INTRODUCTION
Online condition monitoring is mandatory for fault detection and analysis of
power system equipments. Condition monitoring is continuously measurement of
related quantities such as currents, voltages, active and reactive powers, temperatures,
harmonics and etc. Using online monitoring is possible to recognize and remove
the faults. Furthermore, the original reasons of the occurred faults are determined
from the monitored quantities. Insulation is one of the most important parts
of a high voltage device. It is shown that most observed failures in power devices
arise from insulation failures (Di Lorenzo del Casale et
al., 2000) which can cause a total breakdown (Boggs
and Densley, 2000), although in the beginning stages, only Partial Discharges
(PDs) occur (Boggs, 1990). For condition monitoring
of power devices insulation, PD signals detection can be used. Based on the
magnitude and occurrence rate of PDs, the condition of the insulation can be
determined and sudden insulation outages in power system can be prevented. PDs
are signals that do not completely bridge the insulation. In XLPE cables, the
PDs are occurred in the air filled cavities and in the oil power transformers;
they are occurred in the bulbs filled with air, humidity and voids in the paper
insulation. In addition, in the power transformers, surface discharge on the
contaminated bushings, corona discharge on the conductors arrived to the bushing
and windings in the oil occur (Nattrass, 1988; Dong
et al., 1999). The insulation strength of these cavities and bulbs
are less than other parts of the insulation and it cause PD occurrence. PD signals
are current impulses with high frequency content and very short pulse width.
For detection of PDs, the electrical and nonelectrical techniques can be used.
Acoustic sensors such as microphones installed on the transformer tank are nonelectrical
method used for PDs detection (Kreuger, 1964). According
to Lundgaard (1992), the sensitivity of the electrical
methods is higher than the nonelectrical approaches and in PD detection of
the power apparatus, it is better to use electrical methods by measuring current
impulses. PD detection in the power equipments can be done in offline and online
modes. In the online mode, because of the availability of different quantities
such as currents, voltages, temperatures and etc, with PD signals, fault detection
is instantly performed. Additionally, the trend of the PD signals is monitored
and the preventive operation is done in an appropriate situation. However, in
the offline mode, the measurements are performed in discrete times and PDs may
be occurred between the times. Extension of PD signals may be occurred rapidly
and resulted in the total breakdown and insulation failure (Stone,
1991). In power systems, different noises such as radio waves, power electronic
firing pulses, corona and switching waves affect the PDs and make online PDs
detection difficult. Signal processing methods must be applied for removing
the noises from PD signals. So far, many researches were done for denoising
the PDs in power transformers (Zhang et al., 2007).
Wang et al. (2001) mentions high pass filter
and wavelet transform as two methods which are used for noise removing in power
transformers. In addition, wavelet transform is used for denoising the PDs
in both distribution and power transformers (Ghaffarian
et al., 2008). Ming and Birlasekaran (2002)
and Satish and Nazneen (2003) discuss the use of wavelet
transform for noise reduction of different discharge signals. Moore
et al. (2006) has used wireless wideband radiofrequency measurements
for detection of the PD signals in power transformers. Zhou
et al. (2005) mentioned noise removing of the power transformer by
using chaotic algorithm. In this study for noise reduction, since broadcast
radio signals have a symmetrical probability density function, the effects of
the noises are compensated by taking a large number of measurements using the
antenna array and finding the mean value of the distribution. These measurements
were then processed and the PDs are detected.
In this study the Bhattacharyya distance was used for PD detection in the power transformers as a new method.
PD DETECTION CIRCUIT
For online PD detection of high voltage power transformers, the circuit of Fig. 1 can be used. The circuit consists of a copper strip, ground wire, High Frequency Current Transformer (HFCT), coaxial cable and an oscilloscope.
The copper strips are connected to the bushings. The equivalent circuit model
of a bushing can be presented as several series capacitors. The copper strip
is connected to these capacitors in series. These capacitors have large impedances
in the power frequency and filter high voltage currents. However, the frequencies
of PDs are high and can be passed from these capacitors. In some transformers,
where a bushing tap is available, the copper strip is not required. The PD signals
transmit to the ground through the ground wire. In the measurement circuit,
the ground wire is passed in the HFCT and then connected to the ground. When
the PD is occurred in a transformer, it travels and goes to the ground through
the bushing tap (copper strip) and the ground wire. Based on the ampere law,
PD currents generate the magnetic field in the HFCT and induce a current proportional
to the PD magnitude in the secondary winding of the HFCT.

Fig. 1: 
Online PD signals detector circuit of a power transformer 
The induced current is connected to the oscilloscope using a coaxial cable.
The presented PD signals on the oscilloscope screen include noises. The noisy
PD signals are recorded and transferred to a PC for denoising.
BHATTACHARYYA DISTANCE METHOD
This section presents the Bhattacharyya distance technique for denoising and
detection of the PD signals. This method is applied for epileptic seizure detection
and phone clustering by Niknazar et al. (2010)
and Mak and Barnard (1996), respectively. The statistical
and mathematical model of PD signal is investigated in the following subsection.
Then, detection and denoising algorithm based on Bhattacharyya distance will
be proposed.
Statistical and mathematical model of PD signals: The mathematical form of the PD signals can be presented as follows:
Where:
where, a_{k} is the magnitude of PD signals, t_{k }is the time that PD signals are occurred, δ(t) is impulse function and s(t) is the reference PD signal which depends on the occurrence time of the PD. This signal has a finite period time T. In the other words:
The time difference between t_{k} and t_{j} is considered, so the s(tt_{k}) and s(tt_{j}) have no overlapping. Considering the assumption, the PD signal (x_{pd}) is zero at most times and only at the short duration after the t_{k} is not zero and the s(t) exists.
The mathematical model of the noisy PD signal (y_{pd}) can be presented as bellow:
where, n(t) is an additive noise. The nature of the PD signals is so that two states would be considered for the noisy PD signals (y_{pd}) as follows:
• 
At the time t, when the PD signals (s(t)) are zero and only
the noises exist 
• 
At the time t, when the PD signals (s(t)) with the noises (n(t)) exist 
• 
On the other hand, the mathematical form of this fact is presented in
Eq. 5 
For detection of the PD signals, it is required to distinguish the two above states using a statistical distance. For statistical distance definition, probability distribution function of noisy signal (y_{pd}(t)) is required. To obtain this function, it is considered that the noise n(t) is independent of the PD signals and the PD signal is deterministic. With these two assumptions, the noisy signal probability density function would be as bellow:
where, p_{y}(y_{pd}) is the noisy signal probability density function and p_{n}(n(t)) is the probability density function of the noise n(t). In this stage, it is considered that the noise has the Gaussian distribution with zero mean and σ^{2} variance, N(0,σ^{2}) and with this assumption, the probability mass function of the noisy signal would be as Eq. 7:
It can be concluded that the two probability density functions are different only in mean values. As a result, for the detection of PD signals, the mean values can be used. However, the mean value of the PD signal is dependent on the PD signal which is not available. In this stage, PD signal recognition is required and for this purpose the statistical distance between the two distributions is obtained.
Bhattacharyya distance: The Bhattacharyya distance is the theoretical distance between two Gaussian distributions and is equivalent to the up limit of the classified error. For two distributions, i.e., p(x) and q(x), the Bhattacharyya distance is defined as follows:
where, D_{B} is Bhattacharyya distance, m_{i} and P_{i}
are the mean value and covariance matrix of the distribution, respectively and
P = (P_{1}+P_{2})/2. The first term in Eq. 8,
is the ability of separation of the two distributions due to the difference
between the distribution mean values and the second term is the ability of decomposition
of the two distributions because of the difference in the covariance matrix
of the two distributions. From point of the classification, the classification
error between two classes is obtained as bellow:
where, p_{w1} and p_{w2} are the probability occurrence of the classes, w_{1} and w_{2}, respectively.
Proposed algorithm for detection and Denoising of PD signals: The main idea for detection and denoising is statistical similarity measurement between the two investigated states in Eq. 7. Hence, for denoising of the PD signals based on the Bhattacharyya distance, the probability distribution functions p(x) and q(x) are defined as follows.
The probability density function p(x) is for the state with only noises. Thus,
p(x) = N(0,σ^{2}). In other words, m_{1} = 0, P_{1}
= σ^{2}. The Gaussian distribution is considered for the noises
and σ^{2} is estimated from the Eq. 10 (Donoho
and Johnstone, 1994):
where, W_{1}^{D} is the detail coefficients of the first scale of the wavelet transform. Considering the assumption of the stationary characteristic of the statistical distribution of the noises in all times, the parameter of p(x) for each signal is adjusted for one time and is fixed in all times.
The probability density function q(x) is for the state with PD signals and
noises. The signal, z(t), is defined as Eq. 11 and 12
for estimation of the parameters, m_{2} , P_{2} at arbitrary
time, t_{0}.
where, T_{w} is length of PD signal sample. It is considered that the
signals are ergodic and the parameters m_{2} and P_{2} are estimated
as Eq. 13 and 14, respectively:
For the PD signals detection based on the Bhattacharyya distance, the follow
algorithm is proposed. The sampling rate of the PD signals is f_{s}.
In this study, 100 MHz is considered for the sampling frequency of the PD signals
(N_{w} is number of PD signals).
Using the technique, with inserting a simple threshold on the detection index, the location of the PD signals can be detected. In the noisy signal, the Detection Index (DI) is very small, when the PDs don't exist and it is significant, when the PDs exist. Based on this fact, denoising of the PD signals is performed in Eq. 15:
When there is no PD signal, with high gain, the noises are reduced but in the times that the PD is available, the noises are not reduced, so the locations of the PD signals are determined. In this method with reduction of the noises around the PD signals, these PDs can be detected successfully. In fact, in this technique, the noises in the times that the PD is available, is not removed. For obtaining PD signal with high quality and without any noises, it can be used from other typical denoising techniques on the y_{pd}(t) only in the time durations that DI(t) has significant values. The proposed technique is simple and successfully detects the PD signals. Implementation of the method for denoising of the different PD signals is given in the next section.
IMPLEMENTATION OF THE METHOD TO PD SIGNALS
In this stage, the proposed technique is implemented on different PD measured signals of a power transformers and the effectiveness of the method is investigated.
PD in the 20 kV distribution transformer: The voltages up to 40 kV are
applied to the 20 kV side of an old distribution transformer. In this condition,
the PD is occurred and the recorded PD signals are presented in Fig.
2. Using the MATLAB software, different Gaussian noises (low and high) are
added to this signal. The proposed method for removing the existence noises
is used and the denoised PD signals are extracted. It is presented in Fig.
3 and 4.
From the Fig. 3 and 4, it is shown that the noise removing is successfully done using of the Bhattacharyya distance method.
PD arisen from an air filled bubble in the oil: In this stage, several
air filled bubbles in the oil are made and with applying high voltage, PD is
occurred. Recorded PD signals are added with the low and high Gaussian noises.
The proposed method is applied and the denoised PD signals are extracted. These
signals are presented in Fig. 5 and 6. It
is deduced from the figures that the proposed technique can successfully denoise
the PD signals arisen from an air filled bubble in oil.

Fig. 2: 
PD in 20 kV distribution transformer 

Fig. 3(ad): 
Denoising of PD (a) original signal, (b) Noisy signal, (c)
Denoised signal and (d)
Bhattacharyya in the 20 kV distribution transformer (low noise addition) 

Fig. 4(ad): 
Denoising of PD (a) original signal, (b) Noisy signal, (c)
Denoised signal and (d)
Bhattacharyya in the 20 kV distribution transformer (high noise addition) 

Fig. 5(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from air filled bubbles in the oil (low noise
addition) 

Fig. 6(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from air filled bubbles in the oil (high noise
addition) 
PD arisen from fixed metallic particle in the transformer oil: In this
stage, a fixed metallic particle is inserted in the transformer oil. The PD
signals occur with applying high voltage. Then the recorded signals are added
with low and high Gaussian noises. The proposed method is applied and the denoised
PD signals are extracted. They are presented in Fig. 7 and
8. From these figures it can be concluded that the proposed
technique can successfully denoise the PD signals arisen from a fixed metallic
particle in transformer oil.
PD arisen from single void: In this stage only one void exists in the
transformer oil. Then with applying high voltage, the PD signals are occurred
and recorded. These signals are added to the low and high Gaussian noises. Then
using the proposed method, the denoised PD signals are extracted.

Fig. 7(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from fixed metallic particles (low noise addition) 

Fig. 8(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from fixed metallic particles (high noise addition) 
They are presented in Fig. 9 and 10. It
is deduced from these figures that the proposed technique can successfully denoise
the PD signals arisen from single void in transformer oil.
PD arisen from multiple voids in the oil: In this stage, multiple voids
(more than one) exist in the transformer oil. Then with applying high voltage,
the PD signals are occurred and recorded. These signals are added to the low
and high Gaussian noises. Then, using of the proposed method the denoised PD
signals are extracted. They are presented in Fig. 11 and
12. It is deduced from these figures that the proposed technique
can successfully denoise the PD signals arisen from multiple voids in transformer
oil.
Surface discharge: In this stage, the surface discharge signals that
occur as a result of the bushing surface contamination are recorded. The low
and high Gaussian noises are added to the surface discharge signals.

Fig. 9(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from single void in the oil (low noise addition) 

Fig. 10(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from single void in the oil (high noise addition) 

Fig. 11(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from multiple voids in the oil (low noise addition) 

Fig. 12(ad): 
Denoising of PD signals (a) Original, (b) Noisy, (c) Denoised
and (d) Bhattacharyya arisen from multiple voids in the oil (high noise
addition) 

Fig. 13(ad): 
Denoising of surface discharge signals (a) Original, (b)
Noisy, (c) Denoised and (d) Bhattacharyya (low noise addition) 
Then, the proposed technique is applied and denoised signals are extracted.
These signals are presented in Fig. 13 and 14.
It is deduced from these Fig. 13 and 14
that the proposed technique can successfully denoise the discharge signals.
Corona discharge arisen from needle: In a power transformer, the corona
discharge may occur on the arrival conductors to the bushings and it results
in ionization of the air around the conductors. In this stage, a high voltage
is applied to a needle and the corona discharge occur on the air around top
of the needle. The corona discharge signals are recorded and added with low
and high Gaussian noises. Then using the proposed technique, denoising is performed
and the corona discharge signals are extracted. These signals are presented
in Fig. 15 and 16. From the results, it
can be concluded that the proposed technique can successfully denoise the corona
signals.
Corona discharge between the needle and ground in the air: In this stage,
a high voltage is applied to a needle and the corona discharge occur between
the needle and the ground in the air around the needle.

Fig. 14(ad): 
Denoising of surface discharge signals (a) Original, (b)
Noisy, (c) Denoised and (d) Bhattacharyya (high noise addition) 

Fig. 15(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and (d) Bhattacharyya of a needle in the air (low noise addition) 
The corona discharge signals are recorded and added with low and high Gaussian
noises. Then, using the proposed technique, denoising is performed and the
corona discharge signals are extracted. These signals are presented in Fig.
17 and 18. It is deduced from the results that the proposed
technique can successfully denoise the corona signals.
Corona discharge between the needle and ground in the oil: In this stage,
a high voltage is applied to a needle and the corona discharge occur between
the needle and the ground in the oil around the needle. The corona discharge
signals are recorded and added with low and high Gaussian noises. Then, using
the proposed technique, denoising is performed and the corona discharge signals
are extracted.

Fig. 16(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and
(d) Bhattacharyya of a needle in the air (high noise addition) 

Fig. 17(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and
(d) Bhattacharyya between a needle and ground in air (lownoise addition) 

Fig. 18(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and (d) Bhattacharyya between a needle and ground in air (highnoise
addition 

Fig. 19(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and (d) Bhattacharyya between a needle and ground in the oil
(low noise addition) 

Fig. 20(ad): 
Denoising of corona discharge signals (a) Original, (b) Noisy,
(c) Denoised and (d) Bhattacharyya between a needle and ground in the oil
(high noise addition) 
These signals are presented in Fig. 19 and 20
with low and high noise additions, respectively. It is deduced from the figures
that the proposed technique can successfully denoise the corona signals.
CONCLUSION
In this study, a new method based on the Bhattacharyya distance is proposed
to detect PD signals and remove different noises from the PD signals in high
voltage power transformers. This method is applied to different discharge signals,
including PD in the 20 kV distribution transformer, PD in air filled bubbles
in the transformer oil, PD arisen from fixed metallic particles, PD arisen from
single void, PD arisen from multiple voids, surface discharge, corona discharge
in the air, corona discharge between the needle and ground in the air and corona
discharge between the needle and ground in the oil. It is concluded from the
results that this technique can successfully denoise different PD signals.