Abstract Transformers must be monitor continuously and so destroyer discharges detect correctly. Partial discharge is one of the important destroys. For detecting the type of partial discharge, the received signals from oscilloscope must be denoised. Wavelet is one of the important ways, for denoising. Signal to Noise Ratio (SNR) was used as major way for choosing the best wavelet functions for denoising the signals in abstracts. Here we use two another ways for finding the best wavelet function for denoisig the signals, with insist on two different artificial discharge signals. Firs way is called Maximum Likelihood. And second way is called Minimum Least Square. In first way correlation between the denoised signal and origin signal gives us a likelihood coefficient. The high likelihood coefficient, the best wavelet function for denoising discharge signals. In second way we confirm our results with another way. We decrease the denoised signals from the origin signals. It is clear the littler results, mean the better wavelet function for denoising discharge signals.
Key words: Partial discharge, Corona, Surface discharge, Signal to Noise Ratio (SNR), Minimum least square, Maximum likelihood
1 Introduction
Nowadays there are few methods for lo-cating the partial discharge and fault type of the oil transformers. However at the case of dry distribution transformers, there are many dif-ferent methods to use because of the easy access to its coils. At this type of transformers, coil is placed in the mold of solid insulated resin and its peripheral surface is accessible.
Mounting capacitive sensors on the sur-face of the bobbin is one of the effective me-thods for locating the partial discharge and recognizing fault type for dry distribution transformers. By detection of the partial dis-charge signals through the capacitive sensors the location and type of the partial discharge is possible [2].
There are different devices to measure partial discharge. These devices have different usage and abilities. Because of the different techniques of monopulses measuring, and using different UWB device and applying an especial kind of partial discharge, various important information was recorded. Devices and schematic of the measurement system with ultra wideband is shown at Fig. 1. Detecting circuit of this system has very ultra wideband and is able to detect the waveform of PD mo-nopulse at the time domain.
Fig. 1. Schematic of the measurement system with ultra wideband
At this measuring system, passing through detection impedance inside the detector, PD current pulses are converted into an electrical signal. These signals are amplified by a variable gain amplifier and then converted into an optical signal by a sensor. It imposes lower noise signals on PD signals at the transmission line, so gives better signal to noise ratio (SNR).
After transmission through an optical ca-ble, subsequently this optical signal is con-verted into an electrical signal by a sensor is sampled by digital oscilloscope with the rate of 100 MS/S .this electrical signal is recorded by a computer for further investigation. At this measuring system, oscilloscope is triggered by occurrence of each PD pulse. Detected signals are stored at each measuring channel.
2 PD Testing conditions:
We used needle on insulation paper and grounded for generating corona discharge. The distance between needle and paper was set at 2 mm. At three referenced below conditions the tests results have been recorded.
a) For corona discharge:
Measurement 1:
Calibration: 167 pC
Primary side voltage: 105V
Calibration and measurement:
G20dB: on GPD: 50;
Measurement 2:
Calibration: 400 pC
Primary side voltage: 165V.
Calibration and measurement:
G20dB: on GPD: 0;
Measurement 3:
Calibration: 1970 pC
Primary side voltage: 165V.
Calibration and measurement:
G20dB: off GPD: 20;
b) For surface discharge of needle on insulation paper and grounded plate.
Measurement 1:
PD inception voltage: 30 volt on LV side of dry type transformer.
Calibration with 30 pC
Calibration and measurement setting:
G20dB: on, GPD: 140;
Measurement 2:
PD inception voltage: 50 volt on LV side of dry type transformer.
Calibration with 50 pC
Calibration and measurement setting:
G20dB: on, GPD: 140;
3 PD fault types and denoising them
Corona, surface discharge and discharge of the holes inside insulation are three impor-tant types of PD fault are shown at Fig. 2 [1]. To study efficiency of the different patterns for recognizing and classifying these faults, ar-tificial partial discharge faults happened on each of them were stored. It is obvious that each of the information and features obtained from the waveform of partial discharge pulses have different efficiency and ability determine the fault type, so these features should be re-liable enough in order to reach exact and cor-rect results.
a)
b)
c)
Fig. 2. Different arrangements of various kinds of partial discharge
a) Discharge of the holes inside insulation
b) Corona
c) Surface discharge
So, because of the reliability importance, pulses containing superficial charges and sim-ilar to PD, at three different conditions were applied by a calibrator to ten experiments for each condition, and were measured by a de-tector joint to capacitive sensor. At this paper denoising the partial discharge of corona dis-charge and surface discharge of needle on in-sulation paper and grounded plate will be stu-died and considered. Monopulses that are de-tected by UWB device during 6 experiments, with 3 different condition for corona discharge (each condition was done 2 times) and 3 ex-periments with same conditions for surface discharge of needle on insulation paper and grounded plate are delivered and shown at Fig. 3 , Fig. 4.
The noise of the surrounding ambient mixed with discharge signal should be isolated for detection of partial discharge signal.
a)
b)
c)
d)
e)
f)
Fig.3. Monopulses, detected by UWB device during 6 ex-periments for corona discharge (mV/mSec)
a,b) two Monopulses of first test
c,d) two Monopulses of second test
e,f) two Monopulses of third test
a)
b)
c)
Fig.4. Monopulses, detected by UWB device during 3 ex-periments for surface discharge of needle on insulation paper and grounded plate (mV/mSec)
a) Monopulse of first test
b) Monopulse of second test
c) Monopulse of third test
Usually, noise type is Environmental noise. Noises of the amplifiers also are this type. These noises are called White Noise. These kinds of noises follow Gaussian distri-bution and their average equals zero [1].
Partial discharge contains high frequen-cies near 10 MHz. For isolation of this signal from noise if only frequency domain is take into consideration, then the time factor will not be available and hence detecting the time of the fault will not be done. Because of this matter, one method that cover both time and frequency factor is indeed, in order to isolate the signal and noise from each other. This method is called Wavelet transfer. Wavelet method in-cludes various wavelet functions. By applying each of these wavelet functions, it is possible to omit the noise. But using some of these wavelet functions may cause to lose details or parts of original signal. The optimum wavelet function is that similar to original signal. At this condition, the isolated signal will be more similar to the main signal. At most of similar papers, after denoising, usually the main signal power to two signal difference power ratio is considered as determinate factor. Also, the number of surfaces is determined by trial and error method.
Here we use two another ways for defin-ing the best wavelet function for denoising the signals. We use some practical signals for de-noising them as followed way:
1- We denoise the signal by using speci-fied wavelet functions, firstly.
2- Correlation between the denoised sig-nal and origin signal gives us a likelihood coefficient. It is clear The high likelihood coefficient, the best wavelet function for de-noising discharge signals.
3-In this step we confirm our results with another way. We decrease the denoised signal from the origin signal. Then calculate the power of result signal. It is clear the littler result, the better wavelet function for denoising discharge signals.
To study efficiency of the different pat-terns for recognizing and classifying these faults, artificial partial discharge faults hap-pened on each of them were stored. It is ob-vious that each of the information and features obtained from the waveform of partial dis-charge pulses have different efficiency and ability determine the fault type, so these fea-tures should be reliable enough in order to reach exact and correct results.
both of mentioned methods and SNR way reach same result. But the advantage of men-tioned methods, will be clearer when the do-main magnitude of white noise is litter in compared with the origin signal, or noise be-come more irregular during the spend time. We are always trying to maximize oscillation probability. In practical tests, using the SNR filter is usual. Input signal is complex signal, with S (&fnof
, furrier transfer. Response to the filter is shown with h (t). So transfer function is H (&fnof. Output voltage can obtain as bellow:
(1)
tM, is the time, witch the output voltage domain is maximum. This time is important, because the maximum value causes the maximum os-cillation. The power of output noise is:
(2)
The SNR at time tM, can calculate as:
(3)
According to the Schwartz theorem:
(4)
With supposing:
We have:
(5)
So:
(6)
So the output of filter will be:
4 The experimental results
At this experiment, partial discharge re-sulted from corona discharge and surface dis-charge of needle on insulation paper and grounded plate. The method that has been used for optimum selection of the wavelet function in order to omit the noise is as below:
1) First, the main signal has been denoised by the specified wavelet function.
2) We correlate the denoised signal and origin signal. It gives us a likelihood coeffi-cient. The high likelihood coefficient, the best wavelet function for denoising discharge sig-nals. This way is known as maximum likelihood method.
3) At this step, second norm of the dif-ference between main signal and denoised signal is obtained. It is obvious that how much the second norm magnitude is small, the se-lected wavelet function is better. This way is known as minimum least square method.
After receiving partial discharge signal, it is denoised with 37 wavelet function and at 5 surface and step 2 and 3 are done. Fig. 7 and Fig. 8 shows the second norm of the difference between main signal and denoised signal for corona discharge and surface discharge of needle on insulation paper and grounded plate, ordinary.
As it is seen for corona discharge, values of wavelet function number 76, 6, 131, 166, 36, 81, 161, 71, 116, 111, 26 are smaller and for surface discharge of needle on insulation paper and grounded plate values of wavelet function number 11, 21, 46, 41, 56, 136, 126, 86, 141, 171, 176 are smaller. These values for each experiment are available at table 1.
Fig. 9 and Fig. 10 shows the coefficients between main signal and denoised signal for corona discharge and surface discharge of needle on insulation paper and grounded plate.
As it is seen, wavelet functions number 76, 6, 131, 166, 36, 81, 161, 71, 116, 111, 26 have greater values than others for corona discharge and wavelet functions number 11, 21, 46, 41, 56, 136, 126, 86, 141, 171, 176 have greater values than others for discharge and surface discharge. These values for each ex-periment are shown at table 1, 2, 3, 4. Fig. 5 shows main artificial corona discharge signal and denoised signals resulted with level 4 bior 2.2, level 4 db 3, level 4 rbio2 2.6, level 4 and 8 rbio2 3.1 wavelet functions. Also it is recom-mended not to use rbio2 3.1 wavelet functions.
Also Fig. 6 shows main artificial surface discharge of needle on insulation paper and grounded plate signal and denoised signals resulted with level 4 coif2, level 4 db4, level 4 bior2.8, level 4, 8 rbio2 3.1 wavelet functions, and it is recommended not to use rbio2 3.1 wavelet functions.
The wavelet functions that are mentioned below are offered to be used for corona dis-charge.
1) bior2.2, Level 4 2) db3, Level 4
3) rbio2 2.6, Level 4 4) rbio2 4.4, Level 4
5) sym4, Level 4 6) bior2.4, Level 4
7) rbio2 3.9, Level 4 8) coif5, Level 4
9) bior4.4, Level 4 10) bior3.9, Level 4
11) db8, Level 4
And below wavelet functions are offered to be used for surface discharge of needle on insulation paper and grounded plate.
1) coif2, Level 4 2) bior2.8, Level 4
3) rbior2 2.6, Level 4 4) rbior2 5.5, Level 4
5) rbior2 6.8, Level 4 6) rbior2 2.8, Level 4
7) bior6.8, Level 4 8) sym8, Level 4
9) sym6, Level 4 10) db6, Level 4
11) db4, Level 4
a)
b)
c)
d)
e)
f)
Fig.5. corona discharge signals (mV/mSec)
a) Origin signal
b) Denoised signal with bior2.2, level 4
c) Denoised signal with db3, level 4
d) Denoised signal with rbio2 2.6, level 4
e) Denoised signal with rbio2 3.1, level 4
f) Denoised signal with rbio2 3.1, level 8
Key words: Partial discharge, Corona, Surface discharge, Signal to Noise Ratio (SNR), Minimum least square, Maximum likelihood
1 Introduction
Nowadays there are few methods for lo-cating the partial discharge and fault type of the oil transformers. However at the case of dry distribution transformers, there are many dif-ferent methods to use because of the easy access to its coils. At this type of transformers, coil is placed in the mold of solid insulated resin and its peripheral surface is accessible.
Mounting capacitive sensors on the sur-face of the bobbin is one of the effective me-thods for locating the partial discharge and recognizing fault type for dry distribution transformers. By detection of the partial dis-charge signals through the capacitive sensors the location and type of the partial discharge is possible [2].
There are different devices to measure partial discharge. These devices have different usage and abilities. Because of the different techniques of monopulses measuring, and using different UWB device and applying an especial kind of partial discharge, various important information was recorded. Devices and schematic of the measurement system with ultra wideband is shown at Fig. 1. Detecting circuit of this system has very ultra wideband and is able to detect the waveform of PD mo-nopulse at the time domain.
Fig. 1. Schematic of the measurement system with ultra wideband
At this measuring system, passing through detection impedance inside the detector, PD current pulses are converted into an electrical signal. These signals are amplified by a variable gain amplifier and then converted into an optical signal by a sensor. It imposes lower noise signals on PD signals at the transmission line, so gives better signal to noise ratio (SNR).
After transmission through an optical ca-ble, subsequently this optical signal is con-verted into an electrical signal by a sensor is sampled by digital oscilloscope with the rate of 100 MS/S .this electrical signal is recorded by a computer for further investigation. At this measuring system, oscilloscope is triggered by occurrence of each PD pulse. Detected signals are stored at each measuring channel.
2 PD Testing conditions:
We used needle on insulation paper and grounded for generating corona discharge. The distance between needle and paper was set at 2 mm. At three referenced below conditions the tests results have been recorded.
a) For corona discharge:
Measurement 1:
Calibration: 167 pC
Primary side voltage: 105V
Calibration and measurement:
G20dB: on GPD: 50;
Measurement 2:
Calibration: 400 pC
Primary side voltage: 165V.
Calibration and measurement:
G20dB: on GPD: 0;
Measurement 3:
Calibration: 1970 pC
Primary side voltage: 165V.
Calibration and measurement:
G20dB: off GPD: 20;
b) For surface discharge of needle on insulation paper and grounded plate.
Measurement 1:
PD inception voltage: 30 volt on LV side of dry type transformer.
Calibration with 30 pC
Calibration and measurement setting:
G20dB: on, GPD: 140;
Measurement 2:
PD inception voltage: 50 volt on LV side of dry type transformer.
Calibration with 50 pC
Calibration and measurement setting:
G20dB: on, GPD: 140;
3 PD fault types and denoising them
Corona, surface discharge and discharge of the holes inside insulation are three impor-tant types of PD fault are shown at Fig. 2 [1]. To study efficiency of the different patterns for recognizing and classifying these faults, ar-tificial partial discharge faults happened on each of them were stored. It is obvious that each of the information and features obtained from the waveform of partial discharge pulses have different efficiency and ability determine the fault type, so these features should be re-liable enough in order to reach exact and cor-rect results.
a)
b)
c)
Fig. 2. Different arrangements of various kinds of partial discharge
a) Discharge of the holes inside insulation
b) Corona
c) Surface discharge
So, because of the reliability importance, pulses containing superficial charges and sim-ilar to PD, at three different conditions were applied by a calibrator to ten experiments for each condition, and were measured by a de-tector joint to capacitive sensor. At this paper denoising the partial discharge of corona dis-charge and surface discharge of needle on in-sulation paper and grounded plate will be stu-died and considered. Monopulses that are de-tected by UWB device during 6 experiments, with 3 different condition for corona discharge (each condition was done 2 times) and 3 ex-periments with same conditions for surface discharge of needle on insulation paper and grounded plate are delivered and shown at Fig. 3 , Fig. 4.
The noise of the surrounding ambient mixed with discharge signal should be isolated for detection of partial discharge signal.
a)
b)
c)
d)
e)
f)
Fig.3. Monopulses, detected by UWB device during 6 ex-periments for corona discharge (mV/mSec)
a,b) two Monopulses of first test
c,d) two Monopulses of second test
e,f) two Monopulses of third test
a)
b)
c)
Fig.4. Monopulses, detected by UWB device during 3 ex-periments for surface discharge of needle on insulation paper and grounded plate (mV/mSec)
a) Monopulse of first test
b) Monopulse of second test
c) Monopulse of third test
Usually, noise type is Environmental noise. Noises of the amplifiers also are this type. These noises are called White Noise. These kinds of noises follow Gaussian distri-bution and their average equals zero [1].
Partial discharge contains high frequen-cies near 10 MHz. For isolation of this signal from noise if only frequency domain is take into consideration, then the time factor will not be available and hence detecting the time of the fault will not be done. Because of this matter, one method that cover both time and frequency factor is indeed, in order to isolate the signal and noise from each other. This method is called Wavelet transfer. Wavelet method in-cludes various wavelet functions. By applying each of these wavelet functions, it is possible to omit the noise. But using some of these wavelet functions may cause to lose details or parts of original signal. The optimum wavelet function is that similar to original signal. At this condition, the isolated signal will be more similar to the main signal. At most of similar papers, after denoising, usually the main signal power to two signal difference power ratio is considered as determinate factor. Also, the number of surfaces is determined by trial and error method.
Here we use two another ways for defin-ing the best wavelet function for denoising the signals. We use some practical signals for de-noising them as followed way:
1- We denoise the signal by using speci-fied wavelet functions, firstly.
2- Correlation between the denoised sig-nal and origin signal gives us a likelihood coefficient. It is clear The high likelihood coefficient, the best wavelet function for de-noising discharge signals.
3-In this step we confirm our results with another way. We decrease the denoised signal from the origin signal. Then calculate the power of result signal. It is clear the littler result, the better wavelet function for denoising discharge signals.
To study efficiency of the different pat-terns for recognizing and classifying these faults, artificial partial discharge faults hap-pened on each of them were stored. It is ob-vious that each of the information and features obtained from the waveform of partial dis-charge pulses have different efficiency and ability determine the fault type, so these fea-tures should be reliable enough in order to reach exact and correct results.
both of mentioned methods and SNR way reach same result. But the advantage of men-tioned methods, will be clearer when the do-main magnitude of white noise is litter in compared with the origin signal, or noise be-come more irregular during the spend time. We are always trying to maximize oscillation probability. In practical tests, using the SNR filter is usual. Input signal is complex signal, with S (&fnof
, furrier transfer. Response to the filter is shown with h (t). So transfer function is H (&fnof. Output voltage can obtain as bellow:(1)
tM, is the time, witch the output voltage domain is maximum. This time is important, because the maximum value causes the maximum os-cillation. The power of output noise is:
(2)
The SNR at time tM, can calculate as:
(3)
According to the Schwartz theorem:
(4)
With supposing:
We have:
(5)
So:
(6)
So the output of filter will be:
4 The experimental results
At this experiment, partial discharge re-sulted from corona discharge and surface dis-charge of needle on insulation paper and grounded plate. The method that has been used for optimum selection of the wavelet function in order to omit the noise is as below:
1) First, the main signal has been denoised by the specified wavelet function.
2) We correlate the denoised signal and origin signal. It gives us a likelihood coeffi-cient. The high likelihood coefficient, the best wavelet function for denoising discharge sig-nals. This way is known as maximum likelihood method.
3) At this step, second norm of the dif-ference between main signal and denoised signal is obtained. It is obvious that how much the second norm magnitude is small, the se-lected wavelet function is better. This way is known as minimum least square method.
After receiving partial discharge signal, it is denoised with 37 wavelet function and at 5 surface and step 2 and 3 are done. Fig. 7 and Fig. 8 shows the second norm of the difference between main signal and denoised signal for corona discharge and surface discharge of needle on insulation paper and grounded plate, ordinary.
As it is seen for corona discharge, values of wavelet function number 76, 6, 131, 166, 36, 81, 161, 71, 116, 111, 26 are smaller and for surface discharge of needle on insulation paper and grounded plate values of wavelet function number 11, 21, 46, 41, 56, 136, 126, 86, 141, 171, 176 are smaller. These values for each experiment are available at table 1.
Fig. 9 and Fig. 10 shows the coefficients between main signal and denoised signal for corona discharge and surface discharge of needle on insulation paper and grounded plate.
As it is seen, wavelet functions number 76, 6, 131, 166, 36, 81, 161, 71, 116, 111, 26 have greater values than others for corona discharge and wavelet functions number 11, 21, 46, 41, 56, 136, 126, 86, 141, 171, 176 have greater values than others for discharge and surface discharge. These values for each ex-periment are shown at table 1, 2, 3, 4. Fig. 5 shows main artificial corona discharge signal and denoised signals resulted with level 4 bior 2.2, level 4 db 3, level 4 rbio2 2.6, level 4 and 8 rbio2 3.1 wavelet functions. Also it is recom-mended not to use rbio2 3.1 wavelet functions.
Also Fig. 6 shows main artificial surface discharge of needle on insulation paper and grounded plate signal and denoised signals resulted with level 4 coif2, level 4 db4, level 4 bior2.8, level 4, 8 rbio2 3.1 wavelet functions, and it is recommended not to use rbio2 3.1 wavelet functions.
The wavelet functions that are mentioned below are offered to be used for corona dis-charge.
1) bior2.2, Level 4 2) db3, Level 4
3) rbio2 2.6, Level 4 4) rbio2 4.4, Level 4
5) sym4, Level 4 6) bior2.4, Level 4
7) rbio2 3.9, Level 4 8) coif5, Level 4
9) bior4.4, Level 4 10) bior3.9, Level 4
11) db8, Level 4
And below wavelet functions are offered to be used for surface discharge of needle on insulation paper and grounded plate.
1) coif2, Level 4 2) bior2.8, Level 4
3) rbior2 2.6, Level 4 4) rbior2 5.5, Level 4
5) rbior2 6.8, Level 4 6) rbior2 2.8, Level 4
7) bior6.8, Level 4 8) sym8, Level 4
9) sym6, Level 4 10) db6, Level 4
11) db4, Level 4
a)
b)
c)
d)
e)
f)
Fig.5. corona discharge signals (mV/mSec)
a) Origin signal
b) Denoised signal with bior2.2, level 4
c) Denoised signal with db3, level 4
d) Denoised signal with rbio2 2.6, level 4
e) Denoised signal with rbio2 3.1, level 4
f) Denoised signal with rbio2 3.1, level 8
