Partial Discharge Signals Using Gabor Wavelet Transform Biology Essay

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The main aim of the paper is to discuss an extremely efficient method for denoising and detection of partial discharge (PD) signals generated in high voltage power transformers. Partial discharges in power transformers is a well known common phenomena and its value should not exceed a given specified limit as per standard. The most commonly occurring phenomena relate to wedge type, float type, corona type and internal. In this paper, corona type partial discharge generated using ultra high frequency (UHF) antenna and recorded on digital oscilloscope from simulated model is presented. The samples are subjected to FFT analysis. Gabor wavelet transform is used to obtain the time ~ frequency relation to remove the noise present in the PD. The multiplication factor (k) is also calculated for all frequencies ranging from 1 Hz to 1 GHz in order to evaluate the time varying current waveform at any particular frequency. Finally, the signal is reconstructed with all dominant frequencies after the removal of noise present in the signal.


Partial discharge is an electrical power discharge that fills the small gaps of the insulation between any two or more conducting electrodes or surfaces. This leads to sudden failure of the system particularly when electric field strength exceeds the breakdown strength of that portion of the insulating material. The Partial discharge may occur at any time and any point in the insulation of the system. Hence, the main objective of the partial discharge detection is to analyze the insulation condition and to suggest proper remedial action to avoid the sudden failure of the system if required.

The equipment condition can also be identified with the help of partial discharge testing and subsequently suitable action can be taken to enhance the electrical reliability. It is already proved that the partial discharges are the primary reason behind many high voltage equipment failures. Therefore, in the event of a trouble with high voltage equipment with regard to insulation, generally partial discharge evaluation is recommended.

The analysis of partial discharge is made to predict the insulation degradation well in advance, which arises due to natural circumstances or by accelerated aging of the HV apparatus or sometimes due to manufacturing or installation failures. It is a predictive test to improve the reliability of operation. Another added advantage of conducting such partial discharge diagnostic test is that, it doesn't affect the normal operation of the equipment under test and at the same time allows us to solve the problem if exist.

Therefore, it is essential to determine the type of discharge present to identify its severity. One of the major problem with PD detection is with noise contamination. The reason is that both PD and noise signals have high frequency components making it very difficult to distinguish them from noises. Therefore, denoising a given noise corrupted PD signal is an important issue to be considered in partial discharge detection. Several papers have already been published by many researchers and proposed various efficient techniques for denoising of PD signals with different types of noise involved[1-5]. Different algorithms are also reported for PD pattern classification. Most of the techniques discussed above needs denoised PD pulses to determine the type of PD occurred and almost all denoising schemes needs an expert operator[6].

The test equipment used for laboratory test as per the standard is not suitable for site, due to the presence of strong electromagnetic radiation in the neighborhood. Since any equipment shifted to site undergoes vibration during transport, it is likely that either a portion of insulation would have been affected or inter-gaps between live parts would have altered.

In order to assure the reliability of operation, it is compulsory that proper diagnostic test to be carried out at site. Thus, a suitable diagnostic technique is required to be evolved. The partial discharge diagnostic (PDD) using acoustic and ultrasonic are the two latest methods currently being used by the researchers at site for detection of PD inside transformer. However, the confidence level of proper detection including location and identification of various types of PD are rather low[7].

The present paper deals with the diagnostic of corona type discharge in a model simulation experiment. The ultra high frequency discharge signal emanating from the partial discharge is detected by suitable UHF antenna and later it is amplified to obtain the measurable pulse. The recorded pulse is analyzed for all of its dominant frequency components. The time ~ magnitude characteristic of pulse for every dominant frequency is calculated using Gabor wavelet transform. In order to ascertain the accuracy of computation the pulse is reconstructed. The ratio of the peak magnitude of each pulse for every frequency is calculated to obtain a relationship for similar comparison with other corona type of discharge for future use. However, the present analysis has been carried out for one typical discharge of corona type. The method of detection and wavelet analysis for wedge type of partial discharge are discussed by Sudarshanam et. al.[8] and float type discharge has been reported by Ramprasad et. al[7].


In order to generate PD data for corona type of discharge a chamber made of steel is used. A PD generating model as shown in Fig.1.a. to Fig.1.d. is used for all experimental studies. In order to simulate oil corona the set up used is similar to Fig. 1.b. However, the plate is unscrewed so that the holding rod directly seen by the lower grounded plate. A voltage is applied at H.V electrode marked C and gradually increased until PD starts. Then the PD signal recorded using UHF CT, which is shown in Fig. 2.a. In this paper, the analysis was carried out using the values of the above signal.

Fig.1.a. Test tank with antenna and simulator

Fig.1.b. Discharge simulator Assembly

Fig.1.c. Discharge simulator Assembly for corona PD generation

Fig.1.d. UHF Signal measurement systems


An UHF antenna is used to detect the acoustic signal emanated from PD and later it is amplified and recorded on a storage oscilloscope. One typical signal recorded by an UHF detector of small and big is given in Fig.2.a. and Fig.2.b. respectively. The total time of recording is limited to one micro second with 1000 samples. It is found that duration of 102.4 µsec is adequate to represent signal up to 500 MHz.

The frequency response obtained from PD signal of Fig.2.a. is given in Fig.3[9]. The dominant frequencies are seen from the FFT analysis are (5, 9, 14, 20, 69 and 250) MHz. A similar result and analysis for Wedge type discharge has been reported by Sudarshanam [8] and Float type discharge has been reported by Ramprasad et. al. [7].


In Fourier theory, a signal is represented as sum of, a possibly infinite, sines and cosines and it is called as Fourier expansion. The information obtained from the above expansion is good enough to analyze the given signal when it is stationary. However, the main disadvantages of Fourier expansion arise when the signal being analyzed is non stationary. Because, it provides only frequency resolution and doesn't give time resolution, which is also important to identify the signal component when exist for short duration on time scale.

Fig.2.a. UHF signal from floating type of PD by small antenna

Fig.2.b. UHF signal from floating type of PD by big antenna

Fig.3. FFT of the UHF signal corresponding to Fig.2.a.

Although the short-time Fourier Transform overcomes the time location problem to a large extent, it does not provide multiple resolutions in time and frequency, which is an important characteristic for analyzing transient signal containing both high and low frequency components.

The limitations of Fourier methods can be overcome wavelet analysis by employing analyzing functions that are local both in time and frequency. Unlike Fourier analysis, which uses one basis function, wavelet analysis relies on wavelets of rather wide functional form. The wavelet functions are generated in the form of translation and dilation of fixed function. The basis wavelet is termed as a mother wavelet. The wavelet transforms are categorized into continuous wavelet transform(CWT) and discrete wavelet transform(DWT). For further details refer [10-13].



The following mother wavelet integral and wavelet equation has been chosen in order to analyze the signal obtained from the experimental set up mentioned above and is given by the wavelet



Where, a = scale parameter

b = translation parameter

f = frequency

The Gabor wavelet equation has been selected to carry out the present work i.e denoising and analysis of corona PD signal, and is given by the following equation


where, σ2 is a constant and controls the band of frequencies to be identified. The necessary and sufficient condition for a function to become wavelet is discussed in detail by Rao et. al.[14]. Using the wavelet function defined in equation (3) and (4), the time ~ magnitude characteristic of the signal for all dominant frequencies are calculated for most appropriate values of signals.

In order to evaluate the time varying current waveform at any particular frequency, it is necessary to determine the multiplication factor (k). This factor converts the wavelet transform of the time waveform at a particular scale parameter 'a' into the transient current waveform for the corresponding frequency[13].

For every dominant frequency there exists a signal in time domain. All the dominant frequencies are calculated using the Gabor wavelet transform and are plotted from Fig.10 (a) to (f). The signals corresponding to each frequency are multiplied by a scale factor 'k' to obtain the signal with true magnitude. The reconstructed signal using all such individual signals added is shown in Fig.11. A comparison between original signal and reconstructed signal suggests the extent of accuracy of calculation[15].







Fig.4 Component signal for various frequencies

(a)5MHz (b)9MHZ ( c)14MHz (d)20MHz (e)69MHz (f)250MHz

Fig.5.a. Reconstructed signal of corona type of PD

Fig.5.b. FFT of the reconstructed signal corresponding to Fig.5.a.

Validity of the Model

The main objective of the present analysis is to segregate all the dominant frequencies present in the corona waveform so that the noise contaminated with the actual PD signal can be eliminated. In the process of evaluating the time varying current waveform at a particular frequency, the multiplication factor (k) is required to be calculated and it depends on the selection of σ2 value used to control the band of frequencies. This factor is used to convert the wavelet transform of the transient corona waveform at a particular scale parameter 'a' into the transient current waveform for the corresponding frequency (f = 1/2πa).

The σ2 value is increased slowly from 2 to 1024 until output waveform (wavelet transform of the input waveform) at a particular scale parameter matches with the input /original waveform. To confirm the validity of σ2 value and the multiplication factors at different frequencies, a sinusoidal signal with an amplitude of 1 p.u. for various frequencies ranging from 1 Hz to 1 GHz are considered. The variation of k values with σ2 at a particular frequency 20 MHz are shown in Table 1. Similarly, Table 2 shows the k values for different frequencies at a particular value of σ2 value 256. From Table 1 and Table 2, it is clear that when σ2 increases the k value decreases and also it is observed that k2/f is constant for any given σ2 value. Similar results are generated for σ2 value from 2 to 1024 in steps of 2 powers and frequencies ranging from 1 Hz to 1 GHz. The corresponding graph of σ2 Vs k2/f is shown in Fig 6. From the simulation results generated the minimum value of σ2 has been identified as 53.5, to satisfy the necessary condition that the average value of the mother wavelet function at any frequency is zero[16]. Nevertheless, it is found that there is a possibility of evaluating a waveform comprising of a band of frequencies or frequency cluster with reasonable accuracy, by using a σ2 value less than the above minimum value.

Table 1 . Variation of k w.r.t. σ2

Frequency (MHz)









64 128
















Table 2. Variation of k w.r.t. Frequency.


Frequency (MHz)

























Fig 6: k2/f Vs σ2


The nature of the corona waveforms is such that, transient current amplitudes for the frequency content close to 9 MHz has a major contribution compared to the other frequencies (refer Fig. 3). Fig. 4 shows the transient waveforms evaluated at different dominant frequencies of the corona signal. As can be seen from Fig. 4-a, σ2 = 64 is enough to evaluate accurately the transient waveform at 5 MHz. To evaluate the transient waveform at 5 MHz, σ2 = 4, is selected initially and it is observed from FFT analysis that it is not only associated with the signal of 5 MHz frequency component but also with the frequencies 5 and 9 MHz. However, the transient waveform evaluated at the same frequency with σ2 = 64, appear to be accurate (shown in Fig. 4-a). Thus, accurate evaluation of the transient waveforms at the required frequencies (except low frequency content in the order of a few MHz) from the corona waveform is observed to be possible with σ2 > 53.5. The transient waveform that was calculated at a frequency of 20 MHz with σ2 =256, is found to be accurate shown in Fig. 4.d.

For further validation of the model to be established, the amplitudes of all dominant frequencies can be compared from the frequency spectrums of original and reconstructed signal. The reconstructed signal is obtained by adding all dominant signals at different frequencies. A dominant frequency[17,18] may suggest a high magnitude with short duration or a low magnitude with long duration existence. It is this characteristic that is utilized by wavelet transform to identify a particular type of signal. Typically from Fig. 4(a) to (f) show the time ~ magnitude values for all dominant frequencies. There are several other frequencies which are not so clear from FFT diagram, but they exist and contribute to the main signal. It is rather complex to determine if the related frequency is due to a true signal or caused due to windowing or truncation [14,19]. it is seen that higher contribution comes either from a few low frequency (5, 9 MHz) components or a few very high frequency (69, 250 MHz) components. The remaining frequencies have very low contribution in the main signal. Such characteristic can be utilized for identifying the range of frequencies which contribute to a given type of discharge. By using these results as a basis for analyzing partial discharges, corona waveforms obtained at different locations of prototype model of high power transformer are used.


The paper deals with the denoising and analysis of PD signals from a corona type of discharge. The FFT analysis is carried out on the UHF signal recorded in time domain for 1 micro second duration with 1000 samples using small antenna. Any frequency whose magnitude is at least greater than or equal to 10% of maximum peak is considered as dominant frequency and for all such dominant frequencies the actual time domain contribution is calculated using Gabor wavelet. The multiplication factor (k) is also calculated for all frequencies ranging from 1 Hz to 1 GHz in order to evaluate the time varying current waveform at any particular frequency. Finally, all the dominant frequency signals are added to obtain original PD signal. The wavelet method is observed to be very useful in eliminating noise contaminated. If large number of such corona type UHF signals are available, it is possible to obtain an empirical relation to identify this type of discharge with internal PD, surface PD or corona.


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