Morten Lerche, s031889
Circuit Breaker Characteristics in
Medium Voltage Equipment under
Various Network Configurations
MSc project, June 2009
Morten Lerche, s031889
Circuit Breaker Characteristics in
Medium Voltage Equipment under
Various Network Configurations
MSc project, June 2009
Circuit Breaker Characteristics in Medium Voltage Equipment under Various Network
Configurations,
This report was prepared by
Morten Lerche, s031889
Supervisor
Lektor Joachim Holbøll
Technical University of Denmark
Department of Electrical Engineering
Centre for Electric Technology (CET)
Elektrovej 325
building 325
DK-2800 Kgs. Lyngby
Denmark
www.elektro.dtu.dk/cet
Tel:
(+45) 45 25 35 00
Fax:
(+45) 45 88 61 11
E-mail: cet@elektro.dtu.dk
Release date:
Category:
30. June 2009
1 (public)
Edition:
First
Comments:
This report is part of the requirements to achieve the Master
of Science in Engineering (MSc) at the Technical University of
Denmark. This report represents 35 ECTS points.
Rights:
c
Morten
Lerche, 2009
Preface
This Master’s thesis was prepared at the Technical University of Denmark
(DTU).
The work is conducted at the Department of Electrical Engineering, Centre
for Electric Technology at DTU.
The work done in this project continues the work performed by Örn I.
Björgvinssonin in his MSs project in 2006. My supervisor has been lector
Joachim Holbøll from Department of Electrical Engineering, which I would
like to thank for guidance, support and inspiration throughout my project.
A thanks should also be directed to engineer assistant Freddie Fahnøe and
operation techinan Flemming Juul Petersen from Department of Electrical
Engineering who have both contributed with great help during the laboratory tests.
I would also like thank my fellow studens and specially PhD student Iván
Arana, for theoretical discussions during the project.
Kgs. Lyngby 2009-06-30
——————————————–
Morten Lerche, s031889
mortenler@gmail.com
Summary
This Master’s thesis presents an investigation of the transient overvoltages
generated by a vacuum circuit breaker. A theoretical model of vacuum circuit breakers is investigated and the parameters used to describe the vacuum
circuit breaker in a simulation model is described.
A series of laboratory test were made in order to examine the transients
created by the breaker and to calculate the parameters which are used to
describe the vacuum circuit breaker in the simulation model. The laboratory setup consists of a transformer, a cable, a vacuum circuit breaker and
a capacitive load. During the tests the cable lenght was varied to study how
network changes effects the transient overvoltages. The load was varied in
order to determine some parameters for the simulation model. The tests
shows that the transient recovery voltage created by a switching operation
is highly dependent on the system configuration. Further more it is shown
how the transient recovery voltage and the breaking angle effects the number reignitions of the vacuum arc.
A simulation model of the laboratory setup is designed and used to test the
vacuum breaker model and the parameters found. The simulations shows the
slower transients and the prestrikes, but the lack of detail in the simulation
model makes the results less precise than desired.
Dansk Resumé
Dette kandidatspeciale præsenterer en undersøgelse af de transiente overspændinger som genereres af vakuumbrydere. En teoretisk model af vakuumbryderen bliver undersøgt og de parametre som bruges til at beskrive
vakuumbryderen i en simuleringsmodel beskrives.
En serie af laboratorietest blev udført for at kunne undersøge de transienter
som bryderen danner og udregne de parametre som bruges til at beskrive
bryderen i simuleringsmodellen. Laboratorieopstillingen består af en transformer, et kabel, en vakuumbryder og en kapacitiv belastning. Under forsøgene blev længden af kablet varieret for at undersøge hvordan ændringer i
netværket påvirker de transiente overspændinger. Belastningen blev varieret for at kunne bestemme nogle af de parametre til simuleringsmodellen.
Forsøgene viser at ”the transient recovery voltage” som dannes ved en skifte
operation er afhænging af netwærks konfigurationen. Derudover vises det
hvordan ”the transient recovery voltage” og brydevinklen påvirker antallet
af gentændinger af vakuum lysbuen.
En simuleringsmodel af laboratorieopstillingen bliver designet og denne model
bruges til at teste vakuumbryder modellen samt de fundne parametre. Simuleringerne viser de langsomme transienter og antændinger af vakuum lysbuen
under en lukke operation, men på grund af manglende detaljeringsgrad i
simuleringsmodellen bliver resultaterne ikke så præsise som ønsket.
List of Acronyms
Acronym
VCB
TRV
RRDS
RDDS
HF
AC
DC
Meaning
Vacuum Circuit Breaker
Transient Recovery Voltage
Rate of Recovery of Dielectric Strength
Rate of Decay of Dielectric Strength
High Frequency
Alternating Current
Direct Current
List of Symbols
Symbol
R
L
C
G
I
V
Vm
t
φ
ω
θ
τ
fT RV
fT RV 10
Unit
Ω
H
F
S
A
V
V
t
rad
rad/s
rad
s
Hz
Hz
fT RV 100
Hz
Ich
|i|
α
β
U
A
B
A
A
s
–
V
V /µs
V
t0
Cc
Dd
topen
s
s
tclose
s
A
µs2
A
µs
Meaning
Resistance
Inductance
Capacitance
Conductance
Current
Voltage
Voltage amplitude
time
Phase angle
Angular frequency
Phase angle at breaker closing time
Time constant
Frequency of transient recovery voltage
Frequency of transient recovery voltage
in the system using the 10m cable
Frequency of transient recovery voltage
in the system using the 100m cable
The chopping current level
Amplitude of current
Contact material constant
Contact material constant
Dielectric withstand
Rate of rise of dielectric strength
Breaker transient recovery voltage
just before current zero
Time of contact seperation
Breaker constant
Breaker constant
Time of a opening operation
of the VCB
Time of a closing operation of the VCB
Symbol
Rclosed
Unit
Ω
Ropen
Ω
VLoad
V
VT rans
V
Vopen
V
Vvacuum
fopen
V /mm
Hz
fopen10
Hz
fopen100
Hz
Z
ex
Ω
–
Vm
Sm
V
VA
Meaning
Resistance over VCB contacts
in closed position
Resistance over VCB contacts
in open position
Voltage measured on the
load side of the VCB
Voltage measured on the
transformer side of the VCB
Dielectric withstand of the
VCB in open position
Dielectric withstand of vacuum
Frequency of the oscillating transient
caused by a VCB opening
Frequency of the oscillating transient
caused by a VCB opening when 10m
cable is used
Frequency of the oscillating transient
caused by a VCB opening when 100m
cable is used
Impeadance of the HTT transformer
Short circuit impeadance of the
transformer
Rated voltage level of transformer
Rated load of transformer
Contents
Preface
vii
Summary
ix
Dansk Resumé
xi
List of Acronyms
xiii
List of Symbols
xv
1 Introduction
1
1.1
Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2
Methods and restrictions . . . . . . . . . . . . . . . . . . . . .
3
1.3
Outline of Report . . . . . . . . . . . . . . . . . . . . . . . . .
4
2 Switching Transients
5
2.1
Closing Circuit Transient . . . . . . . . . . . . . . . . . . . .
5
2.2
Opening Circuit Transient . . . . . . . . . . . . . . . . . . . .
9
3 Vacuum Circuit Breakers
13
3.1
Construction of Vacuum Circuit Breakers . . . . . . . . . . .
14
3.2
Modelling of Vacuum Circuit Breakers . . . . . . . . . . . . .
16
4 Laboratory Setup
25
4.1
The Existing Setup . . . . . . . . . . . . . . . . . . . . . . . .
25
4.2
Improvements to the Existing Setup . . . . . . . . . . . . . .
30
xviii
5 Laboratory Tests and Results
5.1 Preparatory tests . . . . . . . . . . . .
5.2 Transient Recovery Voltage . . . . . .
5.3 Chopping Current . . . . . . . . . . .
5.4 Reignitions . . . . . . . . . . . . . . .
5.5 High Frequency Quenching Capability
5.6 Closing the circuit . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
33
36
37
41
43
47
51
6 Simulations
57
6.1 Opening the Vacuum Circuit Breaker . . . . . . . . . . . . . . 58
6.2 Closing the Vacuum Circuit Breaker . . . . . . . . . . . . . . 64
7 Discussion
7.1 Voltage Circuit Breaker Model Parameters .
7.2 Opening the Vacuum Circuit Breaker . . . .
7.3 Closing the Vacuum Circuit Breaker . . . .
7.4 Further Work . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
67
67
68
70
72
8 Conclusion
75
References
77
Appendix
79
List of Figures
79
List of Tables
82
A Plotting results
85
B Results of the TRV Calculations
89
C Results of Current Chopping Calculations
91
D Results of the Rate of Rise of Dielectric Strength Calculations
93
E Results of HF Current Quenching Capability Calculations
97
F Results of Rate of Decay of Dielectric Srength
99
Chapter
1
Introduction
In the last part of the 19th century the demand of electric power started
increasing rapidly because of new technical inventions. The increased use
of electrical lighting, the introduction of the DC-motor and railway systems
were just some of the inventions that called for a power system. In 1882
Tomas Edison opened the worlds first power station in New York City, this
is referred to as the beginning of the electric utility industry. From this
starting point and until 1872 the electric utility industry grew at a remarkable pace [3]. In 1885 William Stanley developed the first commercial and
practical transformer and overcame the limitation of maximum distance and
load in the exciting network. The year after the first AC distribution system
was installed in Massachusetts. Nikola Tesla presented the first ideas of a
polyphase AC system in 1888 introducing induction and synchronous motors, and the first transmission of tree-phase alternating current took place
during the international electricity exhibition in Frankfurt in 1891, transmitting power at 12kV over 175km [3].
The industrialization during the 20th century made the electrical infrastructure a critical point. Interconnection of local distribution networks and the
construction of large power plants were some of the main demands created
by the industrialization. These demands have led us to the power networks
we have today, which are designed to transport energy as efficient and reliably, from the producer to the consumer, as possible. To deal with the
challenges of this task many network components have been developed and
some of the main components of today’s power networks are overhead lines,
cables, transformers, circuit breakers and switches.
For many years lightning were the only phenomenon that could create steep
front pulses in the power system and thereby produce high overvoltages [1].
When lightning strokes terminates on or near a power line they create a
2
path between the cloud and the power line or the adjacent earth and hereby
changes the circuit conditions and creates a transient overvoltage. In order
to protect the insulation of the equipment against the lightning overvoltages
surge arresters were used, they kept the voltage on a level that was not
harmful for the protected equipment. The research in this area was stopped
until an increased number of failures were detected on the insulation of the
equipment, even at low voltage levels. It was discovered that these failures
were caused by some of the equipment that had been implemented in the
power network. One of the components that led to failure of insulation was
the breakers used in the electrical grid.
Many types of breakers have been used in the power grid during the years.
In the beginning of the 20th century oil circuit breakers were mainly used. In
1959, SF6 circuit breakers came to the marked, this type of circuit breaker
had several advantages such as long life time and high reliability [15]. The
first vacuum circuit breaker (VCB) was constructed in the 1960s. VCBs
have low maintenance costs, good durability and provide the best breaker
solution for medium voltage below 24kV [1]. But the use of VCBs resulted in
worldwide reports on transformer insulation failures possibly due to switching operations of VCBs, also transformers that had previously passed all
the standard tests and complied to all quality requirements suffered failures
[2]. It has still not been finally proved that the high frequency transients
have a negative influence on the transformer insulation. Some studies give
a description of the phenomenon that produces the high overvoltages internally in the transformer winding, which are potentially responsible for the
transformer insulation failure during the high frequency transients [10]. A
problem of the transformer insulation failure also occured in the wind parks
(WP) Middelgrunden and later at Hornsrev where almost all transformers
had to be replaced with new ones due to the insulation failure [14]. This
problem is suspected to be caused by fast switching breakers as e.g. VCBs.
VCBs are the most used breaker type in the medium voltage area, due to
its excellent breaking abilities and economic advantages. But as mentioned
the VCB also seems to cause some faults in the power network. The physical phenomena in the VCB during a switching operation are very complex,
and therefore the models of VCBs are also very complex. When performing
a switching operation a conducting plasma channel is created between the
breaker contacts, this channel is called the vacuum arc. When the arc is extinguished a transient recovery voltage appears across the terminals and this
voltage can give rise to another breakdown in the vacuum and create a new
conducting plasma channel between the breaker contacts. The arc formed by
the plasma can become unstable and create high frequency currents, which
the breaker must be able to interrupt. The advanced and unstable nature of
the conducting plasma channels does that there is no universal precise vac-
Introduction
3
uum arc model. The models that exist all take into account the stochastic
properties of the phenomena that take place in the breaking process [7].
1.1
Purpose
The purpose of this thesis is to test a VCB and to observe the physical
phenomena that occur in the VCB during the interruption process, especially
the phenomena that cause high frequency transients. Based on laboratory
tests the parameters, that are used to model the VCB, will be determined.
In order to study the laboratory setup it is desirable to make a precise
simulation model of the setup, this simulation model can be used to test
the behaviour of the VCB model and compare it with the tests made on the
VCB.
1.2
Methods and restrictions
The VCB model that is used in this project takes into account the following
stochastic properties of the VCB:
• Current chopping ability.
• Recovery of dielectric strength.
• High frequency current quenching.
In the test setup, used in order to determine these properties of the VCB,
only one phase of the VCB is connected and measurements are performed
on this phase. In order to supply the VCB with high voltages a transformer
is used, the measurements are performed on the high voltage side on the
transformer. In order to change the network configurations, two similar cables with different length are used to connect the VCB and the transformer.
Two capacitive loads are used to load the system, these loads are both 0.5µF
and the maximum load in the system is therefore 1.0µF . This means that
the current running through the VCB during the tests will be rather limited.
When analysing the results of the VCB tests, the main focus will be on
determining the parameters for the VCB model. As these parameters are
mainly determined by the opening process of the VCB most analysis will be
on VCB open operations. As the parameters are mainly described by the
very fast transients created by the VCB the main work will be put in this
area.
The simulations are performed in PSCAD, a model of the laboratory setup
4
1.3 Outline of Report
is created using lumped circuit elements for the transformer and the cable.
This will make the results of the simulations less accurate, but lumped circuit elements are used to be able to finish the simulations within the time
limitations of the project.
1.3
Outline of Report
The structure of the thesis is as follows:
• Chapter 2 : Switching Transients
This chapter will introduce two examples of switching transients ocurring due to an opening and a closing action of an ideal switch. For one
example the full result of the transient current, caused by opening the
switch, will be calculated, where the other example will explain the
areas of interest.
• Chapter 3 : Vacuum Circuit Breakers
In this chapter the design principles of VCBs are described and the
theory behind the vacuum arc will be explained. A model of the VCB
will be introduced and the different parameters of the model will be
explained according to the physical phenomena occurring in the VCB.
• Chapter 4 : Laboratory Setup
A description of the laboratory setup and its components is given in
this chapter. The improvements and adjustment made on the setup
are also described.
• Chapter 5 : Laboratory Tests and Results
This chapter concerns with the performed tests and the treatment of
the test results. In this chapter the parameters of the VCB model
will be calculated and the accuracy of the results will be discussed.
Methods for achieving more accurate results will be discussed.
• Chapter 6 : Simulations
In this chapter the simulation model will be described. The results
from the PSCAD simulation of an opening and a closing operation of
the VCB is analysed.
• Chapter 7 : Discussion
In this chapter a discussion of the achieved results will be made, the
discussion will mainly focus on comparing the simulation results with
the measured results. A description of the further work that is needed
in order to make a fully working model of the VCB will also be given.
• Chapter 8 : Conclusion
This section gives the conclusion.
Chapter
2
Switching Transients
An electrical transient is caused by a sudden change in the circuit conditions [4]. This change could be when a lightning hits the ground near a high
voltage line or when lightning strikes a substation directly. But the most
common transients in the power systems occur as a result of a switching action. This could be when circuit breakers, fuses, disconnectors etc, open and
close in order to switch off parts of the network, interrupt higher currents
and clear faults in the network and hereby secure the network. These switching actions give rise to switching transients. The transient time is usually
very short, in the range of microseconds to milliseconds, but the transients
periods are very important as it is in this period the network components
are subject to the greatest stress. The transients may shorten the lifetime
of the components in the network or in worst case cause a breakdown of the
power system. In this chapter, two switching examples will be examined,
both examples will use an ideal swich to represent a network switch as e.g.
a VCB. An ideal switch acts as a disconnection when open and as a short
circuit when closed and it switches between the two stages instantly. Using
an ideal switch gives a good idea of what happens when a VCB is opened or
closed even though it does not have the same characteristic. An ideal switch
does not have the influence of reignitions and high frequency currents, which
excist in a VCB due to arc instability.
2.1
Closing Circuit Transient
In this example a sinusoidal voltage is switched on to a series connection of
an inductance and a resistance. Figure 2.1 represent the simplest case of a
high-voltage circuit breaker closing into a short-circuited transmission line
or a short-circuited underground cable. The voltage source V represents
the electromotive force from the connected generators [15]. The inductance
L represents the synchronous inductance from the generators, the leakage
6
2.1 Closing Circuit Transient
R
S
L
Vmsin(ωt+θ)
Figure 2.1: An sinusoidal voltage is switched on an RL-circuit.
inductance in the transformers and the inductance of bus bar, cables and
transmissions lines. The resistance R represents the resistive losses of the
network. Since the network consist of linear elements only, the current flowing in the network after closing the switch can be seen as the superposition
of a transient current and a steady-state current. Applying Kirchhoff’s voltage law on the circuit in figure 2.1 gives us the nonhomogeneous differential
equation that represents the circuit after the switch has been closed [15]
R·I +L·
dI
= V,
dt
(2.1)
where V represents the sinusoidal voltage of the source and I is the current
in the circuit.
V
= Vm · sin(ωt + θ)
⇔
V
= Vm · [sin(ωt)cos(θ) + cos(ωt)sin(θ)]
(2.2)
The angle θ is the phase angle at which the switch is closed. The term
sin(ωt+θ) has been rewritten in order to make the solution of the differential
equation easier. The steady state power factor of the load in figure 2.1 is
given by
cos(φ) =
R
R
=p
.
2
|L|
(R + ω 2 · L2 )
(2.3)
The differential equation is solved by the Laplace method. Inserting equation
(2.2) in (2.1) gives
R·I +L·
dI
= Vm · (sin(ωt)cos(θ) + cos(ωt)sin(θ)),
dt
(2.4)
Laplace transforming both sides yields
R · i(s) + L · s · i(s) − L · I(0) = Vm
ω · cos(θ) s · sin(θ)
+ 2
s2 + ω 2
s + ω2
.
(2.5)
Switching Transients
7
Setting I(0) = 0 in figure 2.1 makes it possible to find an expression for the
current
ω · cos(θ) s · sin(θ)
⇔
R · i(s) + L · s · i(s) = Vm
+ 2
s2 + ω 2
s + ω2
ω · cos(θ) s · sin(θ)
Vm
⇔
+ 2
i(s) =
L·s+R
s2 + ω 2
s + ω2
Vm
1
ω · cos(θ) s · sin(θ)
i(s) =
+ 2
.
(2.6)
·
L s+ R
s2 + ω 2
s + ω2
L
In order to transform back into the time domain the equation is rewritten
to the following form
i(s) =
A
B·s
+
,
2
2
(s + α)(s + ω ) (s + α)(s2 + ω 2 )
(2.7)
where the constants
A=
Vm
· ω · cos(θ),
L
B=
Vm
· sin(θ),
L
α=
R
.
L
(2.8)
Equation (2.7) can be transformed back into the time domain when the
following two inverse Laplace transforms are known
L
−1
A
A
= 2
· [e−α·t
2
2
(s + α)(s + ω )
(s + ω 2 )
− cos(ω · t) +
L
−1
α
sin(ω · t)]
ω
B·s
B
= 2
· [−α · e−α·t
2
2
(s + α)(s + ω )
(s + ω 2 )
+ ω · sin(ω · t) + αcos(ω · t)]
(2.9)
(2.10)
Using equation (2.9) and (2.10), equation (2.7) can be transformed into the
time domain
A
B·s
−1
+
i(t) =L
(s + α)(s2 + ω 2 ) (s + α)(s2 + ω 2 )
=
(s2
A
α
· [e−α·t − cos(ω · t) + sin(ω · t)]
2
+ω )
ω
B
+ 2
· [−α · e−α·t + ω · sin(ω · t) + αcos(ω · t)].
(s + ω 2 )
(2.11)
8
2.1 Closing Circuit Transient
Closing a RL−circuit at 90 degrees
0.8
Resultant current I(t)
Steady−state current
Transient current
0.6
0.4
Current[I]
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2
0
20
40
60
80
100
Time[ms]
Figure 2.2: The sinusoidal voltage is switched on to the RL-circuit with a switching angle of 90◦ .
Incerting A and B from (2.8) into equation (2.11) yields
i(t) =
Vm · ω · cos(θ)
α
· [e−α·t − cos(ω · t) + sin(ω · t)]
L · (s2 + ω 2 )
ω
Vm · sin(θ)
· [−α · e−α·t + ω · sin(ω · t) + αcos(ω · t)]. (2.12)
+
L · (s2 + ω 2 )
Equation (2.12) can be simplified by using the power factor described in
(2.3) and inserting α from (2.8), the following expression for the current can
be found [4]
R
Vm
i(t) = √
[sin(ω · t + θ − φ) − sin(ω − φ)e− L ·t ].
R 2 + ω 2 · L2
(2.13)
The first term is the steady-state term, it has an amplitude of Vm /|Z| and
it has a phase angle of −φ with respect to the voltage. The second term is
R
the transient term, it includes an exponential function e− L ·t . At t = 0 the
steady-state term and the transient term are the same but with different
sign, assuring that the current starts in zero when the breaker closes. In
figure 2.2 the transient current, the steady-state current and the resultant
current is shown for a switching angle of θ − φ = 90◦ . As figure 2.2 shows
the transient term starts at its lowest possible value, which is equal to the
amplitude of the current. Opening the breaker at θ − φ = 90◦ gives the
largest transient, on the other hand opening the θ − φ = 0◦ makes the
Switching Transients
9
Closing a RL−circuit at 0 degrees
0.8
Resultant current I(t)
Steady−state current
Transient current
0.6
Current[I]
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
0
20
40
60
80
100
Time[ms]
Figure 2.3: The sinusoidal voltage is switched on to the RL-circuit with a switching angle of 0◦ .
transient term turn zero. This can be seen in figure 2.3. It is seen that the
transient term is zero, which causes the resultant current to be equal to the
steady state current from the moment of contact separation.
2.2
Opening Circuit Transient
When a switch opens in order to switch off parts of the network or clear faults
in the network it can cause high overvoltages in the network. This section
will investigate what happens when interrupting a capacitive current using
an ideal switch. A simple model of the laboratory setup used in this project
is seen in figure 2.4, the inductance of the circuit represents a transformer,
the capacitance C1 represents a cable and the capacitance C2 is the load
of the network. When opening the switch in the system in figure 2.4 the
circuit will only consist of the inductance L and the capacitance C1 . After
the switch has opened, a HF voltage appears across the switch contacts, this
voltage is called the transient recovery voltage (TRV). This transient will
have the frequency
fT RV =
1
√
.
2 · π L · C1
(2.14)
The TRV has no real influence on the switching when using a ideal switch,
but it is of high importance of the switching in real switching devices. In real
10
2.2 Opening Circuit Transient
S
L
Vmsin(ωt+θ)
C1
C2
Figure 2.4: An sinusoidal voltage is switched on an RL-circuit
switching devices the characteristics (amplitude and rate of rise) determines
if the current interruption is successful or fails (reignition of the arc between
the contacts). As seen in eqation (2.14) the frequency of the TRV depends
on the circuit in which the ideal switch or circuit breaker is working. In the
example from figure 2.4, the TRV created by the switch when opening the
circuit could look like the graph in figure 2.5, this figure shows how the TRV
effects the transformer side of the circuit seen in figure 2.4. The TRV can
be harmful for network equipment since its high amplitude can exceed the
voltage level of the system.
As mentioned the circuit in figure 2.4 represents the setup used in this
project. In [11] the capacitance of the cable used is found to be 157.57 ·
10−12 F/m and the in this project the value of L used to represent the transformer is found to be 0.318H (see chapter 6). In this project a 10m and a
100m cable is used, for the 10m cable the frequency of the TRV is expected
to be
fT RV 10 =
1
p
= 7110Hz,
2 · π 0.318H · 157.57 · 10−12 F/m · 10m
(2.15)
and for the 100m cable a frequency of
fT RV 100 =
1
p
= 2248Hz.
2 · π 0.318H · 157.57 · 10−12 F/m · 100m
(2.16)
These TRVs are the only effect of interrupting current with ideal switches,
but as mentioned in the use of real switching devices, such as VCBs, the
TRV can cause reignitions of the conducting arc between the switching contacts. These reignitions can lead to high overvoltages and HF currents in
the system. In order to describe the phenomena of reignitions in VCBs a
more detailed study of the design and principles of the VCB must be made.
This investigation is done in the following chapter.
Switching Transients
11
Simulation of VCB opening
Trans. side voltage[kV]
10
5
0
−5
−10
−15
50
55
60
65
70
75
80
Time[ms]
Figure 2.5: The figure shows the voltage on the transformer side of a VCB under
a opening operation in a circuit with a capacitive load.
12
2.2 Opening Circuit Transient
Chapter
3
Vacuum Circuit Breakers
A circuit breaker is in principle an electrical switch that is designed to protect
the power system [9]. Circuit breakers play an important role in transmission and distribution networks. They must clear faults and isolate faulted
network sections fast and clearly and they are also used for normal load
switching [7]. For a circuit breaker to fulfil its purposes the following is
required [15]:
• It functions as a good conductor in closed position.
• It functions as a good insulator in open position.
• It is able to switch from open to closed in a short period of time.
• It does not cause overvoltages during switching.
• It is reliable in its operation.
When a circuit breaker interrupts a current, an electric arc is usually formed
between the breaker contacts and the current continues to flow in this arc.
The current interruption is performed by cooling the arc plasma so that the
electric arc disappears. Circuit breakers are classified according to the cooling and extinguishing medium used. There are four main types of circuit
breakers namely, oil, air blast, vacuum and SF6 circuit breakers. This thesis
concerns with the functions of a vacuum circuit breaker (VCB).
Vacuum is used as an extinguishing medium for medium voltage circuit
breakers. VCBs have excellent interruption and dielectric recovery characteristics and can interrupt the high frequency currents which results from
arc instability [16]. VCBs are primarily designed for switching operations in
capacitive circuits [12]. The main advantages of the VCB are:
• It has excellent interruption capability.
14
3.1 Construction of Vacuum Circuit Breakers
• It can interrupt high frequency currents, created by arc instability.
• It is completely self-contained and does not need supply of gasses or
liquids.
• It does not need maintenance.
• It is not flammable.
These advantages of the vacuum breaker technique have been the driving
force of VCB development [1]. Due to the fact that there is nothing to
ionize between the contacts in VCBs, the characteristics of the electric arc
in VCBs are different than the electric arc in other types of breakers. VCBs
have a very little arc and the arc extinguishes with small distance between
the breaker contacts [15].
3.1
Construction of Vacuum Circuit Breakers
A VCB consist, like other circuit breakers, of two contacts, a fixed contact
and a moving contact. The moving contact has two positions, one where
it is touching the other contact and one where the two contacts are apart.
When the contacts are touching the VCB is conducting current and when the
contacts are apart the VCB is not conducting current. The two contacts of a
VCB are inside a vacuum chamber. When the moving contact starts to move
away from the fixed contact, an arc is formed between the two contacts and
the VCB does not stop conducting current before this arc is extinguished. In
figure 3.1 the basic concept of the VCB design is shown. The moving contact
is normally moved by a stored-energy operating mechanism, in most cases a
closing and an opening spring [5]. These springs stores the energy to open
and close the VCB, when the closing spring gets released the VCB closes.
During the closing of the VCB the opening spring is charged so that the
VCB is ready to open immediately after the closing operation is over. After
the closing operation is over the closing spring recharges automatically.
3.1.1
Vacuum Arc
The vacuum arc is a key element when analysing the behaviour of a VCB.
The name vacuum arc is not entirely accurate, because an electric arc cannot
exist in vacuum [5]. The arc that appears between the contacts of a VCB is
a result of metal-vapour, ion- and electron emission. After being established
the vacuum arc is relatively stable and will draw energy from the electrical
system until the current reaches a zero crossing and thereby removes the
energy source. When conducting small currents the vacuum arc can become
unstable and extinguish before current zero is reached, this phenomenon is
Vacuum Circuit Breakers
15
Figure 3.1: The design principle of a VCB, showing contacts, arching chamber
and insulation, the picture is taken from [12] page 8.
called current chopping.
Depending on the current level and on the size and shape of the contact
the vacuum arc appears in different ways [5]. At lower currents small spots
on the negative electrode (the cathode) appear. These cathode spots are in
constant movement over the cathode surface. Electrons and ions radiates
from the spots and contributes with around 50A to 150A depending on the
cathode material [15]. The plasma channel formed by the emitted electrons
and ions is called a vacuum arc, this arc connects the cathode and the anode (the positive electrode). After leaving the cathode the arc spreads out
filling almost the entire volume of the vacuum chamber before hitting the
anode. The electrons and ions leave the arc and get collected all over the anode and for this reason the arc is said to be in diffuse mode at lower currents.
When the current is increased the arc takes a different form, the arc be-
16
3.2 Modelling of Vacuum Circuit Breakers
Figure 3.2: A vacuum interrupter with slits in the contacts to avoid uneven erosion of the contact surface, this picture is from [15] page 66.
comes focused on a small area of the anode. These spots are normally
formed around a sharp edge on the contact. Due to the high current density
in these anode spots the contact material evaporates and when the vapour
is ionised it supplies positive ions to the arc. The cathode spots becomes
grouped together, giving the arc a much more defined and columnar appearance and the arc is said to be in constrict mode [5].
3.1.2
Construction of Vacuum Circuit Breaker Contacts
The constrict mode leads to erosion of both contacts, in diffuse mode the
cathode spots leads to evaporation but in the constrict mode melting occurs
at both contacts especially at the anode [5]. To avoid uneven erosion of the
surface of the contacts the arc should be kept in motion or kept burning in
diffused mode. The most common way of avoiding melting is to make slits
in the contacts, as showed in figure 3.2, by doing this the arc is being kept in
diffuse mode. The contact in figure 3.2 provides a axial magnetic field and
it is this field that keeps the arc in diffuse mode. This means that the stress
on the disc shaped contact surfaces is uniform and local melting is avoided
[12].
3.2
Modelling of Vacuum Circuit Breakers
In order to study the behaviour of VCBs it is desirable to describe their
physical phenomena by a mathematical model that can be used for simulations. In this project a breaker model will be investigated and be applied
on the VCB tested in the project. The model used in this project describes
Vacuum Circuit Breakers
17
the VCB according to the follow parameters:
• The chopping current.
• The dielectric withstand.
• The high frequency quenching capability.
The model is developed and described in [7]. The parameters used, and
their effect on the VCB will be described in the following sections.
3.2.1
Current Chopping
Current chopping is a phenomena that can lead to overvoltages, it occurs
when small capacitive and inductive currents are interrupted [1]. When the
vacuum arc is conducting a small current it will become very unstable and
normally it will disappear and cause the current to be interrupted before it
reaches its natural zero. This premature interruption of the current is called
current chopping. The value of the current when the arc extinguishes is
called the chopping current level and is referred to as Ich . Figure 3.3 shows
current chopping during switching of a VCB.
The value of the chopping level depends mainly on the type of contact material used in the breaker but also on the level and form of the current that
is interrupted. The prediction of the actual current chopping value, considering all its dependents is very complex. But in [13] an expression of the
mean chopping level has been estimated
−1
Ich = (2 · π · f · |i| · α · β)(1−β) ,
(3.1)
where
• f = Power frequency.
• |i| = Amplitude of the load current.
• α,β = Contact material constants.
Equation (3.1) is used to calculate the current chopping level of the VCB.
When simulating the VCB the values of α and β are normally consider to
be α = 6.2 · 10−16 s and β = 14.2 [6].
If the current through the breaker is lower than the chopping level, then
the current is chopped immediately after contact separation. During current
chopping the current declines with a very high di/dt (very steep slope) this
produces very high overvoltages due to the inductances in the network. For
18
3.2 Modelling of Vacuum Circuit Breakers
Current Chopping
−3
5
0.5
0
Current[A]
Current[A]
Current Chopping
1
0
−0.5
x 10
−5
−10
−1
−15
−1.5
36
38
40
42
44
46
48
50
44.84
44.85
Time[ms]
44.86
44.87
44.88
44.89
44.9
44.91
44.92
Time[ms]
(a) The current when the breaker opens (b) Zoomed plot at the point of arc extinguish
Figure 3.3: The figure shows the current during an opening of the breaker. As
seen on figure b the current chops around the value 0,005 and jumps
to zero.
this reason current chopping is considered to be a major disadvantage of
the VCB. The current chopping level for VCBs usually varies between 3A
and 8A [1]. When modelling the chopping current it is usually considered
to have a Gaussian distribution with a standard deviation 15% of the mean
chopping current, that is calculated using equation (3.1) [7].
3.2.2
Reignitions
A reignition of the vacuum arc is a temporary electrical breakdown of the
vacuum in the VCB. The dielectric withstand of the VCB is an important
subject in the analysis of the switching transients that occurs due to reignitions in the VCB [1]. When the breaker contacts start to separate the
withstand voltage of the gap starts increasing. During the first millimetre of
separation the withstand voltage increases linearly and here after it increases
proportionally to the square of the distance between the contacts [1]. In the
model that is used in this project a linearly relation between the withstand
voltage and the time after separation is assumed [7]. This relation is seen in
equation (3.2)
U = A(t − t0 ) + B,
where
• t0 = The moment of contact separation.
• A = Rate of rise of dielectric strength.
(3.2)
Vacuum Circuit Breakers
19
Dielectric withstand
80
60
TRV
Breaker withstand voltage
Voltage[kV]
40
20
0
−20
−40
−60
−80
32
33
34
35
36
37
38
Time[ms]
Figure 3.4: The figure shows 5 reignitions of the vacuum arc during contact seperation. When the reignitions occur the TRV jumps to zero. The red
line shows the RDDS of the circuit breaker.
• B = Breaker transient recovery voltage (TRV) just before current zero.
The values of A and B vary from the different VCBs. The constant A describes as mentioned the rate of rise of dielectric strength (RRDS) when the
breaker is opening. When the breaker is closing the constant A describes
the rate of decay of dielectric strength (RDDS). In [16] the value of the constant A is suggested to be between 2V /µS and 50V /µS when B is set to
zero, which is quiet normal when determining the dielectric withstand of the
breaker. The value of the dielectric strength determined in equation (3.2) is
also following a Gaussian distribution with a standard deviation of 15% of
the dielectric mean value [7].
When the contacts separate and the current is interrupted a TRV appears
across the breaker contacts, as described in chapter 2. This TRV is determined by the configuration of the network on both sides of the breaker. If
the value of the TRV exceeds the dielectric withstand of the gap between the
contacts, the arc will be re-established and the breaker will conduct current
again. This causes a high frequency (HF) current to be superimposed on the
power frequency current. This HF current will be extinguished at current
zero and the race between the TRV and the dielectric withstand will begin
again. The relation between the reignitions and the dielectric withstand is
illustrated in figure 3.4 and in figure 3.5 both the restrikes and the HF current is shown.
20
3.2 Modelling of Vacuum Circuit Breakers
Voltage[kV]
High frequency quenching capability
TRV
Breaker withstand voltage
20
0
−20
−40
34.65
34.7
34.75
34.7
34.75
34.8
34.85
34.9
34.95
34.8
34.85
34.9
34.95
Current[A]
0.5
0
−0.5
34.65
Time[ms]
Figure 3.5: The figure shows 3 reignitions of the vacuum arc during contact separation. The figure also shows the high frequency currents caused by
the arc.
The simulation model simulates restrikes by sending a closing signal to the
breaker whenever the TRV exceeds the dielectric strength of the gab [7].
This means that the resistance of the arc is expected to be the same as the
resistance of the VCB in closed position.
3.2.3
High Frequency Quenching Capability
The HF currents that occur after a reignition of the arc are mainly determined by the stray parameters of the VCB. The HF current will be superimposed on the power frequency current and if the HF current has a larger
magnitude than the power frequency current it can cause the current to pass
zeros. Most VCBs have the ability to quench the HF current at a zero crossing, and thereby extinguish the vacuum arc [7]. The VCB cannot extinguish
these HF currents if the di/dt value of the current is too high. Since the
magnitude of the currents is damped quite quickly the di/dt of the current
is also decreasing. When di/dt is small enough the VCB quenches the HF
current at one of its zero crossings. Figure 3.5 shows how a HF current is
created when the vacuum arc is established and how the arc is extinguished
when di/dt of the HF current becomes small enough. The critical value of
di/dt represents the quenching capability of the VCB. A method of determining the quenching capability of a VCB is to model it as a linear function
Vacuum Circuit Breakers
21
with respect to time
di/dt = Cc (t − t0 ) + Dd ,
(3.3)
where
• t0 = The moment of contact separation.
• Cc , Dd = Breaker constants.
Equation (3.3) gives the mean value of the quenching capability and once
again it follows a gaussian distribution where the standard deviation is 15%
of the mean value. The suggested values of the constant Cc is between
−0.034A/µs2 and 1A/µs2 . Some authors describes the HF quenching capability di/dt to be constant, Cc = 0 and suggested values of Dd to be between
100A/µs and 600A/µs [16].
3.2.4
Multiple Reignitions and Voltage Escalation
When the VCB breaks the HF current that has occurred due to a reignition
of the arc, the TRV of the breaker starts rising again. When the TRV
reaches the dielectric withstand of the breaker gab the arc will ignite again
and course another HF current to be superimposed on the power frequency
current. This phenomenon is called multiple reignitions. Figure 3.6 shows
the current of the breaker during multiple reignitions of the vacuum arc.
The occurrence of multiple reignitions depends mainly on tree parameters.
• The arching time of the breaker.
• The RRDS and the dielectric withstand of the breaker.
• The HF current quenching capability.
The two last areas have been discussed in the previous sections, but the
arching time has not been introduced yet. The time between contact separation and first arc extinguishing is called the arching time, in other words
the arching time is the time between contact separation and the time of current chopping. If the arcing time is short then the dielectric strength of the
gap will not have time to reach a high value before the arc is extinguished
and the probability of reignitions is higher. In VCB with high RRDS the
possibly of restrikes will be smaller since the breaker regains its dielectric
withstand faster than breakers with low RRDS.
After some reignitions the VCB does not have a high enough HF quenching
capability to break the HF current at a zero crossing in the last reignition,
this is seen in figure 3.7. Due to this the power frequency takes over and
22
3.2 Modelling of Vacuum Circuit Breakers
Unsuccessful current interruption
0.4
0.3
0.2
Current[A]
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
−0.6
34.4
34.6
34.8
35
35.2
35.4
Time[ms]
Figure 3.6: The figure shows the HF currents caused by 5 reignitions. The last
current cannot be quenched at a zero crossing and therefore the arc
is maintained until the next zero crossing of the current.
Complete breaking operation
Voltage[kV]
100
TRV
Breaker withstand voltage
50
0
−50
−100
32
34
36
32
34
36
38
40
42
44
46
48
38
40
42
44
46
48
Current[A]
1
0.5
0
−0.5
−1
Time[ms]
Figure 3.7: Multible reignitions lead to unsuccessful interruption of the current
at first current zero.
Vacuum Circuit Breakers
23
interruption is effected at the next current zero (around 45ms) as seen in
figure 3.7. As seen in figure 3.7 successful interruption takes place after
the contacts are fully apart and the dielectric withstand has reached its final value. The process of multiple restrikes can lead to voltage escalation,
where every breakdown of the arc can lead to higher and higher voltage at
the load side of the VCB since the TRV is superimposed on the steady state
50 Hz voltage.
3.2.5
Prestrikes
Prestrikes are like reignitions a temporary breakdown of the vacuum dielectric. Prestrikes occur during the closing operation of the breaker. Prestrikes
normally occur during energizing of capacitive loads and are caused by the
same phenomena that cause reignitions during opening operations.
When the VCB contacts starts to move towards each other the dielectric
strength of the gap starts to decrease. As soon as the dielectric withstand
of the VCB becomes smaller than the voltage over the breaker an arc will
ignite and current will flow through this arc. This current consists of a HF
current and a current at power frequency. The arc will be extinguished at a
zero crossing, when di/dt of the HF current becomes lower than the quenching capability of the VCB [1]. The interruption of the HF current causes a
TRV to build up over the breaker. When this voltage reaches the dielectric
strength of the gab another prestrike will occur and the TRV will go to zero
again. Figure 3.8 shows how prestrikes create a HF current and how these
currents are quenched, causing the arc to be extinguished.
This process continues to produce prestrikes until the dielectric withstand
of the VCB is no longer high enough to extinguish the arc. And when the
last HF current is damped the VCB only conducts current at the power
frequency. The slope of the dielectric strength seen in picture 3.8 is called
the rate of decay of dielectric strength (RDDS). RDDS is normally said to
have the same value as RRDS.
24
3.2 Modelling of Vacuum Circuit Breakers
Prestrikes
Voltage[kV]
40
TRV
Breaker withstand voltage
20
0
−20
−40
34.55
34.6
34.65
34.7
34.75
34.8
34.6
34.65
34.7
34.75
34.8
Current[A]
0.4
0.2
0
−0.2
−0.4
34.55
Time[ms]
Figure 3.8: The figure shows 4 reignitions of the vacuum arc during contact separation. The figure also shows the high frequency currents caused by
the arc.
Chapter
4
Laboratory Setup
In 2006 a laboratory setup for investigation of switching transients in wind
turbine systems was made. The setup was completed and modified by Örn
I. Björgvinssonin during his master’s project [11]. The modifications made
by Örn I. Björgvinssonin made it possible to remotely open and close the
VCB and at the same time, measure the voltage over the VCB and the
current through the breaker using a LabVIEW interface. In a preparatory
project [9] the laboratory setup was investigated and some improvements
were implemented on both the measurement system and the control system.
A MATLAB program that processes and shows the measured data was also
constructed.
4.1
The Existing Setup
As mentioned the existing laboratory setup was made to represent a windmill system, in order to examine the switching transients that are created
in such a system [11]. In this project the setup will be used only to examine
how the VCB behaves, and affects the system. These studies will be used
to find the parameters of the VCB that are used in the simulation model.
The high voltage components used in the laboratory setup are:
• A AXA 3BT − 380/45 vario-transformer.
• A HTT 10/0.4kV , 100kV A transformer.
• A 100m and a 10m NKT ”1-conductor PEX-CU 17.5kV” cable.
• A 12kV Siemens vacuum circuit breaker.
• A 0.5µF and a 1.0µF capacitive load.
26
4.1 The Existing Setup
Rogowski Current
Transducer
LabVIEW
LeCroy
Oscilloscope
Ch1
Position
Meter
Ch2
Ch3
Ch4
Switch unit
Voltage
Probe
HTT Transformer
Cable
Voltage
Probe
VCB
Load
Vario-transformer
Net Voltage
High Voltage
Measurement signal
Control Signal
Figure 4.1: The laboratory setup including high voltage components and the control and measurement system
The 3 phases from the vario-transformer are connected to the low voltage
side of the HTT transformer. From the high voltage side of the HTT transformer only one phase is connected to one side of the Siemens VCB via the
100m or 10m NKT cable. The other side of the breaker is loaded with the
capacitive load. In figure 4.1 the high voltage setup is shown. Figure 4.1
also shows the control and measurement system. The main element in this
system is a LabVIEW program that is used to control the VCB and to measure the voltage, current and the position of the VCB moving contact. The
full control and measurement system consist of:
• The labVIEW program.
• A four channel LeCroy LC334 oscilloscope.
• A Hewlett Packard 34970A data acquisition/switch unit.
• Two Tektronix P6015A voltages probes.
Laboratory Setup
27
• A Rogowski current transducer of type CWT03.
• A linear position meter.
A more detailed description of the high voltage components and the control
and measurement components, will be given in the following two sections.
4.1.1
High Voltage Setup
The vario-transformer is a AXA 3BT-380/45 vario transformer with a voltage rating of 3x380V /3x0V − 380V . The transformer has a nominal current
of 45A and is rated at 29.6kV A. The vario-transformer is on the primary
side connected to the power grid and therefore supplied with 380V . The 3
phases from the secondary side of the vario-transformer is connected to the
HTT transformer.
The HTT transformer is a 10/0.4kV wire-wound transformer rated at 100kV A
and has 1136 windings at the high voltage side. The transformer is star connected on both sides. The transformer is a dry type transformer. On the
secondary side of the transformer a cable is connected on one of the three
phases while the other two are left open.
In the project two identical cables with different length are used in order to
create various network characteristic. The cables are ”1-conductor PEX-CU
17.5kV” cables from NKT, the copper conductor has a diameter of 25mm
and the insulation used is polyethylene. Some tests have been made on the
cables in order to determine its losses [11], the main results of these tests
are shown in table 4.1. As seen in table 4.1 the losses in the cable increases
–
R[Ω/m]
L[H/m]
C[F/m]
G[S/m]
50Hz
727.00 · 10−6
239.79 · 10−9
157.57 · 10−12
14.85 · 10−12
1kHz
727.00 · 10−6
239.79 · 10−9
157.57 · 10−12
297.01 · 10−12
500kHz
738.17 · 10−6
239.79 · 10−9
157.57 · 10−12
148.51 · 10−9
1M Hz
770.11 · 10−6
239.79 · 10−9
157.57 · 10−12
297.01 · 10−9
Table 4.1: Cable parameters calculated at different frequencies [11]
when the frequency exceeds 1kHz. The two cables are used to connect the
HTT transformer and the VCB.
The VCB used in this project is a 12kV Siemens ”3AH1 115-2” vacuum
circuit breaker. The breaker has a rated short circuit current of 31.5kV
and a rated normal current of 1250A. In the tests done for this project
the current will not come close to the rated current. The breaker is a 3
phase VCB with a distance of 210mm between the centre of the 3 sets of
28
4.1 The Existing Setup
breaker contacts. The distance between the two VCB contacts in each phase
is in open position 9mm [12]. The operating drive of the VCB is using a
stored-energy mechanism, an opening spring and a closing spring. The closing spring can be charged either electrically, by a motor, or mechanically,
using a handle. It can also be unlatched either electrically by means of the
remote control or mechanically using the local ”CLOSE” pushbutton [12].
When the closing spring unlatches the opening spring automatically charges.
The loads chosen for the setup is a 0.5µF and a 1.0µF load. The reason for this is that the loads should represent a cable network under no-load
conditions, where a very small current flows in the network [11]. The loads
are installed on the frame of the VCB in order to avoid long connections
that can cause undesired transients.
4.1.2
Measurement and Control System
As mentioned the measurement and control system is build up around a
LabVIEW program. This program concerns with controlling the variotransformer, opening and closing the breaker, defining the measurement
settings and saving the measured data. As seen in figure 4.2 the LabVIEW
program communicates with almost all parts of the laboratory setup. In
figure 4.2, a screen shot of the program GUI is shown. The program has 4
graphs that show the measurements done on the high voltage system. In the
middle of the GUI there are 6 control boxes, 4 that control the oscilloscope,
1 that controls the breaker and 1 that controls the vario transformer. On
the right side of the GUI there is a button called Enable which is used to
save the measured data to a .lvm file. A description on how to plot the data
from the saved .lvm file is seen in appendix A.
In order to control the vario-transformer and the VCB the LabVIEW program sends a signal to the ”Hewlett-Packard 34970A data acquisition/switch
unit” via the GPIB interface. The switch unit is equipped with a I/O card
which switches 26V on 4 different channels. This unit is used to control
two relays that sends a 170V dc signal to the VCB, these signal energizes
the two coils which are used for opening and closing the VCB. When the
springs for opening or closing the breaker is unlatches they automatically
latches again using a motor supplied with 230V ac. The ”Hewlett Pacard
34970A data acquisition/switch unit” is also used to send control signals to
the vario-transformer in order to increase or decrease the ratio of the transformer or to bring the secondary side voltage to zero. The fact that it is
possible to increase and decrease the ratio of the vario-transformer enables
the user to control the voltage level in the system.
Laboratory Setup
29
Figure 4.2: Screenshot of the LabVIEW program.
The data measurements in the system are collected in an oscilloscope and
are sent to the LabVIEW program using a GPIB interface. The oscilloscope
used is a ”LeCroy LC334”, which can sample with a frequency of up to
500M S/s. When the LabVIEW program is running it controls the oscilloscope, it can setup the measurement range, it takes care of the trigger mode
and setup, and the program enables the user to choose which measurements
to show on the oscilloscope display.
The voltage measurements are performed by two Tektronix P6015A voltage probes. The probes are set to have a scaling of 1000:1 and they can
tolerate up to 20kV and can measure frequencies up to 75M Hz. The two
probes are placed on each side of the VCB, the probe on the load side of
the VCB is connected to channel 1 on the oscilloscope and the probe on the
transformer side of the VCB is connected to channel 2.
A Rogowski current transducer of type CWT03 is placed to measure the
current that runs through the high voltage system. The current transducer
is placed after the load, meaning that the connection from load to ground
runs through the coil. The current transducer can measure currents from
300mA to 600A and can measure frequencies up to 16M Hz. The output of
the Rogowski current transducer is connected to channel 3 on the oscillo-
30
4.2 Improvements to the Existing Setup
scope.
To measure the distance between the contacts in the VCB a position meter
is used. The position meter is connected to a fibreglass rod which is fastened
to the moving contact of the VCB [11]. When the contact moves, it moves
the fibreglass rod and thereby changes the output from the position meter.
The position meter, is in fact just a variable resistance, and is supplied by a
9V battery, which means that the output from the position meter is between
0V and 9V . The output is connected to channel 4 on the oscilloscope.
4.2
Improvements to the Existing Setup
The first measurements showed the need for some improvements of the setup.
The main improvements made to the setup were adjusting the probe connections, installing a discharging resistance to the load and changing the
setup of the Rogowski current transducer. Some minor adjustments were
also made, e.g. moving the loads closer to the circuit breaker and rewiring
the ground connection from the cable and the load making the connections
as short as possible.
4.2.1
Improving probe connections
The first measurements made on the system gave rise to some strange oscillations. These oscillations were a result of a too movable connection between
the voltage probes and the VCB, when the VCB switches, it does so with
large mechanical forces causing both the VCB and its frame to move. During these movements the voltage probes lost the connections with the VCB
in small time intervals, this causes the voltage oscillations seen in the measurements. This was avoided by fastening the connections as seen in figure
4.3. The result of the new setup can be seen in figure 4.4, where the two
plots show the results of the measurements before and after the new setup
was used. Figure 4.4 also shows the TRV caused be the switching operation, and as seen the shape of the TRV also changes when the probes are
fastened. Before fastening the probes the shape of the TRV were effected
by disturbances and after the improvement the TRV obtains the expected
shape.
4.2.2
Installing discharging resistance
When a test of opening the breaker is made, the voltage on the capacitive
load has to go to zero before the next measurement is taken. For this
reason a discharge resistance is installed in parallel with the capacitor in
order to make the discharging of the capacitor faster. It was estimated that
Laboratory Setup
31
(a) Transformer side
(b) Load side
Figure 4.3: The two pictures show how the probes are fastened to the setup.
Before this was done the probes were connected loosely to the setup
by the hooks on the tip of the probes.
4
HTTP1L100C1x05Dt1−6V5,75kOUT.lvm
x 10
Voltage on trans. side of the VCB [V]
Voltage on trans. side of the VCB [V]
4
HTTP1L100C1x05Dt1−6V5,75kOUT.lvm
1
0.5
0
−0.5
−1
−1.5
−2
0
10
20
30
40
50
1
x 10
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
10
Time[ms]
20
30
40
50
Time[ms]
(a) Before improving the setup
(b) After improving the setup
Figure 4.4: The plots show the voltage measured on the transformer side probe,
before and after fastening the probe. At around 30ms oscillations can
be seen on figure a.
a discharging time of approximately 10 seconds would be suitable, due to
the time used on saving the measurements to the .lvm file. The following
calculations show how the size of the discharging resistance, R, is found
τ = R · C,
setting τ = 5s and C = 0, 5µF gives
R=
5s
= 10M Ω.
0.5µF
As seen from the calculations a 10M Ω resistance gives a time constant of 5
seconds. This means that after 5 seconds the voltage will have decreased to
32
4.2 Improvements to the Existing Setup
Figure 4.5: The picture shows the Rogowski current transducer. In order to
improve the current-to-noise ratio the current measurement is led
through the Rogowski coil 4 times as seen on the picture
37% of the initial voltage, which means that after 10 seconds the capacitor
should be discharged, therefore a 10M Ω resistance is chosen as discharge
resistance.
4.2.3
Improving the Rogwski current transducer setup
The first tests of the laboratory setup showed a low frequency disturbance on
the current measurement. Where this disturbance comes from is unknown,
but since it had quiet a big influence on the current it was decided to improve
the current-to-noise ratio so that the low frequency fault current had less
influence. Therefore the wire conducting the current through the Rogowski
transducer was twisted several times so that it runs through the Rogowski
coil 4 times, increasing the output current by a factor 4, meaning that the
ratio of the Rogowski transducer is changed from 10mV /A to 40mV /A.
In figure 4.5 it can be seen how the new setup of the Rogowski current
transducer looks. A change in the LabVIEW program was made in order to
fit the program to the new voltage-current ratio of the Rogowski transducer.
Chapter
5
Laboratory Tests and Results
The main purpose of the tests is to determine the paremeters that are used
to describe the VCB in the simulation model. All the measurements made
in this project have been made on one phase. The tests have been performed with two different setups, one using the 10m cable to connect the
HTT transformer and the VCB and one using the 100m cable. This is done
in order to observe how the VCB reacts on different configurations of the
network it is operating in.
At both cable lengths tests were made at different voltage levels. The voltages levels were chosen based on the knowledge that the HTT transformer
has a nominal voltage of 5.75kV on the secondary side. This voltage level
was chosen to be the base of the measurements and test series were made
on voltage levels of 20%, 40%, 60%, 80%, 100% and 120% of the 5.75kV .
The reason why the system was tested at different voltage levels was to see
how the voltage level effects the generated transients. In order to calculate
the current chopping level of the breaker, the tests at the low voltage levels
are very useful, since they do not create any significant transients. During the work with the current chopping level it was chosen to make use of
the extra load capacitor in order to increase the current in the system. As
this project mainly concentrates with the very fast transients caused by the
breaking operation the measurement time has been set to 10ms. During
this 10ms, 50000 data measurements are taken, which means that the time
between each measurement, ∆t, is 0.2µs. This gives a good and precise
picture of the fast transients. When analysing the chopping current of the
VCB tests with a measuring time of 50ms is used, since the amplitude of
the current is a parameter in the chopping current calculations and cannot
be read on the 10ms measuremets. A few more measurements, with a measurement time of 50ms, were made to illustrate the breaking process and
measure the opening and closing time of the VCB.
34
In order to observe the effect the arching time has on the VCB and the
TRV it was decided to make several tests on each voltage levels to observe
most possible breaking angles and thereby different arching times. Since it is
not possible to control the breaking angle or the breaking time of the VCB,
random tests were made and for every test the angle was registered. The
voltage sine curve was divide in 8 sections and the testing was continued
until a breaking angle in each section was obtained. The breaking angle was
read on the voltage measurements, this means that with a breaking angle of
0◦ , the VCB opens when the power frequency voltage curve is at the rising
zero crossing. A breaking of 90◦ would mean that the VCB opens when the
voltage is at its maximum. When the breaker closes, the angle at which it
starts conducting current is called the closing angle and is found in the same
way as the breaking angle.
To distinguish between the different test series it was decided to give each
file containing the measurements a name referring to the test setup. An
example of the file name could be:
HT T P 1L100C1x05Dt2 − 7V 5, 75kIN 1
where the meaning of the different parts of the name are:
• HTT : HTT transformer is used.
• P1 : One phase is connected between the HTT transformer and the
VCB.
• L100 : The length of the cable between the HTT transformer and the
VCB is 100m.
• C1x05 : The load on the VCB is capacitive with a size of 0.5µF .
• Dt2-7 : The time step between measurements is 2 · 10−7 s.
• V5,75k : The voltage on the secondary side of the HTT transformer
is 5.57kV .
• IN1: The measurements are taken when the VCB closes.
The HTT transformer and number of phases connected are included in the
filename, even though they are not changed throughout the project. This is
done so that it is easy to make more tests with different setups and compare
the new tests with the ones made in this project in future work on the VCB.
As described in chapter 4, the measurement system takes 4 measurements,
the position of the moving VCB contact, the current, the voltage on the
Laboratory Tests and Results
35
HTTP1L100C1x05Dt1−6V6,9kIN1.lvm
40
8
30
7
20
Current[A]
Distance between VCB contacts[mm]
HTTP1L100C1x05Dt1−6V6,9kIN1.lvm
9
6
5
4
10
0
−10
3
−20
2
−30
1
0
10
20
30
40
−40
50
0
10
Time[ms]
HTTP1L100C1x05Dt1−6V6,9kIN1.lvm
Trans. side voltage[V]
Load side voltage[V]
0.5
0
−0.5
0
10
20
30
50
40
Time[ms]
(c) The load side voltage
HTTP1L100C1x05Dt1−6V6,9kIN1.lvm
4
1.5
1
−1
40
(b) The current
4
x 10
30
Time[ms]
(a) The length of the VCB gab
1.5
20
50
x 10
1
0.5
0
−0.5
−1
0
10
20
30
40
50
Time[ms]
(d) The transformer side voltage
Figure 5.1: Closing the VCB at voltage level 6.9kV , the setup is using the 100m
cable and the load with a capacitance of 0.5µF . The time between
the measurements ∆t is 1 · 10−6 s, and the closing angle is 0◦
load side of the VCB and the voltage on the transformer side of the VCB. In
figure 5.1 the 4 measurements from a closing process of the VCB are shown.
As figure 5.1a shows, the moving VCB contact starts to move towards the
fixed VCB contact after around 20ms. The picture shows a distance between
the contacts is only 7.8mm and not 9mm, this is due to a small calibration
error in the position meter. After around 30ms the distance between the
contacts is 0mm and the VCB starts conducting current, as seen in figure
5.1b. Figure 5.1c and 5.1d show the voltage on both sides of the VCB, the
voltage on the load side is zero until the contacts are together and after that
it follows the transformer side voltage since the VCB forms a short circuit
between the two voltage probes. This measurement is taken at aclosing angle
of about 0◦ . As mentioned this angle can easiest be seen on the transformer
side voltage curve, where a small switching transient appears in the area of
5.1 Preparatory tests
HTTP1L100C1x05Dt1−6V5,75kIN3.lvm
9
8
X: 20.39
Y: 7.688
7
6
5
4
3
2
1
0
10
20
30
X: 32
Y: 1.312
40
50
Time[ms]
(a) Closing the VCB
Distance between VCB contacts[mm]
Distance between VCB contacts[mm]
36
HTTP1L100C1x05Dt1−6V5,75kOUT3.lvm
8
X: 27.6
Y: 7.594
7
6
5
4
3
2
X: 19.89
Y: 1.219
1
0
5
10
15
20
25
30
35
40
45
50
Time[ms]
(b) Opening the VCB
Figure 5.2: The figure shows two plots of the distance between the VCB contacts,
when the VCB is opening and closing.
the rising zero crossing or around 0◦ . As this shows the measurement of the
angle is not very precise and the closing and opening angles decribed will be
approximate values.
5.1
5.1.1
Preparatory tests
Breaker position
The opening time of this type of VCB should be less than 15ms [12] and
previous projects have measured the opening and closing time of the specific
VCB to be around topen = 7ms and tclose = 12ms [9]. In figure 5.2 a
measurement of the distance between the VCB contacts during a closing
and an opening process is seen. In figure 5.2 two data markers are set, these
data markers shows the time and the distance between the contacts and this
data can be used to find the closing and opening time of the VCB.
tclose = 32.001ms − 20.391ms = 11.61ms
topen = 27.602ms − 19.889ms = 7.713ms
The values used for the calculations are more exact than the values seen on
the data markers on the figures. The exact values of the data markers can
be exported to a file in MATLAB and the values from this file are used to
make the calculations, this method was used throughout the project. The
results of the closing and opening time corresponds to the values calculated
in previous projects. As seen of figure 5.2b some vibrations occurs when the
moving breaker contact reach the open position. These vibrations are caused
by the mechanical impact the contact gets when reaching the open position
Laboratory Tests and Results
37
and it stabilise after some time. The used breaker model does not offer an
option to change the opening and the closing time of the VCB. Instead the
model uses a fixed time of 0.55ms as both the opening time and the closing
time of the VCB.
5.1.2
Resistance of the Voltage Circuit Breaker
The simulation model of the VCB uses the resistance of the VCB in open
and closed position as parameters and for this reason these values have to
be measured. Since the resistance in open position is very high and the
resistance in closed position is very small, a normal ohmmeter cannot be
used in the measurement. In order to measure the resistance of the VCB
in open position an insulation tester is used, the tester is a ”Fluke 1520
MegOhmMeter” that can measure a maximum of 4000M Ω. The test of the
open resistance measurement gave
Ropen > 4000M Ω.
In order to measure the resistance of the VCB in closed position a Wheatstone bridge is used. This device is a bridge circuit which consists of 2
known resistors, one adjustable resistor and the last part of the bridge is the
resistor being measured. A 4-point measurement technique, applying both
a current and a voltage over the measured resistance, is used in order to get
the most precise measurement. The measurement of the closed resistance
gave the following result
Rclosed = 200µΩ,
The value of Ropen will be set to 1M Ω in the simulations, since it is the
highest possible value in the simulation model, and Rclosed will be set to the
measured 200µΩ.
5.2
Transient Recovery Voltage
When the VCB contact separates and the vacuum arc extinguishes, a TRV
will arise across the two contacts. This TRV is a critical parameter in the
interruption process, the TRV can either cause the arc to be reestablished
or it can lead to successful interruption. As described in chapter 2, the TRV
is dependent on the network configuration.
The TRV is calculated by using the voltage measurement from the load
side of the VCB and the voltage measurement from the transformer side of
the VCB, like this
T RV = VLoad − VT rans .
(5.1)
38
5.2 Transient Recovery Voltage
HTTP1L100C1x05Dt2−7V5,75kOUT2.lvm
4000
2000
2000
0
0
TRV[V]
TRV[V]
HTTP1L10C1x05Dt2−7V5,75kOUT6.lvm
4000
−2000
−2000
−4000
−4000
−6000
−6000
−8000
3
3.5
4
4.5
5
5.5
6
Time[ms]
(a) Test with 10m cable
6.5
7
−8000
2
2.5
3
3.5
4
4.5
5
5.5
6
Time[ms]
(b) Test with 100m cable
Figure 5.3: The TRV across the breaker contacts using a 10m and a 100m cable.
The breaking angle is in both cases 0◦ .
5.2.1
Frequency of the Transient Recovery Voltage
In chapter 2 it is described how the frequency of the TRV depends on the
network configuration, and should be the same for all breaking angles. Tests
have been performed with two network configurations in order to observe
different frequencies of the TRV. Figure 5.3 shows the TRV in the two network configurations, in both cases the breaking angle is 0◦ . As figure 5.3
clearly shows the tests made with the different cable lengths gives different
frequencies of the TRV. To find the two frequencies a number of measurements were made on the curves. In figure 5.4 the measurement from one test
is shown. As seen in figure 5.4, 7 markers have been placed on the curve,
one marker is placed to show at what time the TRV is damped, and the last
6 markers are placed to find the wavelength of the TRV at different places.
If using the two first markers at the top tips of the TRV it can be found
that the wavelength of the TRV in this area is
λ = 4.2908ms − 4.1808ms = 0.11ms,
and by using the wavelength the frequency can be found
1
1
⇒
= 9090.9Hz
λ
0.11ms
In order to minimise inaccuracy caused by the data measurements, more
data markers are set. The wavelength and the resulting frequencies are
found between the other data markers as well and the mean of the four
frequencies is found. In appendix B the results of all the tests made at
5, 75kV , for both 10m and 100m, is shown. In the full appendix, which is
found on the cd, the measurements and data points used for the calculations are found. The results in tables B.1 and B.2 show the breaking angle,
fT RV =
Laboratory Tests and Results
39
HTTP1L10C1x05Dt2−7V5,75kOUT6.lvm
3000
X: 4.181
Y: 3000
2000
X: 4.291
Y: 1625
1000
X: 4.406
Y: 375
TRV[V]
0
−1000
−2000
X: 5.24
Y: −3000
−3000
X: 4.242
Y: −3625
X: 4.355
Y: −3000
−4000
−5000
−6000
3.5
X: 4.121
Y: −5125
4
4.5
5
5.5
Time[ms]
Figure 5.4: The measurements for calculating the frequency of the TRV when
using a 10m cable in the test. The breaking angle is again 0◦ .
the amplitude, the frequency and the damping time of all the measurements.
The two tables show that the frequency is independent of the breaking angle
and the average value of the frequencies are:
fT RV 10 = 8708, 92Hz
fT RV 100 = 2953, 87Hz.
The results show that when changing from a 100m cable to a 10m cable, the
frequency of the TRV becomes almost 3 times higher. This is a result of the
difference in capacitance and inductance in the two cables. As the cables
used are of same type, the 100m cable has a capacitance and inductance
that is 10 times higher than in the 10m cable, the specific parameters of the
cable can be seen in table 4.1.
5.2.2
Amplitude of the Transient Recovery Voltage
The amplitude of the TRV is a very important parameter as this voltage
can reach values that are higher than the normal peak voltage and thereby
apply a high eletrical stress to components. The amplitude of the TRV is
measured as the first and undamped maximum of the TRV, e.g. in the test
shown in figure 5.4 the amplitude of the TRV is 5125V . In contrast to the
frequency of the TRV, the amplitude of the TRV is dependent of the breaking angle. This dependency can be seen in tables B.1 and B.2. In table 5.1
40
5.2 Transient Recovery Voltage
some of the results from the tests using the 10m cable have been taken out
and sorted by the breaking angle.
From table 5.1 the relation between the breaking angle and the ampliTest nr.
Brk. angle[◦ ]
Amplitude[V ]
12
0
-5500
4
22.5
-5375
3
45
-4875
9
90
0
2
180
5250
8
202.5
4500
7
225
4250
10
247.5
1625
Table 5.1: The table shows the relation between the breaking angle and the amplitude of the TRV. The results are from the tests made at 5.75kV
using the 10m cable.
tude can be seen. When the VCB breaks the voltage close at a maximum
value of the voltage, 90◦ and 270◦ , the amplitude of the TRV is low and
when the VCB breaks the voltage close to a zero crossing, 0◦ and 180◦ , the
amplitude is high. The reason for this is that the VCB conducts a capacitive current, causing the current to lag the voltage with 90◦ . This means
that when the VCB breaks at a high voltage the current that is interrupted
is low and will cause low amplitudes of the TRV. In the best case, if the
interruption happens at a current zero crossing, no TRV will be generated.
When the voltage is around zero at the time of interruption, the current will
be interrupted around its maximum and cause a TRV with high amplitude.
The tables B.1 and B.2 also show that for breaking angles from 90◦ to 270◦
the TRV will start by rising, resulting in a positive first amplitude. Similarly for breaking angles from 270◦ to 90◦ the TRV will start by falling, the
reason for this relation is the direction of the current, which will be opposite
in the two intervals. Table B.1 and B.2 show that there is a clear connection
between breaking angles that are 180◦ apart. They have the same amplitude
but with different sign, this is because measurements that are 180◦ apart are
on the same place of both the voltage and current curve, except from the
fact that one is on the negative part and one is on the positive part. This
similarity has been observed throughout the project.
The tests have shown that the setup with the short cable gave larger TRV
amplitudes. As the short cables also have a larger frequency the rate of rise
of the TRV will be higher when using the short cable. This will lead to more
reignitions, since a circuit where the TRV has a high rate of rise will reach
the dielectric withstand level of the VCB faster than in a setup where the
rate of rise of the TRV is lower.
The tables B.1 and B.2 also show the time it takes for the TRV to be
completely damped. The TRV generated when using the short cable needs
less than half the time to be damped than the TRV generated when using
Laboratory Tests and Results
41
the long cable. The mean value of the damping time is 0.97ms when using
the 10m cable and 2.3ms when using the 100m cable.
5.3
Chopping Current
The current chopping is an undesirable effect of the VCB, since the steep
slope of the current produces the TRV that can cause overvoltages in the
network. As described the current chopping is a result of arc instability
which causes the vacuum arc to be extinguished before reaching a current
zero. The value of the current chopping level is found using equation (3.1).
In order to find the contact parameters α and β, it is necessary to know the
amplitude of the current through the breaker and the current chopping level.
Figure 5.5 shows a measurement of the current when opening the VCB at
voltage level 5.75kV with breaking angle 180◦ using the 100m cable.
As seen in figure 5.5a there is a high spike on the current around 20ms,
this current spike is a result of the HF currents, which occur after arc extinguises. In order to read the amplitude of the current and the current
chopping level a zoomed plot of the current around the breaking time is
needed. In figure 5.5b a plot zoomed around the power frequency current
is shown. As seen the zoomed plot is very blurred and it is hard to make a
precise measurement of the current chopping level and the current magnitude.
This problem occurs when recording the measurements in LabVIEW. In
order to get the full picture the settings of the oscilloscope have to be in a
way so that all data points fit in the plot. For this reason the sensitivity of
the oscilloscope has to be set so that the maximum point of the HF current
is within the measuring range. This means that the measurements get less
accurate and the picture gets blurred. Therefore it is convenient to look at
measurements taken at lower voltage levels, where smaller or almost no HF
currents are produced. In figure 5.6 a plot of the current during a breaking
process is shown. As seen the current is interrupted at around 22ms, before this time the power frequency current (with disturbance) is conducted.
At 22ms the current chopping level is apparently reached and the current
is chopped. After this point the only current comes from discharging the
capacitor and after a short time the current measured in the Rogowski coil
is zero.
The full appendix C on the CD contains the measurements for calculating the values α and β. From the graphs in the full appendix C, it can be
observed that the current chopping occurs at the same time in all measurements. This indicates that the current level is under the level of the chopping
42
5.3 Chopping Current
HTTP1L100C1x05Dt1−6V5,75kOUT1.lvm
5
80
4
60
3
40
2
Current[A]
Current[A]
HTTP1L100C1x05Dt1−6V5,75kOUT1.lvm
100
20
0
−20
1
0
−1
−40
−2
−60
−3
−80
−4
−100
0
10
20
30
40
50
−5
0
Time[ms]
10
20
30
40
50
Time[ms]
(a) Unzoomed plot.
(b) Zoomed plot.
Figure 5.5: The plots shows the current through the VCB at 5, 75kV using a
100m cable. The interruption is made at a breaking angle of 180◦ .
current and therefore the current is chopped instantaneously after contact
separation. In table C.1 the value of α has been calculated when β has the
value 14.3, this is expected to result in a value of α around 6.2 · 10−16 s.
As seen in table C.1 the calculated values of α are very different from the
expected value, and the calculated values vary a lot.
The results from table C.1 indicate that the current is under the current
chopping level of the breaker, which means that the VCB breaks the current
as soon as the contacts separate. Therefore another test series with the extra
capacitor, increasing the load to 1.0µF , was made. These tests can also be
seen in the full appendix C on the CD. The constant α has been calculated
again using the new measurements and the results can be seen in table C.2
the values of α are still very different from the expected value and they still
vary a lot. And since it has not been possible to find a reasonable value of
α no attempts at finding β has been made. The plots of the measurements
and the calculations of the constant α strongly indicates that the current
level in the tests is lower than the current chopping level of the VCB. This
corresponds with the fact that the normal current chopping level for VCBs
usually varies between 3A and 8A. In order to find the parameters of α and
β for the breaker, different types of loads must be used in order to conduct
a current that is larger than the current chopping level. But since only the
small capacitive loads were available standard values of α and β will be used
in the simulation model:
α = 6.2 · 10−16 s
β = 14.2.
Laboratory Tests and Results
43
HTTP1L100C1x05Dt1−6V1,15kOUT6.lvm
0.4
0.3
Current[A]
0.2
0.1
0
−0.1
−0.2
−0.3
0
10
20
30
40
50
Time[ms]
Figure 5.6: The plots shows the current through the VCB at 1, 15kV using a
100m cable. The interruption is made at a breaking angle of 45◦ .
5.4
Reignitions
To find the dielectric withstand of the VCB, the reignitions that occur when
opening the breaker have been studied. After the vacuum arc has been extinguished, the race between the TRV and the dielectric withstand of the
VCB begins. When the TRV exceeds the dielectric withstand of the VCB a
breakdown of the vacuum occurs and creates a conducting path between the
two VCB contacts. When the conducting path is created the TRV jumps
back to zero and does not start to rise again before the arc is extinguished.
In figure 5.7 it is seen how reignitions appears after contact seperation.
Figure 5.7 shows there is a difference in the number of reignitions between
the tests made with the 100m cable and the 10m cable. In figure 5.7 there
is 3 reignitions when the 100m cable is used and around 11 reignitions when
using the 10m cable. It is also seen that the conducting time of the vacuum
arc is a lot shorter when using the 10m cable, with this setup the arc is
extinguished almost instantaneous. The reignitions when using the 100m
cable appear for a longer time, around 0.2ms. The difference is a result of
the different shape of the TRV, as mentioned the TRV has a large rate of
rise in the system when the 10m cable is used. Therefore the TRV will reach
the dielectric withstand of the VCB much faster and create more reignitions
as seen in figure 5.7.
44
5.4 Reignitions
HTTP1L10C1x05Dt2−7V5,75kOUT7.lvm
5000
4000
4000
3000
3000
2000
2000
TRV[V]
TRV[V]
HTTP1L100C1x05Dt2−7V5,75kOUT4.lvm
5000
1000
1000
0
0
−1000
−1000
−2000
−2000
−3000
2.6
2.7
2.8
2.9
3
3.1
3.2
−3000
3.75
3.8
3.85
Time[ms]
(a) 100m cable
3.9
3.95
4
4.05
4.1
4.15
Time[ms]
(b) 10m cable
Figure 5.7: The plots shows the voltage across the breaker contacts during an
opening of the VCB. Both tests have a breaking angle of 225◦ .
5.4.1
Rate of rise of Dielectric Strength
In order to model the VCB it is necessary to know its dielectric withstand.
The dielectric withstand of the breaker can be found by using equation (3.2)
and in order to simplify the calculations the value of the TRV just before
current zero is set to be zero. This means that the dielectric withstand of
the breaker is proportional to the RRDS or the value A used in the simulation model. Figure 5.8 shows how the RRDS of the VCB is found. The
red line on figure 5.8 illustrates how the dielectric withstand is increased
with respect to time. The time t0 is set to zero in the calculations, this
is done because the time of contact separation is not know. This will give
correct results when making the linear regression to find the RRDS, since
the progress of t − t0 is the same as long as t0 is set constant. The data
measurements that are showed in figure 5.8d are used to perform a linear
regression, finding the RRDS of the VCB. In the example on figure 5.8d the
value of the RRDS becomes 24.37V /µS. The full appendix D on the CD
shows the data measurements that have been used to calculate the value of
the RRDS and the tables D.1, D.2, D.3, D.4, D.5 and D.6 shows the results
of the calculations. As the tables show an average value of the RRDS is
found in each of the 6 test series, and these values can be seen in table 5.2.
As it is seen in table 5.2 the calculated values of the RRDS is much smaller
when using the 100m cable than the ones calculated for the 10m cable. The
table also shows that the value of the RRDS seems to be dependent of the
voltage when using the 100m cable, where the calculations of the RRDS are
more constant when the 10m cable is used. The results found in appendix
D also shows a much larger variance of the results using the 100m cable
with many large and small values of the RRDS. This is particularly the case
Laboratory Tests and Results
45
HTTP1L100C1x05Dt2−7V5,75kOUT4.lvm
HTTP1L100C1x05Dt2−7V5,75kOUT4.lvm
5000
4000
4000
3000
3000
2000
TRV[V]
TRV[V]
2000
1000
0
1000
0
−1000
−1000
−2000
−2000
−3000
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
2.8
2.85
Time[ms]
2.9
2.95
3
3.05
Time[ms]
(a) The full measurement
(b) Zoomed plot, showing the reignitions
HTTP1L100C1x05Dt2−7V5,75kOUT4.lvm
HTTP1L100C1x05Dt2−7V5,75kOUT4.lvm
4000
4000
3000
3000
X: 2.885
Y: 2250
2000
TRV[V]
TRV[V]
2000
1000
1000
X: 2.842
Y: 750
0
0
−1000
−1000
−2000
X: 2.81
Y: 468.8
−2000
2.8
2.85
2.9
2.95
3
3.05
2.8
Time[ms]
(c) Dielectric withstand curve
2.85
2.9
2.95
3
3.05
Time[ms]
(d) Points for calculating the RRDS
Figure 5.8: The figure illustrates how the RRDS is calculated from the laboratory
measurements.
Voltage level
4.6kV
5.75kV
6.9kV
Average RRDS
Cable
10m
38.24V /µS
39.39V /µS
36.02V /µS
37.88V /µS
length
100m
18,52V /µS
21,94V /µS
24,50V /µS
21.65V /µS
Table 5.2: The table shows the average RRDS, for the 6 analysed test series and
the average value of the RRDS found for the two cable lengths.
at voltage level 4.6kV and is probably due to the fact that less reignitions
occurs at this voltage level and thereby makes the results vulnerable to measurement mistakes. In the tests using the 10m cable the results are more
close to the average value and only a few results are very different from the
46
5.4 Reignitions
average values.
With basis in these consideration the value of the RRDS that is used in
the simulations, has been chosen. It is decided to choose the value of the
RRDS that was calculated in the tests where the 10m cable is used. This
decision was made because of the lack of stability in the results from the
100m cable tests. Specially the fact that the value of the RRDS increases
when the voltage level (number of reignitions) increases indicate that there
is a lot of inaccuracy in the calculations, and therefore the results using the
10m cable, which creates a lot of reignitions, are used. The value of the
RRDS that will be used when simulating the VCB will therefore be the average of the value found in the 10m cable tests and the value of B will be
zero:
A = 37.88V /µs
B = 0.
This means that the dielectric withstand of the VCB when it is fully open
(after 7.23ms) will be:
Vopen = 37.88V /µS · 7.23ms ·
1000µs
= 273.87kV.
ms
This means that the withstand of the vacuum between the breaker contacts
is:
Vvacuum =
273.87kV
= 30.43kV /mm.
9mm
As seen from the calculations the dielectric withstand of vacuum in the VCB
is approximately 10 times larger that the withstand in air.
5.4.2
Effect of breaking angle
As seen in table 5.1 the breaking angle has an influence in the amplitude
of the TRV. Therefore it is also expected that the breaking angle has an
influence in the number of reignitions that occurs after separating the VCB
contacts. As figure 5.7 shows there is a difference in reignitions in the tests
done with different cables. A closer look at tables D.1, D.2, D.3, D.4, D.5
and D.6 show that the number of reignitions are dependent on the breaking
angle. To illustrate this the results from the test made at 5.75kV with
10m cable have been sorted by the breaking angle and are shown in table
5.3. Table 5.3 shows that the relation between number of reignitions and
breaking angle follows the same pattern as the relation between amplitude
of the TRV and the breaking angle. When the VCB breaks the voltage close
a maximum value of the voltage at 90◦ and 270◦ , the number of reignitions
Laboratory Tests and Results
Test nr.
Brk. angle[◦ ]
Reignitions
6
0
20
5
22.5
18
47
3
45
15
9
90
0
1
180
15
8
202.5
15
7
225
10
10
270
1
Table 5.3: The table shows the relation between the breaking angle and the number of reignitions of the vacuum arc. The results are from the tests
made at 5.75kV using the 10m cable.
is low and close to zero and when the VCB breaks the voltage close to a zero
crossing, 0◦ and 180◦ , the number of reignitions is quiet high. The reason for
this is that the current is capacitive and therefore zero at voltage maximum
and maximum at voltage zero. It is clear that the number of reignitions
must be zero if the VCB opens at a current zero crossing since no current is
interrupted and no vacuum arc is formed. During a current maximum a large
current will be interrupted this creates a TRV with high amplitude which
leads to many reignitions. Tabel 5.3 shows that the number of reignitions
is almost the same at the positive part and the negative part of the curve,
this can again be related to the TRV which had the same amplitude at the
positive part and the negative part.
5.5
High Frequency Quenching Capability
When a reignition of the vacuum arc occurs it will cause a HF current to
be superimposed on the power frequency current. This HF current may be
quenched at one of its zero crossings, if it has a low enough di/dt. If the
current is quenched the TRV will again start rising over the VCB gab and
depending if it reaches the dielectric withstand a new reignition and a new
HF current will be created. In figure 5.9 the TRV and the current through
the VCB is seen. Figure 5.9 is a measurement taken when the 100m cable is
used, in this measurement it is easy to see that when the two first reignition
occur (TRV jumps to 0), the HF current is formed. The third reignition
(after 2940µs) gives only a short appearance of the HF current, which is
quenched after only a half period. It is also seen that the first HF current
(13 periods) is longer than the second HF current (1 21 periods). This phenomenon of shorter lifetime of the reignitions has been observed in almost
all measurements on the 100m cable, but in most of the measurements the
second reignition creates a HF current with a length of 3-7 periods.
As figure 5.9 shows, the magnitude of each HF current is small at the first
reignition and rises from reignition to reignition. In this case the magnitude
starts at around 10A on the first HF current and at the second HF current
the magnitude is around 30A ending at a magnitude of around 80A for the
last HF current. This phenomenon is also observed in all the measurements.
48
5.5 High Frequency Quenching Capability
HTTP1L100C1x05Dt2−7V5,75kOUT8.lvm
TRV[V]
2000
0
−2000
−4000
−6000
2700
2750
2800
2750
2800
2850
2900
2950
3000
2850
2900
2950
3000
Current[A]
100
50
0
−50
−100
2700
Time[us]
Figure 5.9: The plot shows how the reignitions of the VCB create a HF current
that is superimposed on the power frequency current. The test is from
the system with 100m cable and the breaking angle is 292.5◦ .
The frequency of the HF currents is around 400kHz, which means that the
wavelength is only 2.2µs. With this short wavelenght and a ∆t of 0.2µs the
plots of the HF currents do not get as precise as desired. The plots are good
enough to determine the HF current quenching capability, but in order to
get a more precise result the measuring time, when examining HF currents,
should be set down in comming projects.
When the 10m cable is used in the measurement the shape of the HF currents become very different from the ones observed in figure 5.9. The HF
currents that appear in the system using a 10m cable can be seen in figure
5.10. The HF currents seem to be quenched instantly after they appear and
can just be seen as small spikes on the current curve, which occur when the
TRV jumps to zero. Some of the HF currents are quenched even before they
reach their first maximum, and therefore it is not possible to see the increase
in magnitude in the HF currents.
5.5.1
Determining the High Frequency Quenching Capability
Since the HF currents from the tests with the 10m cable have a very short
life time and are often quenched even before the first maximum is reached, it
is not possible to use them when calculating the HF quenching capability of
Laboratory Tests and Results
49
HTTP1L10C1x05Dt2−7V5,75kOUT7.lvm
TRV[V]
5000
0
−5000
3850
3900
3950
4000
4050
3950
4000
4050
Current[A]
50
0
−50
3850
3900
Time[us]
Figure 5.10: The plot shows how the reignitions of the VCB create a HF current
that is superimposed on the power frequency current. The test is
from the system with 10m cable and the breaking angle is 225◦ .
the VCB. Before determining the HF quenching capability of the VCB many
considerations on the approach were made. The two main considerations
were how to determine the constant Cc that appears in equation (3.3) and
the second was how to set the opening time of the VCB, t0 . The value of Cc
can be described as the change in di/dt with respect to time. The value is
therefore found by finding the slopes of the HF current between a maximum
and a minimum point and describe the slopes as a function of time. The
time used to find Cc is in equation (3.3) given as t − t0 . The time t0 should
be the opening time of the breaker, but since this time is not known it, was
decided to set t0 as the time when the HF current starts appearing. When
calculating the value of RRDS the time t0 was set to zero, but in this case
the beginning time of the HF current was chosen, since this time have to be
used anyway when finding the value of Dd . The value of the constant Cc
can now be calculated from the measurements of the HF currents. In figure
5.11, 2 plots are seen, plot 5.11a shows 3 occurrences of HF currents during
a breaking operation and plot 5.11b is a zoomed plot showing the values used
to calculate the HF quenching capability of the VCB. As described the value
of Cc is found by making a linear regression, using the di/dt, found between
the data markers, and the difference between the time of a the zero crossing
and the start time of the HF current. The value of Dd is found simply by
50
5.5 High Frequency Quenching Capability
HTTP1L10C1x05Dt2−7V5,75kOUT8.lvm
HTTP1L100C1x05Dt2−7V5,75kOUT8.lvm
100
25
80
20
60
40
10
Current[A]
Current[A]
X: 2785
X: 2787
X: 2790
Y: 14.06
X: 2795
Y: 12.5X: 2793
Y: 12.5
Y: 10.94
Y: 10.94
X: 2801
X: 2803
Y: 7.812
Y: 7.812
15
20
0
−20
−40
5
X: 2783
Y: −1.562
0
−10
−15
−20
−80
−25
−100
2700
2770
2750
2800
2850
2900
2950
2780
X: 2808
X: 2811
X: 2813
Y: 6.25
Y: 6.25
Y: 6.25
X: 2816
Y: 1.562
2790
2800
2810
2820
2830
Time[us]
3000
Time[us]
(a) Plot showing the reignitions
X: 2806
Y: 7.812
X: 2815
X: 2807 Y: −7.812
X: 2802Y: −9.375
X: 2794
X: 2797
Y: −10.94
Y: −12.5
Y: −12.5
X: 2809
X: 2787
X: 2804Y: −7.812
X: 2812
X: 2784
Y: −15.62
X: 2799Y: −9.375 Y: −9.375
Y: −17.19 X: 2792 Y: −10.94
X: 2789
Y: −12.5
Y: −14.06
−5
−60
X: 2798
Y: 7.812
(b) Zomed plot showing the first reignition
Figure 5.11: The plots shows the data markers used to calculate HF current
quenching capacity of the VCB.
finding the slope between the first two data markers seen on figure 5.11b.
Dd =
A
−1.562 − (−17, 1875)
= −15.626 .
2783, 2 − 2784, 2
µs
In the full appendix E on the CD the measurements and the data used for
calculation of the HF quenching capability of the VCB are found. The results
of the calculations is seen in table E.1, in the printed version, and as seen
the calculations of Cc and Dd are made separately for each reignition. The
results in the table are only results from HF currents that have a appearance
time, which is long enough to give a realistic result (more that 1 period).
The average value of Cc and Dd can be seen in table 5.4. As table 5.4, shows
Arc nr.
Average
Arc 1
A
C[ µs
2]
-0.591
Arc 1
A
D[ µs
]
25.670
Arc 2
A
C[ µs
2]
-1.190
Arc 2
A
D[ µs
]
48.572
Arc 3
A
C[ µs
2]
-1.912
Arc 3
A
D [ µs
]
75.703
Table 5.4: The average results of the calculations of C and D
the values of Cc and Dd both increase depending on the number of reignition
it is calculated for. And as seen in table E.1 in the appendix, the value of the
constants vary a lot even for the calculation done on the same arc number.
When comparing the results to the suggested values presented in chapter 3,
it shows that the lowest value of Cc is pretty far from the suggested negative
value, −0.034A/µs2 and the value of Dd is also far from the suggested values.
Due to the found results, another approach of finding the HF quenching
capability was tried. Instead of looking at the value of di/dt according to
Laboratory Tests and Results
51
equation (3.3) the value was set to be constant. Using this approach the
value of di/dt can be seen as the slope between the last two data pointers
in figure 5.11b, the example from the figure gives
Dd =
−7.8125 − 1.562
A
= 11.718 .
2814.8 − 2815.6
µs
This approach leads to the results seen in table E.2 in appendix E. The
average of the results is shown in table 5.5. As the table shows the results
Arc nr.
Arc 1
A
D[ µs
]
Arc 2
A
D[ µs
]
Arc 3
A
D[ µs
]
Average
13.255
34.03
55.742
Table 5.5: The average results of D when considering di/dt to be constant.
calculated with this approach is again not close to the expected values preA
A
sented in chapter 3, (100 µs
- 600 µs
). Since none of the two approaches gives
results close to the expected values of the HF quenching capability parameters, it could indicate that the quenching capability of the VCB cannot be
calculated when the current through the VCB is very low. Because of the
results the values of the HF current quenching constants, Cc and Dd are set
to the suggested values in [1]
A
µS
µs2
A
Dd = 350 .
µs
Cc = 0
5.6
Closing the circuit
When the contacts in the VCB start moving together the dielectric withstand
of the gab between them starts to get smaller. At one point the dielectric
withstand of the gab will become smaller than the voltage across the contact
and a breakdown of the vacuum will occur.
5.6.1
Prestrikes
This conducting vacuum arc formed by the breakdown will cause the voltage between the breaker contacts to go to zero. In figure 5.12 a plot of the
voltage across the VCB channels and the current during 3 prestrikes of the
breaker is seen. As seen in figure 5.12 the prestrike creates an oscillating
HF current. This current is interrupted at one of its current zeros, when
di/dt is low enough and the voltage over the VCB channels reappears. The
arc appears again the next time the voltage over the contacts reaches the
52
5.6 Closing the circuit
HTTP1L100C1x05Dt2−7V6,9kIN11.lvm
Voltage[V]
5000
0
−5000
−10000
6180
6190
6200
6210
6220
6230
6240
6250
6260
6190
6200
6210
6220
6230
6240
6250
6260
Current[A]
200
100
0
−100
−200
6180
Time[us]
Figure 5.12: The plot shows the voltage across the breaker channels and the current through the breaker when during 3 prestrikes. The test is made
with 100m cable and at a closing angle of 22.5◦ .
decaying dielectric withstand of the VCB.
Prestrikes are also observed in the system using a 10m cable and in the
same way as the reignitions, the prestrikes created in this setup seems to
have a much shorter lifetime. In figure 5.13, 4 prestrikes from measurements
with the 10m cable are seen. In the same way as when the 100m cable is
used the prestrike forces the voltage across the contact to go to zero. After
the restrikes in figure 5.13 the voltage is going more smoothly back to the
previous voltage level than when using the 100m cable. Just after it reaches
the previous voltage level another restrike is created whereas in the case
with 100m cable the voltage across the cannels kept were steady for a while
before another restrike was created.
In the VCB model used in the simulations the rate of decay of dielectric
withstand (RDDS) is set to have the same value as the RRDS. In the description of the VCB model [7] prestrikes are not treated, and therefore it
was decided to examine the RDDS to see if it has the same value as the
RRDS. In appendix F the RDDS in the VCB have been calculated. On the
CD the fulle appendix F is found, this contains the pictures and data used
in the calculation, the result of the calculations is seen in appendix F in the
report. The calculations have only been done at voltage level 5.75kV for the
system using the 10m cable, due to the experiences made when calculating
Laboratory Tests and Results
53
HTTP1L10C1x05Dt2−7V6,9kIN9.lvm
Voltage[V]
10000
5000
0
−5000
5500
5510
5520
5530
5540
5550
5510
5520
5530
5540
5550
Current[A]
100
50
0
−50
−100
5500
Time[us]
Figure 5.13: The plot shows the voltage across the breaker channels and the current through the breaker when during 4 prestrikes. The test is made
with 10m cable and at a breaking angle of 202.5◦ .
the RRDS. Table F.1 show the results of the calculations. As the results
show the average value of the RDDS is found to be 147.1V /µs, this value is
almost 4 times higher than the result of the RRDS which was found to be
37.88V /µs.
This result points out a weakness of the used VCB model and shows a need
of a VCB model where the RDDS is investigated and treated as a individual
parameter.
The results in table F.1 also show how the closing angle affects the number of prestrikes. This can be seen more clearly from table 5.6 where some
results from table F.1 have been picked out and arranged according to the
closing angle. As seen from table 5.6 the closing angle has the opposite effect
Test nr.
Clos. angle[◦ ]
Prestrikes
9
0
0
8
67.5
3
7
90
6
3
112.5
4
4
180
2
5
202.5
4
10
270
6
6
316
2
Table 5.6: The table shows the relation between the opening angle and the number
of prestrikes of the vacuum arc. The results are from the tests made
at 5.75kV using the 10m cable.
on the number of prestrikes than the breaking angle has on the number of
54
5.6 Closing the circuit
HTTP1L10C1x05Dt1−6V6,9kIN1.lvm
HTTP1L10C1x05Dt1−6V6,9kIN3.lvm
10
8
6
0
−10
2
Current[A]
Current[A]
4
0
−2
−4
−20
−30
−6
−40
−8
−10
0
10
20
30
40
50
Time[ms]
(a) Breaking angle 0◦
−50
0
10
20
30
40
50
Time[ms]
(b) Breaking angle 270◦
Figure 5.14: The plots shows the current through the breaker when closing the
circuit at 0◦ and at 270◦ , both measurements are made with 10m
cable.
reignitions. Table 5.6 shows that when closing the breaker at low voltage
and high current the number of prestrikes is low and when closing the VCB
at high voltage and low current the number of prestrikes is high.
5.6.2
Current During Closing
The current during the closing operation of the breaker is expected to be of
the same shape as found in the example in chapter 2. In figure 5.14 the current transients generated by an closing operation, with closing angles of 0◦
and 290◦ is seen. As seen from figure 5.14a the exponential transient term
becomes almost zero and the current follows the power frequency current
immediate after separation, when the closing angle is 0◦ . In figure 5.14b
the closing angle is 270◦ this means that the exponential transient term will
obtain its maximum starting value and after separation lead the current towards the steady state current.
As figure 5.14 shows the current after the closing operation consist of the
exponential transient term and the steady state term, as explained in chapter 2. But as seen in figure 5.14, a higher frequency term is also affecting the
current just after contact separation. This term is caused by the same phenomena that causes the TRV and the oscillating term will have a constant
frequency dependent of the inductances and capacitances in the system. The
frequency of the oscillating transient caused by the closing operation can be
found by using equation 2.14, which is also used to find the frequency of
the TRV. The inductance of the system is the same as in the opening case,
but now the load capacitance (0.5µF ) becomes the dominant capacitance.
Laboratory Tests and Results
55
HTTP1L100C1x05Dt1−6V6,9kIN3.lvm
HTTP1L10C1x05Dt1−6V6,9kIN3.lvm
20
8
0
6
−20
4
Current[A]
Current[A]
−40
2
0
−2
X: 13.47
Y: −1.953
−4
−80
−100
−120
X: 10.36
Y: −4.297
−6
−60
X: 34.52
Y: −125
−140
−8
X: 31.63
Y: −143.8
−160
−10
0
10
20
30
40
Time[ms]
50
−180
0
10
20
30
40
50
Time[ms]
(a) 10m cable
(b) 100m cable
Figure 5.15: The plots shows the current through the breaker when closing the
circuit at 0◦ and at 290◦ . Data measurements are set in order to
calculate the frequency of the oscillating transient.
This means that the frequency of the oscillating transient should be almost
simular for the two cable lengths. In this case we will say that the load capacitance is the only capacitance in the system and the frequency is therefore
expected to be
fopen =
1
√
= 399.14Hz.
2 · π 0.318H · 0.5µF
(5.2)
In figure 5.15 data markers have been placed on the current curves and
from the value of the data markers the frequency of the oscillating transient
can be found. The frequency is only found in these two measurements, as
the results from section 5.2 showed that the frequency of the oscillations is
constant. The 2 frequencies is found to
1
= 390.63Hz
12.84ms − 10.28ms
1
=
= 311.53Hz.
34.66ms − 31.45ms
fopen10 =
fopen100
The results shows that the frequency, for both cable lengths, is almost the
same as the calculated frequency 399.14Hz. For the system using the 100m
cable the frequency is more inaccurate. This is because the capacitance of
the cable is larger in this system and thereby has a larger influence on the
system.
56
5.6 Closing the circuit
Chapter
6
Simulations
To simulate the system it was decided to set up a simulation model in
PSCAD. The VCB model that is used in the simulation of the system is
described in [7]. The model uses the parameters found in chapter 5 to
describe the behaviour of the VCB. In figure 6.1 the setup of the simulation
model for the system is seen.
Figure 6.1: Setup of the system representing the laboratory setup when using the
10m cable.
The ideal voltage generator in the left side of the circuit represents the net
voltage supplying the vario-transformer, the vario-transformer and the cable
leading from the vario transformer to the HTT transformer. The inductance
of 0.318H represents the HTT transformer, the value of the inductance is
found by looking at the nominal load of the transformer. The impedance of
the transformer is calculated to be
Z = ex ·
10kV 2
Vm2
= 0.1 ·
= 100Ω
Sm
100kV A
(6.1)
The factor ex , is the short-circuit impedance of the transformer, this value
is set to be purely resistive and its value is set to 0.1. The inductance of the
58
6.1 Opening the Vacuum Circuit Breaker
transformer can now be found.
Z = 2 · π · f · L ⇒ L = 0.318
(6.2)
The capacitance of 1575.7pF represents the 10m cable, the value of the
capacitance is found according to table 4.1. The box called BRK is the
model of the VCB where the values found in chapter 5 are inserted in order
to represent the VCB used in this project. The box over the VCB called
T imedBreakerLogicClosed@t0 is the control of the VCB, the box enables
the user to open or close the VCB at a specific time. The capacitance of
0.5µF and the resistance of 10M Ω is the load and the discharging resistance.
The signals Eload , Etrans and Iout correspond to the voltage and current
measurements from the laboratory setup and the small boxes over the system
handles the plotting of the simulation results. The measurement Ea is the
voltage across the VCB contacts.
6.1
Opening the Vacuum Circuit Breaker
In the first simulations made with the described system, a breaker opening
is simulated. The breaking time is set to be 50ms, which should give a
breaking angle of 180◦ (measured on the voltage) and should result in some
reignitions of the breaker and a large amplitude of the TRV, as observed in
the laboratory measurements. In figure 6.2 the simulation is seen. As seen
from the simulation the current does not break at 50ms as expected, instead
the vacuum arc remains and the current is not interrupted before it crosses
zero at 55ms. It was discovered that this problem arises due to the current
chopping level. The parameters used to find the current chopping level in
the model of the VCB are α = 6.2 · 10−16 s and β = 14.2. These parameters
should give a chopping level that is more than enough to chop the current
as soon as the VCB contacts separate.
It was tried to change the time of contact separation, to see if the arching time had any influence on the chopping level in the simulation model. It
was discovered that if the VCB opens at current maximum or minimum the
chopping level is set to zero. Therefore the time of contact separation was
set to 0.49ms, the results of running the simulations with the new opening
time of the VCB is seen in figure 6.3. As figure 6.3 shows the VCB has a
current chopping level of 0.0005A for this current, and a oscillating TRV
is created when the current is interrupted, when the oscillation is damped,
the voltage between the VCB contacts follows the transformer side voltage
as expected, with opposite sign due to the orientation of the measurement
of Ea . The damping time of the oscillation is around 10ms, in the tests
with the 10m cable the damping time was only 1ms. The reason for this
difference is probably the lack of detail in the simulation model.
Simulations
59
Simulation of VCB opening
TRV[kV]
10
0
−10
−20
52
54
56
58
60
62
64
66
68
54
56
58
60
62
64
66
68
−4
Current[A]
5
x 10
0
−5
−10
−15
52
Time[ms]
Figure 6.2: Simulation of opening the VCB with the constants found and described in chapter 5. The breaker opens at angle of 180◦ , but current
is not interrupted before 270◦ . The simulation uses the parameters
for the 10m cable.
Simulation of VCB opening
TRV[kV]
10
0
−10
−20
52
54
56
58
60
62
64
66
68
54
56
58
60
62
64
66
68
−4
Current[A]
5
x 10
0
−5
−10
−15
52
Time[ms]
Figure 6.3: This simulation shows the TRV created by an opening operation, the
current is interrupted just before 270◦ . The simulation is for the
system using 10m cable
60
6.1 Opening the Vacuum Circuit Breaker
It was expected to see some reignitions of the vacuum arc, but this is not
seen in the simulation model. The reason why no reignitions occur is that
the TRV never exceeds the dielectric withstand of the VCB. As mentioned
before the lack of detail in the simulation models of the different components
results in a TRV that is not the same as the measured TRV. Therefore it
was decided to use the pi-equivalent circuit model for the cable, to try and
improve the model. This model includes also the inductance and the resistance of the cable from table 4.1. The setup of the new simulation model is
seen in figure 6.4.
Figure 6.4: Setup of the system representing the laboratory setup when using the
pi-equivalent circuit model and the parameters for the 10m cable.
Using the pi-equivalent circuit to model the cable does not make any changes
to the simulation results, the result is still the same as in figure 6.3, with
a damping time of around 10ms. In figure 6.5 a graph of the TRV under
the opening process is shown together with the dielectric withstand of the
VCB. The parameters used to describe the dielectric withstand is set to
A = 37.88V /µs and B = 0 according to the calculations from section 5.4. It
can be seen from figure 6.5, that the problem of the simulations is found in
the shape of the TRV created by the breaking operation. To try and force a
reignition of the VCB, the opening time of the VCB was moved very close to
the time of current chopping, but the amplitude of the TRV does not get a
value that is high enough to make the TRV exceed the dielectric withstand
of the VCB. The difference between the tests and the simulation model is
that, as soon as the VCBs contact seperate in the real tests the current is
chopped and the TRV starts rising. This causes reignitions of the vacuum
arc. In the simulation the current is not chopped at the time of seperation
and the dielectric withstand becomes too high for reignitions to occur.
The simulation model of the VCB is a closed model and its source code
cannot be seen. Therefore it is not possible to investigate the problem of
the current chopping level further. The results of the simulations suggest
that the VCB model always sets the current chopping level under the current level. This would explain why the current is not chopped immediately
Simulations
61
Simulation of VCB opening
25
TRV
Breaker withstand voltage
20
TRV[kV]
15
10
5
0
−5
53.8
53.9
54
54.1
54.2
54.3
54.4
54.5
54.6
Time[ms]
Figure 6.5: The simulation shows the TRV and the dielectric withstand of the
VCB. As seen the time of seperation has been moved to 54ms (270◦ )
to try and force reignitions.
after contact seperation. In order to analyse the problem, the VCB model
should be tested at a higher current level.
Another step of improving the simulation model would be to use the PSCAD
cable model to describe the cable and to transform an already made Simulink
model of the HTT transformer to a PSCAD model in order to get a more
precise model of the system. These opportunities were investigated, but
they were found to be too time consuming to be included in this project.
The VCB model should also be tested at other current levels to see if the
problem with the chopping level is a fault in the model or a result of the low
current level of the VCB.
Instead it was decided to continue using the circuit in figure 6.4 and only
analyse the frequency of the TRV and effect of breaking angle during the
opening operation. As mentioned, figure 6.3 shows the simulated TRV in
the system using a 10m cable. In figure 6.6 the result of a simulation, using
the parameters for the 100m cable is seen. The simulation opens the VCB
contacts after 49ms. Again it is seen that the current does not get chopped
at contact seperation but a vacuum arc conducts the current and it is not
extinguished before the current chopping level, set by the simulation model,
is reached at 55ms. Figure 6.6 shows that the damping problem in the
simulation model becomes more significant when simulating the 100m ca-
62
6.1 Opening the Vacuum Circuit Breaker
Simulation of VCB opening
TRV[kV]
10
0
−10
−20
52
54
56
58
60
62
64
66
68
54
56
58
60
62
64
66
68
−4
Current[A]
5
x 10
0
−5
−10
−15
52
Time[ms]
Figure 6.6: Simulation of opening the VCB in the system with 100m cable, the
current is interrupted at 270◦ .
ble. The TRV created by the breaking process continues to oscillate without
any damping, where the test result showed that the oscillation in this setup
would be completely damped after around 2.3ms. These simulation results
again show the need for a better simulation model of the circuit components.
6.1.1
Frequency analysis
The frequency of the performed simulations was measured in order to make
a comparison of the calculated frequencies and the measured frequencies. In
figure 6.7 the simulations and data points for the frequency calculations are
seen. Using this data the frequencies of the TRV for the two cable lengths
were found to
1
= 7149Hz
54.4ms − 54.25ms
1
=
= 2272Hz
54.92ms − 54.48ms
fT RV 10 =
fT RV 100
These results correspond to the data found in chapter 2 where a circuit representing a transformer and a cable where disconnected from a capacitive load.
The frequencies found in the measurements where fT RV 10 = 8708, 92Hz and
fT RV 100 = 2953, 87Hz. The difference in simulated and measured frequency
can be seen as a result of the lack of detail in the simulation model, as
already described.
Simulations
63
Simulation of VCB opening
5
X: 54.26
Y: 4.362
Simulation of VCB opening
1.5
X: 54.4
Y: 4.223
4
1
3
0.5
TRV[kV]
TRV[kV]
2
X: 54.92
Y: 1.332
X: 54.48
Y: 1.245
1
0
−1
0
−0.5
−2
−3
−1
−4
−5
54
54.5
55
55.5
56
−1.5
54
54.5
Time[ms]
55
55.5
56
Time[ms]
(a) 10m cable
(b) 100m cable
Figure 6.7: The two plots shows the TRV generated in the system using 10m and
100m cable. For both simulations the breaking angle is 270◦ .
Simulation of VCB opening
5
4
4
3
3
2
2
TRV[kV]
TRV[kV]
Simulation of VCB opening
5
1
0
−1
1
0
−1
−2
−2
−3
−3
−4
−4
−5
44
44.5
45
45.5
46
−5
54
Time[ms]
(a) VCB contacts separates at 40ms
54.5
55
55.5
56
Time[ms]
(b) VCB contacts separates at 50ms
Figure 6.8: The simulation shows the TRV when the VCB is set to open at 39ms
and 49ms which results in breaking angles of almost 90◦ and almost
270◦ .
6.1.2
Analysis of breaking angle
As the current chopping level in the simulations cannot be changed, the
breaking angle can only obtain two values. The two possible breaking angles
of the voltage lay just before 90◦ or just before 270◦ . In the simulations
already made the opening time of the VCB has been set to 49ms which
gives a breaking angle of almost 270◦ and to obtain the breaking angle of
almost 90◦ the opening time of the VCB was set to 39ms. Figure 6.8 shows
the result of the simulations performed with the two opening times. The
two simulations in figure 6.8, results in a TRV with the same amplitude but
64
6.2 Closing the Vacuum Circuit Breaker
Simulation of VCB closing
−3
Simulation of VCB closing
3
x 10
0.015
2
0.01
Current[A]
Current[A]
1
0.005
0
−0.005
X: 51.23
Y: −0.003063
X: 58.37
Y: −0.008888
54
−1
−2
X: 55.9
Y: −0.009806
−0.01
−0.015
52
0
56
58
60
X: 53.74
Y: −0.002395
−3
62
Time[ms]
(a) 10m cable
64
66
68
−4
42
44
46
48
50
52
54
56
58
Time[ms]
(b) 100m cable
Figure 6.9: The two plots shows simulations of closing the VCB with both cable
lenghts. The data markers are used to find the frequency of the oscillating transients. The closing angle of the VCB is 270◦ for plot a and
180◦ for plot b.
with different sign. This is similar to the results obtained in the laboratory
tests, where breaking angles that are 180◦ apart have the same amplitude
but with different sign.
6.2
Closing the Vacuum Circuit Breaker
When closing the VCB model, the slow transients, described in chapter
2, the fast oscillating transients, described in section 5.6.2 and prestrikes
of the vacuum arc, that were seen in section 5.6.2, can be seen from the
simulation results. In this section the frequency of the oscillating transients
will be calculated and an analyse of the prestrikes will be made. During the
simulations of the closing operation it was discovered that the prestrikes in
the VCB only occurs when the pi-equivalent model of the cable was used.
This emphasises the importance of the level of detail in the simulation model.
6.2.1
Frequency of Oscillating Transient
The frequency of the oscillation transient is expected to be around 400Hz.
Figure 6.9 shows a plot of the oscillating transient for both cable lenghts,
the frequency of the two setups can be found using the data markers seen
on figure 6.9
Simulations
65
Simulation of VCB closing
Voltage[kV]
15
Voltage between VCB contacts
Breaker withstand voltage
10
5
0
−5
55.2
55.3
55.4
55.3
55.4
55.5
55.6
55.7
55.8
55.5
55.6
55.7
55.8
−3
Current[A]
5
x 10
0
−5
−10
55.2
Time[ms]
Figure 6.10: The plot shows the voltage between the VCB contacts and the current through the VCB just before the VCB contacts meet. As the
plot shows, prestrikes of the VCB occur.
1
= 411.35Hz
58.372msb − 55.941ms
1
fT RV 100 =
= 399.2Hz
53.74ms − 51.235ms
fT RV 10 =
As these results show the two frequencies are both very close the expected
frequency of 400Hz. The calculations shows that the frequencies are not
the same for both cable lenghs, this is as mentioned earlier because the
capacitance and inductance in the system changes a bit when changing the
cable. But since the load capacitance 0.5µF is the dominant capacitance
in the system, the change of cable will not have a very large effect on the
frequency of the oscillations.
6.2.2
Prestrike simulation
A look at what happens very close to the time where the two VCB contacts
meet, shows that some prestrikes occur in the simulation results. These prestrikes take the same shape as expected, and force the voltage betweeen the
VCB contacts to go to zero and after the vacuum arc extinguishes. In figure
6.10 simulated prestrikes from the system using a 10m cable are seen. The
simulation shown in figure 6.10 is made with a cable length of 10m and at
a closing angle of 270◦ . When the voltage between the VCB contacts goes
to zero, because of a restrike, the current starts oscillating. These oscilla-
66
6.2 Closing the Vacuum Circuit Breaker
Simulation of VCB closing
Simulation of VCB closing
3
9
8
2.5
7
6
Voltage[kV]
Voltage[kV]
2
1.5
1
5
4
3
2
0.5
1
0
0
−0.5
50.6
50.7
50.8
50.9
51
51.1
51.2
Time[ms]
(a) Closing angle 180◦
51.3
51.4
−1
55
55.1
55.2
55.3
55.4
55.5
55.6
55.7
55.8
Time[ms]
(b) Closing angle 270◦ e
Figure 6.11: The two plots shows simulations of closing the VCB at different
times, iin the system using the 10m cable. As seen the two different
closing angles causes a different number of prestrikes.
tions are quenched very fast and the voltage between the contacts are led
smoothly back to the previous level. This process repeats it self when more
prestrikes occur.
The voltage plot on figure 6.10 also shows how the dielectric withstand
of the VCB decays and as expected the prestrikes occur when the voltage
between the VCB contacts exceeds the dielectric withstand. The RDDS can
be calculated from the plot and is found to be A = 37.88V /µs, the same
value as the inserted value of RRDS. The VCB contacts start moving together at 55ms and are fully together at 55.55ms, this gives a closing time
of the VCB of 0.55ms. This time is not adjusteble in the model and can
therefore not be set to the value found in the laboratory tests.
In order to investigate if the number of prestrikes were dependent on the
closing angle of the VCB, a number of simulations were made. The relation
between the number of prestrikes and the closing angle was found to be the
same as in the laboratory tests and in figure 6.11 two simulations of a closing
operation are seen. As seen from the plot in figure 6.11, a closing angle of
180◦ on the voltage gives few prestrikes, in this case 1, and a closing angle
of 270◦ gives more prestrikes, in this case 4. So as found in the laboratory
tests, high voltage between the VCB contacts when a closing operation is
started gives many prestrikes and a little voltage between the contacts gives
few prestrikes.
Chapter
7
Discussion
The results obtained in the project will be discussed and compared in this
chapter. First a description of the measurements and calculations, made in
order to find the VCB model parameters will be given. Then a description
and comparison of the calculated, measured and simulated results when
opening and closing the VCB is given. Finally a description of the further
work needed, in order to determine the model parameters of the VCB and
the further work on the simulation model, will be given.
7.1
Voltage Circuit Breaker Model Parameters
The parameters used to model the VCB in the PSCAD simulation model,
were found based on a series of tests. The result of these tests were analysed
and from these analyses the parameters were calculated.
The chopping current was the first parameter of the VCB model that was
treated. The current chopping phenomena were hard to observe at high
voltage levels because of the high current transients created at these levels.
At lower voltage levels the chopping effect was seen quiet clearly and an attempt on calculating the current chopping level of the VCB was made. But
since the laboratory setup conducts a current which is under the current
chopping level of the breaker the value of the parameters α and β could not
be determined for this breaker. The parameters of α and β were therefore
chosen to standard values, which should give a current chopping level of
3A-8A in the simulation model.
An analyse of the reignitions of the vacuum arc was made in order to determine the dielectric withstand of the VCB. As expected the circuit configuration changed the number of restrikes of the vacuum arc, when using
the 100m cable few reignitions were created and when using the 10m cable
68
7.2 Opening the Vacuum Circuit Breaker
many reignitions were created. The analyse of the reignitions showed that
the VCB has a RRDS of 37.88V /µs. This value corresponds to the suggested
value range of RRDS when testing VCBs. The value of the RRDS gives a
maximum dielectric withstand of the vacuum between the VCB contacts
of 30.43kV /mm. In [8] the dielectric withstand of vacuum is stated to be
between 20kVrms /mm and 30kVrms /mm. The rms value in this project is
21.52kVrms /mm, therefore found value of the RRDS of the VCB seems to
be acceptable.
The HF quenching capability of the VCB was also examined and two methods of determening the simulation parameters were used. The methods gave
very different and varying results. When the HF quenching capability is considered to be constant its values should lay between 100A/µs and 600A/s,
which indicate that the result found in this project is wrong. The difference between the calculated value and the expected value, is most likely to
be caused by the current level in the system, and it is expected that tests
conducting larger currents will give better results of the HF quenching capability of the VCB. Due to this, the value of the HF quenching capability
was set to be 350A/s in the simulation model.
The prestrikes during a closing operation of the VCB were also observed
and the RDDS of the VCB was calculated. The value of RDDS is calculated in the same way as the value of RRDS and the RDDS of the VCB was
found to be 147.1V /µs. However it is not possible to set the RDDS in the
simulation model, the value of the RDDS will be set to the the value of the
RRDS, 37.88V /µs.
When inserting the found and decided parameters in the VCB model and
inserting the model in the simulation model of the laboratory setup it was
expected to observe the phenomena, that is described by the VCB theory
and is also seen from the test results.
7.2
Opening the Vacuum Circuit Breaker
The TRV that arises in the system, after a breaking operation, was observed
in both the laboratory tests and in the simulations of the system. In chapter
2 the expected frequency of the TRV was calculated based on the capacitance
of the cable and the inductance of the HTT transformer. The results of these
calculations were fT RV 10 = 7110Hz and fT RV 100 = 2248Hz. A comparison
of the TRV found in the laboratory and the TRV found in the simulations
is seen in figure 7.1. As figure 7.1 shows the measured frequency and the
simulated frequency for the system using 10m cable are almost similar, and
have been calculated to 8708, 92Hz for the measurements and 7149Hz for
Discussion
69
Simulation of VCB opening
TRV[kV]
5
0
−5
54
54.5
55
55.5
56
56.5
Measurement of VCB opening
TRV[kV]
2
1
0
−1
−2
3.5
4
4.5
5
5.5
6
Time[ms]
Figure 7.1: Comparison of the simulated and the measured results of at VCB
opening, when the breaking angle is 270◦ and the 10m cable is used.
the simulations. When using the 100m cable the frequency of the TRV have
been calculated to 2953, 87Hz for the measurements and 2272Hz for the
simulations. As the results shows the simulated value is almost equal to
the value calculated, whereas the measured result is a bit different. This
difference between the measured result and the simulated/calculated result
comes from the lack of detail in the simulation/calculation model. In order
to improve this a more detailed model of both transformer and cable, should
be used in further work with the simulation model.
As figure 7.1 shows the simulation does not apply the right damping to
the system, the measured damping time of the TRV, using the 10m cable,
is 1ms whereas the simulation gives a damping time of 10ms. This is also
caused by the lack of detail in the simulation model. The damping problem
of the simulation model gets worse when switching from the 10m cable to
the 100m cable, where almost no damping is applied to the TRV.
When simulating a opening operation of the VCB it was expected to observe some reignitions of the vacuum arc, but no reignitions were seen. It
was found that these problems were caused by the current chopping level
of the VCB. In the laboratory tests the current is chopped immediately after the contact seperation, since the current level in the tests is under the
current chopping level of the VCB. This was also expected in the simulation, but in the simulation the current chopping level is set to be 0.0005A
70
7.3 Closing the Vacuum Circuit Breaker
with the used values of α and β, where a current chopping level of 3A-8A
is expected. Since it is not possible to see the source code of the simulation
model a investigation of the problem could not be made. But the results
suggest that the current chopping level in the VCB model is always set to
be under the current level.
As explained in the report the rate of rise of the TRV is a very important
parameter in the generation of reignitions of the vacuum arc. Therefore it
is important that the simulation model gives a correct TRV according to
the laboratory measurement, when studying reignitions. When the problems with the current chopping level is solved the simulation model might
be good enough to make a study of reignitions of the vacuum arc. But in
order to get the best results, the problems with the simulation of the TRV
should be solved, this is done by using more accurate models of the transforemr and the cable. PSCAD has a cable model that could be applied in
the simulation setup, a detailed model of the HTT transformer is already
made in Simulink, this model should be transformed to a PSCAD model
and used in the simulation.
7.3
Closing the Vacuum Circuit Breaker
The measurements taken during a VCB closing operation show that the exponential transient term is affecting the current through the VCB in the
way described in section 2.1. The result of two tests is shown in figure 5.14,
one where the VCB closes at 270◦ and one where the VCB closes at 0◦ .
When the VCB closes at a angle of 90◦ or 270◦ the exponential transient
will have maximum effect and when the VCB closes at angles of 0◦ or 180◦
the exponential transient will have minimum effect.
When closing the VCB some fast oscillations occure due to the capacitances
and the inductances of the system. The frequency of these oscillations is
found in the same way as the frequency of the TRV. But when the circuit
is closing the dominant capacitance of the system becomes the load and
the frequency of the oscillations have been calculated considering the load
capaticance to be the only capacitance of the system. The frequency of the
oscillations have been calculated to 399.14Hz for both cable lenghts. When
examining the system using the 10m cable a frequency of 390.63Hz is found
from the measurements and a frequency of 411.35Hz is found in the simulations. And when using the 100m cable a frequency of 311.53Hz is found
from the measurements and a frequency of 399.2Hz is found in the simulations. As seen the measured frequencies and the simulated frequencies are
very similar, only the measurement using the 100m cable is a bit different.
The reason for this is that the capacitance and inductance of the 100m cable
Discussion
71
Simulation of VCB closing
Voltage[kV]
10
5
0
−5
55
55.2
55.4
55.6
55.8
56
Measurement of VCB closing
Voltage[kV]
10
5
0
−5
5.2
5.25
5.3
5.35
5.4
Time[ms]
Figure 7.2: Comparison of prestrikes in simulation and measurement, both plots,
shows the voltage between the VCB contacts. The system uses the
10m cable and have a closing angle of 270◦ .
affects the system and the load capacitance is not as dominating as when
the 10m cable is used.
When simulating a VCB closing operation it was possible to observe the
prestrikes that occur in the VCB. When a prestrike occurs in the simulation it forces the voltage between the contacts to jump to zero and causes a
oscillating HF current. Figure 7.2 shows a plot of the voltage between the
VCB contacts from simulation and from the measurement, during a closing
operation of the VCB. Figure 7.2 shows a clear connection between the measured prestrikes and the simulated pretrikes. In both cases the voltage drops
to zero when a restrike occurs, the created vacuum arc extinguishes almost
immediately and the voltage between the contacts is smootly led back to its
previous level.
The opening time of the VCB and the RDDS are not variable parameters in
the VCB model, this means that the simulation of restrikes is not as precise
as desired. The simulation has a fixed closing time of 0.55ms where the actual closing of the VCB was measured to be 12ms. The RDDS of the VCB
model is set to have the same value as the RRDS, and in this case 37.88V /µs
where the RDDS measured on the VCB was found to be 147.1V /µs. This
means that the voltage in the simulations, does not reach the right level
when recovering after a prestrike, since the slope of the dielectric withstand
72
7.4 Further Work
is too low.
The simulation of the prestrikes showed the same dependency of closing
angle as found in the measurements. Closing angles at high voltages gives
many prestrikes and closing angles at low voltages gives few prestrikes. In
figure 6.11 this is shown by simulating a closing angle of 180◦ (voltage zero
crossing) and 270◦ (voltage maximum) these simulations give 1 and 4 prestrikes respectively. This also shows that 4 is the maximum number of prestrikes in the simulation, the measured results showed a maximum number
of 6 prestrikes (at angle 270◦ ). The difference in the maximum number of
prestrikes for the measurements and for the simulations can be seen in figure
7.2. This difference comes from the difference in closing time and the differene in RDDS between the real VCB and the simulation model of the VCB.
The prestrikes of the VCB can only be simulated in the simulation model
that is using the pi-equivalent model of the cable. This fact shows the importance of a precise simulation model and it suggestes to improve the model
of the transformer and the cable as already described.
The fact that it is possible to simulate the prestrikes in the VCB model,
support the theory that the current chopping level is the reason why the
restrikes of the VCB cannot be simulated.
7.4
Further Work
The results of this project shows the need of some further work, both on the
laboratory setup and on the simulation model. In order to determine the
current chopping level and the HF quenching capability of the VCB, some
test at a higher current level than used in this project are needed. The ideal
scenario would be tests conducting the nominal current of the VCB 1250A.
If this is not possible, tests with a current of at least 8A − 10A (expected
current chopping level) should be applied. Tests done with these currents
should make it possible to find the values of α and β and with the right
values of these parameters the simulation model should be able to produce
restrikes, HF currents etc. From tests with higher currents it is also expected that a more precise value of the quenching capability of the VCB can
be found.
The simulation model also requires some further work in order to fully represent the laboratory setup. In this project the laboratory setup has been
represented by lumped circuit element, in order to improve the model this
should be improved. The HTT transformer has already been modelled in
Simulink in a previous project, so in order to improve the model used in this
Discussion
73
project the Simulink model could be transformed to a PSCAD model and
used. In order to improve the representation of the cable, a PSCAD cable
model should be used.
The above improvements should make it possible to fully test the VCB
model. These tests will determine if the model is fulfilling its purpose or
if changes in the model are required. Changes to the VCB model could be
introducing the RDDS, the opening time and the closing time as variable
parameters.
74
7.4 Further Work
Chapter
8
Conclusion
This project has investigated the generation of high voltage transients from
a vacuum circuit breaker (VCB). The investigation has concerned with theoretical research, expermential tests and simulations studies.
The different physical phenomena of a VCB were investigated, the current chopping level, the dielectric strength and the HF quenching capability.
These phenomena are all described using a mathematical model and the
model includes parameters which determine the behaviour of the specific
VCB. Methods for finding the parameters from test results wer determined
and a series of tests were performed on the VCB.
The result of the tests showed that a transient recovery voltage (TRV) is
created when the VCB is opened. The frequency of the TRV was found to
be dependent of the network setup and when using a 100m cable the frequency was found to be 2953, 87Hz where the 10m cable gave a frequency
of 8708, 92Hz. It was shown that the amplitude of the TRV is dependent
of the VCB breaking angle. The rate of rise and the amplitude of the TRV
were found to have a big influence on the behaviour of the VCB during
current interruption. The two parameters play a big role in the creation
of restrikes in the VCB, the reignitions in the VCB are created whenever
the dielectric strength is exceeded by the TRV. The rate of rise of dielectric
strength (RRDS) during an opening operation was found to be 37.88V /µs.
The parameters for determening the current chopping level could not be
found, as the current in the test setup was under the current chopping level
of the VCB. An attempt of finding the HF quenching capability of the VCB
was made, but the result was very varying, which is also expected to be
because of the low currents level in the tests. The parameters of the current
chopping and the HF quenching capability were therefore set to standart
values in the simulations.
76
Measurements were also taken during closing operations of the VCB, these
measurements showed an exponential current transient and a faster oscillating transient, as expected. The frequency of the fast oscillating transient
was expected to be 399.14Hz for both cable lenghts and was found to be
390.63Hz when the 10m cable was used and 311.53Hz when 100m cable is
used. On the measurement of the closing operation, prestrikes of the vacuum
arc was observed and the RDDS of the VCB was calculated to be 147.1V /µs.
The parameters of the VCB model were inserted in a PSCAD model of
a VCB. The model of the VCB is used in a simulation model that represents the complete laboratory setup. The simulation results in a TRV with
a frequency of 7149Hz for the system with 10m cable and 2272Hz for the
system using 100m cable. During the simulations it was discovered that the
level of the current chopping is always set to be smaller than the current in
system, this meant that the simulations could not reproduce the restrikes of
the vacuum arc seen in the VCB tests. The simulation of a closing action of
the VCB, shows the exponential transient, the oscillating transients and the
prestrikes of the VCB. The RDDS of the VCB found from the tests results
cannot be inserted in the PSCAD model of the VCB, the PSCAD model
uses the value of the RRDS as the value of the RDDS.
In order determine the parameters for modelling the current chopping level
and the HF quenching capability, new tests at higher current level should
be made. In order to get more precise simulation results an improvement of
the simulation model is also required.
Bibliography
[1] Tarik Abdulahovic. Analysis of high-frequency electrical transients in
offshore wind parks. Master’s thesis, Chalmers University of Technology, Department of Energy and Environment Division of Electric Power
Engineering, 2009.
[2] D.J.Clare. Failures of encapsulated transformers for converter winders
at oryx mine. Electron Magazine, March 1991.
[3] J. Duncan Glover and Mulukutla S. Sarma. Power System Analysis
and Design. The Wadsworth Group, 3th edition, 2002.
[4] Allan Greenwood. Electrical Transients in Power Systems. John Wiley
and Sons, inc, 2th edition, 1991.
[5] Allan Greenwood. Vacuum Switchgear. The institution of Electrical
Engineers, 2th edition, 1997.
[6] J. Helmer and M. Lindmayer. Mathematical modeling of the high
fiequency behavior of vacuum interrupters and comparison with measured transients in power systems. XVIIth International Symposium on
Discharges and Electrical Insulation in Vacuum,, July. 1996.
[7] Rao Kondala and Gajjar Gopal. Development and application of vacuum circuit breaker model in electromagnetic transient simulation.
IEEE Power India Confrence, 2006.
[8] F. H. Kreuger. Industrial High Voltage: Fields/Dielectrics/Constructions. Ios Pr Inc, 3th edition, 1991.
[9] Morten Lerche. Optimization of laboratory setup for determination of
breaker characteristics. Msc prepatory project, Technical University of
Denmark, 2008.
78
BIBLIOGRAPHY
[10] A. Mazur, I. Kerszenbaum, and J. Frank. Maximum insulation stresses
under transient voltages in the hv barrel-type winding of distribution
and power transformers. IEEE Transactions on Industry Applications,
1988.
[11] Örn I. Björgvinsson. Theoretic and experimental investigations of
switching transients in wind turbines. Msc project, Technical University
of Denmark, 2006.
[12] Siemens. 3ah vacuum circuit-breakers. Medium-Voltage Equipment,
Catalog HG 11.11, 1999.
[13] Rene Peter Paul Smeets. ow-current behaviour and current chopping
of vacuum arcs. Proefschrift, Technische Universiteit Eindhoven, 1987.
[14] W. Sweet. Danish wind turbines take unfortunate turn. Spectrum,
IEEE, November 2004.
[15] Lou van der Sluis. Transients in Power Systems. John Wiley and Sons,
inc, 1th edition, 2002.
[16] S.M. Wong, L.A. Snider, and E.W.C. Lo. Overvoltages and reignition behaviour of vacuum circuit breaker. International Conference on
Power System Transients, 2003.
List of Figures
2.1
An sinusoidal voltage is switched on an RL-circuit. . . . . . .
6
2.2
The sinusoidal voltage is switched on to the RL-circuit with
a switching angle of 90◦ . . . . . . . . . . . . . . . . . . . . . .
8
The sinusoidal voltage is switched on to the RL-circuit with
a switching angle of 0◦ . . . . . . . . . . . . . . . . . . . . . .
9
2.4
An sinusoidal voltage is switched on an RL-circuit . . . . . .
10
2.5
The figure shows the voltage on the transformer side of a VCB
under a opening operation in a circuit with a capacitive load.
11
The design principle of a VCB, showing contacts, arching
chamber and insulation, the picture is taken from [12] page 8.
15
A vacuum interrupter with slits in the contacts to avoid uneven erosion of the contact surface, this picture is from [15]
page 66. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
The figure shows the current during an opening of the breaker.
As seen on figure b the current chops around the value 0,005
and jumps to zero. . . . . . . . . . . . . . . . . . . . . . . . .
18
The figure shows 5 reignitions of the vacuum arc during contact seperation. When the reignitions occur the TRV jumps
to zero. The red line shows the RDDS of the circuit breaker.
19
The figure shows 3 reignitions of the vacuum arc during contact separation. The figure also shows the high frequency
currents caused by the arc. . . . . . . . . . . . . . . . . . . .
20
The figure shows the HF currents caused by 5 reignitions.
The last current cannot be quenched at a zero crossing and
therefore the arc is maintained until the next zero crossing of
the current. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.3
3.1
3.2
3.3
3.4
3.5
3.6
80
LIST OF FIGURES
3.7
Multible reignitions lead to unsuccessful interruption of the
current at first current zero. . . . . . . . . . . . . . . . . . . .
22
The figure shows 4 reignitions of the vacuum arc during contact separation. The figure also shows the high frequency
currents caused by the arc. . . . . . . . . . . . . . . . . . . .
24
The laboratory setup including high voltage components and
the control and measurement system . . . . . . . . . . . . . .
26
4.2
Screenshot of the LabVIEW program. . . . . . . . . . . . . .
29
4.3
The two pictures show how the probes are fastened to the
setup. Before this was done the probes were connected loosely
to the setup by the hooks on the tip of the probes. . . . . . .
31
The plots show the voltage measured on the transformer side
probe, before and after fastening the probe. At around 30ms
oscillations can be seen on figure a. . . . . . . . . . . . . . . .
31
3.8
4.1
4.4
4.5
The picture shows the Rogowski current transducer. In order
to improve the current-to-noise ratio the current measurement
is led through the Rogowski coil 4 times as seen on the picture 32
5.1
Closing the VCB at voltage level 6.9kV , the setup is using
the 100m cable and the load with a capacitance of 0.5µF .
The time between the measurements ∆t is 1 · 10−6 s, and the
closing angle is 0◦ . . . . . . . . . . . . . . . . . . . . . . . . .
35
The figure shows two plots of the distance between the VCB
contacts, when the VCB is opening and closing. . . . . . . . .
36
The TRV across the breaker contacts using a 10m and a 100m
cable. The breaking angle is in both cases 0◦ . . . . . . . . . .
38
The measurements for calculating the frequency of the TRV
when using a 10m cable in the test. The breaking angle is
again 0◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
The plots shows the current through the VCB at 5, 75kV
using a 100m cable. The interruption is made at a breaking
angle of 180◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
The plots shows the current through the VCB at 1, 15kV
using a 100m cable. The interruption is made at a breaking
angle of 45◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
The plots shows the voltage across the breaker contacts during
an opening of the VCB. Both tests have a breaking angle of
225◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
The figure illustrates how the RRDS is calculated from the
laboratory measurements. . . . . . . . . . . . . . . . . . . . .
45
5.2
5.3
5.4
5.5
5.6
5.7
5.8
LIST OF FIGURES
5.9
81
The plot shows how the reignitions of the VCB create a HF
current that is superimposed on the power frequency current.
The test is from the system with 100m cable and the breaking
angle is 292.5◦ . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
5.10 The plot shows how the reignitions of the VCB create a HF
current that is superimposed on the power frequency current.
The test is from the system with 10m cable and the breaking
angle is 225◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
5.11 The plots shows the data markers used to calculate HF current quenching capacity of the VCB. . . . . . . . . . . . . . .
50
5.12 The plot shows the voltage across the breaker channels and
the current through the breaker when during 3 prestrikes.
The test is made with 100m cable and at a closing angle of
22.5◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
5.13 The plot shows the voltage across the breaker channels and
the current through the breaker when during 4 prestrikes.
The test is made with 10m cable and at a breaking angle of
202.5◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
5.14 The plots shows the current through the breaker when closing
the circuit at 0◦ and at 270◦ , both measurements are made
with 10m cable. . . . . . . . . . . . . . . . . . . . . . . . . . .
54
5.15 The plots shows the current through the breaker when closing
the circuit at 0◦ and at 290◦ . Data measurements are set in
order to calculate the frequency of the oscillating transient. .
55
6.1
6.2
6.3
6.4
6.5
Setup of the system representing the laboratory setup when
using the 10m cable. . . . . . . . . . . . . . . . . . . . . . . .
57
Simulation of opening the VCB with the constants found and
described in chapter 5. The breaker opens at angle of 180◦ ,
but current is not interrupted before 270◦ . The simulation
uses the parameters for the 10m cable. . . . . . . . . . . . . .
59
This simulation shows the TRV created by an opening operation, the current is interrupted just before 270◦ . The simulation is for the system using 10m cable . . . . . . . . . . . .
59
Setup of the system representing the laboratory setup when
using the pi-equivalent circuit model and the parameters for
the 10m cable. . . . . . . . . . . . . . . . . . . . . . . . . . .
60
The simulation shows the TRV and the dielectric withstand
of the VCB. As seen the time of seperation has been moved
to 54ms (270◦ ) to try and force reignitions. . . . . . . . . . .
61
82
LIST OF FIGURES
6.6
Simulation of opening the VCB in the system with 100m cable, the current is interrupted at 270◦ . . . . . . . . . . . . . .
6.7 The two plots shows the TRV generated in the system using
10m and 100m cable. For both simulations the breaking angle
is 270◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.8 The simulation shows the TRV when the VCB is set to open
at 39ms and 49ms which results in breaking angles of almost
90◦ and almost 270◦ . . . . . . . . . . . . . . . . . . . . . . . .
6.9 The two plots shows simulations of closing the VCB with
both cable lenghts. The data markers are used to find the
frequency of the oscillating transients. The closing angle of
the VCB is 270◦ for plot a and 180◦ for plot b. . . . . . . . .
6.10 The plot shows the voltage between the VCB contacts and
the current through the VCB just before the VCB contacts
meet. As the plot shows, prestrikes of the VCB occur. . . . .
6.11 The two plots shows simulations of closing the VCB at different times, iin the system using the 10m cable. As seen
the two different closing angles causes a different number of
prestrikes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1
7.2
Comparison of the simulated and the measured results of at
VCB opening, when the breaking angle is 270◦ and the 10m
cable is used. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of prestrikes in simulation and measurement, both
plots, shows the voltage between the VCB contacts. The system uses the 10m cable and have a closing angle of 270◦ . . . .
62
63
63
64
65
66
69
71
List of Tables
4.1
Cable parameters calculated at different frequencies [11] . . .
27
5.1
The table shows the relation between the breaking angle and
the amplitude of the TRV. The results are from the tests made
at 5.75kV using the 10m cable. . . . . . . . . . . . . . . . . .
40
The table shows the average RRDS, for the 6 analysed test
series and the average value of the RRDS found for the two
cable lengths. . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
The table shows the relation between the breaking angle and
the number of reignitions of the vacuum arc. The results are
from the tests made at 5.75kV using the 10m cable. . . . . .
47
5.4
The average results of the calculations of C and D . . . . . .
50
5.5
The average results of D when considering di/dt to be constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
The table shows the relation between the opening angle and
the number of prestrikes of the vacuum arc. The results are
from the tests made at 5.75kV using the 10m cable. . . . . .
53
B.1 Results of the long TRV. The calculations have been made
for the test where the 10m cable is used and at a voltage level
of 5,75kV . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
B.2 Results of the long TRV. The calculations have been made
for the test where the 100m cable is used and at a voltage
level of 5,75kV . . . . . . . . . . . . . . . . . . . . . . . . . .
90
C.1 Measurements and results of the current chopping analysis.
The data is based on measurements with a load of 0.5µF ,
100m cable and a voltage level of 1.15kV . . . . . . . . . . .
92
5.2
5.3
5.6
84
LIST OF TABLES
C.2 Measurements and results of the current chopping analysis.
The data is based on measurements with a load of 1.0µF ,
100m cable and a voltage level of 1.15kV . . . . . . . . . . .
D.1 The table shows the calculation of the RRDS for the system
using with 100m cable and have a voltage level of 4.6kV . . .
D.2 The table shows the calculation of the RRDS for the system
using with 100m cable and have a voltage level of 5.75kV . . .
D.3 The table shows the calculation of the RRDS for the system
using with 100m cable and have a voltage level of 6.9kV . . .
D.4 The table shows the calculation of the RRDS for the system
using with 10m cable and have a voltage level of 4.6kV . . . .
D.5 The table shows the calculation of the RRDS for the system
using with 100m cable and have a voltage level of 5.75kV . . .
D.6 The table shows the calculation of the RRDS for the system
using with 100m cable and have a voltage level of 6.9kV . . .
E.1 The results of the parameters C and D when expressing the
HF current quenching capability as a linear function. All
tests are made at voltage level 5.75kV in the system using
the 100m cable. . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2 The results of D when considering the HF current quenching
capability to be constant. Again all tests are made with 100m
cable and at voltage level 5.75kV . . . . . . . . . . . . . . . .
92
94
94
95
95
96
96
98
98
F.1 The results of the Rate of decay of Dielectric Strength, the
calculations are made on test results from the system using
the 10m cable and voltage level 5.75kV . . . . . . . . . . . . 100
Appendix
A
Plotting results
The measurements in the LabVIEW program are stored in a .lvm file, this
file concists of six columns. The data stored in each column is
• Column 1, contains the measurement number.
• Column 2, the measurement from channel 4 on the oscilloscope (breaker
position).
• Column 3, the measurement from channel 1 on the oscilloscope (voltage, transformer side).
• Column 4, row 1 the time of the trigging moment.
• Column 5, the measurement from channel 2 on the oscilloscope (voltage, load side).
• Column 6, the measurement from channel 3 on the oscilloscope (current).
MATLAB is used to take the data out of the columns, process it and plot it
in the desired way. Later in this appendix an example of how the results are
plotted is shown, this file is also found on the CD. The concept of the MATLAB file is that it loads a directory containing a number of measurement
results files, .lvm files. The .m file then processes all the measurement files
and saves a picture of the plotted results. The .m file is modified in order
to get the desired plot, these modifications can be a zoom of the x − axis,
plotting the difference between the load side- and transformer side voltage
in order to plot the TRV, etc.
In order to use the matlab file P lot res.m to plot the measured results
it is important that the file is placed in the right directory. The file must be
in the same directory as the folders containing the .lvm files. The file plot.m
86
has two parameters that the user must change to get the wanted plots. The
first one is step time, delta t, this number has to be set in order to get the
right time on the x-axis. Delta t is calculated by the labview program when
the measurements are taken and can also be seen in the filename of the .lvm
file. The second parameter that can be changed by the user is the directory
name. The name must be the name of the directory containing the .lvm
files with the data for which a plot is wanted.
If you have any problem plotting the results or have questions on how to
modify the Matlab file you can send me an email and i’ll try and help you.
The code of the matlab file P lot res.m is seen here
1
2
clc ;
clear a l l ;
3
4
5
6
7
8
9
%Values t h a t has t o be s e t by t h e u s e r
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
d e l t a t =2e −7; %The s t e p time D e l t a t
cd ChoopingCurrent ; % Name o f t h e d i r e c t o r y with t h e ...
results
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
10
11
12
%Loads a l l t h e measurements f i l e s from t h e d i r e c t o r y
d=dir ( ’ ./*. lvm ’ ) ;
13
14
15
16
17
18
%G e n e r a t e s a f o r −l o o p t h a t run through a l l t h e f i l e s
f o r k=1: length ( d ) ;
fname=d ( k ) . name ;
19
20
21
%Loads t h e measurement r e s u l t s t o a matrix
x = csvread ( fname , 1 , 0 ) ;
22
23
24
25
26
%Loads t h e v o l t a g e from t h e p o s s i t i o n meter
v o l t a g e p o s=x ( : , 2 ) ;
%Converts t h e v o l t a g e t o t h e d i s t a n c e between t h e b r e a k e r ...
contacts
d i s t =(9− v o l t a g e p o s ) ∗ 9 / 9 ;
27
28
29
%Loads t h e v o l t a g e o f t h e l o a d s i d e o f t h e b r e a k e r
v o l t a g e l o a d s i d e=x ( : , 5 ) ;
30
31
32
%Loads t h e v o l t a g e o f t h e t r a n s f o r m e r s i d e o f t h e b r e a k e r
v o l t a g e t r a n s s i d e=x ( : , 3 ) ;
33
34
35
%Loads t h e t r o u g h t h e b r e a k e r
c u r r e n t=x ( : , 6 ) ;
Plotting results
87
36
37
38
%Loads and s e t s t h e time a c o r d i n g t o t h e s t e p time
time=d e l t a t ∗x ( : , 1 ) ∗ 1 0 ˆ 3 ;
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
%Opens a new f i g u r e
F=f i g u r e ;
%S e t s t h e f i l e n a m e o f t h e p l o t t o t h e name o f t h e measurement ...
f i l e followed
%by R e s u l t
f i l e n a m e =[ fname ( 1 : length ( fname ) −4) ’ Breakerpos ’ ] ;
T i t l e=fname ;
%P l o t s t h e d i s t a n c e between t h e b r e a k e r c o n t a c t s a s a f u n c t i o n ...
o f time
plot ( time , d i s t ) ;
%S e t s t h e x−a x i s t o t h e l e n g t h o f t h e time v e c t o r
xlim ( [ 0 time ( end ) ] )
%Adding a t i t l e t o t h e f i g u r e
t i t l e ( T i t l e , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
%Adds l a b e l s t o t h e a x i s
xlabel ( ’ Time [ ms ] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
ylabel ( ’ Distance between VCB contacts [ mm ] ’ , ’ FontWeight ’ , ’ bold ’ , ...
’ Fontsize ’ , 1 6 ) ;
%Saves t h e p l o t a s a png f i l e under t h e f i l e name
print (F , ’- dpng ’ , f i l e n a m e ) ;
s a v e a s ( gcf , [ fname ( 1 : length ( fname ) −4) ’ Breakerpos . fig ’ ] )
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
%New f i g u r e f o r p l o t t i n g t h e t r a n s f o r m e r s i d e v o l t a g e
F=f i g u r e ;
%P l o t s t h e l o a d s i d e v o l t a g e a s a f u n c t i o n o f time
plot ( time , v o l t a g e t r a n s s i d e ) ;
%S e t s t h e f i l e n a m e o f t h e p l o t t o t h e name o f t h e measurement ...
f i l e followed
%by R e s u l t
f i l e n a m e =[ fname ( 1 : length ( fname ) −4) ’ Voltagetransside ’ ] ;
T i t l e=fname ;
%S e t s t h e x−a x i s t o t h e l e n g t h o f t h e time v e c t o r
xlim ( [ 0 time ( end ) ] )
%Adding a t i t l e t o t h e f i g u r e
t i t l e ( T i t l e , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
%Adds l a b e l s t o t h e a x i s
xlabel ( ’ Time [ ms ] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
ylabel ( ’ Trans . side voltage [V] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’...
,16) ;
%Saves t h e p l o t a s a png f i l e under t h e f i l e name
print (F , ’- dpng ’ , f i l e n a m e ) ;
s a v e a s ( gcf , [ fname ( 1 : length ( fname ) −4) ’ Voltagetransside . fig ’ ] )
79
80
81
82
83
%New f i g u r e f o r p l o t t i n g t h e l o a d s i d e v o l t a g e
F=f i g u r e ;
%P l o t s t h e l o a d s i d e v o l t a g e a s a f u n c t i o n o f time
plot ( time , v o l t a g e l o a d s i d e ) ;
88
84
85
86
87
88
89
90
91
92
93
94
95
96
97
%S e t s t h e f i l e n a m e o f t h e p l o t t o t h e name o f t h e measurement ...
f i l e followed
%by R e s u l t
f i l e n a m e =[ fname ( 1 : length ( fname ) −4) ’ Voltageloadside ’ ] ;
T i t l e=fname ;
%S e t s t h e x−a x i s t o t h e l e n g t h o f t h e time v e c t o r
xlim ( [ 0 time ( end ) ] )
%Adding a t i t l e t o t h e f i g u r e
t i t l e ( T i t l e , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
%Adds l a b e l s t o t h e a x i s
xlabel ( ’ Time [ ms ] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
ylabel ( ’ Load side voltage [V] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’...
,16) ;
%Saves t h e p l o t a s a png f i l e under t h e f i l e name
print (F , ’- dpng ’ , f i l e n a m e ) ;
s a v e a s ( gcf , [ fname ( 1 : length ( fname ) −4) ’ Voltageloadside . fig ’ ] )
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
%New f i g u r e f o r p l o t t i n g t h e l o a d s i d e v o l t a g e
F=f i g u r e ;
%P l o t s t h e l o a d s i d e v o l t a g e a s a f u n c t i o n o f time
plot ( time , c u r r e n t ) ;
%S e t s t h e f i l e n a m e o f t h e p l o t t o t h e name o f t h e measurement ...
f i l e followed
%by R e s u l t
f i l e n a m e =[ fname ( 1 : length ( fname ) −4) ’ current ’ ] ;
T i t l e=fname ;
%S e t s t h e x−a x i s t o t h e l e n g t h o f t h e time v e c t o r
xlim ( [ 0 time ( end ) ] )
%Adding a t i t l e t o t h e f i g u r e
t i t l e ( T i t l e , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
%Adds l a b e l s t o t h e a x i s
xlabel ( ’ Time [ ms ] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
ylabel ( ’ Current [A] ’ , ’ FontWeight ’ , ’ bold ’ , ’ Fontsize ’ , 1 6 ) ;
%Saves t h e p l o t a s a png f i l e under t h e f i l e name
print (F , ’- dpng ’ , f i l e n a m e ) ;
s a v e a s ( gcf , [ fname ( 1 : length ( fname ) −4) ’ Current . fig ’ ] )
end
118
119
120
121
122
%Returns t o t h e top d i r e c t o r y with t h e measurement f o l d e r s
cd . .
Appendix
B
Results of the TRV
Calculations
The pictures contaning the data points used for the calculations is found
on the cd. The PDF file named F ull Appendix.pdf contains the pictures
showing the data and the results of the calculation. The appendix seen in
the printed version only shows tabels contaning the calculation results. To
get the full appendix, just send me an email and i will send the file.
90
Test nr.
1
2
3
4
5
6
7
8
9
10
11
12
Average
Breaking angle[◦ ]
180
180
45
22.5
22.5
0
225
202.5
90
247.5
247.5
0
–
Amplitude[V ]
5000
5250
-4875
-5375
-5500
-5125
4250
4500
0
1625
1625
-5500
–
Frequency[Hz]
8739.824137
8827.700477
8502.21631
8753.602989
8750.663754
8729.068075
8717.853469
8941.000094
–
8473.056716
8587.166059
8775.923838
8708.915993
Time to damp[ms]
0.9876
1.1586
1.0652
1.0742
0.9426
1.119
1.0884
1.0278
–
0.9932
1.0114
1.19
0.9700
Table B.1: Results of the long TRV. The calculations have been made for the test
where the 10m cable is used and at a voltage level of 5,75kV
Test nr.
1
2
3
4
5
6
7
8
9
10
Average
Breaking angle[◦ ]
22.5
0
67.5
202.5
315
135
180
225
90
337.5
–
Amplitude[V ]
-4218.75
-4500
-3000
3843.75
-1875
3468.75
4500
3468.75
468.8
-3937.5
–
Frequency[Hz]
2914.948534
2978.72869
2948.610075
2881.742751
2951.113172
2866.342232
3047.715332
2945.719274
3053.748933
2950.057835
2953.872683
Time to damp[ms]
2.4964
2.5916
2.7594
2.6422
1.902
2.422
2.472
2.493
–
2.4624
2.30162
Table B.2: Results of the long TRV. The calculations have been made for the test
where the 100m cable is used and at a voltage level of 5,75kV
Appendix
C
Results of Current Chopping
Calculations
The pictures contaning the data points used for the calculations is found
on the cd. The PDF file named F ull Appendix.pdf contains the pictures
showing the data and the results of the calculation. The appendix seen in
the printed version only shows tables contaning the calculation results.
92
Test nr.
i
Ich
1
2
3
4
5
6
0,28905
0,3086
0,2734
0,28905
0,2969
0,2818
0,1797
0,1484
0,2266
0,1875
0,1641
0,1016
α
(when β = 14, 3)
6.3249·106
75.517·106
306.03·106
3.59·106
20.60·106
12.76·109
Table C.1: Measurements and results of the current chopping analysis. The data
is based on measurements with a load of 0.5µF , 100m cable and a
voltage level of 1.15kV
Test nr.
i
Ich
1
2
3
4
5
6
0,54295
0,5547
0,53905
0,5547
0,5742
0,5625
0,3828
0,4688
0,1953
0,4141
0,2734
0,4062
α
(when β = 14, 3)
144.29
9.54
1120844.08
49.65
11995.84
63.26s
Table C.2: Measurements and results of the current chopping analysis. The data
is based on measurements with a load of 1.0µF , 100m cable and a
voltage level of 1.15kV
Appendix
D
Results of the Rate of Rise of
Dielectric Strength Calculations
The pictures contaning the data points used for the calculations is found
on the cd. The PDF file named F ull Appendix.pdf contains the pictures
showing the data and the results of the calculation. The appendix seen in
the printed version only shows tables contaning the calculation results.
94
Test nr.
1
2
3
4
5
6
7
8
9
10
11
12
13
Average A
Breaking angle[◦ ]
0
225
247.5
337.5
22.5
202.5
22.5
315
0
45
0
292.5
315
–
Number of reignitions
2
2
2
3
3
3
2
0
3
2
2
0
2
–
A [V/µ S]
26.46
20.83
21.94
19.17
23.85
19.44
12.23
–
10.464
9.97
32.71
–
6.58
18.52
Table D.1: The table shows the calculation of the RRDS for the system using
with 100m cable and have a voltage level of 4.6kV .
Test nr.
1
2
3
4
5
6
7
8
9
10
Average A
Breaking angle[◦ ]
0
0
67.5
225
315
135
0
202.5
90
337.5
–
Number of reignitions
3
2
2
3
2
2
2
3
0
2
–
A [V/µ S]
21.83
–
16.54
24.37
24.72
9.62
34.10
24.06
–
20.27
21.94
Table D.2: The table shows the calculation of the RRDS for the system using
with 100m cable and have a voltage level of 5.75kV .
Results of the Rate of Rise of Dielectric Strength Calculations
Test nr.
1
2
3
4
5
6
7
8
9
10
11
Average A
Breaking angle[◦ ]
135
180
247.5
315
67.5
22.5
157.5
0
0
0
45
–
Number of reignitions
5
6
2
3
3
4
4
4
5
4
3
–
95
A [V/µ S]
28.82
25.66
10.20
22.43
24.13
31.73
20.68
21.45
26.60
27.23
31.64
24.50
Table D.3: The table shows the calculation of the RRDS for the system using
with 100m cable and have a voltage level of 6.9kV .
Test nr.
1
2
3
4
5
6
7
8
9
10
Average A
Breaking angle[◦ ]
22.5
292.5
225
90
90
225
22.5
135
67.5
225
–
Number of reignitions
15
8
8
4
0
6
11
5
6
9
–
A [V/µ S]
44.29
47.94
29.71
23.54
–
37.90
54.27
34.78
51.78
58.20
38.24
Table D.4: The table shows the calculation of the RRDS for the system using
with 10m cable and have a voltage level of 4.6kV .
96
Test nr.
1
2
3
4
5
6
7
8
9
10
11
12
Average A
Breaking angle[◦ ]
180
180
45
22.5
22.5
0
225
202.5
90
270
270
0
–
Number of reignitions
15
13
15
10
18
20
10
15
0
1
1
17
–
A [V/µ S]
31.00
42.82
35.16
38.90
34.68
42.69
39.85
40.35
–
–
–
49.02
39.39
Table D.5: The table shows the calculation of the RRDS for the system using
with 100m cable and have a voltage level of 5.75kV .
Test nr.
1
2
3
4
5
6
7
8
9
10
11
12
Average A
Breaking angle[◦ ]
247.5
45
112.5
202.5
0
247.5
202.5
0
315
45
0
225
–
Number of reignitions
8
15
12
17
23
7
23
19
17
19
5
5
–
A [V/µ S]
36.88
34.61
43.45
42.91
39.10
37.36
35.91
39.19
34.82
44.93
24.17
18.57
36.02
Table D.6: The table shows the calculation of the RRDS for the system using
with 100m cable and have a voltage level of 6.9kV .
Appendix
E
Results of HF Current
Quenching Capability
Calculations
The pictures contaning the data points used for the calculations is found
on the cd. The PDF file named F ull Appendix.pdf contains the pictures
showing the data and the results of the calculation. The appendix seen in
the printed version only shows tables contaning the calculation results.
98
Arc number
Arc 2
Arc 2
A
A
C[ µs
D[ µs
]
2]
Test nr.
Arc 1
A
C[ µs
2]
Arc 1
A
D[ µs
]
1
2
3
4
5
6
7
8
9
10
11
12
Average
-0.294
-0.489
-0.52524
-0.48529
-1.684
-0.316
-0.705
-0.429
-0.437
-0.114
-0.87
-0.74513
-0.59125
9.375
31.25
27.34375
36.45
29.296
5.580
21.484
15.626
17.188
9.766
117.188
85.938
25.67046
-0.668
-1.436
–
–
-2.182
-1.774
-0.673
–
–
-0.588
-0.609
-1.597
-1.19084
33.2
50.78
–
–
52.734
85.937
14.5
–
51.563
19.531
85.938
42.969
48.57241
Arc 3
A
C[ µs
2]
Arc 3
A
D [ µs
]
-0.705
-3.272
–
–
–
–
1.898
–
-2.174
-1.512
–
–
-1.9121
62.5
103.516
–
–
–
–
51.563
–
125
35.938
–
–
75.70312
Table E.1: The results of the parameters C and D when expressing the HF current
quenching capability as a linear function. All tests are made at voltage
level 5.75kV in the system using the 100m cable.
Test nr.
Arc number
Arc 1 Arc 2
Arc 3
A
A
A
D[ µs
]
D[ µs
]
D[ µs
]
1
2
3
4
5
6
7
8
9
10
11
12
Average
7.812
19.531
11.718
11.718
24.553
6.696
12.695
11.718
12.695
6.696
21.875
13.021
13.255
28.125
15.625
–
–
33.854
29.017
26.041
29.513
93.75
12.276
45.312
26.785
34.03
60.937
107.142
–
–
–
–
30.273
47.991
32.366
–
55.742
Table E.2: The results of D when considering the HF current quenching capability
to be constant. Again all tests are made with 100m cable and at
voltage level 5.75kV
Appendix
F
Results of Rate of Decay of
Dielectric Srength
The pictures contaning the data points used for the calculations is found
on the cd. The PDF file named F ull Appendix.pdf contains the pictures
showing the data and the results of the calculation. The appendix seen in
the printed version only shows tables contaning the calculation results.
100
Test nr.
1
2
3
4
5
6
7
8
9
10
Average A
Breaking angle[◦ ]
112.5
90
112.5
180
202.5
315
90
67.5
0
270
–
Number of Prestrikes
3
4
4
2
4
2
6
3
0
6
–
A [V/µ S]
125.97
149.23
136.35
240.38
103.86
174.54
147.37
130.79
–
115.37
147.1
Table F.1: The results of the Rate of decay of Dielectric Strength, the calculations
are made on test results from the system using the 10m cable and
voltage level 5.75kV
www.elektro.dtu.dk
Technical University of Denmark
Department of Electrical Engineering
Centre for Electric Technology (CET)
Elektrovej 325
Building 325
DK-2800 Kgs. Lyngby
Denmark
Tel:
(+45) 45 25 35 00
Fax:
(+45) 45 88 61 11
Email: cet@elektro.dtu.dk