District GIS for Tamilnadu GIS Nagapattinam GIS DIV.NIC,TNSC.
CHAPTER-III MODELING OF 245kV GIS SYSTEM FOR...
Transcript of CHAPTER-III MODELING OF 245kV GIS SYSTEM FOR...
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CHAPTER-III
MODELING OF 245kV GIS SYSTEM FOR
ESTIMATION AND SUPPRESSION OF VFTOs
3.1 INTRODUCTION
An accurate representation of each component of a system is
essential for a reliable simulation of its transient performance. This
representation must be done taking into account the frequency range of
the transients to be simulated. Very fast transients (VFT) belong to the
highest frequency range of the power system. The simulations are
suitable for frequencies varying from 100 KHz to 100MHz [13]
Due to the travelling nature of the transients the modeling of GIS
makes use of electrical equivalent circuits composed of lumped elements
and especially by distributed parameter lines, surge impedances and
travelling times. Disconnector switches are used primarily to isolate
operating sections of high voltage installations from each other as a
safety measure. In addition, they must also be able to perform certain
switching duties such as load transfer from one bus bar to another
busbaror off load connection or disconnection of bus sections, circuit
breakers etc. The connection or disconnection of energized but unloaded
substation sections involve the disconnector having to switch small
capacitive currents, typically few mA[21]. During closing and opening
operations the voltages develop across the switching contacts which
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subsequently collapse in a series of spark discharges often in extended
sequences. Within just nanoseconds, the channel of such a spark
discharge rapidly establishes a conducting bridge across the contacts.
Lasting few hundreds of micro seconds, it momentarily connects the
potential equalization is accompanied by transient oscillations with very
high frequencies in the adjacent GIS elements, giving to VFTOs. The
frequency and amplitudes depends up on the layout of the GIS network.
The estimation of these transients and rise times are very important in
order to design insulation levels[14]. The fast transients over voltages are
generated during switching operation of disconnectors. VFTO generated
in a GIS should be considered as an important factor in the insulation
design. In EHV class voltages, VFTOs can reach to high amplitudes
and steepness, the insulation failures of 500kV transformers due to
effect of VFTO have happened several times [15]. Hence it is important
to estimate and suppress these over voltages for protection of internal
systems. The simulation depends on the quality of the model of each
individual GIS component. In order to achieve reasonable results in GIS
structures highly accurate models for each internal equipment and also
for components connected to the GIS are necessary.
The disconnector spark itself has to be taken into account by
transient resistance according to the toepler’s equation and subsequent
arc resistance of a few ohms. The wave shape of the over voltage surge
due to disconnector switch is affected by all GIS elements. Accordingly,
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the simulation of transients in GIS assumes an establishment of the
models for the bus, bushing, elbow, transformers, surge arresters,
breakers, spacers, disconnectors and enclosures and so on. One of the
ways is avoiding dangerous layout of GIS and dangerous operation
procedures of the disconnectors however; this brings a big limitation to
the design and control operation of GIS. Another way is to use high
speed disconnector, but there will be a problem of high trapped charge
on the floating electrode[23]. The exisisting method of suppressing
VFTOs is resistance switching. In this method a resistor of range 400Ω to
500Ω is fitted to disconnector[29,31], in this method in the event of
restriking the resistor is inserted in the circuit, so that ,the over voltages
can be suppressed, but this method is complicated in structure and has
reduced reliability and also the probability of failure of resistors are
great. Therefore this method needs to combine practical considerations.
Another method is using R-C filter circuits, this method has been
widely used in vacuum circuit breakers to suppress over voltages of
arcing, the R-C filters can be applied to suppress the VFT, but in this R-
C filter absorbs high frequency components, consumes the energy of
VFTO, but selection of R and C for different ratings applications is
difficult[18]. Another method suggested by Hongsheng Li is use of metal
oxide arrester but this can inhibit the amplitude of the VFTO, but cannot
inhibit its steepness and high frequency oscillations.
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In this chapter, first suppression effect of VFTOs has been verified
with switching resistor across the disconnector switch and secondly the
suppression effect of VFTOs verified with new technique of application of
ferrite rings on bus bar. The frequency spectrums are also obtained
using FFT technique. The results obtained from the above methods are
compared.
In this chapter, the single line diagram of 245kV GIS and its
description is given in section 3.2. The representations of important GIS
components are given in section 3.3. The modeling of GIS components is
given in section 3.4. Calculation of various parameters for modeling is
given in the section3.5 A 245kV GIS system considered for modeling to
estimate VFTOs is presented in section 3.6 The EMTP-RV model of the
system given in section 3.7 The Simulation of the EMTP-RV GIS model to
estimate transients due to disconnector switch 1 closing operation with
fixed arc resistance is given in section 3.7.1. The Simulation of the
EMTP-RV GIS model to estimate transients due to disconnector closing
operation with variable arc resistance given in section3.7.2. The
Simulation of the EMTP-RV GIS model to estimate transients due to
disconnector opening operation with fixed arc resistance given in section
3.7.3. The simulation of the EMTP-RV GIS model to estimate transients
due to disconnector opening operation with variable arc resistance given
in section3.7.4. The Simulation of the EMTP-RV GIS model to estimate
transients due to disconnector opening operation with variable arc
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resistance and trapped charges is given in section 3.7.5. The GIS
simulation model with DS2 opening operation and variable arc resistance
is given in the section 3.7.6. The results of various simulations are given
in the section 3.8.1. The transients on source side and load side of the
disconnector switch with different trapped charges are given in the 3.8.2.
Summary is given in the section 3.9. Various methods for suppression of
VFTOs in GIS systems are discussed in section3.10. The VFTO
suppression using resistance switching is discussed in 3.10.1. The FFT
analysis of reduced VFTOs given in section 3.10.2. Single phase
equivalent circuits of 245kV GIS system with opening and closing
resistance given in 3.10.3. Simulation results with opening and closing
resistance are presented in the section3.10.4. The VFTO suppression
using ferrite rings given in 3.11. The simulation results are given in the
section 3.14. The summary is given in the section 3.15.
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3.2 A TYPICAL 245kV GAS INSULATED SUBSTATION
Fig 3.1 Single-line diagram of 245kV GIS
3.3 REPRESENTATION OF IMPORTANT GIS COMPONENTS
a) Bus ducts: bus duct can be represented as a loss less transmission
line for a range of frequencies lower than 100MHz. The surge impedance
is calculated from the physical dimensions of the duct (using Eq 3.4).
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The Experimental results show that the propagation velocity in GIS duct
is close to 95% of the speed of light other devices such as closed
disconnectors can also be modeled as lossless transmission lines.
b) Surge arresters: A surge arrester model is taken into account the
steep front wave effect. The voltage developed across the arrester for a
given discharge current increases, and reaches crest prior to crest of the
discharge current. A detailed model is represent each internal shield and
block individually, and the travel times along shield sections as well as
capacitances between these sections as well as capacitances between
blocks and shields, and the blocks themselves. The detailed model is
shown in the table. Usually the switching operations do not produce
voltages high enough to cause MOAs to conduct its capacitance is taken
into account.
c) Circuit breakers: The representation of circuit breakers is very
complicated in GIS systems because of its internal irregularities. In
addition , circuit breakers with several chambers contain grading
capacitors as these components are not arranged symmetrically, a circuit
breaker has a different transient response depending up on which
terminal is connected to the surge source. A closed circuit breaker can
be represented as a lossless transmission line. The surge impedance is
calculated from the diameters of the conductor and enclosure. The effect
of grading capacitors can be ignored. The representation of a closed
circuit breaker is more complicated because the electrical length is
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increased and the speed of progression is decreased due to the effects of
the higher dielectric constant of the grading capacitors. If the
intermediate voltages are needed, the breaker is divided into as many
sections as there are interrupters, all connected by the grading
capacitors. A simple model consists of two equal lengths of bus
connected by a capacitor with a value equivalent to the series
combination of sections are calculated from the physical dimensions of
the breaker
d) Disconnector switches: Closed disconnectors are modeled as a
transmission line with distributed parameters. Capacitance of the
switching contacts towards the ground is considered. Disconnectors in
open condition are represented with inter electrode capacitance of the
switching contacts towards the ground is considered.
e) Earth switches: Earth switches can be modeled as lumped
capacitance to ground.
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3.4 MODELING OF GIS COMPONENTS
ELEMENT MODEL EQUIVALENT
CIRCUIT
CHARACTERISTI
CS
BUS DUCT
Transmission line with
distributed parameters.
Loss in transmission line
because of skin
effect.(Neglected)
Loss free
distributed
parameter
transmission line
SPACER Lumped Capacitance
towards the ground.
C > 20pf
ELBOW
Transmission line with
distributed parameters
and capacitance added
in between the line.
Parameters
depending on the
ratio between
conductor and
enclosure radius.
Value of the
capacitance C
depending on the
system topology.
CABLE
Transmission line with
distributed parameters.
Each end of cable is
terminating with a
lumped capacitance.
The values are
Depends up on
voltage rating of
GIS
CURRENT
TRANSFORMER
Lumped capacitance
towards the ground
The values are
Depends up on
voltage rating of
GIS
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CAPACITIVE
VOLTAGE
TRANSFORMER
Lumped capacitance
towards the ground
BUSHING
(Capacitively
Graded Bushing)
Transmission line of
varying surge
impedances are
connected in series
Zg1, Zg2,.. are
variable surge
impedance in SF6
side. Za1, Za2, …
are variable surge
impedance in air
side.
SURGE
ARRESTER
Arrester capacitance is
considered. Protection
characteristic connected
in parallel with arrester
capacitance
In case of VFT
(0.5µs) the
protection
characteristic is
corrected in
reference to the
characteristic for
the surge 8/20µs.
Inductance of
grounding
connection is
taken into account.
POWER
TRANSFORMER
Lumped capacitance
towards the
ground.Inductive branch
toards ground is
neglected due to a very
high impedance at very
high
frequencies.Nonlinear
behavior of the core is
neglected
Value of
capacitance
depends on the
transformer type,
voltage level,
winding connection
and winding type.
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DIS-CONNECTOR
CLOSED
Transmission line with
distributed parameters.
Capacitance of the
switching contacts
towards the ground is
considered.
Parameters
depending on the
ratio between
conductor and
enclosure radius.
Value of
capacitance C
depends on the
system topology.
DIS-CONNECTOR
OPENED
Inter electrode
capacitance of the
switching contacts
towards the ground is
considered.
C includes spacer
capacitance also.
EARTH
SWITCHING
Lumped capacitance
towards the ground.
SPARK
RESISTANCE (in
case of DS
operation)
It is a non-linear
function of time. It varies
according to the
Toepler’s Spark Law
if t < 1µs, R = 0 Ω
if t > 1µs, R varies
from 0 to 5 Ω
SPARK
(earth fault)
Spark resistance varies
according to Toepler’s
Spark Law. L is the
inductance of the spark
channel.
R is in the range of
1 to 3 Ω
CIRCUIT
BREAKER (C.B)
CLOSED
Transmission line with
distributed parameters
equivalent capacitance of
switching contacts
The surge
Impedance of C.B
bus duct is less
than 70 Ω because
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towards the ground is
considered.
of additional
capacitance.
CIRCUIT
BREAKER (C.B)
OPENED
The capacitance between
switching contacts is
considered. C.B bus duct
is represented with
distributed parameters
on both sides of the
contacts.
The length of bus
duct on both sides
of contacts is
equal. The inter
electrode
capacitance incase
of C.B is high,
because of large
arc of the contacts.
3.5 CALCULATION OF VARIOUS PARAMETERS OF GIS
3.5.1 Calculation of Inductance
The inductance of the bus duct can be calculated by using the formula
[16] given below:
Where r1, r2, r3, r4, are the radii of the conductors in the order of decreasing
magnitude and ‘l’ is the length of the section.
−∗
∗+
+
+
××= 1
r
rln
r
r-1
r
r
2 r
rln
r
rln
r
rln 0.001 L
2
1
2
1
2
2
1
2
3
4
1
2
3
1l
3.1
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Fig 3.2 Cross section of typical GIS System
3.5.2 Calculation of Capacitance in micro farads
The Capacitance is calculated with the assumption that the conductors
are Cylindrical. Capacitance is calculated by using the standard formulae
given below:
0
1 0
2 * * *
2 .3 * ln
r lC
b
a
π ε ε∗=
3.2
Where εo = 8.854 * 10-12, εr = 1
b = Outer Cylinder Radius
a = Inner Cylinder Radius
l = Length of the Section
3.5.3 Calculation of Capacitance due to Spacer
Spacers are used for supporting the inner conductor with reference
to the outer enclosure. They are made with Alumina filled epoxy
material whose relative permittivity (εr) is 4. The thickness of the
spacer is assumed to be the length of the capacitance for calculation.
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3.5.4 Calculation of Short Circuit Inductance(mH) &
Resistance
Assuming a short circuit fault level of 2000MVA for 245kV system
voltage, Inductance and Resistance are calculated as follows: In the
derivation of short circuit inductance and resistance, the GIS
considered for the study is 200MVA,22.8/220Kv with leakage
reactance of 10%. The symmetrical short circuit MVA will be about 8
to 12 times the rated MVA capacity of the ttransformer.
S V * ph =phI
⇒ phV
S =phI
And V
I * X Z% =
⇒ I
V * %Z X =
But L * f * * 2 X Π=
⇒ f * * 2
X
Π=L
And it is assumed that R = XL
3.5.5 Calculation of Inductance due to Load
For 200MVA, 245KV transformer with 10% impedance and 0.8 power
factor the inductance is calculated as follows:
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P Cos * I * V * 3 =φ
⇒ φ
=Cos * V * 3
P I
And V
I * X Z% =
⇒ I
V * %Z X =
But L * f * * 2 X Π=
⇒ f * * 2
X L
Π=
3.5.6. Calculation of Variable Arc Resistance
Based on earlier studies in SF6 gas, Toepler’s Spark Law is valid for
calculation of Variable Arc Resistance. The Variable Arc Resistance due to
Toepler’s formulae [5] is given below
= ∗ +
3.3
Where KT = Toepler’s Constant
= 0.005 volt.sec/m for SF 6 under Uniform Field conditions
L = Spark Length in meters
qo = Initial Charge or Charge at the instant of breakdown
t = Spark collapse time in sec.
The value of time varying spark resistance R (t), is calculated until
it reaches a value of 1 to 5 ohms. The integral in the denominator sums
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up the absolute value of current ‘i’ through the resistance R (t) over the
time beginning at breakdown inception. Thus, it corresponds to the
charge conducted through the spark channel up to time‘t’.
Initial charge qo is an important parameter while considering the non-
uniform fields. But the field between the disconnector contacts is almost
uniform. Therefore qo is very small.
3.5.7 Surge Impedance
A typical 245kV gas insulated bus duct in the substation
considered has an inner conductor of 3.6 inches (8.9cm) and its
grounded outer sheath has a diameter of about 12inches (30.5cm). The
surge impedance of the 245kV SF6 bus can be calculated from the
following formula [6]
= 138√
3.4
Where Z= surge impedance in Ω
= inner radius of outer sheath
= radius of inner conductor
K= permittivity of dielectric (unity for SF6)
Hence, for a typical 245kV Gas insulated bus, the surge impedance is
about 75Ω
Ω== 8.739.8
5.30log
1
138Z
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3.6 TYPICAL SECTION OF SEGREGATED-PHASE 245kV GIS SYSTEM
Fig.3.3 Single line diagram of typical section of segregated-phase
245kV GIS system
T - Generator transformer E.S - Earthing Switch B1 = Air –to- SF6 Gas Bushing C.B- Circuit Breaker L.A - Lightning arrester C.T- current Transformer P.T - Potential Transformer B2 = SF6 Gas - to – XLPE cable
Table.3.1 Dimensions of 245kV GIS system
Name of the GIS component Distance
in meters
Air-to-SF6bushing(From DS1)
12.6
Lightning arrester(From DS1)
11.3
Potential transformer(From DS1)
9.5
Earth switch(From DS1)
1.5
Current transformer(From DS2) 1.5
Earth switch(From DS2) 2.0
Potential transformer(From DS2) 9.5
SF6-to-XLPE cable termination
13.5
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3.6.1 Description of the circuit
A typical section of 245kV GIS substation has been considered
for VFTO study. Its single line diagram is shown in Fig. 3.3; a complete
EMTP-RV electrical equivalent models have been developed for the GIS
system.
A substation has 200MVA, 22.8kV/220kV transformer and the
over head line from transformer is connected to 245kV GIS system
through an Air-to-SF6 gas bushing. The length of the over head line is
about 20meters. The typical 245kV GIS system consisting of lightning
arrester, instrument transformers, and high speed earthing switch and
SF6 gas to air bushing and SF6 gas to XLPE cable termination have
shown in the diagram. The surge impedance of the over head line is
considered as 350Ω with wave velocity of 300m/µs.
Due to the travelling wave nature of the VFT the modeling of
GIS makes use of electrical equivalent circuits composed by lumped
elements and especially by distributed parameter lines, defined by surge
impedances and travelling times. The power transformer is assumed as a
source side and load side of the disconnector switch being operated.
It is assumed that, initially the load side circuit breaker is
operated. The fast transient over voltages results at both load side and
source side of the disconnector switch. The switching of capacitive
current is difficult; under these conditions restrikes occurs and cause
large number of transients on the supply and load side. The variations of
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transient voltages at Air-to-SF6 gas bushing, load side & source side are
calculated during disconnector Switch1 operation and transient voltages
at XLPE cable termination has been estimated during Disconnector
switch2 opening and closing operations using EMTP-RV. The step size
for the analysis taken as 0.1ns and stop time is selected between 5 to
8µsec. In the circuit a great deal of restrikes occurs across the switching
contacts when disconnectors are operated. These restrikes lead to
generation of VFTO; Consequently VFTO appears in the circuit. Due to
random nature of trapped charge at the commencement of disconnector
opening or closing two important parameters variable arc resistance and
trapped charge on the floating bus bar are considered during estimation
of VFTO.
The transients generated due to the operation of a disconnector switch1
have been simulated by the injection of a unit step voltage source. The
patterns of transient voltages at air to gas bushing are estimated during
Disconnector switch 1 closing and opening operations with fixed and
variable arc resistance. The patterns of transient voltages at SF6-to-XLPE
cable termination is estimated during Disconnector switch2 opening
operation the results are presented. The patterns of transient voltage at
source side, load side have been analyzed. The trapped charge is varied
from -0.1p.u to -1p.u. insteps of 0.1p.u. (1 p.u = Vm (ph))
The electrical equivalent models with trapped charge are given
in the Fig. 3.5.9 to Fig 3.5.18. The simulation waveforms are given in
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section 3.8.1. The patterns of transient voltages at SF6-to-XLPE cable
termination during Disconnector switch 2 opening is presented in the
Fig.3.42. The VFTOs on source side with different trapped charges are
presented in the Table 3.1. The VFTOs on load side with different trapped
charges are presented in the table 3.2. The VFTOs at air to SF6 gas bushing
during opening and closing operation of DS1 are given in the table 3.3.
The disconnector switches DS1, DS2 and circuit breaker arrangement as
shown in the diagram.
The disconnectors are of motor driven, with rated voltage is
245kV and rated short-time current 40/50kA 3sec.
Earth switches are located on either side of the disconnector
switches. The rated voltage is 245kV, rated short time current 40/50kA
3sec, Method of operation is motor driven, Bus bar type is segregated
phase, Rated voltage is 245kV,Rated current is 2500/3150A, Rated short
time current rating is 40/50kA,The rated gas pressure is 0.6Mpa.
The ratings of the circuit breaker are, Rated voltage is 245kV, Rated
current is 1250/2500/3150A rated breaking current 40/50A, rated gas
pressure is about 0.6MPa and method of operation is motor driven with
spring. The instrument transformers are located with in the bay. Their
secondary connections are routed through a gas-tight bushing plate to a
terminal box.
The pressurized SF6 gas in the module serves as the primary
insulation. The high voltage connection to the switchgear is established
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by means of conductor, which is supported by means of a gas-tight
bushing plate to the terminal box.
The surge arrester consists of metal oxide resistors with a non-
linear current/voltage characteristic. The arrester is flange-joined to the
switchgear via gas tight bushing. In the tank of the arrester module,
there is an inspection hole, through which the internal conductor can be
inspected. At the bottom there are the connections for gas monitoring,
arrester testing, and an operation counter. The SF6gas/air termination is
a combination of an angle type module and an outdoor/ SF6 bushing.
The surge impedance of the 245kV XLPE-600 Cable is taken as 30Ω and
wave velocity of 103.8m/µs.
3.7 EMTP-RV MODEL OF THE SECTION OF 245KV GIS SYSTEM
Fig. 3.4 EMTP-RV model of the section of 245kV GIS system
92
The EMTP-RV equivalent circuit representation of typical
245kV GIS system is shown in Fig.3.4. According to their internal design
all parts of the GIS have been represented thoroughly by line sections
with the corresponding surge impedance and travelling times. The
VFTOs during opening and closing operation of the disconnector switch1
are simulated and estimated for various conditions. The variable arc
resistance with respect to time is given in the software according to
customised equation.
3.7.1 GIS (EMTP-RV) model of DS1 closing operation with fixed arc
resistance (Rarc=0.5Ω)
Fig3.5 The Electrical equivalent network of the GIS system during
disconnector switch 1 closing with fixed arc resistance.
The trapped charge equivalent is considered by assigning different
voltage values to VL i .e from -0.1 to -1 pu. This can be considered as
equivalent magnitude of trapped charge.
VS =VFTO at Source side
VL = VFTO at Load side
Vagb = VFTO at Air-to- SF6 bushing
Z Z Z Z
ZZZZ ZZ
250 75 75 75
75 75 757575 30
+2nF
C1 +
0.003nF
C2 +
0.003nF
C3 +
0.2nF
C4 +
0.1nF
C5 +
0.0045nF
C6 +
0.003nF
C8
+
0.003nF
C10
+
0.003nF
C11 +
0.0045nF
C12 +
0.005nF
C13 +
0.003nF
C14 +
0.003nF
C15 +
0.0045nF
C16 +
0.1nF
C17
+
0.5
r
+
0.003nF
C7
+
1 /_0
+ C9
0.0
05
nF
+0.4nF
C18
VM+
VS
?v
VM+
VL
?v
VM+
?v
VM+
?v
Vagb+
0|2.5ms|0
DS1
93
VS =VFTO at Source side
VL = VFTO at Load side
Vagb = VFTO at Air-to- SF6 bushing
Z Z Z Z
ZZZZ ZZ
250 75 75 75
75 75 757575 30
+2nF
C1 +
0.003nF
C2 +
0.003nF
C3 +
0.2nF
C4 +
0.1nF
C5 +
0.0045nF
C6 +
0.003nF
C8
+
0.003nF
C10
+
0.003nF
C11 +
0.0045nF
C12 +
0.005nF
C13 +
0.003nF
C14 +
0.003nF
C15 +
0.0045nF
C16 +
0.1nF
C17
+
0.5
r
+
0.003nF
C7
+
1 /_0
+ C9
0.0
05
nF
+
0.4nF
C18
VM+
VS
?v
VM+
VL
?v
VM+
?v
VM+
?v
Vagb+
-1|2.5ms|0
DS1
3.7.2 GIS model of DS1 closing operation with variable arc resistance
Fig.3.6 The Electrical equivalent network of the GIS system during
disconnector switch 1 closing with variable arc resistance
3.7.3 GIS simulation model of DS1 opening operation with fixed arc
resistance
Fig. 3.7 The Electrical equivalent network of the GIS system during
disconnector switch 1 opening with fixed arc resistance.
VS =VFTO at Source side
VL = VFTO at Load side
Vagb = VFTO at Air-to- SF6 bushing
Z Z Z Z
ZZZZ ZZ
250 75 75 75
75 75 757575 30+2nF
C1 +
0.003nF
C2 +
0.003nF
C3 +
0.2nF
C4 +
0.1nF
C5 +
0.0045nF
C6 +
0.003nF
C8
+
0.003nF
C10
+
0.003nF
C11 +
0.0045nF
C12 +
0.005nF
C13 +
0.003nF
C14 +
0.003nF
C15 +
0.0045nF
C16 +
0.1nF
C17
+
0.5
r
+
0.003nF
C7
+
1 /_0
+ C9
0.0
05
nF
+
0.4nF
C18
VM+
VS
?v
VM+
VL
?v
VM+
?v
VM+
?v
Vagb+
0|2.5ms|0
DS1
R(t)+0
Rt1
94
3.7.4 GIS simulation model of DS1 opening operation with variable
arc resistance
Fig3.8 The Electrical equivalent networks of the GIS system during
disconnector switch 1 opening with variable arc resistance
3.7.5 GIS simulation models of DS1 opening operation with variable
arc resistance and with trapped charge of -0.1p.u to -1p.u
Fig.3.9 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with -0.1 p.u. trapped
charge
VS =VFTO at Source side
VL = VFTO at Load side
Vagb = VFTO at Air-to- SF6 bushing
Z Z Z Z
ZZZZ ZZ
250 75 75 75
75 75 757575 30
+2nF
C1 +0.003nF
C2 +
0.003nF
C3 +
0.2nF
C4 +
0.1nF
C5 +
0.0045nF
C6 +
0.003nF
C8
+
0.003nF
C10
+
0.003nF
C11 +
0.0045nF
C12 +
0.005nF
C13 +
0.003nF
C14 +
0.003nF
C15 +
0.0045nF
C16 +
0.1nF
C17
+
0.5
r
+
0.003nF
C7
+
1 /_0
+ C9
0.0
05
nF
+
0.4nF
C18
VM+
VS
?v
VM+
VL
?v
VM+
?v
VM+
?v
Vagb+
-1|2.5ms|0
DS1
R(t)+0
Rt1
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
95
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
Fig3.10 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with- 0.2 p.u. trapped
charge
Fig3.11 The Electrical equivalent network of the GIS system during opening
operation of disconnector switch 1 with -0.3 p.u. trapped charge
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
96
Fig. 3.12 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with -0.4 p.u. trapped
charge
Fig.3.13. The Electrical equivalent network of the GIS system during opening
operation of disconnector switch 1 with -0.5 p.u. trapped charge.
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
97
Fig. 3.14 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with -0.6 p.u. trapped
charge
Fig. 3.15 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with -0.7 p.u. trapped
charge
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
98
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
Fig.3.16 The Electrical equivalent network of the GIS system during opening
operation of disconnector switch 1 with -0.8 p.u. trapped charge
Fig.3.17 The Electrical equivalent network of the GIS system during opening
operation of disconnector switch 1 with -0.9 p.u. trapped charge
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30
+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF
+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
99
Fig.3.18 The Electrical equivalent network of the GIS system during
opening operation of disconnector switch 1 with -1 p.u. trapped
charge.
3.7.6 GIS simulation model of DS2 opening operation with variable
arc resistance
Fig.3.19 The EMTP-RV equivalent network of the GIS system during closing
operation of disconnector switch 2 with -1pu trapped charge.
VS =VFTO at Source side
VL = VFTO at Load side
VB = VFTO at SF6-to- XLPE cable termination
Z Z Z Z
ZZZZ ZZ
250 75 75 75
7575 7575
75 30+
C1
2nF +C2
0.003nF
+C3
0.003nF
+C4
0.2nF
+C5
0.1nF
+C6
0.0045nF
+C7
0.003nF
+ C8
0.003nF
+ C9
0.003nF
+ C10
0.0045nF
+ C11
0.005nF
+ C12
0.003nF
+ C13
0.003nF
+ C14
0.0045nF
+ C15
0.1nF
+R1
0.5
+ C16
0.003nF+
1 /_0
+
0.0
05
nF
C
17
+C18
0.4nF
VM+
?v
VSVM+
?v
VL+
DS1
?v
-1|1E15|0
VM+
m4
?v
R(t)+0
Rt1
250 75 75 75 75
75 75 75 75 30
z z z z z
z z z z z
VS = VFTO at source side
VL = VFTO at load side
Vxlpe = XLPE cable termination
VS VL
+
2nF
C1 +
0.2nF
C4 +
0.1nF
C5 +
0.0045nF
C6 +
0.003nF
C7 +
0.003nF
C8 +0.003nF
C9
+
0.003nF
C10
+
0.003nF
C11
+
0.0045nF
C12 +
0.005nF
C13 +
0.003nF
C14 +
0.003nF
C15 +
0.0045nF
C16 +
0.1nF
C17 +
0.4nF
C18
+
0.0
05
nF
C
19
+
1 /_0
AC1 +
0.003nF
C3+
0.003nF
C2
+1ms|2.5ms|0
DS2
R(t)+0
Rt1VM+
?v
Vxlpe
3.8 RESULTS OF THE SIMULATION
Fig. 3.20 VFTO at Air
DS1 with fixed arc resistance.
Fig. 3.21 VFTO at Air
the DS1 with variable arc resistance.
100
RESULTS OF THE SIMULATIONS
VFTO at Air-to-SF6 bushing during the opening operation of the
DS1 with fixed arc resistance.
VFTO at Air-to-SF6 bushing during the opening operation of
the DS1 with variable arc resistance.
SF6 bushing during the opening operation of the
operation of
101
Fig. 3.22 VFTO at Air-to-SF6 bushing during the closing operation of the
DS1 with fixed arc resistance.
Fig. 3.23 VFTO at Air-to-SF6 bushing during the closing operation of the
DS1 with variable arc resistance.
Fig. 3.24 VFTO at source side of DS1 with variable arc resistance and
trapped charge of
Fig. 3.25 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.1p.u.
102
at source side of DS1 with variable arc resistance and
trapped charge of- 0.1p.u.
at load side of DS1 with variable arc resistance and trapped
0.1p.u.
at source side of DS1 with variable arc resistance and
at load side of DS1 with variable arc resistance and trapped
Fig. 3.26 VFTO at sou
charge of -0.2p.u.
Fig. 3.27 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.2p.u
103
at source side of DS1 with variable arc resistance and trapped
0.2p.u.
at load side of DS1 with variable arc resistance and trapped
0.2p.u.
rce side of DS1 with variable arc resistance and trapped
at load side of DS1 with variable arc resistance and trapped
Fig. 3.28 VFTO at source side of DS1 with variable arc resistance and
trapped charge of
Fig. 3.29 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.3p.u.
104
at source side of DS1 with variable arc resistance and
trapped charge of -0.3p.u.
at load side of DS1 with variable arc resistance and trapped
0.3p.u.
at source side of DS1 with variable arc resistance and
at load side of DS1 with variable arc resistance and trapped
Fig. 3.30 VFTO at source side of DS1 with variable arc resistance
trapped charge of
Fig. 3.31 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.4p.u.
105
at source side of DS1 with variable arc resistance
trapped charge of -0.4p.u.
at load side of DS1 with variable arc resistance and trapped
0.4p.u.
at source side of DS1 with variable arc resistance and
at load side of DS1 with variable arc resistance and trapped
106
Fig. 3.32 VFTO at source side of DS1 with variable arc resistance and
trapped charge of -0.5p.u.
Fig. 3.33 VFTO at source side of DS1 with variable arc resistance and
trapped charge of -0.5p.u.
Fig. 3.34 VFTO at source side of DS1 with variable arc resistance and
trapped charge of
Fig. 3.35 VFTO at load side of DS1 wi
charge of -0.6p.u.
107
at source side of DS1 with variable arc resistance and
trapped charge of -0.6p.u.
at load side of DS1 with variable arc resistance and trapped
0.6p.u.
at source side of DS1 with variable arc resistance and
th variable arc resistance and trapped
Fig. 3.36 VFTO at source side of DS1 with variable arc resistance and
trapped charge of
Fig. 3.37 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.7p.u.
108
at source side of DS1 with variable arc resistance and
trapped charge of -0.7p.u.
at load side of DS1 with variable arc resistance and trapped
0.7p.u.
at source side of DS1 with variable arc resistance and
at load side of DS1 with variable arc resistance and trapped
109
Fig. 3.38 VFTO at source side of DS1 with variable arc resistance and
trapped charge of -0.8p.u.
Fig. 3.39 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.8p.u.
110
Fig. 3.40 VFTO at source side of DS1 with variable arc resistance and
trapped charge of -0.9 p.u.
Fig. 3.41 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -0.9p.u.
111
Fig. 3.42 VFTO at source side of DS1 with variable arc resistance and
trapped charge of -1 p.u.
Fig. 3.43 VFTO at load side of DS1 with variable arc resistance and trapped
charge of -1 p.u.
112
Fig. 3.44 VFTO at SF6 – to – XLPE cable termination during opening of DS2
With variable arc resistance and trapped charge of -1 p.u.
113
3.9 FAST FOURIER TRANSFORM (FFT) ANALYSIS OF VERY FAST
TRANSIENT OVER VOLTAGES
In this section, the frequency spectrums of voltage transients are
obtained using FFT algorithm. The Fourier transform has long been a
principle analytical tool in such diverse fields as linear systems, Optics,
Probability theory, Quantum physics, Antennas and Signal analysis.
However, a similar statement is not true for the Discrete Fourier
transform (DFT). But with the development of the Fast Fourier transform
(an algorithm that efficiently computes the DFT) many facets of scientific
analysis have been completely revolutionized. The Fourier Integral is
defined by the expression:
( ) ∫+∞
∞−
Π−= dtetsfS ftj 2)( (3.5)
Where s (t) is the waveform to be decomposed into the sum of
sinusoids, S (f) is the Fourier Transform of set, and 1−=j . Typically, s
(t) is a function of the variable time and S (f) is a function of the variable
frequency. The Fourier Transform identifies or distinguishes the different
frequency sinusoids and their respective amplitudes, which combine to
form an arbitrary waveform. The Inverse Fourier Transform is defined as
∫+∞
∞−
Π= dtefSts ftj 2)()( (3.6)
Inversion transformation allows the determination of a function of
time from its Fourier transform. The validity of equations (3.5) and (3.6)
114
depend upon certain conditions as if s(t) is integral in the sense
∫+∞
∞−
∞<)(ts (3.7)
Then its Fourier transform S(f) exists and satisfies the inverse
Fourier transform. It is to be noted that the above condition is a
sufficient but not a necessary for the existence of a Fourier transform.
If s(t) = β(t) sin(2πft+α), where f and α rare arbitrary constants. If
β(t+k) < β(t) for | t | > λ > 0, then function s(t)/t is absolutely integrable
in the sense of equation (3.7) then S(f) exists and satisfies the Inverse
Fourier Transform equation (3.6).
3.9.1: Discrete Fourier transforms
1,.....,2,1,0,)()/(1
0
/2 −== ∑−
=
−NnekTgkTnG
N
K
Nnkj π (3.8)
The above expression relates N samples of time and N samples of
frequency by means of the continuous Fourier Transform. “The Discrete
Fourier Transform (DFT) is then a special case for the Continuous
Fourier Transform (CFT)”. If it is assumed that the N samples of the
original function g (t) are one period of a periodic waveform, the Fourier
Transform of this periodic function is given by the N samples computed
by equation (3.8).
115
3.9.2: Inverse Discrete Fourier Transforms
∑−
=
Π −==1
0
/2 1,...,2,1,0,)/(/1)(N
n
NnkjNnekTnGNkTg (3.9)
The above discrete inversion formula exhibits periodicity in the
same manner as the Discrete Transform (DT); the period is defined by N
samples of g(kT). This property results from the periodic nature of
ej2πnk/N.
Properties:
(l) Linearity x (t) + h (t) ↔ X (f) + H (f)
(2) Symmetry H(t) ↔ h(-f)
(3) Time scaling h (kt) ↔ 1/k H (f/k)
(4) Frequency scaling1/k h (t/k) ↔ H(kf)
(5) Time shifting h (t-to) ↔ H (f) ej2πft0
(6) Frequency shifting h (t) e j2πft0 ↔ H (f-fo)
(7) Convolution x(t) h(t) ↔ x(T)h(t- T)dT
The above properties for the Continuous Fourier Transform can be
simply restated with the appropriate notation for the discrete Fourier
transform, as the latter is a special case of the former.
3.9.3: Fast Fourier Transform (FFT):
Consider the discrete Fourier transform
∑ −== − 1,....,2,1,0,)()( /2
0 NnekxnXNnkj π (3.10)
Where we have replaced kT by 'k' and n/NT by 'n' for convenience
of notation. We note that equation (3.10) describes the computation of N
116
equations. For example, if N = 4 and if we let
NjeW
/2π−= (3.11)
Then equation (3.10) can be written as
0
0
0
0
0
0
0
0 )3()2()1()0()0( WxWxWxWxX +=== (3.12)
3
0
2
0
1
0
0
0 )3()2()1()0()1( WxWxWxWxX +===
6
0
4
0
2
0
0
0 )3()2()1()0()2( WxWxWxWxX +===
9
0
6
0
3
0
0
0 )3()2()1()0()3( WxWxWxWxX +===
Equation (3.12) can be more easily represented in matrix form
=
)3(
)2(
)1(
)0(
)3(
)2(
)1(
)0(
0
0
0
0
9630
6420
3210
0000
X
X
X
X
WWWW
WWWW
WWWW
WWWW
X
X
X
X
(3.13)
or more compactly as
X(n) = Wnk Xo(k) (3.14)
Examination of equation (3.13) reveals that since W and possibly
Xo(k) are complex, then N2 complex multiplications and N(n-l) complex
additions are necessary to perform the required matrix computation.
“The FFT owes its success to the fact that the algorithm reduces the
number of multiplications and additions required in the computation of
equation”. To illustrate the FFT algorithm, it is convenient to choose the
number of sample points of Xo (k) according to the relation N= 2r where
'r' is an integer. From the choice of N= 4 = 2r = 22, we can apply the FFT
to the computation of equation (3.13). The first step in developing the
117
FFT algorithm for this example is to rewrite equation (3.13) as
=
)3(
)2(
)1(
)0(
1
1
1
1111
)3(
)2(
)1(
)0(
0
0
0
0
123
202
321
X
X
X
X
WWW
WWW
WWW
X
X
X
X
(3.15)
Matrix equation (3.15) was derived from (3.13) by using the
relationship Wnk = WnkmodN. Recall that [nk mod (N)] is the remainder
upon division of nk by N;
hence if N = 4, n = 2 and k = 3 then
W6 = W2 (3.16)
Since, Wnk+W6 = exp[(-jπ/4)(6)] = exp[-j3π]
exp[-jπ] = exp[(-jπ/4)(6)] = W2 = WnkmodN (3.17)
The second step in the development is to factor the square matrix
in the equation (3.15) as follows:
=
)3(
)2(
)1(
)0(
010
001
010
001
110
100
001
001
)3(
)1(
)2(
)0(
0
0
0
0
2
2
0
0
3
1
2
0
X
X
X
X
W
W
W
W
W
W
W
W
X
X
X
X
(3.18)
For the present, it suffices to show that multiplication of the two
square matrices of equation (3.18) yields the square matrix of equation
(3.15) with the exception that rows 1 and 2 have been interchanged. It is
to be noted that this interchange has been taken into account in
equation (3.18) by rewriting the column vector X(n); let the row
118
interchanged vector be denoted by
=
)3(
)1(
)2(
)0(
)(1
X
X
X
X
nX (3.19)
One should verify that equation (3.18) yields equation (3.15) with
the interchanged rows as noted above. This factorization is the key to the
efficiency of the FFT algorithm. Having accepted the fact that equation
(3.18) is correct, although the results are scrambled, one should then
examine the number of multiplications necessary to compute the
equation. The final equation can be re written as:
=
)0(
)0(
)0(
)0(
010
001
010
001
)3(
)2(
)1(
)0(
0
0
0
0
2
2
0
0
1
1
1
1
X
X
X
X
W
W
W
W
X
X
X
X
(3.20)
i.e. column vector x1(k) is equal to the product of the two matrices
on the right in equation (3.18). Element x1(0) is computed by one
complex multiplication and one complex addition
3.9.4: WEIGHTING FUNCTIONS
A weighting function, w (n), is a sequence of numbers that is
multiplied by input data prior to performing a Discrete Fourier
Transform (DFT) on that data. Weighting (also called window) functions
reduce sidelines of DFT filters and widen main lobes while, fortunately,
not altering the locations of the centers of the filters.
Weighting function selection can be made early in the design process
119
because the choice of FFT algorithm and their functions are independent
of each other. Choice of a weighting function to provide the specified side
lobe level is done without concern for the FFT algorithm that will be used
because they work for any length FFT and they work the same for any
FFT algorithm. They do not alter the FFTs ability to distinguish two
frequencies. The performance measures of weighting functions and
comparison are given in [44].
The different types of weighting functions used are:
(1) Rectangular: for n = 0 to N-l, ω(n) = 1
The rectangular weighting function is just the plain FFT without
modifying the input data samples. The peak of the highest side lobe is
only 13 dB below the main-lobe response, and the side lobe peaks do not
drop off rapidly. This makes it poor for signals with multiple frequency
components that have amplitudes that are more than 6 dB different from
each other.
(2) Triangular: for n = 0 to N/2, w (n) = 2*n/N
n = N/2+1 to N-1, w(n) = 2*(N-n)/N
The triangular window function is used to provide side lobes and
straddle loss lower than the rectangular function. The outstanding
characteristic of this window function is the smaller number of side lobes
than the others.
(3) Sine-lobe: for n = 0 to N-1, w (n) = sin(nπ/N)
The sine-lobe window function provides improved side lobe performance.
120
For power of two FFTs, this window function has a computational
advantage over triangular window function because the coefficients are
the same one as used to compute the FFT.
(4) Hanning: for n = 0 to N-l, w(n) = 0.5*[1-cos(nπ/N)]
The Hanning window function is slightly more complicated to compute
than the sine-lobe. The peaks of its side lobes fall off 50% faster than the
triangular and sine-lobe functions.
(5) Sine-cubed: for n = 0 to N-l, w(n) = sin3(nπ/N)
The sine-cubed function is a natural extension to the side-lobe window
function, but with values that are not used for the complex
multiplications between powers of two building blocks.
(6) Sine to the fourth: for n = 0 to N-l, w(n) = sin4 (nπ/N)
(7) Hamming: for n = 0 to N-l, w(n) = 0.54 – 0.46.cos(2nπ/N)
(8) Blackman:
for n = 0 to N-l , w(n) = 0.42 – 0.5*cos(2nπ/N) = 0.08* 0.08* cos(4nπ/N)
(9) Three-sample Blackman-harries:
(a) For n = 0 to N-l, w (n) = 0.449595 – 0.49364* cos(2nπ/N) = 0.05677*
cos(4nπ/N)
(b) For n = 0 to N-l, w (n) = 0.42323- 0.49775* cos(2nπ/N) = 0.07992*
cos(4nπ/N)
(10) Four-sample Blackman-harries:
(a) For n = 0 to N-l,
w(n)=0.40217 - 0.49703 * cos(2nπ/N) + 0.09892* cos(4nπ/N) - 0.00188*
121
cos(6nπ/N)
(b) For n = 0 to N-l,
w (n) = 0.35875- 0.48829* cos(2nπ/N) + 0.14128* cos(4nπ/N) - 0.01168*
cos(6nπ/N)
The following factors significantly influence the transfer function:
Finite record length:
During the conversion from the analog to digital domain, the
Nyquist criterion must be satisfied. It specifies that all signals should be
sampled by at least twice; preferably ten times the highest frequency
component in the signal. So, this stipulates the minimum limit on the
sampling frequency for a given sampling speed. Higher record lengths
result in an increase in digitizer costs and are also higher record lengths
are accompanied by a decrease in signal-noise ratio.
Quantization:
“The process by which the analog signals are converted to their
digital from is called Quantization". This is an irreversible process, and
can be defined as a nonlinear mapping from the domain of continuous
amplitude inputs onto one of a countable number of the possible output
levels. This results in the so called quantization error, which is the main
cause for the deviation of the signals from the ideal nature.
Windowing:
A very popular signal processing method, namely, windowing is
used to avoid leakage effects due to abrupt truncation of signals. This is
122
a deliberate smoothing of the abrupt truncation of the impulse tail
caused by the finite length of the digital record.
In this chapter the fast Fourier transform (FFT) technique has been
employed to identify the dominant frequencies of the fast transient
voltages. The frequency spectrum has been calculated by considering the
VFTO waveform for the duration of 0.4µs and 0.5µs. The Fourier
transform and Fast Fourier transform, types of Fourier transforms and
weighting functions as well as their application are discussed. The
MATLAB 7.1 is used for this analysis. The time-domine data (APPENDIX-
I) of corresponding signal is transferred to Signal processing tool box in
MATLAB7.1 The corresponding results are presented in the section 3.9.5.
3.9.5 FFT analysis of VFTOs
Fig. 3.45 Frequency spectrum of VFTO at Air-to-SF6 bushing during the
opening operation of the DS1 with fixed arc resistance
123
Fig. 3.46 Frequency spectrum of VFTO at Air-to-SF6 bushing during the opening
operation of the DS1 with variable arc resistance.
Fig.3.47 Frequency spectrum of VFTO at Air-to-SF6 bushing during the
closing operation of the DS1 with fixed arc resistance
Fig.3.48 Frequency spectrum of
closing operation of the DS1 with
Fig.3.49 Frequency spectrum of
arc resistance and trapped charge of
124
Frequency spectrum of VFTO at Air-to-SF6 bushing during the
closing operation of the DS1 with variable arc resistance
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.1p.u.
SF6 bushing during the
arc resistance
source side of DS1 with variable
Fig.3.50 Frequency spectrum of
resistance and trapped charge of
Fig.3.51 Frequency spectrum of
arc resistance and trapped charge of
125
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.1p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.2p.u.
load side of DS1 with variable arc
source side of DS1 with variable
Fig.3.52 Frequency spectrum of
resistance and trapped charge of
Fig.3.53 Frequency spectrum of
arc resistance and trapped charge of
126
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.2p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.3p.u.
load side of DS1 with variable arc
source side of DS1 with variable
Fig.3.54 Frequency spectrum of
resistance and trapped charge of
Fig.3.55 Frequency spectrum of
arc resistance and trapped charge of
127
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.3p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.4p.u.
load side of DS1 with variable arc
source side of DS1 with variable
Fig.3.56 Frequency spectrum of
resistance and trapped charge of
Fig.3.57 Frequency spectrum of
arc resistance and trapped charge of
128
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.4p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.5p.u.
side of DS1 with variable arc
source side of DS1 with variable
Fig.3.58 Frequency spectrum of
arc resistance and trapped charge of
Fig.3.59 Frequency spectrum of
arc resistance and trapped charge of
129
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.5p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.6p.u.
side of DS1 with variable
source side of DS1 with variable
Fig.3.60 Frequency spectrum of
resistance and trapped charge of
Fig.3.61 Frequency spectrum of
arc resistance and trapped charge of
130
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.6p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.7p.u.
DS1 with variable arc
source side of DS1 with variable
Fig.3.62 Frequency spectrum of
resistance and trapped charge of
Fig.3.63 Frequency spectrum of
arc resistance and trapped charge of
131
Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -0.7p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.8p.u.
with variable arc
source side of DS1 with variable
Fig.3.64 Frequency spectrum of
resistance and trapped charge of
Fig.3.65 Frequency spectrum of
arc resistance and trapped charge of
132
Frequency spectrum of VFTO at load side of DS1 with vari
resistance and trapped charge of -0.8p.u.
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -0.9p.u.
load side of DS1 with variable arc
source side of DS1 with variable
Fig.3.66 Frequency spectrum of
arc resistance and trapped charge of
Fig.3.67 Frequency spectrum of
arc resistance and trapped charge of
133
Frequency spectrum of VFTO at source side of DS1 with
arc resistance and trapped charge of -0.9p.u
Frequency spectrum of VFTO at source side of DS1 with variable
arc resistance and trapped charge of -1p.u.
source side of DS1 with variable
source side of DS1 with variable
134
Fig.3.68 Frequency spectrum of VFTO at load side of DS1 with variable arc
resistance and trapped charge of -1p.u.
Fig.3.69 Frequency spectrum of VFTO at at SF6 – to – XLPE cable
termination during opening of DS2 with variable arc resistance and
trapped charge of -1 p.u.
135
3.9.6 The transients on source side and load side of the
Disconnector switch with different trapped charges.
Table 3.2 VFTOs on source side with different trapped charges
S.No
Trapped
charge in
p.u
Source side
voltage in p.u.
Rise Time in
(ns)
Highest
frequency
In MHz
1
-0.1 1.61 19.27
11
2 -0.2
1.82 21.27
12.6
3 -0.3 1.93
26.73
14.1
4 -0.4 1.97
26.92
13.7
5 -0.5 2.31
27.12
17.4
6 -0.6 2.37
28.12
21.6
7 -0.7 2.39
28.21
28.1
8 -0.8 2.48
28.78
39.1
9 -0.9 2.71
33.40
39.7
10 -1
2.72
39.20
41.2
136
Table 3.3 VFTOs on load side with different trapped charges
S.No
Trapped
charge in
p.u
Load side
voltage in p.u.
Rise Time in
(ns)
Highest
frequency
In MHz
1
-0.1 1.97 19.27
9
2
-0.2
2.13 21.27
13.1
3 -0.3 2.21
26.73
14.7
4 -0.4 2.27
26.92
17.0
5 -0.5 2.42
27.12
19.1
6 -0.6 2.43
28.12
26.3
7 -0.7 2.69
28.21
29.7
8 -0.8 2.74
28.78
29.1
9 -0.9 2.76
29.34
37
10
-1 2.81 39.20
44
137
Table 3.4 VFTOs at air to SF6gas bushing during opening and closing
operation of DS1
VFTO at air to gas bushing
during DS1 opening operation
VFTO at air to gas bushing
during DS1 closing operation
VFTO
in p.u.
Rise time
in ns
Frequency
In MHz
VFTO
in p.u.
Rise time
in ns
Frequency
In MHz
With fixed arc
resistance
2.31
2.29
11.7
2.19
29.11
24.9
With variable arc
resistance
2.21
2.11
11.1
1.92
25.32
19.7
The Fig 3.20 to Fig.3.23 shows VFTO waveforms at Air-to-SF6 bushing.
Similarly from Fig3.24 to Fig.3.43 shows VFTO waveforms at source side
and load side of DS1 with different values of trapped charges. The
Fig3.45 to Fig3.69 shows the various frequency spectrums obtained at
various locations of the system with different trapped charges. The
results are tabulated in tables 3.2 and 3.4 respectively.
In the case of variable arc resistance the system acts as more oscillatory
circuit there is a superposition of transient state, with some damping
effect results slight decrease in VFTO.
138
3.10 VARIOUS METHODS FOR SUPPRESSION OF VFTOs IN GIS
SYSTEMS
3.10.1 VFTO Suppression Using Opening and Closing Resistor across
Disconnector Switch
During switching operation of disconnector switches and earth
faults in GIS systems very fast transient over voltages occurs and will
stress adjacent equipment and secondary equipment in GIS [39]. With
the increasing of GIS voltage levels, the effect of VFTO should be taken
into consideration. Hence it is advisable to suppress these over voltages
for protection of secondary equipment [40]. One of the exisistng methods
of suppressing these over voltages is by insertion of resistor during
switching. Usually the resistance parameter ranges from 400-500Ω will
be used in this method [41]. In the present application, a resistor of
500Ω is connected in parallel to the disconnector switch and a switch is
connected in series with the resistor. The switch connected in series with
the resistor is closed at the time of maximum voltage is obtained during
second restrike/prestrike at load end. The trapped charge of -0.1p.u,-
0.5p.u&-1p.u are considered for the computation of VFTOs with
resistance switching
139
3.10.2 Fast Fourier Transform (FFT) Analysis of reduced transient
over voltages
In this chapter the fast Fourier transform (FFT) technique has
been employed to identify the dominant frequencies of the transient
voltages. The frequency spectrum has been calculated by considering the
VFTO waveform for the duration of 0.4µs and 0.5µs. The Signal
Processing Tool box in MATLAB 7.1 is used for this analysis. The time
domine data of corresponding signal is transferred into the MATLAB 7.1
as an input file and the corresponding frequency spectrums are
obtained. The results are given in section 3.10.4.
140
3.10.3 Single Phase Equivalent Circuits of 245kV GIS System
with Opening and Closing Resistor
Fig.3.70(a) DS1 opening operation with variable arc resistance and with -
0.1p.u trapped charge and resistance Switching
Fig. 3.70(b) DS1 closing operation with variable arc resistance and with- 0.1
trapped Charge and resistance switching
141
Fig. 3.70(c) DS1 opening Operation with variable arc resistance and trapped
charge of -0.5 p.u. and resistance switching.
Fig. 3.70(d) DS1 closing Operation with variable arc resistance and trapped
charge of -0.5 p.u. and resistance switching
142
Fig. 3.70(e) DS1 opening operation with variable arc resistance and trapped
charge of -1p.u. and resistance switching
Fig. 3.70(f) DS1 closing operation with variable arc resistance and trapped
charge of -1p.u. and resistance switching
143
3.10.4 Simulation Results with opening and closing Resistance
Fig. 3.71(a) VFTO at source side of the DS1 opening operation variable
arc resistance and trapped charge of -0.1p.u and switching
resistance across DS
Fig. 3.71(b) FFT of VFTO waveform during opening of DS1 with variable
arc resistance and trapped charge of- 0.1p.u with
resistance switching
144
Fig. 3.71(c) VFTO at source side of the DS1 closing operation with variable
arc resistance and trapped charge of -0.1p.u and switching
resistance
Fig. 3.71(d) FFT of VFTO waveform during closing of DS1 with variable arc
& trapped charge of -0.1p.u resistance and resistance switching
145
Fig. 3.71(e) VFTO at source side of the DS1 opening operation with
variable arc resistance with trapped charge of- 1p.u and
with resistance switching
Fig.3.71 (f) FFT of VFTO waveform during DS1 opening operation with variable
arc resistance with trapped charge of -1p.u and with resistance
switching
146
Fig.71(g) VFTO at source side of the DS1 closing operation with variable
arc resistance with trapped charge of -1p.u and with resistance
switching
Fig. 3.71(h) FFT of VFTO waveform during DS1 closing operation with variable
arc resistance with trapped charge of -1p.u and with resistance
switching
147
Fig. 3.71(i) VFTO at source side of the DS1 opening operation with
variable arc resistance with trapped charge of- 0.5p.u and
with resistance switching
Fig. 3.71(j) FFT of VFTO waveform during DS1 opening operation with
variable arc resistance with trapped charge of -0.5p.u and
with resistance switching
148
Fig. 3.71(k) VFTO at source side of the DS1 closing operation with variable arc
resistance with trapped charge of- 0.5p.u and with resistance
switching
Fig. 3.71(l)FFT of VFTO waveform during DS1 opening operation with variable
arc resistance with trapped charge of -0.5p.u and with resistance
switching
149
3.11 VFTO SUPPRESSION USING FERRITE RINGS
In this section, a new technique is proposed for the suppressing of
VFTOs by high frequency magnetic rings known as ferrite rings. These
ferrite rings are very effective in inhibiting the high frequency
components of transient over voltages[40] . The ferrite rings are
connected to the bus bars near the disconnector contacts can effectively
resist the steep rise time travelling waves passing through and consumes
energy from the waves [22,40]. The characteristics and design features of
ferrite rings for high voltage applications are discussed in detail. The
mathematical modeling of ferrite rings has been done. The Fig.3.72 (a) to
Fig.3.72(d) shows EMTP-RV equivalent circuits with ferrite ring
equivalents. The simulation results during opening and closing
operations are presented in the Fig. 3.73(a) to Fig. 3.73(l). The proposed
technique is experimentally verified and it is discussed in detail in the
next chapter.
Ferromagnetic rings can be utilized to effectively suppress the
amplitude of VFTO generated with in GIS [23], however selection of
ferromagnetic materials for high voltage applications is of extreme
significance. The ferrite material chosen must have different
characteristics of saturation, magnetic conductivity, and frequency
response and loss characteristics. All these parameters influence the
VFTO suppression effect. The ferrite material is chosen such that the
magnetic flux density is maximum. The magnetic conductivity parameter
150
is complex and nonlinear. The suppressing effect on VFTO is determined
by equivalent inductance of Ferro magnetic ring that relate to the size
and the magnetic conductivity of ferrite ring. The energy loss of the
ferrite ring can know from the equation 3.11.1[22]
! =
√" µ ℎ $%& 3.21
µ is magnetic hysteresis conductivity
H is magnetic field strength
h is magnetic hysteresis coefficient
F is magnetization frequency
V is volume of the ferrite ring
3.11.1 Equivalent characteristics
The suitable ferrite rings can be connected to bus bar of GIS
systems to limit the magnitudes of VFTOs generated due to disconnector
operations. The equivalent circuit of the ferrite ring fixing it on the GIS
conductor bar is equivalent to connecting impedance and inductance
between the disconnector and bus bar. The simulation circuit for VFTO
studies is inductance of the ferrite coil parallel to resistance of the coil.
The effect of reflected waves is neglected.
151
3.11.2 Losing characteristics of ferrite rings
The ferrite ring fixed on GIS conductor should have no influence
on the power frequency electric current and the most loss of the ferrite
ring produces at high frequency, so the energy of the VFTO can be
absorbed. The loss of unit volume of ferrite material is
P = Pe + Ph +Pc 3.22
Total power loss can be expressed as
' = &()* 3.23
K is constant
f is frequency
B is flux density; n and m are the Index parameters, from above equation
the loss of the ferrite ring is in direct proportion to f and B.
3.11.3 Design aspects of ferrite rings
Mn-Zn ferrite is chosen as its high magnetic saturation Bs i.e.
about Bs > 47mt at 250C and the core shape selected is toroid. Ferrite
characteristics as a function of operating conditions. When selecting a
ferrite rings it is necessary to consider some important application
aspects.
The frequency where maximum attenuation is needed will
determined the material requirements. The most suitable ferrite would
offer the highest impedance levels at the very high frequencies, which
usually cover an abroad spectrum core shape, which is usually defined
by bus bar type and size. Installation requirements to decide on an entire
152
or split core type. Attenuation/impedance level of maximum suppression
the Mn-Zn material (3S4) is selected for present application. It can
suppress very high frequencies order of MHz [40]. With MnZn-Ferrite
precise control of material composition has resulted in an increase of its
resistivity to a value of 103Ω m. The additional advantage of 3S4 is that it
does not have nickel which is a heavy metal and therefore a potential
hazard to the environment. Also, its high permeability gives it excellent
high-frequency characteristics.
3.11.4 Specifications of 3S4 ferromagnetic material
S.NO. Symbol Conditions Value Unit
1
µi 25oC;10KHz;0.1mT
1700
mT
2 B 25oC;10KHz;250A/m 300 mT
3 --- 100oC;10KHz;250A/m 140 ---
4 Z 25oC;3MHz ≥25 Ω
5 --- 25oC;30MHz ≥60 ---
6 --- 25oC;100MHz ≥80 ---
7 25oC;300MHz ≥90 ---
8 ρ DC; 25oC =103 ---
9 Tc ---- ≥110 Ωm
10 Density ---- =4800 Kg/m3
153
3.11.5 Impedance behavior of 3S4-Ferrite cores
The inside diameter is fixed by the GIS bus bar dimensions. The
ferrite rings should fit closely around the bus bar to avoid loss of
impedance. Impedance increases mainly with the length of a bus bar or
the number of shields. It depends linearly on length and only
logarithmically on the outer dimensions. The most suitable ferrite core
will be the largest type with an outer diameter matching the bus bar
outer dimensions. If large inner diameter (not fitting the bus bar) and
their shorter length are compensated by using more than one turn. The
Z is proportional to N2, where N is number of turns. It is not
recommended to use more than 2 turns on ferrite core. Although the
higher number of turns results in more impedance. The parasitic inner
winding capacitance, which is also proportional to the number of turns,
will decrease the results in a worse performance at very high frequencies.
Location:
The position of ferrite rings is very important for the best
performance in the application. The ferrite rings are connected near the
disconnector switch in the GIS system.
Material and size
The impedance curve can be divided from a pure material curve
can be derived from a pure material curve, the so called complex
permeability curve. As impedance consists of a reactive and a resistive
part, permeability should also have two parts to represent this. The real
154
partµ,) corresponds to the reactances, and the imaginary part ( µ" the
losses.
= ./0µ, − .µ"23
= wµ"3 + ./µ,3 3.24
Z = R+jx, R = w µ,3 & X= wµ"3
Magnitude of Impedance (Z) = √ + 4 = w3 5 µ, + µ,, Where / = 2п&
L0 = µ 7 89:9
µ = 4п ∗ 10<=
N = Number of turns
>? = Effective area
@? = Effective length
In high power rating applications the ferrite ring can be equivalent
to simply from with uniform magnetic field. It can be similar to a thin
ring ‘dr’. The different magnetic field line length and ferrite ring section
can be expressed with one equivalent length 3? and area >?. The total
magnetic field go through the each section, the equivalent inductance 3A is 3A = µµAB 89
C9
3.25
and equivalent resistance E = ℎ&3AFC9
3.26
Here µA is the relative initial magnetic conductivity h is the magnetic
hysteresis coefficient, “N’s the number of rings. The ferrite ring is
155
composed of a lot of ideal thin rings dr. So lN=2пrH, and the section area
as dA = a.dr then the differential inductance is
3 = 7H@ = 7 H
I. 2пr = 7 ) K I 2пr
From B = µµAI , the initial differential inductance is
3A = µµA7 LпM
by adding all the rings, the inductance of the ferrite ring is
3A = NONA7 K2P B L
A 3.27
Using the similar method the resistance can be obtained as
E = ℎ & 3A7 @ 1A − 1
LB LA
3.28
The initial magnetic conductivity of µA of the Mn-Zn ferrite is
between 2000 and 10,000 and its magnetic hysteresis coefficient scale
ERS" is about 0.1*10<T>/V If the equivalent impedance and inductance of
the ferrite ring are calculated as 70Ω and 0.02mH using above
equations. If the frequency is 100MHz, initial magnetic conductivity is
3000. Magnetic hysteresis coefficient is 0.18 ∗ 10<T > VW , the dimensions
of the ferrite ring are K = 3.33 ∗ 10<% m , L= 9.68*10-3m, ri =19.37*10-3m.
156
VS = VFTO at Source voltage
VL = VFTO at Load voltage
VSF6AGB= VFTO at Air to Gas Bushing
+
2nF
C1
+
0.003nF
C19+
0.003nF
C20
+
0.2nF
C21
+
0.1nF
C22
+
0.0045nF
C23
+
0.003nF
C24
+
0.003nF
C25 +
0.003nF
C26 +
0.0045nF
C27 +
0.005nF
C28 +
0.003nF
C29 +
0.003nF
C30 +
0.0045nF
C31 +
0.1nF
C32
+
0.5
R2
+ RLC
250,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
30,0,0
+
1 /_0
+ C3
4
!v0
.00
5n
F
+ RLC
75,0,0
+
0.4nF
C35
VM+
VL
?v
+
0.003nF
C33
+0.02mH
L2
+
70
R1
VM+
VS?v R(t)+
Rt1
0
+-1|10ms|0
SW1
3.12 EMTP-RV EQUIVALENT CIRCUITS OF 245kV GIS SYSTEM WITH
APPLICATION OF FERRITE RINGS
Fig. 3.72(a) DS1 opening Operation with variable Arc Resistance and trapped
charge of -1p.u. and Ferrite rings.
Fig. 3.72(b) DS1 closing Operation with variable Arc Resistance and trapped
charge of- 1p.u. and Ferrite rings
VS = VFTO at Source voltage
VL = VFTO at Load voltage
VSF6AGB= VFTO at Air to Gas Bushing
+
2nF
C1
+
0.003nF
C19
+
0.003nF
C20
+
0.2nF
C21
+
0.1nF
C22
+
0.0045nF
C23
+
0.003nF
C24
+
0.003nF
C25 +
0.003nF
C26 +
0.0045nF
C27 +
0.005nF
C28 +
0.003nF
C29 +
0.003nF
C30 +
0.0045nF
C31 +
0.1nF
C32
+
0.5
R2
+ RLC
250,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
30,0,0
+
1 /_0
+ C3
4
!v0
.00
5n
F
+ RLC
75,0,0+
0.4nF
C35
VM+
VL
?v
+
0.003nF
C33
+0.02mH
L2
+
70
R1
VM+
VS?v
+
1ms/10ms/0
SW1
R(t)+
Rt1
0
157
VS = VFTO at Source voltage
VL = VFTO at Load voltage
VSF6AGB= VFTO at Air to Gas Bushing
+
2nF
C1
+0.003nF
C19
+
0.003nF
C20
+
0.2nF
C21
+
0.1nF
C22
+
0.0045nF
C23
+
0.003nF
C24
+
0.003nF
C25 +
0.003nF
C26 +
0.0045nF
C27 +
0.005nF
C28 +
0.003nF
C29 +
0.003nF
C30 +
0.0045nF
C31 +
0.1nF
C32
+
0.5
R2
+ RLC
250,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
30,0,0
+
1 /_0
+ C3
4
!v0
.00
5n
F
+ RLC
75,0,0
+
0.4nF
C35
VM+
VL
?v
+
0.003nF
C33
+0.02mH
L2
+
70
R1
VM+
VS?v R(t)+
Rt1
0
+-1|10ms|0
SW1
VS = VFTO at Source voltage
VL = VFTO at Load voltage
VSF6AGB= VFTO at Air to Gas Bushing
+
2nF
C1
+
0.003nF
C19
+
0.003nF
C20
+
0.2nF
C21
+
0.1nF
C22
+
0.0045nF
C23
+
0.003nF
C24
+
0.003nF
C25 +
0.003nF
C26 +
0.0045nF
C27 +
0.005nF
C28 +
0.003nF
C29 +
0.003nF
C30 +
0.0045nF
C31 +
0.1nF
C32
+
0.5
R2
+ RLC
250,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
75,0,0
+ RLC
30,0,0
+
1 /_0
+ C3
4
!v0
.00
5n
F
+ RLC
75,0,0+
0.4nF
C35
VM+
VL
?v
+
0.003nF
C33
+0.02mH
L2
+
70
R1
VM+
VS?v
+
1ms/10ms/0
SW1
R(t)+
Rt1
0
Fig. 3.72(c) DS1 opening Operation with variable Arc Resistance and trapped
charge of - 0.5p.u. and Ferrite rings
Fig. 3.72(d) DS1 closing Operation with variable Arc Resistance and trapped
charge of -0.5p.u. and Ferrite rings
3.13 SIMULATION RESULTS
RINGS.
Fig.3.73(a) VFTO at source side of the DS1 opening operation with variable
arc resistance
Fig. 3.73(b) FFT of VFTO waveform during opening of DS1 with variable
Arc resistance and ferrite rings on bus bar.
158
RESULTS WITH APPLICATION OF FERRITE
VFTO at source side of the DS1 opening operation with variable
resistance, trapped charge of -0.1p.u and ferrite rings
FFT of VFTO waveform during opening of DS1 with variable
resistance and ferrite rings on bus bar.
WITH APPLICATION OF FERRITE
VFTO at source side of the DS1 opening operation with variable
ferrite rings.
FFT of VFTO waveform during opening of DS1 with variable
159
Fig. 3.73(c) VFTO at source side of the DS1 closing operation with variable
arc resistance, trapped charge of -0.1p.u and with ferrite rings.
Fig. 3.73(d) FFT of VFTO waveform during DS1 closing operation with variable
arc resistance with trapped charge of -0.1p.u and with ferrite rings.
160
Fig. 3.73(e) VFTO at source side of the DS1 opening operation with variable arc
resistance with trapped charge of -1p.u and with ferrite rings
Fig. 3.73(f) FFT of VFTO waveform during DS1 closing operation with variable
arc resistance with trapped charge of -1p.u and with ferrite rings.
161
Fig. 3.73(g) VFTO at source side of the DS1 closing operation with
Variable arc resistance with trapped charge of- 1p.u with ferrite
rings Application on bus bar
Fig. 3.73(h) FFT of VFTO waveform during DS1 closing operation with
Variable arc resistance with trapped charge of -1p.u and
With ferrite rings
162
Fig. 3.73(i) VFTO at source side of the DS1 opening operation with variable arc
resistance with trapped charge of -0.5p.u with ferrite rings
Fig. 3.73(j) FFT of VFTO waveform during DS1 opening operation with variable
arc resistance with trapped charge of -0.5p.u and with ferrite rings
163
Fig. 3.73(k) VFTO at source side of the DS1 closing operation with variable
Arc resistance with trapped charge of -0.5p.u with ferrite rings
Fig.3.73(l) FFT of VFTO waveform during DS1 closing operation with variable
Arc resistance with trapped charge of -0.5p.u and with ferrite
rings.
164
3.14 RESULTS
The switching operations in a Gas Insulated Systems leads to very
fast transient Over voltages , these over voltages propagates with in the
GIS chambers with very steep wave front and very high amplitude, and
also stress the equipments in GIS and reduce the reliability of the
switchgear equipment. Such over voltages may cause some faults in GIS
and interrelated components, such as transformers. For knowing the
peak values of VFTO the EMTP-RV software is used, and simulations
have been carried out by designing suitable equivalent circuits and its
models. The parameters like arc resistance and trapped charge on
floating electrode are very important parameters in VFTO estimation.
Different values of trapped charges and variable arc resistance model are
considered for simulations.
There are some deficiencies in the existing suppressing methods.
The exisisting technique for suppression of VFTOs in GIS systems is by
using opening and closing resistance across the disconnector
switch(DS), this method is called resistance switching. There are certain
difficulties are present with this method. usually the Bus ducts are filled
with SF6 Gas at certain pressure in the GIS systems, because of this,
the installation of resistors is difficult in GIS systems as in air blast
circuit breakers. The resistance switching can result material
decompositions and byproducts in the gas, which can increase the
particle contamination and partial discharge problems in GIS systems.
165
VFT have a very short rise time in the range of 4 to 100 ns, and followed
by high frequency oscillations in the range of a few hundreds of
kilohertz to about a few tens of megahertz. The resistance switching
mechanism is not suitable because of large response time during
nanoseconds. In this chapter, a new method is proposed by using high
frequency magnetic rings for suppressing VFTO near by the source has
been researched. In this method ferromagnetic rings are mounted on
the conductors linked to the disconnectors to effectively suppress both
the amplitudes and steepness of VFTOs. The results are compared with
results obtained with resistance switching method. The results are
validated by the experimental results.
In this chapter, first EMTP-RV models of 245kV GIS
system with opening and closing resistance have been developed as
shown in Fig.3.70(a) to 3.70(f) The suppression effect is observed .The
VFTO plots and corresponding frequency spectrums are given in the
Fig.3.71(a) to 3.71(l)
In the next case EMTP-RV models of 245kV GIS system with ferrite
ring equivalent have been developed. They are given in Fig. 3.72(a)
to3.72(d) The VFTO plots and corresponding frequency spectrums are
given in Fig.3.73(a) to 3.73(l) The results are summarized in the Tables
3.5 to 3.7
166
Table 3.5 VFTOs without suppression methods:
S.NO.
Mode of
operation of
Disconnector
switch
Arc
resistance
Type
Trapped
charge
in p.u
Peak
amplitude
of VFTO
in p.u
Rise
time
(ns)
Highest
frequency
componenet
MHz
1 Opening
operation Variable -0.1 1.61 17.16 11.11
2 Closing
operation Variable -0.1 1.72 19.27 11.79
3 Opening
operation Variable -0.5 2.31 27.12 17.41
4 Closing
operation Variable -0.5 2.69 37.12 43.12
5 Opening
operation Variable -1 2.72 39.20 41.22
6 Closing
operation Variable -1 2.89 29.73 39.17
167
Table 3.6 VFTOs suppression with opening and closing resistance:
S.NO.
Mode of
operation of
Disconnector
switch
Arc
resistance
Type
Trapped
charge
in p.u
Peak
amplitude
of VFTO
in p.u
Rise
time
(ns)
Highest
frequency
componenet
MHz
1 Opening
operation Variable -0.1 1.41 24.11 11.01
2 Closing
operation Variable -0.1 1.52 21.13 11.19
3 Opening
operation Variable -0.5 2.11 39.12 17.13
4 Closing
operation Variable -0.5 2.21 48.91 43.01
5 Opening
operation Variable -1 2.17 41.21 40.91
6 Closing
operation Variable -1 2.29 47.39 34.17
168
Table 3.7 VFTOs suppression with ferrite rings on bus bar:
S.NO
.
Mode of
operation of
Disconnector
switch
Arc
resistance
Type
Trapped
charge in
p.u
Peak
amplitude
of VFTO
in p.u
Rise
time
(ns)
Highest
frequency
componen
et
MHz
1 Opening
operation Variable -0.1 1.31 69.11 5.11
2 Closing
operation Variable -0.1 1.22 73.11 9.21
3 Opening
operation Variable -0.5 1.61 65.1 11.13
4 Closing
operation Variable -0.5 1.71 97.16 12.16
5 Opening
operation Variable -1 1.69 98.81 14.92
6 Closing
operation Variable -1 1.51 89.31 11.91
169
3.15 SUMMARY
A simulation models are developed using EMTP-RV for the computation
of the VFTO phenomena. The main advantage of such model is to enable
the transient analysis of GIS systems. A spark collapse time is correctly
simulated by the variable resistance. A GIS system comprising of
spacers, bus bars and disconnectors have been considered for modeling
into electrical network. Cone insulators used for supporting inner
conductor against outer enclosure are assumed to be disk type for
approximate calculation of spacer capacitance. The bus duct capacitance
is calculated using formulae for concentric cylinders. The entire bus
length is modeled as distributed pi-network.
The transients due to switching operations with fixed arc resistance
and for variable arc resistance were calculated. It is observed that the
transients obtained with fixed arc resistance having higher than
magnitudes obtained with variable arc resistance. It is also found that
the magnitudes of the transients at both load side and source side of the
disconnector switch increases with trapped charge on the floating
electrode. It is also found that, the rise times are increased with trapped
charge value. The VFTO magnitudes are estimated at locations air-to-SF6
gas bushing and SF6-to-XLPE cable termination during switching
operations of DS1 and DS2.
170
The peak voltages and rise times are obtained
and presented. The trapped charge magnitude depends up on speed of
operation of the circuit breaker. The trapped charge varied from the
value -0.1p.u. to -1p.u. on floating electrode. It is observed that, for any
length of GIS it was found that the transients due to variable arc
resistance give lower value of peak voltages than that obtained with fixed
arc resistance. It was found that the highest frequency component
increases with increase in the trapped charge on floating electrode.
The switching operations in a GIS systems leads to very fast
transient Over voltages (VFTO), these over voltages propagates with in
the GIS chambers with very steep wave front and very high amplitude,
There are some drawbacks in the existing suppressing methods. The
exisisting techniques for suppression of VFTOs in GIS systems is by
resistance swicthing across the disconnector switch(DS). There are
certain difficulties are present with this method. In this chapter, a new
method that using high frequency magnetic rings suppressing VFTO
near by the source has been researched. In this ferromagnetic rings can
be mounted on the conductors linked to the disconnector to effectively
suppress both the amplitudes and steepness of VFTOs. The results are
compared with results obtained with existing method. The results are
validated by the experimental results.
For knowing the peak values of VFTO the EMTP-RV software is
used, and simulations have been carried out by designing suitable
171
equivalent circuits and its models. The parameters like arc resistance
and trapped charge on floating electrode are very important parameters
in VFTOs estimation. Different values of trapped charges and variable
arc resistance model are considered for simulations.
On the basis of plots, the following conclusions are drawn
1. From Fig.3.45, It is observed that, during opening operation of DS,
VFTO maximum peak and principal frequency component is increased.
2. From Fig.3.67, It is observed that, during closing operation of
Disconnector switch the trapped charge effect is more considerable.
3. From Fig.3.50 to From Fig.3.67, the Peak amplitudes of VFTOs and
rate of rise of first peak have been increased proportionately with the
trapped charge on the floating electrode.
4. From Fig.3.50 to From Fig.3.67, a Wide band of frequencies are
observed, the transient voltages oscillates between two dominant
frequencies around 11MHz and 50MHz
5 From Fig.3.51 to From Fig.3.67 With every decrease in trapped charge
value, damping of VFTO increases
6. From Fig.3.54 to From Fig.3.67With increasing of trapped charge
magnitude, the frequency of transient oscillations has been increased.
7. Comparing results Table3.5 and Table3.6, with the resistance
switching method the VFTO suppressed to 13% to 29% maximum.
8. Comparing results Table3.5 and Table 3.7, with the high frequency
magnetic rings (ferrite rings) method of suppressing VFTOs it is
172
observed that the magnitudes are suppressed by 30% to 69%
maximum.
9. Comparing results from Table3.5 and Table3.7 the high frequency
components are very much reduced with ferrite rings. This can reduce
interference effects to GIS secondary circuits, and can increase the
reliability of the system.
As seen from the above results and discussions, with the proposed
method for suppression of fast transients is advantageous, when ferrite
material is carefully selected for particular voltage and current ratings.
However, this method would not increase the complexity of the structure
of the GIS and it can play a role in the protection of GIS equipment
inside the bus bar. The protection range against high frequency
transients is larger than all exisisting methods.