Electrical Power and Energy Systems 73 (2015) 192–199

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Application of Gabor–Wigner transform to inspect high-impedancefault-generated signals

http://dx.doi.org/10.1016/j.ijepes.2015.05.0100142-0615/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +886 6 2757575x32506; fax: +886 6 234 5482.E-mail address: clhuang@mail.ncku.edu.tw (S.-J. Huang).

Jiang-Yong Cheng a, Shyh-Jier Huang a,⇑, Cheng-Tao Hsieh b

a Department of Electrical Engineering, National Cheng Kung University, Tainan 70101, Taiwanb Department of Electrical Engineering, Kun Shan University, Tainan 70101, Taiwan

a r t i c l e i n f o a b s t r a c t

Article history:Received 28 June 2014Received in revised form 4 May 2015Accepted 5 May 2015Available online 19 May 2015

Keywords:Gabor–Wigner transformHigh-impedance faultsCross-terms

The Gabor–Wigner transform was adopted in this study to explore the electric signals generated byhigh-impedance faults (HIFs). This method excels at detecting non-stationary signals and featuring highresolutions, while the effects of cross-term problem of Wigner distribution can be meanwhile decreased.To confirm the feasibility of this method, the approach was tested under different scenarios with compar-isons to practical waveforms. Test results support the practicality of the method for the inspection ofhigh-impedance fault-generated signals.

� 2015 Elsevier Ltd. All rights reserved.

Introduction

High-impedance faults often occur when an overhead groundwire is broken and falls to a ground with high resistance, such asa tar road, cement floor, grass, or sand. When this fault occurs,the magnitude of current is low because impedances of somegrounds are very high. Therefore, it may not be easy to detect suchfaults solely by using traditional protection devices. Worst of all, anelectric wire falling on a high-impedance fault may produce arcs,endangering the personal safety and causing property damages[1–5]. From perspectives of public safety and operational reliabil-ity, an effective detection of high-impedance faults serves as a veryimportant topic to study.

In the last decades, several researches have been devoted to thisfault detection study. Some studies were focused on adjusting theover-current protection devices [6]. Yet, if the device was notcarefully designed, errors may occur due to the short ofsignal-discrimination capability. A grounding relay was appliedto detect; however, under an extremely unbalanced load or multi-ple grounding contacts, a sufficient reliability was hard to reach[7]. Based on the second-order [8], the third-order [9,10], and thehigh-frequency harmonics current [11], the changes in harmoniccurrents of feeders were closely tracked, anticipating the featuresof high-impedance fault would be better comprehended.Subsequently, signal processing methods including Kalman filters[12], artificial neural networks (ANNs) [13,14], and decision trees

[15] were also proposed. Among these methods, although theKalman filter was applied in the inspection of non-stationary sig-nals, it came with the demerits of requiring great amounts of com-putation and additional efforts for accuracy of parameters. As forthe application of ANNs, it needs to build complex non-linear sys-tems by learning examples. If the number of samples was insuffi-cient or training procedures were inappropriate, the probabilityof detection will be highly affected. It is worth mentioning thatmost signal-processing approaches utilized the Fourier transformas the analysis basis; however, by transforming all the informationin time domain to frequency domain, relationships between timeand frequency were found difficult to grasp, hence causing the dif-ficulty of visualizing event dynamics. By automatically adjustingthe window function to adapt to the required resolution, the wave-let transform was emerged, by which both time and frequencyinformation were simultaneously presented [16–19]; yet an inap-propriate selection of the mother wavelet may still affect the com-putation performance.

In this study, a Gabor–Wigner transform (GWT) is proposed todetect high-impedance faults. This method is expected to integratethe merits of Gabor transform (GT) with Wigner distribution suchthat the fault-detection performance can be significantlyenhanced. On one hand, the Wigner distribution was witnessedto own the characteristics of higher time–frequency resolutionand energy concentration, but on the other hand, its cross-termsproblem may hinder a further development. Although theGaussian-like window function of Gabor transform was provedsuitable for analyzing non-stationary signals [20], it came with alimited degree of resolution. Therefore, by combining the merits

J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199 193

of these two methods as a whole, the method suggested in thisstudy will not only solve the cross-term problem, but also exhibitthe advantage of higher resolution for the visualization of events.Features of this method include the following:

(1) The proposed method is very simple in concept and easy toimplement. It is capable of zooming in the area of interest fora clearer visualization.

(2) With the increasing concern of power system faults, the pro-posed method can be extended as a useful tool in addition toexisting approaches.

(3) The method is beneficial to analyze any non-stationary sig-nals, presenting a high potential of inspecting otherdisturbances.

The organization of this paper is made as follows:Section ‘Proposed method’ introduces the proposed method, Section ‘Detecting process’ shows the detection process, Section ‘Testresults’ provides the test results, and Section ‘Conclusion’ presentsa conclusion.

Proposed method

The Gabor transform

Among several time–frequency analysis approaches, theshort-time Fourier transform is one of the most used tools to inves-tigate the non-stationary signals. The most significant differencebetween the short-time Fourier transform and the Fourier trans-form is the use of windows function w(s) in limited time. By mov-ing the windows function on the time axis and spectrogram of theFourier transform, the time–frequency analysis of the signal maybe comprehended. The short-time Fourier transform is defined as

STFTðt;xÞ ¼Z 1

�1wðsÞf ðt þ sÞe�jxsds ð1Þ

where t is a sliding variable of time, x is the frequency, s is the sig-nal function in the time-domain, and w(s) is the window function.The Gabor transform (GT) can be seen as a type of short-timeFourier transform, which replaces the window function withGaussian function as shown below

GTðt;xÞ ¼ffiffiffiffiffiffiffi1

2p

r Z 1

�1gðsÞf ðt þ sÞe�jxsds ð2Þ

where g(s) is the Gaussian function and the duration of g(t) window is2T along with T = 1/60 [s]. This Gabor transform detects the time andfrequency of a non-stationary signal simultaneously, yet its analyzingperformance is easily affected by the window width. A narrow win-dow may hinder from the sufficient resolution to distinguish thosesignals with similar frequencies, while a wide window may causethe difficulty of immunity from neighboring high-frequency distur-bances [21,22]. Special attentions are suggested to ensure the

Freq

uenc

y (H

z)

Time (s)

Freq

uenc

y (H

z)

Tim

(a) (

Fig. 1. The time–frequency spectrum of real sign

effectiveness of Gabor transform, hence motivating the inclusion ofWigner distribution proposed in this study.

The Wigner distribution

The Wigner distribution depicts the energy density of a signal inthe time–frequency plane. In the calculation process, thetime-domain signal f(t) is used twice, which is also called bilinearanalysis. Since the Wigner distribution comes with a higher time–frequency resolution and energy concentration, it is often used inengineering applications which is defined as

WDðt;xÞ ¼Z 1

�1f t þ s

2

� �f � t � s

2

� �e�jxsds ð3Þ

For example, after the employment of (3), a signal of f(t) = cos2

x1t + cos2 x2t will bring the auto terms of cos2 x1t and cos2 x2talong with the cross terms of cos(x1 + x2)t + cos(x1 �x2)t, yetthe frequency of x1 + x2 and x1 �x2 is away from that of theoriginal signal. In other words, the nuisance of cross terms formedduring the calculation of Wigner distribution, possibly leading tothe insufficient signal discernment.

The Gabor–Wigner transform

In view of GT short of clarity along with Wigner distribution of across terms problem, an approach combining these two transformsbut without these demerits have been proposed [21], in which themethod is called Gabor–Wigner transform (GWT) with the expres-sion made below:

GWTðt;xÞ ¼ GTAðt;xÞWDBðt;xÞ ð4Þ

where A and B are constants. When the prime number of the GT isgreater than that of the Wigner distribution, the GWT is inclined tothe GT. When the prime number of the GT is lower than that of theWigner distribution, the GWT is inclined toward the Wigner distri-bution. Thus, it is necessary to select an appropriate prime numberfor the GT and the Wigner distribution. Based on the suggestions,this study set the values of A and B at 2.6 and 0.6 [21].

Through the employment of this approach, the study made sim-ulations on various signals to verify its applicability and reliability.First, three types of signals were used to verify the resolution oftime–frequency analysis: Example 1 is focused on real signals;Example 2 on complex signals; and Example 3 on multiple com-plex signals. This is followed by the application of GWT to analyzesignals of high-impedance faults by comparing analysis resultsbetween the GT and the Wigner distribution.

Example 1 (Real signals). This test focuses on real signals. Theequation is assumed as follows:

f ðtÞ ¼ cosð6t � 0:05t2Þ ð5Þ

Fig. 1(a–c) individually shows the results of GT, Wigner distribution,and GWT. The horizontal axis represents time and the vertical axis

Freq

uenc

y (H

z)

e (s) Time (s)b) (c)

als. (a) GT. (b) Wigner distribution. (c) GWT.

194 J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199

represents frequency. Analyzed values are displayed by variousshades of color. Lighter colors represent greater values, and darkercolors represent lower values.

Fig. 1(a) shows the results of GT. Although it does not have across terms problem, the resolution is lower. Fig. 1(b) shows theWigner distribution. Although it has a higher resolution, it has across terms problem. Fig. 1(c) shows the proposed approach com-bining the advantages of both: a better resolution and an elimina-tion of cross terms.

Because of asymmetrical characteristics of Fourier transform, iff(t) is a real function, then the Wigner distribution andGabor–Wigner distribution will generate both positive and nega-tive frequencies, in which a negative frequency does not havephysical meaning. However, to clearly demonstrate the crossterms, the negative frequency is partially shown.

The selected prime numbers A and B in (7) are 2.6 and 0.6,respectively. The two functions are then multiplied byGT2.6(t,x)WD0.6(t,x). To verify if the selected prime number isappropriate, smaller prime numbers of the GT and the Wigner dis-tribution are compared. In Fig. 2(a), where the selection in the GWTis GT2.6(t,x)WD0.06(t,x), the spectrum is inclined to the GT func-tion and has a lower resolution. In Fig. 2(b), where the selectionis GT0.4(t,x)WD0.6(t,x), the spectrum is inclined to the Wignerdistribution and has a cross terms problem.

Freq

uenc

y (H

z)

Time (s)(a)

Fig. 4. The effects of the prime number on the GWT. (a) The prime number of th

Freq

uenc

y (H

z)

Time (s)

(a)

Fig. 2. The effects of the prime number on the GWT. (a) The prime number of t

Freq

uenc

y (H

z)

Time (s)

Freq

uenc

y (H

z)

T

(a)

Fig. 3. The time–frequency spectrum of complex si

Example 2 (Complex signals). This example uses a complex signal.It is defined as

f ðtÞ ¼ ej0:15t3 ð6Þ

Fig. 3(a–c) shows the results by using GT, Wigner distribution andGWT, where the horizontal axis represents the time and the verticalaxis represents the frequency. Calculated values are displayed byvarious shades of colors, where the lighter color is for a larger valueand the deeper color for a smaller one. From this example, theresults of GT does not have cross terms problem, but the resolutionis seen to be the lowest. The Wigner distribution has a higher reso-lution, yet its cross terms lead to an unexpected line draw. Only theplot of Fig. 3(c) owns a sufficient resolution while the cross termsproblem is solved as well.

The prime numbers in the complex signals in the GT and theWigner distribution are 2.6 and 0.6, respectively. By multiplyingthe two functions, GT2.6(t,x)WD0.6(t,x) is obtained. To verify if theselected prime number is appropriate, smaller prime numbers ofthe GT and the Wigner distribution are compared. Fig. 4(a) showsthat when the function in the GWT is GT2.6(t,x)WD0.06(t,x), thespectrum is inclined toward the GT and has lower resolution.Fig. 4(b) shows that when the window function is GT0.4(t,x)WD0.6(t,x), the spectrum is inclined toward the Wigner distributionand has cross terms problems.

Freq

uenc

y (H

z)

Time (s)

(b)

e GT is greater. (b) The prime number of the Wigner distribution is greater.

Freq

uenc

y (H

z)

Time (s)

(b)

he GT is larger. (b) The prime number of the Wigner distribution is larger.

ime (s)

Freq

uenc

y (H

z)

Time (s)

(b) (c)

gnals. (a) GT. (b) Wigner distribution. (c) GWT.

Fig. 7. The detection flow diagram.

J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199 195

Example 3 (Multiple complex signals). This example uses multiplecomplex signals. The equation is

f ðtÞ ¼ eðj0:0015t4þj0:06t3�j0:3t2þjtÞ ð7Þ

Fig. 5, the waveform of using the GT, the Wigner distribution, andthe GWT are all depicted. The horizontal axis represents time, andthe vertical axis represents frequency. Analyzed values are displayedby various shades of color. Lighter colors represent greater values,and darker colors represent lower values. Except from an additionaldraw caused by the cross terms as shown in Fig. 5(b), both of Fig.5(a) and (c) are able to demonstrate the resultant frequency distri-bution on the time axis; yet the resolution of Fig. 5(c) is a better one.

To verify if the selected prime number is appropriate, a lowerprime number of the GT and a lower prime number of the Wignerdistribution are compared. In Fig. 6(a), when the selected primenumber in GWT is GT2.6(t,x)WD0.06(t,x), the spectrum is inclinedtoward the GT function and has a lower resolution. In Fig. 6(b), whenthe selected window function is GT0.4(t,x)WD0.6(t,x), the spectrumis inclined toward the Wigner distribution and has a cross termsproblem.

The examples show that the GWT not only has a higher resolu-tion, but also overcomes the cross terms problem in the Wignerdistribution. It is also worth noting that for a polyharmonic signalincluding harmonics of 60 Hz, 120 Hz, 180 Hz, the harmonic of120 Hz will be still distorted by the cross-term solved with 60 Hzand 180 Hz harmonics. Although this situation appears very sel-dom, yet special attentions may need to be paid for such rare cases.As for the GWT applied for the inspection of high-impedance faultsin this study, it comes with a high suitability when compared tosome published techniques. In the following sections, the GT, theWigner distribution, and the GWT will be compared to verify theapplicability of GWT for the HIF investigated in this study.

Detecting process

Fig. 7 presents the GWT flow diagram, where T represents theduration of HIF cycles and Tth denotes the threshold values set in

Freq

uenc

y (H

z)

Time (s)(a)

Fig. 6. Effects of the prime number on the GWT. (a) The prime number of the

Freq

uenc

y (H

z)

Time (s)

Freq

uenc

y (H

z)

Tim

(a) (

Fig. 5. The time–frequency spectrum of complex si

this study for determining duration of HIF cycles. The HIFs at30 kHz were sampled before the high-impedance signals were ana-lyzed. The sampling frequency of, 30 kHz which was sufficient forenabling HIF signal analysis, and 300,000 sampling points wereobtained. The GWT was applied to the sampled signals to conductcomputation and analysis. When the GWT analysis and computa-tion were completed, the HIF duration (i.e. Tth) was determined.When the selected values of Tth were excessively low, non-HIF sig-nals might be erroneously considered HIF signals. Conversely,when the selected values of Tth were extremely high, HIF detectionwas delayed. Therefore, to select appropriate Tth values, this studyadopted the Tth value (i.e., Tth = 5) used by [23] as the thresholdvalue. When the detected signal did not exceed the set thresholdvalue, the signal was considered to be a non-HIF signal and thedetection continued by sampling next piece of data. When thedetected signals exceeded the threshold value, they wereconsidered HIF signals. This process enabled the precise detectionof the exact time when HIFs occurred, thereby preventing result

Freq

uenc

y (H

z)

Time (s)(b)

GT is greater. (b) The prime number of the Wigner distribution is greater.

e (s)

Freq

uenc

y (H

z)

Time (s)

b) (c)

gnals. (a) GT. (b) Wigner distribution. (c) GWT.

100 MVA

Load161 kV

30 MVA161 kV / 22.8kV Overhead feeder

5-kM

HIF Modle

∞

Fig. 8. The HIF single-line diagram of the power distribution system.

196 J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199

misinterpretation. To verify that the proposed method was appro-priate for detecting HIFs, experiments were conducted; theseexperiments are discussed in the following section.

Test results

In this section, the experimental results are provided. First, theHIF signals in cement flooring and arc furnace load switches weredetected and compared. This was set as the baseline and used tocompare HIF and non-HIF signals. Subsequently, because the HIFelectric current in various substances differ [24], this methodwas used to detect the HIFs in various substances (i.e., cement,

Cur

rent

(p. u

.)

Time (s)

Fault Begins

0.1

0

0.20.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Freq

uenc

y (H

z)

Am

plitude (p. u.)

(a)

(c)

Fig. 9. The time–frequency diagram of the HIFs in the cement ground: (a) The HIF waveand (d) GWT time–frequency diagram.

wet sand, wet soil, and wet meadow soil). The study [24] indicatedthat the HIF current of cement was the lowest followed by the HIFcurrent of wet sand. The HIF current of wet meadow soil was high.All experiments consisted of single line-to-ground faults. HIFs incement were detected on sunny days. In addition, HIFs in wet sand,wet soil, and wet meadow soil were detected on rainy days.Moreover, all of the signals were obtained by conducting actualmeasurements, rather than simulations.

Experiment 1: The HIFs in cement

Fig. 8 shows an HIF single-line diagram of the power distribu-tion system at Southern Taiwan Science Park. In this diagram, a161 kV bus is used to transfer electricity from a substation contain-ing 161/22.8 kV to an overhead feeder of 5 km, and finally to theload. HIFs were detected in the overhead feeder (Fig. 8). In thisexperiment, the ground was cement, the weather was sunny, andthe temperature was approximately 32 �C. The obtainedsingle-line diagram data is presented in Fig. 8.

The HIF current waveforms in cement are presented in Fig. 9(a).The horizontal axis represents time [s] and the vertical axis repre-sents electric current (p.u.).

To verify the HIF detection efficacy of the proposed method, theHIF signal of cement (Fig. 9(a)) was analyzed and computed usingthe Gabor transform (GT), Wigner distribution (WD), and the GWT.Fig. 9(b), (c), and (d) show the time–frequency analysis diagramsobtained using the GT, WD, and the GWT, respectively. The hori-zontal axes represent time [s] and the vertical axes represent thefrequency (Hz) of the HIF signals. The second vertical axes repre-sent the amplitude values (per-unit value) obtained by conductinganalysis. When amplitude was high, the frequency spectrum colorsbrightened. Conversely, when the amplitude was low, the fre-quency spectrum colors were dim. The symmetry characteristicsof the Fourier transform were previously introduced in

0.10

0.20.3

0.4

0.50.60.7

0.80.91

Time (s)

Freq

uenc

y (H

z) Am

plitude (p. u.)

0.1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

Time (s)

Freq

uenc

y (H

z)

Am

plitude (p. u.)

(b)

(d)

forms in cement; (b) GT time–frequency diagram; (c) WD time–frequency diagram;

Am

plitu

de (p

. u.)

Time (s)

Fault Begins

Fig. 10. The cement HIF amplitude detected using the GWT.

J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199 197

Section ‘Proposed method’. When f(t) represented a real numberfunction, the time–frequency diagrams obtained by applying theGT, WD, and GWT all showed both positive and negative frequen-cies. The negative frequencies were not physically meaningful forthe real number signals. However, although the negative frequencyin this experiment was �60 Hz, the negative frequencies were dis-played to exemplify the presence of cross terms.

As mentioned in Section ‘Proposed method’, regarding thetime–frequency diagram shown in Fig. 9(b), using the GT cannotsimultaneously maintain high resolution in the time and frequencydomains, thus resulting in the poor resolution in either domain. InFig. 9(b), to detect HIFs, satisfactory time resolution was presented,which resulted in the poor frequency resolution. The electric powerfrequency provided by the Taiwan Power Company is typically60 Hz. In the time–frequency diagram, the frequency spectrum dis-tributed near 60 Hz is broad, thereby showing the low-frequencyresolution of this method. When analyzing HIFs, thelow-frequency resolution affected detection and therefore wasinapplicable to detecting HIFs. Fig. 9(c) presents the time–fre-quency diagram derived by using the WD. As mentioned inSection ‘Proposed method’, the WD yields high time and frequencyresolutions. However, the WD has the disadvantage of producingcross terms. Hence, as shown in the time–frequency diagrams,noise signals that were caused by the cross terms were detectedwhen using frequencies other than 60 Hz. Because the WD offersa high time–frequency resolution, the width of the WD frequencyspectrum distributed near 60 Hz was smaller than that producedusing the GT. In addition, as shown in the figures, when the fre-quency was 0 Hz, the GT method yielded cross terms noise signals,which influenced the HIF detection results. Thus, the GT was alsounsuitable for detecting HIFs. Fig. 9(d) shows the GWT time–fre-quency analysis diagram. Based on the theories introduced inSection ‘Proposed method’, the GWT yields a high time–frequencyresolution. The figure shows that the GWT derived frequency spec-trum width distributed near 60 Hz was smaller than that derived

Cur

rent

(p. u

.)

Time (s)

(a)

Fig. 11. Transient switching events: (a) The current waveforms of transie

by applying the GT. However, the GWT does not present crossterms. Hence, the time–frequency diagrams show that noise sig-nals were detected only when the frequency was 60 Hz.However, because time–frequency diagrams cannot show theexact time or amplitudes of the HIFs, plotting frequency spectrumwaveforms at 60 Hz was required to exhibit the HIF times andamplitudes.

The time–frequency diagrams show that compared with the GTand WD, the GWT is a superior method. Fig. 10 shows the ampli-tudes of the waveforms presented in Fig. 9(d) at a 60 Hz frequency.Based on this figure, before 0.04 s (t), the value of the detected cur-rent was 0. The current could only be detected after t = 0.04 s.Additionally, the value exceeded the set threshold value (i.e., 5cycles) and were thus determined to be HIFs. Moreover, becauseof the high impedance in cement, the HIF current was low. At0.04–0.14 s, the amplitude value was approximately 0.1 p.u., whichwas a low value. This figure shows that the GWT can be used toaccurately detect the occurrence of HIFs, without delaying thedetection of the HIF occurrence intervals. Hence, the proposedmethod is suitable for detecting HIFs.

The results of Experiment 1 were used to present the GT, WD,and GWT differences. In addition to accurately detecting HIF timeof occurrence, the GWT does not misjudge non-HIF signals.Hence, the GWT is suitable for HIF detection. To further ensure thatthe GWT precisely detect HIFs in various substances, switchingevents and overhead feeders were used to measure the signals inwet sand, wet soil, and wet meadow soil. The measurement resultswere used to determine whether the GWT could accurately detectthe HIF occurrence times.

Experiment 2: Transient switching events

Under normal system operations, switching events related toarc furnaces or other transient phenomena may distort the currentwaveforms. Therefore, these phenomena must be distinguishedfrom the HIFs. Fig. 11(a) shows the current waveforms of a 35%loaded arc furnace that was connected to the system. Based on thisfigure, transient switching events occurred at approximately 0.038,0.08, 0.105, and 0.14 s.

Fig. 11(b) presents the current values obtained using GWT anal-ysis. At 0–0.14 s, all the amplitude values obtained by applying theGWT were 0, indicating that the GWT did not erroneously considertransient switching events as HIFs.

Experiment 3: The HIFs in wet sand

In Experiment 3, the contact ground was wet sand (Fig. 12(a));the current value began to increase at 0.05 s. This indicated that anHIF occurred. However, this signal cannot be used to indicate thedifferences between the HIFs in wet sand and cement. Therefore,the GWT was used to distinguish the various substances.

Am

plitu

de (p

. u.)

Time (s)

(b)

nt switching events and (b) the amplitude obtained using the GWT.

198 J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199

Fig. 12(b) shows the signal amplitude after the current was ana-lyzed and computed using the GWT. The results indicate that theGWT could detect when the HIFs began occurring. The signal beganat .05 s and continued for five cycles, indicating that this was anHIF signal. In addition, a comparison of wet sand and cementshowed that when t = 0.14 s, the amplitude was 0.3 p.u. Becausethe impedance of wet sand was smaller than that of cement, theHIF current in wet sand was greater than that in cement. The figurealso indicates that the wet sand yielded higher amplitude than thatof cement.

Experiment 4: The HIFs in wet soil

In this experiment, the measured ground was wet soil. Fig. 13(a)shows the HIF waveforms, indicating that, the current value beganto rapidly increase at approximately 0.05 s, indicating the occur-rence of HIFs.

Fig. 13(b) shows the HIF signal analysis and computation resultsobtained using the GWT. In this figure, the horizontal axis repre-sents time and the vertical axis represents amplitude. Before

Cur

rent

(p. u

.)

Time (s)

Fault Begins

(a)

Fig. 13. The HIFs in the wet soil ground: (a) The HIF waveforms

Cur

rent

(p. u

.)

Time (s)

Fault Begins

(a)

Fig. 14. The HIFs of wet meadow soil: (a) The HIF current waveforms

Cur

rent

(p. u

.)

Time (s)

Fault Begins

(a)

Fig. 12. The HIFs of wet sand: (a) The HIF waveforms of w

0.05 s, the GWT amplitude was 0 p.u., because HIF was notdetected. At 0.05 s, the HIFs began occurring, as demonstrated bythe increased amplitude in Fig. 13(b). At 0.14 s, the amplitudewas measured at 0.37 p.u. and remained at this level for more thanfive cycles. Hence, this phenomenon was considered to be an HIF. Aprevious study [24] indicated that the HIF current in wet soil washigher than that in cement and wet sand. The amplitude displayedin this figure was also higher than that for cement and wet sand,thereby verifying the accuracy of the results.

Experiment 5: The HIFs in wet meadow soil

The final experiment in this study was conducted to measurethe HIF of wet meadow soil. The curves in Fig. 14(a) are the wave-forms of the HIF currents. The current is displaying at a per-unitvalue. Based on this figure, the approximate occurrence time ofHIFs was 0.05 s.

Fig. 14(b) shows the current values that were computed usingthe GWT. Based on the figure, the HIFs in wet meadow soiloccurred at .05 s, which indicated the detection accuracy. The

Am

plitu

de (p

. u.)

Time (s)

Fault Begins

(b)

of wet soil and (b) the amplitude obtained using the GWT.

Am

plitu

de (p

. u.)

Time (s)

Fault Begins

(b)

wet meadow soil and (b) the amplitude obtained using the GWT.

Am

plitu

de (p

. u.)

Time (s)

Fault Begins

(b)

et sand and (b) the currents obtained using the GWT.

J.-Y. Cheng et al. / Electrical Power and Energy Systems 73 (2015) 192–199 199

current value remained elevated for five cycles after 0.05 s., verify-ing that the signal was an HIF signal. In addition, at 0.14 s, the HIFcurrent in the wet meadow soil was 0.7 p.u. Thus, the impedance inwet meadow soil is lower than that in cement, wet sand, and wetsoil. The results in the figure indicated that the amplitude in wetmeadow soil was also higher than that in cement, wet sand, andwet soil.

The results of the five experiments show that the GWT canaccurately detect the HIF occurrence time in various substances.Additionally, non-HIF signals were not erroneously considered tobe HIF signals. These experimental results verify that in additionto the mentioned advantages, the GWT can be used to detect HIFs.

Conclusion

This study applied the GWT method for inspecting thehigh-impedance fault generated signals. This proposed approachis proved to be effective to solve the cross-term problems ofWigner transform as well. Compared with the conventionalFourier transform, this proposed GWT method owns a potentialof extending to analyze other non-stationary signals so as to fore-warn the occurrence of power quality events with a higher effi-ciency. At this time, we are assessing the possibility ofimplementing the GWT method through hardware design, antici-pating a further enhancement of monitoring performance. Theresults will be reported in the near future.

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