Stochastic noise removal on partial discharge measurement
for transformer insulation diagnosis
Author
Chan, Jeffery, Ma, Hui, Saha, Tapan, Ekanayake, Chandima
Published
2014
Conference Title
2014 IEEE Power & Energy Society General Meeting Proceedings
Version
Accepted Manuscript (AM)
DOI
https://doi.org/10.1109/PESGM.2014.6938913
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Stochastic Noise Removal on Partial Discharge
Measurement for Transformer Insulation Diagnosis
Jeffery C. Chan, Student Member, IEEE, Hui Ma, Member, IEEE, Tapan K. Saha, Senior Member, IEEE, Chandima
Ekanayake, Member, IEEE
The University of Queensland
Brisbane, Australia
j.chan@uqconnect.edu.au, huima@itee.uq.edu.au, saha@itee.uq.edu.au, chandima@itee.uq.edu.au
Abstract—Measurement of partial discharge (PD) paves a way
for transformer insulation diagnosis. However, noise always
interferes with PD signals and can jeopardize the diagnostic
reliability. Therefore, it is necessary to adopt signal processing
techniques to remove noise from collected signals. Among
various types of noise, stochastic noise is considerably difficult to
remove due to its similarity with PD signals. This paper
proposes an effective method, which adopts fractal dimension
and entropy analyses to remove stochastic noise. To verify the
proposed method, PD measurements have been performed on a
number of experimental models and a substation transformer.
Results prove that PD signals can be extracted while the noise
can be eliminated from collected noise-corrupted signals by
using the proposed method. A comparison with a wavelet
transform-based noise removal method has also been made in
the paper.
Index Terms—De-noising, entropy, fractal dimension, partial
discharge (PD), transformer.
I. I
NTRODUCTION
Transformer is one of the most crucial assets in electricity
networks and the transformer’s health conditions highly
depend on its insulation system. Partial discharge (PD)
measurement is an effective method for evaluating the
insulation system [1], [2]. However, PD signals collected from
PD measurements in substation environment are always
overwhelmed by a variety of interference and noise. This can
pose significant difficulties in recognizing PD patterns
generated from corresponding insulation defects in a
transformer and making explicit diagnosis on its insulation
system.
There are different types of noise that can exist during PD
measurements, such as white noise, periodic impulsive and
sinusoidal noise, and stochastic noise [3]-[6]. Among the
above types of noise, stochastic noise is considerably difficult
to remove and limited research works have been reported in
the literature. In [7], neural network is used to remove
stochastic noise. However, this method requires a training
process to create a database for classifying PD pulses
generated by different PD sources. For those situations that
collected PD signals do not belong to the database can induce
misclassifications. The major difficulty on removing
stochastic noise is due to its similarity in frequency
characteristics with PD signals [6]. Therefore, conventional
methods such as notch filtering and gating method are not able
to provide an effective filtering for stochastic noise.
Recently, wavelet transform attains a high attention on
removing noise from collected signals for PD measurements
[3]-[6]. The principle of wavelet transform is based on signal
decomposition through selected wavelet functions. PD signals
can be separated from noise in the decomposed signals with
different frequency scales. By applying thresholds to the
decomposed signals and performing signal reconstruction, PD
signals can be retrieved while noise can be removed. However,
frequency scales of stochastic noise can be the same as those
of PD signals. This implies that PD signals may not be
distinguished from stochastic noise using wavelet transform.
Since no research works address this issue, this paper (Section
V) examines the capability on using wavelet transform for
removing stochastic noise.
This paper proposes a hybrid of fractal dimension and
entropy analyses for effectively distinguishing and extracting
PD signals from collected signals corrupted by stochastic
noise. Fractal dimension is a method to describe complex
shapes, such as coastlines and mountains, by using fractal sets
[9], while entropy is a measure of uncertainty in a signal. In
the proposed method, fractal dimension is used to separate PD
signals from the noise, which locates in distinctive power
cycles from the PD signals. Meanwhile, entropy is calculated
to distinguish and extract PD signals from the noise, which
distributes over the power cycles with PD signals.
The paper is organized as follows. Section II presents
experimental set-up of PD measurements. Section III provides
a brief introduction on fractal dimension and entropy. Section
IV describes the proposed method on stochastic noise removal
and PD signal extraction from raw signals (i.e. noise-corrupted
signals) collected from PD measurements. Section V presents
This work was supported by the Australia Research Council (ARC) on
Linkage Grant.
results by applying the proposed method to measured signals
obtained from both experimental models and a substation
transformer. A comparison with a wavelet transform-based
noise removal method is also provided. Section VI concludes
the paper.
II. E
XPERIMENTAL
S
ET
-
UP
The PD measurement set-up used in this paper is based on
IEC 60270 standard (Fig. 1) [10]. In the set-up, V is a voltage
source, C
a
is a test object (i.e. a PD experimental model or a
transformer), C
k
is a coupling capacitor, Z is measuring
impedance, and M is a data acquisition and processing system.
PD experimental models simulate PD sources using different
configurations (Fig. 2). The model shown in Fig. 2a simulates
discharge with flat cavity by putting four pressboards
(diameter = 40 mm) together in transformer oil with a cavity
(diameter = 15 mm) at the center. The model shown in Fig. 2b
simulates corona with 50 mm distance between a needle and
grounding. The model shown in Fig. 2c placed in air simulates
surface discharge by using one pressboard putting between the
needle and grounding. These experimental models were used
to generate both single and multiple PD sources.
Figure 1. PD measurement set-up.
(a) Discharge with flat
cavity
(b) Corona
(c) Surface
discharge
Figure 2. PD experimental models.
III. I
NTRODUCTION ON
F
RACTAL
D
IMENSION AND
E
NTROPY
A. Fractal Dimension
The concept of fractal dimension refers to changes of a
pattern’s details with respect to the scales used for measuring
this pattern. A number of methods including box-counting,
variance, and spectral methods are used for calculating fractal
dimension [11]. This paper adopts box-counting for its
simplicity and efficiency [12]. Fractal dimension (FD) of a
signal in Euclidean space is defined as [13]:
)1log(
)(log
lim
0
ε
ε
=
→ε
N
FD
(1)
where
)(εN
is the least number of boxes with side length
ε
to cover the signal.
A PD source caused by a particular insulation defect can
exhibit a unique PD pattern. Due to its ability of representing
various patterns and describing complex shapes, fractal
dimension has been used for feature extraction and recognition
of PD sources [13], [14]. This paper makes use of fractal
dimension to remove and quantify severity of noise.
B. Entropy
When PD signals and noise merge together, fractal
dimension alone may not be able to recover PD signals and
thus entropy is used. Entropy is a measure of disorder in a
random variable. A larger value of entropy relates to more
chaotic data [15]. For a signal
[
]
n
xxxX ,...,,
21
=
, its entropy,
(
)
XH
, is defined as:
( )
∑
=
−=
n
i
ii
xpxpXH
1
2
)(log)(
(2)
where
)(
i
xp
is the probability mass function of
i
x
.
This paper adopts entropy to find how abundant
information is in each box of fractal dimension. This can help
to differentiate PD signals from noise. Next section will
provide more details on the application of fractal dimension
and entropy for stochastic noise removal on PD measurements.
IV. P
ROPOSED
M
ETHOD ON
S
TOCHASTIC
N
OISE
R
EMOVAL
Fig. 3 depicts the flowchart of the proposed stochastic
noise removal method for PD measurements. Firstly, a
collected one-dimensional (1D) noise-corrupted signal
consisting of both PD signal and stochastic noise is
transformed into a two-dimensional (2D) signal. In this
transformation, the original signal in a power cycle is
converted to 512 x 512 pixels for accurately representing the
signal while still maintaining reasonable processing time in
subsequent fractal dimension and entropy calculations. Then,
fractal dimension is calculated on the transformed 2D signal in
each power cycle with different side lengths of boxs, 2
x
, where
[
]
nx ,...,2,1=
. If severe noise presents in a particular power
cycle, the value of fractal dimension in this power cycle is
different from that of others. Thus, it is able to indicate the
present of noise. Subsequently, the noise can be removed by
discarding the signal in the power cycle with noise and
selecting the signals in other cycles.
Figure 3. Proposed stochastic noise removal method.
Since noise may locate in every or most of power cycles
with similar fractal dimension values, using fractal dimension
alone may not be able to completely distinguish and separate
PD signals from noise. Moreover, even at the situations that
fractal dimension can distinguish noise appearing at most of
power cycles; it is still not wise to discard all signals located
in those power cycles. Therefore, entropy is calculated in each
box within each power cycle.
For a signal generated by stochastic noise, if it locates in a
particular box in a power cycle, it is unlikely present at the
same box in other power cycles when compared with PD
signals. Based on this assumption, entropy value of the noise
in each box is not as high as that of PD signals. After adding
entropy values of the same box for every power cycle together
and using color to represent the sum (the highest to lowest
values are represented by a colormap ranging from red, orange,
yellow, cyan, to blue), PD signals (i.e. noise-removed signals)
can be identified and subsequently extracted from noise-
corrupted signals.
V. R
ESULTS AND
D
ISCUSSIONS
To evaluate the proposed method on stochastic noise
removal, PD signals were collected from PD measurements on
the experimental models (Fig. 2). PD signals were also
collected from a PD measurement on a 5 MVA power
transformer for further evaluation of the proposed method. A
comparison with a wavelet transform-based noise removal
method has also been made in this section to justify the
effectiveness of the proposed method.
A. Noise Removal Evaluation on PD Experimental Models
Fig. 4 presents noise removal results on a PD measurement
performed for the PD experimental model of discharge with
flat cavity (i.e. Fig. 2a). From Fig. 4a (original PD
measurement signal), it can be observed that the PD signal
locates periodically in most of power cycles. Severe stochastic
noise occurs at the 1
st
and 2
nd
power cycles where relatively
insignificant noise can be found at the 3
rd
power cycle. The
stochastic noise was generated by occasional discharges from
the transformer supplying voltage to the PD measurement
system and the coupling capacitor in the measurement circuit
(Fig. 1). This is because both the transformer and coupling
capacitor have been used for more than 20 years and cannot be
regarded as discharge free.
Fig. 4b presents normalized results of fractal dimension in
each power cycle with different side lengths of boxes. The
numbers in Fig. 4b represent the power cycles’ numbers. From
the figure, it can be seen that fractal dimensions from the 1
st
to
the 3
rd
cycles are separated from those of other cycles in most
of side lengths. The fractal dimension of the 3
rd
cycle
containing minor noise is close to those from the 4
th
to the 10
th
cycles. By contrast, fractal dimensions of the 1
st
and 2
nd
cycles
containing severe noise are relatively far from those from the
4
th
to the 10
th
cycles. These results can be used for
distinguishing and separating PD signals from noise.
By rejecting signals in the first three power cycles and
combining the signals in the remaining cycles into one cycle,
phase-resolved partial discharge (PRPD) pattern can be
obtained (Fig. 4d). PRPD patterns reveal signals distribution
with respect to phase angles of applied test voltages [8]. Fig.
4c is the original PRPD without applying the proposed noise
removal method. It can be seen that PD pattern in the original
PRPD is contaminated by stochastic noise. This demonstrates
that the original PRPD cannot fully represent the PD pattern
caused by the corresponding insulation defect (i.e. discharge
with flat cavity) and thus may not be suitable for transformer
insulation diagnosis.
(a) Original signal
(b) Fractal dimension
(c) Original phase-resolved partial
discharge (PRPD)
(d) Noise-removed phase-resolved
partial discharge (PRPD)
Figure 4. Noise removal results of discharge with flat cavity.
(Note: The numbers in Fig. 4b represent power cycles' numbers)
The results in Fig. 4 prove that fractal dimension used by
the proposed method is capable of identifying and removing
stochastic noise. It can also indicate severity of noise by
comparing its value of signal in each power cycle. For those
signals that noise is located in every power cycle and the
signals themselves have similar values of fractal dimensions,
entropy is employed to further eliminate the noise. The results
of applying entropy for removing noise are presented in Fig. 5.
(a) Original signal
(b) Original signal (magnified)
(c) Original phase-resolved partial
discharge (PRPD)
(d) Noise-removed phase-resolved
partial discharge (PRPD, magnified)
Figure 5. Noise removal results of corona.
(Note: In Fig. 5d the pulses in blue color are stochastic noise)
PD signal
In Fig. 5, the PD signal is caused by corona (Fig. 2b).
During the measurement, the applied voltage was below 5 kV
and distance between the needle and grounding was kept at
50 mm. The purpose of such arrangement is to generate
corona with small amplitudes (when compared with the noise)
for evaluating performance of the proposed noise removal
method on revealing small-amplitude PD signals. From the
original signal and its magnification (Fig. 5a and Fig. 5b),
noise can be observed in most of power cycles. In contrast,
the discharge signals (indicated by red arrows, Fig. 5b) are
hardly identified due to their relatively small amplitudes.
Though some noise can be identified in some power cycles
and removed with fractal dimension calculation, other noise
still presents in the remaining power cycles (since the signals
in these power cycles have similar fractal dimension values).
Through calculating entropy in each box of fractal dimension
in each cycle and then combining all entropy values into a
single cycle, noise-removed PRPD is obtained (Fig. 5d). PD
signal is clearly identified (the pulses represented by blue
color are stochastic noise). However, in the original PRPD
without applying the proposed noise removal method, PD
signal is submerged in noise (Fig. 5c).
Fig. 6 presents noise removal results on a PD measurement
performed for the PD experimental model due to surface
discharge (Fig. 2c). It again demonstrates the applicability of
the proposed method on removing the stochastic noise and
extracting PD signals.
(a) Original signal
(b) Original signal (magnified)
(c) Original phase-resolved partial
discharge (PRPD)
(d) Noise-removed phase-resolved
partial discharge (PRPD)
Figure 6. Noise removal results of surface discharge.
In field PD measurements of transformers, multiple PD
sources may always co-exist. Therefore, it is necessary to
evaluate the performance of the proposed method on PD
measurements of multiple PD sources. Fig. 7 presents noise
removal results on multiple PD sources, which combine
discharge with flat cavity and corona. Fig. 8 presents the
results of another multiple PD sources, which combine
discharge with flat cavity and surface discharge. It can be seen
from both figures that the propose method can effectively
remove stocahstic noise while PD signals generated by
multiple PD sources can be retrieved.
(a) Original signal
(b) Original signal (magnified)
(c) Original phase-resolved partial
discharge (PRPD)
(d) Noise-removed phase-resolved
partial discharge (PRPD)
Figure 7. Noise removal results of discharge with flat cavity and corona.
(a) Original signal
(b) Original signal (magnified)
(c) Original phase-resolved partial
discharge (PRPD)
(d) Noise-removed phase-resolved
partial discharge (PRPD)
Figure 8. Noise removal results of discharge with flat cavity and surface
discharge.
B. Noise Removal Evaluation on a Substation Transformer
The proposed method is also applied to extract PD signals
collected from a PD measurement on a 5 MVA power
transformer with 22 kV test voltage as shown in Fig. 9.
It can be seen that the original PD signal is immersed in
noise and hardly to be identified (Fig. 9a to Fig. 9c). On the
contrary, PD signal can be revealed by using the proposed
method (Fig. 9d). The PD signal located near the negative
cycle may be related to corona, while the PD signal located in
both negative and positive cycles may be generated by internal
discharge.
