-EMTP
ATP-EMTP (Alternative Transients Program) is a non-commercial simulation
tool for the calculation of electromagnetic transients in specific. It is mainly
based on the efforts of H.W. Dommel during his time at the Munich Institute
of Technology in the early 1960s and later at BPA (Bonneville Power Administration) in the United States where he continued his work on the program. At
present ATP-EMTP is the most widely used Electromagnetic Transients Program in the world [30].
3
Chapter 1
Both simulation software packages are used in this thesis to validate the
dynamical short-circuit currents in the Dutch grid model.
1.3
Thesis Outline
This thesis will first treat relevant theory on the topic of transients and shortcircuit calculations in chapter 2. Chapter 3 describes how parts of the Dutch
transmission grid are modeled for EMT analysis. It focuses on the validation
and model description of relevant power system components. A study on the
technical aspects of several fault current limiting reactors is presented in chapter
4. This chapter also comprises the model description of an oil-immersed series
reactor based on manufacturing parameters. A thorough insight in SC materials and a comparison of SCFCL topologies is given in chapter 5. The same
chapter describes how an EMT model of a SCFCL is established. Chapter 6
contains the case study, where the explored fault current limiting measures will
be tested on substation Maasbracht 380. Finally chapter 7 gives conclusions
and recommendations for future work.
4
CHAPTER
2
Fault Currents
Relevant aspects on power system faults are treated in this chapter. It covers elementary theory on fault currents, short-circuit calculations and transient
recovery voltages.
2.1
Basic Theory
2.1.1
Anatomy of a Short-circuit
To get an thorough understanding of the short-circuit current behavior in a
power system, the LR-circuit in figure 2.1 is evaluated. The short-circuit is of
a predominant inductive character as most of the energy is stored in the magnetical field of power systems components. The inductance L could represent
the inductance of synchronous generators, transformers or transmission lines for
example. Losses in the power system, such as iron losses, are represented by
the resistance R. By applying Kirchoff’s law, the nonhomogeneous equation of
the circuit is obtained:
U = Û sin(ωt + ϕ) = Ri + L
di
dt
L
(2.1)
R
U
Figure 2.1: Voltage source connected to a LR series circuit
5
Chapter 2
The short circuit can be initiated at any time instant by the circuit breaker and
therefore has a phase angle between 0 and 180 degrees (or 0 and π). The general
solution is found by solving the characteristic equation:
Ri + Lκ = 0
(2.2)
The eigenvalue of the characteristic equation is declared as κ. By solving equation (2.2) for κ, the result is κ = −(R/L). Subsequently the general solution
for equation (2.1) is:
ih (t) = C1 e−(R/L)t
(2.3)
By substituting a general expression in equation (2.1), the particular solution
is found:
ip (t) = A sin(ωt + ϕ) + B cos(ωt + ϕ)
(2.4)
Now A and B van be defined:
A=
R2
RÛ
+ ω 2 L2
B=−
R2
ωLÛ
+ ω 2 L2
Then the particular solution is:
Û
ωL
ip (t) = √
sin ωt + ϕ − tan−1
R
R 2 + ω 2 L2
(2.5)
(2.6)
Resulting in the complete solution, which is the total of the general and the
particular solution:
i(t) = ih (t) + ip (t)
i(t) = C1 e
−(R/L)t
Û
ωL
−1
+√
sin ωt + ϕ − tan
R
R2 + ω 2 L2
(2.7)
(2.8)
Before the switch closes, the magnetic flux in the inductor L is zero as a result
of the law of the conservation of flux. Therefore we may omit the R/L term,
resulting in:
Û
ωL
i(0) = C1 + √
sin ϕ − tan−1
(2.9)
R
R 2 + ω 2 L2
C1 can now be derrived and yields:
(
)
Û
ωL
i(t) = e−(R/L)t √
sin ϕ − tan−1
R
R 2 + ω 2 L2
Û
ωL
−1
+√
sin ωt + ϕ − tan
R
R2 + ω 2 L2
(2.10)
The term exp[−(R/L)t] is known as the DC component and eventually damps
out. The expression between the brackets is a constant and its outcome is
6
Fault Currents
Top envelope
2√2Ik=2√2I´´k
A
ip
2√2I´´k
d.c. compnent id.c. of the short-circuit current
Time
Bottom envelope
Figure 2.2: Short-circuit current of a far-from-generator short circuit with constant
AC component
determined by the instant of the fault current (closing of the circuit). It means
that the magnitude of the DC component depends on this closing instant. If the
fault occurs at the current-zero crossing, than there is no DC component and
the current reaches an immediate steady state. This is called a symmetrical
current. If the fault instant is shifted plus or minus 90 degrees with respect
to the zero-crossing, it will reach the maximum amplitude. This is called an
asymmetrical current and an example is given in figure 2.2. The short-circuit
can be characterized by parameters as is done by IEC 60909. This will be
discussed in the next sub-section.
2.1.2
The Short-circuit Characterized by the IEC 60909
The IEC 60909 defines the short-circuit current with parameters that are very
commonly used during the planning, design and operation of electrical power
systems. The IEC 60909 makes the distinction between far-from-generator and
near-to-generator faults. The behavior of the short-circuit current in both cases
00
is shown in figures 2.2 and 2.3. Where Ik is the initial symmetrical short circuit
current, ip is the peak short circuit current, idc is the decaying DC aperiodic
component and A is the initial amplitude of the DC aperiodic component. Figure 2.2 refers to a short-circuit far-from generating units and is characterized by
a constant value of the symmetric AC periodic component. Figure 2.3 refers to
a short circuit near a synchronous generator and is characterized by a variable
value of the symmetric AC periodic component. The decaying AC component
is a direct result of the varying reactance of the synchronous machine during a
short circuit. The waveform is divided in three distinct time periods. The substransient period, lasting only for the first few cycles and where the amplitude
decays rapidly, the transient period that takes a longer time, during which the
amplitude decays considerably more slowy and finally the steady state period,
during which the amplitude of the current stays constant. The parameters that
determine the amplitude of the short-circuit waveform are the substransient re7
Chapter 2
Top envelope
A
2√2Ik
ip
2√2I´´k
d.c. compnent id.c. of the short-circuit current
Time
Bottom envelope
Figure 2.3: Short-circuit current of a near-to-generator short circuit with decaying
AC component
00
0
actance, X , the transient reactance, X and the synchronous reactance, X,
respectively.
2.1.3
The Transient Recovery Voltage
The TRV is the voltage which appears across the circuit breaker terminals when
it opens and interrupts a current. This voltage comprises both power frequency
and transient components and depends on the type of fault, the location of the
fault and the type of circuit being switched. An example of a three-phase-toground fault is given in figure 2.4. The transformer is represented by a short
circuit reactance, Lt and its windings capacitance by a capacitor to ground Ct ,
see figure 2.4c for the one-phase representation. The resulting voltage over the
circuit breaker is plotted in figure 2.4c. Vl is equal to zero, as it is connected
to ground. The TRV Vs increases to E with 1.0 per unit and can reach a peak
value of 2.0 per unit without damping in the circuit. In practical situations this
value is significantly lower due to iron and copper losses.
The frequency of the TRV is related to the response of the system on each
side of the breaker. In this example where Vl is connected to the ground the
oscillating frequency results in:
f=
1
√
2π Lt Ct
(2.11)
The rate of rise and peak value of the TRV are related to the type of fault being
interrupted. And
8
Fault Currents
Three-Phasetoground fault
G
(a)
+
E
Lt
Ct
−
(b)
Vs
Vl
2E (no damping)
Vs
E
Vs & Vl
Vl
(c)
Figure 2.4: The TRV for a three phase to ground fault: (a) one-line representation,
(b) one-phase representation, (c) TRV waveform, [51]
.
2.2
Short-circuit Calculations
2.2.1
Analysis of Grid Faults
The most important grid faults1 in a three-phase system are categorized in table
2.5 [28, 51]. Their profound description is beyond the purpose of this thesis,
however the most important characteristics are shortly treated hereafter. The
three-phase-to-ground fault is defined as a simultaneous short-circuit across all
three phases. This means that the conductors are loaded symmetrically; it is a
balanced fault and therefore can be solved on a per phase basis. The remaining
conductors carry the same fault current except from phase shift. It occurs
infrequently, however it is the most severe type of fault that can occur in a
power system.
The line-to-line, the double line-to-ground and the line-to-ground shortcircuit are unsymmetrical faults. The single-line-to-ground short-circuit is the
most frequent occuring fault in a power system.
2.2.2
Symmetrical Components
Literature describes various methods for the solution of unbalanced faults. However the theory of symmetrical components introduced by C. L. Fortescue in
1918 is the most used, since it simplifies the solution of unbalanced circuits by
transforming them in to several balanced circuits [21]. This makes it possible
to treat the short-circuit on a per-phase basis. It assumes the network has a
symmetrical structure (i.e. transposed overhead lines); however acceptable accuracy is provided in the case of an untransposed network. A vector for three
1 If
the fault impedance Zf = 0, the fault is called a bolded or solid fault.
9
Chapter 2
Circuit diagram of the
short-circuit
Fault
Three-phase-to-ground
a
b
c
a
b
c
Ia+Ib+Ic=0
Va=Zf Ia
Vb=Zf Ib
Vc=Zf Ic
+
- Va
Vb
Vc
Line-to-line
Boundary
conditions
Zf
Ia
+
- Va
Ib
Ic
Ic
Ib
Vb
Vc
Ia=0
Ib=-Ic
Vb-Vc=Zf Ib
Zf
Ia=0
Double line-to-ground
a
b
c
+
- Va
Ib
Vb
Vc
Zf
Zg
Ib
Ia=0
Vb=(Zf+Zg)Ib+Zg Ic
Vc=(Zf+Zg)Ic+ZgIb
Ia+Ib
Ia=0
Single line-to-ground
a
b
c
Ib=Ic=0
Va=Zf Ia
+
- Va
Vb
Vc
Zf
Ia
b=0 Ic=0
Figure 2.5: Possible faults in a three-phase network
10
Fault Currents
phase currents can be expressed as:
  
 
 

Ia
Ia,0
Ia,1
Ia,2
Iabc =  Ib  =  Ib,0  +  Ib,1  +  Ib,2 
Ic
Ic,0
Ic,1
Ic,2
(2.12)
where a = ej2π/3 and the subscripts 0, 1 and 2 respectively refer to the zero
sequence, positive sequence and negative sequence components. Note that a−1 =
a2 and a3 = 1. The zero sequence components are in phase and can be denoted
as:
I0 ≡ Ia,0 = Ib,0 = Ic,0
(2.13)
and the remaining phase sequences as:
I1 ≡ Ia,1 = Ib,1 = Ic,1
(2.14)
I2 ≡ Ia,2 = Ib,2 = Ic,2
(2.15)
and:
Resulting in:

1
Iabc = 1
1
1
a2
a
 
I0
1
a  I1  = AI012
a2
I2
(2.16)
where:
I012
 

I0
1
= I1  , A = 1
I2
1
1
a2
a

1
a
a2
(2.17)
where A is the symmetrical component transformation matrix (SCTM) that
transforms the sequence components I012 into the phasor currents Iabc . Conversely the sequence components can be derived from the phasor currents by:
I012 = A−1 Iabc
(2.18)
where the inverse of A-1 is expressed as:


1 1 1
1
A−1 = 1 a a2 
3
1 a2 a
(2.19)
Substituting equation 2.19 into 2.18 yields:


1 1 1
I012 = 1 a a2  Iabc
1 a2 a
(2.20)
00
When calculating the initial symmetrical short-circuit current Ik and the symmetrical short-circuit current Ik , the positive, negative and zero-sequence equivalent circuits are converted by network reduction into equivalent short-circuit
11
Chapter 2
impedances Z0 , Z1 and Z2 at the location of the fault. When applying the
method of equivalent circuits, each network component is represented by a specific sequence circuit as is widely explained in references [28, 51, 53].
The symmetrical current components I0 , I1 and I2 can be calculated once
the positive, negative and zero-sequence equivalent circuits are reduced to equivalent short circuit impedances at the fault location. Hereby taking into account
contraints imposed by the faults, such as the interconnection between positive,
negative and zero sequence equivalent circuits.
The symmetrical component equations provide the possibility to calculate
steady-state short circuit currents for several types of faults, however do not
include the pre-fault conditions.
2.2.3
The Superposition Method
The superposition method is also referred to as the complete method and is an
exact method for the calculation of steady-state short circuit currents. It consists of the superposition of two steady-state operating conditions and requires
the following three steps:
1. The pre-fault voltages and currents are calculated. The calculation is
based on the load-flow solution of the specified network. The operating
conditions are taken into account as well (e.g. transformer tap positions,
generator exitation conditions and circuit breaker status).
2. In this step the pre-fault voltage at the fault location with negative sign is
applied to the passive network. This means that there is only one voltage
source connected while the internal voltage sources of the generators are
short-circuited. Then the steady-state currents and voltages are determined using the load-flow calculation.
3. Finally both conditions are superposed resulting in a zero voltage at the
fault location. The accuracy depends on the correctness of the pre-fault
conditions. Additionally the operating conditions are sometimes difficult
to determine (i.e. active and reactive power, bus voltages and tap settings
for transformers).
The procedure of the superposition method is illustrated in figure 2.6.
2.2.4
The IEC 60909 Method
The IEC short-circuit calculation method is generally accepted in Western Europe and is based on the method of an equivalent source at the fault location. It
is derived from the superposition method as is discussed in sub-section 2.2.3. It
has the aim of accomplishing a close-to-reality short circuit calculation without
the need of preceeding load-flow calculations and actual operating conditions.
Regarding the principle of superposition, the IEC 60909 method does not require the pre-fault load flow solutions and pre-fault operating conditions. The
most important simplifications compared to the superposition method are given
hereafter:
ˆ Nominal conditions are assumed for the whole network, i.e. Ui = Un,i
12
Fault Currents
Generation
a)
Xdi’’
Ei
F
Electrical
power system
UbF
Pre-fault
voltage
+
F
Xdi’’
b)
Electrical
power system
Generation
c)
Xdi’’
Ei
=
UbF
F
Ik’’
Electrical
Fault
power system location
Figure 2.6: Principle of the superposition method. (a) Pre-fault operating condition,
(b) Operation with applied negative pre-fault voltage at the short circuit
location, c) Short circuit condition obtained by superposing a and b
ˆ Load currents are neglected, i.e. Iop =0
ˆ The simulation network is simplified, loads are not considered in the positive and negative sequence network.
From these simplifications figure 2.6c can be approximated as figure 2.6b because
the pre-fault operating conditions are considered to be insignificant under the
following assumptions:
ˆ During normal operation (pre-fault condition) the currents are much smaller
in magnitude than the prospective2 short circuit currents
ˆ In general power systems have an inductive behavior and the current lags
the bus voltage with a power factor of about 0.9. However during a short
circuit the current lags the bus voltage with a much lower power factor
(i.e. phase shift close to 90◦ ).
Therefore the nominal operating current and the short circuit current can be
approximated in steady-state condition by the phasors as shown in figure 2.7.
00
From figure 2.7 it is clear that when the ratio Ik /Ip becomes higher the ap00
proximation of Isc ≈ Ik will improve considerably. This means that in the vast
majority of short circuit calculations the operating conditions may be neglected.
The IEC 60909 method defines the nominal power system voltage to be one
p.u.. This means that the pre-fault voltage, Uf , at the fault location is equal
to Un . However in some cases the system voltage may be significantly higher,
therefore a correction factor c is incorporated. This factor is applied on the
nominal voltage at the fault location and consequently the pre-fault voltage
results in: Uf = cUn . The correction factor, c, can be determined according to
2 The prospective short-circuit current is the current that would flow if the short circuit
was replaced by an ideal connection (negligible impedance) without any change of the supply
[5]
13
Chapter 2
Uf
I sc ≈ I k''
Ip
I k''
Figure 2.7: Pre-fault current and short-circuit current. Pre-fault bus voltage, Uf ,
00
pre-fault operating current, Ip , steady state short circuit current, Ik ,
total short-circuit current after superposition, Isc
Q
Non-rotating load
A
T
~
L
HV
LV
tr :1
k3
~
F
Non-rotating load
ZQ
Q
Un
A
ZT
F
ZL
~
cU n
3 ZQ ZT
ZL
cU n
3
Ik
Figure 2.8: Principle of the equivalent voltage source method
table 2.1, taking into account that the highest voltage does not differ from the
rated value by more than +5% in low-voltage systems and +10% in high-voltage
systems. When calculating maximum short circuit currents cmax is used and for
the calculation of minimum short circuits currents cmin is applied. The relevant
IEC 60909 short circuit values are treated:
00
ˆ initial symmetrical short circuit current Ik
ˆ symmetrical short circuit current Ik
ˆ peak short-circuit current ip
ˆ DC component of the short-circuit current iDC
00
Initial symmetrical short-circuit current Ik
00
The initial symmetrical short-circuit current, Ik , is the RMS value of the AC
symmetrical component of the prospective short-circuit current at the instant
00
of the fault. The short-circuit
current, Ik , is determined by using the equivalent
√
voltage source, cUn / 3, which is defined as the voltage of an ideal source applied
at the short-circuit location in the positive sequence system, at the fault location
F. All other sources are neglected. All network feeders such as synchronous and
asynchronous machines are replaced by their internal impedances. Line capacitances, shunt admittances and non-rotating loads are ignored. The equivalent
voltage source method is depicted in figure 2.8. For a three-phase-to-ground
14
Fault Currents
Nominal voltage
Un
Low voltage
100V to 1000V
(IEC 60038, table I)
Voltage factor c for the calculation of
maximum
minimum
short circuit currents short circuit currents
cmax 1
cmin
1.053
1.104
0.95
Medium voltage
> 1 kV to 35 kV
(IEC 60038, table III)
1.10
1.00
High voltage2
> 35 kV
(IEC 60038, table IV)
1.10
1.00
1
2
3
4
cmax Un should not exceed the highest voltage Um for equipment of power
systems
If no nominal voltage is defined cmax Un = Um or cmax Umin = 0.9Um should
be applied
For low-voltage systems with tolerance of +6%, for example systems renamed
from 380V to 400V
For low-voltage systems with tolerance of +10%
Table 2.1: Voltage factor c
fault the initial symmetrical short-circuit current can be calculated according
to:
00
cUn
Ik3 = √
3Zk
(2.21)
where Zk is value of the equivalent short-circuit impedance (in fact this is the
Thevenin impedance) at the location of the fault F. From here it is possible
to calculate the short-circuit current according to the equivalent voltage source
method at location F by only using the nominal voltage. To be sure the results
are on the safe side the voltage factor c according to table 2.1 and correction
factor KG for the correct calculation of the generator impedance is applied.
Symmetrical short-circuit current Ik
The symmetrical short-circuit current, Ik , is the RMS The calculation depends
on wether the fault is far from or near to the generator. When the fault location
00
is far from the generator, Ik , is assumed to be equal to the initial value of Ik . If
the fault occurs near to the generator several paramaters are taken into account
such as the excitation type, automatic voltage regulation, machine type and
saturation effects [5].
15
Chapter 2
Peak short-circuit current ip
The peak short-circuit current, ip , is the maximum instantaneous value of the
prospective short-circuit current. For the calculation the IEC 60909 makes the
distinction between radial and meshed networks. In case of a radial network,
ip , is defined as the sum of all contributions to the fault:
X
ip =
ipi
(2.22)
i
where each contribution of ipi is calculated by:
√ 00
ipi = κi 2Iki
(2.23)
The coefficient κi depends on the R/X ratio of each contributing branche. For
meshed networks the behavior of the short-circuit current is influenced by the
network as a whole. Therefore the peak value is directly calculated through:
√ 00
(2.24)
ip = κ 2Ik
For both types of networks (radial and meshed) the IEC 60909 suggests three
different methods, A, B, or C to compute the equivalent coefficient κ:
κ = 1.02 + 0.98e−3R/X
(2.25)
A In this method the equivalent coefficient κ is determined from the smallest
R/X ratio of all branches in the network. In this way ip is estimated on
the safe-side (maximum peak-value).
B In this method the equivalent coefficient κ is determined from the R/X ratio
of the positive-sequence short-circuit impedance at the fault location. It is
multiplied by a factor 1.15 to cover inaccuracies caused by different R/X
ratios in parallel branches.
C In this method the equivalent coefficient κ is determined according to:
R
Rc fc
=
X
Xc f
(2.26)
where fc = 20 Hz for a nominal frequency of f = 50 Hz or fc = 24 Hz for
a nominal frequency of f = 60 Hz. And Zc = Rc + jXc is the equivalent
impedance of the system as seen from the short-circuit location for the
assumed frequency fc . Subsequently κ is found by equation 2.25.
Method C is recommended in meshed networks [5].
Direct current component of the short-circuit current iDC
The maximum DC component iDC of the short-circuit current is calculated
according to:
√ 00
iDC = 2Ik e−2πf tR/X
(2.27)
where f is the nominal frequency, t is the time and R/X is the ratio for radial
networks or an equivalent ratio for meshed networks. For meshed networks the
R/X ratio is determined according to equation 2.26 described in method C.
However instead of using the ratio fc /f , fc is calculated from the ratio fc /f
depending on f · t from table 2.2.
16
Fault Currents
f ·t
<1
< 2.5
<5
< 12.5
fc /f
< 0.27
< 0.15
0.092
0.055
Table 2.2: fc /f ratios for DC component computation in meshed networks
2.3
The First Pole-to-clear Factor
The first pole-to-clear factor (FPTC) is a funtion based on the grounding arrangements of the power system. It is defined as: “the ratio between the power
frequency voltage across the first clearing pole before current interruption in the
other poles, to the power frequency voltage occurring across the pole or poles
after the interruption in all three poles” [13]. The mathematical description of
the FPTC factor is given in equation 2.29 and is derived from the sequence
circuits for a double-line-to-ground fault as is described in [51].
kpp = 3
Z2 Z0
Z1 (Z2 + Z0 ) + Z2 Z0
(2.28)
Since the behavior of a power system is mainly inductive during a short circuit,
Z0 , Z1 and Z2 may be replaced by X0 , X1 and X2 respectively. Assuming
the fault is relatively far away from the generators, we can write for X1 = X2 .
However for generator circuit breakers (GCB) special conditions apply with
respect to grounding conditions and TRV’s [47, 48]. When including the star
point of a transformer with complex impedance Zn = Rn + jXn the zerosequence impedance becomes Z0 = 3Zn + jX0 . Substituting Z0 in equation
2.29 yields:
kpp = 3
3Rn + jX0 + 3Xn
jX1 + 2 [3Rn + j(X0 + 3Xn )]
(2.29)
This means that in ungrounded systems the value of the neutral impedance, Zn ,
is infinite and consequenly the FPTC factor results in 1.5. For solidly grounded
systems where, Zn = 0, the FPTC factor becomes:
kpp =
2.4
3X0
X1 + 2X0
(2.30)
The IEC 62271-100
The circuit breaker is considered to clear the fault successfully if the recovery
of the dielectric strength across the breaker poles is faster than the recovery
of the voltage across it. The specified TRV withstand capability of the circuit
breaker is defined by the IEC 62270-100 [6]. The IEC characterises the TRV by
two envelopes; The two-parameter envelope (Uc , t3 ) for circuit breakers with a
nominal rated voltage up to 100 kV at all values of the breaking current and for
breakers with a rating of 100 kV and above if the short-circuit current is equal or
less than 30% of the rated breaking current. And by the four-parameter method
(U1 , t1 ,Uc , t2 ) which applies for all other cases. From these characteristics, the
so-called Limiting envelopes can be deduced in which the circuit breaker is able
17
Chapter 2
Resistance
Reactance
Ratio
IEC criterion
R0 = 0.673 Ω
X0 = 7.978 Ω
X0 /X1 = 1.550
0 < X0 /X1 < 3
R1 = 0.351 Ω
X1 = 5.145 Ω
R0 /X1 = 0.130
0 < R0 /X1 < 1
Table 2.3: Values for the sequence circuits of the TenneT 380 kV network
to handle the imposed voltage stresses of the TRV. The two-parameter and fourparameter limiting envelopes are depicted in figure 2.9 and are characterized by
the values given in table 2.4 and 2.5 respectively. The rate-of-rise is the same
for both the 420 kV and 550 kV circuit breaker although the dielectric strength
of the 550 kV breaker is higher. Therefore selecting a 550 kV circuit breaker
instead of a 420 kV breaker does not make sense when it comes to the initial
steepness of the TRV.
When evaluating the TRV, the IEC 62271 standard makes the distinction between solidly earthed systems and non-solidly earthed systems. The IEC states
that a system is effectively earthed if the ratio of the zero-sequence reactance
to the positive reactance (X0 /X1 ) is positive and less than 3 and the ratio of
zero-sequence resistance to that of the positive-sequence reactance (R0 /X1 ) is
positive and less than 1. This criterion is related to the FPTC-factor and is
discussed in sub-section 2.1.3 The Transient Recovery Voltage. Accordingly the
380 kV network of TenneT TSO is assessed on these ratio’s. They were calculated through the means of the IEC 60909 method in PowerFactory. The results
are given in table 2.3. From here it can be concluded that the 380 kV transmission network of TenneT is effectively earthed. The test duties are defined
as T10, T30, T60 and T100. Where the number stands for the percentage of
the breaking current of the circuit breaker. This means that for a 63 kA circuit
breaker the test duties can be translated into the following nominal breaking
currents:
ˆ T10 corresponds with a nominal breaking current of 6.3 kA
ˆ T30 corresponds with a nominal breaking current of 18.9 kA
ˆ T60 corresponds with a nominal breaking current of 37.8 kA
ˆ T100 corresponds with a nominal breaking current of 63 kA
18
Fault Currents
Voltage
Uc
Voltage
Uc
U′
U1
U′
td
t′
t3
td t ′ t1
Time
t2
Time
Figure 2.9: IEC Two- and four-parameter limiting envelopes
Test
duty
FPTC
factor
Time
kpp
First
ref.
voltage
u1
Time
Time
delay
Rateof-rise
t1
TRV
peak
value
uc
t2 , t 3
td
(kV)
(µs)
(kV)
(µs)
(µs)
u1 /t1 ,
uc /t3
(kV/µs)
(p.u.)
T100
1.3
334
167
624
668
2-(47)
2
T60
1.3
334
111
669
666
2-33
3
T30
1.3
-
-
687
137
21
5
T10
1.3
-
-
682
97
15
7
Table 2.4: Standard values of prospective transient recovery voltage for a 420 kV
CB, effectively earthed system [6]
Test
duty
FPTC
factor
Time
kpp
First
ref.
voltage
u1
Time
Time
delay
Rateof-rise
t1
TRV
peak
value
uc
t2 , t 3
td
(kV)
(µs)
(kV)
(µs)
(µs)
u1 /t1 ,
uc /t3
(kV/µs)
(p.u.)
T100
1.3
438
219
817
876
2-(61)
2
T60
1.3
438
146
876
876
2-44
3
T30
1.3
-
-
899
180
27
5
T10
1.3
-
-
893
128
19
7
Table 2.5: Standard values of prospective transient recovery voltage for a 550 kV
CB, effectively earthed system [6]
19
CHAPTER
3
The Model
his chapter describes how the TenneT transmission network is modeled in
T
PowerFactory and ATP-EMTP. It covers the methodology, validation and
limitations of the grid models. Finally a comprehensive survey describes the
relevant power system components with respect to EMT analysis.
3.1
Grid Model
The primary aim of the grid model is facilitating the EMT short-circuit analysis
in chapter 6: Case Study Maasbracht 380. Therefore surrounding 380 kV and
150 kV transmission networks of the substation are modeled. The grid models have been established with reference to the 2020 scenario of TenneT. The
2020 scenario is in a large extent based on the TenneT Vision2030 document
which involves all possible future reinforcements for the Dutch transmission
grid. Such as the new interconnection to Germany, Doetinchem - Niederhein,
and the South-West 380 kV project [3, 12]. A geographic overview of the modeled part of the grid is given in figure 3.1. How the grid is modeled in detail
will be discussed in the following sub-sections. The relevant data for the EMT
models, such as the generator, transformer and line parameters, were retrieved
from the PowerFactory IEC 60909 model, primarily intended for steady-state
short-circuit calculations. This informational database is continuously updated
and maintained by the Asset Management department of TenneT. All relevant
power system component parameters are included in Appendix E Grid Parameters.
3.1.1
Initial study
Based on an initial study it has been determined that at substation Maasbracht
380 the three-phase-to-ground short-circuit is the most severe fault which may
occur. This represents the worst case scenario and is the criterion for TenneT
to protect their substations and relating equipment.
21
Chapter 3
NorNed
NorNed 2
COBRA
380 kV Transmission line
Eemshaven
220 kV Transmission line
150 kV Transmission line
110 kV Transmission line
Cross border line
Gronau
Vierverlaten
DC interconnector
Louwsmeer
Cable or line under construction
Meeden
Diele
Zeyerveen
Oudehaske
Hoogeveen
Ens
Hessenweg
Beverwijk
Hengelo
Gronau
Diemen
Dodewaard
Maasvlakte
Brit Ned
Waddinxveen
Krimpen
Wesel
Geertruidenberg
Boxmeer
Borssele
Weert
Van Eyck
Zandvliet
Maasbracht
Rommerskirchen
Siersdorf
Figure 3.1: A geographic overview showing the TenneT 380 kV network modeled in
PowerFactory EMT and ATP-EMTP (indicated in yellow)
22
The Model
3.1.2
Topology of the Dutch Grid Model
The PowerFactory IEC 60909 model provided by Asset Management is used as
a reference for establishing network equivalent sources at appropriate boundaries.Locations at which the system became very “stiff” served as a boundary
[24]. This can be interpreted as the location where the impedance is high in
comparison to the rest of the grid, such as transformers. Another reasoning was
that the further away from the location of the fault, the less impact the fault
has. Resulting in more modeling liberties at remote points. At last the shape of
the grid model played an important role. It did not contain any loops in order
to rule out any back feeding short-circuit currents. This was evident for the
determination of the equivalent sources.
As a result the boundaries for the 380 kV grid are picked at the locations
Krimpen and Hengelo and at all points where this grid is connected to the underlying 150 kV grid. With respect to grounding conditions it is trivial that each
380 / 150 kV transformer neutral was incorporated. Therefore the transformers
are modeled with the equivalent sources at the LV-side.
Substation Maasbracht 150 has been modeled in more detail, due to the
presence of the Claus CC-B generator. Its subtransient reactance has considerable influence on the behavior of the fault current at substation Maasbracht
380.
At last the 380 kV cross border lines where modeled. For the Belgium
TSO Elia is was possible to derive equivalent sources for substations Zandvliet
and Van Eyck with help of the ENTSO-E,, formerly known as UCTE, trans
boundary informational data included in the PowerFactory IEC 60909 model.
However with respect to the interconnections to Germany this was not the case,
this will be discussed in more detail in subsection 3.1.5 Limitations.
An overview of the grid models which are established in the software packes
ATP-EMTP and PowerFactory are given in Appendix C Overview of the Grid
Models.
3.1.3
Validation
The two independent models in PowerFactory and ATP-EMTP are validated for
00
00
single-phase-to-ground, Ik1 , fault current and three-phase-to-ground, Ik3 , fault
current according to figure 3.2. The validation process can be described in the
following manner:
1. The simulation results are based on the input data from the equivalent
sources and the power system components parameters. These parameters
were retrieved from the PowerFactory IEC 60909 model which served as
an informational database.
2. The actual validation was done by comparing the single-phase-to-ground,
00
00
Ik1 , fault currents and three-phase-to-ground, Ik3 , fault currents computed
from the PowerFactory IEC60909 model, with that of the EMT grid models built in PowerFactory EMT and ATP-EMTP. Faults where initiated at
different points in the Dutch grid to give a thorough comparison between
the different models. The results are presented in table 3.1. The table
shows that the difference between the models is between 2% and 8%.
23
Chapter 3
EMT grid models
Validation Ik¨
Input of grid model
parameters
PowerFactory EMT
Results
PowerFactory
IEC 60909
Validation i(t)
Results
ATP-EMTP
TRV Study
Validation Ik¨
Figure 3.2: EMT grid model validation principle
Substation
IEC 60909
00
00
Ik3
Ik1
(kA) (kA)
PowerFactory EMT
00
00
Ik3
Ik1
(kA)
(kA)
ATP-EMTP
00
00
Ik3
Ik1
(kA) (kA)
Borssele
32.4
33.2
32.3
31.8
32.2
31.1
Doetinchem
45.8
37.7
45.4
35.5
45.5
35.4
Dodewaard
35.4
28.8
35.1
27.7
35.0
27.5
Geertruidenberg
57.7
48.4
57.5
47.2
57.3
47.1
Maasbracht
70.5
55.0
69.1
53.2
68.4
53.4
Table 3.1: A comparison of the foreseen initial three-phase-to-ground fault currents,
00
00
Ik3 , and the single-phase-to-ground fault currents, Ik1 , between the IEC
60909 grid model, PowerFactory EMT grid model and the ATP-EMT grid
model at a number of buses
3. Secondly the correctness of the dynamical short-circuit currents was evaluated by initiating a single-phase-to-ground and three-phase-to-ground
fault at several locations in the grid. For substation Maasbracht 380 a
comparison is given in figure 3.3 for phase b of the dynamical short-circuit.
From there it is clear that differences are marginal (within 5%) and only
visible when the DC component damps out.
Conclusion
The demonstrated deviations are considered to be acceptable for the purpose of
the case study since the deviations fall within the expected margins that these
models will have with respect to the real power system. Secondly the EMT
software packages PowerFactory and ATP-EMTP are validated to each other
and with respect to the IEC 60909 short-circuit calculation method.
24
The Model
Three Phase fault current comparison
×105
2
1.5
Current [A]
1
0.5
0
−0.5
−1
ATP-EMTP phase b
PowerFactory phase b
−1.5
−2
0
0.05
0.1
0.15
0.2
Time [s]
Figure 3.3: Bolted three-phase-to-ground short-circuit current comparison of phase
b between PowerFactory and ATP-EMTP. The fault has been initiated
at substation Maasbracht 380
3.1.4
TRV Study
The TRV study is based on the ATP-EMTP grid model because of time contraints associated with this thesis. It turned out to be very time consuming
modeling the fault current limiting measures presented in this thesis both in
PowerFactory and ATP-EMTP. Since ATP-EMTP has a long tradition and
history in the computation of electromagnetic transients, it was the preferred
software package. In addition it has to be mentioned that many references in
the technical documentation of PowerFactory refer to the EMTP Theory Book
[19], which has been written by one of the originators of ATP-EMTP, Hermann
W. Dommel. However in a potential follow-up study it would be higly recommended to implement the fault current limiting measures in PowerFactory and
subsequently accomplish the validation with ATP-EMTP.
3.1.5
Limitations
As stated earlier, information regarding the grids of neighboring TSO’s is rather
limited. This is especially the case for transmission lines to Germany, where only
the three-phase-to-ground and single-phase-to ground currents were provided.
In conjunction with TenneT the R/X ratios of table 3.2 are assumed. It is
apparent that there are no line parameters available and consequently this may
influence the computation of the TRV and the dynamical short-circuit current.
However it is still possible to derive an equivalent circuit based on the theory
of symmetrical components. We may write for a bolted three-phase-to-ground
25
Chapter 3
00
00
Cross border line
substation
Ik3
(kA)
Ik1
(kA)
R/X
Maasbracht - Siersdorf
Maasbracht
10.8
8.06
0.1
Maasbracht - Rommerskirchen
Maasbracht
7.9
6
0.1
Doetinchem - Niederrhein
Doetinchem
16.36
13.21
0.1
Table 3.2: Fault current contribution from neighboring countries for the year 2020,
provided by TenneT TSO department Asset Management
short-circuit, defined as asymmetrical fault:
00
Un
Ik3 = √
3Z1
(3.1)
Where Un is the line-to-ground voltage and Z1 the positive sequence impedance.
From Z1 and a predefined R1 /X√
1 ratio it is possible to derive the values for R1
and X1 respectively. With Z = R2 + X 2 we can derive for X1 :
X1 = p
Z1
1 + (R1 /X1 )2
And for R1 :
q
R1 = Z12 − X12
For the single-phase-to-ground fault one can write:
√
00
3U
Ik1 =
Z1 + Z2 + Z3
(3.2)
(3.3)
(3.4)
Assuming the fault is relatively far away from the generator it is allowed to
equate the positive-sequence and negative-sequence impedance (Z1 = Z2 ), [28,
53]. This assumption makes it possible to derive the Z0 /Z1 ratio from equations
3.1 and 3.4:
00
Z0
I
= 3 k3
00 − 2
Z1
Ik1
(3.5)
Another limitation of equation 3.5 is the fact that it does not take into account
the mutual couplings of transmission lines. From equation 3.5 it possible to
derive Z0 . An overview of the parameters for the equivalent sources is given in
table E.6 in Appendix E Grid Parameters.
3.2
Modeling of Power System Components
In this section a comprehensive survey is given on the topic of power system
components EMT modeling. The choice of which components to include in the
Dutch grid model has been determined according to the recommendations of
26
The Model
the IEC 60071-4 [4]. There is a large amount of literature available which gives
a thorough insight on the modeling of power system components. The reader is
invited to review the relevant literature, appropriate references are included in
the bibliography section. It has to be noted that ATP-EMTP and PowerFactory
are using two different integration methods (equation solvers); the trapezoidal
rule and the Newton-Raphson algorithm, respectively [49].
3.2.1
Circuit Breakers
During normal operation the circuit breaker is in closed position and a nominal
current is flowing through the contacts. However the circuit breaker is designed
for its main task: interrupting fault currents and isolating faulted parts of the
grid. The circuit breakers opens its contacts when it receives a tripping signal
from the protectional relays, normally this is within the order of five periods (100
ms) after the fault has occurred. The contact separation causes the generation
of an arc and the current interruption is successful when the arc plasma between
the breaker contacts is sufficiently cooled down.
The IEC 62271-100 Annex F states that the influence of the circuit-breaker
characteristics on the prospective TRV may be excluded [6]. This means that
the circuit breaker acts as an ideal conductor (zero impedance) when closed and
as an open circuit when opened (infinite impedance). However for the sake of
comprehension the main circuit-breaker modeling methodologies are discussed
hereafter.
1. The simplest circuit breaker model is based on an ideal switching action
that is completely independent of the arc. It is represented by an ideal
switch that opens its contacts at the instant defined by the user. Subsequently the fault current is interrupted at the current-zero crossing. This
model is adequate in EMT studies where the breaker arc interaction with
the enclosed network may be excluded. This method is prescribed in the
IEC 62271-100 Annex F document, where the voltage across the breaker
is to be compared with the pre specified TRV withstand envelopes.
2. A more elaborate model represents the circuit breaker as a time-varying
conductance or resistance whose variation is determined by the breaker’s
characteristic. The arc parameters of the breaker are measured during experiments in a High-voltage test facility or from precomputed TRV curves.
Such a model can represent the effect of the arc on the system. Conversely
this is not the case and therefore more advanced arc models are required.
3. The most advanced models employed for EMT simulations are the socalled Black box models. The arc is described by differential equations and
gives the relation between the arc conductance and several parameters
such as arc voltage and arc current. These models have the ability to
represent both the effect of the arc on the system and the effect of the
system on the arc. Most models are used to study the arc re-ignitions
due to insufficient dielectric withstand capabilities between the breaker
contacts. Others are used to study the thermal behavior and period of
the breaker. Two classical black box models are treated with the following
27
Chapter 3
variables:
g c,m
τ c,m
P0
us
if
=
=
=
=
=
Conductance of the arc, S
Time constant of the arc, s
Steady-state power loss of the arc, W
Steady state arc voltage, V
Prospective fault current, A
The Mayr model is given in equation 3.6 and is most suitable for studying
the behavior of the arc conductance in the high-current time interval,
when the plasma temperature is relatively high (8000 K or more) [37].
!
i2f
1
dgm
=
− gm
(3.6)
dt
τm P0
The Cassie model is given in equation 3.7 and is applicable for the calculation of the arc in the vicinity of current-zero, when the temperature of
the plasma is relatively low (below 8000K) [14].
!
i2f
1
dgc
=
− gc
(3.7)
dt
τc u2s gc
Both PowerFactory and ATP-EMTP do not include the elaborate and advanced
circuit breaker models by itself. However many third-party resources are available which describe the implementation of non-linear arc models in EMT simulation software [22, 23, 50].
3.2.2
Generators
How synchronous machines are modeled depend very much on the type of transient study. With respect to the first few cycles of a short-circuit the representation of a voltage source behind a subtransient reactance Xd” can be considered as
reasonably accurate. However this thesis also has the aim to validate the dynamical short-circuit current of two EMT software packages, therefore a considerable
fault current timeframe has to be taken into account. Meaning that an accurate
generator model is preferred. Both PowerFactory and ATP-EMTP include a
general-purpose generator model which is based on Park’s transformation from
abc phase variables to dq0 components. This is a reference frame in which the
self and mutual machine inductances are constant. This is advantageous as the
stator and rotor equations of the synchronous machine contain inductance terms
which vary with angle θ which in turn varies with time. This makes it rather
complex to solve the machine and power system variables. In PowerFactory the
generator model is represented by the “standard” EMT model, in ATP-EMTP
this is the SM58 or SM59 model. Both include the possibility to add saturation
characteristics. For further reference please see [1, 19, 31, 46].
3.2.3
Transmission Lines
Usually electrical devices are analyzed through the theory of lumped or concentrated models, with constant parameters for the resistance, capacitance and
28
The Model
inductance. In reality these parameters are distributed in any circuit or piece of
equipment. Whether the circuit is modeled by lumped or distributed elements
depends on the purpose of the model. For steady state analysis a lumped element representation is adequate as the 50 Hz wavelength is considerably long.
However for transient analysis this is no longer the case and the effect of traveling waves has to be incorporated.
A PI section represents the transmission line by a branch of lumped elements.
An example of a PI section with mutual couplings for a three-phase system is
given in figure 3.4. When the travel time is less than the solution of the time
step, PI sections are suitable for EMT calculations. Considering the length of
most transmission lines, distributed models are preferred. Unlike lumped elements, distributed models have the unique property to support traveling waves
of current and voltage. Only the key elements of transmission line theory is
given in the subsequent derivations. For a complete overview on this matter,
the author suggests the following literature [24, 51]: The velocity of the current
and voltage waves traveling along a lossless circuit can be expressed with:
v=√
1
LC
The inductance can be approximated by:
µ d
0
L=
ln
2π
r
(3.8)
(3.9)
And the capacitance with the approximation:
C=
2π0
!
d
ln
r
(3.10)
Substituting equation (3.9) and (3.10) into equation (3.8) yields:
v=√
1
µ0 0
(3.11)
Equation (3.11) shows that the wave velocity is independent of the line geometry.
It is solely dependent on the relative permeability and relative permittivity of
the conductor. The ratio of the amplitude of a single voltage wave to its current
wave on a transmission line is called the characteristic impedance, Z0 .
r
L
Z0 =
(3.12)
C
Unlike the wave velocity, v, the characteristic impedance depends upon the line
geometry. Since the transmission line also has a reflected wave, the characteristic
impedance does not represent the impedance measured on the line. The theory
of wave reflection and refraction is discussed hereafter.
Normally when an electromagnetic wave propagates along a transmission
line, there is a strict “proportionality” between the voltage and the current wave.
This proportionality is called the characteristic impedance of the line. When
the wave arrives at a discontinuity, such as an open circuit or short-circuit, the
29
Chapter 3
ia
va
ib
vb i
c
vc
R
vá
R
vb́
R
vć
Figure 3.4: Representation of a three-phase transmission line by a PI section
characteristic impedance changes. But due to the proportionality the wave has
to be “adjusted”. This adjustment consists of the initiation of two new wave
pairs. At the discontinuity a part of the energy is let through and a part of
the energy travels back in form of an electromagnetic wave. The total amount
of energy in the electromagnetic waves remains constant, such that the voltage
to current proportionalities are preserved, as demanded by the characteristic
equation. The magnitude of the reflected voltage wave at a discontinuity with
characteristic impedance ZA and ZB on the incident side and refractive side,
respectively, is described by equation (3.13):
V2 =
ZB − ZA
V1 = ρ1
ZB + ZA
(3.13)
The refracted voltage wave is defined as (3.13):
V3 =
2ZB
V1 = α1
ZB + ZA
(3.14)
Where V1 is the incident wave, V2 is the reflected wave and V3 is the refracted
wave. ρ and α are defined as the reflected and refracted coefficient respectively.
A suitable line model based on the traveling wave principle is the Bergeron’s
routine integrated within ATP-EMTP and PowerFactory [10]. It is based on the
constant frequency method, the line is treated as lossless but distributed series
resistance is added in lump form. This model gives acceptable results, provided
that R/4 Z0 . For high frequency studies, the Bergeron’s model may not be
adequate [39]. Other models, such as the JMarti routine, include the frequency
dependant characteristics of a transmission line. However physical dimensions
of the line are required (i.e. conductor radius, and conductor positions) [36].
3.2.4
Transformers
A complete EMT model for transformers would require every winding being
represented, including all mutual couplings, both inductive and capacitive. In
practice such an extensive model is undesirable. In short, the purpose of the
simulation determines the type and extent of the transformer model.
If for example the accuracy of the simulation is within the microseconds
range, no significant current is able to penetrate the windings because of its
inductance. As a result currents are displaced and flow into the capacity of the
windings. Therefore if the transformer has to be accurately modeled with respect to the initial voltage distribution, capacitive elements have to be included
[24].
30
The Model
When carrying out switching studies, with respect to TRV’s caused by vacuum circuit breaker re-ignitions, a capacitive model would not suit the needs
[45]. If the transformer is switched in at no-load, the model should represent
the influence of the transformer winding and core. Possible re-ignitions contain oscillations with different frequency components, resulting in a variable
transformer winding impedance.
Considering the case study in chapter 6 where the transient behavior of the
series reactor and SCFCL is evaluated, a transformer model results in a simplified case. The ATP-EMTP BCTRAN transformer model and the PowerFactory
standard transformer model, the standard will suit the criteria for the short
circuit current and TRV calculations as described in the IEC 62271-100 Annex
F. The transformer models in ATP-EMTP and PowerFactory will be addressed
accordingly.
ATP-EMTP model
The BCTRAN routine is part of the ATP-EMTP and embodies a three-phase
two-winding or three-winding transformer. It is based on a matrix representation containing two matrices R and L. These represent the transformer with
respect to excitation and short-circuit tests for zero and positive sequences. To
get a understanding of the matrix representation concept, a single phase twowinding transformer will be considered. It is described by following steady state
phasor equations:
V1
Z11 Z12 I1
=
(3.15)
V2
Z21 Z22 I2
The matrix in equation (3.15) is symmetric. The characteristic parameters are
visualized in figure 3.5. L11 and L22 are the self inductance of windings 1
and 2 respectively. L12 and L21 represents the mutual inductance between the
windings. [Z] is described by:
Zij =
Vi
Vj
(3.16)
When applying the trapezoidal rule to solve the matrix in equation (3.15), it
has to be rewritten in the form of the following differential equation:
V1
R11 R12 I1
L11 L12 d I1
(3.17)
=
+
V2
R21 R22 I2
L21 L22 dt I2
The differential matrix representation is the fundament of the BCTRAN routine
and is extended in severals ways to model a complete transformer adequately.
Extensions are the impedance matrix containing self and mutual impedances,
related to the positive and zero-sequence values for example. The full circumscription of the BCTRAN model is given in [19].
PowerFactory model
The exact operating principle of the PowerFactory EMT transformer model is
undisclosed. However an equivalent circuit of the 2-winding 3-phase transformer
is supplied in the transformer technical reference manual of PowerFactory, it is
31
Chapter 3
i1
v1
L1
R1
L2
L12
R2
i2
v2
Figure 3.5: A simplified transformer model in the ATP-EMTP BCTRAN routine
Figure 3.6: Equivalent circuit of the 2-winding 3-phase transformer model in DIgSILENT PowerFactory
depicted in figure 3.6 [20]. It is assumed, based on the references made in the
technical reference manual that the transformer model makes use of a similar
solving principle as compared to ATP-EMTP. The PowerFactory model provides
the possibility to include transformer winding capacitances in contrast to the
transformer model of ATP-EMTP.
32
CHAPTER
4
Fault Current Limiting Reactors
ault current limiting reactors are applied in power systems to reduce shortF
circuit currents to levels within the electromechanical and thermal withstand capabilities of power system components. Fault current limiting reactors
can be installed at different points in the grid and they are mostly referred to
their location and application. In this chapter two types of reactors will be
discussed:
ˆ The series reactor; in series with incoming or outgoing feeders or used to
tie together two independent buses
ˆ The neutral grounding reactor; installed between the neutral of a transformer and the earthing point
4.1
Applications of Reactors
4.1.1
Series Reactors
Series reactors are placed in line with incoming or outgoing lines or feeders.
Or can used to tie together two independent buses. The main advantage is
the ability to reduce the single-line-to-ground fault and three-phase-to-ground
fault current to desired levels. The maximum limiting capability depends on
physical limitations of the reactor. Other benefits are the improvement of the
primary bus voltage during faults and reduction of the current-interrupting duty
of circuit breakers. However series reactors have the contradictory property of
limiting fault current on the one hand but increasing the magnitude of the TRV
on the other hand. This will become clear in sub-section 6.3.
The required impedance to limit the three-phase fault current is calculated
by either equation 3.1 or 3.2:
XCLR =
VLL ((1/ISC,af ter ) − (1/ISC,bef ore ))
√
3
(4.1)
33
Chapter 4
2
XCLR = VLL
((1/M V ASC,af ter ) − (1/M V ASC,bef ore ))
(4.2)
where:
XCLR
VLL
ISC af ter,bef ore
=
=
=
M V ASC af ter,bef ore
=
4.1.2
reactance of the current limiting reactor, Ω
rated line-to-line voltage, kV
value of the short circuit current after and before
the fault, kA
value of the short circuit power after and before
the fault, MVA
Neutral Grounding Reactors
Neutral grounding reactors are installed in between the star point of a transformer or generator and the earth grounding point. The implementation is most
effective where generators are solidly grounded since then the single-line-toground fault in most cases exceeds the magnitude of the three-phase-to-ground
fault [40]. They are able to limit the single-phase-to-ground faults and do not
limit symmetrical faults. Another drawback is the rate-of-rise of the TRV of
the unfaulted phases. This may form an issue as a result of the X0 /X1 ratio
that could exceed the critical value of an effectively earthed system. This drawback can be partly overcome when applying neutral grounding resistances in
the power system.
Thanks to the fact that only one neutral grounding reactor is needed per
transformer or generator, the investment costs for neutral grounding reactors are
rather low in comparison with series reactors. When comparing operating losses,
neutral grounding reactors are also in favor when taking into consideration that
only single-line-to-ground faults are limited.
4.2
4.2.1
Technical Aspects of Series Reactors
Air-core Reactors
Thanks to their linear behavior of inductance versus current, air-core reactors
have been traditionally in favor regarding current limiting applications. Generally its mechanical construction is fully encapsulated, aiming on a higher withstand level to fault currents. A modern encapsulated Air-core reactor is depicted
in figure 4.1. The primary source of acoustic noise is the radial vibration of the
winding due to AC current flowing through the winding. Air-core reactors carrying only power frequency produce noise at twice the fundamental frequency.
The acoustic noise will substantially increase when the reactor’s current spectrum includes multiple harmonics; “n” harmonic currents can generate at most
n2 forcing frequencies [26].
The magnetic field of an air-core reactor is not constrained and occupies
the space around the reactor. Although the magnetic field decreases with the
distance from the reactor, it still may play an significant role with respect to
safety and health. An important factor is the distance to metal parts, for
example fences, grounding mesh grids or concrete reinforcements. There should
be sufficient distance to metal parts because of the eddy current losses that
34
Fault Current Limiting Reactors
Figure 4.1: Encapsulated Air-core reactor
may be induced and as a result unwanted heating may occur. The European
Directive 2004/40/CE defines the maximum levels of electromagnetic fields that
workers should be exposed to. These levels depend on the frequency as the effect
on the human body depends as well on the frequency. In the range from 25 to
800 Hz the electrical field must be below 500 (V/m) and the magnetic induction
below 5000 (uT).
4.2.2
Oil-immersed Reactors
Unlike air-core reactors, oil-immersed reactors do not suffer from high external
magnetic fields thanks to the mechanical construction of a closed tank filled
with mineral oil. Therefore it is safe to carry out maintenance work in the
proximity of the air-core reactor. The active part consists of paper-insulated
coils with copper windings. The magnetic circuit is based on end-shields with the
reactor coils in between. The sound sources from oil-immersed reactors are more
complex compared to air-core reactors. It depends on the design approach and
includes combinations of and contributions from magnetic and non-magnetic
shieldings, windings and core. The key is to minimize and avoid mechanical
resonance to reduce sound levels. Additional benefits of oil-immersed reactors
are the straightforward installation of noise reduction measures. Where for aircore reactors this is far more complex due to the construction above ground.
Oil-immersed reactors are also more robust since the active parts, such as the
windings, are immersed in oil and therefore benefit from paper-oil insulation.
At last oil-immersed reactors can be tested according IEC standards, as most
manufacturers of air-core reactors do not own their own test facilities. This is
35
Chapter 4
Figure 4.2: Oil-immersed reactor with external cooling
an important benefit for TSO’s to ascertain their quality checks.
4.3
A Practical Model
4.3.1
Technical Parameters
For the EMT model of the series reactor, practical data from a 400kV - 4000A
three phase series reactor was obtained. The information was acquired from a recently commissioned project in the TenneT transmission network: MaasvlakteWesterlee. Here two series reactors will be installed to compensate the system
impedance with the rest of the transmission network. Information regarding
the construction of the series reactor, was obtained by a factory visit by KEMA
and TenneT [27].
36
Fault Current Limiting Reactors
Cs
Rs
CE /2
Ls
CE /2
Figure 4.3: Per phase equivalent circuit
8 Ohm
L
(mH)
Lsat
(mH)
Rs
(mΩ)
Cs
(pF)
Creactor
(pF)
27.06
23.87
26.15
10...500
1000
Table 4.1: Equivalent circuit parameters
Technical Specifications
System voltage:
Test voltages:
Nominal current:
Nominal impedance:
Minimum impedance at
full short circuit:
Losses at 4000A:
Cooling stages:
Um = 420 kV
BIL = 1425 kV / SIL = 1050 kV / AC = 630 kV
I = 4000 A
8Ω
XSAT = 7.5 Ω
1255 kW
ONAN up to 2000 A
ONAF up to 2500A
ODAF up to 4000A
Cbushing = 1330pF
(4.3)
CE /2 = Cbushing + Creactor /2
(4.4)
where:
L
Lsat
Rs
Cs
Creactor
=
=
=
=
=
unsaturated reactance, mH
saturated reactance, mH
series resistance, mΩ
winding capacitance, pF
reactor capacitance, pF
The model is based on an impedance of 8 Ω. This value translates in an
unsaturated reactance of 27.03 mH and a series resistance of 26.15 mΩ. The
impedance of 8 Ω is adequate to limit the fault current within the limits of
the proposed 63 kA circuit breakers at station Maasbracht 380. The saturation
characteristics where modeled by taking into account two inductors in series:
37
Chapter 4
I
(A)
Flux-linkage
(Wb-turn)
Knee point (end of linear section)
10100
43.95
Saturated section
55000
68.29
Table 4.2: Saturation characteristics
Return limb
Coil
Coil
Coil
Return limb
Upper yoke
Bottom yoke
Figure 4.4: Encapsulated Air-core reactor
ˆ a linear 22.68 mH inductor, representing the air path of the magnetic
circuit
ˆ a non-linear 4.35 inductor, representing the iron core part of the magnetic
circuit
The saturation characteristics of the 4.35 mH saturable inductor are given in
table 4.2. The saturatation is relatively mild thanks to the particular construction of the reactor. The magnetic circuit consists partly of an iron path when
the flux passes the bottom and upper yoke and the two return limbs as can be
seen in figure 4.4. The main reactance is formed by the flux that passes through
the path of the coils, splits in the iron tank and the mineral oil that has the
same permeability as air. Thus when the iron path goes into saturation it has
a marginally impact on the total impedance.
4.3.2
ATP-EMTP Model of the Series Reactor
The series reactor was modeled in ATP-EMTP and based on the circuit diagram
depicted in figure 4.3. The 4.35 mH saturable inductor was represented by a
TYPE-98 nonlinear current-dependent inductor, its non-linear characteristic is
given in figure 4.5. The 22.68 mH inductor was represented by the model of an
ideal inductor in ATP-EMTP. The following parasitic capacitances that have
been provided by the series reactors’ manufacturer were incorporated:
ˆ Winding capacitance (Cs ) of 500 pF
38
Fault Current Limiting Reactors
ˆ Terminal capacitance (CE /2) of 1830 pF
Figure 4.5: Non-linear characteristic of the saturable inductor
39
CHAPTER
5
Superconducting Fault Current Limiters
he state when a conductor experiences zero-resistance, superconductivity,
T
was discovered by the Dutch physicist Heike Kamerlingh Onnes in 1911.
He observed that the resistance of mercury when cooled to a temperature of
4.2 K, almost disappeared [43]. The discovery in 1986 of superconductors with
transition temperatures above the boiling point of nitrogen has renewed the
interest in large-scale applications. These are the so-called High temperature
superconductors (HTS) and were discovered by Karl Müller and Johannes Bednorz. They are known by their relatively high critical temperature above 30
K.
5.1
Superconducting Materials
SC materials are characterized by a three-dimensional graph in which the current density, temperature and magnetic field are plotted respectively [11]. If
one of these parameters exceeds the critical levels of the operating area, the
SC material will experience a superconducting-to-normal (S/N) transition. The
highest temperature at which the SC material is not experiencing electrical resistivity is called the critical temperature Tc . The maximum current the SC
Magnetic
field, B
Bc
Critical
surface
Current
density, J
Jc
Tc
l
Temperature, T
Figure 5.1: Superconductor critical
surface is a function of
the magnetic field B,
current density J and
temperature T.
41
E [V/cm]
Chapter 5
N-value
E=1µV/cm
Current [A]
Ic
Figure 5.2: V-I curve of a superconductor
can carry before superconducting-to-normal transition takes place, is called the
critical current density Jc or critical current Ic . Ic is derived from the definition of “a voltage drop along the length of a wire as a function of its current”
[29]. The industry accepted practice is to define the SC’s critical current as
a function of the current that produces a voltage drop of 1µV/cm along the
conductor. At last the critical magnetic field at which the SC material loses
superconductivity is defined as Hc . To the V-I curve where the S/N transition
for a given SC test sample is plotted, a power law can be fitted as depicted in
figure 5.2. This power law is given in equation 5.1. Where E(I) is the voltage
drop across the superconductor, Ec is the electric field criterion at 1µV/cm, T
is the temperature dependency and I is the current flowing through the SC. N
is the SC material dependent exponent and influences the coefficient of the V-I
curve. This power law is quite accurate since the heating process is adiabatic
and independent of the behavior between the SC’s material and the cryogenic
system.
N (T )
I
E(I) = Ec
(5.1)
Ic
Since the discovery of HTS materials in the 1980’s, research has increased with
respect to the application of fault current limiting purposes. HTS materials have
come to be known as second generation (2G) superconductors as these materials
where discovered after the introduction of the so-called low-temperature superconductors (LTS). HTS are cooled with liquid nitrogen LN2 and have a critical
temperature above 30 K. This is a great advantage compared to LTS’s which
usually operate very close to their critical temperature at 4.2K and therefore
very sensitive to temperature changes. Consequently the refrigeration system,
which mainly consists of external tanks filled with LN2 or He, must have a higher
capacity. By using HTS for FCL applications, instead of LTS - refrigerations
costs can be decreased by a factor of 10 [60].
Most used HTS materials come in bulk or thin film, the most important
SC’s for FCL applications are discussed below:
YBa2 Cu3 O7
Yttrium-barium-copper-oxide typically referred to as YBCO was discovered in 1987 [34]. Its critical temperature, Tc is equal to 93 K. It comes in
42
Superconducting Fault Current Limiters
bulk form or can be applied in the form of YBCO CC, where CC stands
for coated conductor. YBCO CC has an improved (larger) contact area
with the cryogenic environment. This facilitates easier and faster heat
transport in comparison with bulk material and therefore recovery times
are improved. In some cases YBCO CC is also referred to as (RE)BaCuO,
where RE stands for rare-earth material.
Bi2 Sr2 Ca1 Cu2 O8
Bismuth-strontium-calcium-copper-oxide typically referred to as BSCCO
2212 or Bi 2212 was discovered in 1988 [25]. Its critical temperature, Tc
is equal to 95 K.
Bi2 Sr2 Ca2 Cu3 O10
Typically referred to as BSCCO 2213 or Bi 2213 with a critical temperature Tc of 107 K.
MgB2
Magnesium-diboride discovered in 2001 with a critical temperature, Tc ,
of 39 K [60]. It’s a relatively new discovered SC material and the price
per unit length is significantly lower, as will be discussed in chapter. Conversely the cryogenic system needs to have a higher cooling capacity, as the
critical temperature, Tc , is much lower. This results in higher operating
costs, but it is imaginable that in some cases the total cost of ownership of
an SCFCL with MgB2 is lower in comparison with systems where YBCO
or Bi 2212 is applied.
YBCO CC, is the most promising SC for FCL applications because it has a
high critical current density and a good temperature stability. The four main aspects which are leading in the design and choice of a HTS material are addressed
accordingly:
1. Recovery time of the SCFCL
The time needed for a SCFCL to cool down below the critical temperature
after S/N transition is called the recovery time. The recovery time depends
on the thermal capacity of the cryogenic zone and the amount of dissipated
heat during a fault. This is an critical factor in the design and application
of HTS materials and has consequences on the operation and protection
of the power system.
The recovery interval is in most cases within the order of several seconds
for thin film SC’s and in the order of minutes for bulk SC material and
primarily depends on the magnitude and duration of the fault [7, 33].
During this period, the fault current limiter is still acting as an impedance.
The recovery delay can be reduced by using YBCO CC.
2. Maximum limiting period of the SCFCL
During a fault the SC elements and cryogenic system is dissipating energy in the form of heat. Thus the duration of the fault limiting period
is directly related the amount of dissipated heat. The SC material can be
damaged by overheating and the fault must be cleared within reasonable
time [57, 58]. The maximum limiting period of the SCFCL can be calculated. This is done as an example in section 5.4.1 Design Aspects of a
SCFCL.
43
Chapter 5
3. Hot-spots in the SC material
Hot-spots are local power dissipations in the SC material when stressed
by a fault current. They are caused by electrical inhomogeneities and are
the weak spots of the SC material. Consequently an uneven distribution
of the fault current will occur, resulting in the so-called hot spots. This
is an exponential process as can be estimated from the characteristics of
the SC material.
5.2
Costs of SC Materials
A major drawback of SCFCL’s is the price of SC materials and the investment
of crygogenic cooling systems. Currently the price of copper ranges between
25 euro/kA-m to 50 euro/kA-m. To compete with the price of copper, the
price-performance-ratio of SC materials has to increase. At present the price
of LTS SC wire is 150 euro/kA-m while the price for HTS SC wire is in the
order of 200-300 euro/kA-m. For the long term it is expected that the price
of LTS wire will drop to 50 euro/kA-m and for the HTS wire it will decrease
to 10 euro/kA-m. The costs of SC materials are determined by three factors:
productions costs, equipment costs and the costs of the SC raw material. Future
improvements of the production process could lead to increased yields and quality of the SC materials, which will most probably result in cost reductions and
quality enhancement. The overall price of SCFCL’s can be reduced by these
enhancements as lower AC losses in the SC material would result in smaller
cryogenic systems and therefore an improved business case and lower costs of
ownership [16].
5.3
5.3.1
SCFCL Topologies
Resistive Type
Resistance
The resistive type SCFCL is based on the non-linear behavior of the superconducting material. The transition from the superconducting state to the normal
conducting state is called the “quench”. During normal operation or superconducting state, the resistance of the superconductor, RHTSC is negligible. In case
of a fault, the short-circuit current supersedes the critical current density and
critical temperature of the superconductor and consequently will develop a resistive
characteristic
as
shown
in
5.3.
The resistance Rp placed in parallel
to the superconductor as depicted in
figure 5.4 is needed to protect the suNormal conductor
perconductor from “hot spots”. This
parallel resistance is in fact a metalized thin-sheet wire which is contacted all over the length of the super
Superconductor
conductor. This will also help protect
the superconducting alloy from over
Tc
Temperature
voltages if RHTSC rises too rapidly.
Figure 5.3: Evolution of the SC’s resistiv- The fault has to be cleared by the cirity as a function of tempera- cuit breaker, CB, in order to limit the
ture
44
Superconducting Fault Current Limiters
Rp
Ls
Rs
RHT SC
Limiter
iF
CB
Zf
U
Figure 5.4: Electrical circuit of resistive type SCFCL
Figure 5.5: 110kV Resistive type SCFCL from Siemens; 1. FCL, 2. LN2 refill tank,
3. bushings, 4. busbars, 5. voltage transducer [8]
maximum temperature of the superconductor.
These kind of the SCFCL’s are fail safe and can be built compact with
marginal impedance during normal operation. Drawbacks are the cryogenic
losses from the current leads and bushings that cause heat losses due to thermal
conduction. Another drawback is the recovery time, which is in the order of
seconds to minutes. An overview of planned and recently commissioned resistive
type SCFCL pilot projects is given in Appendix B, Overview of SCFCL projects.
5.3.2
Saturated Iron Core
The operating principle of the saturated iron core, also refererd to as DC biased
core FCL can be explained through the behavior of a non-linear inductor. The
impedance L,sat is a function of the length l of the flux path, the cross-sectionial
area A, the number of turns N and the relative permeability of the core µ. By
driving the magnetic core into saturation the inductance value L of the inductor
decreases and the B-H working point can be manipulated as is depicted in figure
45
Chapter 5
B
5.6. The principle of operation of a saturated core FCL is independent on the
type of material used for the inductor, for instance copper or SC material.
However, AC losses and inductor size are greatly reduced when SC material is
applied for the windings of the inductors. The values of the inductance in the
Bsat
A
l
ΔB µ=ΔB/ΔH
ΔH
Linear region
Saturated region
H
N
Hsat
Figure 5.6: Non-linear B-H curve
Figure 5.7: Magnetic circuit of a core
with wounded inductor
saturated and unsaturated case can be approximated by the following equations
[38]:
L = µ0 µr
N 2A
;
l
Lsat = µ0 µr,sat
N 2A
l
(5.2)
where:
L
Lsat
µ0
µr
µr,sat
=
=
=
=
=
unsaturated reactance, mH
saturated reactance, mH
permeability of air
unsaturated relative permeability of the core
saturated relative permeability of the core
The core can be saturated by an additional winding conducting a DC current
or could be biased by using a permanent magnet. The winding of the inductor
is placed in series with the line and conducts the AC current. During normal
operation the AC current iac must be low enough to keep the core fully saturated.
In case of a fault the magnitude of the AC current will drive the inductor out of
saturation and into the region of high relative permeability on the B-H curve.
The fault current is quenched in the magnetic core. This results in an immediate
recovery after a fault. Less SC material is needed which results in another
benefit, a smaller cryogenic system. A drawback is the large size of the system,
due to the dimension of the iron core.
When the magnetic core in figure 5.7 is driven into saturation it will only
limit the fault current for one polarity and not the full AC current. When using
a single magnetic core the fault current would desaturate in one half-cycle and
driven further in saturation the second half-cycle. To resolve this issue, two
magnetic cores in opposite direction can be employed [9]. This setup is depicted
magnetically in figure 5.9 and electrically in figure 5.8. Also the waveforms for
a bipolar saturated core FCL are given in figure 5.10, where both iron cores are
driven into saturation. This causes the magnetic circuits to operate around the
magnetic fields HDC1 and HDC2 respectively.
Drawbacks are the relatively large footprint; equal to a transformer with
the same power rating. And the need for an auxiliary DC source or permanent
46
Superconducting Fault Current Limiters
Rs
iac Ls
L1
iF
L2
U
DC
CB
Limiter
DC
Zf
Figure 5.8: Electrical circuit of saturated iron core SCFCL
I dc Ndc
i ac
Nac
Ndc
Nac
ac line
Figure 5.9: Magnetic circuit of saturated iron core SCFCL
magnet to bring the core into saturation. Applying a permanent magnet in a
380 kV FCL is not feasible at this moment and probably will not be in the
future. An overview of planned and recently commissioned saturated iron core
type SCFCL pilot projects is given in Appendix B, Overview of SCFCL projects.
5.3.3
Magnetic Shielded Core
The magnetic shieldeld core SCFCL or often referred to as inductive type
SCFCL, is a two-winding transformer consisting of a short-circuited secondary
winding. The secondary winding reflects zero-resistance to the primary windings
during normal conditions. An representing electrical circuit is given in figure
5.12. The magnetic shielded core concept was originally invented by Dersch
[18].
The construction of the magnetic shielded iron core is based on a conventional primary winding around an iron core and SC cylinder in between. The
cylinder consists of several melt casted SC elements, which form the magnetic
shielding. During normal operation the induced current in the superconducting
cylinder is lower than the critical current of the SC magnetic shield, therefore
serving as a short-circuited secondary winding. The residual impedance is limited to the losses in the primary winding Rl and the stray inductance Lσ between
the primary winding and the SC cylinder. The electrical circuit of the magnetic
shielded iron core SCFCL during short-circuit operation is given in figure 5.13.
During a quench the short-circuit current exceeds the critical current of the SC
cylinder and therefore will develop a resistance. The flux generated by the primary windings is penetrating the iron core and the limiting impedance is formed
by magnetizing inductance Lh and the resistance RHTSC . Whether the current
47
Chapter 5
L1 =
dB1
dH1
HDC1
H1
B1
H1
U0
iac
Δv = (L1 + L2 )
di ac
dt
t
H2
B2
H2
HDC2
L2 =
dB2
dH2
Figure 5.10: Wave forms of the bipolar saturated core SCFCL [35].
48
Superconducting Fault Current Limiters
Superconductor
N
Figure 5.11: Magnetic circuit of the magnetic shielded iron core SCFCL
limitation is predominantly resistive or inductive is determined by the factor
ω(Lh − Lσ ) > N 2 RHT SC . If both terms are comparable then the limitation
is of a mixed type [55]. The resistance of the SC cylinder is reflected by the
squared winding ratio of N1 /N2 times RHTSC . This factor can be derived by
the following equations:
U1 =
N2
U2
N1
(5.3)
I2 =
N1
I1
N2
(5.4)
By multiplying equation (5.3) by equation (5.4):
U2 I2 = U1 I1
By dividing equation (5.3) by equation (5.4):
2
U1
N1
= R1 =
RHT SC
I1
N2
(5.5)
(5.6)
It is advantageous that the SC material is exhibited to large currents but low
voltages, this reduces the effect of hot-spots. Also the lack of current leads to
the cryogenic compartment reduces the effect of heat losses. A drawback is the
recovery time of several seconds to minutes, because the quench takes place in
the SC material. This is similar to resistive type SCFCL’s where the quench also
takes place in the SC material. Another drawback is size, which is similar to the
weight and volume of a transformer with the same power rating. An overview
of planned and recently commissioned magnetic shielded core type SCFCL pilot
projects is given in Appendix B, Overview of SCFCL projects.
5.3.4
Solid State FCL’s
Other topologies are based on the application of high-power semiconductors.
With their fast turn-off capability, semiconductors such as IGCT’s, GTO’s and
IGBT’s are the ideal breakers. Major drawbacks for 380 kV applications are
size (several football fields, comparable to a HVDC substation), on-state losses,
requirement of auxiliary circuits (e.g. turn-off snubbers), limited blocking voltage and reduced breaking current capabilities. Therefore solid state FCL’s are
not in the scope of this document. However for low voltage applications semiconductors can be applied as a feasible solution in FCL applications.
49
Chapter 5
iac Ls
Rs
Rl
CB
L1
i2
L2
Zf
U
Limiter
RHT SC
Figure 5.12: Electrical circuit of the magnetic shielded iron core SCFCL
Ls
Rs
R1
Lh
Lσ
iF
CB
i2
Limiter
U
RHT SC
Zf
Figure 5.13: Electrical circuit of the magnetic shielded iron core SCFCL during
short-circuit
5.3.5
Overview of Different SCFCL Types
To conclude, a comparative summary of several SCFCL types is given in table
5.1. At present novel (SC)FCL’s like described in the foregoing subsections are
not commercially available. It is difficult to predict which SCFCL will be the
most promising for the future. In any case fast current limitation is achieved
with all SCFCL types. The main differences are covered by the parameters:
recovery-time, fail-safeness, normal operation losses and size. The main requirements for SCFCL’s are:
ˆ Fast quenching
ˆ Fast recovery
ˆ Ability to self recover
ˆ Fail-safe and reliable operation
ˆ Low AC and cryogenic losses
ˆ Compact and light weight
ˆ Low investment costs and economic operation
The most compact solution is offered by the resistive type, however the problems
regarding the effects of hot-spots first have to be overcome. With respect to fast
recovery, the saturated iron core is the most promising since the quench does not
take place in the SC. Considering the fact that the effect of hot spots is greatly
50
Superconducting Fault Current Limiters
Losses
Fail safe
Amount of
superconductor
Size
Recovery
Resistive
SC
AC
losses and
current lead
losses
Yes
Medium
Small
Few seconds
up to minutes
Saturated
iron core
Iron
core
losses and
primary
conductor
losses
No
Small
Large
Immediate
Magnetic
shielded
core
Iron
core
losses and
primary
conductor
losses
Yes
Small
Large
Immediate
Solid state
Semiconductor No
AC losses
May
be
equipped
without SC
material
Depends on
voltage level
Immediate
Table 5.1: Comparative summary of SCFCL concepts
reduced and no auxiliary DC circuits are needed, today the magnetic shielded
core is the most promising solution for transmission level voltages. This concept
will be translated into a model for ATP-EMTP in the case study Maasbracht
380. Additional comparative summaries of SCFCL concepts are given in [35, 54].
5.4
A Practical Model for a Shielded Core SCFCL
5.4.1
Design Aspects of a SCFCL
The basic principles of designing a SCFCL are relatively simple. Most important
parameters are the maximum permissible fault current Ilim , fault duration ∆t
and temperature rise ∆T of the SC material. It is assumed that the heat
resistivity and capacity are temperature independent. In equations 5.7 and 5.8
the limiting resistance R and limiting current Isc are given respectively [29].
R=
U
ρ`
=
Isc
A
s
Isc = A
C∆T
ρ∆t
(5.7)
(5.8)
The corresponding maximum permissible electric field during limitation is given
in equation 5.9 and is independent of the cross sectional area, A.
r
ρC∆T
Esc =
(5.9)
∆t
51
Chapter 5
Figure 5.14: E(j) characteristics for different Bi 2212 samples @65 K. [32].
where:
R
U
`
∆T
∆t
A
C
Isc
Esc
=
=
=
=
=
=
=
=
=
SCFCL resistance during fault, mΩ
system rms voltage, V
length of SC material, m
maximum permissible temperature rise, ◦ C
maximum permissible fault duration time, s
cross sectional area, m2
specific heat of SC and stabilizer
maximum permissible SC fault current, A
maximum permissible SC electric field during limitation, V/m
By solving these equations the minimum conductor volume is obtained. The
minimum conductor value can also be approximated by equation 5.10 [44].
V olume =
Isc U ∆t
C∆T
(5.10)
This means that in the case of a 380 kV limiter with Isc = 4000A, a limited
fault current for 0.1 seconds (five periods @50 Hz) and a 100 K maximum
permissible temperature rise in a bulk volume with the approximate specific
heat value of 2 × 106 J/m3 K, results in 0.76 m3 of SC material per phase.
The minimum cross sectional area A, can be determined by equation 5.8 or
directly from test samples of bulk (Bi 2212 / Bi 2213) SC material depicted in
figure 5.14. In short the cross sectional area has to be large enough to reduce
the SC losses, but small enough to ensure a fast transition from superconducting
state to normal state. Finally the length of the SCFCL determines the total
limiting resistance R.
5.4.2
ATP-EMTP Model of the Magnetic Shielded Core
SCFCL
The non-linear behavior of the SC material is temperature dependent which
again is a function of the fault-current. The temperature rise versus time can
52
Superconducting Fault Current Limiters
Function of the resistance R
10
Resistance [Ω]
8
6
4
2
0
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time [s]
Figure 5.15: Evolution of the resistance as a function of time
be calculated under the assumption that the heating effect due to the transition
from superconducting state to normal state is adiabatic. In other words the
heat dissipated in the SC material will not be transferred to the coolant in such
a short notice.
It was found rather complex to model a temperature dependent resistance
which was again a function of the fault current. In particular it was difficult
to achieve an equilibrium between the evolution of the resistance and the fault
current.
Instead a more pragmatic way was selected to model the magnetic shielded
core SCFCL. It was accomplished by a time dependent resistance evolution
connected to the secondary winding of an ideal transformer. It is assumed that
the behavior of the magnetic shielded core SCFCL is predominantly resistive.
The model is built up with use of the MODELS1 block set in ATP-EMTP.
The TACS controlled resistor is driven by the function RHT SC = 25t0.35 which
is an output of the MODELS block set to the TACS resistor. The rise time of
the resistance evolution is derived from the quenching behavior of an YBCOcoated conductor in [56]. The aim is to compare the quenching behavior of
the magnetic shielded core SCFCL with that of the series reactor prestented
in chapter 4. Therefore the maximum limiting resistance is defined to be 8 Ω
at the moment of the interruption of the circuit breaker. The complete source
code written in FORTRAN is listed in Appendix A.
The evolution of the resistance on the primary side (line side) of the magnetic
shielded core is given in figure 5.15.
1 MODELS
is the internal FORTRAN based programming language of ATP-EMTP
53
CHAPTER
6
Case Study Maasbracht 380
he construction of substation Maasbracht 380 was part of the first steps
T
towards the realization of the Dutch 380 kV transmission grid which has
been put in operation between 1969 and 1970 [52]. Over time the substation
expanded due to the construction of more and more incoming supplying lines
and outgoing feeders. Its most recent expansion is the commissioning of three
CHP units, CC-C 1-3 which account for 280 MW each. The construction of
three more CHP’s, CC-D 1-3 is planned for 2014 [42]. The sum of six CHP’s
are part of the modernization project at the “Claus centrale”, a Power plant
which is owned by Essent NV, an electric utility provider in the Netherlands.
In the near future it is foreseen that the substation will exceed its maximum
short-circuit withstand levels, to overcome this problem buses A and B1 are
planned to be split. In this way the fault current levels are reduced. This
measure will be explained in more detail in sub-section 6.1. The preferable
outlook for substation Maasbracht 380 is given in the form of an one-line diagram
in figure 6.1. The diagram includes all supplying lines and outgoing feeders, the
present and future fault current contributions are given in table 6.1. The short00
circuit withstand levels for the substation are known to be for Ik = 51kA and for
ip = 125kA. However measures are taken to upgrade the short-circuit withstand
00
levels on a short notice to Ik = 63kA with a corresponding ip = 171kA.
6.1
Splitting the Substation Into Sub Grids
The entire transmission system of TenneT is built according to the n−1 reliability criterion. This means that in each grid one component can fail without loss
of supply since the remaining components are still able to transfer the power.
In general this principle is referred to as redundancy and has the aim to increase reliability and availability. At substations redundancy is achieved by the
1 Due to environmental constraints at substation Maasbracht 380 the extension of bus bar
B is renamed to C. However bus bar B and C can be seen as a whole.
55
Chapter 6
CC-C 1-3
CC-A
Dodewaard
Eindhoven
KV 2
CC-D 1-3
KV 1
C
B
A
CC-B
TR401
Van Eyck
Elia
TR402
Selfkant
Amprion
TR404
TR403
150 kV Network
MBT 150
Figure 6.1: Overview of substation Maasbracht 380 with possible location of
(SC)FCL in coupling bay KV 1
CB
A
B
Figure 6.2: Parallel bus bars coupled through bus-coupler circuit breakers
Type
Name
Ik3
(kA)
Total
00
Ik3
(kA)
Ik1
(kA)
Total
00
Ik1
(kA)
CC-A
3.44
3.44
1.98
1.98
CC-C 1-3
1.61
4.83
0.89
2.67
CC-D 1-3
1.61
4.83
0.89
2.67
Lines (to)
Eindhoven
7.15
14.3
5.40
10.80
Lines (to)
Dodewaard
4.97
9.94
4.02
8.04
Lines (to)
Selfkant
18.7
18.7
14.1
14.1
Lines (to)
Van Eyck
9.6
9.6
7.9
7.9
Transformers
Total
MBT TR401-TR404
1.22
4.88
70.52
1.64
6.56
55.02
00
Generator
Generators
Generators
1
1
00
Effective from the year 2018.
Table 6.1: Overview of the fault current contributions at MBT 380, calculated
through the IEC60909 method
56
Case Study Maasbracht 380
CB 1
CB 4
CB 2
A´
A
B´
B
CB 3
Figure 6.3: Two bus bars sections longitudinal coupled through circuit breakers CB
2 and CB 3
coupling of two (or more) bus bars. An example is given in picture 6.2 where
two parallel bus bars are connected through a bus-coupler circuit breaker. If,
for example a short-circuit occurs at bus A, or in one of the supplying lines
or outgoing feeders connected at that time to bus A, it is possible to exclude
the faulting parts from the substation and subsequently transfer the unharmed
phases to bus B.
To decrease the fault current contribution at substation Maasbracht 380
it is possible to split the bus bars A and B as mentioned earlier. This can
be done in two ways. The first possibility is best explained through figure
6.2 and is achieved by splitting the parallelly coupled bus bars. This results
in bus bars A and B operating independently from each other. Assuming that
supplying lines and outgoing feeders are equally distributed over buses A and B,
the fault current levels are reduced with approximately 50%. According to table
6.1 this results in approximately 35 kA for a three-phase-to-ground fault and
approximately 27.5 kA for a single-phase-to-ground fault. This is within todays
electromechanical and thermal limits of substation Maasbracht 380. It is obvious
that this measure can be effectuated immediately without additional efforts and
costs. This is a great advantange, however serious drawbacks are present. With
this measure the substation has lost its n − 1 reliability. Consequently this
implies that if one bus bar is out of service due to maintenance, the short
circuit withstand level on the remaining bus bar is exceeded. Therefore it is
advised to implement this measure only on a temporary basis. The second
method of substation splitting is based on the one-line diagram in picture 6.3
where two parallel bus bars can be longitudinal coupled through CB 2 and
CB3. This way of “sectioning” reduces the short-circuit levels since there are
less supplying lines and outgoing feeders connected to each section. The n − 1
reliability criterion is maintained and the option to join bus bars makes the
substation more flexible. Sections can be separated if the short-circuit current
contribution is too high or joined if one bus bar is out of service for example.
One can think of many more scenarios where this flexibility comes to assistance.
With respect to existing substations the drawbacks are clear; It demands the
reallocation of supplying lines and outgoing feeders which is considered to be
costly and results in unequally loaded buses. At last it has to be taken into
account that when two energized sections are being joined by the bus-section
circuit breakers, the phase angle and voltage difference between the sections has
57
Chapter 6
to be within predefined limits. Otherwise (too) large compensating currents will
flow that may harm the power systems’ equipment.
6.2
EMT Model of Substation Maasbracht 380
Substation Maasbracht 380 has been modeled in more detail with regard to the
capacitances associated with power system components, such as the bushings,
CT’s, CVT’s and bus bars. These capacitances play an important role in the
initial voltage rise of the TRV and have been estimated according to Annex B
of C37.011 - Application Guide for Transient Recovery Voltage for AC HighVoltage Circuit Breakers [15]. The capacitances of the cables have been derived
from the IEC 60909 informational database that has been provided by the Asset
Management department.
The remaining two fault current limiting measures in this thesis, being the
series reactor and the magnetic shielded core SCFCL will be studied in the
following sections. Both FCL’s are placed in coupling bay KV 1 of substation
Maasbracht 380, aiming on reaching a maximum efficacy of the limiter. It is
assumed that supplying lines and outgoing feeders are equally distributed over
the substation.
It is important to note that all subsequent transient switching studies are
carried out with all power system components energized to the maximum system
voltage. Meaning the 380 kV system is energized up to 420 kV, or approximately
1.1 p.u. voltage. In this way the largest possible short-circuit current is being
initiated.
The circuit breakers are configured in such a way that the full bus bar is
cleared when a fault occurs at substation Maasbracht 380. Meaning that every
supplying line and outgoing feeder is disconnected from the faulting bus bar
when a short-circuit occurs. It is assumed that the circuit breakers act within
two periods, which equals 40 milliseconds in a 50 Hz power system. The time
between the instant of the fault and the short-circuit interruption is set to be
short, representing the worst case scenario for the circuit breaker.
6.3
6.3.1
EMT Study Series reactor
Results
To initiate a starting point of this EMT study, a three-phase bolted line-toground fault has been initiated at bus bar A of substation Maasbracht 380.
The resulting fault current is shown in figure 6.4, with ip = 171 kA and I” k =
68.4 kA. After adding the series reactor of 8 Ω in the coupling bay, the threephase-to-ground fault current is limited to a value of ip = 141 kA and I” k =
62.4 kA. These results are within the electromechanical and thermal limits of
substation Maasbracht 380. Figure 6.5 illustrates the limited fault current. The
instantaneous change of the fault current to 0 A at t = 0.1 seconds is the result of
the switching action by the circuit breaker and is set on purpose to evaluate the
TRV. The circuit breaker opens and the current is interrupted at current-zero.
The current of I” k = 16.9 kA through the series reactor and associated circuit
breaker in the coupling bay suits the IEC T30 test duty criteria, the waveforms
are given in figure 6.6. In figure 6.7 the full three-phase TRV’s are depicted,
58
Case Study Maasbracht 380
×105
2
Three Phase fault current
Phase a
Phase b
Phase c
1.5
Current [A]
1
0.5
0
−0.5
−1
−1.5
−2
0
0.05
0.1
0.15
0.2
Time [s]
Figure 6.4: Three-phase-to-ground fault current
where in figure 6.8 the magnified function of the TRV is given. Unfortunately the
TRV exceeds the 420 kV and 550 kV IEC T30 envelopes of the circuit breaker.
The TRV plots of the remaining phases are given in Appendix D Resulting Plots
TRV Study. It can be concluded that the implementation of a 550 kV circuit
breaker in place of a 420 kV circuit breaker does not make sense since the initial
dielectric strength of both breakers is the same. In the next sub-section 6.3.2,
measures are presented to reduce the rate-of-rise-of-recovery voltage (RRRV).
6.3.2
Insertion of Damping Capacitors
A convenient solution to suppress the RRRV would be the insertion of damping
capacitors close to the series reactor, as stated in references [15, 17]. The damping capacitors can be implemented as being Y-connected capacitances or as a
series-connected capacitances across the reactor. At substation Maasbracht 380
the approach of the Y-connected capacitance has been chosen since this option
is most favorable with regard to practical aspects. By gradually increasing the
value of the capacitor a satisfactory result for the RRRV was obtained. The
result of the damped TRV is given in figure 6.9. Depending on the type of
capacitor (polypropylene or oil-impregnated paper) the capacity may vary between 0.055 uF and 0.065 uF. The TRV plots of the remaining phases are given
in Appendix D Resulting Plots TRV Study.
59
Chapter 6
×105
2
Three Phase fault current
Phase a
Phase b
Phase c
1.5
Current [A]
1
0.5
0
−0.5
−1
−1.5
−2
0
0.05
0.1
0.15
0.2
Time [s]
Figure 6.5: Limited three-phase-to-ground fault current
×104
5
Three Phase fault current
Phase a
Phase b
Phase c
4
3
Current [A]
2
1
0
−1
−2
−3
−4
−5
0
0.05
0.1
0.15
0.2
Time [s]
Figure 6.6: Three-phase fault current through the circuit breaker and series reactor
in the coupling bay
60
Case Study Maasbracht 380
Transient Recovery Voltage
×105
5
4
3
Voltage [V]
2
1
0
−1
−2
Phase a
Phase b
Phase c
−3
−4
−5
0.08
0.09
0.1
0.11
0.12
0.13
0.14
Time [s]
Figure 6.7: Three-phase transient recovery voltage
Transient Recovery Voltage
×105
9
8
550
Phase c
7
420
Voltage [V]
6
5
4
3
2
1
0
0.0944
0.0945
0.0946
0.0947
0.0948
0.0949
0.095
Time [s]
Figure 6.8: Undamped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase c
61
Chapter 6
Transient Recovery Voltage
×105
9
550
Phase c
8
7
420
Voltage [V]
6
5
4
3
2
1
0
0.0944
0.0945
0.0946
0.0947
0.0948
0.0949
0.095
Time [s]
Figure 6.9: Damped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase c
6.4
6.4.1
EMT Study Magnetic Shielded Core SCFCL
Results
The current limiting behavior of the magnetic shielded iron core is of a resistive
type and was discussed in subsection 5.4.2 ATP-EMTP Model of the Magnetic
Shielded Core SCFCL. The quenching behavior is given in picture 6.10, the
three-phase-to-ground fault current is limited to value of ip = 130 kA and I” k
= 61.4 kA. These results are within the electromechanical and thermal limits
of substation Maasbracht. Again the current is interrupted at t = 0.1 seconds,
to evaluate the TRV. The current and TRV fall within IEC test duty T30 as is
depicted in figure 6.11 and 6.12. It can be concluded that no additional measures
are needed to control the RRRV. Accordingly there is no need for upgrading the
circuit breaker. The TRV plots of the remaining phases are given in Appendix
D Resulting Plots TRV Study.
62
Case Study Maasbracht 380
×105
2
Three Phase fault current
Phase a
Phase b
Phase c
1.5
Current [A]
1
0.5
0
−0.5
−1
−1.5
−2
0
0.05
0.1
0.15
0.2
Time [s]
Figure 6.10: Limited three-phase-to-ground fault current
×104
5
Three Phase fault current
Phase a
Phase b
Phase c
4
3
Current [A]
2
1
0
−1
−2
−3
−4
−5
0
0.05
0.1
0.15
0.2
Time [s]
Figure 6.11: Three-phase fault current through the circuit breaker and magnetic
shielded core SCFCL in the coupling bay
63
Chapter 6
Transient Recovery Voltage
×105
0
−1
−2
Voltage [V]
−3
−4
−5
−6
420
−7
−8
550
Phase a
−9
0.0863
0.0864
0.0865
0.0866
0.0867
0.0868
0.0869
Time [s]
Figure 6.12: TRV with T30 capability envelope for 420 kV and 550 kV breaker,
phase a
64
CHAPTER
7
Conclusion and Recommendations
7.1
Conclusion
When analyzing power system short-circuit current reduction measures it is
evident to rely on close-to-reality grid models. Two independently operating
EMT grid models were established in ATP-EMTP and DIgSILENT PowerFactory. Both models were validated to each other, by comparing dynamical
short-circuit currents, and with respect to the initial symmetrical short-circuit
currents computed through the IEC 60909 model provided by the Asset Management department of TenneT. The identified deviations of 2-8% were within
the expected margins that these models will have to the real network.
Three different short-circuit current reduction methods were considered. At
first the air-core reactor and oil-immersed reactor were examined. From the
perspective of magnetic fields, noise, footprint and robustness the oil-immersed
series reactor is the preferred topology to limit fault currents in the transmission network. An EMT model based upon practical parameters confirmed the
successful quench of the short-circuit current. However special measures were
required to control the RRRV. Additional drawbacks are size and electrical
losses which may account up to 1.2 MW for an 8 Ω, 400 kV oil-immersed series
reactor.
The second measure has the specific interest of many system operators
thanks to its desirable electrical characteristics: the SCFCL. At present several
pilots are in progress and numerous have been successfully completed, however
no SCFCL has become commercially viable yet. The most promising topologies
have been investigated and led to the EMT model of a magnetic shielded core
SCFCL. Simulations demonstrated a successful quench and in comparison to
the series reactor no additional measures were required to reduce the RRRV.
Finally several methods of substation splitting were investigated. To increase
the fault current withstand levels on the short term, splitting two parallel coupled bus bars is justified. However for the long term this imposes a serious
threat to the reliability of the power system as it violates the n − 1 reliability
65
Chapter 7
criterion. To overcome this limitation it is possible to separate the substation
into a number of sections. In this way fault levels are reduced while a redundant
substation is maintained. A severe drawback of “sectioning” is the reallocation
of supplying lines and outgoing feeders which is very expensive.
With respect to substation Maasbracht 380 all three measures are advisable.
Whether to implement a series reactor or SCFCL in the coupling bay mainly
depends on the question if TenneT wants to invest in a innovative pilot or rather
sticks to a concept which have been proven over years. In any case it has to
be noted that if one of the bus bars is out of service the remaining bus bar
could still exceed its fault current withstand level. To address this limitation
substation Maasbracht 380 has to be separated into subsections or FCL’s can
be placed in supplying lines and / or outgoing feeders.
7.2
Recommendations for Future Work
This section covers the recommendations for future work and are listed in order
of preference.
ˆ Implementation of a real time short-circuit calculation system: this is the
first suggestion to the transmission network of TenneT. At present most
fault current studies and operational decisions at TenneT are based on
worst case scenarios. By knowing the actual fault current contribution,
the operation of a more reliable and (cost) efficient transmission network
would be in reach. At substation Maasbracht 380 such a system could
make the difference between upgrading in the near future or leaving the
substation unchanged at present.
ˆ Economic feasibility study on the fault current limiting measures presented
in this thesis: three fault current limiting measures were investigated in
this thesis, however the main focus was on the electrical characteristics
while the economical consequences also play an important role in the decision making process. How do operating costs relate to the investment
costs of the presented measures for example? Especially the SCFCL would
be of interest for a subsequent study since its relies on a cryogenic system
that may account for additional operating costs.
ˆ Collaborations between neighboring TSO’s with respect to the exchange of
short-circuit calculation parameters; during the modeling stage of this thesis it became clear that only a limited amount of information was available
regarding the interconnections with neighboring TSO’s. R/X ratios were
estimated and transmission lines have been omitted. However these simplifications could significantly differ from reality. For example this means
that the accuracy of the simulated short-circuit current peak values and
the correctness of grounding conditions of the power system could deviate substantially. The author suggests the establishment of collaborations
between neighboring TSO’s with respect to the exchange of short-circuit
calculation parameters.
66
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71
APPENDIX
A
Source Code ATP-EMTP MODELS Block Set
73
APPENDIX
B
Overview of SCFCL Projects
75
Appendix B
RSE, A2A
RSE, A2A
factory in Japan, 2008
project stopped
San Dionigi, Italy Q4,
2011, Q3 2012
CESI PowerLab Milano,
Italy January, 2011
Italy / 2005
Test location and date(s)
Resistive
Resistive
Resistive
Resistive
Resistive
Type
3-phase
3-phase
3-phase
1-phase
3-phase
3-phase
Phase
11 kV, 0.1 kA, 1.9 MVA
10 kV, 0.6 kA, 10 MVA
10 kV, 0.4 kA, 7 MVA
6.6 kV, 0.6 kA, 6.9 MVA
9.0 kV, 1 kA, 15.6 MVA
9.0 kV, 0.22 kA, 3.9 MVA
3.2 kV, 0.22 kA, 1.2 MVA
Unfaulted line rating
Bi2212 Melt cast bifilar
coil, LN2
Bi2212 Melt cast bifilar
coil, @73 K, LN2
Bi2212 Melt cast bifilar
coil, @66 K, LN2
REBaCuO tape, LN2
REBaCuO tape, LN2
Bi2223 tape, LN2
Bi2223 tape, LN2
Bi2223 tape, LN2
Superconductor
Table B.1: Table containing recent SCFCL projects [59]
Toshiba, Fujikura
Shanghai ss TBD 2012
Resistive
3-phase
11 kV
Participants
Gan-Shan
Shanghai,
Shanghai Jaioting University
Netphen ss, Netphen, DE,
April 2004 - April 2005
Resistive
3-phase
(now
Nexans Superconductors,
RWE
BamberBridge ss, Preston, UK, October, 2009
March 2010
Resistive
RICERCA
Nexans Superconductors,
Electricity
Northwest,
ASL
Liverpool, UK, Q2 2011
CESI
RSE)
Nexans Superconductors,
Scottish Power, ASL
76
Resistive
Icheon ss Korea, Q1 2011
Factory
Project
2011
Central Networks East,
Rolls-Royce, HyperTech,
E.ON, ASL, ETI
KEPRI, KEPCO, LSIS
KEPRI, KEPCO, LSIS
Korea,
March,
Resistive
Loughborough, Leicestershire, UK, 2012-2014
Nexans France and 14
other participants all in
ECCOFLOW
test,
ended
Resistive
PowerLab test in Milano
June 2012 / ENDESAs
ss bus-tie on Majorca
Spain followed up by a ss
(LV power transformer) in
Kosice, Slovakia, Q3 2012
Dec 2013
Resistive
Resistive
Boxberg Station, Cottbus,
DE, September, 2009 31
December 2011
Nexans Superconductors,
Vattenfall Ag, KIT, BTU,
University of Dortmund
Resistive
Boxberg Station, Cottbus,
DE
Nexans Superconductors,
Vattenfall Ag, BTU
3-phase
3-phase
3-phase
3-phase
3-phase
3-phase
22.9 kV, 0.630 kA
22.9 kV, 0.630 kA
11 kV, 1.25 kA, 24 MVA
24 kV, 1.0 kA, 41.6 MVA
11 kV, 0.8 kA, 15 MVA
11 kV, 0.8 kA, 15 MVA
Bi2223 tape 344S, LN2 3
Bar, He @76 K
Bi2223 tape 344S, LN2 3
Bar, He @76 K
MgB2 wire
REBaCuO tape, LN2
REBaCuO tape, LN2
Bi2212 Melt cast bifilar
coil, @65 K, LN2
Overview of SCFCL Projects
77
Appendix B
Krzhizhanovsky
Power
Engineering
Institute,
Lebedev
Physical Institute
Zenergy, CE Electric,
ASL
Zenergy, CE Electric,
ASL
Zenergy, SoCalEd
EDF Energy Networks, E.ON, GridOn,
Wilson Transformer
Innopower, Southern
Power
Lab
scale
test,
Moscow,
Russia,
2010
T.b.a., UK, 2012
Scunthorpe, UK, Q2Q3 2011
Shandin
Substation, San Bernadino,
California,
USA,
November,
2009
October 2010
NewHaven
Substation, East Sussex,
UK, 2012-2014
Puji ss, southwest
China, 2007
Resistive (shielded core)
Saturated core
Saturated core
Saturated core
Saturated core
Saturated core
1-phase
3-phase
3-phase
3-phase
3-phase
3-phase
0.001 kV, 0.002 kA
33 kV, 1.25 kA, 72
MVA
11 kV, 1.25 kA, 26
MVA
12 kV, 1.2 kA, 25
MVA
11 kV, 0.8 kA, 15
MVA
35 kV, 1.5 kA, 90
MVA
REBaCuO
Bi2223 tape, @30 K,
conduction cooled
Bi2223 tape, @20 K,
conduction cooled
Bi2223 tape, @68 K,
LN2 boil-off recondense
T.b.d.
Bi2223 tape, LN2 deliver, store, boil-off
78
Saturated core
Saturated core
Shigezhuang ss, Tianjin,
China, Q4 2011
Steubencville,
USA, 2012
Zenergy, AEP
Ohio,
Resistive
InnoPower
BC,
PowerTech,
Canada, Q2 2011
Resistive
Shielded core
Siemens, Nexans, AMSC
Netphen,
Augsberg, Bavaria, DE
Q3 2012 to Q3 2013
Netphen ss,
DE
Bruker,
Augsberg
ENSYSTROB,
RWE,
Nexans (Hurth), KIT
Areva,
Stadtwerke,
Energie
3-phase
3-phase
1-phase
1-phase
1-phase
138 kV, 1.3 kA, 310
MVA
220 kV, 0.75 kA, 280
MVA
115 kV, 1.2 kA
110 kV, 1.85 kA
6.4 kV, 2 kA, 22 MVA
Bi2223,
conduction
cooled, @20-30 K
Bi2223 tape, LN2 deliver, store, boil-off
REBaCuO tape, LN2
Bi2212 Melt Cast Tubes
Monofilar, LN2
REBaCuO LN2
Overview of SCFCL Projects
79
APPENDIX
C
Overview of the EMT Grid Models
81
GT-MDK380 W
Krk-XZA_BS11 grs
L380/B0.1
L380/B0.0
XZA_BS11
GT-MDK380 Z
MDK-KRK380 Z
Krk-XZA_BS11 wit
MDK-KRK380 W
0
~
G
BSL150/BB1
BSL150/BB2
Wind op Zee BSL
0
~
G
Sloe20
Sloe10
KRK-BSL380 GS
XZA_GT11
TR Sloe20
GT150/A
Bsl Tr401
AC Voltag..
V
~
11
Tr-A8
3
GT150/B
V
~
TBG380/B
TBG380/A
1
BSL-TBG380 Z
BSL-TBG380 W
AC Voltag..
11
Gtb-LC401
11
~
G
Kerncentrale BSL
1
Gtb-LC402
Tr kerncentrale BSL
MDK380/B
TR Sloe10
11
EHV380/A
EHV380/B
EHVO15/A
EHVO15/B
GT-TBG380 G
GT-TBG380 Z
TBN150/A
TBN150/B
11
11
11
AC Voltag..
V
~
TBG TR2
11
11
AC Voltag..
V
~
Ehv Tr401 Ehv Tr402 Ehv Tr403 Ehv Tr404
11
TBG TR1
V
~
G
~
CCC5
G
~
CCC6
CCC4
G
~
0
1
Dod-Co1
AC Voltag..
DOD380/B
DOD380/A
BMR150/BOXM
MBT380/A
MBT380/B
Z
W
LGK150/BB2
LGK150/BB1
Tr-CCC6
Gt-Tr402 Gt-Tr401
Tr-CCC5
MDK380/A
KRK-BSL380 Z
Bsl Tr402
Bmr Tr404
Tr-CCC4
11
MBT150/A
MBT150/B
BMRT/BB1
BMRT/BB2
11
KIJ-GT380 Z
TBG-EHV380 G
V
~
0
Dtc-LC403
AC Voltag..
Dtc-LC402
11
Dtc Tr402
Mbt Tr402
11
BMR-DOD Z
Dtc Tr403
MBT-BMR W
DTC380/B
DTC380/A
MBT-BMR Z
V
~
BMR-DOD W
V
~
AC Voltag..
Mbt Tr401
DOD150/B
11
Dod-LC402
Dod-Dtc wt
DOD150/A
Dtc-Hgl zw
Dod-Dtc zt
0
12
Dod Tr402
Dtc-Hgl wt
0
11
12
Mbt Tr403 Mbt Tr404
11
AC Voltag..
V
~
HGLO11/BB1
HGLO11/BB2
Dod Tr403
Dod-LC403
V
~
TR CC-B
12
V
~
AC Voltag..AC Voltag..
V
~
~
G
CCA
V
~
13
Hgl Tr403
AC Voltag..
13
Hgl Tr401
Dod Tr404
AC Voltag..
3
AC Voltag..
Tr-CCA
GTB380/B
GTB380/A
~
G
~
G
CCC1
13
~
G
CCC2
Hgl Tr402
Tr-CCC1
A8
G
~
HGL380/B
HGL380/A
Tr-CCC2
82
CC-B
KIJ380/B
KIJ380/A
~
G
CCC3
MBT380..
Appendix C
Figure C.1: A overview showing the TenneT 380 kV network modelled in PowerFactory
DIgSILENT
Tr-CCC3
TBG-EHV380 Z
GT-TBG380 W
KIJ-GT380 W
TBG-EHV380 W
Overview of the EMT Grid Models
Figure C.2: A overview showing the TenneT 380 kV network modelled in ATPEMTP
83
APPENDIX
D
Resulting Plots TRV Study
D.1
Series Reactor
85
Appendix D
Transient Recovery Voltage
×105
9
8
550
Phase a
7
420
Voltage [V]
6
5
4
3
2
1
0
0.0995
0.0996
0.0997
0.0998
0.0999
0.1
0.1001
Time [s]
Figure D.1: Undamped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase a
Transient Recovery Voltage
×105
0
−1
−2
Voltage [V]
−3
−4
−5
−6
420
−7
−8
550
Phase b
−9
0.0982
0.0983
0.0984
0.0985
0.0986
0.0987
0.0988
Time [s]
Figure D.2: Undamped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase b
86
Resulting Plots TRV Study
Transient Recovery Voltage
×105
9
8
550
Phase a
7
420
Voltage [V]
6
5
4
3
2
1
0
0.0995
0.0996
0.0997
0.0998
0.0999
0.1
0.1001
Time [s]
Figure D.3: Damped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase a
Transient Recovery Voltage
×105
0
−1
−2
Voltage [V]
−3
−4
−5
−6
420
−7
−8
550
Phase b
−9
0.0982
0.0983
0.0984
0.0985
0.0986
0.0987
0.0988
Time [s]
Figure D.4: Damped TRV with T30 capability envelope for 420 kV and 550 kV
breaker, phase b
87
Appendix D
D.2
88
Magnetic Shielded Core SCFCL
Resulting Plots TRV Study
Transient Recovery Voltage
×105
0
−1
−2
Voltage [V]
−3
−4
−5
−6
420
−7
−8
550
Phase b
−9
0.0928
0.0929
0.093
0.0931
0.0932
0.0933
0.0934
Time [s]
Figure D.5: TRV with T30 capability envelope for 420 kV and 550 kV breaker, phase
b
Transient Recovery Voltage
×105
9
8
550
Phase c
7
420
Voltage [V]
6
5
4
3
2
1
0
0.0898
0.0899
0.09
0.0901
0.0902
0.0903
0.0904
Time [s]
Figure D.6: TRV with T30 capability envelope for 420 kV and 550 kV breaker, phase
c
89
APPENDIX
E
Grid Parameters
91
Table E.1: Generator parameters
xq
p.u.
0,31
0,355
0,355
0,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
xd
p.u.
0,22
0,242
0,242
0,1746
0,1746
0,1746
0,1746
0,1746
0,1746
0,2
0,2
0,2
xd
p.u.
0,3
0,5
0,5
0,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
0,3
xq
p.u.
0,22
0,242
0,242
0,2
0,2
0,2
0,2
0,2
0,2
0,2
0,2
0,2
xq
p.u.
0,889462
1,74413
1,74413
1
1
1
1
1
1
1
1
1
Td
s
0,029806
0,034085
0,034085
0,04365
0,04365
0,04365
0,04365
0,04365
0,04365
0,05
0,05
0,05
Td
s
0,057831
0,115942
0,115886
1
1
1
1
1
1
1
1
1
Tq
s
0,1012
0,06776
0,06776
0,05
0,05
0,05
0,05
0,05
0,05
0,05
0,05
0,05
Tq
s
00
xd
p.u.
2,49
2,07
2,071
2
2
2
2
2
2
2
2
2
0
xrl
p.u.
2,6
2,3
2,3
2
2
2
2
2
2
2
2
2
00
xl
p.u.
0
0
0
0
0
0
0
0
0
0
0
0
0
rstr
p.u.
0,18
0,18
0,1
0,1
0,1
0,1
0,1
0,1
0,1
0,1
0,1
0,1
00
Pow.Fact.
0,001
0,00011
0,00011
0,001
0,001
0,001
0,001
0,001
0,001
0,001
0,09
0,09
0
App.Pow.
MVA
0,8
0,78
0,78
0,8
0,8
0,8
0,8
0,8
0,8
0,8
0,85
0,85
00
Name
775
770
770
343
343
343
343
343
343
3125
524
524
0
A8
CC-B
CC-A
CCC1
CCC2
CCC3
CCD1
CCD2
CCD3
BSL
Sloe10
Sloe20
92
93
HV-rtd.Pow.
MVA
500
500
500
500
500
450
450
450
500
500
450
450
450
450
450
350
350
350
450
450
450
500
500
500
Name
Bmr Tr404
Bsl Tr401
Bsl Tr402
Bsl Tr403
Dod Tr402
Dod Tr403
Dod Tr404
Dtc Tr402
Dtc Tr403
Ehv Tr401
Ehv Tr402
Ehv Tr403
Ehv Tr404
Gt-Tr401
Gt-Tr402
Hgl Tr401
Hgl Tr402
Hgl Tr403
Mbt Tr401
Mbt Tr402
Mbt Tr403
Mbt Tr404
TBG TR1
TBG TR2
500
500
500
500
500
450
450
450
500
500
450
450
450
450
450
350
350
350
450
450
450
500
500
500
MV-rtd.Pow.
MVA
167
167
167
167
167
150
150
150
167
167
150
150
150
150
150
115
115
115
150
150
150
167
167
167
LV-rtd.Pow.
MVA
380
380
380
380
380
380
380
380
380
380
380
380
380
380
380
381
381
381
380
380
380
380
380
380
HV-rtd.Volt.
kV
150
150
150
150
150
150
150
150
150
150
150
150
150
150
150
117
117
117
150
150
150
150
150
150
MV-rtd.Volt.
kV
Table E.2: Transformer parameters
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
10
10
10
50
50
50
50
50
50
LV-rtd.Volt.
kV
20,5
20,5
20,5
20,5
20,5
18
18,2
18,2
20,5
20,5
18,2
18
18
18
18
16,1
16,1
16,1
18
18
18,2
20,5
20,5
20,5
HV-MV-Shc.Volt.
%
5,8
5,8
5,8
5,8
5,8
5,7
5,8
5,8
5,8
5,8
5,8
5,7
5,7
5,7
5,7
6,74
6,74
6,74
5,7
5,7
5,8
5,8
5,8
5,8
MV-LV-Shc.Volt.
%
Name
13,7
13,7
13,7
13,7
13,7
12,4
12,7
12,7
13,7
13,7
12,7
12,4
12,4
12,4
12,4
8,4
8,4
8,4
12,4
12,4
12,7
13,7
13,7
13,7
LV-HV Shc.Volt.
%
1140
1140
1140
1140
1140
1540
1250
1250
1140
1140
1250
1540
1540
1540
1540
630
630
630
1540
1540
1250
1140
1140
1140
HV-MV Cop.Los.
kW
235
235
235
235
235
290
255
255
235
235
255
290
290
290
290
153
153
153
290
290
255
235
235
235
MV-LV Cop.Los.
kW
260
260
260
260
260
360
270
270
260
260
270
360
360
360
360
177
177
177
360
360
270
260
260
260
LV-HV Cop.Los.
kW
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
HV-Vec.Grp.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
HV-Ph.Shift
*30deg
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
YN
MV-Vec.Grp.
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
MV-Ph.Shift
*30deg
Table E.3: Transformer parameters, continued
Bmr Tr404
Bsl Tr401
Bsl Tr402
Bsl Tr403
Dod Tr402
Dod Tr403
Dod Tr404
Dtc Tr402
Dtc Tr403
Ehv Tr401
Ehv Tr402
Ehv Tr403
Ehv Tr404
Gt-Tr401
Gt-Tr402
Hgl Tr401
Hgl Tr402
Hgl Tr403
Mbt Tr401
Mbt Tr402
Mbt Tr403
Mbt Tr404
TBG TR1
TBG TR2
94
95
Length
km
41,7
41,7
120
120
45,4
45,4
58,65
58,65
51
51
19
19
23
23
23
57,9
57,9
41,4
41,4
40,9
40,9
40,9
Name
BMR-DOD W
BMR-DOD Z
BSL-TBG380 W
BSL-TBG380 Z
Dod-Dtc wt
Dod-Dtc zt
Dtc-Hgl wt
Dtc-Hgl zw
EHV-MBT W
EHV-MBT Z
GT-MDK380 W
GT-MDK380 Z
GT-TBG380 G
GT-TBG380 W
GT-TBG380 Z
MBT-BMR W
MBT-BMR Z
MDK-KRK380 W
MDK-KRK380 Z
TBG-EHV380 G
TBG-EHV380 W
TBG-EHV380 Z
0,969704
0,970228
1,776
1,776
1,155497
1,155497
1,491021
1,491021
1,191047
1,191047
0,478929
0,478929
0,539353
0,539353
0,529098
1,346384
1,346384
1,04356
1,04356
0,959111
0,959111
0,940874
R1
Ω
11,42179
11,42121
27,84
27,84
12,37199
12,37199
16,04022
16,04022
13,96164
13,96164
5,25375
5,25375
6,849686
6,849686
6,848017
15,85909
15,85909
11,44765
11,44765
12,18053
12,18053
12,17756
X1
Ω
0,546171
0,546185
0,61389
0,61389
0,788722
0,788722
0,665231
0,665231
0,251057
0,251057
0,27993
0,27993
0,280661
0,758352
0,758352
0,54704
0,54704
0,497788
0,497788
0,499088
C1
µF
0,315494
0,315547
0,367692
0,367692
0,462944
0,462944
0,361112
0,361112
0,144499
0,144499
0,184947
0,184947
0,192146
0,438058
0,438058
0,314857
0,314857
0,328885
0,328885
0,341686
C0
µF
Table E.4: Transmission line parameters
4,435373
4,459465
3,827423
3,827423
6,386832
6,386832
5,18715
5,18715
2,002156
2,002156
2,410311
2,410311
2,360048
6,149535
6,149535
4,362593
4,362593
4,286161
4,286161
4,19678
R0
Ω
30,43955
30,39635
29,23587
29,23587
41,87643
41,87643
35,25316
35,25316
13,14126
13,14126
16,68108
16,68108
17,14094
42,31007
42,31007
28,63412
28,63412
29,66331
29,66331
30,48106
X0
Ω
Name
380
50
50
50
50
6
6
6
50
50
Nom.Volt.
kV
150
45
45
45
45
1
1
1
75
75
Qmax
Mvar
150
0
0
0
0
250
250
250
0
0
L
Hz
2,939149
84,88263
84,88263
84,88263
84,88263
84,88263
84,88263
84,88263
84,88263
84,88263
C
uF
26,45234
0
0
0
0
0
0
0
0
0
Capacitance C1
uF
3,306543
0
0
0
0
84,88263
84,88263
84,88263
0
0
Capacitance C2
uF
383,0329
176,8388
176,8388
176,8388
176,8388
4,774649
4,774649
4,774649
106,1033
106,1033
L
mH
900
0
0
0
0
0
0
0
0
0
Par.Resist.
Ω
Table E.5: Shunt parameters
Dod-Co1
Dod-LC402
Dod-LC403
Dtc-LC402
Dtc-LC403
Ens Spoel 1
Ens Spoel 2
Ens Spoel 3
Gtb-LC401
Gtb-LC402
96
Table E.6: Parameters for the equivalent sources
Name
R0
Ω
X0
Ω
R1
Ω
X1
Ω
BMR150
BSL150
DOD150
EHVO150
GTB150
HGLO110
HGLO380
KIJ380
LGK150
MBT150
Niederrhein
Rommerskirchen
Siersdorf
TBN150
Van Eyck 1
Van Eyck 2
Zandvliet
1,2
2,44
3,53
0,3
0,37
0,45
1,19
0,59
5,11
0,59
4,01
9,02
6,76
0,59
1,5
2,83
0,19
9,3
12,15
18,81
3,17
3,21
2,84
10,25
5,85
25,17
4,55
40,11
90,22
67,61
4,54
17,23
29,03
2,51
1,73
0,11
0,31
0,57
0,15
1,13
0,66
0,27
0,69
0,37
1,47
3,04
3,23
0,38
4,82
2,95
0,28
11,15
3,91
3,47
5,05
2,61
5,72
7,3
6
5,62
3,73
14,71
30,44
32,33
3,61
39,35
31,95
3,22
97