16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
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Parametric Analyses on Impulse Voltage Generator
and Power Transformer Winding for Virtual High
Voltage Laboratory Environment
Sachin Kumar, N K Kishore and B Hemalatha
Indian Institute of Technology Kharagpur
Kharagpur-721302, India.
Abstract—This paper presents the development work done
for virtualization of a typical high voltage laboratory, especially
named as virtual high voltage laboratory. The main objective of
the paper is to develop an understanding of impulse voltage
generator’s ciruit parameters’ effect on the standard output
waveforms. The most significant part includes analyses of various
internal constraints which cannot be easily estimated in a high
voltage laboratory. The motive is to - analyze the effects of
different parameters involved in the respective impulse voltage
generator and equivalent power transformer winding circuits
and show the results graphically. To accomplish this motto,
parametric analyses are carried out on the effects of different
parameters for impulse voltage generator and power transformer
winding, along with desired outputs.
Index Terms—Impulse voltage generator, marx generator,
parametric analyses, power transformer winding, virtual high
voltage laboratory.
Table I
T IME PARAMETERS WITH TOLERANCES FOR
SOME STANDARD IMPULSE
WAVEFORMS
Type of impulse
LI voltage
SI voltage
Impulse current
Impulse current
Front Time Tf (µs)
1.2±30%
250±30%
4.0±10%
8.0±10%
Tail Time Tt (µs)
50±20%
2500±20%
10±10%
20±10%
particular experiment from the list, GUI prompts input values. After submitting the input values mathematical analyses
algorithm of impulse voltage generator (IVG) circuit in this
particular case is run and displays output waveform with the
help of JAVA programming. So, present paper deals with the
parametric analyses of IVG and impulse testing on power
transformer winding equivalent which is useful in VHVL
environment to get the standard waveforms.
I. I NTRODUCTION
OMPUTER simulation plays an important role in engineering course teaching. Nowadays, a variety of softwares like MATLAB, AutoCAD, and PSCAD are available
to simulate electrical circuits; but fail to provide the actual
feel of a physical laboratory. Also most of these softwares
come with commercial license at a high price, thus restricting
their availability but virtual high voltage laboratory (VHVL)
is a web based [1,2,3,4,5] application which not only serves
as a good tool for teaching but also enables a student to
understand the influence of the circuit parameters on the output
of the various experiments. VHVL can also act as a guide
for the testing engineer to arrive at the values of the desired
parameters to get a standard output waveform as listed in
Table I [6]. VHVL prompts user to achieve the standard
Lightning Impulse (LI) or Switching Impulse (SI) parameters
by providing facility to vary the circuit parameters through
graphical user interface (GUI).
C
Figure 1.
Proposed Scheme of VHVL.
II. I MPULSE VOLTAGE G ENERATOR
A. Marx generator
Marx generators [7] are at the core of impulse voltage tests
of HV equipment. The classical Marx generator nominally
produces a pulse in the form of a double exponential function.
Fig. 1 presents a proposed scheme of VHVL which constitutes home page links for various experiments. By selecting
V (t) = V [exp(−αt) − exp(−βt)]
Sachin Kumar is a recent graduate of M.Tech. in Electrial Engineering from
Indian Instutute of Technology Kharagpur, Kharagpur 721302 India (email:
sackumaarc@gmail.com).
N K Kishore is Professor of Electrical Engineering with Indian Institute of
Technology Kharagpur, Kharagpur 721302 India (email: kishor@iitkgp.ac.in).
B Hemalatha is Principal System Manager with Indian Institute of Technology Kharagpur (email: hema@adm.iitkgp.ernet.in).
where V(t) is the instantaneous value of output impulse
voltage, and V is the voltage that is stored across the generator
capacitor (Cg ) (for a multistage generator V is the sum of
the charging voltages of all stages), α and β are inverse time
constants in µs. Fig. 2 [8] shows an equivalent of n ≤ 20
stage Marx generator which generates the impulse voltage for
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
(1)
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
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testing of transformers, where the front and tail time of the
impulse voltage are important; therefore one must observe the
effect of the wave-shaping control elements on the voltage
waveform. The dependence of the shape of the waveform
on the resistors Rf (front resistor) and Rt (tail resistor) can
be checked by changing the values of these resistors. These
resistors control the wave-front and wave-tail of the output
impulse voltage waveform. The basic principle of operation of
the Marx generator is that the generator capacitors are charged
in parallel with a HV dc source and discharged in series
through load (here capacitive, Cl ) with the means of triggering
spark gaps (SG). Hence an impulse voltage is obtained across
the load which is standardised as shown in Fig. 3.
corresponding to 50% of the peak value, and it is t4 . O’t4 is
defined as fall or tail time (Tt ).
Figure 3.
Standard waveform of an impulse voltage generator.
B. Single stage impulse voltage generator circuit
Fig. 5 shows single – stage equivalent of IVG circuit.
Circuit contains front resistor (Rf ) and tail resistor (Rt )
with small internal inductancesLf and Lt offered by Rf and
Rt respectively. These inductances are incorporated in the
equivalent circuit to give the VHVL a more realistic feel.
Solution for the circuit is obtained using differential equations
approach and then the corresponding algorithm is developed.
Differential equations and appropriate boundary conditions
V(t=0) = 0 and ( dV
dt )(t=0) = 0 are formulated as follows:
Loop i1 :
Z
Z
1
1
di2
+ Rf ∗ i2 +
i1 dt + Lf
i2 dt = V
(2)
Cg
dt
Cl
Loop i2 :
Lf
1
di2
+ Rf ∗ i2 +
dt
Cl
Z
i2 dt = Lf
d(i1 − i2 )
+ Rt ∗ (i1 − i2 )
dt
(3)
output voltage:
V (t) =
Figure 2.
Typical Scheme of a Marx Generator.
Referring to the waveshape in Fig. 3, the peak value A is
fixed and referred to as 100% value. The point corresponding
to 10% and 90% of the peak values are located on the front
portion (points C and D). O’ is taken as the virtual origin.
1.25 times the interval between times t1 and t2 corresponding
to points C and D is defined as the front time (Tf ), i.e.
1.25*(O’t1 -O’t2 ).1 The point E is located on the wave tail
1 Due
to oscillation in the initial portion, front is defined this way.
1
Cl
Z
i2 dt
(4)
After solving Eqn. 2 and Eqn. 3 for current i2 and putting
i2 ’s value in Eqn. 4 output voltage is obtained. The algorithm
for single-stage IVG for generation of impulse voltage is
shown in Fig. 4, is employed in virtual laboratory environment
[14].
1) Single stage impulse voltage generator - Algorithm :
Based on the mathematical analyses of circuit shown in Fig.
4, algorithm for the implementation of the VHVL is developed.
The flowchart shown in Fig. 4 explains the algorithm of
parametric analyses for impulse voltage generation. The first
task is to track peak voltage of waveform which is accomplished by comparing present and previous sample values
which are continuously stored. At an instant when previous
value is greater than the present value, the sample data of
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
525
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Figure 4.
Algorithm for generation and parametric analyses of single-stage impulse voltage generator.
previous value is stored as the value of peak voltage. After
tracking peak voltage, time for 10%, 90% and 50% of peak
voltage are determined. This provides waveform parameters
to be compared with standard listed in Table I. Finally, a plot
between voltage vs. time with front and tail time values is
displayed with the help of JAVA programming.
transformer winding models are taken and analyzed through
simulation. The results enable students to test a transformer in
vitual laboratory environment, and a test engineer to arrive at
required configuration of the generator for an impulse test.
To accomplish the above discussion present paper deals with
the parametric analyses of an equivalent model of a power
transformer winding with an application of impulse voltage.
A. Power transformer winding equivalent
Figure 5.
Equivalent circuit of single stage impulse voltage generator.
III. I MPULSE VOLTAGE G ENERATOR A PPLICATION
A power transformer [9], a vital and expensive piece
of equipment in a power system, requires critical attention
from the standpoint of its insulation design and performance
under both steady state and transient stress. Therefore, this
assessment is carried out through impulse tests. This study
is carried out using transformer model to be incorporated
in VHVL. Since, the virtualization involves simulation so,
Fig. 6 shows an equivalent of one phase winding of a
three-phase transformer [11]. In this model 2 , each stage (one
turn of winding) is modeled by series resistance (Rs ), selfinductance (Ls ), shunt resistance (Rsh ), series capacitance
(Cs ) and ground capacitance (Cg ). The typical voltage and the
neutral current waveform for A phase during impulse voltage
testing is shown in Fig. 7 and Fig. 8 respectively.
Cg represents the equivalent capacitance of primary and
secondary windings; Csh is the capacitance between primary
and secondary windings; Ls is equivalent leakage inductance
of the primary and secondary windings; Rs is equivalent
resistance of the primary and secondary windings; Rsh is
the core exciting impedance-composed of a resistance and
inductance.
2 This paper presents transformer winding model of the frequency range
of 10 kHz to few MHz which is helpful in internal resonance studies. And
the experiments in this frequency range reveal remarkable overvoltages. So,
necessary to model a transformer accordingly, as explained in [12].
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
526
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tail resistor value only leads to increment in tail time but there
is no change in peak voltage and front time as summarised in
Table III.
Figure 6.
Equivalent model for a Power Transformer winding.
Figure 7. Typical voltage waveform at A phase terminal during impulse
voltage testing for power transformer.
Fig. 11 shows the impulse voltage waveforms of Marx
circuit for different values of load capacitor. Slight change
in load capacitor value leads to increment in peak voltage and
tail time but there is no change in front time as summarised
in Table IV.
Figure 9.
Variation of impulse voltage with front resistance Rf .
Figure 10.
Variation of impulse voltage with tail resistance Rt .
Figure 11.
Variation of impulse voltage with load capacitance Cl .
Figure 8. Typical neutral current waveform at A phase terminal during
impulse voltage testing for power transformer.
In the present paper, the data [12,13] for one phase of
a 220 kV/35 kV, 50 MVA three phase transformer are as
follows:
• series resistance per turn = 1 Ω;
• self inductance per turn = 1.65 mH;
• shunt resistance per turn = 1 kΩ;
• series capacitance per turn = 2 nF;
• ground capacitance per turn = 2 pF.
IV. R ESULTS
A. Marx Generator
Fig. 9 shows the impulse voltage waveforms of Marx
circuit for different front resistor values. Small increment in
front resistor value leads to negligible increment in tail time
but a significant change in peak voltage and front time as
summarised in Table II.
Fig. 10 shows the impulse voltage waveforms of Marx
circuit for different values of tail resistor. Significant change in
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
527
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Table II
VARIATION OF OUTPUT VOLTAGE WAVEFORM OF M ARX GENERATOR WITH
FRONT RESISTANCE R f
a
V
(kV)
50
Cg
(µF )
0.6
Rf
(Ω)
10
Rt
(Ω)
120
Cl
(nF)
2
Vp
(kV)
143.60
Tf
(µs)
1.39
Tt
(µs)
45.40
b
50
0.6
11
120
2
143.30
1.43
45.45
c
d
e
50
50
50
0.6
0.6
0.6
12
13
14
120
120
120
2
2
2
143
142.85
142.65
1.47
1.51
1.55
45.46
45.52
45.54
curve
Figure 12. Variation of impulse voltage for single stage impulse voltage
generator with front inductance Lf .
Table III
VARIATION OF OUTPUT VOLTAGE WAVEFORM OF M ARX
TAIL RESISTANCE R t
CIRCUIT WITH
a
V
(kV)
50
Cg
(µF )
0.6
Rf
(Ω)
10
Rt
(Ω)
120
Cl
(nF)
2
Vp
(kV)
143.60
Tf
(µs)
1.39
Tt
(µs)
45.40
b
c
d
e
50
50
50
50
0.6
0.6
0.6
0.6
10
10
10
10
122
124
126
128
2
2
2
2
143.60
143.60
143.60
143.60
1.39
1.39
1.39
1.39
46.10
46.76
47.37
48
curve
Table IV
VARIATION OF OUTPUT VOLTAGE WAVEFORM
OF M ARX GENERATOR
CIRCUIT WITH LOAD CAPACITANCE C l
a
V
(kV)
50
Cg
(µF )
0.6
Rf
(Ω)
10
Rt
(Ω)
120
Cl
(nF)
2
Vp
(kV)
143.60
Tf
(µs)
1.39
Tt
(µs)
45.40
b
50
0.6
10
120
2.2
143.30
1.43
45.50
c
d
e
50
50
50
0.6
0.6
0.6
10
10
10
120
120
120
2.4
2.6
2.8
143.10
142.90
142.70
1.45
1.49
1.53
45.57
45.72
45.80
curve
Figure 13. Variation of impulse voltage for single stage impulse voltage
generator with tail inductance Lt .
Table V
VARIATION OF IMPULSE VOLTAGE FOR SINGLE STAGE IMPULSE VOLTAGE
GENERATOR WITH FRONT INDUCTANCE L f ( CHARGING VOLTAGE = 100
K V)
a
b
Cg
(µF )
1
1
Rf
(Ω)
112
112
Lf
(nH)
1
10
Rt
(Ω)
70
70
Lt
(nH)
1
1
Cl
(nF)
2
2
Vp
(kV)
97.03
97.03
Tf
(µs)
1.22
1.27
Tt
(µs)
45.30
46.10
c
d
f
e
1
1
1
1
112
112
112
112
102
103
105
106
70
70
70
70
1
1
1
1
2
2
2
2
97.03
97.09
-
1.28
1.34
-
50.14
53.70
-
curve
B. Single stage Impulse Voltage Generator
Fig. 12 shows the impulse voltage waveforms for the different values of front inductance. It is an important consideration
to avoid output waveform distortion. Slight change in front
internal inductance value does not affect peak voltage, front
time and tail time, however, for a large change in inductance
value output waveform shows oscillations as shown in Fig. 10
and summarised in Table V.
It is also an important consideration for getting an error
free standard output waveforms. Fig. 13 shows the impulse
voltage waveforms for the different values of tail inductance.
As inductance increases slightly there is negligible change in
peak voltage, front time and tail time but due to a large change
in inductance value there is a significant change in Vp , Tf and
Tt as summarised in Table VI.
Table VI
VARIATION OF IMPULSE VOLTAGE FOR SINGLE STAGE IMPULSE VOLTAGE
GENERATOR WITH FRONT INDUCTANCE L f ( CHARGING VOLTAGE = 100
K V)
curve
a
b
Cg
(µF )
1
1
Rf
(Ω)
112
112
Lf
(nH)
1
1
Rt
(Ω)
70
70
Lt
(nH)
1
10
Cl
(nF)
2
2
Vp
(kV)
97.03
97.03
Tf
(µs)
1.28
1.28
Tt
(µs)
50.14
50.11
c
1
112
1
70
103
2
97.05
1.33
50.21
d
1
112
1
70
106
2
98.66
1.65
56.78
e
1
112
1
70
107
2
98.79
2.17
121
C. Power Transformer
In order to get power transformer testing analyses results,
simulation studies are carried out by using a MATLAB simulation model. The number of stages is chosen by the user,
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
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dependent on the number of coils of transformer winding,
to simulate the transformer windings (here, it is 3), and the
ladder network for the transformer is constructed in MATLAB
by choosing proper values of the ladder parameters that are
obtained from test results for the transformer. The transformer
is connected to the output of the IVG as the test object as
shown in Fig. 6.
Series inductance and shunt resistor having significant value
affect the output voltage across transformer winding. So,
present paper analyses the variation of these two only. Fig. 12
and Fig. 13 show the voltage waveforms for different values
of shunt resistor and series inductance respectively. As shunt
resistor value is increased the voltage increment is more and as
series inductance value is increased the winding voltage has
very little increment as summarised in Table VII and Table
VIII respectively. The analyses on number of coils are also
done which shows an increment in voltage across transformer
winding as shown and summarised in Fig. 14 and Table IX
respectively.
Figure 16.
Variation in output voltage with number of turns.
Table VII
VARIATION OF OUTPUT VOLTAGE WAVEFORM
WITH R sh
Curve
a
b
c
Rs
(Ω)
Ls
(mH)
Csh
(nF)
Rsh
(kΩ)
Cg
(pF)
1
1
1
1.65
1.65
1.65
2
2
2
1
1.5
2
2
2
2
Table VIII
VARIATION OF OUTPUT VOLTAGE WAVEFORM
WITH L s
Rs
Curve
(Ω)
a
b
c
Figure 14.
Variation in output voltage with shunt resistance Rsh .
OF POWER TRANSFORMER
1
1
1
Number
of
turns
1
1
1
peak
voltage
(kV)
134.20
142.47
146.63
OF POWER TRANSFORMER
Ls
(mH)
Csh
(nF)
Rsh
(kΩ)
Cg
(pF)
Number
of
turns
1.65
1.75
1.85
2
2
2
1
1
1
2
2
2
1
1
1
peak
voltage
(kV)
134.20
135.38
135.90
Table IX
VARIATION OF OUTPUT VOLTAGE WAVEFORM
OF POWER TRANSFORMER
WITH NUMBER OF TURNS
Curve
a
b
c
Figure 15.
Variation in output voltage with series inductance Ls .
Rs
(Ω)
Ls
(mH)
Csh
(nF)
Rsh
(kΩ)
Cg
(pF)
Number
of
turns
1
1
1
1.65
1.65
1.65
2
2
2
1
1
1
2
2
2
1
2
3
peak
voltage
(kV)
134.20
157.90
166.70
V. C ONCLUSIONS
The mutual coordination between present work and VHVL
is to provide a remote access of virtual laboratory with
accomplished parametric analyses, which is most important
for the learning perspective.
This paper is outlined and illustrated a MATLAB model to
generate standard output impulse voltage waveforms of 1.2/50
µs which leads to the simulation analyses on impulse voltage
testing of power transformer winding equivalent.
Students may use power transformer winding equivalent
model to learn about impulse voltage testing, and can simulate
Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.
16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010
529
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different kinds of winding parameters during impulse voltage
testing.
The method considerably reduces the time and cost needed
to teach impulse testing of power transformers. Therefore, it
is very useful for educational purposes where the budget is
limited.
ACKNOWLEDGMENT
Sachin Kumar whole heartedly thanks Professor N.K.
Kishore for providing an opportunity to compose a conference
paper on M.Tech project work, which is one of the most
emerging technology in the field of virtualization. Author takes
this opportunity to express his gratitude to Ministry of Human
Resource development (MHRD), Government of India (GoI)
for sponsoring the project. Author would like to thank Mr.
N.C. Santhosh (Electrical Engineer, Tata Consulting Engineers
Limited, Jamshedpur), Mr. Debasish Mukherjee (Jr. Programmer, Electrical Engineering Department, IIT Kharagpur), Miss
S. Poornima Rao (Web Developer, Electrical Engineering
Department, IIT Kharagpur) and all his colleagues for their
support. Finally, the Department of Electrical Engineering, IIT
Kharagpur for their encouragement.
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Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.