Partial Discharge Signal Denoising using Adaptive Translation Invariant Wavelet Transform-Online Measurement

Abstract

Partial discharge (PD) measurements have emerged as a dominant investigative tool for condition monitoring of insulation in high voltage equipment. But the major problem behind them the PD signal is severely polluted by several noises like White noise, Random noise, Discrete Spectral Interferences (DSI) and the challenge lies with removing these noise from the onsite PD data effectively which leads to preserving the signal for feature extraction. Accordingly the paper is mainly classified into two parts. In first part the PD signal is artificially simulated and mixed with white noise. In second part the PD is measured then it is subjected to the proposed denoising techniques namely Translation Invariant Wavelet Transform (TIWT). The proposed TIWT method remains the edge of the original signal efficiently. Additionally TIWT based denoising is used to suppress Pseudo Gibbs phenomenon. In this paper an attempt has been made to review the methodology of denoising the PD signals and shows that the proposed denoising method results are better when compared to other wavelet-based approaches like Fast Fourier Transform (FFT), Discrete Wavelet Transform (DWT), by evaluating five different parameters like, Signal to noise ratio, Cross-correlation coefficient, Pulse amplitude distortion, Mean square error, Reduction in noise level.

1. Introduction

Partial Discharge is an undesirable phenomenon which reduces the life expectancy of power system apparatus and also causes permanent damage to them. PD normally happens at defect sites such as voids, cavities, cracks, joints and delaminations. It can occur in solids, liquids and gaseous dielectrics. The damage due to the discharge can be estimated depending on the type of discharges; like, internal or surface discharge, termination discharge, corona, electrical treeing, etc [15]. In general, PD does not cause instant breakdown. It indicates the presence of a defect within the insulation which can affect its performance in a long term [14]. The significance of partial discharges on the life of insulation has long been recognized. Due to the repetitive nature and confinement to small regions of PD signal, it is very difficult to denoise them. There are different methods which are used to detect the PD signal namely, Chemical detection, Acoustic detection and Electrical detection [15].

In online PD measurement, noise can occur due to several kinds of sources and can couple with the systems in different ways and with different features. Therefore, it is necessary to denoise by several techniques [5].

It is well known that PD measurements are widely employed in testing power apparatus after manufacture. A most important problem which take part while measuring such PD signals is the ingress of external interferences (the magnitude is high when comparable to PD signal), which mainly affects the sensitivity and reliability of the acquired PD data. The external interferences in PD measurement are DSI which arises from power line carrier communication systems, Periodic pulse shaped interferences are from power electronic devices or other periodic switching etc, and Stochastic pulse shaped interferences are from infrequent switching operations or lightning, arcing between adjacent metallic contacts etc. while adding together to the above sources. Other possible noises which take part in the PD measuring devices are, random noise, periodic pulse currents and other pulsive interferences [4].

Due to the occurrence of different interferences in the PD signal, it is necessary to extract those original signals from noisy signal. In the last few years, several techniques were introduced to denoise the PD signals effectively. But it could be realized in either the time domain or in the frequency domain. Once the signal processing is done in the frequency domain, the time domain information is lost. Recently, the wavelet transform (WT) was recognized as a powerful tool for PD processing because it preserves both time and frequency domains information. Several authors perform their PD denoising methods by enhancing the wavelet transform techniques [13].

Of all the external interferences mentioned above, DSI can be identified and eliminated in frequency domain. Periodic pulse shaped interferences can be gated-off in time domain to some extent. But, it is very difficult to identify and suppress the gaussian or white interferences as they have many characteristics in common (both in time and in frequency) with the PD pulses [4]. Thus, the enhanced method is used in this work to suppress these interferences in the PD signal.

In [3] continuous wavelet (CWT) based denoising method is employed in separating PD pulses from electrical noise successfully. In [4] the removal of noises (Periodic, Discrete Spectral Interference and Stochastic) from the PD signals by using Multi-resolution signal analysis is explained. In [7] the complexity of WT is explained, and an improved methodology is used named as DWT is employed with better denoising effect for partial discharge measurement. In addition, a full ac cycle data recovery can be achieved instead of focusing only on recovering individual PD pulse, since the frequency range of PD signal is around MHz [15].

In [6] the ten different denoising techniques namely, Fast Fourier Transform, Low-pass filters, Wigner-Ville Distribution, Short-Time Fourier Transform, Least Mean Squares, Frequency-Domain Adaptive Filtering using DFT, Recursive Least Squares, Exponentially-Weighted Recursive Least Squares, Matched Filtering, Notch filtering, Wavelet-based Thresholding, are used to denoise the PD signals in an effective manner.

The greatest advantage of this proposed method TIWT remain in the edge of the original signal efficiently and reduces the impulsive noise to some extent, meanwhile at the same instant it will suppress Pseudo-Gibbs phenomenon (an artificial interference is generated due to wavelet based denoising techniques). This paper mainly deals with the procedure of Lifting the wavelet coefficient in order to denoise the signals. Moreover the effectiveness of the proposed TIWT denoising technique is evaluated by six different parameters namely, Signal to noise ratio, Signal to reconstruction error ratio, Cross-correlation coefficient, Pulse amplitude distortion, Mean square error, Reduction in noise level.

The paper is organized as follows: Section 2 presents the Characteristics of PD signal, Onsite PD measurements, Wavelet Transform and Translation Invariant Wavelet Transform. Section 3 discusses the steps involved in denoising techniques. Section 4 shows the Generation of Simulated PD signal and different types of noise. Section 5 describes the details related to Evaluated parameters. Section 6 presents the Results and Discussion. Section 7 shows the Conclusion.

 

2. Characteristics of PD Signal

Partial discharge reproduces on the external circuitry as shape and temporal parameters depend on factors like the type and location of the defect, the size of the equipment under test, the distance between the discharge site and the sensor and the type of the measurement system. The pulse amplitudes are usually in the range of micro- to milli-volts, which makes them very difficult to detect under noisy conditions [1]. The characteristics and detection of PD can afford information on the location, nature and extent of degradation [8].

2.1. Onsite partial discharge measurement

During onsite PD measurement, interference can occurs in three different forms as mentioned below: (i) continuous sinusoidal noise (DSI), (ii) pulse-type noise (repetitive and random pulses) and (iii) white noise. The ability to separate PDs from such interference clearly shows the behaviour and characteristics of defects in the system. Reducing white noise from the onsite measurements will yield high PD sensitivity. Removing DSI and pulse-like noise from on site measurement will improve the measurement accuracy. Thus for high accuracy of PD measurement, it is necessary to reject the noise by the monitoring system [11]. In denoising, the signal immersed in noise there is an inevitable PD signal loss. The proposed TIWT method is more efficient in processing high noise levels.

The Fig. 1 shows the experimental setup of PD measurements. A variable voltage source up to 7.5kV is applied across the plane to plane configurations. The emitted PD signal is measured across 50 ohm resistor using HV coupling capacitor. Thus the signal is recorded by using digital oscilloscope at a sampling rate of 2giga samples / second. Recorded readings are interfaced by GPIB interface. Then the collected data is denoised by using TIWT.

Fig. 1.Experimental setup

2.2 Wavelet transform

Wavelet Transform of a function is the improved version of Fourier transform. Fourier transform is a powerful tool for analyzing the components of a stationary signal. But it failed to analyze the non stationary signal where as WT allows the components of a non-stationary signal to be analyzed. WT is broadly divided into three classes: CWT, DWT and Multiresolution Based techniques [16].

The general block diagram in Fig. 2 shows the working scheme of DWT, where the two filter pairs namely, low pass and high pass filters respectively, are adopted from a mother wavelet. When the given input signal is decomposed using DWT, the signal under analysis is fed in to the two filters using a down-sampling algorithm, thus we yield approximations and details coefficients. Details about the above DWT applications are mentioned in the paper [7].

Fig. 2.Schematic representation of discrete wavelet transform

The main aim of this paper is to find out the advantages of WT compared to Fourier transform. Generally, wavelets are purposefully crafted to have specific properties that make them useful for signal processing.

2.3 Translation invariant wavelet transform

When PD signal is extracted from noisy signal using DWT, Pseudo Gibbs phenomena will present in the neighbourhood of discontinuities of the extracted signal. The reconstructed denoised signal will appear undershoot and overshoot around the singularity alternatively. The peak values are not inherent in the original signal. They are caused by the artificial interference in transforming process. The above problem was solved by using the proposed TIWT method. The proposed method is based on Fast Lifting Scheme to perform the denoising techniques. This is shown schematically in the Fig. 3.

Fig. 3.Block diagram of signal decomposition

Any DWT, the input signal is partially split into, Approximations: low-frequency components of the input signal (x) and Details: high-frequency components of (x) , which are defined by a term Details (d) and Approximations (s) [2]. In proposed method, Lifting Scheme decomposition is performed in the forward transform namely, Splitting, Prediction and Updated [12].

a) Split

In this step, the original signal x(n) is divided into two disjoint subsets namely, the even indexed points xe (n) , and the odd indexed points xo (n) . The both sequences are highly correlated. This similarity will lead to predict and update as mentioned below.

b) Predict

From the splitted signals as mention above, this step determines the detail d(n) coefficient of the original signal x(n) in the wavelet decomposition using (1). Using prediction operator P, xo (n) is predicted from xe (n) .

c) Update

This step determines the approximation coefficient s(n) of the original signal x(n) using (2). To obtain s(n) , an updated operator U is applied on the detail coefficients and the result is added to xe (n) .

The original signal is recovered from its approximations and detailsalong the wavelet decomposition tree. In each step, the inverse transform is done by the following steps namely, Inverse Update, Inverse Prediction and Merging is shown in Fig. 4.

Fig. 4.Block diagram of signal reconstruction

Inverse Update (Inverse primary lifting)

Inverse Prediction (Inverse dual lifting)

Merging

The odd and even indexed points are determined by using (3) and (4). Finally the indexed points are merged using Eq. (5)

 

3. Steps Involved In Wavelet Denoising

The procedure involves in denoising the signals are broadly classified into three steps [7]:

3.1 Decomposition

Choose a wavelet, choose a level N and compute the wavelet decomposition coefficients of the signals at levels from 1 to N.

3.2 Select threshold detail coefficients

For each level from 1 to N, select a threshold and apply a soft or hard threshold to the detail coefficients. wavelet denoising methods can be carried out using either hard or soft thresholding.

a) Threshold determination fot hard thresholding:

Hard thresholding processes data in such a way that those wavelet coefficients whose absolute values are greater than the threshold are kept and those less than or equal to the threshold are set to zero.

b) Threshold determination for soft thresholding:

Soft thresholding sets the wavelet coefficients below the threshold to zero. The coefficients greater than threshold are kept and then shrunk towards zero.

In comparison, hard thresholding is preferred in PD denoising due to the higher coefficients values associated with discharge events being kept without any modification and thus yielding an improved PD signal to noise ration [3].

3.3 Reconstruction

To reconstruct a signal it is necessary to use original approximation coefficients and modified detail coefficients from levels 1 to N.

 

4. Generation of PD Signal

As suggested by Hao Zhang et al [10] the Damped Exponential Pulse (DEP) and Damped Oscillation Pulse (DOP) had been numerically simulated for PD denosing. These waveforms are expressed by Eqs. (8) and (9), and the simulated waveform is shown in Figs. 5 and 6.

where A is the pulse peak value t1, t2 are the time constants that determine typical PD pareameters such as pulse rise time, pulse width and pulse decay time. fc is the oscillatory feequency of the DOP type pulse.

Fig. 5.Simulated DEP pulse

Fig. 6.Simulated DOP pulse

In general PD signals are in the mV range [4]. The frequency range of PD pulse is around MHz [9]. PDs are normally low-level pulses with fast rise time and short duration, typically no more than a few hundred nano-seconds [10].

4.1 Simulated noisy signals

a) White Noise:

A noise produced by a stimulus containing all of the audible frequencies of vibration, white noise is a good masking agent.

b) Discrete spectral interferences:

Some examples are from communication and amplitude modulation / frequency modulation, radio emissions.

c) Random nose:

Some examples are from switching operations or lightning or RF corona emitted from HV equipment [3].

All the above noses are simulated and shown in the Fig. 7.

Fig. 7.Simulated noise signal

 

5. Evaluated Parameters

During denoising in addition to removing the noise components from the PD pulse, the signal component whose frequency is very close to the interfering frequency ranges also gets removed to some extent. Meanwhile it is important to define that the signal component to be improved suffers from both attenuation and distortion. These two characters may be quantified by defining the pulse amplitude and the correlation coefficient. A satisfactory noise control method should reject or suppress all the interferences and noise with minimum attenuation and distortion of the PD pulse. In order to compare the performance of various methods, the following indices have been considered [4].

5.1 Signal to Noise Ratio (SNR)

a) SNR (1) is defined as [4]

where s(i) is the simulated PD signal, n(i) is the simulated noise signal and N the number of samples in Eq. (10.a). The SNR (1) determines the values before denoising. It is important to define that the value of SNR (1) should be less than SNR (2) in order to define the effectiveness of the denoising techniques.

b) SNR (2) is defined as

where s(i) is the PD reference signal, y(i) the denoised signal and N the number of samples in Eq. (10.b), It determines the effectiveness of the denoising method by relating the original signal energy to the reconstruction error energy.

5.2 Signal to Reconstruction Error Ratio (SRER)

b) The SRER is defined as

where s(i) is the original PD onsite signal, y(i) the denoised signal and N the number of samples in Eq.(11). It determines the performance of the denoising techniques during onsite measurement.

5.3 Cross-correlation coefficient Rxy

The cross-correlation is defined as [4]

Where x(n) is the original reference signal, y(n) is the denoised signal and N the number of samples in Eq. (12). Rxy indicates the degree of similarity between the original and the denoised signals.

5.4 Pulse Amplitude Distortion (PAD)

PAD is determined by

where xmax is the amplitude of the reference PD pulse and ymax the amplitude of the denoised pulse equation (13). In cases where several pulses are involving then mean value was computed.

5.5 Mean Square Error (MSE)

MSE is determined by,

It is used to assess the effectiveness of the algorithm. MSE is defined by Eq. (14), where n is again the length of the signal; f represents the original sample whilst R stands for the reconstructed data.

5.6 Reduction in Noise Level (RNL)

RNL is determined by,

As in practical records, there is no such reference signal x(i) to compute SNR, only the extent of noise suppressed can be estimated. Eq. (15) is used to find the reduction in noise level. In this z(i) is the noisy signal acquired, y(i) is the denoised signal and n is the number of samples.

In general a good denoising strategy should result in a high signal to noise ratio and signal to reconstruction error ratio, a high cross correlation coefficient and reduction in noise level, a low pulse amplitude distortion and a low Mean square error.

 

6. Results and Discussions

Four PD pulse sequences were simulated using the procedure explained in Section 3 and one onsite surface discharge in oil PD data are taken and explained in section 2.These sequences are called Signal-1, Signal-2, Signal-3, Signal-4 and Signal-5 comprise the following components [4]:

Signal-1: DEP type PD pulse with equal amplitude + white noise (Noise immersed in signal).

Signal-2: DEP type PD pulse with equal amplitude + additive white noise (Signal immersed in noise).

Signal-3: DOP type PD pulse with equal amplitude + white noise (Noise immersed in signal).

Signal-4: DOP type PD pulse with equal amplitude + additive white noise (Signal immersed in noise).

Signal-5: On-site surface discharge in air PD signal.

Signal-1 is a sequence of 6 PD pulses of amplitude 0.6650 mV and length of the signal is 378, where as white noise amplitude is 0.6507 mV. Thus the Signal-1 with less magnitude of white noise is combined to DEP signal.

Signal-2 is a sequence of 6 PD pulses of amplitude 0.6650 mV and length of the signal is 378 where as white noise amplitude is 0.8907 mV. Thus the Signal-2 with high magnitude of white noise is combined to DEP signal.

Signal-3 is a sequence of 6 PD pulses of amplitude 0.6264 mV and length of the signal is 378where as white noise amplitude is 0.6150 mV. Thus the Signal-3 with less magnitude of white noise is combined to DOP signal.

Signal-4 is a sequence of 6 PD pulses of amplitude 0.6264 mV and length of the signal is 378 where as white noise amplitude is 0.8139 mV. Thus the Signal-4 with high magnitude of white noise is combined to DOP signal.

Signal-5 is a on-site PD pulse, where the sinusoidal signal in kV range and the particular PD signal will be in mV range. Thus the Signal-5 consists of three different types of interferences namely, white, random, DSI.

To evaluate the effectiveness of the PD signal denoising method the results were compared with FFT using wiener filter and other wavelet-based PD denoising procedures. The wiener filter is adjusted to the power spectrum of the PD signal. The wavelet-based method is based on decomposition level is proposed by H. Zhang et al [10, 11]. For further reference the methods and their identifications are listed in Table 1.

Table 1.Different denoising techniques

Thus the above denoising methods are applied to the DEP and DOP and their parameters to be evaluated are discussed in the section 4.

The Fig. 8 shows the denoising of signal 1 using the methods listed in Table 1. In the FFT method, the signal is denoised to some extent, but they fail to return the originality of the signal. The pulse amplitude value is high. When wavelet based method is used for denoising purpose, it retains the originality of the signal, but there is an introduction of artificial interference. TIWT method overcomes the above problem and shows better results comparing to other metheods. The effectives of the method is studied by evaluated the parameters discussed in section V and they are listed in Table 2.

Fig 8.Simulated DEP Signal polluted with white noise and denoised with different techniques

Table 2.Numerical evaluation of signal 1

Since FFT and Wavelet based denoise techniques are effectives only for the elimination of gaussian part of noise, it shows low cross correlation coefficient values. The proposed TIWT method reduces the Pseudo Gibbs Phenomenon. This method shows better SNR value and high Cross Correlation Coefficient because it retains the originality of the signal after denoising.

The similar analysis is performed for signal 2 and its denoised signals are shown in Fig. 9.

Fig 9.Simulated DEP Signal polluted with additive white noise and denoised with different techniques

In FFT denoising techniques the noise is reduced to some extent but, the originality of the simulated DEP signal is lost. At the same instant when wavelet based method is used for denoising, the oscillations are more in the output signal. For this signal 2 also TIWT shows better results.

The numerical results for signal 2 are shown in Table 3. The SNR (1) has negative value which indicates that the noise content is too high. The TIWT shows high SNR value and cross correlation coefficient and low pulse amplitude distortion and MSE value. The proposed TIWT method does not reproduce any oscillation as in WT method.

Table 3.Numerical evaluation of signal 2

The methods listed in Table 1 is used for denoising the signal 3 and its denoised signal is shown in Fig. 10.

Fig. 10Simulated DOP Signal polluted with white noise and denoised with different techniques

In this wavelet based denoising methods fail to reproduce the original. Thus from the Fig. 10 TIWT will reduce the artificial interference and retains the originality of the signal and shows better results when comparing other techniques.

The numerical results for signal 3 are shown in Table 4. The method A reduces the noise to some extent but the cross correlation value is low. The TIWT shows high SNR value, high cross correlation coefficient, low pulse amplitude distortion and low MSE value. And also there is no artificial interference generation.

Table 4Numerical evaluation of signal 3

The Fig. 11 shows the denoising of signal 4 using the methods listed in Table 1. Due to the presence of high SNR (1) value, FFT denoising techniques contains more oscillations and the relation between original and denoise signal is entirely different. Once wavelet based method is used for denoising means the original signal content is lost. When wavelet based hard and soft thresholding is used for denoising means it fails to reduce the noise to some extent. For this signal 4 also TIWT shows better results by comparing the original and denoised signal.

Fig. 11Simulated DOP Signal polluted with additive white noise and denoised with different techniques

The numerical results for signal 4 are shown in Table 5. The SNR (1) negative value which determines the noise content is too high compared to PD signal. While analysing the methods (A-I) SNR (2) value is low and the PAD value is also high because, of high SNR (1) value. The TIWT shows high SNR value and cross correlation coefficient and low pulse amplitude distortion and MSE value. The proposed TIWT method reduces the Pseudo Gibbs phenomenon.

Table 5Numerical evaluation of singal 4

The Fig. 12 clearly shows that different denoising techniques applied to Signal 5. FFT denoising techniques fails to denoise the unwanted spikes in the real time data. As mentioned, the soft thresholding techniques introduces Pseudo Gibbs phenomenon to the denoised signal. Thus proposed TIWT method reduces the three different possibility of interferences in onsite measurements and extract the types and behaviour of PD signal and shows better performances when compared to other techniques.

Fig. 12Onsite Surface Discharge in oil PD measurements with external interference and denoised with different techniques

The numerical results for signal 5 are shown in Table 6. The SRER value increases gradually from different denoising methods (A -J) which determine the effectiveness of denoising the onsite PD measurements. The reduction in noise level is also too high. Thus among the different techniques, TIWT shows better result.

Table 6.Numerical evaluation of signal 5

In the Figs. 13 and 14, there are four sub-figures representing the four benchmark signals, respectively. It can be visually appreciated that a great amount of noise has been suppressed. Thus by comparing the four sub figures in the plot for signal 1, 2, 3 and 4 (under noise immersed in signal and signal immersed in noise) conditions, the proposed method TIWT (pink colour) will resembles the original signal to some extent, where soft thresholding (blue colour) introduces pseudo Gibbs phenomenon. Hence the proposed method performs the better performance to simulation as well as in measured signal.

Fig.13.Comparison of three different denoising techniques in a single plot for Signal 1 and 3

Fig. 14.Comparison of three different denoising techniques in a single plot for Signal 2 and 4

 

7. Conclusion

In this proposed method, TIWT is used to denoise the PD signal in a more effective manner. By evaluating the five different parameters it clearly shows that the proposed denoised method shows high SNR, which compares the original PD reference signal with denoised signal. It is important to define that the SNR (2) value should be greater than the SNR (1) value and it shows the effectiveness of the denoising techniques. Then the cross correlation value is high, which determines the relation between original PD reference signal with denoised signal. The Pulse Amplitude Distortion value is low, it compares the amplitude of PD original signal and the denoised signal. If the PAD value is zero, the amplitude of original and denoised PD signal is same. The RNL shows high value, which describes how efficiently the noise is eliminated from the PD noisy signal. Finally the MSE is low, which determines the error level in the denoised level techniques. Meanwhile for the onsite PD measurements TIWT will reduce the three different noise to some extent and shows high SRER value and high RNL values. Thus among the ten different methods TIWT method shows better quality denoise signals, when compared to the other denoising techniques. Acknowledgement