research article fault line selection method of small...

Research ArticleFault Line Selection Method of Small Current toGround System Based on Atomic Sparse Decomposition andExtreme Learning Machine

Xiaowei Wang1 Yanfang Wei1 Zhihui Zeng1 Yaxiao Hou2 Jie Gao1 and Xiangxiang Wei1

1School of Electrical Engineering and Automation Henan Polytechnic University Jiaozuo 454000 China2School of Electrical Engineering and Automation Harbin Institute of Technology Harbin 150001 China

Correspondence should be addressed to Xiaowei Wang proceedings126com

Received 13 October 2014 Accepted 28 November 2014

Academic Editor Sergiu Dan Stan

Copyright copy 2015 Xiaowei Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposed a fault line voting selection method based on atomic sparse decomposition (ASD) and extreme learningmachine (ELM) Firstly it adopted ASD algorithm to decompose zero sequence current of every feeder line at first two cycles andselected the first four atoms to construct main component atom library fundamental atom library and transient characteristicatom libraries 1 and 2 respectively And it used information entropy theory to calculate the atom libraries the measure values ofinformation entropy are got It constructed four ELM networks to train and test atom sample and then obtained every networkaccuracy At last it combined the ELM network output and confidence degree to vote and then compared the vote number toachieve fault line selection (FLS) Simulation experiment illustrated that the method accuracy is 100 it is not affected by faultdistance and transition resistance and it has strong ability of antinoise interference

1 Introduction

For small current to ground system FLS study focus is faultline identified when single phase to ground fault occurredat this moment the fault current is weaker and Petersencoil to ground mode also has the features Therefore theconventional method with using current amplitude size andphase information is difficult to obtain satisfactory results

In recent years modern signal processing technologyused FLS to get fault characteristic information such aswavelet transform [1] 119878 transform [2] mathematical mor-phology [3] Hilbert-Huang transform (HHT) [4] Pronyalgorithm [5] and Hough transform [6] Besides the com-mon method of FLS criterion had artificial neural networks[7] support vector machines [8] and Bayesian classification[9]

Zero sequence current was decomposed by wavelet trans-form and calculated wavelet modulus maxima to determinearrival time of traveling waversquos head and then compared the

amplitude and polarity of every feeder line at this time toachieve FLS [1] It used 119878 transform to get modulus value andphase angle of every frequency range and comparedmodulusvalue and phase angle to obtain characteristic frequency andvoting mechanism respectively the experiments indicatedthat the method could not only judge the fault line accuratelybut also obtain the FLS confidence degree [2] Paper [10]used 119878 transform to get transient fault feature and based onthe frequency point of transient maximum energy it chosecharacteristic frequency sequence therefore the criterionwith relative entropy values of multiple combination modesdetermined the fault section Paper [3] proposed a novelmethod which was based on mathematical morphology themethod included two aspects one used morphological filtersto preprocess the data and removed the noise impact forFLS at the maximum extent and the other adopted morpho-logical operators to detect the denoised signal with mutantaspect to judge the fault line Paper [4] calculated transient

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 678120 19 pageshttpdxdoiorg1011552015678120

2 Journal of Sensors

instantaneous power by Hilbert-Huang transform (HHT)and got fault direction well the method took advantage oftransient high-frequency component at lower sampling rateIt tried to divide the zero sequence current signal into severalsegments to ensure good continuity and smaller mutationat every subsegment and Prony algorithm was appliedto choose transient dominant component with maximumenergy principle and then calculated the relative entropy andvoted by preliminary vote and 119896 values check to judge thefault line [5] Hough transform was adopted to constructwhole mutant direction angle which indicated overall trendof zero sequence current at initial stage and FLSwas achievedby distinguishing the direction angle [6] Paper [7] replacedordinary neurons with rough neurons and fuzzy neuronsto identify 10 kinds of fault type the method improvedthe training speed and reduced training samples and faultidentification accuracy was enhanced It used correlationcoefficient of zero sequence voltage and charge as charac-teristic input to construct FLS process which was based ontransient zero sequence 119876-119880 features the method adoptedsupport vector machine algorithm with small sample [8]For incomplete information of fault diagnosis [9] adoptedevidence uncertainty reasoning and compared abnormalevents to reduce computation amount

This paper proposed a novel FLS method which wasbased on combination of ASD and ELM Firstly it usedatomic sparse algorithm to decompose zero sequence currentof every feeder line and extracted the first four atomsto construct fault sample library respectively besides itcalculated information entropy measure of every libraryThen it trained the ELM network to improve network outputaccuracy At last fault votingwas adopted to vote every feederline and compared the values and then the fault line wasjudged Simulation results showed that the accuracy rate ofproposed method is 100 and had strong ability of antinoiseinterference

The remaining of this paper is organized as follows InSection 2 we analyzed the physical characteristics of zerosequence current In Sections 3 and 4 the theory of time-frequency atom decomposition and ELM work principle arepresented respectively In Section 5 test signals analysis isgiven in the paper In Section 6 we chose the characteristicatoms of zero sequence current In Section 7 the FLS meth-ods are proposed In Section 8 example analysis is appliedto verify the proposed method In Section 9 we discussedthe applicability of the method In Section 10 the paper iscompleted with conclusions and future directions

2 Physical Characteristics Analysis

Transient zero sequence circuit of single phase to ground faultis shown in Figure 1 where 119862

0and 119871

0are zero sequence

capacitance and inductance respectively 119877119892is transition

resistance of grounding point 119877119901and 119871

119901are equivalent

resistance and inductance of arc suppression coil and 119890(119905) iszero sequence voltage

When the fault occurred in compensation networkFigure 1 the transient zero sequence current flows through

i0t Rg

e(t)i0Lt

Lp

Rp

L0

i0Ct

C0

Figure 1 Transient zero sequence equivalent circuit of single phaseto ground

fault location [11 12] the calculation is shown in the followingformula

1198940119905= 1198940119871119905

+ 1198940119862119905

= 119868119871119898

cos120593119890minus119905120591119871 + 119868119862119898

times (120596119891

120596sin120593 sin120596119905 minus cos120593 cos120596

119891119905) 119890minus120575119905

(1)

where 1198940119871119905

and 1198940119862119905

are inductance component and capaci-tance component of transient zero sequence current 119868

119871119898and

119868119862119898

are initial value of inductance current and capacitancecurrent respectively 120596 is angular frequency 120596

119891and 120575

are oscillation angle frequency and attenuation coefficientof transient zero sequence current capacitance componentrespectively 120591

119871is decay time constant of inductance current

and 120593 is initial phase of fault line120596119891and 120575 calculations are shown in the following formula

respectively

120596119891= radic

1003816100381610038161003816100381610038161003816100381610038161003816

1

11987101198620

minus (119877119892

21198710

)

21003816100381610038161003816100381610038161003816100381610038161003816

(2)

120575 =119877119892

21198710

(3)

Transient zero sequence current is comprised of sinu-soidal function from formula (1) and its waveform has atten-uation characteristics It can be seen from formula (2) and (3)that oscillation angle frequency 120596

119891is influenced by 119871

0 1198620

and 119877119892 attenuation coefficient 120575 is also influenced by 119871

0and

119877119892 when transition resistance 119877

119892increased 120596

119891decreased

and 120575 increased it reflected that wave oscillation trend ofzero sequence current becomes slow and the attenuation timebecome fast and then transient processwill end soon and intosteady state Therefore if it could extract accurately transientcomponent to achieve FLS exactly at the large resistanceto ground fault it will be an important index to test theapplicability of the FLS methods

Figure 2 is zero sequence current of actual distributionnetworkwhen overhead line 1 caused fault it can be seen fromFigure 2 that whether the overhead line cable line or hybridline its zero sequence current has oscillation attenuationcharacteristics

Journal of Sensors 3

300

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(a) Overhead line 1

20

10

0

minus10

minus200 0005 001 0015 002

i 0t

(A)

t (s)

(b) Overhead line 2

100

50

0

minus50

minus1000 0005 001 0015 002

i 0t

(A)

t (s)

(c) Hybrid line

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(d) Cable line

Figure 2 Transient zero sequence current

3 Time-Frequency AtomDecomposition Theory

31 Decomposition Methods For continuous signal 119891(119905) isin

119867 119867 is Hilbert space and transformed 119891(119905) into 119891(119899) itsprocess is discretization [13ndash15]Defined atomdictionary119863 =

(119892119903)119903isinΓ

Γ is group of parameters 119903 119892119903= 1 Choose the atoms

to match the signal 119891(119899) from atom dictionary119863 that is themaximum inner product between119891(119899) and all atoms 119892

(1199030)(119899)

meet the following formula10038161003816100381610038161003816⟨119891 (119899) 119892(1199030)

(119899)⟩10038161003816100381610038161003816= sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)

The signal could be decomposed by the best matchingatom 119892

(1199030)(119899) component and the residual signal 119877119891(119899) and

the calculation expression is shown in the following formula

119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)

(119899) + 119877119891 (119899) (5)

In (5) 119877119891(119899) approached along 119892(1199030)

(119899) direction Obvi-ously 119892

(1199030)(119899) and 119877119891(119899) were orthogonal therefore the

following formula was got1003817100381710038171003817119891(119899)

1003817100381710038171003817

2=10038161003816100381610038161003816⟨119891(119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119891(119899)

1003817100381710038171003817

2 (6)

Because atom dictionaries are over completeness theoptimal solution could be turned to suboptimal solution thatis choose the approximation atom to a certain extent Thecalculation is shown in

10038161003816100381610038161003816⟨119891 (119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)

In formula (7) 0 le 120572 le 1 decompose 119877119891(119899) andchose the best matching atom 119892

(1199031)(119899) from atom dictionary

make 1198770119891(119899) = 119891(119899) iterative 119896 times the 119896 time residualcomponent 119877119896119891(119899) could be expressed as

119877119896119891 (119899) = ⟨119877

119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) + 119877

119896+1119891 (119899) (8)

The signal 119891(119899) decomposed 119898 times and its expressionis shown in

119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899) + 119877

119898119891 (119899) (9)

Therefore signal energy 119891(119899)2 could be expressed in

1003817100381710038171003817119891(119899)1003817100381710038171003817

2=

119898minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891(119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899)

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119898119891(119899)

1003817100381710038171003817

2

(10)


02

015

01

005

0

minus005

minus01

minus015

minus02

Am

plitu

de

Sampling point50 100 150 200

(a) Time-frequency diagram

04

035

03

025

02

015

01

Am

plitu

de


(b) Wigner-Ville distribution

Figure 3 Gabor atoms time-frequency diagram and Wigner-Ville distribution 119904 = 26 119906 = 128 120585 = 1205872

In (10) 119892(119903119896)

(119899)meet the formula

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903⟩10038161003816100381610038161003816 (11)

If it decomposed 119898 times to meet the accuracythen stop the decomposition Because the residualcomponent 119877119898119891(119899) tends to 0 119891(119899) could be expressed bychosen atoms It was shown in

119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) (12)

The similarity degree119862119898between original signal119891(119899) and

constructed signal 119891119898(119899) is shown in

119862119898=

⟨119891 (119899) 119891119898(119899)⟩

1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)

1003817100381710038171003817

(13)

Because 119892119903 = 1 calculated Wigner-Ville distribution of

formula (12) it could get

119882119891(119899 119897)

=

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903119896(119899)⟩

10038161003816100381610038161003816

2

119882119892119903119896(119899 119897)

+

119872minus1

sum

119896=0

119872minus1

sum

119898=0119898 =119896

⟨119877119896119891 (119899) 119892

119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892

119903119898(119899)⟩

sdot 119882 [119892119903119896(119899) 119892

119903119898(119899)] (119899 119897)

(14)

In (14) 119882119892119903119896(119899 119897) is Wigner-Ville distribution of atom

119892119903119896(119899) and 119897 is discretization frequency variable The last item

in (14) is cross terms of every atom Mallat eliminated thecross terms and got the energy distribution in

119864119891 (119899 119897) =

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816

2

119882119892(119903119896)

(119899 119897) (15)

In (15) |⟨119877119896119891(119899) 119892(119903119896)

(119899)⟩|2 is energy intensity and 119864119891(119899 119897) is

density function of 119891(119899) energy distribution

32 Gabor Atoms Gabor atoms are constructed by Gaussenergy function with telescopic translation and modulationtransform and its expression is shown in the followingformula

119892119903(119905) =

1

radic119904119892 (

119905 minus 119906

119904) 119890119895120585119905 (16)

The expression of corresponding real Gabor atom isshown in the following formula

119892(119903120601)

(119905) =1

radic119904119892 (

119905 minus 119906

119904) cos (120585119905 + 120601) (17)

In (17) 119892(119905) is standard Gauss signal and is equalto 214119890minus1205871199052

119904 is scale parameter 1radic119904 is atom normalizationparameter and 119906 120585 and 120601 are parameters of time shiftfrequency modulation and phase

Parameter 119903 is equal to (119904 119906 120585) and its discretizationtreatment is 119903 = (119886

119895 119901119886119895Δ119906 119896119886

minus119895Δ120585) where 0 lt 119895 le log

2119873

0 le 119901 le 1198732minus119895+1 0 le 119896 le 2

119895+1 and 119873 is sampling pointswhere 119886 = 2Δ119906 = 05 andΔ120585 = 120587 120601 is discrete as120601 = Vsdot1205876where 0 le V le 12 V is integer

Single atom time-frequency diagram and Wigner-Villedistribution of Gabor atom are shown in Figure 3

It can be known that Gabor atom has the best time-frequency aggregation in Figure 3 and utilized sparse signalrepresentation to fully reveal signal time-frequency charac-teristicsThe deficiency of Gabor atom is that atom frequency


Gabor atoms

Original signal

Normalization

Obtain the best atom bymatching pursuit

Residual signal

Does it meet the termination

End

Delayelement

Atoms index

Identificationprocess

Storage unit

Optimization process byNewton downhill method

conditionNo

Yes

Figure 4 Atomic sparse decomposition process

is not changed with time and the division way of time-frequency plane belongs to lattice segmentation CompareFigures 2 and 3 it is known that the similarity degree betweenGabor atom waveforms and zero sequence currents is higherand therefore adoptsmatching pursuitway tomatch it couldnot only accurately extract the fault feature components butalso save a large number of calculation time Hence it usedGabor atoms to extract the fault features in the paper

4 ELM Work Principle

Extreme learning machine is a novel feed-forward neuralnetwork [16ndash18] which is assumed to have119873 training sample(x119896 119905119896)119873

119896=1 its expression is shown in (16)

119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)

In (18) xk b and 119900119896 are input vector hidden layer bias andnetwork output respectivelyWin is input weight linked inputnode and hidden layer node120596 is output weight linked hiddenlayer node and output node 119891 is hidden layer activationfunction and its form is Sigmoid function generally and 119873

is sample numberAt the beginning of training Win and b randomly

generated and remain unchanged it only needs to trainoutput weight 120596 Assume that feed-forward neural networkapproached training samplewith zero error that issum119873

119896=1119900119896minus

119905119896 = 0 ThereforeWin b and 120596meet the formula

120596119879119891 (Winxk + b) = 119905

119896 119896 = 1 2 119873 (19)

Formula (19) is written to matrix form that is H120596 = Twhere

H =[[

[

119891(Winx1 + b1) sdot sdot sdot 119891(Winx1 + b

119898)

d


119898)

]]

]119873times119898

(20)

In (20) H and 119898 are output matrix and node number ofhidden layer respectively andT is expected output vector and

it could be expressed as T = [1199051 1199052 119905

119873]119879 If the activation

function of hidden layer is infinitely differentiable and thenumber of hidden layer node met the relationship 119898 le 119873 itcould approach training sample with small training error 120596value is calculated by pseudoinverse algorithm generally [19]

The training process of single-hidden layer feed-forwardneural network (SLFN) is equivalent to calculating leastsquares solution of linear system it is shown in

H minus T = min120596

H120596 minus T (21)

In (21) is least squares solution ofminimumnorm ofH120596 =T H+ is generalized inverse of hidden layer output matrixH For feed-forward neural network smaller weights havestronger generalization ability For all least squares solutionof equation H120596 = T has the smallest norm number thatis = H+T le 120596 where

forall120596 isin 120596 | H120596 minus T le Hz minus T forallz isin 119877119873times119898 (22)

From (22) not only can ELM achieve the minimum trainingerror but it also has stronger generalization ability than thetraditional gradient descent algorithm There is only one H+for the generalized inverse H+of matrix H so the value isunique

5 Test Signal Analysis

Given the test signal there are three frequency componentswhich have different time scale intervals the calculation is asfollows

119904 (119905) =

9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s

38119890minus119905 sin (100120587119905)

+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s

(23)

We added 20 db Gauss white noise to the signal and veri-fied anti-interference ability of atom decomposition methodFor original signal it should be normalized the signal isdivided by its Euclid norm [20] The decomposition processwas shown in Figure 4


01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Gabor atom 1st iteration

t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u) Gabor atom 2nd iteration

t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u) Gabor atom 3rd iteration

t (ms)

(c)

Figure 5 The first second and third atoms

005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)

Original signalConstructed signal

Figure 6 Comparison of original signal and constructed signal by20 iterations

Identification method frequency center 119865 is equaled to1198911199041205852120587 119891

119904is sampling frequency start time is 119879

119904= 119906 minus 1199042

end time is119879119890= 119906+1199042 120601 is phase angle and the amplitude is

equaled to atom normalization amplitude to multiply actualenergy value which is Euclid norm

Set 119891119904= 1 kHz simulation time and sampling points

areequaled to 05 s and 500 respectively Before the decom-position the normalization equation is shown in

119904119892 (119899) =

119904 (119899)

119904 (119899) (24)

In (24) 119904(119899) is discrete signal of 119904(119905) 119904119892(119899) is normalization

expression of 119904(119899) 119904(119899) is Euclid norm and its value is927915

Set iteration number as 20 and decompose 119904119892(119899) by

atomic algorithm Figure 5 shows atom 1 atom 2 and atom 3generated by iteration respectively and all atoms in Figure 5are normalized results Comparison of original signal andconstructed signal is shown in Figure 6 it indicated that thedifference of two signals is smaller by 20 iteration numbersThe residual component amplitude is only 10minus3 in Figure 7and further shows that the accuracy is satisfied atomicdecomposition requirement

001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)

Figure 7 Residual component decomposed by 20 iterations

The parameters of atom 1 atom 2 and atom 3 areshown in Table 1 Notably every atom decomposed by atomicalgorithm does not have physical meaning it just indicateddistribution characteristics of time scales Hence the atomicparameters in Table 1 are needed for identification processingand we transformed it to indicate local features of originalsignal it is shown in Table 2

We observed the amplitude frequency and phase valueof atoms in Table 2 it could know that the atoms 12 and 3 represent 9119890minus119905 sin(150120587119905) 38119890minus119905 sin(100120587119905) and28119890minus05119905 sin(70120587119905) of original signal respectively by identi-

fication processing For atom 1 because the actual end time is200ms and the calculated end time is 1877268ms deviationis 122732ms But for atoms 2 and 3 comparing the calculatedstart time with actual start time the deviations are 14297msand 78642ms respectively the difference is smaller

Time-frequency analysis by 20 iteration number decom-position is shown in Figure 8 we can see that the atoms couldindicate local characteristics of nonstationary test signalsaccurately including frequency segment time interval andfrequency components energy compared to the traditionalFFT spectrum cross interference and noise interference canbe suppressed effectively and the calculation accuracy is alsohigher than FFT


Table 1 Characteristic parameters of every atom

Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 2276520 729008 04709 minus20125 009032 3083047 3527226 03150 minus22285 003803 3168729 3663006 02200 minus18173 00281

Table 2 Local characteristic parameters of test signal

Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 90112 749841 minus20125 mdash 18672682 37921 501592 minus22285 1985703 mdash3 28041 350319 minus18173 2078642 mdash

500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15

Time-frequency distribution based on matching pursuit

5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)

Figure 8 Time-frequency representation of test signal

006004002

0minus002minus004minus006

0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)

Figure 9 Fitting waveform of overhead line 1198782

6 Choose Characteristic Atom of ZeroSequence Current

To verify ASD algorithm extracting fault feature componentsability in distribution network it gives the feeder fault asexample by ASD set the iteration number as 4 hence the

zero sequence current fitting waveform of overhead line isshown in Figure 9

The similarity between constructed signal and originaloverhead line 119878

2signal is higher by 4 iterations and the

fitting accuracy meets the requirements The first four atomsrsquowaveform and specific parameters are shown in Figure 10 andTables 3 and 4 respectively

Combined with Figure 10 and Table 4 atom 1 waveformshows oscillation attenuation trend both waveform andenergy value have higher similarity with original signal andit indicated major information of original signal thereforeatom 1 is defined asmain components atom and its frequencyvalue is equal to 4729299Hz Atom 2 is defined as funda-mental atom and its frequency value is 509554Hz Atom 3and atom 4 all show oscillation attenuation trend but theirfrequency values are different from atom 1 they are equal to17786624Hz and 11767516Hz respectively and all the highfrequency components therefore it is defined as transientcharacteristic atoms 1 and 2 respectively

Zero sequence current fitting waveform of cable line1198784is shown in Figure 11 the first four atoms are shown

in Figure 12 and the parameters of every atom are shownin Tables 5 and 6 Combining Figure 12 and Table 6 it isknown that atom 1 of cable line is main components atomand its frequency is equal to 4729299Hz Therefore thefrequencies of fundamental atom and transient characteristicatoms 1 and 2 are equal to 493631Hz 11751592Hz and23662420Hz respectively Comparing Figures 10 and 12 itgot different characteristic of transient characteristic atomsbetween overhead line and cable line

Comparing Figures 10(c) 10(d) and Figures 12(c) 12(d)respectively for cable line oscillation attenuation trend oftransient characteristic atoms is more obvious its oscillationprocess is shorter than overhead line Because the capacitanceto ground value of cable line is larger than overhead line inactual distribution network it got different oscillation processof fault current

7 Fault Line Selection Methods

71 Atom Dictionary Measure Based on Information EntropyIndex Information entropy canmeasure uncertain degree ofevent the information entropy value is larger it indicated that


004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4

Figure 10 Zero sequence current characteristic atom of overhead line 1198782

Table 3 Every atom characteristic parameters of overhead line 1198782

Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 3941 times 104 minus27094 times 105 00297 15419 003852 115 times 106 minus26135 times 106 00032 minus21710 000483 41957 times 104 minus16524 times 105 01117 09501 001224 297 times 103 minus17133 times 103 00739 12609 00135

004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)


Figure 11 Fitting waveform of cable line 1198784

uncertain degree is larger that is random characteristics ofevent are stronger therefore the credibility applied to faultdiagnosis is lower [21 22] According to the characteristicsof single phase to ground fault one fault feature is morereliable the fault difference of fault line and healthy lineis larger and its information entropy value is smaller itindicated that certain characteristics of FLS result basedon the fault characteristics are larger Therefore it usedinformation entropy to measure uncertain characteristics ofevery feature To evaluate certain degree of sample library byatoms it adopted information entropy theory to calculate inthe paper the details are as follows

Firstly calculate the ratio of atom library and atom librarysum it is shown in

120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)

In (25) 119871(119896) is atom library it can be main component atomlibrary fundamental atom library and transient characteris-tic atom library 120582(119896) is probability reflected every line faultand the calculation formula of information entropy is shownin

119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)

In (26) information entropy reflected characteristicsinformation content of samples and the value is larger itindicated that sample in the atom library has more uncer-tainty hence the fault characteristic component is less andthe credibility is lower On the contrary the credibility ofatom library is higher

Figures 13(a) 13(b) 13(c) and 13(d) are informationentropy value of main components atom fundamental atomtransient characteristic atoms 1 and 2 it can be seen fromFigure 13 that information entropy values of most atoms aresmaller and reflected certainty of the sample is stronger andit applied to FLS which has more credibility however theentropy values of some samples are larger it reflected thatcertainty of the samples is weak and the credibility is lowerTo evaluate credibility of every atom the statistical method isadopted to measure the information entropy the details areas follows

Step 1 We selected the maximum entropy value of atomlibraries 1 2 3 and 4 expressed as 119867

1max 1198672max 1198673maxand 119867

4max compared the four values and determined themaximum entropy value119867max


005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4

Figure 12 Zero sequence current characteristic atom of cable line 1198784

2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)

Figure 13 Information entropy value of every atom library

Input layerHidden layer1205961 1205731 S1

S2S3

Sn120573Hn

T

Snminus11205964H

Figure 14 ELM network topology structure

Step 2 We calculated 119867119867max and then counted samplenumber of every atom library which is less than 120583 (in thepaper 120583 = 001)

Step 3 We took sample number by Step 2 to divide totalnumber of samples and got information entropy measure ofatom library

The information entropymeasure value can evaluate datacredibility of every atom library with FLS the measure valueis smaller and it indicated that the sample uncertainty issmaller and the certainty is larger therefore the credibilitywith FLS is higher On the contrary the value is largerindicated certainty is smaller and the credibility is lower

72 Confidence Degree of Fault Line Selection Judgmentresults did not add additional constraints in the past FLSmethod it only required to show the fault line symbol andthe symbol output results have the following disadvantages

(1) It can not reflect significant degree of fault featureWhen the fault occurred if fault feature is obvious theFLS is very reliable on the contrary the fault feature isweak and the resultsmay bewrong but the differenceis hard to reflect in symbol FLS method


Zero sequencecurrent signal

Atomic sparsedecomposition

Main componentatoms

Fundamental waveatoms

Number 1 of characteristic atoms

Calculating measure values ofatoms information entropy

Training ELM1network




The trained ELM1model




Calculating correct rateof every ELM network

Faultvote

transient


transient

Fault lineselection

results

Fault line selectioncredibility

Figure 15 Basic framework of fault voting

Table 4 Zero sequence current local characteristic parameters of overhead line 1198782

Atoms Amplitude Frequency shiftHz Phaserad Start timems End timems1 38654 4729299 15419 102568 mdash2 00485 509554 minus21710 155897 mdash3 12352 17786624 09501 85679 mdash4 13446 11767516 12609 95879 225625

(2) It can not provide fault indication information ofother lines

(3) It is not conducive to usemultiple criteria comprehen-sivelyWhen usingmultiple criteria to select fault lineit is not viable to vote results of several criteria simply[23ndash25]

This paper proposed a novel FLS method based on atomlibrary fusion ideas its purpose is not to give FLS resultsby every criterion simply it quantitatively measured faultsymptom degree of every line by every atom characteristicand then trained the ELM to make decision Finally itadopted vote to get the results

It has given concept of FLS confidence degree in thepaper the confidence degree is defined as real variables thatis used to measure atom samples certainty and ELM trainingaccuracy its scope is [0infin) The confidence degree value ofatom library is larger it indicated that vote weight of the atomlibrary is larger The calculation is shown in

Confidence degree

= information entropy measure of atom library

times ELM network accuracy

(27)

73 Fault Line SelectionModel of ELM Based on the acquiredmain component atom fundamental atom and transientcharacteristic atom of group119882 the ELM network is trainedThere are three steps for the initial judgment of FLS in ELMnetwork

Step 1 Normalize the inputoutput training samples of group119882 which is limited to [0 1] and randomly offer the input

weights and hidden layer threshold of the input neurons andthe 120591 hidden layer neurons120596

120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)

Step 2 According to the generalized inverse matrix theory ofPenrose Moore the output weights of the network with theleast square solution are calculated in an analytical way 120573

120591=

[1205961205911 120573

12059112]119879 and well-trained ELM network is obtained

from which the nonlinear mapping relations between everysample atom and fault conditions in the line can be shown

Step 3 Given a set of fault atomic sample input data theinitial selection of fault line is presented based on the well-trained ELM networkThe accuracy rate of test set is adoptedto test the result of the initial selection [26 27]

Based on the above analysis the ELM network topologyestablished in this paper is shown in Figure 14

74 Fault Vote Mechanism According to the theory of infor-mation entropy measure and FLS confidence degree thepaper proposed the basic framework as shown in Figure 15

From Figure 15 the four atoms correspondingly com-posed atom library as fault training samples and input it tocorresponding ELM network to train and then according toELM network output and FLS confidence degree to achievethe fault vote finally it judged the FLS results [28 29]Based on the vote principle of society it proposed fault voteselection way based on confidence degree the specific stepsare as follows

Step 1 Firstly set that every line is healthy line in otherwords assume that there is no fault


Start

U0(t) gt 015Un

Obtaining zero sequence current of every branch line

Decomposed zero sequence current byatomic algorithm

network respectively

Is it the healthy line

Numerical size comparison

Judge the line ashealthy line

Judge the line asfault line

Display storageprinting

End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm

Adjusting arc suppressioncoil away from the

resonance point

Atom 1 atom 2 atom 3 and atom 4

TV is broken

Input the ELM1 ELM2 ELM3 and ELM4

multiplied ldquo1rdquo multiplied ldquo minus1rdquo

Arc suppression coil is series resonant

To vote ldquoyesrdquo the confidence value To vote ldquonordquo the confidence value

Are the ldquoyesrdquo votes more than the ldquonordquo votes

Figure 16 Fault line selection process

Table 5 Every atom characteristic parameters of cable line 1198784

Atoms Scale 119904pu Location shift 119906pu Frequency shift 119908Hz Phaserad Atom amplitude1 36216 times 104 minus22767 times 105 00297 14440 005132 13019 times 104 24196 times 103 00031 minus20734 000653 23151 times 104 minus15341 times 105 00738 minus18505 001234 46146 times 103 minus48524 times 103 01486 09955 00043

Step 2 When a line is judged as healthy line by ELM networkoutput the confidence degree value is multiplied ldquo1rdquo whichis consistent with Step 1 assumption hence voted ldquoagreerdquo Onthe other hand when a line is judged as fault line by ELMnetwork output the confidence degree value is multipliedldquominus1rdquo which is deviated from Step 1 assumption hence votedldquoagainstrdquo

Step 3 When ELMnetwork judgment is completed comparethe vote number value of ldquoagreerdquo and ldquoagainstrdquo and thenwhenldquoagreerdquo value is larger than ldquoagainstrdquo judge the line as healthyline on the contrary the line is judged as fault line

The specific process of FLS is shown in Figure 16

8 Example Analysis

In this paper the ATP-EMTP is used to simulate a singlephase to ground fault and the simulation model is shown inFigure 17 The parameters of simulation model are as follows[30]

In order to simplify the analysis the power supply adoptsideal source therefore the internal impedance of the sourceis 0

Overhead line positive-sequence parameters are 1198771=

017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero

sequence parameters are 1198770= 023Ωkm 119871

0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2

Overhead line Overhead line Load

SourceTransformer

Current probe

Voltage probe

Switch

Grounding resistance

Overhead line

Overhead line Overhead line

Cable line Cable line

Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V

Figure 17 ATP simulation model

Cable line positive-sequence parameters are 11987711

=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero

sequence parameters are11987700= 193Ωkm119871

00= 548mHkm

and 11986200= 143 nFkm

The overhead lines 1198781and 119878

2are 135 km and 24 km

respectively Cable line 1198784is 10 km Hybrid line 119878

3is 17 km

where the cable line is 5 km and the overhead line is 12 kmTransformer is 110105 kV connection mode indicates

that the primary side is triangle connection and the secondside is star connection Primary resistance is 040Ω induc-tance is 122Ω secondary resistance is 0006Ω inductanceis 0183Ω excitation current is 0672A magnetizing flux is2022Wb magnetic resistance is 400 kΩ Load all are delta119885119871= 400 + j20Ω Petersen coil 119871

119873= 12819mH 119877

119873=

402517ΩSampling frequency119891

119904is equal to 105Hz simulation time

is 006 s and the single phase to ground fault occurred at002 s Based on the simulation model when the initial phase

angle is 0∘ the transition resistance is 1Ω 10Ω 100Ω 1000Ωor 2000Ω respectively the single phase to ground fault testsare carried out at the points of 5 km and 10 km in line 119878

1

9 km and 17 km in line 1198783 and 6 km and 10 km in line 119878

4

with the arc suppression coil to ground (overcompensation is10) The zero sequence current signals of four feeder lineswhich are chosen from2 circles after the fault can be collectedfor each fault and the total number is 4 times 5 times 2 times 3 = 120After the atomic decomposition of these 120 zero sequencecurrent signals the first 4 atoms of each group are picked outrespectively to comprise a main component atomic librarya fundamental atomic library and two transient atomiclibraries Each library contains 120 atomic samples the first100 samples of which are taken as the training set and the last20 samples of which as the test set [31]

According to the ELM theory when the number ofhidden layer neurons equals the number of the training setsamples then for any119882in and 119887 ELM can approximate to the


Table 6 Zero sequence current local characteristic parameters of cable line 1198784

Atoms Amplitude FrequencyHz Phaserad Start timems End timems1 336181 4729299 14440 115875 mdash2 42596 493631 minus20734 148956 mdash3 80605 11751592 minus18505 86987 2156144 28179 23662420 09955 94893 284462

Table 7 Fault voting result of overhead line 1198781under 0∘

Faultlocationkm

TransitionresistanceΩ

Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results

Fault lineselectionresults

10 100

Overheadline S1

09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times (minus1) 34441 gt 0 Vote S1 isfault line

Overheadline 119878

2

09667 times 1 0855 times 1 08358 times (minus1) 07866 times (minus1) 18217 gt 16224 Vote 1198782is

healthy lineHybrid line1198783

09667 times 1 0855 times 1 08358 times 1 07866 times 1 34441 gt 0 Vote 1198783is

healthy line

Cable line 1198784

09667 times 1 0855 times 1 08358 times 1 07866 times (minus1) 26575 gt 07866 Vote 1198784is

healthy line

5 1000

Overheadline S1


Overheadline 119878

2



09667 times 1 0855 times (minus1) 08358 times 1 07866 times 1 25891 gt 0855 Vote 1198783is

healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784

09667 times 1 0855 times 1 08358 times (minus1) 07866 times 1 26083 gt 08358 Vote 1198784is

healthy line

5 2000

Overheadline S1

09667 times (minus1) 0855 times (minus1) 08358 times (minus1) 07866 times 1 26575 gt 07866 Vote S1 isfault line

Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Table 8 Fault voting result of hybrid line 1198783under 0∘

Faultlocationkm




17 100

Overheadline 119878

1


healthy lineOverheadline 119878

2


healthy lineHybrid lineS3

09667 times (minus1) 0855 times 1 08358 times (minus1) 07375 times (minus1) 254 gt 0855 Vote S3 isfault line

Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

training samples with no deviation and the calculation resultis the best Therefore four ELM networks are used to trainthe fault atomic samples in four atomic libraries respectivelyof which the input layer neurons are 4000 the hidden layerneurons are 100 and the output layer neuron is 1

According to the information entropy theory the valuesof information entropy of main component atomic libraryfundamental atomic library and transient atomic libraries1 and 2 are calculated as 09667 095 09833 and 09833respectively In addition after the ELM networks train everyatom library the accuracy rate of the 4 test sets of ELMnetwork is 100 90 85 and 80 Therefore according

to formula (27) the confidence degree of every atomic libraryis 09667 0855 08358 and 07866 Table 7 shows the votingresults of fault in overhead line 119878

1when the initial phase angle

is 0∘ According to the fault votingmechanism assuming thatall the branch lines are healthy lines if the line checked by theELMnetwork is a healthy line thenmultiply the line selectioncredibility by ldquo1rdquo which shows ldquoagreerdquo if the line checkedis a fault line then multiply the line selection credibility byldquominus1rdquo which shows ldquoagainstrdquo Finally FLS is achieved throughthe comparison between the votes of ldquoagreerdquo and of ldquoagainstrdquoAs can be seen from Table 7 at different fault distance anddifferent grounding resistance value the fault in overhead line


Table 9 Fault voting result of cable line 1198784under 0∘

Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line

Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times (minus1) 33508 gt 0 Vote S4 isfault line

6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line

Cable line S4 09667 times (minus1) 07125 times (minus1) 09341 times (minus1) 07375 times 1 26133 gt 07375 Vote S4 isfault line

1198781is accurately checked out through the comparison of the

values above even if the grounding resistance value is as highas 1000Ω

Table 8 offers the selection result of hybrid line 1198783when

the initial fault phase is 0∘ An experiment of fault line underthe end of the high resistance ground is made to furtherverify the accuracy of this method Similarly the entropyvalue of the main component atomic library fundamentalatomic library and transient component atomic libraries 1and 2 at this time is 09667 095 09833 and 09833 andthe accuracy rate of the four test sets after being trained bythe ELM network is 100 90 85 and 75 therefore the

corresponding confidence degree of every atomic library is09667 0855 08358 and 07375 Table 8 shows that evenwhen the fault occurs at the distance of 17 km under 2000Ωthe voting result is 3395 gt 0 which indicates that fault occursin line 119878

3

Table 9 offers the selection result of cable line 1198784when

the initial fault phase is 0∘ The entropy value of every atomiclibrary is 09667 095 09833 and 09833 the accuracy rate ofthe test sets after the atomic libraries are trained by the ELMnetwork is 100 75 95 and 75 therefore the confidencedegree of every atomic library is 09667 07125 09341 and07375 The voting results prove that the method proposed


Table 10 Information entropy value of every atom library

Main componentatom library

Fundamental atomlibrary

Transientcharacteristic atomlibrary number 1


Information entropyvalue 09792 09583 09861 09861

Table 11 Test result of every ELM network

Samples styleELM

Correct samplesnumbertotal number Accuracy rate

Main componentatom library 2324 958333

Fundamental atomlibrary 2024 833333


2124 875


1924 791667

Total 8396 864583

in this paper can select fault line accurately when groundingfault of cable line occurs

9 Applicability Analysis

Since the distribution network is exposed to the outdoorenvironment when the fault occurs the current signalscollected contain large amounts of noise which is a negativefactor for FLS In order to test the antinoise interferenceability of the method proposed in this paper a strong noise of05 db is added to the zero sequence current signals Figures18(a) and 18(b) present the zero sequence current waveformsof overhead line 119878

1when grounding fault occurs at 10Ω

and 2000Ω It shows that when the added noise is 05 dbcompared with Figure 2 the zero sequence current signalsof each line have changed greatly and there are lots of burrson the waveforms due to noise interference which makes thetransient characteristics of fault line almost undistinguishableand which is harmful for FLS [32ndash34] The zero sequencecurrent signals of each line are much weaker in Figure 18(b)since it represents grounding fault under high resistance withnoise interference Therefore whether or not accurate FLS ofweak signals can be achieved with strong noise interferenceis important for testing the applicability of the proposedmethod Table 10 shows the entropy values of each atomiclibrary with noise interference and Table 11 is the testingresults of each ELM network

It can be seen from Table 11 that with the added 05 dbnoise the overall accuracy of line selection of a single atomiclibrary of ELM network can only reach 864583 withoutconsidering measuring instrument error electromagneticinterference and other factors and the accuracy of the

selection method based on one single fault characteristicis not successful in practice with all kinds of complicatedconditions in consideration So the method proposed in thispaper tries to select fault line through fault voting of multipleatomic library fusion Table 12 is the fault selection results ofeach linewith strong noise interferencewhen the initial phaseangle is 0∘

Table 12 shows that with the added 05 db noise themethod based on multiple atomic libraries of ELM modelcan still accurately select the fault line without the influenceof transition resistance fault distance and other factorsCompared with the results based on one single atomic libraryshown in Table 11 effectively fusing with a variety of faultcharacteristics this method improves the correct rate of FLSwith its excellent fault tolerance and robustness

10 Conclusions

A fault voting selection method based on the combinationof atomic sparse decomposition and ELM is proposed in thispaper The following are the conclusions of the research

(1) ASD breaks through the idea of fixed complete basisto decompose signal it utilizes signal features todecompose signal by choosing adaptively appropriatebase of atom library Because the ASD has adaptiveanalytical and sparse characteristics the algorithmhas outstanding advantage of fault feature extractionof power system the atoms extracted not only restorethe main characteristic of initial signal well but alsoapply to judge the fault line with ELM networkconveniently

(2) It could get the unique optimum solution by sethidden layer neurons number of ELM network anddoes not need to adjust connectionweight and hiddenlayer threshold We construct four ELM networksand train and test each sample atom library toimprove the accuracy of every sample test set andit provided the base for FLS at next step Throughour research we found that ELM network has fastlearning speed good generalization performanceand less adjustment parameters it better applied tothe fault diagnosis field of power system

(3) Information entropy can measure the confidencedegree of every sample library combined the ELMnetwork accuracy to establish FLS confidence degreeand then constructed fault vote selection mechanismby ELM network output and confidence degree valueAs can be seen by voting the accuracy of the methodis 100 and it is not affected by fault distance


Table 12 Fault voting result with strong noise

(a) Fault voting result of overhead line 1198781

Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1

09384 times 1 07986 times (minus1) 08217 times (minus1) 07807 times (minus1) 2401 gt 09384 Vote S1 isfault line

Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

(b) Fault voting result of hybrid line 1198783

Faultlocationkm




5 500

Overheadline 119878

1



2



09384 times (minus1) 07986 times (minus1) 08217 times 1 07807 times (minus1) 25177 gt 08217 Vote S3 isfault line

Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

(c) Fault voting result of cable line 1198784

Faultlocationkm


Feeder linestyle Atom 1 Atom 2 Atom 3 Atom 4 Voting results Fault line

selection results

4 200

Overheadline 119878

1



2


healthy lineHybridline 119878

3


healthy lineCable lineS4

09384 times (minus1) 07986 times 1 08217 times (minus1) 07807 times (minus1) 25408 gt 07986 Vote S4 is faultline

8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)

(a) 10Ω to ground fault

0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)

(b) 2000Ω to ground fault

Figure 18 Zero sequence current with strong noise

and transition resistance value besides the methodcan accurately achieve FLS with 05 db strong noiseinterference

(4) Because ASD algorithm adopts matching pursuit wayto find the best atom in decomposition process itneeds a large number of inner product operations soit needs to spend a long time Therefore the futurework is how to reduce matching pursuit calculationtime

Notations

ASD Atomic sparse decompositionELM Extreme learning machineFLS Fault line selectionHHT Hilbert-Huang transform

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by National Natural Science Fund(61403127) of China Science and Technology Research(12B470003 14A470004 and 14A470001) of Henan ProvinceControl Engineering Lab Project (KG2011-15 KG2014-04) ofHenan Province China and Doctoral Fund (B2014-023) ofHenan Polytechnic University China

References

[1] X Dong and S Shi ldquoIdentifying single-phase-to-ground faultfeeder in neutral noneffectively grounded distribution systemusing wavelet transformrdquo IEEE Transactions on Power Deliveryvol 23 no 4 pp 1829ndash1837 2008

[2] J Zhang Z He and Y Jia ldquoFault line identification approachbased on S-transformrdquo Proceedings of the CSEE vol 31 no 10pp 109ndash115 2011

[3] J Ren W Sun M Zhou and A Cao ldquoTransient algorithm forsingle-line to ground fault selection in distribution networksbased on mathematical morphologyrdquo Automation of ElectricPower Systems vol 32 no 1 pp 70ndash75 2008

[4] T Cui X Dong Z Bo and A Juszczyk ldquoHilbert-transform-based transientintermittent earth fault detection in noneffec-tively grounded distribution systemsrdquo IEEE Transactions onPower Delivery vol 26 no 1 pp 143ndash151 2011

[5] XWWang JWWu and R Y Li ldquoA novel method of fault lineselection based on voting mechanism of prony relative entropytheoryrdquo Electric Power vol 46 no 1 pp 59ndash64 2013

[6] H Shu L Gao R Duan P Cao and B Zhang ldquoA novelhough transform approach of fault line selection in distributionnetworks using total zero-sequence currentrdquo Automation ofElectric Power Systems vol 37 no 9 pp 110ndash116 2013

[7] S Lin ZHe T Zang andQQian ldquoNovel approach of fault typeclassification in transmission lines based on roughmembershipneural networksrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 30 no 28 pp 72ndash79 2010

[8] S Zhang Z-Y He Q Wang and S Lin ldquoFault line selectionof resonant grounding system based on the characteristicsof charge-voltage in the transient zero sequence and supportvector machinerdquo Power System Protection and Control vol 41no 12 pp 71ndash78 2013

[9] Q Li and J Z Xu ldquoPower system fault diagnosis based onsubjective Bayesian approachrdquo Automation of Electric PowerSystems vol 31 no 15 pp 46ndash50 2007

[10] X-W Wang S Tian Y-D Li T Li Y-J Zhang and Q Li ldquoAnovel fault section location method for small current neutralgrounding system based on characteristic frequency sequenceof S-transformrdquo Power System Protection and Control vol 40no 14 pp 109ndash115 2012

[11] XWWang Y XHou S Tian Y-D Li J Gao andX-XWei ldquoAnovel fault line selectionmethod based on time-frequency atomdecomposition and grey correlation analysis of small current toground systemrdquo Journal of China Coal Society 2014


[12] H-S Zhao L-X Yao L-F Ke and L Wu ldquoA novel method forfault line selection and location in distribution systemrdquo PowerSystem Protection and Control vol 38 no 16 pp 6ndash10 2010

[13] S G Mallat and Z Zhang ldquoMatching pursuits with time-frequency dictionariesrdquo IEEE Transactions on Signal Processingvol 41 no 12 pp 3397ndash3415 1993

[14] L Lovisolo E A B da Silva M A M Rodrigues and PS R Diniz ldquoEfficient coherent adaptive representations ofmonitored electric signals in power systems using dampedsinusoidsrdquo IEEE Transactions on Signal Processing vol 53 no10 part 1 pp 3831ndash3846 2005

[15] L Lovisolo M P Tcheou E A B da Silva M A M Rodriguesand P S R Diniz ldquoModeling of electric disturbance signalsusing damped sinusoids via atomic decompositions and itsapplicationsrdquo EURASIP Journal on Advances in Signal Process-ing vol 2007 Article ID 29507 2007

[16] X Zhang J Liang F Zhang L Zhang and B Xu ldquoCombinedmodel for ultra short-term wind power prediction based onsample entropy and extreme learning machinerdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 33 no 25 pp33ndash40 2013

[17] Q YuanW Zhou S Li andD Cai ldquoApproach of EEGdetectionbased on ELM and approximate entropyrdquo Chinese Journal ofScientific Instrument vol 33 no 3 pp 514ndash519 2012

[18] F Y Wu X F Le and D L Nan ldquoA short-term wind speedprediction model using phase-space reconstructed extremelearning machinerdquo Proceedings of the CSU-EPSA vol 25 no 1pp 136ndash141 2013

[19] G B Huang Q Y Zhu and C K Siew ldquoExtreme learningmachine theory and applicationsrdquoNeurocomputing vol 70 no1ndash3 pp 489ndash501 2006

[20] J J Jia Q W Gong X Li Q Y Guan and S L Chen ldquoSingle-phase adaptive recluse of shunt compensated transmission linesusing atomic decompositionrdquo Automation of Electric PowerSystems vol 37 no 5 pp 117ndash123 2013

[21] Q Jia L Shi N Wang and H Dong ldquoA fusion method forground fault line detection in compensated power networksbased on evidence theory and information entropyrdquo Transac-tions of China Electrotechnical Society vol 27 no 6 pp 191ndash1972012

[22] L Fu Z Y He R K Mai and Q Q Qian ldquoApplicationof approximate entropy to fault signal analysis in electricpower systemrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 28 pp 68ndash73 2008

[23] Q-Q Jia Q-X Yang and Y-H Yang ldquoFusion strategy forsingle phase to ground fault detection implemented throughfault measures and evidence theoryrdquo Proceedings of the CSEEvol 23 no 12 pp 6ndash11 2003

[24] H R Karimi P J Maralani B Lohmann and B Moshirildquo119867infin

control of parameter-dependent state-delayed systemsusing polynomial parameter-dependent quadratic functionsrdquoInternational Journal of Control vol 78 no 4 pp 254ndash2632005

[25] S Yin S X Ding A Haghani H Hao and P Zhang ldquoAcomparison study of basic data-driven fault diagnosis andprocess monitoring methods on the benchmark TennesseeEastman processrdquo Journal of Process Control vol 22 no 9 pp1567ndash1581 2012

[26] H M Yang L Huang C F He and D X Yi ldquoProbabilisticprediction of transmission line fault resulted from disaster ofice stormrdquo Power System Technology vol 36 no 4 pp 213ndash2182012

[27] H R Karimi ldquoA computational method for optimal con-trol problem of time-varying state-delayed systems by Haarwaveletsrdquo International Journal of Computer Mathematics vol83 no 2 pp 235ndash246 2006

[28] H Zhang Z He and J Zhang ldquoA fault line detection methodfor indirectly grounding power system based on quantumneural network and evidence fusionrdquo Transactions of ChinaElectrotechnical Society vol 24 no 12 pp 171ndash178 2009

[29] H R Karimi ldquoRobust Hinfin filter design for uncertain linearsystems over network with network-induced delays and outputquantizationrdquo Modeling Identification and Control vol 30 no1 pp 27ndash37 2009

[30] Z Kang D Li andX Liu ldquoFaulty line selectionwith non-powerfrequency transient components of distribution networkrdquo Elec-tric Power Automation Equipment vol 31 no 4 pp 1ndash6 2011

[31] S Yin H Luo and S X Ding ldquoReal-time implementation offault-tolerant control systems with performance optimizationrdquoIEEE Transactions on Industrial Electronics vol 61 no 5 pp2402ndash2411 2014

[32] X WWang J Gao X X Wei and Y X Hou ldquoA novel fault lineselectionmethod based on improved oscillator system of powerdistribution networkrdquo Mathematical Problems in Engineeringvol 2014 Article ID 901810 19 pages 2014

[33] H R Karimi N A Duffie and S Dashkovskiy ldquoLocalcapacity 119867

infincontrol for production networks of autonomous

work systems with time-varying delaysrdquo IEEE Transactions onAutomation Science and Engineering vol 7 no 4 pp 849ndash8572010

[34] X W Wang X X Wei J Gao Y X Hou and Y F WeildquoStepped fault line selection method based on spectral kurtosisand relative energy entropy of small current to ground systemrdquoJournal of Applied Mathematics vol 2014 Article ID 726205 18pages 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



instantaneous power by Hilbert-Huang transform (HHT)and got fault direction well the method took advantage oftransient high-frequency component at lower sampling rateIt tried to divide the zero sequence current signal into severalsegments to ensure good continuity and smaller mutationat every subsegment and Prony algorithm was appliedto choose transient dominant component with maximumenergy principle and then calculated the relative entropy andvoted by preliminary vote and 119896 values check to judge thefault line [5] Hough transform was adopted to constructwhole mutant direction angle which indicated overall trendof zero sequence current at initial stage and FLSwas achievedby distinguishing the direction angle [6] Paper [7] replacedordinary neurons with rough neurons and fuzzy neuronsto identify 10 kinds of fault type the method improvedthe training speed and reduced training samples and faultidentification accuracy was enhanced It used correlationcoefficient of zero sequence voltage and charge as charac-teristic input to construct FLS process which was based ontransient zero sequence 119876-119880 features the method adoptedsupport vector machine algorithm with small sample [8]For incomplete information of fault diagnosis [9] adoptedevidence uncertainty reasoning and compared abnormalevents to reduce computation amount

This paper proposed a novel FLS method which wasbased on combination of ASD and ELM Firstly it usedatomic sparse algorithm to decompose zero sequence currentof every feeder line and extracted the first four atomsto construct fault sample library respectively besides itcalculated information entropy measure of every libraryThen it trained the ELM network to improve network outputaccuracy At last fault votingwas adopted to vote every feederline and compared the values and then the fault line wasjudged Simulation results showed that the accuracy rate ofproposed method is 100 and had strong ability of antinoiseinterference

The remaining of this paper is organized as follows InSection 2 we analyzed the physical characteristics of zerosequence current In Sections 3 and 4 the theory of time-frequency atom decomposition and ELM work principle arepresented respectively In Section 5 test signals analysis isgiven in the paper In Section 6 we chose the characteristicatoms of zero sequence current In Section 7 the FLS meth-ods are proposed In Section 8 example analysis is appliedto verify the proposed method In Section 9 we discussedthe applicability of the method In Section 10 the paper iscompleted with conclusions and future directions

2 Physical Characteristics Analysis

Transient zero sequence circuit of single phase to ground faultis shown in Figure 1 where 119862

0and 119871

0are zero sequence

capacitance and inductance respectively 119877119892is transition

resistance of grounding point 119877119901and 119871

119901are equivalent

resistance and inductance of arc suppression coil and 119890(119905) iszero sequence voltage

When the fault occurred in compensation networkFigure 1 the transient zero sequence current flows through

i0t Rg

e(t)i0Lt

Lp

Rp

L0

i0Ct

C0

Figure 1 Transient zero sequence equivalent circuit of single phaseto ground

fault location [11 12] the calculation is shown in the followingformula

1198940119905= 1198940119871119905

+ 1198940119862119905

= 119868119871119898

cos120593119890minus119905120591119871 + 119868119862119898

times (120596119891

120596sin120593 sin120596119905 minus cos120593 cos120596

119891119905) 119890minus120575119905

(1)

where 1198940119871119905

and 1198940119862119905

are inductance component and capaci-tance component of transient zero sequence current 119868

119871119898and

119868119862119898

are initial value of inductance current and capacitancecurrent respectively 120596 is angular frequency 120596

119891and 120575

are oscillation angle frequency and attenuation coefficientof transient zero sequence current capacitance componentrespectively 120591

119871is decay time constant of inductance current

and 120593 is initial phase of fault line120596119891and 120575 calculations are shown in the following formula

respectively

120596119891= radic

1003816100381610038161003816100381610038161003816100381610038161003816

1

11987101198620

minus (119877119892

21198710

)

21003816100381610038161003816100381610038161003816100381610038161003816

(2)

120575 =119877119892

21198710

(3)

Transient zero sequence current is comprised of sinu-soidal function from formula (1) and its waveform has atten-uation characteristics It can be seen from formula (2) and (3)that oscillation angle frequency 120596

119891is influenced by 119871

0 1198620

and 119877119892 attenuation coefficient 120575 is also influenced by 119871

0and

119877119892 when transition resistance 119877

119892increased 120596

119891decreased

and 120575 increased it reflected that wave oscillation trend ofzero sequence current becomes slow and the attenuation timebecome fast and then transient processwill end soon and intosteady state Therefore if it could extract accurately transientcomponent to achieve FLS exactly at the large resistanceto ground fault it will be an important index to test theapplicability of the FLS methods

Figure 2 is zero sequence current of actual distributionnetworkwhen overhead line 1 caused fault it can be seen fromFigure 2 that whether the overhead line cable line or hybridline its zero sequence current has oscillation attenuationcharacteristics


300

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(a) Overhead line 1

20

10

0

minus10

minus200 0005 001 0015 002

i 0t

(A)

t (s)

(b) Overhead line 2

100

50

0

minus50

minus1000 0005 001 0015 002

i 0t

(A)

t (s)

(c) Hybrid line

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(d) Cable line





(119892119903)119903isinΓ



(1199030)(119899)


(119899)⟩10038161003816100381610038161003816= sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)




119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)

(119899) + 119877119891 (119899) (5)





1003817100381710038171003817

2=10038161003816100381610038161003816⟨119891(119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119891(119899)

1003817100381710038171003817

2 (6)


10038161003816100381610038161003816⟨119891 (119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)




119877119896119891 (119899) = ⟨119877

119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) + 119877

119896+1119891 (119899) (8)


119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899) + 119877

119898119891 (119899) (9)


1003817100381710038171003817119891(119899)1003817100381710038171003817

2=

119898minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891(119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899)

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119898119891(119899)

1003817100381710038171003817

2

(10)


02

015

01

005

0

minus005

minus01

minus015

minus02

Am

plitu

de



04

035

03

025

02

015

01

Am

plitu

de




In (10) 119892(119903119896)


10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903⟩10038161003816100381610038161003816 (11)


119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) (12)



119862119898=

⟨119891 (119899) 119891119898(119899)⟩

1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)

1003817100381710038171003817

(13)



119882119891(119899 119897)

=

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903119896(119899)⟩

10038161003816100381610038161003816

2

119882119892119903119896(119899 119897)

+

119872minus1

sum

119896=0

119872minus1

sum

119898=0119898 =119896

⟨119877119896119891 (119899) 119892

119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892

119903119898(119899)⟩

sdot 119882 [119892119903119896(119899) 119892

119903119898(119899)] (119899 119897)

(14)




119864119891 (119899 119897) =

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816

2

119882119892(119903119896)

(119899 119897) (15)

In (15) |⟨119877119896119891(119899) 119892(119903119896)




119892119903(119905) =

1

radic119904119892 (

119905 minus 119906

119904) 119890119895120585119905 (16)


119892(119903120601)

(119905) =1

radic119904119892 (

119905 minus 119906

119904) cos (120585119905 + 120601) (17)




119895 119901119886119895Δ119906 119896119886


2119873

0 le 119901 le 1198732minus119895+1 0 le 119896 le 2





Gabor atoms

Original signal

Normalization


Residual signal


End

Delayelement

Atoms index


Storage unit


conditionNo

Yes






119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)




119896=1119900119896minus


120596119879119891 (Winxk + b) = 119905

119896 119896 = 1 2 119873 (19)


H =[[

[


119898)

d


119898)

]]

]119873times119898

(20)







H120596 minus T (21)






119904 (119905) =

9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s

38119890minus119905 sin (100120587119905)

+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s

(23)



01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(c)


005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)





119904= 119906 minus 1199042





119904119892 (119899) =

119904 (119899)

119904 (119899) (24)





001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)











500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










300

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(a) Overhead line 1

20

10

0

minus10

minus200 0005 001 0015 002

i 0t

(A)

t (s)

(b) Overhead line 2

100

50

0

minus50

minus1000 0005 001 0015 002

i 0t

(A)

t (s)

(c) Hybrid line

200

100

0

minus100

minus2000 0005 001 0015 002

i 0t

(A)

t (s)

(d) Cable line





(119892119903)119903isinΓ



(1199030)(119899)


(119899)⟩10038161003816100381610038161003816= sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (4)




119891 (119899) = ⟨119891 (119899) 119892(1199030)(119899)⟩ 119892(1199030)

(119899) + 119877119891 (119899) (5)





1003817100381710038171003817

2=10038161003816100381610038161003816⟨119891(119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119891(119899)

1003817100381710038171003817

2 (6)


10038161003816100381610038161003816⟨119891 (119899) 119892

(1199030)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

1003816100381610038161003816⟨119891 (119899) 119892119903⟩1003816100381610038161003816 (7)




119877119896119891 (119899) = ⟨119877

119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) + 119877

119896+1119891 (119899) (8)


119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899) + 119877

119898119891 (119899) (9)


1003817100381710038171003817119891(119899)1003817100381710038171003817

2=

119898minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891(119899) 119892

(119903119896)(119899)⟩ 119892

(119903119896)(119899)

10038161003816100381610038161003816

2

+1003817100381710038171003817119877119898119891(119899)

1003817100381710038171003817

2

(10)


02

015

01

005

0

minus005

minus01

minus015

minus02

Am

plitu

de



04

035

03

025

02

015

01

Am

plitu

de




In (10) 119892(119903119896)


10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903⟩10038161003816100381610038161003816 (11)


119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) (12)



119862119898=

⟨119891 (119899) 119891119898(119899)⟩

1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)

1003817100381710038171003817

(13)



119882119891(119899 119897)

=

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903119896(119899)⟩

10038161003816100381610038161003816

2

119882119892119903119896(119899 119897)

+

119872minus1

sum

119896=0

119872minus1

sum

119898=0119898 =119896

⟨119877119896119891 (119899) 119892

119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892

119903119898(119899)⟩

sdot 119882 [119892119903119896(119899) 119892

119903119898(119899)] (119899 119897)

(14)




119864119891 (119899 119897) =

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816

2

119882119892(119903119896)

(119899 119897) (15)

In (15) |⟨119877119896119891(119899) 119892(119903119896)




119892119903(119905) =

1

radic119904119892 (

119905 minus 119906

119904) 119890119895120585119905 (16)


119892(119903120601)

(119905) =1

radic119904119892 (

119905 minus 119906

119904) cos (120585119905 + 120601) (17)




119895 119901119886119895Δ119906 119896119886


2119873

0 le 119901 le 1198732minus119895+1 0 le 119896 le 2





Gabor atoms

Original signal

Normalization


Residual signal


End

Delayelement

Atoms index


Storage unit


conditionNo

Yes






119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)




119896=1119900119896minus


120596119879119891 (Winxk + b) = 119905

119896 119896 = 1 2 119873 (19)


H =[[

[


119898)

d


119898)

]]

]119873times119898

(20)







H120596 minus T (21)






119904 (119905) =

9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s

38119890minus119905 sin (100120587119905)

+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s

(23)



01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(c)


005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)





119904= 119906 minus 1199042





119904119892 (119899) =

119904 (119899)

119904 (119899) (24)





001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)











500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










02

015

01

005

0

minus005

minus01

minus015

minus02

Am

plitu

de



04

035

03

025

02

015

01

Am

plitu

de




In (10) 119892(119903119896)


10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816= 120572 sup120574isinΓ

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903⟩10038161003816100381610038161003816 (11)


119891 (119899) =

119898minus1

sum

119896=0

⟨119877119896119891 (119899) 119892(119903119896)

(119899)⟩ 119892(119903119896)(119899) (12)



119862119898=

⟨119891 (119899) 119891119898(119899)⟩

1003817100381710038171003817119891 (119899)1003817100381710038171003817 sdot1003817100381710038171003817119891119898 (119899)

1003817100381710038171003817

(13)



119882119891(119899 119897)

=

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

119903119896(119899)⟩

10038161003816100381610038161003816

2

119882119892119903119896(119899 119897)

+

119872minus1

sum

119896=0

119872minus1

sum

119898=0119898 =119896

⟨119877119896119891 (119899) 119892

119903119896(119899)⟩ ⟨119877119898119891 (119899) 119892

119903119898(119899)⟩

sdot 119882 [119892119903119896(119899) 119892

119903119898(119899)] (119899 119897)

(14)




119864119891 (119899 119897) =

119872minus1

sum

119896=0

10038161003816100381610038161003816⟨119877119896119891 (119899) 119892

(119903119896)(119899)⟩

10038161003816100381610038161003816

2

119882119892(119903119896)

(119899 119897) (15)

In (15) |⟨119877119896119891(119899) 119892(119903119896)




119892119903(119905) =

1

radic119904119892 (

119905 minus 119906

119904) 119890119895120585119905 (16)


119892(119903120601)

(119905) =1

radic119904119892 (

119905 minus 119906

119904) cos (120585119905 + 120601) (17)




119895 119901119886119895Δ119906 119896119886


2119873

0 le 119901 le 1198732minus119895+1 0 le 119896 le 2





Gabor atoms

Original signal

Normalization


Residual signal


End

Delayelement

Atoms index


Storage unit


conditionNo

Yes






119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)




119896=1119900119896minus


120596119879119891 (Winxk + b) = 119905

119896 119896 = 1 2 119873 (19)


H =[[

[


119898)

d


119898)

]]

]119873times119898

(20)







H120596 minus T (21)






119904 (119905) =

9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s

38119890minus119905 sin (100120587119905)

+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s

(23)



01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(c)


005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)





119904= 119906 minus 1199042





119904119892 (119899) =

119904 (119899)

119904 (119899) (24)





001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)











500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Gabor atoms

Original signal

Normalization


Residual signal


End

Delayelement

Atoms index


Storage unit


conditionNo

Yes






119900119896= 120596119879119891 (Winxk + b) 119896 = 1 2 119873 (18)




119896=1119900119896minus


120596119879119891 (Winxk + b) = 119905

119896 119896 = 1 2 119873 (19)


H =[[

[


119898)

d


119898)

]]

]119873times119898

(20)







H120596 minus T (21)






119904 (119905) =

9119890minus119905 sin (150120587119905) 0 le 119905 le 02 s

38119890minus119905 sin (100120587119905)

+28119890minus05119905 sin (70120587119905) 02 s lt 119905 lt 05 s

(23)



01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(c)


005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)





119904= 119906 minus 1199042





119904119892 (119899) =

119904 (119899)

119904 (119899) (24)





001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)











500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










01

0

minus0150 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(a)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(b)

002

0

minus002

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p


t (ms)

(c)


005

0

minus005

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)





119904= 119906 minus 1199042





119904119892 (119899) =

119904 (119899)

119904 (119899) (24)





001

0005

0

minus0005

minus001

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)Residues

t (ms)











500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














500

450

400

350

300

250

200

150

100

50

f(H

z)

90

75

60

45

30

15


5

0

minus5

50 100 150 200 250 300 350 400 450 500

Am

plitu

de (p

u)

t (ms)


006004002


0005 001 0015 002 0025 003 0035 004


t (s)

Am

plitu

de (p

u)















004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










004002

0

minus004minus002

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004Am

plitu

de (p

u)

t (s)

(b) Atom 2

001

0

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

0010

minus001

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(d) Atom 4




004002

0minus002

minus006minus004

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)





120582 (119896) =119871 (119896)

sum119873

119896=0119871 (119896)

(25)


119867 = minus

119873

sum

119896=0

120582 (119896) ln 120582 (119896) (26)




1max 1198672max 1198673maxand 119867



005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










005

0

minus0050005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(a) Atom 1

50

minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(b) Atom 2

510

0minus5

times10minus3

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

(c) Atom 3

20

minus2

0005 001 0015 002 0025 003 0035 004

t (s)

Am

plitu

de (p

u)

times10minus3

(d) Atom 4


2

1

0

minus1

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(a)

2

1

0

minus1

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(b)

4

2

0

minus2

times105

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(c)

1

0

minus1

minus2

times106

Entro

py v

alue

0 20 40 60 80 100 120

Sample number

(d)



S2S3

Sn120573Hn

T

Snminus11205964H










Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Main componentatoms













Faultvote

transient


transient

Fault lineselection

results









Confidence degree



(27)




120591= [1205961120591 1205962120591 1205963120591 1205964120591]119879 (120591 isin 119867)


120591=

[1205961205911 120573









Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start

U0(t) gt 015Un









End

YesYes

Yes

Yes

Yes

No

No

No

No

No

Return

TV alarm


resonance point


TV is broken












8 Example Analysis




017Ωkm 1198711= 12mHkm and 119862

1= 9697 nFkm zero


0= 548mHkm

and 1198620= 6 nFkm


SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










SI

I

I

I

I

I

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

LineZ-T

RLC

RLC

RLC

RLC

Hybrid line S3

Overhead line S1

Overhead line S2


SourceTransformer

Current probe

Voltage probe

Switch


Overhead line



Cable line

Arcsuppression

coil

+U

+Uminus

+Uminus

I

I

I

Cable line S4

IV V V



=0193Ωkm 119871

11= 0442mHkm and 119862

11= 143 nFkm zero


00= 548mHkm

and 11986200= 143 nFkm




3is 17 km



119873= 12819mH 119877

119873=





1


4







Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Faultlocationkm




10 100

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 1000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

5 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 2000

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line



Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Faultlocationkm




17 100

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 1000

Overheadline 119878

1



2




Cable line 1198784


healthy line

9 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line

17 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line








Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Faultlocationkm




10 100

Overheadline 119878

1



2




healthy line


6 1000

Overheadline 119878

1



2




healthy line


10 1000

Overheadline 119878

1



2




healthy line


6 2000

Overheadline 119878

1



2




healthy line


10 2000

Overheadline 119878

1



2




healthy line







3











Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















Samples styleELM





2124 875


1924 791667

Total 8396 864583









10 Conclusions








Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Faultlocationkm




5 5

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line

10 500

Overheadline S1


Overheadline 119878

2




healthy line

Cable line 1198784


healthy line


Faultlocationkm




5 500

Overheadline 119878

1



2




Cable line 1198784


healthy line

14 2000

Overheadline 119878

1



2




Cable line 1198784


healthy line


Faultlocationkm



selection results

4 200

Overheadline 119878

1



2



3




8 10

Overheadline 119878

1



2



3





0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 001 002 003 004minus200

minus100

0

100

200

300

t (s)

i 0t

(A)


0 001 002 003 004minus15

minus10

minus5

0

5

10

15

t (s)

i 0t

(A)





Notations




Acknowledgments


References









































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article fault line selection method of small...

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