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Original filename: Partial Discharge Analysis in High-Frequency Transformer Based on High-Frequency Current Transducer.pdf
Title: Partial Discharge Analysis in High-Frequency Transformer Based on High-Frequency Current Transducer
Author: Jun Jiang, Mingxin Zhao, Chaohai Zhang, Min Chen, Haojun Liu and Ricardo Albarracín

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energies
Article

Partial Discharge Analysis in High-Frequency
Transformer Based on High-Frequency
Current Transducer
Jun Jiang 1, * ID , Mingxin Zhao 1 , Chaohai Zhang 1 , Min Chen 2 , Haojun Liu 2
and Ricardo Albarracín 3
1

2
3

*

Jiangsu Key Laboratory of New Energy Generation and Power Conversion, Nanjing University of
Aeronautics and Astronautics, Nanjing 211106, China; dobby12345678@163.com (M.Z.);
zhangchaohai@nuaa.edu.cn (C.Z.)
State Grid Zhejiang Electric Power Co. Ltd., Research Institute, Hangzhou 310014, China;
ncepucm@163.com (M.C.); hhjjll@163.com (H.L.)
Departamento de Ingeniería Eléctrica, Electrónica, Automática y Física Aplicada, Escuela Técnica Superior
de Ingeniería y Diseño Industrial, Universidad Politécnica de Madrid, Ronda de Valencia 3, 28012 Madrid,
Spain; ricardo.albarracin@upm.es
Correspondence: jiangjun0628@163.com; Tel.: +86-158-5183-0677

Received: 14 July 2018; Accepted: 26 July 2018; Published: 1 August 2018




Abstract: High-frequency transformers are the core components of power electronic transformers
(PET), whose insulation is deeply threatened by high voltage (HV) and high frequency (HF).
The partial discharge (PD) test is an effective method to assess an electrical insulation system. A PD
measurement platform applying different frequencies was set up in this manuscript. PD signals
were acquired with a high-frequency current transducer (HFCT). For improving the signal-to-noise
(SNR) ratio of PD pulses, empirical mode decomposition (EMD) was used to increase the SNR by
4 dB. PD characteristic parameters such as partial discharge inception voltage (PDIV) and PD phase,
number, and magnitude were all analyzed as frequency dependent. High frequency led to high PDIV
and a smaller discharge phase region. PD number and magnitude were first up and then down as the
frequency increased. As a result, a suitable frequency for evaluating the insulation of high-frequency
transformers is proposed at 8 kHz according to this work.
Keywords: partial discharge (PD); high-frequency transformers; power electronic transformers (PET);
partial discharge inception voltage (PDIV)

1. Introduction
To establish a smart grid, it is necessary to accomplish electronic power conditioning and control
of electric power production and distribution [1]. In this trend, electronic-based power devices are
migrating from the on/off control to a modern control, such as the direct control (DC) microgrid
(DCMG) [2] and railway traction systems [3], etc. Power electronic transformers (PET), functioning as
energy routers in the power grids at various voltage levels have gained widespread concern. Since PET
is a combination of power electronics and high frequency (HF) transformers, it has a great capacity
to convert electrical energy with different electrical characteristics and to make reactive power
compensation for the system. To reduce the space share of PET, the operating frequency of PET
is designed mainly to a few thousand hertz [4–6], much higher than the conventional power frequency
of 50/60 Hz. The more severe working conditions of high power, high voltage, and high frequency
threaten the insulation of PET [7]. As a core component of PET, HF transformers play a role in isolating
and transmitting power, the insulation of which is particularly important. Damaged insulation of HF
Energies 2018, 11, 1997; doi:10.3390/en11081997

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Energies 2018, 11, 1997

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insulation of HF transformers not only has low energy conversion efficiency but also leads to power
failures of the power and electronic equipment [8], further causing the whole crash of PET.
transformers not only has low energy conversion efficiency but also leads to power failures of the
Partial discharge (PD) in high‐voltage (HV) equipment is deemed as one of the most significant
power and electronic equipment [8], further causing the whole crash of PET.
phenomena to be investigated for determining defects and degradation in electrical insulation and
Partial discharge (PD) in high-voltage (HV) equipment is deemed as one of the most significant
an apparatus’s lifetime. Similar to the conventional HV power apparatus, scholars have paid
phenomena to be investigated for determining defects and degradation in electrical insulation and an
attention to PD in high‐frequency transformers to determine whether there is a fault and to evaluate
apparatus’s lifetime. Similar to the conventional HV power apparatus, scholars have paid attention
the health status.
to PD in high-frequency transformers to determine whether there is a fault and to evaluate the
The frequency dependence of PD sources has been taken into account and a model developed
health status.
in order to study the effect of applying higher frequency (50 to 600 Hz) on the behavior of PD activity
The frequency dependence of PD sources has been taken into account and a model developed in
[9]. Experimental research has been carried out [10] in the range of 50 to 1000 Hz. However, according
order to study the effect of applying higher frequency (50 to 600 Hz) on the behavior of PD activity [9].
to field experiences of oscillating waves ranging from 20 Hz to several hundred hertz, the frequency
Experimental research has been carried out [10] in the range of 50 to 1000 Hz. However, according to
of the power source makes little difference to PD activities [11–13]. More research has been done at
field experiences of oscillating waves ranging from 20 Hz to several hundred hertz, the frequency
higher frequencies. A semi‐square voltage of 2 kHz has been used in [14]; even tens of kilohertz (kHz)
of the power source makes little difference to PD activities [11–13]. More research has been done at
repetitive pulse‐width modulation (PWM), such as HV pulses stressed on power electronic devices,
higher frequencies. A semi-square voltage of 2 kHz has been used in [14]; even tens of kilohertz (kHz)
is considered important for the reduction of the insulation reliability and its life cycle [10,15]. As to
repetitive pulse-width modulation (PWM), such as HV pulses stressed on power electronic devices,
the high‐ frequency transformer in PET, the non‐sinusoidal waveform is not suitable for the voltage
is considered important for the reduction of the insulation reliability and its life cycle [10,15]. As to
step‐up/step‐down [7]. As a result, the sinusoidal waveform with more than 1000 Hz should attract
the high- frequency transformer in PET, the non-sinusoidal waveform is not suitable for the voltage
more attention.
step-up/step-down [7]. As a result, the sinusoidal waveform with more than 1000 Hz should attract
As is well known, PD detection and the diagnosis of low‐frequency power transformers depend
more attention.
on various techniques on which there have been extensive studies [16–20]. Several PD detection
As is well known, PD detection and the diagnosis of low-frequency power transformers depend on
methods have been developed according to the physical properties of the insulation system, which
various techniques on which there have been extensive studies [16–20]. Several PD detection methods
accompany PD activity, such as current pulse method [21], ultrasonic detection, ultra‐high‐frequency
have been developed according to the physical properties of the insulation system, which accompany
(UHF) detection, and the optical method [22,23]. However, the lower frequency limit of conventional
PD activity, such as current pulse method [21], ultrasonic detection, ultra-high-frequency (UHF)
pulse current methods is close to that in the high‐frequency transformer, the ultrasonic detection is
detection, and the optical method [22,23]. However, the lower frequency limit of conventional
not sensitive enough because of the complex acoustic impedance, the UHF signals are affected by
pulse current methods is close to that in the high-frequency transformer, the ultrasonic detection
communication signals, and there is still no known experience with optical measurements in this
is not sensitive enough because of the complex acoustic impedance, the UHF signals are affected by
kind of electrical equipment. In this sense, the wide‐band current method is proposed to be a good
communication signals, and there is still no known experience with optical measurements in this kind
choice for PD detection in high‐frequency transformers [24]. This paper is structured as follows. In
of electrical equipment. In this sense, the wide-band current method is proposed to be a good choice
Section 2, the measurement setup is described. The denoising process of empirical mode
for PD detection in high-frequency transformers [24]. This paper is structured as follows. In Section 2,
decomposition is depicted in Section 3; the signal‐to‐noise (SNR) ratio of the PD signal is increased
the measurement setup is described. The denoising process of empirical mode decomposition is
by 4 dB. In Section 4, PD results and discussions are described, covering which parameters were
depicted in Section 3; the signal-to-noise (SNR) ratio of the PD signal is increased by 4 dB. In Section 4,
frequency‐dependent and how the parameters (PD phase region, PD number, PD magnitude, etc.)
PD results and discussions are described, covering which parameters were frequency-dependent and
varied at different frequencies. The conclusions about appropriate conditions for testing HF
how the parameters (PD phase region, PD number, PD magnitude, etc.) varied at different frequencies.
transformers are presented in Section 5.
The conclusions about appropriate conditions for testing HF transformers are presented in Section 5.
2. Partial Discharge Measurement Setup
2. Partial Discharge Measurement Setup
Insulation defects of HF transformers are caused by many factors, of which free metal particles
Insulation defects of HF transformers are caused by many factors, of which free metal particles
often cause suspension potential or even suspension discharge. Suspension discharge is the greatest
often cause suspension potential or even suspension discharge. Suspension discharge is the greatest
number of partial discharges [14,25]. A schematic diagram of a typical HF transformer is shown in
number of partial discharges [14,25]. A schematic diagram of a typical HF transformer is shown in
Figure 1.
Figure 1.

Figure
Figure1.1.2-D
2‐Dschematic
schematicdiagram
diagramofofa atypical
typicalhigh-frequency
high‐frequency(HF)
(HF)transformer.
transformer.

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The structure of HF transformers are similar to conventional transformers.
HF
consist
of a magnetic
core, to
copper
windings,
and insulation parts. However,
Thetransformers
structure of HF
transformers
are similar
conventional
transformers.
the special
operating consist
conditions
morecore,
demand
onwindings,
the core material,
winding
distribution,
HF transformers
of a place
magnetic
copper
and insulation
parts.
However,
and
insulation
performance.
To achieve
highdemand
efficiency
energy
conversion
and high
power density,
the special
operating
conditions
place more
oninthe
core material,
winding
distribution,
and
a
high
frequency
through
the
magnetic
core
has
been
selected
and
a
compact
winding
design
was
insulation performance. To achieve high efficiency in energy conversion and high power density, a
considered
[7,26].
A large
of coils
restrictive
volume
the winding
inter-turndesign
insulation
high frequency
through
thenumber
magnetic
core in
hasa been
selected
and amakes
compact
was
gain
strong
electrical
stress,
and
additional
insulation
failures
should
be
taken
into
consideration
considered [7,26]. A large number of coils in a restrictive volume makes the inter‐turn insulation gain
in
HF transformers.
cardboard
coordination
has been
adopted
the insulation
for
strong
electrical stress,Insulating
and additional
insulation
failures should
be taken
intoasconsideration
in HF
transformers
and the
hot spots
(the most has
likely
point
of suspension
discharge)
were in the
transformers. [27],
Insulating
cardboard
coordination
been
adopted
as the insulation
for transformers
winding
HFhot
transformers
a suspension
discharge
modelwere
underininsulating
cardboard
[27], andofthe
spots (the [28].
mostTherefore,
likely point
of suspension
discharge)
the winding
of HF
was
designed[28].
to imitate
theasuspended
of a high-frequency
transformer
[29],
transformers
Therefore,
suspension discharge
discharge model
under insulating
cardboard winding
was designed
as
shown the
in Figure
2. discharge of a high‐frequency transformer winding [29], as shown in Figure 2.
to imitate
suspended

Figure
Figure 2.
2. Partial
Partial discharge
discharge test
test platform
platform for
for aa high‐frequency
high-frequency transformer.
transformer.

In the test platform, voltage output was provided to suspend the discharge model in series with
In the test platform, voltage output was provided to suspend the discharge model in series with
a resistance of 10 MΩ by the power supply (CTP2000, Suman, Nanjing, China). A high‐precision high‐
a resistance of 10 MΩ by the power supply (CTP2000, Suman, Nanjing, China). A high-precision
frequency current transformer (HFCT), type iHFCT‐54 (Innovit, Xi’an, China), connected to the
high-frequency current transformer (HFCT), type iHFCT-54 (Innovit, Xi’an, China), connected to the
oscilloscope (DLM2034 with a high sample rate of 2.5 GS/s and high bandwidth of 350 kHz,
oscilloscope (DLM2034 with a high sample rate of 2.5 GS/s and high bandwidth of 350 kHz, Yokagawa,
Yokagawa, Tokyo, Japan) collected the whole signals.
Tokyo, Japan) collected the whole signals.
One of the core devices in the test platform is the PD model. The large potential difference
One of the core devices in the test platform is the PD model. The large potential difference between
between the two parallel brass plates with a 35 mm gap provided a strong electric field in the air
the two parallel brass plates with a 35 mm gap provided a strong electric field in the air medium.
medium. Thus, the metal suspended in the strong electric field by the insulating paperboard and
Thus, the metal suspended in the strong electric field by the insulating paperboard and support
support carried a floating potential. Suspension discharges were generated due to the large potential
carried a floating potential. Suspension discharges were generated due to the large potential difference
difference between the suspended metal and HV side brass plate, but with a small gap of 2 mm. The
between the suspended metal and HV side brass plate, but with a small gap of 2 mm. The other core
other core device was HFCT, shown in Figure 1. It is a magnetic core surrounded by a multi‐turn
device was HFCT, shown in Figure 1. It is a magnetic core surrounded by a multi-turn conductive
conductive coil. After a discharge, a large amount of charge moves rapidly toward the defect until it
coil. After a discharge, a large amount of charge moves rapidly toward the defect until it discharges
discharges again. This process is cyclic and generates a high‐frequency current in the circuit. The
again. This process is cyclic and generates a high-frequency current in the circuit. The magnetic field
magnetic field generated by the rapid current change passes through the magnetic core, resulting in
generated by the rapid current change passes through the magnetic core, resulting in an induction
an induction voltage of the coil, which is the signal output of the HFCT. The iHFCT‐54 sensor has
voltage of the coil, which is the signal output of the HFCT. The iHFCT-54 sensor has high accuracy,
high accuracy, and the detection frequency range can reach 0.3~100 MHz. There is no electrical
and the detection frequency range can reach 0.3~100 MHz. There is no electrical connection between
connection between the measurement circuit and the measured current. With a front fastening, the
the measurement circuit and the measured current. With a front fastening, the iHFCT-54 used in the
iHFCT‐54 used in the non‐intrusive detection method can realize online monitoring of PD. The
output characteristic of this HFCT is shown in Figure 3.

Energies 2018, 11, 1997

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non-intrusive detection method can realize online monitoring of PD. The output characteristic of this
HFCT 2018,
is shown
in Figure
3.
Energies
11, x FOR
PEER REVIEW
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Figure 3.
3. Output
Outputcharacteristic
characteristic of
of an
an iHFCT‐54
iHFCT-54 sensor.
sensor.
Figure

3.
3. Denoise
Denoise Processing
Processing of
of PD
PD Signal
Signal
A
A typical
typical PD
PD current
current signal
signal is
is shown
shown in
in Figure
Figure 44 when
when the
the power
power supply
supply exerted
exerted aa peak‐to‐peak
peak-to-peak
amplitude
output
amplitude
of of
HFCT
is
amplitude of
of 20
20 kV
kVand
andfrequency
frequencyofof44kHz
kHzsinusoidal
sinusoidalvoltage.
voltage.The
The
output
amplitude
HFCT
U
HFCT
.
is UHFCT .
PD
PD activity
activity was
was detected
detectedon
onboth
bothpositive
positiveand
andnegative
negativeaxes
axesin
inaaperiod,
period,according
accordingto
toFigure
Figure4.4.
U
attained
a
peak‐to‐peak
value
of
1.61
V
with
noise
of
0.232
V,
which
reduced
the
PD
magnitude
UHFCT
attained
a
peak-to-peak
value
of
1.61
V
with
noise
of
0.232
V,
which
reduced
the PD
HFCT
accuracy.
An
improved
signal‐to‐noise
ratio
(SNR)
of
PD
signal
is
required.
Consequently,
empirical
magnitude accuracy. An improved signal-to-noise ratio (SNR) of PD signal is required. Consequently,
mode
decomposition
(EMD) was
usedwas
to improve
the SNR the
in this
becausebecause
of its merits
empirical
mode decomposition
(EMD)
used to improve
SNRmanuscript
in this manuscript
of its
on
processing
nonlinear
and
non‐stationary
signal.
merits on processing nonlinear and non-stationary signal.

Figure 4.
4. Typical
partial discharge
discharge (PD)
(PD) current
current and
and voltage
voltage signal
signal under
under ff =
= 44 kHz
= 20 kV.
Figure
Typical partial
kHz and
and U
Up‐p
p-p = 20 kV.

3.1.
3.1. Process
Process of
of Empirical
Empirical Mode
Mode Decomposition
Decomposition
EMD
dealing
with
nonlinear
non‐stationary
signals
because
it hasitgreat
self‐
EMDhas
hasan
anadvantage
advantageinin
dealing
with
nonlinear
non-stationary
signals
because
has great
adaptability.
EMD
is
based
on
the
Hilbert–Huang
transform.
The
Hilbert–Huang
transform
assumes
self-adaptability. EMD is based on the Hilbert–Huang transform. The Hilbert–Huang transform
that
all data
simple internal
modes called
intrinsic
mode functions
(IMFs)
assumes
thatcontain
all datadifferent
contain different
simple oscillation
internal oscillation
modes
called intrinsic
mode functions
[29].
In [29].
this way,
data are
superimposed
by many
different
IMFs IMFs
whose
amplitude
and
(IMFs)
In thiscomplex
way, complex
data
are superimposed
by many
different
whose
amplitude
frequency
vary
as
a
function
of
time.
Based
on
such
an
assumption,
the
process
of
EMD
to
process
and frequency vary as a function of time. Based on such an assumption, the process of EMD to process
signals is shown in Figure 5.
signals is shown in Figure 5.

Energies 2018, 11, 1997
Energies
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2018, 11,
11, xx FOR
FOR PEER
PEER REVIEW
REVIEW

5 of 13
55 of
of 13
13

Set
Set aa variance
variance of
of expectations
expectations as
as SS
Calculate
Calculate the
the maximum
maximum and
and minimum
minimum
values
values of
of the
the signal
signal hhi‐1
i‐1 in
in local
local interval
interval
ii is
is the
the number
number of
of iteration
iteration

Fitting
Fitting the
the maximal
maximal point
point envelope
envelope curve
curve aaii
Fitting
Fitting the
the Minimum
Minimum point
point envelope
envelope curve
curve bbii
m=(a
m=(aii+b
+bii)/2
)/2
hhii(t)=h
(t)=hi‐1
i‐1(t)‐m(t)
(t)‐m(t)

ii == ii +1
+1

Variance
Variance of
of all
all h(t)
h(t) obtained
obtained before
before is
is SDi
SDi
No
No

Yes
Yes
hhii(t)=IMF
(t)=IMF11

Figure
5. Process
diagram of
empirical mode
decomposition processing
signals.
Figure
signals.
Figure 5.
5. Process
Process diagram
diagram of
of empirical
empirical mode
mode decomposition
decomposition processing
processing signals.

A
A variance
variance SS is
is set
set associated
associated with
with the
the expected
expected noise
noise reduction.
reduction. Then,
Then, the
the upper
upper and
and lower
lower
A variance S is set associated with the expected noise reduction. Then, the upper and lower
envelope
envelope of
of the
the original
original signal
signal is
is obtained
obtained by
by calculating
calculating the
the local
local maximum/minimum.
maximum/minimum. The
The upper
upper
envelope of the original signal is obtained by calculating the local maximum/minimum. The upper
envelope
envelope is
is denoted
denoted as
as aaii while
while the
the lower
lower is
is bbii.. m
m is
is the
the arithmetic
arithmetic mean
mean of
of aaii and
and bbii.. The
The residual
residual signal
signal
envelope is denoted as ai while the lower is bi . m is the arithmetic mean of ai and bi . The residual signal
extracted
extracted from
from some
some information
information is
is represented
represented by
by h.
h. If
If the
the variance
variance of
of all
all hh obtained
obtained before
before SD
SDii is
is
extractedS,
from some
information
is represented
by h. Ifisthe
variance
of all h obtained
before SDi is less
less
less than
than S, then
then the
the first
first IMF
IMF will
will equal
equal hhii,, and
and the
the hhi+1
i+1 is the
the new
new pending
pending signal
signal S.
S.
thanThe
S, then the
first IMF
will equal
h , andoriginal
the hi+1signal
is the new pending
signalisS.
The total
total sum
sum of
of IMFs
IMFs can
can match
matchi the
the original
signal perfectly.
perfectly. The
The IMF
IMF is especially
especially effective
effective on
on
The
total
sum
of
IMFs
can
match
the
original
signal
perfectly.
The
IMF
is
especially
effective on
the
the local
local nonlinear
nonlinear distortion
distortion of
of the
the waveform,
waveform, showing
showing potential
potential signaling
signaling processes
processes and
and revealing
revealing
the local nonlinearchange
distortionthe
of the waveform,
showing potential signaling processes and revealing
the
the instantaneous
instantaneous change of
of the process
process as
as aa whole.
whole.
the instantaneous change of the process as a whole.
3.2.
Analysis of
Noise Reduction
on PD
Signal
3.2.
3.2. Analysis
Analysis of
of Noise
Noise Reduction
Reduction on
on PD
PD Signal
Signal
After
PD
current
signal
was
carried
(Figure
6)
were
obtained.
After
signal was
was carried
carried out
out by
by EMD,
EMD, the
the denoising
denoising results
results (Figure
(Figure 6)
6) were
wereobtained.
obtained.
After PD
PD current
current signal
out
by
EMD,
the
denoising
results

Figure 6. Original
Original signaland
and denoisesignal
signal of HFCT.
HFCT.
Figure
Figure 6.
6. Original signal
signal and denoise
denoise signal of
of HFCT.

As shown
shownin
Figure
6,
denoised
signal
has corrected
been
corrected
toextent,
some in
extent,
terms of
As
6,
denoised
signal
has
to
terms
of
As
shown
ininFigure
Figure
6, the
thethe
denoised
signal
has been
been
corrected
to some
some
extent,
in
terms in
of Equation
Equation
Equation
(1), for SNR.
(1),
for
(1),
for SNR.
SNR.
USp− pmax
SNR = 20 log10 U
(1)
UpSpSp−‐‐pppmax
max
UN
max
20
log
SNR
=
(1)
SNR = 20 log1010
(1)
U
UNp
max
Np‐‐ppmax

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2018, 11,
11, x1997
Energies 2018, 11, x FOR PEER REVIEW

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At t = 40 μs, the peak‐to‐peak amplitude of the original signal was 1.61 V. At t = 170 μs, the peak‐
At
4040
μs,µs,
theofthe
peak‐to‐peak
amplitude
of the
1.61
V. At
= V.
170
μs,t the
peak‐
Attamplitude
t= =
amplitude
signal
was
1.61
At
= 170
µs,
to‐peak
thepeak-to-peak
original signal
was 0.79
V.oforiginal
Atthe
t = original
40signal
μs, thewas
amplitude
of tthe
denoised
signal
to‐peak
amplitude
of
the
original
signal
was
0.79
V.
At
t
=
40
μs,
the
amplitude
of
the
denoised
signal
the
peak-to-peak
amplitude
of
the
original
signal
was
0.79
V.
At
t
=
40
µs,
the
amplitude
of
the
was 1.32 V. At t = 170 μs, the amplitude of the denoised signal was 0.65 V. Therefore, noise reduction
was
1.32
At t =was
170 linear
μs, the
amplitude
of
the amplitude
denoised
signal
was
0.65
Therefore,
noise
reduction
denoised
signal
1.32
V.relationship
At
t = 170 µs,
the
of thesignal
denoised
was 0.65
V.
Therefore,
does
not V.
change
the
between
the current
andV.signal
PD
magnitude.
SNR
of the
does
not
change
the
linear
relationship
between
the
current
signal
and
PD
magnitude.
SNR
of the
noise reduction
notin
change
the linear
original
signal isdoes
shown
Equation
(2): relationship between the current signal and PD magnitude.
original
signal
is shown
in is
Equation
(2):
SNR of the
original
signal
shown in
Equation (2):
1.61
SNR = 20 log 10 1.61 = 17 dB
(2)
0.23 = 17 dB
SNR = 20 log 101.61
(2)
SNR = 20 log10 0.23 = 17 dB
(2)
0.23
SNR of the denoised signal is shown in Equation (3):
SNR of the denoised signal is shown in Equation (3):
SNR of the denoised signal is shown in Equation (3):
1.32
SNR = 20 log 10 1.32 = 21 dB
(3)
0.12 = 21 dB
SNR = 20 log 10 1.32
(3)
SNR = 20 log10 0.12 = 21 dB
(3)
Comparing Equation (2) and Equation (3), SNR0.12
increased by 4 dB for PD current signals after
Comparing
Equation After
(2) and
Equation (3),relationship
SNR increased
by 4 PD
dB current
for PD current
signals
after
the EMD
noise reduction.
denoising,
between
output
by
theafter
HFCT
Comparing
Equation (2) and
Equationthe
(3), SNR increased
by 4 dB
for PD current
signals
the
the
EMD
noise reduction.
After denoising,
relationship between PD current output by the HFCT
and
PD
magnitude
wasAfter
obtained
(Figure
7).the
EMD
noise
reduction.
denoising,
the
relationship between PD current output by the HFCT and
and PD magnitude was obtained (Figure 7).
PD magnitude was obtained (Figure 7).

Figure 7. The response of the high‐frequency current transformer (HFCT) at a PD magnitude of 20 pC.
Figure7.7.The
Theresponse
responseofofthe
thehigh‐frequency
high-frequencycurrent
currenttransformer
transformer(HFCT)
(HFCT)atataaPD
PDmagnitude
magnitudeofof2020pC.
pC.
Figure

The peak‐to‐peak UHFCT was 40 mV when applied at 20 pC charge to PD model. A linear
The
HFCT
mV
when
applied
atatHFCT
20
charge
to
The peak‐to‐peak
peak-to-peak
Umagnitude
was4040
mV
when
appliedof
20 pC
pC(U
charge
to PD model. A
A linear
linear
HFCTwas
HFCT) can be obtained.
relationship
between PDU
(Q)
and
the response
) )can
relationship
relationship between
between PD
PD magnitude
magnitude (Q)
(Q) and
and the
the response
response of HFCT (UHFCT
canbebeobtained.
obtained.
HFCT
4. Results and Discussion
4. Results
Resultsand
andDiscussion
Discussion
4.
This section describes how the applied frequency influences the PD characteristics. The statistics
Thissection
section describeshow
how theapplied
appliedfrequency
frequency influences
influences the PD
PD characteristics. The
Thestatistics
statistics
of theThis
PD results describes
for 100 periodsthe
applying variable
frequencies ofthe
4 kHz,characteristics.
6 kHz, 8 kHz, 10 kHz,
and
of
the
PD
results
for
100
periods
applying
variable
frequencies
of
4
kHz,
6
kHz,
8
kHz,
10 kHz,
of
the
PD
results
for
100
periods
applying
variable
frequencies
of
4
kHz,
6
kHz,
8
kHz,
10
kHz,
and
12 kHz are shown in this section.
and
12 are
kHzshown
are shown
insection.
this section.
12
kHz
in this
4.1.
Partial
Discharge
Inception
Voltage
at
Different
Frequencies
4.1.Partial
PartialDischarge
DischargeInception
InceptionVoltage
Voltage at
at Different
Different Frequencies
Frequencies
4.1.
The
partial
discharge
inception
voltage
(PDIV)
at
different
frequencies
was
detected
multiple
The partial
partial discharge
discharge inception
inception voltage
voltage (PDIV)
(PDIV) at
at different
different frequencies
frequencies was
was detected
detected multiple
multiple
The
times
at
each
frequency.
The
amplitude
of
PDIV
is
U
inc, as shown in Figure 8.
times at
at each
each frequency.
frequency. The
The amplitude
amplitude of
of PDIV
PDIV is
is U
Uinc
asshown
shownin
inFigure
Figure8.8.
inc, ,as
times

Figure8.8.Partial
Partialdischarge
dischargeinception
inceptionvoltage
voltageat
atdifferent
different frequencies.
frequencies.
Figure
Figure 8. Partial discharge inception voltage at different frequencies.

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The measurement results in Figure 8 show that Uinc was in a range at a fixed frequency. An
The measurement results in Figure 8 show that Uinc was in a range at a fixed frequency. An
increasing tendency of the range was evident while increasing the frequency. At 8 kHz, the
The measurement
results
in was
Figure
8 show
that increasing
Uinc was in
range at a At
fixed
frequency.
increasing
tendency of the
range
evident
while
thea frequency.
8 kHz,
the
distribution range of Uinc was minimal with a high measurement accuracy.
An
increasing
tendency
of
the
range
was
evident
while
increasing
the
frequency.
At
8
kHz,
distribution range of Uinc was minimal with a high measurement accuracy.
the distribution range of Uinc was minimal with a high measurement accuracy.
4.2. Results of PD Spectrum at
Different Frequencies
4.2. Results of PD Spectrum at Different Frequencies
4.2. Results
of PD
Spectrum at
Frequencies
The basic
parameters
forDifferent
characterizing
PD patterns are phase angle (Φ) in degrees, discharge
The basic parameters for characterizing PD patterns are phase angle (Φ) in degrees, discharge
magnitude
(Q) inparameters
pC, and number
of discharges (N).
A patterns
3‐D pattern
is phase
shown in
Figure 9a in
and phase‐
The basic
for of
characterizing
magnitude
(Q) in pC,
and number
discharges (N).PD
A 3‐D
patternare
is shown
inangle
Figure(Φ)
9a and degrees,
phase‐
resolved
partial
discharge
(PRPD)
is
presented
in
Figure
9b.
discharge
magnitude
(Q)
in
pC,
and
number
of
discharges
(N).
A
3-D
pattern
is
shown
in
Figure
9a
resolved partial discharge (PRPD) is presented in Figure 9b.
and phase-resolved partial discharge (PRPD) is presented in Figure 9b.

(a) Φ‐Q‐N 3‐D plots for PD at f = 6 kHz
(a) Φ‐Q‐N 3‐D plots for PD at f = 6 kHz

(b) Phase‐resolved partial discharge at f = 6 kHz
(b) Phase‐resolved partial discharge at f = 6 kHz

Figure 9. Typical PD plots at f = 6 kHz.
Figure
Figure9.9.Typical
TypicalPD
PDplots
plotsatatf f= =6 6kHz.
kHz.

4.2.1. PD Q‐Φ Scatter Plot at Different Frequencies
4.2.1. PD Q‐Φ Scatter Plot at Different Frequencies
4.2.1. PD Q-Φ Scatter Plot at Different Frequencies
The main detection parameter of PD is PD magnitude (Q), which is the basis of other detection
The main detection parameter of PD is PD magnitude (Q), which is the basis of other detection
The main
detection
ofin
PDFigure
is PD 10
magnitude
(Q), whichstatistic
is the basis
of other
detection
parameters.
The
PD U‐Φparameter
scatter plot
is the distribution
diagram
of discharge
parameters. The PD U‐Φ scatter plot in Figure 10 is the distribution statistic diagram of discharge
parameters.
The
PD
U-Φ
scatter
plot
in
Figure
10
is
the
distribution
statistic
diagram
of
discharge
magnitude in each phase.
magnitude in each phase.
magnitude in each phase.

(a) f = 4 kHz
(a) f = 4 kHz

(b) f = 6 kHz
(b) f = 6 kHz

(c) f = 8 kHz
(c) f = 8 kHz

(d) f = 10 kHz
(d) f = 10 kHz
Figure 10. Cont.

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(e) f = 12 kHz
(e) f = 12 kHz
Figure 10. PD l Q‐Φ Scatter Plot at different frequencies
Figure
Figure 10.
10. PD
PD ll Q‐Φ
Q-Φ Scatter
Scatter Plot
Plot at
at different
different frequencies
frequencies

As shown in Figure 10, the scattered pattern of PD current in the semi‐axes was an ‘hourglass’
AsAs
shown
in Figure 10,
the scattered
pattern of waist
PD current
in thinner.
the semi‐axes
was anthat
‘hourglass’
shape.
the frequency
the ‘hourglass’
became
This means
the PD
As shown
in Figure increased,
10, the scattered
pattern of PD current
in the semi-axes
was an ‘hourglass’
shape.
As
the
frequency
increased,
the
‘hourglass’
waist
became
thinner.
This
means
that
the PD
magnitude
in
the
low
frequencies
was
more
polarized.
shape. As the frequency increased, the ‘hourglass’ waist became thinner. This means that the PD
magnitude in the low frequencies was more polarized.
magnitude in the low frequencies was more polarized.
4.2.2. PD N‐Φ Spectrogram at Different Frequencies
4.2.2. PD N‐Φ Spectrogram at Different Frequencies
4.2.2. PD N-Φ Spectrogram at Different Frequencies
The PD N‐Φ spectrogram illustrates the PD proper phase displaying the occurrence time of PD.
The PD11
N‐Φ
spectrogram
illustrates
the PD proper
phase
displaying
the occurrence
time
of PD.
Figure
shows
that almost
no PD occurred
near the
power
zero crossing
point. PDtime
current
N‐
The PD N-Φ
spectrogram
illustrates
the PD proper
phase
displaying
the occurrence
of PD.
Figure
11
shows
that
almost
no
PD
occurred
near
the
power
zero
crossing
point.
PD
current
N‐
Φ spectra
an almost
‘M’ shape,
often
callednear
a “rabbit
ear” shape.
A transformation
of the
Figureappeared
11 showsasthat
no PD
occurred
the power
zero crossing
point. PD current
Φ
spectra
appeared
as
an
‘M’
shape,
often
called
a
“rabbit
ear”
shape.
A
transformation
of
the
spectrogram
the semi‐period
a right
an acute
triangle
with increasing
N-Φ spectra in
appeared
as an ‘M’from
shape,
oftentriangle
called ato“rabbit
ear”
shape.occurred
A transformation
of the
spectrogram
in the
semi‐period
from distribution
a right triangle
to an acute
triangle
occurred
increasing
frequency.
From
Figure
11, PD phase
information
as atriangle
phase region
andwith
phase
center is
spectrogram
in the
semi-period
from a right triangle
to an acute
occurred
with
increasing
frequency.
From1.Figure 11, PD phase distribution information as a phase region and phase center is
shown
in Table
frequency.
From Figure 11, PD phase distribution information as a phase region and phase center is
shown in Table 1.
shown in Table 1.

(a) f = 4 kHz
(a) f = 4 kHz

(b) f = 6 kHz
(b) f = 6 kHz

(c) f = 8 kHz
(c) f = 8 kHz

(d) f = 10 kHz
(d) f = 10 kHz
Figure 11. Cont.

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(e) f = 12 kHz
Figure
Figure 11.
11. PD
PD N‐Φ
N-Φ Spectrogram
Spectrogram at
at different
different frequencies.
frequencies.
Table 1. The partial discharge (PD) phase region and displacement phase center at different
Table 1. The partial discharge (PD) phase region and displacement phase center at different frequencies.
frequencies.
Frequency
Frequency

4 kHz
4 kHz
6 kHz
6 kHz
8 kHz
8 kHz
10 kHz
10 kHz
12 kHz
12 kHz

Positive
Positive
Phase
Region
(°) (◦ ) Phase
Phase
Region
PhaseCenter
Center(°)(◦ )
(30,(30,
150)150)
6060
(30,(30,
150)150)
5555
(50,(50,
150)150)
7575
(50,(50,
150)150)
8080
110
(60,(60,
150)150)
110

Negative
Negative
◦)
PhaseRegion
Region((°)
Phase
Center
Phase
Phase
Center
(◦ )(°)
(200,
340)
230
(200, 340)
230
(200, 330)
330)
(200,
220220
(200,
340)
(200, 340)
250250
(200,
300)
(200, 300)
230230
(200,
230230
(200, 280)
280)

PD
PD phase
phase distribution
distribution was
was closely
closely related
related to
to the
the polarity
polarity of
of power
power and
and frequency.
frequency. The
The frequency
frequency
increase
led
to
three
phenomena
on
the
PD
phase
distribution:
increase led to three phenomena on the PD phase distribution:

Initial PD discharge phase in the positive semi‐period gradually shifted to the right, the end PD

Initial PD discharge phase in the positive semi-period gradually shifted to the right, the end PD
phase fluctuated at 150°, and the PD phase region decreased;
phase fluctuated at 150◦ , and the PD phase region decreased;

Initial PD phase in the negative semi‐period fluctuated at 200°◦ and the end PD phase gradually

Initial PD phase in the negative semi-period fluctuated at 200 and the end PD phase gradually
shifted to the left, giving rise to the decreasing PD phase region;
shifted to the left, giving rise to the decreasing PD phase region;

Positive discharge center phase shifted to the right with increasing frequency; the negative
• discharge
Positive discharge
center
shiftedaround
to the 230°.
right with increasing frequency; the negative
center phase
wasphase
maintained
discharge center phase was maintained around 230◦ .
4.2.3. PD Statistical Data at Different Frequencies
4.2.3. PD Statistical Data at Different Frequencies
The average magnitude of each discharge (Qave) and N at two polarities of power were detected
The average magnitude of each discharge (Qave ) and N at two polarities of power were detected
through statistics. The sum of PD magnitude in 100 periods was marked as Qall. The PD parameters
through statistics. The sum of PD magnitude in 100 periods was marked as Qall . The PD parameters
are shown in Table 2.
are shown in Table 2.
Table
2. Partial
characteristic parameters.
parameters.
Table 2.
Partial discharge
discharge characteristic
Polarity
Polarity
Positive
Positive
Negative
Negative

Frequency 4 kHz
Frequency
4 2042
kHz
N
ave (pC)
1235
QN
2042
Qave (pC)
1235
N
2261
2261
ave (pC)
1235
QN
Qave (pC)
1235
N
4303
Positive and Negative
4303
all (μC)
5.3
QN
Positive and Negative
Qall (µC)
5.3

6 kHz 8 kHz 10 kHz 12 kHz
6 kHz 3703
8 kHz 2839
10 kHz 1717
12 kHz
1924
1019
1216
1924
3703 9142839 867 1717
1019
1216 2262914 1241 867
2634
3450
2634
3450 9172262 886 1241
1006
1241
1006
1241 5101917 2958 886
4559
6523
4559
6523 4.75101 2.6 2958
4.6
8.0
4.6
8.0
4.7
2.6

According to Table 2, Qave and N values at two polarities of power were approximated at each
According
to Table of
2, Q
N little
values
at two
of power
were approximated
frequency.
The polarity
power
had
effect
on polarities
PD number
and magnitude.
N and Qallatineach
100
ave and
frequency.
The
polarity
of
power
had
little
effect
on
PD
number
and
magnitude.
N
and
Q
periods are shown in Figure 12.
all in
100 periods are shown in Figure 12.

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10 of 13
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Figure
in test.
test.
Figure 12.
12. PD
PD number
number and
and magnitude
magnitude at
at different
different frequencies
frequencies in

The wave of PD numbers and magnitudes exist in an ascent stage at lower frequencies and tend
The wave of PD numbers and magnitudes exist in an ascent stage at lower frequencies and tend
to decline at higher frequencies, resulting in a frequency‐induced inflection point.
to decline at higher frequencies, resulting in a frequency-induced inflection point.
4.3. Frequency‐Dependant PD Number and Magnitude
4.3. Frequency-Dependant PD Number and Magnitude
PD
number and magnitude are the main parameters describing PD. Therefore, an analysis on
PD number and magnitude are the main parameters describing PD. Therefore, an analysis on
changing the PD number and magnitude is described in this part.
changing the PD number and magnitude is described in this part.
Space charge distribution directly determines the characteristics of the partial discharge. The
Space charge distribution directly determines the characteristics of the partial discharge.
frequency mainly affects PD by affecting the polarization degree and the diffusion process of the
The frequency mainly affects PD by affecting the polarization degree and the diffusion process of the
space charge. Under AC voltage, the movement of charged particles occurs in the air medium
space charge. Under AC voltage, the movement of charged particles occurs in the air medium between
between the electrodes in the discharge model, causing the air to polarize. The degree of polarization
the electrodes in the discharge model, causing the air to polarize. The degree of polarization can be
can be represented by g [20]:
represented by g [20]:
2
εw
ε w 2ττ
(4)
g =g γ= +
γ +1 + w22τ 22
(4)
1+ w τ
where g is an equivalent parameter of space-charge polarization in air (fS/m); γ is the conductivity of
where g is an equivalent parameter of space‐charge
polarization in air (fS/m); γ is the conductivity
air (fS/m) where γ = 0.0231 fS/m at 25 ◦ C, 110 kPa; ε is the relative dielectric constant (F/m) where
0.0231
fS/mkPa;
of
(fS/m)
at w
25is°C,
kPa; electric
ε is the
relative
dielectric
constant (F/m)
12 F/mγat=25
◦ C, 110
ε =air
8.86
× 10−where
the110
applied
field
angular
frequency.
−12
110 kPa; wIt tends
is the to
applied
electric
fieldofangular
frequency.
where
× 10 F/m at 25 °C,parameter.
g isε a=8.86
frequency-dependent
increase
because
the increase
in frequency.
A high
a strengthenedparameter.
air polarization,
the unevenness
of the in
electric
field.
g isga means
frequency‐dependent
It tendsintensifying
to increase because
of the increase
frequency.
PDhigh
occurs
easily awhen
the electric
is non-uniform.
Therefore,
high frequency
results
in afield.
high PD
A
g means
strengthened
airfield
polarization,
intensifying
the unevenness
of the
electric
numbereasily
and magnitude.
However,
the polarization
process
space charge
takes
certain
occurs
when the electric
fieldbecause
is non‐uniform.
Therefore,
high of
frequency
results
in a ahigh
PD
amount
of
time.
Once
the
period
at
high
frequency
less
than
polarization
time,
the
polarization
effect
number and magnitude. However, because the polarization process of space charge takes a certain
of spaceofcharge
no longer
occupies
the frequency
dominantless
position
in affecting time,
the partial
discharge effect
at an
amount
time. Once
the period
at high
than polarization
the polarization
over-high
frequency.
of
space charge
no longer occupies the dominant position in affecting the partial discharge at an over‐
high Discharge
frequency.is a neutralization process of charged particles. When PD occurs, most of the charged
particles
are neutralized
and release
energy.
handful
of charged
particles
are retained
Discharge
is a neutralization
process
of A
charged
particles.
When
PD occurs,
most ofon
theinsulated
charged
surfaces, are
called
the retention
[21].
SpaceAcharge
diffuses
along particles
the cutoffare
surface
under
action
particles
neutralized
andeffect
release
energy.
handful
of charged
retained
on the
insulated
of an electric
field
theeffect
electrodes.
The dissipation
process
of space
charges
is described
by
surfaces,
called
thebetween
retention
[21]. Space
charge diffuses
along
the cutoff
surface
under the
Equation
(5):electric field between the electrodes. The dissipation process of space charges is described
action
of an
− ∆t
by Equation (5):
N (t + ∆t) = N (t)e τd
(5)
q

q

Δt

where Nq is the number of space charge; ∆t is the discharge−interval
of PD (s); τd is the time between
(5)
Nq (t + Δt) = Nq (t)e τ d
the occurrence of the power voltage amplitude larger than PDIV and the first discharge [22]:

where N q is the number of space charge; Δt is the discharge
!!−1 of PD (s); τ d is the time

interval
ρ
U −β
between the occurrence of the
voltage
τd power
= Vvoi
Cd φd amplitude
p 1 − larger than PDIV and the first discharge [22]:
(6)
p
Uinc

 U
ρ
 p  1 − 
 p    Uinc

τ d =  Vvoi Cdφd 











(6)

where U is the amplitude of the source (V); Vvoi is the equivalent gas volume exposed to electric field
(m³); Cd is the radiation ionization coefficient; Φd is the radiation quantum flux density (Wb); ρ is

Energies 2018, 11, 1997

11 of 13

the gas density (kg/m³); p is the intensity of air pressure (Pa); U inc is the value of PDIV (V). β is a
positive constant.
where U is the amplitude of the source
(V); V is the equivalent gas volume exposed to electric field
The value of Cd × Φd is 2 × 106 kg−1·s−1 invoiair and p = 110 kPa. The value of ρ/p is 10−5 kg·m−3·Pa−1 at
(m3 ); Cd is the radiation ionization coefficient; Φd is the radiation quantum flux density (Wb); ρ is
U
3 ); p is the intensity of air pressure
the25gas
(Pa); Uincincrease
is the value
of U
PDIV
(V).increases
β is a
τ d is a(kg/m
°C.density
monotonic
decreasing function of
. Frequency
causes
and
inc
Uinc
positive constant.
The value
of Cd ×
106 kg−1 ·Therefore,
s−1 in air τandincreases
p = 110 with
kPa. anThe
value of
ρ/p is
Φd is 2U×decreases.
according
to Figure
8; thus,
increasing
frequency.
d
U

5

3

1

U
10 kg·m ·Pa at 25 C. τd is aincmonotonic decreasing function of U . Frequency increase causes
inc

U
Uinc
and increases
according
to Figure
8; thus,
Therefore,
with an increasing
Meanwhile,
a rapid
change
of voltage
results
in a decrease
in Δt .τdNincreases
Uinc decreases.
q is a monotone decreasing
frequency. Meanwhile, a rapid change of voltage results in a decrease in ∆t. Nq is a monotone
function of Δt over τ . N gradually increases due to the decrease of Δt and the increase of τ ,
decreasing function of ∆t dover qτd . Nq gradually increases due to the decrease of ∆t and the increase of d
the voltage
voltage changes
changes after
after a
τd ,meaning
meaningthat
thatspace
spacecharges
charges are
are intrinsically
intrinsically insulated.
insulated. The
The polarity
polarity of
of the
half‐cycle but
but space
spacecharge
chargeremains
remainson
onthe
theinsulating
insulatingsurface,
surface,resulting
resultingininananelectric
electric
field
that
a half-cycle
field
that
is is
opposite
to
the
power
source
and
suppresses
the
partial
discharge.
opposite to the power source and suppresses the partial discharge.
up,
as shown
in 13,
Figure
13, a theoretical
(f0) exists. The impact of the
ToTo
sumsum
up, as
shown
in Figure
a theoretical
frequency (ffrequency
0 ) exists. The impact of the polarization
polarization
effecteffect
and retention
effect on PD
are approximately
opposite.
effect
and retention
on PD magnitude
aremagnitude
approximately
equivalent butequivalent
opposite. but
Therefore,
Therefore,
the
maximum
PD
magnitude
was
reached
at
f
0
.
the maximum PD magnitude was reached at f 0 .

f0

Polarization
process

Retention
effect

Figure
Theoretical
analysis
number
and
magnitude
at different
frequencies.
Figure
13.13.
Theoretical
analysis
of of
PDPD
number
and
magnitude
at different
frequencies.

The theoretical results of frequency‐dependent PD are consistent with the test results. When
The theoretical results of frequency-dependent PD are consistent with the test results.
f < f 0 , the polarization process is greater than the retention effect, so that the number and magnitude
When f < f 0 , the polarization process is greater than the retention effect, so that the number and
of PD increase
with anwith
increase
in frequency.
WhenWhen
, the
polarization
process
was
f > ff0 >
magnitude
of PD increase
an increase
in frequency.
f 0 , the
polarization
process
wasnot
effectcaused
causedonly
onlythe
thePD
PD
number
and
notaccomplished
accomplishedininthe
thesemi‐period.
semi-period. Therefore,
Therefore, the retention effect
number
and
magnitude
increase
with
increasing
frequency.
magnitude
to to
increase
with
increasing
frequency.
5. 5.
Conclusions
Conclusions
In In
this
manuscript,
to to
detect
partial
discharges
at at
different
this
manuscript,a abroadband
broadbandHFCT
HFCTwas
wasused
used
detect
partial
discharges
different
frequencies
from
4
kHz
to
12
kHz.
EMD
was
used
for
denoising
pulses.
As
a
result,
the
SNR
frequencies from 4 kHz to 12 kHz. EMD was used for
As a result, the SNR ofofthe
thedata
datawas
wasincreased
increasedbyby4 4dB.
dB.After
Afterfurther
furtherstatistical
statistical
analysis,
the
phenomena
Q-Φ
scatter
analysis,
the
phenomena
of of
PDPD
Q‐Φ
scatter
plot
plot
and
PDN‐Φ
N-Φspectrogram
spectrogramininphase,
phase, number,
number, and magnitude
region
and
PD
magnitudewere
wereanalyzed.
analyzed.The
ThePD
PDphase
phase
region
was
monotone,
decreasing
to to
a frequency
range
of of
4 kHz
to to
12 12
kHz.
The
PDPD
number
and
magnitude
was
monotone,
decreasing
a frequency
range
4 kHz
kHz.
The
number
and
magnitude
first increased and then decreased in the specific frequency range. Air medium polarization process
and retention effect determined PD number (N) and magnitude (Q) at different frequency values.
Finally, a frequency of 8 kHz was selected in this special case, being a suitable working frequency for
detecting insulation defects with high precision of the acquisition of the PDIV values and obtaining
the best amplification effect for insulation defects. Regarding the suspension PD model at various
working frequencies, the PDIV value was lower and the PD magnitude and number were larger at the

Energies 2018, 11, 1997

12 of 13

same voltage level. Thus, 8 kHz can be used to assess insulation status of HF transformers with the
consideration of frequency-dependent effects.
Author Contributions: J.J. and M.Z. conceived and designed the experiments and algorithm; M.Z. performed
the experiments; Z.C. and M.C. analyzed the data; H.L. and R.A. provided the insight and technical expertise to
improve the quality of this paper; M.Z. and J.J. wrote the paper.
Funding: This research was funded in part by the Fundamental Research Funds for the Central Universities
(NOs. XCA17003-04, NS2018027), Natural Science Foundation of Jiangsu Province (BK20170786), the State Key
Laboratory of Alternate Electrical Power System with Renewable Energy Sources (Grant No. LAPS17012) and
State Grid Zhejiang Electric Power Co. Ltd. (5211DS17001C).
Conflicts of Interest: The authors declare no conflict of interest.

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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
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