Chromatic processing for feature extraction of PD-induced UHF signals in GIS

1 Introduction

Partial discharge (PD) that can lead to insulation deterioration of materials of electrical equipment,may occur in gas-insulated switchgears (GIS) and transformers subjected to high-voltage stresses.Online PD detection can effectively discover the incipient faults and improve the power system security [1],[2].As the components of GIS are integrated in enclosed metal tanks,the ultrahigh frequency (UHF) detection method has become a commonly used technique to detect PDs because of their high sensitivity and comparative immunity to noise [3],[4].PDs in GIS emit electromagnetic (EM) waves in the range of UHF.Internal or external antennas can receive PDinduced UHF signals for additional diagnoses [5].Feature extraction of UHF signal has attracted extensive scientific attention [6],[7].The statistical features of discharge phase (φ),amplitude (q),and count (N) yield good defect recognition performance [8],[9].Some other methods used time-resolved PD signals rather than the statistical features of the φ-q-N pattern.Li et al.used short-time Fourier transform (STFT) to obtain the time-frequency distribution of UHF signals,and extract Hu’s invariant moments as a very concise feature vector [10].Long et al.presented an optimized variational mode decomposition algorithm to decompose the UHF signal into several band-limited modes from which the effective components were identified [11].In recent years,deep learning was also extensively applied to UHF signal processing and PD pattern recognition [12],[13].This study presents the chromatic methodology for feature extraction of PD-induced UHF signals based on color science concepts,and investigates key factors that affect the algorithmic outcomes.

2 Chromatic methodology

The purpose of signal feature extraction is the description of a complex signal in a simple manner.At the same time,the results reflect the critical characteristics of the signal.The essence of the color is also a signal type.Thus,many methods exist for the quantification of chromaticity based on color science [14],[15].One of these methods,the chromatic method,simply represents the color based on the values of the coordinates H,L,S whereby H is the hue,S is the saturation,and L is the lightness.In addition to the quantitative description of the color,the chromatic method is also used to monitor the particulates by passing white light through a test microfiber filter,and by detecting the chromatic changes with a camera [16].Furthermore,this method can discriminate different types of liquors by broadband optical absorption spectra [17],and measure the concentration of dissolved gases in the transformer oil due to partial discharges [18].As the chromatic methodology contributed effective results in chemical detection,this simple and valid feature-extraction approach was utilized in PD detection [19],[20].

The three nonorthogonal processors are a significant part of the chromatic methodology.Processor responses R(P),G(P),and B(P),are functions of the parameter P,which can be time,frequency,or sequence.F(P) is the amplitude of a signal that varies with P.The output of a processor X(P) addressing the signal F(P) is

The outputs of three processors are denoted by R,G,B,which are similar to the outputs of tristimulus filters of the human eye.

The three chromatic parameters H,L,S are transformed from the outputs of three processors according to the following algorithms,

where

The values H,L,and S obtained by the chromatic methodology have good consistency with the average frequency,the signal energy content and the (RMS bandwidth)2,

The chromatic methodology (Equations 1-7) provides a more efficient algorithm which can be used instead of the complicated Equation (8)-(10) [19].

For the human eye,the parameter H (Hue) represents the most dominant wavelength,the parameter L (Lightness) corresponds to the signal strength,and the parameter S (Saturation) determines the spectral spread.The values of coordinates H,L,S can be simply represented as two points,i.e.,in the forms of the H-S or H-L polar diagrams.H is the azimuthal coordinate (0°-360°),while L and S are radii [21].

3 Chromatic processing of frequency-domain signal

3.1 Experimental setup

The experimental GIS tank is designed according to a 252 kV GIS bas-bar type with one high-voltage conductor.The planer equiangular spiral antenna is adopted as the internal UHF sensor [4].To simulate the actual running situation of poor contact,the floating electrode defect is installed in the GIS tank artificially.Two adjacent copper nuts are fixed on an insulated bolt,which is mounted on the central conductor as shown in Fig.1(a).The artificial PD defect and the UHF sensor are in different GIS chambers.The defect is arranged in the four-way tank under the bushing based on which the upper terminal is connected to the high-voltage source.There is an epoxy spacer separating the two chambers.The partial discharge UHF signals are recorded when the pressure of the SF6 is 0.1 MPa.In practice,the attenuation characteristic of the UHF signal varies when defects are located at different angles with respect to the antenna [22].Therefore,in this investigation,the artificial defect is oriented at 0°,90°,and 180° with respect to the antenna.Fig.1 shows the internal antenna and different defect positions.

Fig.1 Positions of the defect and UHF sensor

3.2 Feature extraction of UHF signal in chromatic space

The internal antenna is connected to the digital oscilloscope by a coaxial cable.The energy of the UHF signal is mainly distributed in tens of nanoseconds [1],[2],[23].Signal durations in the range of 0-100 ns were acquired in this study.Fig.2 shows the waveform of the UHF signal in the time domain and the Fourier transform (FFT) outcome with N = 1000 points.In the spectrogram,there are peaks at 700 MHz and 1.1 GHz approximately,and the energy thus,is mainly distributed within these frequency bands.

The UHF band ranges from 300 MHz to 3 GHz.The energy in the band spanning 0 to 300 MHz is considered low and can be neglected,as shown in Fig.2(b).Thus,the frequency range from 0 to 3 GHz is covered by three processors R,G,B as shown in Fig.3.Each processor is a Gaussian function (11),

Fig.2 UHF signal waveform

where a is the amplitude of the pulse,b is the position of the peak, is the width of half peak value.

The amplitude of the processor is 1,and the width of half peak value is 0.5 GHz.The center positions of the three pulses are 0.75 GHz,1.5 GHz,and 2.25 GHz respectively.They are all the same except the center position.The amplitude of the intersection point of two adjacent pulses is 0.2115.The processors in Fig.3 are referred to be Processor 1 (P-1) types.

Fig.3 Gaussian processor (P-1)

The H,L,and S values are calculated by three processors outputs R,G,B following (1),and the three coordinates are represented in the biconical chromatic space [24].It is often preferable to display H,L,S as two two-dimensional (2D) polar diagrams rather than as a three-dimensional (3D) diagrams to simplify the observation of the trend patterns.Fig.4 is the H-S polar diagram showing the coordinates of UHF signals when defects occur at 0°,90°,and 180°.

The UHF signals induced by artificial defects were recorded 30 times at each angle.It is obvious that the points of the three angles are separated into three regions.Points at 0° and 180° are located at the circumference of S = 0.8.H values of 0° are less than 180°.Meanwhile,the points at 180° are more concentrated at H = 30.However,the points at 90° are different from the other two angles.The characteristic of 90° is zonal distribution.The S values are in the 0.4 to 0.8 region,and the H values from 35 to 70.

Fig.4 H-S polar diagram of UHF signals of different defect positions processed by P-1

Fig.4 indicates the signal of the 0° defect differs from that at 180°,while the bandwidths of the two angles are almost the same.However,the dominant wavelengths (frequency) of the signals of the 90° defects are greater than 0° and 180°.This reveals that the UHF signal at 90° has more high-frequency components.Points at 90° have a bigger bandwidth distribution region.It provides an overview showing that the intensity of the same frequency component varies in different discharge processes.According to the zonal distribution,the signal has a narrower bandwidth if the frequency is lower,i.e.,the signal has more high-frequency components at the opposite end of the distribution belt.The distribution rules of the UHF signal on the H-S plane can be used to distinguish different angles between the PD defect and the UHF sensor.

4 Effects of the processor

In color science,visual images perceived by the human eye are dependent upon the processor characteristics.For example,modifying the spectral response of the blue processor makes the blue component appear in the basic image as stronger or weaker.The processor characteristics can also influence the results processed by the chromatic methodology in the frequency domain,such as their degree of nonorthogonality,their profile form,width,and relative amplitudes.The influences of the chromatic processors of the UHF signal are studied in this chapter.

In Chapter 3,P-1 is a group of three Gaussian pulses with a full-width-at-half maximum value of 0.5 GHz.Owing to the fact that the amplitude of the Gaussian function decreases rapidly as a function of the independent variable (when it has values farther from the center of the function),the amplitude becomes approximately equal to zero when it is far enough.Three Gaussian functions can be assumed symmetrical in the frequency range of 0 to 3 GHz.The processor overlaps with the adjacent processor.The width of the overlapping area and the amplitude of the intersection point vary depending on the profile form of the processors.The amplitude of the intersection point of P-1 is 0.2115,and the overlapping area is small.Compared with P-1,another type of processor is designed,known as Processor 2 (P-2),with a different profile,as shown in Fig.5.The center positions of the three Gaussian pulses are at 0.5,1.5,and 2.5 GHz,respectively,and the amplitude of the intersection point is 0.4786.A primary difference between P-1 and P-2 is that the R and B processors are shifted to the left and the right,respectively,for uniform distribution from 0 to 3 GHz.These two pulses are asymmetrical in the y direction from 0 to 3 GHz,and the functions are cut off when the amplitude is 0.5 approximately.

Fig.5 Gaussian processor (P-2)

Parameters H,L,S are features of the UHF signal in the chromatic space.H corresponds to the dominant frequency,and L corresponds to the signal strength.However,their relationship is nonlinear and segmented.Thus,it is difficult to be expressed mathematically.To study the H and L responses to the frequency,this work designed a graphic method based on the Dirac function.Assume an infinitely narrow (monochromatic) signal in the frequency domain with a spectrum denoted by a Dirac function δ(f0).In other words,this signal only contains a specific frequency component of f0.The chromatic transformation of the signal yields the parameters H and L,which are responses at f0.The response curves of H and L can be gained by varying f0 from 0 to 3 GHz as illustrated in Fig.6.

Fig.6 is the comparison of the H response of P-1 and P-2 from 0 to 3 GHz.Both curves increase monotonically,and each frequency point corresponds to a well-determined H value.The average frequency of the UHF signal can be solved by the H response curve.The H response curve of P-1 is flat at the beginning and at the end,and the slope is also close to zero in the middle part.The curve is quite steep at the other two parts.For P-2,the H response curve has a good linearity except at the frequency bands of 0-0.5 GHz and 2.5-3 GHz.It can be observed from the processor profiles in Figs.3 and 5 that if there is one dominant processor function at a specific frequency value,i.e.,the amplitude of this processor is considerably larger than other adjacent pulse functions,and the slope of the H response curve at this frequency value is close to zero.By contrast,the slope of the H response curve increases at instances in which the processors overlap.Furthermore,if the width of the overlapping area decreases,the H response curve becomes steep as Fig.6 shows.In other words,the H response curve of P-1 rises faster than P-2 from 1.0 to 1.25 GHz.

Fig.6 H response curves of P-1 and P-2 from 0 to 3 GHz

The steep response curve provides regions with higher sensitivity.The processors can be wider or shifted to adjust the overlapping width to increase the response sensitivity assuming that signals to be processed are mainly discriminated at the specific frequency range.If the spectrum of the signal distributes over the entire frequency range,it is better to provide a more uniform sensitivity throughout the region just like P-2.

Fig.7 illustrates the L response curves of P-1 and P-2 from 0 to 3 GHz.The L response of P-2 is greater than P-1 in the entire frequency range.L denotes the average of the R,G,B processor outputs like (3) shows.Therefore,the L value is related to the amplitudes of processors at the same frequency point.The wider the processor,the greater will be the increase in the amplitude of the function at the same position.The L response increases as well.The L response curve of P-1 is decreased considerably at two places.In contrast,The L response curve of P-2 is smoother owing to the wider overlapping area.The overlapping area of adjacent processors can make up for the diminished processor’s response.As the responses of the R and B P-1 processors drop almost to zero at margins of the frequency range,the L response curve also falls to zero.However,the R and B processors of P-2 are cut off at 0 and 3 GHz,the L response is not zero at the margin of the frequency range.The amplitude of the L response is related to the width and location of the processor.If a more uniform L response distribution is required,the overlapping area of adjacent processors should be wider.

Fig.7 L response curves of P-1 and P-2 from 0 to 3 GHz

Fig.8 indicates the distribution of UHF signals of different defect angles on the H-S plane processed by P-2.The relative distribution tendency applies for the entire range,but the average H value increases compared with P-1.This is attributed to the fact that the dominant frequency component of the UHF signal ranges from 0.5 to 1.5 GHz,wherein the H response of P-2 is greater than that of P-1.In addition,the average S value decreases slightly.The three regions of the three types of the PD defect overlap with each other because of the H response of P-2 has a smaller slope than that in P-1 for frequencies from 0.5 to 1.5 GHz.The lower sensitivity in this region forces the three groups of processed points to be closer to each other.

Fig.8 H-S polar diagram of UHF signals of different defect positions processed by P-2

The chromatic coordinates of the three groups of UHF signals are plotted on the H-S polar diagram by averaging the H and S value,as shown in Fig.9.The chromaticity changes,and the distance between any two points in the graph are defined by (12),

Fig.9 Three groups of averaging H-S coordinates processed by P-1 and P-2

The chromaticity changes of the UHF signals on different angle positions are listed in Table1.When the overlapping area of processors becomes wider,the sensitivity of H response reduces,and then the average distance between different types of UHF signals decreases.This is against the discrimination of different PD defects.

Table1 Chromaticity changes of UHF signals on different angle positions

Processor dHS 0°-90° 0°-180° 90°-180°P1 0.5366 0.2285 0.3882 P2 0.4324 0.1876 0.3150

Fig.10 compares the averaging parameter L in the cases of P-1 and P-2.The relative position of the two adjacent copper nuts has tiny and inevitable differences when the artificial defects are mounted at three different angles.Therefore,the amplitude and energy of the UHF signals are also diverse.The main purpose of this chapter is to investigate the influence of the processor feature on the chromatic representation of UHF signals.Thus,the L value is normalized by considering that the value of L in the case of P-1 as 100%.The L values of P-2 are approximately equal to 150% for the three angle positions.In other words,the L response of P-2 is greater than that in P-1,as demonstrated in Fig.10.

Fig.10 Comparison of averaging parameter L of P-1 and P-2

Meanwhile,the statistical calculation can help study the effect of the processor.Fig.11 shows the standard deviation of parameter H.There are minor differences between P-1 and P-2 when the defect is at 0° or 180°,while the standard deviation of P-2 is much more than that of P-1 at 90°.There are more high-frequency components in the UHF signal at 90°,and these components are in the frequency band around 1.5 GHz.The H response curve of P-2 is steeper than that of P-1 at 1.5 GHz.As a result,P-2 discriminates the UHF signal at 90° better and the H values are more dispersed.

Fig.11 Standard deviation of parameter H of P-1 and P-2

Fig.12 shows the standard deviation of parameter S.Likewise,there is a minor difference between P-1 and P-2 when the defect is at 0° or 180°.However,the standard deviation of P-1 is greater than P-2 at 90°.In addition,the changes of the standard deviations of H and S are inversely proportional,i.e.,more dispersed H values make the S values more concentrated.They are inconsistent and cannot reach the optimal result at the same time.Therefore,it is important to choose suitable processor features for PD defect classification based on the consideration of the spectra of different UHF signals and parameter response curves.

Fig.12 Standard deviation of parameter S of P-1 and P-2

5 Time-stepping processing

The PD-induced signal is a nonstationary signal,and its frequency component varies with time.The specific time at which the frequency component occurs is not clear when the Fourier transform is used.To overcome this disadvantage,the time-frequency analysis and wavelet transform were proposed to process the UHF signal [25],[26],[27].The results shown above are features of the signal in the frequency domain using the chromatic method.To obtain the features of the frequency component that varies with time,chromatic methodology with time-stepping processing is proposed in this section.

A rectangular window is used to extract the time domain signal that is transferred to the frequency domain.The chromaticities H,L,and S are obtained from the spectrum using chromatic method according to (2)-(4).Subsequently,the rectangular window is shifted along the time axis as Fig.13 shows.The processing is repeated until the end of the waveform.The width of the rectangular window and the length of stepping are determined by the sampling rate,signal length,and the expected time-frequency distribution.The obtained parameters H,L,and S that vary with time can be plotted as H-t,L-t, and S-t curves.In addition,the H-L and H-S curves can also been plotted as polar diagrams.

Fig.13 Rectangular window and time stepping

The P-1 processor is selected in this section.The width of the rectangular window is 50 ns,and the time step is 5 ns for the three groups of the UHF signal at different angle positions.Fig.14 shows the H-L curves in the same polar diagram with the normalized parameter L.The trends of the H-L coordinates vary with time,as indicated by the arrows in Fig.14.The tracks of each angle position are enveloped in the dotted line.The UHF signals of the angles change as L decreases owing to the fact that the dominant energy occurs at the early parts of the signal and decreases over time.The parameter H at 0° and 180° changes slightly over time,while the H value at 90° increases first and then drops.This means that the high-frequency component concentrates in the later part of the waveform,and there is a lower frequency component in the initial part.Therefore the track channel for 90° is wider than the other two angles.The time-frequency distribution characteristics of the UHF signal is obtained by the chromatic time-stepping processing.

Fig.14 Track channels of UHF signals at different positions

6 Applications

To classify the PD defect patterns,three typical defects,floating electrode,metal protrusion,and particle on the spacer surface,are mounted in the GIS tank.As Fig.15 shows,the defects are all at 90° position.One hundred groups of UHF signals are recorded in each pattern.The support vector machine (SVM) was applied for classification.Chromatic methodology compresses each UHF signal into a tri-vector.In each pattern,60 random groups of signals constituted the training set,and the other 40 were the test set.The classification results of the three patterns based on the chromatic parameters H, L,and S are listed in Table2,and the average recognition rate is 90%.

Fig.15 Three typical partial discharge (PD) defect patterns

Table2 Classification of three partial discharge (PD) defect patterns

PD defect pattern Number of recognitions Recognition rates Floating electrode 40 100%Metal protrusion 37 92.5%Particle on spacer surface 31 77.5%Total 108 90%

7 Discussion

The features of UHF signals can be extracted in the chromatic domain as several simple parameters.The parameters describe the dominant frequency,strength,and the spectral spread of the signal just like the human eye perceives color.The processor plays a critical role in chromatic processing.This work discusses the influences of the width and relative positions of the processors.The process of the chromatic methodology is summarized in the form of a flow chart in Fig.16.

Fig.16 Flow chart of the chromatic methodology

The PD-induced UHF signal is acquired in the GIS tank by UHF sensors.From one viewpoint,the signal is transferred to the frequency domain,while from another viewpoint,the width of the rectangular window and the length of the time step are determined.Subsequently,the upper and lower limits of the frequency bands fL and fH are determined.The next step is to choose the features of processors according to the spectrum,such as the profile of the function,the width,the overlapping height,and symmetry.The major step of the chromatic methodology follows next.The outputs of the processors R,G,and B,are calculated using numerical integration,and the chromatic parameters H,L,and S are obtained.The representation in chromatic space includes important features of the UHF signal and a sparse representation type.It can be used in the PD classification algorithms.

8 Conclusion

This study proposes a feature extraction method of UHF signals using the chromatic methodology in color science.Three types of artificial defects are installed in the GIS tank at the angle positions of 0°,90°,and 180°,respectively.The features of UHF signals in chromatic space are extracted,and the feasibility of the algorithm is verified.The coordinates of the three types of UHF signals have significant differences in chromatic space so that this method can be used for the discrimination of PD defects.The processors influence the results processed by the chromatic methodology,such as their degree of nonorthogonality,their profile form,width,and overlapping height.This work makes suggestions to the processor feature selection.Time-stepping processing was studied.This led to the formulation of the rules of the UHF signalfrequency characteristics that varied with time.Finally,the process and options of the chromatic methodology were summarized.In the future,the classification of different PD defects and the location of the PD source using chromatic methodology will be researched.

Acknowledgments

This work was supported by National Key Research and Development Program of China (2018YFB0905000).

Declaration of Competing Interest

We declare that we have no conflict of interest.