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Novel Simulation Technique of Electromagnetic Wave Propagation in the Ultra High Frequency Range within Power Transformers .pdf



Original filename: Novel Simulation Technique of Electromagnetic Wave Propagation in the Ultra High Frequency Range within Power Transformers.pdf
Title: Novel Simulation Technique of Electromagnetic Wave Propagation in the Ultra High Frequency Range within Power Transformers
Author: Takahiro Umemoto and Stefan Tenbohlen

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sensors
Article

Novel Simulation Technique of Electromagnetic Wave
Propagation in the Ultra High Frequency Range
within Power Transformers
Takahiro Umemoto 1, *
1
2

*

and Stefan Tenbohlen 2

Advanced Technology R&D Center, Mitsubishi Electric Corporation, Amagasaki 6618661, Japan
Institute of Power Transmission and High Voltage Technology, University of Stuttgart, 70569 Stuttgart,
Germany; stefan.tenbohlen@ieh.uni-stuttgart.de
Correspondence: Umemoto.Takahiro@df.MitsubishiElectric.co.jp

Received: 6 November 2018; Accepted: 27 November 2018; Published: 3 December 2018




Abstract: Diagnoses of power transformers by partial discharge (PD) measurement are effective
to prevent dielectric failures of the apparatus. Ultra-high frequency (UHF) method has recently
received attention due to its various advantages, such as the robustness against external noise and the
capability of PD localization. However, electromagnetic (EM) waves radiated from PD tend to suffer
attenuation before arriving at UHF sensors, because active part of the transformer disturbs the EM
wave propagation. In some cases, that results in poor detection sensitivity. To understand propagation
and attenuation characteristics of EM waves and to evaluate the detection sensitivity quantitatively,
a computational approach to simulate the EM wave propagation is important. Although many
previous researches have dealt with EM wave simulation for transformers, validations of those
simulations by comparing with the experimental ones have seldom been reported. In this paper,
cumulative energies, signal amplitudes and propagation times of EM waves were measured using a
630 kVA transformer. EM wave propagation was computed using the time-domain finite integration
technique and the results were compared with the experimentally obtained ones. These simulation
results showed good agreement with the experimental ones. The results can serve as guidelines to
improve the efficiency of UHF PD detection and offer the possibility to achieve optimal placement of
UHF sensors in power transformers.
Keywords: power transformers; partial discharges; electromagnetic wave simulation; UHF PD
measurement; UHF antennas

1. Introduction
Power transformers are key components in power systems and their dielectric failures severely
influence the system operation [1–3]. Continuous activity of partial discharge (PD), which might occur
within the transformers due to undesirable local electric field enhancement, is one of the main causes
of transformer failures, hence diagnoses based on PD measurement is a promising method to assess
the condition of the apparatus [4].
Although various PD measurement techniques have been proposed and developed over a long
period [5–8], the ultra-high frequency (UHF) method, that is, detecting electromagnetic (EM) waves
in the UHF range (300 MHz–3 GHz) radiated due to a short rise time of the PD current pulse, has
recently received much attention [9,10]. Attractive advantages are, for example, the robustness against
external noise [11,12] and the capability of PD localization by using time-difference of arrival (TDOA)
between multiple UHF sensors [13,14]. Due to these advantages, the UHF method is suitable for
factory acceptance tests (FAT) and site acceptance tests (SAT), as well as on-line diagnoses [15].

Sensors 2018, 18, 4236; doi:10.3390/s18124236

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However, the EM waves radiated from PD tend to suffer severe attenuation within the transformer
before arriving at UHF sensors. In some cases, this results in low detection sensitivity of the PD signals,
especially when the active part of the transformer (e.g., windings, core and leads) disturb the EM
wave propagation [16,17]. Furthermore, localization based on TDOAs also leads to large errors due
to the roundabout propagation path of the EM waves. In order to understand the propagation and
attenuation characteristics of EM waves within transformers and to evaluate PD detection sensitivity
as well as the propagation time quantitatively, a computational approach to simulate the EM wave
propagation is essential.
Simulation of the EM wave propagation in gas insulated switchgears (GIS) has been studied for
more than 15 years and their results were compared with the theoretical or experimental ones for
validation [18–20]. On the other hand, simulation for power transformers has also been investigated
by many researchers [13,15,21–23]. In Reference [21], influences of transformer windings and
insulation papers on amplitudes of the EM waves propagating through them were discussed based
on only numerical computation. In Reference [22], the propagation times of PD induced EM signals
within power transformer were computed in order to improve the accuracy of PD localization. In
Reference [23], the signal amplitudes of EM waves were computed as a function of UHF sensor
positions based on the simulation using an actual transformer model. However, the validity of the
EM wave simulation was not discussed, hence the appropriate computational conditions were still
unclarified. Considering the above fact, validations of simulations of EM wave propagation and those
simulated results by comparing with the experimental ones using actual transformer structures have
been seldom reported, therefore the validations are insufficient.
The objective of this paper is to propose the simulation of EM wave propagation, including
the detailed simulation conditions, which are validated by the experimental results using actual
transformers. First, validations of antenna modeling methods, an exciting signal as well as a model
of a transformer tank were evaluated by measurement with an empty transformer tank (i.e., without
active parts of a transformer). Second, cumulative energies of the EM waves, their signal amplitudes
and propagation times to each UHF sensors were investigated by simulation and measurement
using a distribution transformer for validating the transformer modeling. For both investigations,
the simulated results showed good agreement with the measured ones. Thus, the authors successfully
validated this novel simulation technique.
The rest of this paper is organized as follows: Section 2 presents the experimental setup and
measurement system of UHF signals, including a transformer structure. Detailed EM simulation
methods and 3-D modeling technique are described in Section 3. In Section 4, both simulated and
measured results are compared and the validity of the simulation is discussed, while conclusions and
future work suggestions are presented in Section 5.
2. Experimental Method
2.1. UHF Sensors and EM Wave Source
Figure 1 illustrates a schematic diagram of a steel tank of 1350 kVA transformer and positions of
four UHF drain valve sensors [11,12] and a monopole antenna in the first experiment. Inside dimension
of the transformer tank was 1720 mm in length, 760 mm in width and 1550 mm in height, respectively.
There was a hole with 100 mm in diameter on the top of the tank, through which a monopole antenna
was inserted and used as an EM wave source. Note that in this experiment, the transformer tank was
not filled with the insulating oil.
On the wall of the tank, there are two DN50 and two DN80 gate valves. Four UHF drain valve
sensors, named A, B, C and D, were mounted with each gate valve, as shown in Figure 2. Figure 3
shows an image of the UHF sensor [4]. A probe (top of the UHF sensor) has a truncated cone shape.
The detailed dimension of the probe will be described later in Section 3.2. The antenna factor (AF),
which indicates sensitivity of the sensor, was described in Reference [12]. The probes of the sensors

FOR PEER REVIEW
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from the monopole antenna and detected by these UHF sensors were digitized and recorded by an
(top
portion(LeCroy,
of the sensors)
100
mm NY,
intoUSA,
the tank,
results20inGS/s)
a high
sensor
oscilloscope
WaveProwere
7300,inserted
Chestnut
Ridge,
3 GHzwhich
bandwidth,
without
sensitivity
and
is
suitable
for
the
comparisons
with
the
simulated
results.
EM
wave
signals,
radiated
any analog filter and amplifier.
fromAthe
monopole
antenna
these
UHFinsensors
were
by an
monopole
antenna
of 20and
mmdetected
in lengthby
and
1.3 mm
diameter
wasdigitized
used as anand
EMrecorded
wave source,
oscilloscope
(LeCroy,
7300,
Chestnut Ridge,
NY, USA,
3 GHz
20 GS/s)
without
instead
of a typical
PDWavePro
source (e.g.,
a needle-plane
electrode
system)
sincebandwidth,
it radiates stable
EM waves
any analogamplitudes
filter and amplifier.
regarding
and frequency spectra. The antenna was excited by a voltage pulse generator
A Engineering,
monopole antenna
of 20 mmLDC-7/UHF,
in length andWatertown,
1.3 mm in diameter
was
used as
an Ω
EM
wave cable
source,
(Doble
UHF calibrator
MA, USA)
through
a 50
coaxial
instead
of a typical
PDmm
source
(e.g.,The
a needle-plane
electrode
system)
since itwas
radiates
of
approximately
2000
length.
output voltage
of the pulse
generator
set to stable
60 V. EM waves
In theamplitudes
first experiment,
time-domain
signals
cumulative
energies
the EM
waveforms
regarding
and frequency
spectra.
The and
antenna
was excited
by a of
voltage
pulse
generator
detected
by the four UHF
were
evaluated toWatertown,
validate theMA,
modeling
of antenna,
signal
(Doble
Engineering,
UHF sensors
calibrator
LDC-7/UHF,
USA) through
a 50exciting
Ω coaxial
cable
and
the transformer
tank
in length.
the EM The
wave
simulation.
of approximately
2000
mm
output
voltage of the pulse generator was set to 60 V.

1720
Sensor B

Sensor C
DN80 gate valve

100

160

140

1270

760

Monopole antenna
(EM wave source)
115

115

DN50 gate valve
Sensor D

Sensor A
(a) Top view

1720

130

Sensor A
Coaxial cable

200
1000

115
140

Sensor C
1550

Sensor B
160
200

115
90

Sensor D

Monopole antenna
(EM wave source)

(b) Side view
Figure 1.
1. Schematic
Schematicdiagram
diagramofofaatransformer
transformertank
tankand
andantenna
antennapositions
positions(for
(for
the
first
experiment).
Figure
the
first
experiment).

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In the first experiment, time-domain signals and cumulative energies of the EM waveforms
detected by the four UHF sensors were evaluated to validate the modeling of antenna, exciting signal
and
the
transformer
tank
in the EM wave simulation.
Sensors
2018,
18, xx FOR
FOR PEER
PEER
REVIEW
of 16
16
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2018,
18,
REVIEW
44 of

DN80 gate
gate valve
valve
DN80
UHF sensor
sensor
UHF

Figure 2.
2. UHF
UHF drain
drain valve
valve sensor
sensor mounted
mounted with
with aa DN80
DN80 gate
gate valve.
valve.
Figure

Figure 3.
3. An
An image
image of
of the
the UHF
UHF drain
drain valve
valve sensor
sensor [4].
[4].
Figure

2.2.
Active
Part
of
the
Transformer
2.2. Active
Active Part
Part of
of the
the Transformer
Transformer
2.2.
The
active
partof
ofaaathree-phase
three-phase630
630kVA
kVAdistribution
distributiontransformer,
transformer,which
which
mainly
composed
The active
active part
part
of
three-phase
630
kVA
distribution
transformer,
which
isis
mainly
composed
of
The
is
mainly
composed
of
of
high
and
low
voltage
windings,
an
iron
core
and
leads,
was
utilized
for
the
second
experiment.
high and
and low
low voltage
voltage windings,
windings, an
an iron
iron core
core and
and leads,
leads, was
was utilized
utilized for
for the
the second
second experiment.
experiment. Note
Note
high
Note
thattransformer
the transformer
inexperiment
the experiment
is larger
normally
used
active
part,
that the
the
transformer
tank tank
usedused
in the
the
experiment
is larger
larger
thanthan
normally
used
for for
thisthis
active
part,
in
that
tank
used
in
is
than
normally
used
for
this
active
part,
in
in
order
to
allow
the
UHF
sensors
to
be
inserted
deeply
into
the
tank,
resulting
in
improved
sensitivities.
order to
to allow
allow the
the UHF
UHF sensors
sensors to
to be
be inserted
inserted deeply
deeply into
into the
the tank,
tank, resulting
resulting in
in improved
improved sensitivities.
sensitivities.
order
There
There are
are four
four high
high voltage
voltage (HV)
(HV) and
and two
two low
low voltage
voltage (LV)
(LV) cylindrical
cylindrical windings
windings in
in one
one phase
phase
There
are
four
high
voltage
(HV)
and
two
low
voltage
(LV)
cylindrical
windings
in
one
phase
and
each
HV
and
LV
winding
consists
of
156
and
57
layers,
respectively.
However,
the
HV
winding
and
each
HV
and
LV
winding
consists
of
156
and
57
layers,
respectively.
However,
the
HV
winding
and each HV and LV winding consists of 156 and 57 layers, respectively. However, the HV winding
of
one
phase
was removed.
removed.The
Theinnermost
innermostdiameter
diameterof
the
LV
windings,
the
outermost
diameter
of one
one phase
phase was
was
removed.
The
innermost
diameter
ofof
the
LV
windings,
the
outermost
diameter
of
of
the
LV
windings,
the
outermost
diameter
of
of
HV
windings
and
their
height
areapproximately
approximately207
207mm,
mm,350
350mm
mmand
and780
780mm,
mm,respectively.
respectively.
thethe
HV
windings
and
their
height
are
approximately
207
mm,
350
mm
and
780
mm,
respectively.
the
HV
windings
and
their
height
are
Three
identical
monopole antennas
antennasof
of20
20mm
mmin
length,described
describedin
Section
2.1,
were
also
used
Three identical
identical monopole
monopole
antennas
of
20
mm
ininlength,
length,
described
inin
Section
2.1,
were
also
used
as
Three
Section
2.1,
were
also
used
as
as
EM
wave
sources
in
this
second
experiment.
These
antennas
were
set
around
the
windings
EM wave
wave sources
sources in
in this
this second
second experiment.
experiment. These
These antennas
antennas were
were set
set around
around the
the windings
windings at
at
EM
at
different
heights
and
in
different
positions
before
the
active
parts
were
installed
into
the
transformer
different
heights
and
in
different
positions
before
the
active
parts
were
installed
into
the
transformer
different heights and in different positions before the active parts were installed into the transformer
tank.
The
detailed
structure
of
this
transformer
and
the
positions
of
three
monopole
antennas
will
be
tank. The
The detailed
detailed structure
structure of
of this
this transformer
transformer and
and the
the positions
positions of
of three
three monopole
monopole antennas
antennas will
will be
be
tank.
illustrated
illustrated in
in Section
Section 3.1,
3.1, as
as aaa 3-D
3-D computational
computational model.
model.
illustrated
in
Section
3.1,
as
3-D
computational
model.
In
ofof
the
EM
waves
from
each
monopole
antenna
to the
In this
thissecond
secondexperiment,
experiment,propagation
propagationtimes
times
of
the
EM
waves
from
each
monopole
antenna
to
In
this
second
experiment,
propagation
times
the
EM
waves
from
each
monopole
antenna
to
sensors
were
also
measured
in
addition
to
signal
amplitudes
and
their
cumulative
energies.
Figure
4
the sensors
sensors were
were also
also measured
measured in
in addition
addition to
to signal
signal amplitudes
amplitudes and
and their
their cumulative
cumulative energies.
energies.
the
illustrates
the measurement
setup for propagation
times of thetimes
EM waves,
which
the output
of the
the
Figure 44 illustrates
illustrates
the measurement
measurement
setup for
for propagation
propagation
times
of the
thein
EM
waves,
in which
which
the
Figure
the
setup
of
EM
waves,
in
pulse
generator
and
the
EM
wave
signals
were
simultaneously
measured.
The
propagation
times
of
output of
of the
the pulse
pulse generator
generator and
and the
the EM
EM wave
wave signals
signals were
were simultaneously
simultaneously measured.
measured. The
The
output
the
EM
waves
were
calculated
as
the
time
difference
of
arrival
between
both
signals,
considering
the
propagation times
times of
of the
the EM
EM waves
waves were
were calculated
calculated as
as the
the time
time difference
difference of
of arrival
arrival between
between both
both
propagation
signal
propagation
time
within
the
coaxial
cables.
signals,
considering
the
signal
propagation
time
within
the
coaxial
cables.
signals, considering the signal propagation time within the coaxial cables.

Sensors 2018, 18, 4236
Sensors 2018, 18, x FOR PEER REVIEW

Active parts of the
transformer

5 of 16
5 of 16

Coaxial cable
Pulse generator
(Doble, LDC-7/UHF)
Oscilloscope
(LeCroy, WavePro 7300)

Coaxial cable
Monopole antenna
UHF drain valve sensor
(EM wave source) The EM wave
propagation path
(it propagates around a center winding in this figure)
Figure
Figure 4.
4. Measurement
Measurement setup
setup for
for propagation
propagationtimes
timesof
ofthe
theEM
EMwaves.
waves.

2.3. Denoising of the Cumulative Energies
2.3. Denoising of the Cumulative Energies
Cumulative energies of the EM wave signals are commonly used not only to evaluate the
Cumulative energies of the EM wave signals are commonly used not only to evaluate the PD
PD signal strength quantitatively but also to determine the arrival times of the PD signals for
signal strength quantitatively but also to determine the arrival times of the PD signals for the
the localization [21,24]. Cumulative energy E(t) of a discrete voltage waveform can normally be
localization [21,24]. Cumulative energy E(t) of a discrete voltage waveform can normally be
calculated as,
t
calculated as,
∆t
V 2 (i · ∆t)
E(t) = ∑ t
· ∆t
(1)
Z
2
i =0t
V (i  t )
(1)
E (at
t ) t== i∆t. Z and ∆t 
t an impedance of the measurement
where V(i∆t) is a voltage of the EM signal
are
Z
i =0
circuit (usually 50 Ω) and a sampling period, respectively
[21,25]. However, in this experiment, some
measured
signals
showedoflow
(signalattot =noise
dueare
toan
theimpedance
severe attenuation
of the EM
where V(iΔt)
is a voltage
theSNR
EM signal
iΔt. Zratio)
and Δt
of the measurement
waves
the deflation
andareflection,
resulting
in calculation
errors
of the cumulative
energies. some
circuitby
(usually
50 Ω) and
sampling period,
respectively
[21,25].
However,
in this experiment,
In thissignals
research,
in order
evaluate
thetocumulative
for the of
low
measured
showed
lowtoSNR
(signal
noise ratio)energies
due to accurately
the severe even
attenuation
theSNR
EM
waveforms,
background
noise
components
on the
deleted as,energies.
waves by the
deflation and
reflection,
resulting
incumulative
calculation energies
errors of were
the cumulative
In this research, in order to evaluate the cumulative energies accurately even for the low SNR
t
∆t on 2the cumulative energies were deleted as,
waveforms, background noise components
V (i · ∆t)
E(t) = ∑
· ∆t − A · t
(2)
Z
i =0 t



V (i  t )
(2)
where A is a compensation factor of E
the
noise,
(t )background
=
 which
t − A  tcan be obtained as a slope of the
Z at the sensor. Figure 5 shows an example of the
i = 0arrives
cumulative energy before the EM wave signal
measured
waveform, its cumulative
calculated
by which
(1) andcan
the be
denoised
cumulative
where A isEM
a compensation
factor of theenergy
background
noise,
obtained
as a slopeenergy
of the
calculated
by
(2),
respectively.
Without
this
denoising
procedure,
the
cumulative
energy
continues
cumulative energy before the EM wave signal arrives at the sensor. Figure 5 shows an example of the
to
increase EM
evenwaveform,
before theits
EM
wave signal
arrives
and after
sufficiently
attenuates,
which leads
to
measured
cumulative
energy
calculated
byit(1)
and the denoised
cumulative
energy
large
errors
in
the
total
energy
(i.e.,
the
convergence
energy).
In
a
case
of
Figure
4,
the
cumulative
calculated by (2), respectively. Without this denoising procedure, the cumulative energy continues
energies
at 100
nsbefore
with and
thesignal
denoising
areand
10.6after
fJ and
16.3 fJ, respectively.
Thewhich
relative
error
to increase
even
thewithout
EM wave
arrives
it sufficiently
attenuates,
leads
to
islarge
approximately
53.8%.
errors in the total energy (i.e., the convergence energy). In a case of Figure 4, the cumulative
t



2

energies at 100 ns with and without the denoising are 10.6 fJ and 16.3 fJ, respectively. The relative
error is approximately 53.8%.

Sensors 2018, 18, 4236
Sensors 2018, 18, x FOR PEER REVIEW

6 of 16
6 of 16

0.02

18

Signal amplitude (V)

14

0.01

12
10

0

8
EM wave signal
Cumulative energy before denoising
Denoised cumulative energy

-0.01
-0.02
-40

-20

0

20

40

60

80

100

120

140

6
4
2

Cumulative energy (fJ)

16

0

160

Time (ns)
Figure 5. Measured EM waveform and its cumulative energy before and after denoising procedure.
Figure 5. Measured EM waveform and its cumulative energy before and after denoising procedure.

3. Simulation Technique of the EM Wave Propagation
3. Simulation Technique of the EM Wave Propagation
3.1. 3-D Modeling of the Transformer
3.1. 3-D Modeling of the Transformer
The EM wave propagation within the transformer was simulated by using the CST Microwave
The
EM wave
propagation
within
thecalculation
transformer
simulated
by using
the finite
CST Microwave
Studio software
with
transient solver.
The
in was
the software
is based
on the
integration
Studio
with transient
solver.
The calculation
in the software
based
on the finite
integration
theory software
(FIT), in which
the Maxell’s
equations
are numerically
solved, is
not
in differential
forms
used in
theory
(FIT), in which
the Maxell’s
equations
are numerically
solved,
not[23,27].
in differential forms used
the finite-difference
time-domain
(FDTD)
method
[26] but integral
forms
in theFigure
finite-difference
time-domain
(FDTD)
method
[26]
but integral
forms [23,27].
6 shows a 3-D
computational
model,
which
simulates
the transformer
tank and the active
Figure
6 shows
a 3-D computational
model,
which
simulates the
and1.the
active
part of
the 630
kVA transformer,
which was
used in
the experiment
as transformer
illustrated intank
Figure
Basically,
part
of
the
630
kVA
transformer,
which
was
used
in
the
experiment
as
illustrated
in
Figure
1.
the structure of the active part and its size in this model are the same as the actual ones. However, HV
Basically,
the structure
of theboth
active
part and
its size inon
this
same
asnot
themodeled
actual ones.
and LV leads,
which connect
windings
to bushings
themodel
top ofare
thethe
tank,
were
due
However,
HV and LV
leads, which
connect both
to bushings
top of the cylinder
tank, were
to their complicated
structures.
Furthermore,
eachwindings
winding was
modeledonasthe
a conductive
to
not
modeled
due
to
their
complicated
structures.
Furthermore,
each
winding
was
modeled
as
a
make the model simple and reduce the computational time drastically. This simplification is possible,
conductive
to of
make
model simple
reduce
drastically.
This
because thecylinder
windings
this the
transformer
used and
in this
studythe
arecomputational
the cylindricaltime
type,
hence there
is
simplification
is
possible,
because
the
windings
of
this
transformer
used
in
this
study
are
the
no oil gap between each layer. In fact, there are quite small gaps between conductors because of
cylindrical
type,and
hence
there
is nocan
oiltheoretically
gap between
each layer.
In fact,
there
are quite
small
gaps
layer-insulation
the EM
waves
propagate
through
them
to some
extent.
However,
between
conductors
because
the layer-insulation
and
the EM
can theoretically
propagate
these propagating
paths
can beofignored
in this research
because
thewaves
EM waves
attenuate severely
and
through
them
to
some
extent.
However,
these
propagating
paths
can
be
ignored
in
this
research
cannot be detected experimentally. The validations of this transformer modeling will be discussed in
because
the EM waves attenuate severely and cannot be detected experimentally. The validations of
Section 4.2.
this transformer
modeling
will monopole
be discussed
in Section
The positions
of the three
antennas
(EM4.2.
wave sources) are also indicated in Figure 6.
The
positions
of
the
three
monopole
antennas
(EM
wave
are the
alsocenter
indicated
in Figure
6.
Two of them, named positions 1 and 2, are located at the same sources)
side around
windings
but at
Two
of them,
named
positions
1 and 2,position
are located
same side of
around
the center windings but
different
heights.
Another
EM source,
3, is at the other
the windings.
at different heights. Another EM source, position 3, is at the other side of the windings.

Sensors 2018, 18, 4236

7 of 16

Sensors 2018, 18, x FOR PEER REVIEW

7 of 16

Sensor B
Sensor A
Core

Metal poles

1550

Sensor C

Windings

760

Sensor D

1720

(a) Perspective view (a part of the tank walls is set to be transparent)
Position 3

245

350

Position 1

Position 2

(b) Top view of the active parts
950

Position 2

780
620
385

Position 3
355

Position 1

(c) Side view of the active parts
Figure6.6.3-D
3-D
computational
model
transformer
and
positions
of the
three
monopole
antennas.
Figure
computational
model
of of
thethe
transformer
and
positions
of the
three
monopole
antennas.

Sensors 2018, 18, 4236

8 of 16

Sensors 2018, 18, x FOR PEER REVIEW

8 of 16

3.2.
3.2.Antenna
AntennaModeling
Modeling
AAfeeding
feedingmethod
methodofofan
anantenna
antennafor
forthe
thesimulation
simulationhas
hasnot
notbeen
beenestablished
establishedyet,
yet,although
althoughseveral
several
methods
have
been
proposed
[28–32].
In
this
paper,
the
gap
feeding
method
[33,34]
methods have been proposed [28–32]. In this paper, the gap feeding method [33,34]was
wasapplied
appliedtoto
simulate
simulateboth
boththe
themonopole
monopoleantenna
antennafor
forradiating
radiatingthe
theEM
EMwaves
wavesand
andthe
theUHF
UHFsensors
sensorsfor
forreceiving
receiving
them,
due
to
its
simplicity.
In
this
feeding
method,
a
coaxial
cable
to
feed
the
antenna
was
not
modeled,
them, due to its simplicity. In this feeding method, a coaxial cable to feed the antenna was not
while
the feeding
(e.g., voltage
source)
was introduced
at the
gap between
a probe
(e.g., monopole)
modeled,
while port
the feeding
port (e.g.,
voltage
source) was
introduced
at the
gap between
a probe
and
grounded
conductor.
(e.g.,
monopole)
and grounded conductor.
Figure
models of
of the
themonopole
monopoleand
andUHF
UHF
antennas
with
feeding.
Figure 77 illustrates
illustrates models
antennas
with
the the
gapgap
feeding.
The
The
monopole
in
the
simulation
model
was
20
mm
in
length
and
1.3
mm
in
diameter
with
monopole in the simulation model was 20 mm in length and 1.3 mm in diameter with aaplate
plate
conductor
conductorhaving
havingan
anarea
areaofof1010mm
mm××10
10mm.
mm. The
Theprobe
probeof
ofthe
theUHF
UHFsensor
sensorwas
wasaacircular
circulartruncated
truncated
cone
shape
with
a
bottom
diameter
of
30
mm,
a
top
diameter
of
10
mm
and
a
height
cone shape with a bottom diameter of 30 mm, a top diameter of 10 mm and a heightofof30
30mm
mmand
anditit
had
ofof
3030
mm.
The
gap
lengths
of the
feeding
portport
were
set to
for
hadaaconductor
conductorwith
witha adiameter
diameter
mm.
The
gap
lengths
of the
feeding
were
set0.5
tomm
0.5 mm
both
the
monopole
and
UHF
sensors
and
their
impedance
was
set
to
50
Ω.
An
exciting
voltage
signal
for both the monopole and UHF sensors and their impedance was set to 50 Ω. An exciting voltage
was
applied
to the feeding
port of the
antennaantenna
and the and
received
voltage voltage
waveform
across
signal
was applied
to the feeding
portmonopole
of the monopole
the received
waveform
the
portthe
of the
sensors
were analyzed.
across
portUHF
of the
UHF sensors
were analyzed.
10

10

30

Feeding port
(0.5 mm gap)

10

Feeding port
(0.5 mm gap)

20
30
1.3

30

(a) Monopole antenna

(b) UHF sensor

Figure7.7.Modeling
Modelingofofthe
themonopole
monopoleand
andUHF
UHFsensors.
sensors.
Figure

3.3.
3.3.Other
OtherComputational
ComputationalConditions
Conditions
Table
Table11presents
presentsconductivity,
conductivity,relative
relativepermittivity
permittivityand
andpermeability
permeabilityofofthe
thematerials
materialsused
usedininthe
the
EM
wave
simulation.
On
the
surface
of
the
copper
of
the
transformer
windings,
oil-impregnated
paper
EM wave simulation. On the surface of the copper of the transformer windings, oil-impregnated
0.3
mm0.3
thick
was
set was
as a set
coating
materialmaterial
to represent
the layerthe
insulation
of the windings.
paper
mm
thick
as a coating
to represent
layer insulation
of the windings.
Table 1. Material properties used in the simulation.
Table 1. Material properties used in the simulation.
Material
Material
(Model Component)

Conductivity (S/m)

Relative Permittivity

Relative Permeability

Conductivity (S/m) Relative Permittivity Relative Permeability
(Model Component)
Air
0
1
1
Air
0
1
1
Copper

1
6.0 × 107
Copper
(winding model)
6.0 × 107

1
Paper
(winding
model)
3.9
1
1.0 × 10−14
(layer-insulation)
Paper
1.0 × 10−145
3.9
1
Silicon steel
(layer-insulation)

6000
1.0 × 10
(core)
Silicon
steel
Steel
5
1.0

6000

500
5.0××10
105
(core)
(tank)
Steel
5.0 × 105

500
(tank)
When a voltage pulse is applied to an antenna, the voltage waveform at the antenna terminal
is determined both by the frequency-dependent input impedance of the antenna and characteristic
Whenof
a voltage
pulse
is applied
to an antenna,
voltage
waveform
the antenna
impedance
the coaxial
cable
[35]. Generally,
it is notthe
easy
to determine
theatactual
excitingterminal
signal ofis
determined
both
the frequency-dependent
impedance
of the antenna
characteristic
the
antenna. In
thisby
research,
the exciting voltageinput
waveform
was determined
basedand
on the
reflected
impedance of the coaxial cable [35]. Generally, it is not easy to determine the actual exciting signal of
the antenna. In this research, the exciting voltage waveform was determined based on the reflected

voltage waveform from the open-ended top of the antenna, as proposed in Reference [25]. The
amplitude and rise time (10–90%) of the exciting signal applied for the simulation were set to 60 V
and 0.8 ns, respectively.
The hexahedral mesh was used in this computation. The frequency range and cell numbers per
wavelength were set to 0–1500 MHz and 30, respectively. This results in approximately 76,000,000
Sensors 2018, 18, 4236
total mesh cells. The time durations of the simulation were set to 800 ns for the first experiment
without the active parts and 100 ns for the second experiment. At these times, the EM waves,
propagating within the tank, attenuated sufficiently to evaluate the convergence cumulative energies.

9 of 16

voltage waveform from the open-ended top of the antenna, as proposed in Reference [25]. The
amplitude
and rise time
(10–90%)
ofResults
the exciting
signal applied for the simulation were set to 60 V and
4. Evaluations
of the
Simulated
and Discussions
0.8 ns, respectively.
Validations ofmesh
the Antenna
and Transformer
Tank Modeling The frequency range and cell numbers per
The4.1.
hexahedral
was used
in this computation.
thesetfirst
step, theMHz
EM and
wave30,
propagation
in the
tank
without
the active parts76,000,000
of the
wavelength For
were
to 0–1500
respectively.
This
results
in approximately
total
transformer
was
simulated
and
the
results
were
compared
with
the
measured
ones
in
order
to
mesh cells. The time durations of the simulation were set to 800 ns for the first experiment without the
remove the influence of the active parts and validate the modeling technique of the monopole and
active parts
and 100 ns for the second experiment. At these times, the EM waves, propagating within
UHF sensors as well as the transformer tank.
the tank, attenuated
sufficiently to evaluate the convergence cumulative energies.
Figures 8 shows an example of the simulated and measured EM waveforms by sensor A. In this
figure, the signal amplitudes of both the simulated and measured values were normalized by the

4. Evaluations
ofsignal
the Simulated
Results
and Figure
Discussions
maximum
strength of each
waveform.
8a,b show the entire waveforms up to 800 ns and
the enlargements of the first 50 ns, respectively. From these figures, it can be seen that the attenuation

4.1. Validations
and Transformer
ModelingEM waveforms by the simulation and
degrees of
of the
the Antenna
signal amplitudes
and the Tank
time-domain

showed quite good agreement with each other, especially for the first 10 ns in Figure
Formeasurement
the first step,
the EM wave propagation in the tank without the active parts of the transformer
8b. Such a good agreement of the simulated waveform with the measured one has never been
was simulated
and
the
results were compared with the measured ones in order to remove the influence
reported before.
of the activeFigure
parts9and
validate
the modeling
technique
of the monopole
UHF
sensors
as well as
compares
the simulated
and measured
cumulative
energies for and
the four
UHF
sensors.
the transformer
tank.
In this figure,
the cumulative energies were normalized by the values by sensor A. Both the simulated
and measured
showed of
a similar
trend that the
sensors
A and BEM
showed
the lowestby
and
highestA. In this
Figure
8 showsresults
an example
the simulated
and
measured
waveforms
sensor
sensitivities,
respectively,
although
the
maximum
error
between
the
simulated
and
measured
results by the
figure, the signal amplitudes of both the simulated and measured values were normalized
was about 21% for sensor B. Figure 10 shows cumulative energies as a function of time for the four
maximum signal strength of each waveform. Figure 8a,b show the entire waveforms up to 800 ns
UHF sensors. Although convergence values of the cumulative energies by the simulation and
and themeasurement
enlargements
of the
50 ns, especially
respectively.
From
figures,
it can
be degree
seen that the
showed
somefirst
differences,
for sensor
B asthese
expected
from Figure
9, the
attenuation
degrees
of the
signal amplitudes
and
the time-domain
EM waveforms
bywith
the the
simulation
of increase
in the
cumulative
energies in the
simulation
showed reasonable
agreement
measured ones.
and measurement
showed quite good agreement with each other, especially for the first 10 ns in
Baseda on
the agreement
results of theof
first
in Figures
8–10,
it can be said
Figure 8b. Such
good
theexperiment,
simulatedpresented
waveform
with the
measured
one that
has the
never been
modeling techniques of the monopole and the UHF sensors, the exciting voltage waveform as well
reported before.

Signal amplitude (arb. unit)

as the tank modeling, including the material properties, are reasonable.
1

0.5

0

-0.5

Simulation

Measurement
-1
0

100

200

300

400

500

600

700

800

Time (ns)
Sensors 2018, 18, x FOR PEER REVIEW

Signal amplitude (arb. unit)

(a) Simulated and measured entire waveforms up to 800 ns.
1
Simulation
Measurement

0.5

0

-0.5

-1
0

10

20

30

40

50

Time (ns)
(b) Enlargement of the waveforms at the first 50 ns.

umulative energies (p. u.)

8. Examples
of the
simulatedand
and measured
waveforms
by sensor
A.
FigureFigure
8. Examples
of the
simulated
measuredEM
EM
waveforms
by sensor
A.

2.5
2
1.5
1
0.5

Measurement

10 of 16

Sensors 2018, 18, 4236

unit)
(arb.
amplitude
Signal
unit)
(arb.
amplitude
Signal

Sensors 2018, 18, x FOR PEER REVIEW
Sensors 2018, 18, x FOR PEER REVIEW
1
1

10 of 16
10 of 16

Simulation
Measurement
Simulation
Measurement

0.5
0.5

10 of 16

energies
Cumulative
energies
u.) u.)
Cumulative
(p. (p.

Figure 9 compares 0the simulated and measured cumulative energies for the four UHF sensors.
0
In this figure, the cumulative
energies were normalized by the values by sensor A. Both the simulated
and measured results -0.5
showed a similar trend that the sensors A and B showed the lowest and highest
sensitivities, respectively,
-0.5 although the maximum error between the simulated and measured results
was about 21% for sensor
-1 B. Figure 10 shows cumulative energies as a function of time for the four UHF
sensors. Although convergence
values
energies
by the40simulation50and measurement
10of the cumulative
20
30
-1 0
30 from Figure
40 9, the degree
50
showed some differences, 0especially 10
for sensor B20asTime
expected
of increase in
(ns)
the cumulative energies in the simulation showed reasonable
Time (ns) agreement with the measured ones.
Enlargement
of the presented
waveformsinatFigures
the first8–10,
50 ns.it can be said that the
Based on the results of(b)
the
first experiment,
(b) Enlargement of the waveforms at the first 50 ns.
modeling techniques
ofExamples
the monopole
and the UHF
sensors, the
voltage
waveform
as well as
Figure 8.
of the simulated
and measured
EMexciting
waveforms
by sensor
A.
the tank modeling,
including
theof
material
properties,
are reasonable.
Figure
8. Examples
the simulated
and measured
EM waveforms by sensor A.
2.5
2.5
2
2
1.5
1.5
1
1
Measurement
0.5
Measurement
0.5
Simulation
0
Simulation
C
A
B
D
0
A
B sensorsC
D
UHF
UHF sensors

energy
Cumulative
(p.(p.
energy
u.)u.)
Cumulative

Figure 9. Simulated and measured cumulative energies as a function of the UHF sensor positions.
Figure 9. Simulated and measured cumulative energies as a function of the UHF sensor positions.
Figure 9. Simulated and measured cumulative energies as a function of the UHF sensor positions.

2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0 0
0

Dotted: measurement, solid: simulation
Dotted: measurement, solid: simulation
B
B
C
C

D
D
100
100

200
300
200 Time (ns)
300

A
A
400
400

500
500

Time (ns)

Figure 10. Cumulative energies as a function of time for the four UHF sensors.
Figure 10. Cumulative energies as a function of time for the four UHF sensors.
10.the
Cumulative
a function of time for the four UHF sensors.
4.2. Propagation Figure
Times of
EM Wavesenergies
within as
a Transformer

4.2. Propagation Times of the EM Waves within a Transformer
As the nextTimes
step, of
the
partswithin
of theatransformer
4.2. Propagation
theactive
EM Waves
Transformer were installed into the tank. In order to
As
the
next
step,
the
active
parts
of
the
transformer
installed
the tank.propagation
In order to
validate the size and positions of the transformer windingwere
model
in the into
simulation,
As the size
nextand
step,
the active
parts
of the transformer
wereininstalled
into thepropagation
tank. In order
to
validate
positions
of
the
transformer
winding
model
the
simulation,
times of the EM waves from the EM wave sources to each sensor were computed and compared times
with
validate
the
size and
positions
of
the transformer
winding
model
incomputed
the simulation,
propagation
times
of
the
EM
waves
from
the
EM
wave
sources
to
each
sensor
were
and
compared
with
the
the experimental and theoretically calculated ones. In the experiment, the propagation times were
of the EM waves
the EM wave
sourcesones.
to each
were computed
and compared
with
the
experimental
andfrom
theoretically
calculated
In sensor
the signal
experiment,
propagation
times
were
obtained
by simultaneous
measurement
of the exciting
and thethe
resultant
EM wave
signals,
experimental
and theoretically
calculated
ones.
In the signal
experiment,
the
propagation
times
were
obtained
by simultaneous
measurement
ofsystematically
the exciting
and the
resultant
wave
signals,
where
arrival
times of the EM
waves were
calculated
based
on theEM
Energy
criterion
obtained
by
simultaneous
measurement
of
the
exciting
signal
and
the
resultant
EM
wave
signals,
where arrival
method
[8,21]. times of the EM waves were systematically calculated based on the Energy criterion
where arrival
of the EM waves were systematically calculated based on the Energy criterion
method
[8,21]. times
Theoretical
propagation times were calculated, assuming the transformer windings as simple
method [8,21].
cylindrical obstacles [36]. Figure 11 illustrates geometrical model of the propagation path around a

Sensors 2018, 18, 4236

11 of 16

cylinder and its 2-D projection. In a 2-D projection, we assume coordinates of the EM wave source and
UHF sensor as (xm , ym ) and (xs , ys ). Then, θ 1 , θ 2 , θ 3 and θ 4 illustrated in Figure 11 can be expressed as,
θ1 = tan−1 (ym /xm )
θ2 = tan−1 (

(3)

q

xm 2 + ym 2 − r2 /r )
q
θ3 = tan−1 ( xs 2 + ys 2 − r2 /r )

(4)

θ4 = tan−1 (ys /xs )

(6)

(5)

where r is a radius of the cylindrical obstacle. Considering the height difference in 3-D, the propagation
distance from the source to the sensor, LAD , is expressed as,
1/2

( xm 2 + ym 2 − r2 )
+ r · ( π − θ1 − θ2 − θ3 − θ4 )
o1/2
i
1/2
2
2
2
+( xs + ys − r )
+ ( z m − z s )2

L AD =



(7)

where zm and zs denote z coordinates of the EM wave source and the sensor, respectively [36].
Theoretical propagation time considering the obstacles can be calculated by LAD /c, where c is the light
Sensors 2018,
18,case.
x FOR PEER REVIEW
12 of 16
speed
in this
z

EM wave source
(xm, ym, zm)

D

UHF sensor
(xs, ys, zs)
x

A
y
Diameter: r

θ1
A
EM wave source
(xm, ym)

θ4
θ2
B

θ3

C

x
D
UHF sensor
(xs, ys)

Figure
Figure 11.
11. Propagation
Propagation path
path of
of the
the EM
EM waves
waves around
around aa cylindrical
cylindrical obstacle
obstacle and
and its
its 2-D
2-D projection.
projection.

Propagation time (ns)

Figure 12 shows propagation times of the EM waves, obtained by the simulation, the experiment
9.5
and theoretical calculation described above as functions of positionsSimulation
of the UHF sensors and the EM
Theoretical
8.5
wave sources. For comparison, direct propagation times were also plotted, which were calculated
Direct propagation
based on the Euclidian
7.5 distance between an EM source and a UHF sensor divided by the light speed.
Measurement
It can be seen that the
6.5simulated and theoretically calculated propagation times showed quite good
agreement for all UHF sensors and the source positions, while in some cases, there are some differences
5.5
of about 1 ns between the simulated results and those calculated assuming direct propagation. This fact
4.5
indicates that the influences
of the active part on the propagation times were accurately simulated and
thus the modeling of3.5
the transformer active part, mainly the positions and size of the windings, was
successfully validated.
2.5
It should be noted that some measurement results (e.g., sensor C in EM source position 1 or sensor
1.5
A in EM source 3) showed
large
A Berrors
D AtheBother
D A These
D caused by the roundabout
C from
C results.
B C were
propagation path and resulting severe attenuations of the EM waves, which made the arrival of the
EM source: 3
EM source: 2
EM source: 1
UHF sensors (A-D) and EM source positions (1-3)
Figure 12. Propagation times of the EM waves by the simulation, experiment and theoretical
calculations.

Diameter: r

θ1

θ4

A

x

θ3

θ2

D

Sensors 2018, 18, 4236

12 of 16

EM wave source
(xm, ym)

UHF sensor
(xs, ys)

C

B

EM signals unclear. These large errors in the determination of the arrival time will lead to a critical PD
Figureerror,
11. Propagation
path of on
the the
EM location
waves around
a cylindrical
obstacle andinits
2-D projection.
localization
so the influence
accuracy
will be evaluated
future
works.
9.5

Simulation
Theoretical
Direct propagation
Measurement

Propagation time (ns)

8.5
7.5
6.5
5.5

4.5
3.5
2.5
1.5

A

B

C

D

EM source: 1

A

B

C

D

EM source: 2

A

B

C

D

EM source: 3

UHF sensors (A-D) and EM source positions (1-3)
Figure 12. Propagation times of the EM waves by the simulation, experiment and theoretical calculations.
Figure 12. Propagation times of the EM waves by the simulation, experiment and theoretical
calculations.Energies and Signal Amplitudes as a Function of Sensor Positions
4.3. Cumulative

Finally, cumulative
energies
signal amplitudes
of the
EM wave
signals from the simulations
4.3. Cumulative
Energies and
Signaland
Amplitudes
as a Function
of Sensor
Positions
were evaluated by comparing with those from the experimental using the active parts of the transformer
Finally, cumulative energies and signal amplitudes of the EM wave signals from the simulations
in order to validate the newly developed simulation technique.
were evaluated by comparing with those from the experimental using the active parts of the
Figure 13 shows the entire and the first 30 ns of the time-domain EM waveforms, which were
transformer in order to validate the newly developed simulation technique.
obtained by sensor C at the EM wave source position 3, respectively. The signal amplitudes of both the
Figure 13 shows the entire and the first 30 ns of the time-domain EM waveforms, which were
simulated and measured values were normalized by the maximum signal strength of each waveform.
obtained by sensor C at the EM wave source position 3, respectively. The signal amplitudes of both
From Figure 13a, the attenuation degree of the EM waves as a function of time agreed well with
the simulated and measured values were normalized by the maximum signal strength of each
the measured one. Furthermore, the EM waves attenuated sufficiently within 100 ns, while in the
waveform. From Figure 13a, the attenuation degree of the EM waves as a function of time agreed
first experiment without the active parts, it took more than 500 ns as shown in Figure 8a. This rapid
well with the measured one. Furthermore, the EM waves attenuated sufficiently within 100 ns, while
attenuation was caused by increasing the reflection and diffraction of the EM waves due to the active
in the first experiment without the active parts, it took more than 500 ns as shown in Figure 8a. This
parts. Also, Figure 13b indicates that the waveforms both by the simulation and measurement were
rapid attenuation was caused by increasing the reflection and diffraction of the EM waves due to the
quite similar up to 50 ns. These agreements in Figure 13a,b suggest that the modeling of the active part
active parts. Also, Figure 13b indicates that the waveforms both by the simulation and measurement
of the transformer is reasonable.
were quite similar up to 50 ns. These agreements in Figure 13a,b suggest that the modeling of the
Figures 14 and 15 show the simulated and measured cumulative energies and signal amplitudes
active part of the transformer is reasonable.
as functions of the source and the sensor positions, respectively. In both figures, the vertical axes were
Figures 14 and 15 show the simulated and measured cumulative energies and signal amplitudes
normalized by the values from sensor A at the source position 1. For both cumulative energies and
as functions of the source and the sensor positions, respectively. In both figures, the vertical axes were
signal amplitudes, on the whole, the simulated results show a similar trend to the measured results.
However, the cumulative energies show better agreement, because the signal amplitudes tend to be
strongly affected by resonances of the EM waves, which are difficult to simulate accurately.
As shown in Figures 12–15, the propagation times of the EM waves, the time-domain EM
waveform and signal strength (i.e., cumulative energies and their amplitudes) as a function of the
sensor position by the simulation showed reasonable agreement with the measured ones. Thus,
the newly developed simulation technique for the EM wave propagation has been successfully
validated. Furthermore, it firstly enables us to investigate the sensitivities of PD measurement as a
function of UHF sensor positions for actual transformers by computation.
The authors believe that this simulation technique will contribute to further investigations for the
optimization of the UHF sensor positions, their numbers as well as the type of sensor, by applying the
antenna modeling technique described in Section 3.2 and the sensitivity investigation as a function of
sensor positions in Section 4.3.

Sensors 2018, 18, x FOR PEER REVIEW

13 of 16

Signal amplitude (arb. unit)

normalized by the values from sensor A at the source position 1. For both cumulative energies and
signal amplitudes, on the whole, the simulated results show a similar trend to the measured results.
However,
the
cumulative energies show better agreement, because the signal amplitudes tend
be
Sensors
2018, 18,
4236
13 to
of 16
strongly affected by resonances of the EM waves, which are difficult to simulate accurately.
1
Simulation
Measurement

0.5
0
-0.5
-1
0

20

40

60

80

100

Time (ns)

Signal amplitude (arb. unit)

(a) Simulated and measured entire waveforms up to 100 ns.

1
0.5

0
-0.5

Simulation
Measurement

-1
0

10

20

30

Time (ns)
(b) Enlargement of the waveforms at the first 30 ns.
Figure13.
13.Example
Exampleofofthe
thesimulated
simulatedand
andmeasured
measuredEM
EMwaveforms.
waveforms.(EM
(EMwave
wavesource
sourceposition
position3,3,UHF
UHF
Figure
14 of 16
sensorC).
C).
sensor

Sensors 2018, 18, x FOR PEER REVIEW

Cumulative energies (arb. unit)

2
As shown in Figures
12–15, the propagation times of the EM waves, the time-domain EM
Simulation
waveform and signal strength (i.e., cumulative energies and their amplitudes) as a function of the
sensor position by the1.5
simulationMeasurement
showed reasonable agreement with the measured ones. Thus, the
newly developed simulation technique for the EM wave propagation has been successfully validated.
Furthermore, it firstly enables
us to investigate the sensitivities of PD measurement as a function of
1
UHF sensor positions for actual transformers by computation.
The authors believe
0.5 that this simulation technique will contribute to further investigations for
the optimization of the UHF sensor positions, their numbers as well as the type of sensor, by applying
the antenna modeling 0technique described in Section 3.2 and the sensitivity investigation as a
B C4.3.D A B C D A B C D
A Section
function of sensor positions in

EM source: 1

EM source: 3

EM source: 2

UHF sensors (A-D) and EM source positions (1-3)

Signal amplitudes (arb. unit)

Figure
and
EM
wave
source.
Figure14.
14.Simulated
Simulatedand
andmeasured
measuredcumulative
cumulativeenergies
energiesfor
foreach
eachUHF
UHFsensors
sensors
and
EM
wave
source.
1.4
1.2

1
0.8
0.6

0.4
Simulation
Measurement

0.2
0

A

B

C

D

A

B

C

D

A

B

C

D

C

0

B

A

C

D

EM source: 1

A

B

C

D

A

B

C

D

EM source: 3

EM source: 2

UHF sensors (A-D) and EM source positions (1-3)
Sensors 2018, 18, 4236

14 of 16

Signal amplitudes (arb. unit)

Figure 14. Simulated and measured cumulative energies for each UHF sensors and EM wave source.
1.4
1.2

1
0.8
0.6

0.4
Simulation
Measurement

0.2
0

A

B

C

D

EM source: 1

A

B

C

D

EM source: 2

A

B

C

D

EM source: 3

UHF sensors (A-D) and EM source positions (1-3)
Figure 15. Simulated and measured signal amplitudes for each UHF sensors and EM wave source.
Figure 15. Simulated and measured signal amplitudes for each UHF sensors and EM wave source.

5. Conclusions
5. Conclusions
The authors have proposed a simulation technique for EM wave propagation within transformers
The authors
have proposed
a simulation
for EM wave
propagation
and validated
the simulated
results by comparing
withtechnique
those experimentally
obtained,
using a 630within
kVA
transformers
and
validated
the
simulated
results
by
comparing
with
those
experimentally
obtained,
distribution transformer.
using
a 630
kVA distribution
transformer.
First,
validities
of modeling
methods for a monopole antenna as an EM wave source, UHF
First,
validities
of
modeling
methods
a monopole
as with
an EM
wave source,
UHF
sensors as well as the transformer tank
werefor
investigated
by antenna
comparing
experimental
results
sensors with
as well
the transformer
investigated
comparing
with experimental
results
obtained
an as
empty
transformer tank
tank.were
Consequently,
the by
simulated
time-domain
EM waveforms,
obtained
with
an
empty
transformer
tank.
Consequently,
the
simulated
time-domain
EM
waveforms,
the attenuation rate of EM wave strengths and cumulative energies as a function of UHF sensor
the attenuation
rate of
EM wavewith
strengths
and cumulative
energies
as amodeling
function methods
of UHF sensor
position
showed good
agreement
the measured
ones. Therefore,
those
were
position
showed
good
agreement
with
the
measured
ones.
Therefore,
those
modeling
methods
were
successfully validated.
successfully
validated.
Second, propagation times, signal amplitudes and cumulative energies of the EM waves were
Second,
propagation
times, signaland
amplitudes
cumulativeby
energies
thekVA
EMdistribution
waves were
evaluated
by simulation,
measurement
theoreticaland
consideration
using aof630
evaluated
by
simulation,
measurement
and
theoretical
consideration
by
using
a
630
kVA
distribution
transformer in order to confirm the validation of the modeling of the active parts of a transformer.
transformer
in
order
to
confirm
the
validation
of
the
modeling
of
the
active
parts
of
a
transformer.
As a result, the simulated EM waveforms, their propagation times, cumulative energies and signal
As a result,
simulated
EM sensor
waveforms,
their
propagation
times,
cumulative
and signal
amplitudes
asthe
a function
of UHF
position
showed
reasonable
agreement
with energies
the experimentally
amplitudes
as
a
function
of
UHF
sensor
position
showed
reasonable
agreement
with the
the
and theoretically obtained ones. This suggests that the computational conditions, including
experimentally
and theoretically
obtained
ones. This suggests that the computational conditions,
modeling
of the transformer
structure
were appropriate.
including
the
modeling
of
the
transformer
structure
were appropriate.
Based on these results, this newly developed simulation
technique, proposed in this paper, will
Based
on
these
results,
this
newly
developed
simulation
proposed
in this
paper,
contribute to the optimization of the UHF sensor positions andtechnique,
their numbers
as well
as the
typewill
of
contribute
to
the
optimization
of
the
UHF
sensor
positions
and
their
numbers
as
well
as
the
type
of
UHF sensors to obtain the desired PD detection sensitivity for power transformers.
UHF sensors to obtain the desired PD detection sensitivity for power transformers.
Author Contributions: T.U. conceived and performed the experiments, analyzed the data and wrote the paper;
S.T. offered valuable suggestions and guidance.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflict of interest.

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